1D and 2D Magnetization in Electrical Steels under Uniaxial Stress Viatcheslav Permiakov
Promotoren: prof. dr. ir. J. Melkebeek, prof. dr. ir. L. Dupré Proefschrift ingediend tot het behalen van de graad van Doctor in de Toegepaste Wetenschappen Vakgroep Elektrische Energie, Systemen en Automatisering Voorzitter: prof. dr. ir. J. Melkebeek Faculteit Ingenieurswetenschappen Academiejaar 2004 - 2005
ISBN 90-8578-022-5 NUR 961, 967 Wettelijk depot: D/2005/10.500/22
Acknowledgement
1
Acknowledgement
The author kindly thanks the two promoters, Prof. Jan Melkebeek and Prof. Luc Dupré, for a chance to obtain an internationally recognized degree from Ghent University, Belgium, and for a great help with improving my English writing skills when preparing the Ph.D thesis. The author would like to thank the following people for their contribution to the current research and many discussions we had: Jehudi Maes, engineer at PICANOL BELGIUM Dimitre Makaveev, engineer at BOMBARDIER BELGIUM Marc De Wulf, researcher at OCAS, ARCELOR GROUP Josef Ghijselen, engineer at INVERTO BELGIUM Jan Declercq, head R&D at PAUWELS INTERNATIONAL Tony Moses, head of Wolfson Center, Cardiff, UK Fausto Fiorillo, research director at IEN, Torino, ITALY Martin J. Sablik, senior researcher in San Antonio, TX, USA Johannes Sievert, senior researcher at PTB, GERMANY Philip Beckley, senior researcher at European Steels, UK Special thanks to a former colleague from Urals Technical University, Alexander Pulnikov, for his contribution to this study. Voor de administratieve taken kon ik steeds terecht bij Ingrid Dubois. Bij technische problemen stonden Christian Vervust en Fernand De Boever steeds paraat. This work was financially supported by the STWW-project IWT 980357, the Interuniversity Attraction Poles project IAP-P5/34, the GOA-project 99-200/4, the FWO-project G.0322.04. The author would like to thank the project partners, participating in the above mentioned R&D projects. The work is devoted to my parents, as it is them who gave me the birth and the education for life. Спасибо моим родителям за то, что дали мне возможность получить лучшее образование и путевку в жизнь.
2
Summary
Summary The aim of this study is to expand the knowledge about electromagnetic behaviour of non-oriented and grain-oriented electrical steels, used in all parts of Great Chain of Energy Transformation. This study deals with the effects of uniaxial stress on magnetic properties of electrical steels. The work consists of two major parts. The first part defines the framework of the present study. The second part starts from a 1D study, followed by a more complex 2D magnetization in electrical steels. Chapter 1 is an introduction, positioning the subject of this study. A better understanding of various production procedures leads to a more accurate prediction of energy losses and the "building factor". Chapter 2 deals with the analysis of the working conditions, affecting the behaviour of electrical steel in actual machines. A detailed study is performed for 2D magnetic conditions in induction machines, from theoretical and experimental point of view. The iron energy losses depend on magnetic flux patterns as well as on mechanical stresses. Chapter 3 presents the art of magnetic measurements, followed by the choice of the magnetic measurement technique employed in the present study. The advanced magnetomechanical setup created in EELAB allows to control and maintain sinusoidal induction and to carry out an unique range of 2D magnetic measurements under 1D stress. Evidently, the extensive know-how in magnetic measurements created by the team of EELAB, where the author had the chance to reside for five years, has contributed to this doctoral research. Chapter 4 is an investigation of the simplest 1D case of uniaxial magnetization at uniaxial stress. A physically sound explanation is presented for the stress effects. The loss separation is applied for a statistical characterization of electrical steels under magnetomechanical conditions. Although some effects of stresses are known in literature, a few new aspects are presented. Chapter 5 deals with the complex 2D magnetic measurements under uniaxial compression and tension. This chapter of the study includes both alternating magnetization and rotational magnetization. Chapter 6 concludes this study with the recommendations on how the energy loss in various electrical steels can behave under stress, as well as what other subjects are related to the present study. The author hopes that the work has extended the know-how of EELAB as well as has consolidated the position of EELAB worldwide.
Contents
3
CONTENTS Acknowledgement
1
Summary
2
Contents
3
List of Symbols
7
1. INTRODUCTION. 1.1. Energy transformation. 1.2. Energy losses and magnetism. 1.2.1. The history of magnetism. 1.2.2. Magnetic materials and domain theory. 1.2.3. Application of magnetic materials in energy transformation. 1.3. Electrical steels. 1.3.1. Lamination. 1.3.2. Resistivity and various alloys. 1.3.3. Grain size and orientation of grains. 1.3.4. Production of electrical steels. 1.4. Stress effects in electrical steels. 1.4.1. Production stress in electrical steels. 1.4.2. The effect of punching. 1.4.3. The effect of core building. 1.5. Engineering choice of electrical steels.
9 9 10 11 15 18
2. WORKING CONDITIONS OF ELECTRICAL STEELS. 2.1. Standard characteristics of electrical steel. 2.2. Target research of working conditions in electrical steels. 2.2.1. Target research in grain-oriented steels. 2.2.2. Target research in non-oriented steels. 2.3. 2D magnetic working conditions in induction machines. 2.4. 2D mechanical working conditions in induction machines. 2.5. Conclusions.
31 32 36 36 39 40 51 56
20 21 21 22 24 25 26 26 28 29
4
Contents
3. MAGNETIC MEASUREMENTS UNDER STRESS. 3.1. Standard magnetic measurements in electrical steels. 3.1.1. Epstein frame. 3.1.2. Single sheet tester. 3.1.3. DC magnetic measurements of iron and steel. 3.1.4. Magnetic measurement techniques used in standard methods. 3.2. State of the art in 2D magnetic measurements. 3.2.1. 2D single sheet testers. 3.2.2. Shift to a horizontal rotational single sheet tester. 3.2.3. Typical operational algorithm for magnetic measurements. 3.3. Magnetic measurements under stress. 3.4. 2D magnetic measurement system under stress. 3.4.1. The mechanical subsystem of the 2D setup. 3.4.2. The magnetic subsystem of the 2D setup. 3.4.3. Magnetic measurement technique. 3.4.4. Waveform control. 3.5. Magnetic measurement procedure. Operational software. 3.6. Sample preparation. 3.7. Conclusions.
59 60 60 62 64 65
4. 1D MAGNETIC MEASUREMENTS UNDER STRESS. 4.1. Uniaxial measurements in electrical steels. 4.1.1. Uniaxial magnetization in grain-oriented steels. 4.1.2. Uniaxial magnetization in non-oriented steels. 4.1.3. Uniaxial magnetization at tensile plastic deformation. 4.1.4. Uniaxial magnetization in semi-processed and annealed steels. 4.1.5. Uniaxial distorted magnetization under stress. 4.1.6. Experimental results of 1D measurements: preliminary tendencies. 4.2. The magnetomechanical effect: theoretical approach. 4.2.1. Energy theory and domain structures. 4.2.2. Applied stress and domain theory. 4.2.3. Levels of understanding: microscopic, domain, macroscopic. 4.2.4. Explanation of various effects: the cross points in
107 108 110 114 119
68 71 74 79 81 86 90 92 98 101 103 105 105
122 126 129 130 130 135 137 139
Contents two quadrants. Explanation of various effects: the critical tensile stress. 4.2.6. Explanation of various effects: the plastic deformation. 4.3. Statistical theory of energy losses. 4.3.1. Classical loss. 4.3.2. Hysteresis loss. 4.3.3. Excess loss. 4.3.4. Loss separation technique. 4.4. Separation of losses under applied stress. 4.5. Conclusions. 4.2.5.
5 140 141 143 144 145 145 146 148 153
5. 2D MAGNETIC MEASUREMENTS UNDER STRESS. 5.1. Vector magnetization under uniaxial mechanical load. 5.2. 2D magnetic measurements in electrical steels 5.2.1. Justification of the 1D measurements in Chapter 4. 5.2.2. Alternating magnetization at 0 and 90 degrees with uniaxial stress. 5.2.3. Circular rotational magnetization. 5.2.4. Energy loss at 2D magnetization under stress. 5.2.5. 2D magnetization under tensile plastic deformation. 5.3. 2D magnetomechanical effect in literature. 5.4. Ratios between rotational and alternating losses. 5.5. Conclusions.
155 156 157 161 163
6. STRESS EFFECTS IN ELECTRICAL STEELS. 6.1. Conclusions of the present study. 6.1.1. The art of 2D magnetomechanical measurements. 6.1.2. The 1D magnetomechanical measurements. 6.1.3. The 2D alternating magnetomechanical measurements. 6.1.4. The 2D rotational magnetomechanical measurements. 6.1.5. The parameters and the stress effects. 6.2. Extensions of the present study. 6.2.1. Residual stresses. 6.2.2. NDE: non-destructive evaluation. 6.2.3. Magnetostriction.
183 186 186 187 188
166 171 174 176 179 180
188 189 190 190 191 191
6
Contents 6.2.4. Biaxial stresses. 6.3. Applications of the present research. 6.3.1. Magnetomechanical measurements in soft magnetic materials. 6.3.2. Recommendations to manufacturers of electrical steels. 6.3.3. Recommendations to manufacturers of power transformers. 6.3.4. Recommendations to manufacturers of rotating machines. 6.4. Which engineering choice of section 1.5 is better? 6.5. Conclusions.
191 192 192 192 192 193 193 194
List of International Publications
195
List of Attended Conferences and Awards
197
Bibliography
199
List of Symbols
7
LIST OF SYMBOLS General notations: • • • • •
Scalars: A. Vectors: A (the symbol in bold). Components of the vectors, or their projections on main axes: Ax. Time variations of the scalars: A(t). Various parameters: V0, Wh.
Symbols: Symbol α ρ
Φ µ µ0
µ0M a B Br D E f G H Hc I J lm M N NS P S t T Tc
Definition Any angle between vectors [deg] Mass density [kg/m3] Magnetic flux [Wb] Magnetic permeability Permeability of free space equal to 4π10-7 [H/m] Magnetic polarization [T] Axis ratio of ellipse, varies from 0 to 1 Magnetic flux density [T] Remanence [T] Electric flux density [C/m2] Electrical field [V/m] Magnetizing frequency [Hz] Parameter equal to 0.1357 Magnetic field [A/m] Coercive field, or coercive force [A/m] Electric current [A] Electric current density [A/m2] Mean magnetic path length [m] Magnetization [A/m] Number of turns of a magnetizing winding Effective turns of a search coil, e.g. the H coil Power loss [W/kg] Cross sectional area [m2] Time [sec] Period [sec] Curie temperature [K]
8
List of Symbols U V V0 Vsensor W
Induced emf in a search coil [V] Voltage of the excitation windings [V] Parameter related to microstructure [A/m] Voltage measured by the needle probes [V] Energy loss [J/ m3]
Abbreviations: emf rms 1D 2D AC DC GO NO RD RSST SST TD
Electromotive force Effective value, stands for "root-mean-square" One-dimensional Two-dimensional Alternating current Direct current Grain-oriented steel Non-oriented steel Rolling direction Rotational single sheet tester Single sheet tester Transverse direction
Introduction
9
There are no such things as applied sciences, only applications of science. Louis Pasteur (1822 - 1895) Engineering is the science of economy, of conserving the energy, kinetic and potential, provided and stored up by nature for the use of man. The task is to utilize this energy so that there may be the least possible waste. William A. Smith, 1908.
CHAPTER 1. INTRODUCTION. 1.1. Energy transformation. One of the fundamental features of energy is its ability to be transformed or converted from one form of energy into another. Different forms of energy have been discovered during the modern history of mankind. It is also believed that some forms of energy are yet to be discovered. The curiosity of human nature was a driving force towards the practice of how to employ different forms of energy. One of the causes of the industrial revolution was the knowledge of how to transform energy and how to control that transformation. The next natural step is making knowledge useful for individual and society needs. One of the universal forms of energy is electrical energy. It is easy to produce, easy to transport, and most important, easy to convert from one form of energy into another. The Russian engineer DolivoDobrovolsky was the first to create the complete chain of AC electrical energy transformation, including a three-phase induction machine. In 1891, he presented the AC system at the World Electrotechnical Show in Frankfurt. Today, the majority of energy systems are built based on a similar chain of AC energy transformation as shown in Fig. 1.1.
Fig. 1.1. Energy transformation in Great Chain of Energy Transportation.
10
Chapter 1.
A schematic chain of electrical energy transportation consists of a generator, which transforms mechanical energy into electrical energy, a step-up transformer, which converts the AC energy from low voltage to high voltage, a line or a grid, which transports electrical energy, a series of step-down transformers, and finally, an electrical energy consumer, as shown in Fig. 1.1. The major consumers of electrical energy are electrical motors, which transform electrical energy into mechanical work. The schematic energy chain shown in Fig. 1.1 looks fine, however, it hides a side effect of energy transformation. Whether electrical energy is transformed into mechanical energy or mechanical energy into electrical energy or electrical energy into electrical energy, there is always some part of the energy which is lost during the transformation. In electromagnetic energy conversion, an important part of this energy loss is due to the magnetic core of the converting device. Here, the questions of efficiency and economical value arise. How crucial is that part of energy for the transformation process? What is the cost of the energy loss? What are the ways to improve the system efficiency? How to predict what happens in case of new designs or when new materials are used? What will be the energy loss when the existing technology of electrical machine production is modified? 1.2. Energy losses and magnetism. When considering a typical chain of electrical energy transformation, two types of electrical machines can be distinguished. One type transforms mechanical energy into electrical energy, or vice versa, i.e. generators and motors. Another type transforms AC electrical energy of one value into another, i.e. transformers. Here and later, both rotating and stationary electromagnetic energy converters, i.e. motors and transformers, are called "machines". Due to the fact, that those two types of electrical machines participate in the majority of electrical energy transformation, new knowledge about these machines is very valuable to the industrial and scientific society. The energy conversion in transformers and induction machines is based on electromagnetic principles. In order to understand why this principle was chosen in the majority of electrical machines, one should take a brief look at the historical development of scientific ideas, which were the foundation of all electromagnetic applications.
Introduction 1.2.1.
11
The history of magnetism.
"Once upon a time some sheep shepherds in Magnesia region of Turkey found that their iron-shod staffs became attracted to certain rocks. A regional name was attached to the effect and “magnetism” entered the world vocabulary" [Beckley02]. The effect was first used in a primitive navigation compass, which consisted of a piece of natural rock called lodestone, or “leading stone”. Later it was observed that steel needles rubbed by a natural magnet themselves became magnetized and formed a much more convenient compass component. Since then the art of magnetism expanded into a science starting from the studies of Gilbert (1544–1603) and Galileo (1564–1642), and continued by Faraday (1791–1867). As in most disciplines, the theory of magnetism started from statistical observations and a lot of experiments. Gilbert’s book, published in 1600, was the first work on magnetism in Europe. His experiments with some magnets led to the idea of magnetic poles. He discovered that like poles repel each other and unlike attract. He likened the polarity of the magnet to the polarity of the Earth. A “north seeking” pole is the end of a magnet that points to the Earth’s north magnetic pole when freely suspended, for example, in a compass. In 1819 Oersted (1777–1851) discovered the deflection of a compass needle by electric current flowing in a conductor. The magnitude and direction of this influence is related to the size and the direction of the current involved. This discovery of a fundamental connection between electricity and magnetism engaged the scientific community and led to a brainstorm in electrodynamics research by scientists such as Ampere (1775–1836). His experiments showed that the deflection of a compass relative to an electrical current obeyed the right hand rule. He also showed that parallel wires with current in the same direction attract, those with current in opposite directions repel. A series of experiments by Faraday showed that time-varying magnetism would induce electric current in a nearby electric circuit. Furthermore, Faraday first suggested that a time-varying current would induce electromotive forces, or emfs, in a separate conductor system. He first proposed that magnetism was a circular force and invented the term “lines of force”. Faraday’s laws expressed the electromagnetic environment, as it is known today. First, when a conductor moves with respect to a magnetic field, an emf is developed in that conductor.
12
Chapter 1.
Second, the magnitude of the developed emf is proportional to the rate of change of the magnetic flux. He also believed in the possibility of “the production of any one power from another, or the conversion of one into another.” Faraday concepts of relating magnetism and electricity were then used to make the first transformers. The invention of the dynamo in 1865 naturally followed and began the era of electricity and electromagnetism. In 1860 mathematician Maxwell (1831–1879) from the Cavendish laboratory formulated the fundamental principles of electromagnetic fields. In 1856 he wrote "On Faraday's Lines of Force", in which he translated Faraday's theories into mathematical form, presenting the lines of force as imaginary tubes containing an incompressible fluid. In 1861 he published "On Physical Lines of Force", in which he treated the lines of force as real entities, based on the movement of iron filings in a magnetic field and using the analogy of an idle wheel. In 1865, he published "On a Dynamical Theory of the Electromagnetic Field". Maxwell's formulation of electricity and magnetism was published later in "A Treatise on Electricity and Magnetism", which included the formulas today known as the Maxwell Equations. Those principles became the backbone of further developments in theoretical and applied electromagnetism. Here, a brief evaluation is presented. Macroscopic electromagnetic phenomena are often described by the following vector fields, which can be space and time dependent: E - electrical field [V/m] D - electric flux density [C/m2] H - magnetic field [A/m] B - magnetic flux density [T] These vector fields are not independent, but interconnected by Maxwell’s equations:
∂B ( Faraday ' s ∂t ∂D ∇× H = J + ( Ampere' s ∂t ∇ ⋅ D = γ (electric Gauss ∇ ⋅ B = 0 ( magnetic Gauss ∇× E = −
(1.1)
law)
law)
(1.2)
law) law)
(1.3) (1.4)
Here, J is the current density vector [A/m ], while γ [C/m ] equals the charge density. It is well known that these vectors are connected through the constitutive laws. 2
3
Introduction
13
To recall some terminology necessary for this work, one must define the magnetic field and magnetization. The phenomenon of magnetic field can be described by its action [Jiles91]. The torque on a compass needle, which is an example of a magnetic dipole, is the most familiar property of a magnetic field. The strength of the field of force is called the magnetic field strength H. It has direction as well as strength. The direction is that in which a north pole, subjected to magnetic field, tends to move, or that indicated by the north-seeking end of a small compass needle placed at the point. The Faraday’s "lines of induction" pass from a magnetized material into the air at a north pole, enter again at a south pole, and pass through the material from the south pole back to the north to form a closed loop. The total number of lines crossing a given area S is a measure for the magnetic flux Φ in that area. According to Faraday's theory, the rate of change of the magnetic flux Φ generates an emf in a closed circuit through which the flux passes. The magnetic flux per unit area is the flux density, or magnetic induction B. B = µ0 H
(1.5)
Here, the factor µ0 = 4π10-7 [H/m] is called permeability of free space. In order to describe the magnetic properties of materials, one must have a quantitative measure of magnetization M, which is the material response to the field. Both H and M contribute to the induction lines, which is defined by the following relation: B = µ0 (H + M)
(1.6)
Here, H and M are generally vectors. Electrical currents outside the material generate the magnetic field H. The magnetization M is generated by the uncompensated spin and orbital momentum of electrons within the material [Jiles91]. In the technical literature, the vector expression (1.6) is often reduced to a scalar one, assuming the three vectors being parallel. When a piece of unmagnetized iron is brought near a magnet or is subjected to a time-varying magnetic field, the magnetization in the iron due to the magnetic field is described by a magnetization curve, as shown in Fig. 1.2. This curve is obtained by plotting the magnetization M or the magnetic induction B against the field strength H. Such curves are of fundamental importance for describing the magnetic properties of materials, especially for considering electrical steels.
14
Chapter 1.
For most materials, if the field strength is first increased from zero to a given value and then decreased again, as indicated by the arrows of Fig. 1.3, the original curve is not retraced. The induction “lags behind” the field and follows a characteristic curve, shown by the broken line in Fig. 1.3. This phenomenon was named “hysteresis” by Ewing (1855-1935) in 1891, and the characteristic curve was called a hysteresis loop.
Fig. 1.2. Initial magnetization curve and permeability for iron [Jiles91].
Fig. 1.3. Initial magnetization curve (solid) and hysteresis loop (dotted). 1 gauss = 10-4 T, and 1 oersted = (1000/4π)A/m = 79.58 A/m. [Bozorth51].
Introduction
15
When considering the initial magnetization curve, the ratio B/H is called the permeability µ. For ferromagnetic materials the ratio µ/µ0 is much larger than 1 [Borzorth51]. For a BH loop symmetrical to the origin, the absolute value of the induction at H = 0 is called the remanence Br for that loop. It represents the magnetization obtained after applying a field to the specimen and then removing it. The absolute value of H for which B = 0 is called the coercive field Hc. The coercive field is the field needed to bring the magnetization from the remanence to zero. It represents the magnitude of the field that must be applied to a material in order to reverse its magnetization. Coercive field, remanence and permeability are often used as a measure of quality of the material. The ferromagnetic materials (hereafter, magnetic materials) have been divided into soft and hard magnetic materials, having a low or high value of Hc, respectively. Soft magnetic materials are easy to magnetize due to a low coercive field. An additional parameter of basic importance in the characterization of soft magnetic materials is the power loss P. For electrical steels studied here, the electromagnetic power loss P [W/kg] is proportional to the area of the BH loop [Sievert84] obtained at a time periodic flux: 1 T dB (t ) (1.7) P= H (t ) dt dt ρT ∫0 Here, ρ is the density of the material, T is the period of the cycle, f is the magnetizing frequency. For simplicity, the electromagnetic power loss P is also called "power loss" or "total power loss". 1.2.2.
Magnetic materials and domain theory.
The scientific explanation for mechanisms behind the magnetism was developed historically. A ferromagnetic material has long been regarded as an assemblage of small permanent magnets. Ewing together with Weber (1804–1891) assumed that each atom was a permanent magnet free to turn in any direction about its center. When the material is unmagnetized, the magnets are arranged with random orientation. When it is magnetized, they are lined up with their axes approximately parallel. The nature of this small magnet has been the subject of a number of studies during many years. In 1907, based on earlier works carried out by Ampere, Weber and Ewing, physicist Weiss (1865–1940) concluded that ferromagnetic
16
Chapter 1.
materials must be fully magnetized at all times. Below a critical temperature, or the Curie temperature Tc, the magnetic moments spontaneously attain long-range order and the material acquires a substantial spontaneous magnetization Ms. In case of iron, where Tc ~ 103 K, the molecular field is estimated to be 109 A/m. Thus, well below Tc, the moments are nearly perfectly aligned. In iron, at room temperature, this gives a spontaneous polarization µ0M of order of 2 T. The molecular field hypothesis explains the main aspects of the temperature dependence of the spontaneous magnetization. However, it seemed if there exists such an enormous internal field, one could expect the material to be spontaneously magnetized to saturation under all circumstances. How can a hysteresis loop exist at all? It seems impossible that the external field of 100 A/m can reduce the magnetization of the material to zero, if it confronted with the internal fields of 109 A/m. Weiss proposed to resolve this difficulty by dividing the material into regions of many atoms, called “magnetic domains”. In each domain, the molecular field dictates the degree of magnetic moment alignment. However, the orientation of spontaneous magnetization can vary from domain to domain. Therefore, when magnetization is averaged over large volumes with many domains, the result, mainly determined by the relative orientation and volume of domains, can be very different from the spontaneous magnetization, and even close to zero [Bozorth51]. The history of the comprehension of magnetic materials in the twentieth century has been the history of the elaboration of Weiss’ ideas. It took many years before quantum mechanics could give some microscopic interpretation of the molecular fields. In fact, magnetic domains are the result of the complex balance of several competing energy terms, a balance by no means trivial to treat theoretically [Bertotti98]. However, a number of modern techniques allow producing magnetic domain images to prove their physical existence in magnetic materials. In this study, a simplified interpretation of the domain theory is used to investigate other phenomena. The evolution of magnetic domains is shown in Fig. 1.4. Generally, when the field is applied externally, a rearrangement of the domain structure takes place, mainly due to domain wall movement. The domains with magnetization approximately pointing in the direction of the applied field are energetically favoured. After the magnetic field changes its sign from negative to positive, the domains with magnetization pointing in the direction of the applied field expand
Introduction
17
by consuming unfavourable surrounding domains, as shown in Fig. 1.4. There are four kinds of magnetization processes, namely, reversible and irreversible wall movements and reversible and irreversible domain rotations. Considering a hysteresis loop obtained for an electrical steel, three mechanism are usually present: reversible and irreversible wall movement and reversible rotation. Fig. 1.4 depicts only domain wall movement under the application of a positive external field, starting from the appearance and the growth of the favourable domains, reaching the coercive field and growing up to the disappearance of unfavorable domains. At high field, a single domain practically occupies the whole space. Fig. 1.5 depicts the simple case of domains aligned with the external field direction. When a strong external magnetic field appears, the magnetic domains with the same orientation as the external field grow in size, while opposite 180-degree domains shrink. It moves the socalled “domain walls” to enlarge the favourable domains that are coaxial with the external field H, see Fig.1.5.
Fig. 1.4. BH loop. Domains changes due to magnetization [Bertotti98].
18
Chapter 1.
Fig. 1.5. Domain theory: a) energy stored in a field, reduction of energy by subdivision into lower energies, b) optimal energy storage in a group of domains in iron, c) domain wall movement at strong external field H [Beckley02]. 1.2.3.
Application of magnetic materials in energy transformation.
The unique property of ferromagnetic materials lies in the ability to develop a large magnetic flux by comparatively small applied magnetic field. In soft magnetic materials the crystal structure facilitates a response to applied fields and makes it reversible. Consequently, the magnetization process requires a small amount of energy. Those properties have been successfully exploited in electromagnetic devices, such as transformers and rotating machines. In the nineteenth century there was an enormous engineering activity in the US and Europe, surrounding the invented induction machine. The knowledge of machine design and performance prediction progressed rapidly. At the end of the 19th century, Edison laboratory developed a range of electromagnetic applications. Started with Edison, Tesla (1856–1943) was the first to use AC current in a two-phase electrical generator, a power transformer and MHz frequency devices. Twenty years after the Tesla patents, in 1907, Smith surveyed the loss separation methods used today in motor design [Glew98]. Taking a brief look back to section 1.1, it was stated that the energy transformation is inevitably related to some energy losses.
Introduction
19
Indeed, a century ago, engineers have named the main sources of energy losses in induction machines. Generally, there are two main components of energy losses in induction machines and transformers: “copper” losses in the windings and “iron” losses in the magnetic core. To answer the questions of section 1.1, the designer of a machine must make a choice about the ratio between the copper and iron loss. In many cases, conventional techniques are applied to help engineers make that choice and to compromise between the two losses. This book is about the “iron” energy losses only. The iron energy loss is an inevitable inefficiency of the electromagnetic energy transformation, which is present in all parts of the Great Chain of Energy Transformation, such as generators, transformers or electrical motors. Without magnetic material present, the energy transformation would become hundreds and thousands times more difficult and costly. In other words, the performance of magnetic material in the machine is crucial for energy conversion with optimal energy loss. Another choice the engineer should make is the choice of design technology. For many years, engineers applied various computational parameters and coefficients, based on years of experience (empirical) rather than on pure science. The design methods have been developed to a major extent since the first machine was built. The computer era made the calculations easier. However, many assumptions of older design techniques have survived the changes. As a result, it happens sometimes that the machine shows worse characteristics when built in comparison with the theoretical design. Iron energy loss are entered into the design model from standard properties of electrical steels. This is one of the reasons for the incorrect prediction of (iron) energy losses, i.e. the so-called “building factor” [Dupre03]. The building factor defines the ratio of the actually measured iron losses in the machine and the energy losses calculated under standard conditions. The building factor is usually larger than 1. The main reasons for that are discussed in Chapter 2 of this book. The last choice, or in fact, the first step in every design, is the choice of the electrical steel grade to be used in the device, see section 1.5. For a century, scientists and material engineers did their best to produce cost-effective materials for various purposes. Today, Fe-Si steels are applied in the majority of electromagnetic devices. According to [Schoppa00], about 80% of the produced soft magnetic materials are
20
Chapter 1.
non-oriented Fe-Si steels, about 16% are grain-oriented Fe-Si steels, and only about 4% of all soft magnetic materials are other materials. Although electrical steels only are the subject of this study, the dependencies, presented in this book, have a more general outcome towards other magnetic materials [Turgut03]. One may note that the value of this 4% other magnetic materials is about 20% of the total costs of soft magnetic materials, produced in the world [Schoppa00]. 1.3. Electrical steels The history of the development of electrical steels starts from using cast iron and wrought iron due to its availability in the earliest times. However, the permeability of cast iron is not very good, see Fig. 1.6.
Fig. 1.6. Magnetic curves of Fe materials at moderate applied fields [Beckley02]. Due to large eddy currents induced in solid cores as magnetization changes, modern electromagnetic cores are produced as laminations of thin steel sheets. During the twentieth century, electrical steels have been constantly improved to better permeability and smaller energy losses. Among the parameters to improve, there are electrical resistivity, thickness of sheet, grain size, texture, etc.
Introduction 1.3.1.
21
Laminations.
Iron is a good electrical conductor, so that if solid iron is being used as a magnetic core, the surface of the iron could be considered as a lowresistance short-circuit enclosing the core. It leads to a considerable amount of energy, dissipated in the solid core. The method to reduce the eddy currents is to reduce the thickness of the sheets. This leads to an increase of the production costs, moreover, very thin lamination reduces the percentage of the space occupancy by the steel, when stacking the laminations. Also, the surface acts as a primary source of domain pinning sites, which increase some of the energy loss components. Despite those drawbacks, the majority of electromagnetic devices uses electrical steels with thickness of 0.2 to 1.0 mm [Beckley02]. 1.3.2.
Resistivity and various alloys.
As seen from Fig. 1.7, the maximum resistivity can be obtained when silicon is added to the alloy of iron. Indeed, at 3% silicon the resistivity of iron alloy raises 5 times, and at 6% almost 8 times in comparison with the case of absence of silicon. Aluminum also raises resistivity very well, but there is a negative side effect of high affinity of aluminum for oxygen [RosYanez03]. Carbon cannot be used due to the formation of nonmagnetic carbides at 100 °C, which reduce the mobility of the domain walls [Devine96]. Other elements were tested, but silicon remains the preferable alloying element to increase resistivity. When the silicon content increases up to 6.5%, magnetostriction and related problems of noise and vibration diminish to a negligible level. Unfortunately, high silicon steels are difficult to produce costeffectively. The diffusion annealing after hot dipping is a feasible solution [RosYanez03]. The hot dipping production route can result in an increased silicon content, either constant over thickness of the steel sheet, or varying over thickness with a lower content in the center and a higher content at the surface of the lamination. Hot dipping by diffusion annealing is a relatively new and costeffective process that increases the Si and Al content to obtain better magnetic properties of electrical steel [RosYanez03].
22
Chapter 1.
Fig. 1.7. Resistivity of additions of various elements to iron [Bozorth51]. 1.3.3.
Grain size and orientation of grains.
Grain boundaries are prime pinning sites for domain wall movement. Impurities such as sulfur or carbon also pin domain walls. The larger the grains, the smaller the number of grain boundaries per unit volume, the smaller the overall amount of obstruction of wall movement. Large grains can be obtained by annealing at a temperature of around 850 °C. The iron lattice has favorable directions for magnetization. As illustrated in Fig. 1.8, those directions can be exploited for uniaxial magnetic flux applications, such as transformers. In 1930, Goss developed grain orientation processing, i.e. suitably applied cold rolling and heat treatment regimes, resulting in a selective growth of grains, having their easy directions in the strip rolling direction. It was believed for a long time that the larger the grains, the better. However, with the advent of high-frequency power supplies, using pulse width modulation, the size of grains has to be optimized to avoid extra losses. Those extra energy losses occur in large grains mainly due to large domain wall spacing, associated with micro eddy currents and, consequently, extra losses [Beckley02]. Thus, the optimal grain size depends on the electromagnetic application of the material.
Introduction
23
Fig. 1.8. a) cubic lattice, b) magnetization curves for a single crystal. The [100] direction is the easy cube edge direction, [110] is the hard cube face diagonal direction, and [111] is the hardest cube body diagonal direction [Beckley02]. Electrical steel is a polycrystalline material, having a large amount of grains. The statistical distribution of the orientation of the grains along various directions in the material is called texture. In grain-oriented steel the direction of easy magnetization, or [100] direction in Fig. 1.8, lays in the plane of the sheet, parallel to the RD. The worse direction is the one that makes a 58-degree angle with the RD as it corresponds to the hard magnetic axis of the iron crystal [Bozorth51]. Due to the fact that grain-oriented steel is often used for uniaxial magnetization in the RD, the engineering interest for a 2D study for these materials is limited. Nevertheless, there remains a scientific interest in 2D behavior of grain-oriented steels. In contrast, nonoriented steels are widely used under complex 2D magnetic conditions. Generally, non-oriented steels are assumed to
24
Chapter 1.
be completely isotropic in the plane of the sheet. However, this is not the case. There is always a difference in magnetic behaviour for various directions, such as the RD and the TD. 1.3.4.
Production of electrical steels.
The production of electrical steels has always been the interplay between magnetic properties, physical properties, manufacturing methods and production costs. Larger grains, more silicon content, high purification of steel, low carbon content, and other “better quality” parameters depend on workability of technology, as well as how feasible it is to apply one or another costly method to achieve certain goals. Some processes are crucial to one type of electrical steel, but less important to another one. The art of electrical steel production has been gradually developed to minimize the cost and to increase the quality. When a new piece of knowledge about the application of electrical steels appears at the horizon, a change of production process might be a result, in order to improve the output quality of electrical steel. However, it takes sufficient effort to implement new changes to an existing technology. Before making the decision to change the existing or to implement a new technology in electrical steel production, one should take a look at limitations of the technology-in-use. When talking about production, electrical steel is always mechanically rolled. The main objective for rolling is to obtain a given thickness of the sheet in order to decrease energy loss due to eddy currents. Another objective of rolling is to obtain a certain texture, or sheet-plane anisotropy. In a majority of production methods, the steel is rolled in one direction, called then the rolling direction. Consequently, the transverse direction is the direction perpendicular to the RD in the plane of the sheet. It is known that the magnetic properties of non-oriented steel are different in the RD and the TD. Hence, non-oriented electrical steels can be named isotropic only to some extent. The future progress for the soft magnetic sheets lays in the improvement of their texture, and particularly in obtaining large [100] components [Mekhiche96]. Novel techniques such as cross rolling could bring the desired result. The magnetic performance of cross-rolled sheets turns out to be better compared to conventional non-oriented sheets [Mekhiche96].
Introduction
25
Rolling procedures introduce mechanical stresses in the plane of the sheet, which strongly influence the mechanical and especially magnetic properties of electrical steel. In order to reduce the damage from stresses and deformations, the stress relief annealing is often applied to improve magnetic properties of electrical steel sheets. Carbon and sulphur have also very negative effects on the magnetic properties of electrical steel as they act as pinning sites for domain wall movement. When steel is rolled to thin final thickness, it is then often decarburized and desulphurized. To achieve low carbon content the steel is exposed to a decarburizing atmosphere such as wet hydrogen at 800 °C. Carbon diffuses to the surface and reacts with the furnace atmosphere gas. To reduce the sulphur content, the traditional technique of removing liquid slag is applied together with various chemical methods. The stress relief annealing is applied at the final stages of steelmaking. The control parameters are temperature, time, furnace atmosphere, and cooling period. The optimum annealing temperature for electrical steel ranges from 720 °C to 840 °C. The annealing time usually varies between 1.5 to 2.5 hours depending on materials or type of furnace. The cost of these treatments is considerable, but very low sulphur metal, low carbon content as well as reduced stresses, gives excellent magnetic performance [Beckley02]. 1.4. Stress effects in electrical steels. The question of quality control for electrical steels arises each time a new technological process is applied to steel. The quality control of electrical steels particularly implies the control of the magnetic properties, such as energy loss and permeability. The lifetime of electrical steel starts with the steel manufacturer, producing required quality steel. Then, the consumer of electrical steel applies some technological procedures first to make the desired shape of the steel products and then to build the electromagnetic core. The magnetic properties of electrical steel usually deteriorate due to the influence of these procedures on the microstructure. Before electrical steel is finally used in an electrical machine, it is exposed to various mechanical stresses. The influence of stress on magnetic properties of electrical steels often results in a decreased magnetic performance and extra energy losses. Various stress effects are the subject of numerous researches all over the world. Here, the
26
Chapter 1.
summary of most of this research is presented as a preface to this work. 1.4.1.
Production stress in electrical steels.
Rolling with plastic deformation is an inevitable procedure during the production of electrical steels. However, plastic deformation leads to an increased number of defects in the microstructure. Therefore, many thermal treatments are applied as described in section 1.3.4. Stress relief annealing often minimizes the internal stresses from those procedures. To the interest of this study, the magnetic properties of electrical steel just after it is produced are assumed as the “primary” or the standard properties of steel. Those properties, mechanical and magnetic, can be found in various steel catalogues [Nippon92], [Beckley02]. The completing stage of the production process is the coating procedure. The main purpose of coating is to prevent eddy currents between neighbouring steel sheets in a stacked magnetic circuit. Other purposes of coating are to make punching and welding easier and less damaging to the steel sheet, and to prevent corrosion [Lindenmo00]. Coating also decreases the damage to the cutting tools. Sometimes, a special coating is applied to introduce a small tensile force in the preferable direction [Beckley02], [Grimm78]. The recent tendency to apply composite coatings leads to some reduction of coating thickness and improvement of its performance in a lamination stack. It is often the case that the magnetic properties of one roll are different from another, produced e.g. a day later. Moreover, the steel batch can suffer from various stresses due to transportation. When the steel batch comes to the machine factory, there may be a series of magnetic measurements and testing. Those measurements could take into account the actual standard properties for electrical steel grades before the use. 1.4.2.
The effects of punching.
Electrical steel production is finalized in rolls. In order to use it in electromagnetic devices, the electrical steel lamination should have a certain shape, for example, a tooth-tip shape for rotating machines. The required shape is obtained by cutting techniques, such as punching, guillotine, laser cutting, photocorrosion [Emura03]. All these techniques result in various cut edges.
Introduction
27
When the steel sheet is cut, the material properties next to the cutting edge deteriorate drastically. In 1971 Carlberg first suggested that a 1 mm wide degraded area could be expected adjacent to a sheared edge of an electrical steel strip [Moses00]. Schmidt identified a cut-edge hardening region 0.35 mm wide, showing an increase of loss of 30 to 40% and a corresponding induction drop of 70% for the same applied magnetic field strength [Schmidt75]. Nakata stated that the degradation of magnetic properties of non-oriented silicon steel sheet due to cutting is present as far as 10 mm from the cut edge, and that the deterioration is particularly pronounced up to 5 mm from the edge. Despite the differences in early opinions, the engineering society has agreed upon the average affected cut edge, having a width equal or larger than the thickness of the lamination [Beckley02]. There are many cutting parameters that affect mechanical and magnetic properties, such as steel hardness, ductility, ultimate tensile strength, yield strength, coating favorable to burr minimization, grain size, clearance, etc. Burr and clearance have a strong impact on interlayer shortcuts as well as on the cut edge properties [Baudouin03]. A mechanical strain caused by shearing stresses from cutting electrical steel sheets results in a deterioration of the magnetic characteristics of the sheet. One result is that, when magnetized parallel to the cut edge of a sheet the magnetic flux density measured in the cut edge region is less than the flux density in the center of the sample [Moses00]. The steel grades with larger grains ought to be more affected by cutting than the steels with smaller grain or than the steels with less silicon [Schoppa99], [Schoppa00]. There are few methods to improve the magnetic properties after cutting. The magnetic properties may be restored by heat treatment, such as stress relief annealing after punching, as shown in Fig. 1.9. The quality of the punching can be improved as well by an appropriate choice of a cutting technique, which results in less deterioration of the cutting edge. A lot of research has been devoted to improve the quality of cutting and to introduce new cutting techniques. For example, an abrasive waterjet cutting under high pressure could be applied [Schoppa03]. The method has a minor effect on magnetic properties of electrical steel due to lower deformation of the cut edge and a cooling effect of water. Schoppa believes that the abrasive waterjet cutting is the best currently known cutting method for the production of laminations for magnetic cores used in electrical machines.
28 1.4.3.
Chapter 1. The effects of core building.
After the electrical steel is cut into the required shape and before the copper windings are applied in the production process for electrical machines, the stack of laminations is usually built into the stator or the rotor, and then mounted into the frame of the electrical machine. Stress relief annealing can be applied either before the stack of laminations is in the frame, or after it is built into the frame. The effect of heat treatment is very useful to improve the magnetic properties of steel. However, when the lamination is stacked into the frame, new sources of mechanical stress appear. There are different fixing methods, such as automatic stacking, bolting, riveting, gluing, interlocking, laser or electrical bead welding, and die casting of rotors [Beckley02], [Schoppa02]. When considering which technique of core assembly to apply for lamination sheets, there is a compromise between easiness and low cost of the technology and the effect of various stresses and deformations due to assembly on electrical machine parameters. The significance of the stress effects has often been appreciated due to a negative effect on energy losses. The first side effect of the core building is an introduction of interlaminar short circuits, leading to increased eddy currents and energy losses. This is the question of production quality and quality control. Engineers often make a choice of slower or costly technology in order to keep the electrical steel undamaged. Easy welding leads to a short circuit between the laminations. Compared with welding, the influence of interlaminar short circuits by burs on the magnetizing behavior of electrical steels can be practically neglected [Schoppa02]. The second side effect of core building is the production of mechanical stress, mainly compressive stresses. The effect of compressive stress due to assembling is considered further in section 2.1. Generally, the effect of the cutting and the influence of the cut edge is much higher than the effect of core building due to the large flux density coming through the cut edges in the teeth [Schoppa02].
Introduction
29
Fig. 1.9. Cut edges and pictures of grains in grain-oriented steel "as cut" and "after stress relief annealing" [Beckley02]. 1.5. Engineering choice of electrical steels. There are two polar approaches among engineers about which type of nonoriented steels to use in electromagnetic devices. The effect of stress is different in each case. One group of engineers choose semi-processed steels (SP), having poor magnetic properties but at lower cost. The idea of further processes is to improve the magnetic properties. During production and assembling of the electrical machine, SP electrical steel is first cut to the required shape of the lamination and then annealed. The drawback of that approach is the need for costly annealing systems after punching.
30
Chapter 1.
That approach, favorite in the USA, results in a better quality of the electrical steel in the electrical machine, although obtained from initially poor-quality material. Another approach is to use a material having very good magnetic properties and high costs. Those fully-processed (FP) electrical steels are then cut to produce the required shape of sheets. The cutting process, of course, leads to a deterioration of the magnetic properties. That approach, favorite in particular in Europe and Japan, diminishes the quality of initially good electrical steel. It is worth mentioning that the above choice does not exist in grain-oriented steels. Usually, there is no need for annealing due to a high-quality punching and a "step-lap" technique of core assembling that allows magnetic flux passing without cutting edges. This study aims to bring a clear understanding of the effect of mechanical stress on the magnetic properties of electrical steels, applied in both approaches. However, before investigating the stress dependence, the area of working conditions for electrical steel as well as the methods for magnetic measurements are considered.
Working conditions of electrical steels
31
To believe with certainty we must begin with doubting. Stanislaus Lescynski CHAPTER 2. WORKING CONDITIONS OF ELECTRICAL STEELS. The choice of the electrical steel to be used in electromagnetic devices is often made based on steel characteristics, obtained by means of standard methods [IEC 404-2], [IEC 404-3]. These standards are useful to make a primary comparison between various steel grades. However, actual working conditions for electrical steel in electromagnetic devices often differ considerably from the standard ones. This chapter aims to investigate the actual 2D magnetic and mechanical conditions in electrical machines. The main purpose for that investigation is to define the practical area of further research on the stress effect. The measured iron loss in electrical machines usually exceeds the value obtained by a straight multiplication of the weight of electrical steel in the machine with the standard loss density. This difference in losses is generally taken into account by the so-called building factor [Nakata84]. The building factor is the ratio of the measured iron losses in the machine and the losses obtained under standard conditions. The reasons for a building factor greater than 1 are production reasons and design reasons. Production reasons are short-circuits between neighbouring laminations, quality of technology, influence of mechanical and thermal treatment of the material during the construction of the machine, etc. Design reasons are non-uniform flux distribution due to local saturation, harmonics in flux patterns due to the tooth structure or the non-sinusoidal electrical supply, local rotational magnetization and changes of the magnetic characteristics due to various thermal and mechanical stresses present in electrical machines. For many years, engineers have applied various coefficients and techniques in order to predict the performance of electrical steel in electrical machines. These coefficients were developed by decades of experience in electrical machine design. These techniques had many advantages, such as simplicity in obtaining good engineering results, understanding basic relationships, making decisions about design and performance compromises. Disadvantages were a very low accuracy and sometimes unpredictable results or bad machine performance. In the past, as long as heuristic design rules resulted in a machine that worked satisfactory, the design was considered acceptable. Later however,
32
Chapter 2.
design costs and operating costs, i.e. efficiency, got more attention. When advanced calculation methods became possible, many numerical techniques have been developed to predict the design factors mentioned above more accurately. For example, the analysis of local flux patterns and local iron losses has become possible for further investigations of the parameters of electrical machines [Gyselinck00]. The development has usually reached the highest level. Development departments of machine producers say that the cost improvement of one cent results in millions of profit and a competitive advantage on the market. But where to find that one-cent improvement? One of the ways is to take a good look back. Calculation of actual working conditions is still a question of approach. In many cases, rather conventional methods and coefficients are used. For example, a design technique in Russia employs two different magnetization curves for the same electrical steel, one is in the tooth region and the other is in the yoke. Basically, that technique takes into account the change of magnetic properties in the tooth region of electrical machine due to punching. Indeed, new studies worldwide have been investigating the modification of the magnetic properties due to cutting [Nakata92], [Ossart00], [Schoppa99], [Schoppa00], [Fujimura04]. Baudouin and Pulnikov have recently studied in details the effect of punching in electrical steels [Baudouin02], [Pulnikov04]. 2.1 Standard characteristics of electrical steel. As it was mentioned in section 1.4, the primary properties of electrical steels are the result of the steel production process. Basically, the primary state of steel is what a steel manufacturer provides to a steel customer. Output parameters of steel production are: - chemical composition, - thickness and its deviation, - type of coating, - state of heat treatment, - hardness. Chemical composition is sometimes hidden behind other parameters. The final thickness after few stages of rolling usually ranges from 0.2 to 1.0 mm. Coating could be organic or non-organic. The state of heat treatment means either fully processed or semi-processed. The main characteristics of electrical steel grades can be found in the certificate for a steel grade, catalogues of steel manufacturers and
Working conditions of electrical steels
33
other open sources [Beckley02]. Steel manufacturers provide typical physical and mechanical properties as well as typical magnetic properties. Typical physical properties include: - density, - silicon content, - resistivity. The density of electrical steel ranges from 7600 to 7850 kg/m3 [Bozorth51]. The silicon content varies from 1% for low silicon steel to 6.5% for high silicon steel. The resistivity ranges from 10 to 60·10-8 Ω·m. The common silicon composition for electrical steels is about 3%-wt content. It results in an increase of resistivity, see Section 1.3.2. Typical mechanical properties are: - tensile strength, or ultimate tensile strength, - yield strength, or yield point, - elongation, or plastic strain, - hardness, etc. From a practical point of view, the stress-strain characteristic is the true basis for any analysis of mechanical conditions of electrical steels under externally applied uniaxial mechanical load [Iordache03]. A typical stress-strain characteristic is shown in Fig. 2.1.
Fig. 2.1. A typical true tensile stress – true strain characteristic for nonoriented steel at two stages of hardening rate [Iordache03].
34
Chapter 2.
Generally, the mechanical properties of a steel grade depend on the type of electrical steel produced, see Section 1.5. For example, when the steel sheet is annealed, then the number of internal defects of the lattice, which is directly related to the dislocation density of the material, is reduced. Consequently, fully processed electrical steel typically has mechanical properties of a low-deformed material. On the contrary, high dislocation density of semi-processed steel leads to a reduction of tensile strength and a deterioration of other mechanical, and especially, magnetic properties, see Chapter 4. Typical properties for various electrical steels can be found in [Beckley02]. In fully processed non-oriented electrical steels, the ultimate tensile strength usually varies from 300 to 550 MPa. The yield strength is about 15 to 30% less than the tensile strength. On a stress-strain characteristic, the yield point corresponds to the beginning of plastic deformation, or to the 0.2% proof strength. In non-oriented steels, the difference between most mechanical properties in the RD and the TD is very small and usually less than 5%. The elongation on 80 mm gauge length can usually vary from 15 to 40%. Other mechanical properties are less important to the present study. In grain-oriented electrical steels, most physical and mechanical properties are within a similar range as in non-oriented steels. The typical thickness of the sheet varies from 0.23 to 0.5 mm. The typical density is about 7650 kg/m3. The silicon content is usually 2 to 3.4%. The typical resistivity is about 35 to 55·10-8 Ω·m [Bozorth51]. The ultimate tensile stress is different for the RD and the TD, ranging from 300 to 400 MPa. The difference between the RD and TD can be as much as 20%. The yield strength is smaller than the ultimate tensile stress by 8% in the RD to 22% in the TD. The elongation on 80 mm gauge length is 5 to 15% in the RD and 30 to 40% in the TD. The magnetic properties of electrical steels are the most important data in steel catalogues for electrical machine manufacturers. Typical magnetic properties include: - specific core loss at power frequency 50-60 Hz, - DC magnetization, DC hysteresis, DC coercive field, - incremental, or relative permeability, - core loss and permeability at frequencies up to 10 kHz, etc. The core loss is presented either as a few critical values at different induction levels, or as a complete graph. The typical specific core loss, measured in W/kg, is usually taken at an induction of 1.5 T and for the
Working conditions of electrical steels
35
power frequency of 50-60 Hz. From an engineering point of view, the unit W/kg is very useful, when multiplying the core weight to the core loss at different magnetic inductions. Furthermore, a magnetization curve (peak induction versus Ampere-turns) ranging from 0.5 to 1.8 T is easy to use. As a starting point of this discussion, the standard characteristics are considered. The magnetic properties of electrical steels are presented as the results obtained by an Epstein apparatus according to [IEC 404-2] or by a single sheet tester according to [IEC 404-3]. According to [IEC 404-2], half of the samples of the non-oriented steel under study is sheared parallel and half of the samples is sheared transverse to the RD. This practice leads to an averaging of typical magnetic properties in 2D, which is acceptable for the design of electrical machines. Despite a general belief of isotropic non-oriented electrical steel, the anisotropy is present in non-oriented steels. It results in different properties along various directions in the plane of the sheet. The difference is observed not only in mechanical properties as was stated above, but most importantly also in magnetic properties. Thus, any change of the magnetic anisotropy is important to be taken into account for the prediction of the actual performance of the electrical steels. Externally applied stress introduces a considerable change of the magnetic anisotropy, and hence, the stress effect is very significant at actual working conditions of electrical steels. Some extra information and recommendations for final annealing to reduce the degree of internal stress is also provided in catalogues. For example, the following precautions are issued for non-oriented steel by Nippon Steel Corp. [Nippon92]. "During stress-relief annealing, carbon contamination should be prevented, fast and uniform heating of laminations should be pursued, excessive oxidation from the annealing atmosphere should be avoided." Those precautions ought to maintain a high quality of the steel. Modern control techniques, applied by steel manufacturers, result in a better control of the material parameters and characteristics. In fact, fully processed non-oriented and grain-oriented steel, coming from manufacturers, might be considered today as top quality materials, which do not require any further annealing. Although the control of properties is of major interest to electrical steel factories, actual properties of a steel grade could still be different from the typical properties, provided by the manufacturer. There is a strong belief among engineers that the catalogue data only give a
36
Chapter 2.
general idea about the quality of steel grade. Good practice is the actual magnetic investigations of the materials before use. In general, standard parameters are the only information a steel manufacturer provides about its electrical steel grade. It is often the case that the amount of information an engineer requires in order to make a decision about a new design of an electrical machine, is much larger than the data available either from a catalogue or from classical magnetic measurements. For example, a new design requires the application of a compressive stress due to the preferred machine design. The data about the stress effect on the magnetic properties of electrical steel either do not exist, or are hard to find and difficult and costly to obtain. What an engineer should do in that case is first to take into account a general tendency of stress effect on magnetic properties of various steels. Up to now the general rule is that only a small tensile stress could be useful in the direction of the applied magnetic field [Beckley02]. All other in-plane stresses lead to a deterioration of the magnetic properties of electrical steels. This study is to extend the knowledge of the stress effect. Here, the main question arises: what are the target working conditions, mechanical and magnetic, that are of interest for various electrical steels used in different electromagnetic devices? 2.2. Target research of working conditions in electrical steels. Two types of electrical machines, and consequently, two types of electrical steels are considered: non-oriented steels in rotating machines and grain-oriented steels in transformers. In each case, theoretical and practical approaches are applied both from a steel producer and a device constructor point of view. Why use different approaches? The first reason to use these approaches is just to take a different look at the same problem. The second reason is to have a more complete view on possible working conditions of various electrical steels. The third reason is the possibility to make a choice of these working conditions, which are either of most importance, or easier to simulate in a novel measurement setup. Finally, a combined approach can bring a new area of research. 2.2.1. Target research in grain-oriented steels. The first type of considered electrical steels is grain-oriented steel. Grain-
Working conditions of electrical steels
37
oriented steels exhibit excellent magnetic properties when excited along the RD. A typical application of grain-oriented steel is in power transformers. In medium and large transformers the steel sheets are cut in such a way that the magnetic field in the steel laminations should be mainly uniaxial, parallel to the easy axis, i.e. [100] direction of the lamination. Indeed, one of the main objectives in a transformer design is to decrease core losses, and consequently, total energy losses during the energy transformation. The modern construction practice of large transformers requires cutting laminations in a sophisticated way in order to achieve the required core properties and at the same time being economically sound. The lamination of a large transformer core consists of hundreds of sheets, having different dimensions. The cutting line itself is a large automated piece of machinery. The reason to use such an expensive equipment for production of the transformer core is the reduction of core loss. In three phase transformer cores, there are regions where the magnetic field is not directed along the easy axis of the material, such as the T-joints regions and corners. In these regions, magnetic field exhibits an angle with the RD. Moreover, it is known that energy losses are much larger when a nonzero angle between the RD and the magnetic field is present [Dupre00]. The effect of the T-joints regions can be reduced by cutting and stacking techniques, applying larger number of sheets per layer. Further, a special tensile coating is applied to grain-oriented steels to reduce energy loss even more. From a practical point of view, the interest in stress dependence in grain-oriented steel is limited. Generally, the mechanical stress in transformers can be considered in two aspects. The first point is the presence of 2D stresses, e.g. due to the weight of the material, in the plane of the sheet, which are normally avoided by the present technology. Due to mostly uniaxial magnetic flux in the RD of steel, the case of alternating flux in the RD under different phase of in-plane mechanical stress is of great interest. The second point is the presence of the stress orthogonal to the sheet, e.g. due to the clamping of the lamination package. This stress is not considered in the present study. The effect of the orthogonal compression is likely to be similar to the inplane tension [Liorzou99]. The in-plane mechanical stress is usually controlled by the
38
Chapter 2.
construction methods. To control an external stress to the steel core, various constructions are applied to keep the mechanical stress in the core as low as possible (rarely exceeding 2 to 10 MPa). For example, the upper yoke is connected to the lower yoke by external construction bolts and frames to reduce the effect of weight of the upper yoke to vertical parts of the transformer core. If this is not done, the weight of the upper yoke might be sufficient enough to produce compressive stress in the transformer core. The latter should be avoided. The practical interest of further research might be in the investigation of the following combination of working conditions. The alternating magnetic flux is applied in the RD of grain-oriented steel, while the stress is applied in any direction in the plane of the sheet. However, a 1D investigation could be sufficient in grain-oriented steels from an engineering point of view. A further extension of the 1D investigation to an alternating magnetic field in any direction of grainoriented steel can be also considered. From material science point of view, the 2D investigation of the stress dependence of magnetic properties should be of most interest due to the controlled orientation of the grains in that type of soft magnetic material. In other words, it is quite possible to predict the stress dependence in such fine soft magnetic materials as grain-oriented steel. If the prediction, based on physical understanding, could be confirmed experimentally, the stress dependence can be confirmed. The alternating 2D investigation (an unidirectional magnetic excitation for different directions in the plane of the sheet) has been approached by many researchers [Moses81], [Dupre00]. One conclusion is common, i.e. a possibility to predict 2D behavior of grain-oriented steel by limited information about alternating properties in the RD and the TD. The domain theory plays a major role in a prediction of soft magnetic material behavior. A mechanical stress could be applied in the RD as it corresponds mainly with the [100] direction, or the easy cube edge direction. Other directions might also be of interest, for example, the hard axis direction. The magnetic field, on the other hand, could have a complex 2D pattern, ranging from alternating in any directions to elliptical and circular rotational magnetic flux. Many studies have been performed on the 2D behavior of magnetic properties of grain-oriented steels. However, very few studies were about the stress effect on 2D magnetic properties of grain-oriented steels [Moses80], [Moses89].
Working conditions of electrical steels
39
2.2.2. Target research in non-oriented steels. Non-oriented electrical steel is the most common soft magnetic material used in various electrical machines. The main reason to use non-oriented steel is its quasi-isotropic magnetic properties in different directions in the plane of the sheet. The difference between the RD and the TD, or more general, the anisotropy of magnetic properties, is very small and often not taken into account. Therefore, non-oriented steels are usually applied when complex 2D magnetic conditions are present in the electromagnetic device, such as in an induction machine. From a practical point of view, the effect of the 2D mechanical conditions has always been of great interest. Mechanical conditions present in the machine are at least of three different natures: construction, design and operations. The first cause of stress is the effect of various construction technologies. For example, cutting and punching techniques usually lead to a deterioration to a major extent of mechanical and magnetic properties of steel sheets. Next type of technologies is core building, which often results in extra compressive stresses in magnetic cores of the stator and the rotor of an induction machine [Pulnikov04]. For example, rotor laminations can be built on the rotor shaft by means of a thermal expansion technique. The pre-cooled rotor is expanding when reaches ambient temperature. It results in various compressive stresses in the rotor laminations. The same is true for the stator, when the stator core is pressed into the preheated frame. The frame cools down, resulting in a compressive stress up to 50 MPa [Pulnikov04], [DeWulf04]. Other technological reasons are tensile coating, thermal or residual stresses. To predict the consequences of construction technologies, one should carefully assess these technologies and their effects on steel. Many studies have been done about existing technologies and their effects on magnetic properties of electrical steels [Landgraf00], [Emura03]. The second cause is the effect of the design. For example, if a new design is based on using a compressive stress to be applied to the electromagnetic core, the result of such a design would most certainly be worse than expected. If a design engineer would not modify the design properties of the tooth regions, then the performance of the electrical machine could be worse than expected. In other words, a careful combination of technology and design could result in a high quality
40
Chapter 2.
cost-effective machine, having lower energy loss and better performance. The third cause are the various operating conditions in electrical machines. The operating conditions may introduce various effects. One is the ageing effect, when the energy loss increases in time due to migrating carbon and nitrogen atoms in the steel. From a practical point of view, the 2D investigation of the stress dependence of magnetic properties under 1D mechanical stress should be of most interest to different electrical steels. From a material science point of view, the complete 2D investigation of the stress dependence of magnetic properties should be of most interest under both alternating and rotational 2D magnetic conditions. Application of biaxial stresses is a very interesting subject [Alves04]. It could result in a statistical database of knowledge on how energy loss of various non-oriented steels change under mechanical stress. Lately, there has been a tremendous research activity on that matter. Many research centers have been studying the effect of tensile or compressive stresses on energy losses and magnetic properties of various non-oriented electrical steels. Before considering an actual 2D study of electrical steels under stress, the working conditions of steel in the machine should be defined. 2.3. 2D magnetic working conditions in induction machines. To have a deeper insight on 2D magnetic working conditions in induction machines, an extra study was carried out, both from theoretical and experimental point of view.
Type
IP
D100LB
54
No D846 076
kW 3.0
Table 2.1. Parameters of the induction machine. Hz Rpm Y- V Y- A phase T. °C 50
1420
380
6.7
3
80
A 3kW-induction machine was chosen as the first object for the 2D flux study. It is a four-pole induction machine with a closed unskewed squirrel-cage rotor. The main features of this machine is shown in Table 2.1. This induction machine was equipped with search coils, which were built inside the machine, fitted around each stator tooth close to the
Working conditions of electrical steels
41
air-gap. The used data-acquisition of the voltage signals from the search coils was transferring the measurement data to a PC with commercial software. The measurement results were stored in binary format and then integrated by means of software developed in EELAB. Thus, local magnetic fluxes are measured in each tooth of the stator near the air gap. For numerical evaluation of the magnetic working conditions of electrical steels, a 2D finite element dynamic calculation software was used [Gyselinck00]. This software allows the evaluation of local magnetic flux patterns in the same places where the search coils are placed in the machine. The local magnetic flux waveforms obtained from the numerical calculations and the measurements are compared in order to verify the measurement and calculation techniques. This results in information about the magnetic conditions of the electrical steel in different parts of the magnetic core. The stator of the 3kW-induction machine has 36 slots and the rotor has 32 slots. This type of induction machine has three full-pitch slots per phase. Therefore, two teeth lay in one phase and the third tooth is between two phases. Hence, three teeth in a row are sufficient to analyze both measurements and calculations, see Fig. 2.2.
Fig. 2.2. Location of the search coils (black dots), shown in three teeth in a row.
42
Chapter 2.
Fig. 2.3. 3kW induction machine equipped with search coils in EELAB. To obtain the magnetic fluxes as they are present in this induction machine during operational regimes such as no-load and different loads, an electromechanical setup was constructed. The setup for no-load test consists of the 3kW-induction machine without any additional mass on the shaft, an autotransformer, control devices, such as a voltmeter, an amperemeter and a stroboscope, and the dataacquisition system, see also Fig. 2.3. By integrating the voltages induced in the search coils, local magnetic flux waveforms at no-load were obtained, see Fig. 2.4. Flux waveforms at rated load are shown in Fig. 2.5. The set-up for different load regimes consists of two electrical machines, the shafts of which are mechanically connected to each other: the 3kW-induction machine and a shunt generator as a load to this machine. There is again, like in the no-load condition, an autotransformer, a rheostat, excitation shunt circuit with rheostat and amperemeter, control devices, such as voltmeter, amperemeter and stroboscope, and the data-acquisition system. Similar results were obtained for the following series of different loads: 0.25 of rated load, 0.5, 0.625, 0.75, 0.875, 1.0, 1.125, 1.25, 1.375 of rated load. The control of the load was done by measuring rotating speed, according to Table 2.2.
Working conditions of electrical steels Teeth 1
43
Teeth 2
Teeth 3
1.00
0.80
0.60
Flux (mWb)
0.40
0.20
0.00 0
5
10
15
20
25
30
35
40
-0.20
-0.40
-0.60
-0.80
-1.00
Time (ms)
Fig. 2.4. Measured local flux waveforms at no-load in 3 subsequent teeth. Teeth 1
Teeth 2
Teeth 3
1.0
0.8
0.6
Flux (mWb)
0.4
0.2
0.0 0
5
10
15
20
25
30
35
40
-0.2
-0.4
-0.6
-0.8
-1.0
Time (ms)
Fig. 2.5. Measured local flux waveforms at rated load in 3 subsequent teeth. Table 2.2. Load regimes and speed control. Speed, rpm Slip, % Load ratio
1480
1460
1450
1440
1430
1420
1410
1400
1385
1.333
2.667
3.333
4.0
4.667
5.333
6.0
6.667
7.667
0.25
0.5
0.625
0.75
0.875
1.0
1.125
1.25
1.375
44
Chapter 2.
In Fig. 2.4 and Fig. 2.5, "Tooth 1" is located between two phases while "Tooth 2" and "Tooth 3" are located between coils of the same phase. Therefore, the local magnetic flux waveform of Tooth 1 differs from those of Tooth 2 and Tooth 3. In order to analyze more accurately the local magnetic flux waveforms a Fourier analysis was performed for each curve for each working regime. A Fourier analysis results in the separation of the most significant frequencies in the flux waveform, as well as a quantification of their amplitudes and phases. A complete analysis was performed for all working regimes. With varying load, the Fourier coefficients vary as well. However, the set of the most significant frequencies turns out to remain approximately constant. This set consists of 3, 5, 15, 17, 31, 33. These frequencies can be divided into three groups: 3 and 5, 15 and 17, 31 and 33. The first group is due to saturation, the second and the third groups are due to tooth frequencies. The tooth frequencies can be determined by [Vandevelde94]: (2.1) f stator = f 0 ⋅ (1 + k ⋅ (1 − s) ⋅ S rotor / N P )
f rotor = f 0 ⋅ ( s + k ⋅ (1 − s) ⋅ S stator / N P )
(2.2)
Here, f0 is the power frequency, fstator and frotor are the tooth frequencies, s is the slip, Srotor and Sstator are the numbers of teeth of rotor or stator, NP is the number of pole pairs of the machine, and k = …-2, -1, 0, 1, 2… Considering the induction machine having 32 teeth of the rotor and 36 teeth of the stator with 4 poles, eq. (2.1) and (2.2) give: (2.3) f stator = f 0 ⋅ (1 + 16 ⋅ k ⋅ (1 − s))
f rotor = f 0 ⋅ ( s + 18 ⋅ k ⋅ (1 − s))
(2.4)
Taking into account that the no-load regime gives the slip s → 0, the most significant frequencies in the stator are approximately 15, 17, 31 and 33. This set of theoretical frequencies is confirmed by the results of the actual measurements of by the pick-up coils, presented above. Of course, measuring the flux at the tooth tips is not sufficient to estimate local flux patterns, e.g. for different height along a tooth. Although it might be possible to provide a stator tooth with several search coils, divided along its height, this is far from easy to implement. Since the subject of this study is not the extensive experimental evaluation of the magnetic flux patterns in each place of the induction machine, the experimental part is limited to the search coils, placed at the tip of each tooth of the stator. Therefore, the use of the FE software is crucial to predict various magnetic conditions of electrical steel in the
Working conditions of electrical steels
45
considered induction machine. To justify the software for further research of 2D magnetic conditions of electrical steel, a comparison is made between measured and calculated magnetic flux patterns. The latter were calculated in the same places where search coils were measuring the local magnetic fluxes, as shown on the finite element mesh in Fig. 2.6. The compared calculations and measurements were performed for the same operating conditions, according to Table 2.2. For both experimental and computational results, the relevant frequencies are the same: 3 and 5, 15 and 17, 31 and 33. Comparison of the measurements and the computations shows that the deviation of the amplitudes and the phases of the relevant frequencies was found to be of the order of 25%. This deviation may originate from measurement and calculation errors and from different assumptions in the numerical model. Despite this large quantitative deviation for the frequencies, it is assumed that the software could be used for further analysis of 2D magnetic working conditions of electrical steel in the considered induction machine. The FE software output is the magnetic vector potential in the 2D plane. According to the physical interpretation of the magnetic vector potential in 2D field computations with in-plane B and H vectors, the magnetic flux per unit length passing through an arbitrary curve between two points is the difference of the vector potential values in these two points. Thus, local magnetic flux patterns were obtained as a difference of magnetic vector potential values, calculated in two nodes of the mesh as a function of time. The advanced study of 2D magnetic flux patterns in various places of the induction machine, as in Fig. 2.7, is done by means of the software. Local magnetic fluxes are considered for rated load only, as it is the most important working condition. In order to analyze more accurately local magnetic flux waveforms, the Fourier analysis was performed for each waveform. The ratio between the amplitude of each frequency and the fundamental or power frequency has been calculated for the 9 cross sections, shown in Fig. 2.7. The results are given in Table 2.3.
46
Chapter 2.
Fig. 2.6. Finite elements mesh, including the positions of the measuring coils (black dots) around the 3 teeth in a row.
Fig. 2.7. Local magnetic fluxes of the most target interest: Flux 0 to Flux 9.
Working conditions of electrical steels
47
Table 2.3. Highest percentages of the set of frequencies. Results
% at # 3
% at # 5
% at # 15
% at # 17
% at # 31
% at # 33
1
1
# of tooth
1
2
3
1
2
3
1
2
3
1
2
Flux 0 Flux 1 Flux 2 Flux 3 Flux 4 Flux 5 Flux 6 Flux 7 Flux 8 Flux 9
2.5 2.4 2.2 2.0 1.9 1.5 1.5 0.9 0.3 0.4
1.5 1.4 1.8 2.0 2.0 1.4 3.4 0.3 1.0 0.3
0.4 0.4 0.8 0.9 0.9 2.3 1.3 0.5 0.4 0.3
0.8 0.8 1.1 1.2 1.2 1.4 0.3 0.4 0.4 0.5
2.3 2.4 2.7 2.8 2.8 2.6 1.9 1.0 0.3 0.4
1.9 1.8 1.7 1.7 1.7 1.2 1.8 0.6 0.2 0.3
3.3 2.0 0.5 0.3 0.3 0.8 0.9 1.2 1.1 1.0
4.1 3.3 3.0 3.0 2.9 2.3 2.2 1.2 1.3 0.3
4.5 3.7 3.3 3.3 3.3 1.7 3.2 0.5 0.4 1.2
0.3 1.2 2.1 2.3 2.4 1.8 1.7 0.5 0.7 0.5
3.5 2.4 2.0 1.9 1.9 1.4 1.0 0.6 0.3 0.2
3
2
3
2
3
3.6 0.7 0.9 0.8 0.3 0.4 0.3 2.4 0.4 0.7 0.6 0.2 0.3 0.1 2.0 0.2 0.5 0.6 0.3 0.3 0.2 1.8 1.8 0.9 1.5 0.3 0.5 0.4 -
The general conclusion from the data presented in Table 2.3 is as follows. The distortion in magnetic flux patterns appears mainly in a tooth region of the magnetic core of the induction machine. A set of high frequencies induced by by saturation as well as by teeth frequencies are of major importance to the distortion of the magnetic flux in the machine. Therefore, magnetic flux patterns cannot be considered sinusoidal in the tooth region.
Fig. 2.8. Rotational behavior of local flux patterns in points 1 to 15 of stator.
48
Chapter 2. Table 2.4. Axis ratios in the points of Fig. 2.8.
Point #
1
2
3
4
5
6
7
8
9
Tooth1 Tooth2 Tooth3
0.1 0.1 0.1
0.1 0 0.1
0.1 0.1 0.1
0 0 0
0 0 0.1
0 0 0
0 0 0
0 0 0
0.1 0.1 0.1
11
12
13
14
15
0.4 0.3 0.4 0.2 0.4 0.3
10
0.2 0.2 0.2
0.5 0.3 0.3
0.2 0.1 0.1
0 0 0
The FE software is also an important numerical tool for the investigation of the rotational properties of the local magnetic flux patterns. As a first approximation, the local B loci can be described as an ellipse quantified by the maximum axis and by an axis ratio a. The axis ratios a for all points considered in Fig. 2.8 for three subsequent teeth in the stator of the induction machine are collected in Table 2.4. Up to point # 9, the behavior of the magnetic flux is almost uniaxial.
Fig. 2.9. Uniaxial magnetic fluxes in point # 7 for three subsequent teeth.
Fig. 2.10. Elliptical magnetic fluxes in point # 13 for three subsequent teeth.
Working conditions of electrical steels
49
Little rotational effects were found in the tip of the three considered teeth in a row. However, the magnetic flux in points # 10 to 14 exhibits an elliptical behaviour with axis ratios up to a = 0.5. Point #15 has an uniaxial flux. Typical uniaxial and elliptical magnetic fluxes are observed in the middle of the tooth (point # 7), and in the yoke (point # 13), respectively, see Fig. 2.9 and Fig. 2.10. The electrical steel used in that induction machine was semiprocessed steel of 0.5 mm thickness. Steel sheets were first punched to form the stator and rotor laminations, and were then stress relief annealed to reduce the effect of punching. Then the laminations were assembled into a magnetic core of the induction machine. For the calculations described above, the magnetic properties of the laminations were assumed the same for both tooth and yoke regions. Similar studies have been done by other researchers worldwide. For example, IEN Galileo Ferraris in Turin, Italy, have been recently studying rotational fluxes in stator cores [Botta02]. A three-phase stator (Fig. 2.11), taken from a four-pole induction machine, has been equipped with pick-up coils. A barless rotor makes the no-load test better as electrical losses in the rotor bars induced by higher harmonic magnetic fields are not present. A test device, driven by a synchronous motor, has been employed for a thorough investigation of the magnetic behavior of the stator core during the no-load test.
Fig. 2.11. Pick-up coils on the stator (A-L) and rotor (M-O) [Botta02].
50
Chapter 2.
Fig. 2.12. Measured and computed flux density loci at the tooth root [Botta02]. The analysis has been developed under sinusoidal, six-step and twelvestep voltage supplies. Experimental results have been compared with the results provided by the 2D FE model. A good agreement has been found in the prediction of the flux density loci. To study magnetic flux patterns and distortion, several pick-up coils were placed in different parts of the stator, denoted as A, D for the yoke, B, C, F, E for the tooth (Fig. 2.11). The rotor was also equipped with coils to check if there are higher harmonics induced in the rotor core. To study the rotational behavior, two sets of orthogonal coils, denoted as I-L and G-H, were placed on the stator in the region between tooth and yoke. Measured and computed magnetic flux density loci are shown in Fig. 2.12. Here, BL is the tangential component and BI is the radial component of the flux density. The axis ratio a is around 0.3. The last example of the experimental investigation of rotational flux patterns in the stator shows how difficult it is to equip actual electromagnetic devices with pick-up coils in the right places. On the other hand, it shows how the simulation of actual working conditions in a test device could open new areas and extend the experimental results. Finally, a numerical analysis is a very powerful tool to predict the properties of local magnetic flux patterns in an induction machine [Gyselinck00], [Botta02], [Pulnikov04]. Based on the present studies, a measurement setup for the investigation of electrical steels under stress should be capable of creating the following magnetic conditions. First, it should create sinusoidal and distorted magnetic flux patterns in electrical steel.
Working conditions of electrical steels
51
Second, it should create alternating and rotational magnetic fluxes at least up to a = 0.5. 2.4. 2D mechanical working conditions in induction machine. The mechanical conditions under which electrical steel are used in rotating machines strongly depend on the power and the type of the induction machine. Magnetic cores of large machines usually consist of segmented pieces of the stator. The segments are fixed by a trapezoidal or circleshaped fixing element on the outer diameter. These elements introduce negligibly small mechanical stresses on the outer diameter of the stator segment. Nevertheless, there is another source for mechanical stress, present in large induction machines, i.e. an orthogonal compression by means of bolts and grips. The effect of over-compression or undercompression could be significant, but this source of the orthogonal mechanical stress is out of the framework of the current research.
Fig. 2.13. Stator core, combined from a number of electrical steel laminations.
a a)
b) stresses
Fig. 2.14. Assembling compression of stator (a) and rotor (b) [Pulnikov04].
52
Chapter 2.
Medium power induction machines are usually produced from one sheet, so there are no segments. Despite that, the fixation mechanism is very similar to large machines. It does not introduce any mechanical stresses in the plane of the lamination. Low power induction machines usually have a simple circle shape for the outer diameter. The attention of the current research is focused particularly on this case. The magnetic core of the stator or rotor of small induction machine consists of laminations, produced from semiprocessed or fully-processed non-oriented electrical steels, see Fig. 2.13. When a magnetic core of the stator is assembled into a frame of induction machine, various mechanical stresses could be introduced by the assembling procedure, see Fig. 2.14a. Similar stresses could be observed in the rotor core, see Fig. 2.14b. In low power induction machines, the stator core is usually compressed into the heated frame. This is a very simple technology for clamping the stator core, see Fig. 2.14a. The friction between the frame and the stator core is sufficient in order to prevent any movement of the stator. If there was no friction, the stator would rotate under the electromagnetic force. The rotor laminations are usually shrunk on the rotor shaft, which introduces the required friction, see Fig. 2.14b. Few studies have been done to simulate such external compression and its effect on energy losses in induction machine. The effects of radial stress to the flux distribution and power loss were extensively studied in a test device, simulating an induction machine [Moses89]. To generate radial stress, a series of 30 pistons provided pressure on the outer surface of the stator stack of 165 mm diameter. Stress up to 4 MPa was applied by hydraulic pressure built up in a large cylinder connected to the pistons. Two cores used for stator laminations were compared, each produced from the same non-oriented low silicon steel with 0.65 mm thickness. However, one core was annealed and the other one was not annealed. The laminations were magnetized as in an induction motor stator core. The flux density and the local power loss were measured at various flux densities using arrays of search coils. The radial component of the flux in the teeth was checked with search coils looped around every second tooth. Orthogonal search coils were wound through 0.30 mm diameter holes 5 mm apart at predetermined locations in the teeth and the yoke regions of the stator core. Those coils were used to determine the magnetic flux in the stator back under stress, see Fig. 2.15.
Working conditions of electrical steels
53
Fig. 2.15. Flux density at stress free (solid) and 4 MPa (dotted) [Moses89]. The ellipses in Fig. 2.15 signify the presence of rotational flux patterns of varying degree. The largest axis ratio of a = 0.4 was found behind the teeth. The applied stress makes the flux more rotational behind the teeth and less rotational behind the slots. The axis ratio due to the radial stress of 4 MPa was around 0.5 instead of 0.4 at stress-free conditions. The applied stress tends to make the magnetization in radial directions more difficult so the flux is forced further outwards behind the slots and drops behind the teeth [Moses89]. Similar changes were found in the unannealed core at magnetic conditions of 1.0 and 1.3 T at 50 Hz. The stator geometry was divided into 5 regions. Region 1 denotes the teeth and the other 4 are regions of equal width in the core back, as shown in Fig. 2.16. The power loss was measured locally using 0.5 mm thick, 0.5 mm long microchip thermistors. The method based on the rate of change of the temperature was used to estimate the local loss [Thomas80]. The local power loss increases due to stress by 10% to 40%. Initially, the losses are lower behind the slots than behind the teeth because the rotational flux is lower in that region. An application of stress increases the loss more behind the teeth than behind the slots because the stress makes the rotational flux higher as seen in Fig. 2.15.
54
Chapter 2.
Fig. 2.16. Local loss in annealed (left) and unannealed (right) cores [Moses89]. At all regions of the stator yoke a rapid increase occurs at a stress of around 2 MPa, see Fig. 2.16. The loss increases rapidly in regions 2 and 3, i.e. the inner region of the core yoke, where most rotational flux occurs. The stator core assembled from annealed electrical steel shows a higher dependence on stress, see Fig. 2.16 on the left. Although the core made from unannealed steel shows a smaller dependence on stress, the magnitude of the loss is much higher. The described approach of Moses has one large weakness. The applied radial stress is not a proper way to build a stress dependence of power loss in such a complex geometry as the stator core. In order to understand the distribution of actual mechanical stresses in the stator or rotor core, mechanical modeling of radial deformation on the stator should be used to simulate the effect of that deformation into localized mechanical stresses. A FE calculation of mechanical stresses due to the assembling process of the stator core into a heated frame is based on the approach described in [Pulnikov04] or [DeWulf04]. Assuming the frame of the stator has a constant diameter, then a displacement, i.e. the difference between the inner diameter of the house and the outer diameter of the
Working conditions of electrical steels
55
stator core, is numerically applied to the stator core. After cooling down of the frame, the stator core is subjected to a uniform radial compression, which is similar to the above approach of [Moses89]. If a small displacement equal to 20 µm is applied towards the center of the sheet, it results in a mechanical stress distribution as shown in Fig. 2.17. For example, a further displacement of 40 µm leads to twice compressive stresses in certain places of the magnetic core. In fact, the maximum stress was found in the inner region of the core back, where most rotational flux occurs, according to previous case [Moses89]. Moreover, the stress distribution in the yoke consists of both radial and circumferential stresses [Pulnikov04]. Assuming there is no change of the inner diameter of the stator due to the displacement, the maximum stresses are concentrated in the inner region of the core back. The tooth body remains unaffected by these stresses produced by core assembling, see Fig. 2.17. However, the electrical steel at the edge of the tooth is strongly affected by punching and stress relief annealing, see Fig. 1.9. If not annealed, the tooth is subjected to residual stresses as well as deformation at the edge.
70 MPa
90 MPa
Fig. 2.17. Possible compression in stator and rotor cores after assembling.
56
Chapter 2.
The effect of rotor assembling is also important. When a rotor core is shrunk onto a rotor shaft, the compression could reach as much as 90 MPa according to the same approach proposed in [Pulnikov04]. Again, the tooth itself remains unaffected by those stresses, but only affected by the effect of punching, see Fig.2.17. A similar study of the stress due to core assembling has been presented recently by OCAS, Arcelor Group in cooperation with EELAB [DeWulf04]. The press fitting procedure, applied to assemble the stator of the induction machine into the housing, leads to mechanical stresses inside the stator core. The FE computation of radial and tangential stresses has been performed for a thick elastic cylinder loaded by uniform internal and external pressures. According to these computations, a radial displacement of 20 µm, applied externally to the stator core of the induction machine, results in an internal stress of 45 MPa. The radial displacement of 100 µm leads to the stress of 230 MPa. These values of internal stresses that are introduced by the fitting of the stator into the housing of the induction machine can affect the behaviour of electrical steel and the performance of the induction machine. 2.5. Conclusions. Based on theoretical and experimental research regarding the actual working conditions, the following conclusions can be drawn. Firstly, standard magnetic characteristics of electrical steels are very limited. In fact, they give only basic information about the idealistic properties. When it comes to the actual needs of the customers of electrical steels, more information is required in order to design and produce an efficient electromagnetic device. Secondly, each type of electrical steel may be used in different types of electrical machines, and therefore, exhibits different working conditions. Grain-oriented steel used in transformers works mainly under uniaxial magnetic conditions. T-joint regions of transformers are the main exceptions. Here, the magnetic flux patterns are rotational. From a scientific point of view, 2D stress dependence under complex 2D magnetic conditions is of most interest, since grain-oriented steel has a large anisotropy between different directions of the lamination.
Working conditions of electrical steels
57
Non-oriented steels, the most used magnetic material today, are normally working under complex 2D magnetic and mechanical conditions. The study of 2D stress effect on 2D magnetic properties of annealed and unannealed non-oriented steels should be very interesting both from experimental and theoretical point of view. Thirdly, actual magnetic working conditions of electrical steels are usually non-sinusoidal and non-uniaxial. Non-sinusoidal magnetic flux patterns were observed mainly in the tooth regions of the induction machine. Harmonics lead to an extra power loss and should be taken into account. Rotational behavior of the magnetic flux above the teeth may lead to an extra power loss. From an experimental point of view, an elliptical flux with axis ratio a = 0.5 is the largest rotational flux found during studies presented in this Chapter. However, the axis ratio a = 1.0, i.e. circular rotational behavior of magnetic flux is the most extreme theoretical condition for 2D rotational magnetization. Therefore, it is preferable to apply magnetic conditions starting from sinusoidal and distorted uniaxial excitations to elliptical and even circular. Fourthly, mechanical working conditions of electrical steels show complex 3D compressive and tensile elastic stresses, as well as plastic deformations due to punching of the laminations. By eliminating the third dimension from the framework of the present study, complex 2D mechanical working conditions could be simplified to the following options. In grain-oriented steels, the uniaxial stress could be applied in different directions in comparison with the rolling direction of the steel. In non-oriented steels, the uniaxial stress could be applied virtually to any direction, since non-oriented steels could be considered quasiisotropic. Therefore, it is preferable to use uniaxial mechanical stress, applied either as compression or tension up to plastic deformation. Finally, engineering society agreed upon the fact that the actual 2D magnetic measurements are required in order to take into account the effect of rotational magnetic conditions on energy loss in electrical steels [Beckley02]. Advanced experiments have been performed during the last decades, starting from testing machines, simulating 2D magnetomechanical conditions, to advanced 2D measurement systems. The latter give the opportunity to simulate different effects or separate conditions and investigate the magnetic properties of electrical steel samples. Using a sample is more convenient than carrying out measurements inside the induction machine or the power transformer.
58
Chapter 2.
Therefore, the way to study the stress effects in electrical steels is to use advanced measurement setups, suitable for the target study. The next chapter will study conventional and unconventional measurement setups and measurement techniques. The main question will be: which measurement techniques are suitable to simulate the above mentioned working conditions in different kinds of electrical steels?
Magnetic measurements under stress
59 Knowledge is power. Sir Francis Bacon, 1597
CHAPTER 3. MAGNETIC MEASUREMENTS UNDER STRESS "Measurements mean knowledge" [Fiorillo04]. Indeed, measurements are indispensable to science, industry, trade and economy. They are the prerequisite for any conceivable development in production and trade. Actual measurements are the basis for statistical observation, which any science or research is based upon. For electrical steels, magnetic measurements are the primary source of information about the magnetic properties. Measurements are required in all stages of a lifecycle of electrical steels, starting from the production, followed by inspection and trading, as well as in the actual use of electrical steels by electrical machine designers and constructors. Measurements require a good judgment and this is only possible if the underlying scientific issues and their applications are understood. Whatever the specific aim of measurements, there is no shortcut to physically sound experimental methods [Fiorillo04]. The accuracy and reproducibility are the most important key values to evaluate the experimental methods. Measurements are widely used when the measurement standards are fixed. Basic magnetic measurements in electrical steels have been collected in a group of standards IEC 60404. The International Electrotechnical Committee has agreed upon characterization methods for electrical steels, known as [IEC 404-2] and [IEC 404-3]. These standards are applicable to grain-oriented and non-oriented "sheets and strips" for DC and AC measurements at frequencies up to 400 Hz. The engineering society is constantly working on the perfection of existing standards and on the development of new ones. National Metrological Institutes (NMIs) and international metrological and standardization organizations play a key role through the mechanism of an international programme for "intercomparison" by NMIs, such as PTB, IEN, NPL and others [Sievert96]. What happens when there isn't any standard on specific measurements available but required both for science and industry? One approach is to use the standard measurement methods and try to modify them in order to include a new measurement task. For example, a standard system could be extended by one or another
60
Chapter 3.
mechanism or measurement instrument. When the new measurement system is complete, it is calibrated to the standard system. Calibration to the standards gives a great advantage of comparison between new results and proven measurements performed by a standard system. Unfortunately, not every new system can be calibrated to comply with a standard measurement system. Moreover, the method of intercomparison for non-standard techniques gives sometimes rather different measurement results [Sievert96]. The difference, if not explained, could become the obstacle for approval of a new standard by the international standardization institutes. Another approach is more flexible but less reliable than the applied method of the intercomparison of the results. If a new measurement system is so specific that its results are difficult to calibrate to the results of a standard method, then the new system could produce results on a relative basis. It simply means that all measurements are performed in a single system, under the same conditions, by the same instruments and methods. Two requirements the new system must comply with are the accuracy and the reproducibility. If the accuracy of the instruments and parts of a new system is good enough, then the results obtained by the new system could be comparable to each other, i.e. on relative basis only. The reproducibility of the results should lay in a given area of the acceptable error, which might depend on all parts of the system. To start with a new measurement system, first, the conventional methods must be studied thoroughly. 3.1. Standard magnetic measurements in electrical steels. The standards have been mentioned many times. Herewith a brief description of the standard methods is made. 3.1.1. Epstein frame. One of the most used standard is the standard IEC 60404-2 "Magnetic Materials. Part 2: Methods of measurement of magnetic, electrical and physical properties of magnetic sheet and strip." It is also called the "Epstein frame" standard [IEC 404-2]. The Epstein frame is actually an unloaded transformer. It comprises a primary winding, a secondary winding and the specimen to be tested as a magnetic core. The use of the Epstein frame is applicable to
Magnetic measurements under stress
61
flat strip specimens obtained from magnetic sheets and strips of any quality. The frame itself is shown in Fig. 3.1 and it is a closed circuit. The closed circuit is typical for standard characterization of soft magnetic materials and it is applied in several standards IEC 60404-2-3-4-6-10. The magnetic circuit is made of a core constructed with the strips to be tested, assembled in a square, having double-lapped joints to form four branches of equal length and equal cross-sectional area. The steel samples for Epstein frame measurements must be cut burr-free, having a width of 30 ± 0.2 mm and a length of 280 ± 0.5 mm. The average magnetic path length is agreed by the NMIs to be equal to 0.94 m. The number of steel samples to be used in the tests is at least 12 or a quadruple. Furthermore, it is permissible to apply a tangential force of about 1 N to each corner. To measure the polarization µ0M instead of the induction B, an air flux compensation completes the test setup. A mutual inductor for air flux compensation is connected in series with the primary and secondary windings of the Epstein frame. The voltage induced in the secondary winding of the mutual inductor by the primary current does compensate the voltage induced in the secondary winding of the empty Epstein frame by the flux attributed to the primary current. Last but not least, the waveform of the secondary induced voltage shall be controlled sinusoidal, having a form factor of 1.111 within ± 1%.
Fig. 3.1. The Epstein frame according to IEC 60404-2 [IEC 404-2].
62
Chapter 3.
The standard IEC 60404-2 defines several methods to identify the various properties of the test specimens in the Epstein frame. The following methods are described: - determination of specific total losses by the wattmeter method, - determination of magnetic characteristics by the bridge methods, - determination of the magnetic field strength, the excitation current and the specific apparent power, - determination of the magnetic flux density in a DC field, - determination of the density of the magnetic sheet, - determination of the resistivity of the magnetic sheet and strip, - determination of the coefficient of the surface insulation resistance, - determination of the stacking factor, - appendices on air flux compensation, complex permeability and density. The purpose of these methods is to define terms and specify techniques for the measurement of magnetic, electrical and physical properties of a magnetic sheet. 3.1.2. Single sheet tester. The second mostly used standard is IEC 60404-3 "Magnetic materials. Part 3: Methods of measurement of the magnetic properties of magnetic sheet and strip by means of a single sheet tester." It is also called the "SST" standard [IEC 404-3]. Here, the test specimen comprises a sample of the magnetic sheet and is placed inside two windings, an exterior primary winding (the magnetizing winding in Fig. 3.2.) and an interior secondary winding. To minimize the effect of the weight and pressure on the test specimen, the upper yoke shall be provided with a means of suspension which allows part of its weight to be counterbalanced as shown in Fig. 3.2. In order to reduce the effect of eddy currents and provide a more homogeneous distribution of the flux , the yokes are a pair of U-cores or a glued stack of laminations. Each yoke is in the U-form, made up of insulated sheets of grain-oriented silicon steel or nickel iron alloy. The yoke pole faces have a width of 25 ± 1 mm. The air gap between the opposite pole faces of the yokes shall not exceed 0.005 mm in order to form a suitable closed circuit.
Magnetic measurements under stress
63 180 – 300 mm
25 mm
magnetizing winding
secondary winding suspension
test specimen
500 mm
Fig. 3.2. The single sheet tester with counterbalances [Fiorillo04]. The test specimen for the SST shall have a length of at least 500 mm and a width as large as possible but less or equal to the width of the yokes. The standard defines the width of the yokes equal to 500 mm, however, it is recognized that other yoke dimensions can be used. The main condition to modify the dimensions is very simple. The yoke dimensions can be modified provided that the compatibility of the results can be demonstrated. In other words, a researcher could use a smaller SST but the results must be comparable to the results by the standard SST. The sample used in the standard SST may be square, which allows rotating the sample 90 degrees. Thus, only one sample of electrical steel can be used to define the magnetic properties both in the rolling direction and in the transverse direction. The air flux compensation is done in a similar way as in an Epstein frame. The primary winding of the mutual inductor is connected in series with the primary winding of the test apparatus, while the secondary winding of the mutual inductor is connected in series with the secondary winding of the test apparatus. The adjustment of the value of the mutual inductance is done when passing an alternating current through the primary windings in the absence of the specimen in the apparatus, the voltage measured between the non-common terminals of the secondary windings shall be less than 0.1% of the voltage appearing across the secondary winding alone. Thus, the average value of the rectified voltage induced in the
64
Chapter 3.
combined secondary windings is proportional to the peak value of magnetic induction in the test specimen. Furthermore, the waveform of the secondary induced voltage shall be controlled sinusoidal, having a form factor of 1.111 within ± 1%. The standard is applicable at power frequencies to grain-oriented and non-oriented magnetic sheets for: - specific total loss, specific apparent power, r.m.s. value of the magnetic field strength at magnetic induction 1.0 to 1.8 T in grain-oriented steels, - specific total loss, specific apparent power, r.m.s. value of the magnetic field strength at magnetic induction 0.8 to 1.5 T in nonoriented electrical steels, - peak value of the magnetic induction, peak value of the magnetic field strength at magnetic field strength 10 kA/m in grainoriented steels, - peak value of the magnetic induction, peak value of the magnetic field strength at magnetic field strength 1 kA/m in non-oriented steels. Annex B of IEC 60404-3 proposes the non-obligatory calibration of the SST "for those who wish to obtain the correlation between measurements taken by this method and the Epstein frame method" [IEC 404-3]. The calibration consists of the determination of the effective length of its magnetic circuit from the measurement of the specific total loss in the Epstein frame. This calibration should be performed for each grade of material and each magnetic flux density. 3.1.3. DC magnetic measurements of iron and steel. The third standard of interest is the standard IEC 60404-4 "Magnetic materials. Part 4: Methods of measurement of d.c. magnetic properties of iron and steel." This part of a series IEC 60404 specifies the techniques of measuring the DC magnetic properties of steel in a closed magnetic circuit using either the ring or the permeameter method. The ring method is used to obtain the magnetization curve and the hysteresis loop for a magnetic field strength up to 10 kA/m. A higher magnetic field strength could cause an overheating of the test specimen. The latter is a homogeneous unwelded ring with a rectangular or circular cross-section, which ranges from 100 to 500 mm2. A temperature sensor is attached to the test specimen. A secondary winding of insulated copper wire is wound uniformly around
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the core. A magnetizing winding capable of carrying the maximum magnetizing current and of a sufficient number of turns to produce the maximum required magnetic field strength is wound in one or more layers on the core. Various cooling methods can be applied as well. The magnetizing field strength H is proportional to the magnetizing current, the number of turns of the magnetizing winding, and inversely proportional to the path length. 3.1.4. Magnetic measurement techniques used in standard methods. The principles behind the standard methods are defined in the already mentioned Maxwell equations (1.1) – (1.5). Moreover, the standard methods usually employ a closed circuit. What are the advantages and disadvantages of that approach? It all starts from the Ampere's law (1.2). According to this law, the line integral of the magnetic field H along a closed path lm equals the total electrical current through a surface spanned over the path lm, and is given by
∫ H ⋅ dl = I
total
= N ⋅I
(3.1)
Here, N is the number of turns, each carrying a current I. By assuming that H is constant along the closed path lm, the magnetic field strength is given by
H=
N ⋅I lm
(3.2)
The expression (3.2) is used in IEC 60404-4 as a method for measuring the magnetic field strength by the ring method. Here, H is the magnetic field strength in A/m, N is the number of turns of magnetizing winding of the ring, lm is the mean magnetic path length of the ring in meters, and I is the magnetizing current in A. This is the first principle for the magnetic measurements: the field is proportional to the current in the magnetizing winding. The next method is based on Faraday's law, see eq. (1.1). According to this law, the voltage induced in an electrical circuit is proportional to the rate of change of the magnetic flux, linking the circuit. Lenz's law indicates that the induced voltage is in a direction which opposes the flux change producing it. When the physical magnetic flux Φ is passing through a coil of N
66
Chapter 3.
turns, and dΦ /dt is the rate of change of the magnetic flux, then with the average induction B and the cross section S, the induced emf E [in Volt] is given by
E = −N
dΦ dB = − NS dt dt
(3.3)
This is the second principle for the magnetic measurements. The induced voltage is proportional to the time derivative of the magnetic flux density, or dB/dt. The cross section S of the secondary windings in the Epstein frame or the SST is larger than the magnetic cross section Sm of the test specimen. Hence, the air flux in the secondary winding contributes to the voltage induced in that winding. The magnetic flux density B' integrated from the measured secondary voltage (3.3) differs from the magnetic flux density B in the test specimen:
B' = B + µ 0 H
S − Sm S
(3.4)
A series mutual inductor approximately compensates the error from the second term on the right of (3.4) [IEC 404-2]. When the industrial society had realised that using a SST is much easier than using the Epstein frame, in particular when considering the preparation of the test specimens, the research centers developed novel measurement techniques to measure the magnetic field H, because of possible errors arising from the estimation of the magnetic path length lm of the SST or the Epstein frame. Therefore, other methods for measuring the magnetic field strength were required. A practical method is the tangential magnetic field measurement by an H coil [Pfutzner91]. The results obtained by the H coils were compared with the results by the previously used current method. The H coil method is considered a physically sound measurement technique, based on the following principle. If a search coil is placed in an alternating magnetic field in air, the emf U induced in this coil is proportional to the time derivative of the magnetic field, similar to (3.3):
U = − NS ⋅ µ 0
dH dt
(3.5)
Here, the H coil measures the magnetic field strength in the air, passing through the cross section NS. Once the H coil is calibrated to determine the cross section NS, it can be used as a physically sound sensor. Indeed,
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67
when a H coil is placed near to the surface of the sample with its axis parallel to the surface, it can be used to measure H in the sample parallel to the axis of the H coil, as the tangential component of H is continuous at the surface of the specimen. The calibration procedure for the H coil uses the Helmholtz coils, for example, the ones shown in Fig. 3.3. The Helmholtz coils system produces an uniform magnetic field in a central cylinder parallel to the Helmholtz coil axis. This uniform cylinder has a diameter of 50 mm and a length of 50 mm. The search coil is placed on top of the magnetically and electrically non-conducting supporting blocks in the centre of the uniform cylinder. The water-cooled Helmholtz coils system of Fig. 3.3 used in EELAB is capable to create a magnetic induction in the air up to 0.02 T, which corresponds to a magnetic field of 16 kA/m. Rated current in the Helmholtz coils is 35 A at the power frequency of 50 Hz. The NS value of calibrated search coil is proportional to the induced voltage in the search coil, and inversely proportional to the excitation current of the Helmholtz coils system. Due to linearity, the results are independent of the excitation current.
Fig. 3.3. The Helmholtz coils system by Walker Scientific Inc. EELAB.
68
Chapter 3.
3.2. State of the art in 2D magnetic measurements. Starting from the standard methods, the art of advanced magnetic measurements has been recently evolved into a new level of high quality, accuracy and reproducibility. New digital methods have replaced conventional analogue ones in various measurement systems. Today, a modern software package can easily do a job of analogue devices, for example, a job of integrators, when dB/dt is converted into B as from (3.3). Modern measurement systems become more accurate and advanced than ever before. The question of accuracy rises from any kind of measurements, including magnetic ones. Despite the agreement on the standard methods, the engineering society is well aware of the existing systematic errors in the standards. The main cause of these errors is nonhomogeneous magnetic field distribution along the path length. It results from an assumption of the mean magnetic path length lm, equal to 0.94 m in the Epstein frame or 0.45 m in the SST. The errors can be taken into account by extra coefficients. Otherwise, the deviation can be as much as 10%. More about systematic errors can be found in [Sievert84], [Pfutzner91], [Girgis98], [Sievert99]. Why users of standard methods need new measurement systems? One of the reasons is that the dimensions of the test specimens in the standard methods are fixed. When a smaller specimen is under investigation, then a customized SST can be applied. A typical practical example for a smaller SST application is the identification of the properties of a stator lamination of an induction machine. A variety of measurement systems, based on the standard ones, is produced today, as shown in Fig. 3.4. Another application of small SSTs is the characterization of specimens obtained by production methods on laboratory scale [DeWulf03], [RosYanez03]. In order to obtain reliable and accurate data about electrical steel properties using specimens of small dimensions, usually a small SST is calibrated to the standard one. Here, the calibration means the procedure for the determination of the magnetic path length lm for different yoke constructions as in Fig. 3.5. The procedure is based on using the same material in different measurement systems, including the standard such as the Epstein frame or the SST. The power loss, obtained by the Epstein frame or the SST, is considered as the reference for
Magnetic measurements under stress
69
calibration of the miniature SSTs. An accuracy within 5% deviation is quite feasible to achieve [DeWulf03].
Fig. 3.4. Various systems for punched parts and strips. Source: Brockhaus.net.
Fig. 3.5. Dimensions of various miniature single sheet testers [DeWulf03].
70
Chapter 3.
Small dimensions are fairly good reasons for using miniature measurement systems, based on standard methods or novel measurement techniques. However, the main reason to choose a new measurement system is the limit of both magnetic and mechanical working conditions of standard magnetic measurements. Indeed, standard measurements by the Epstein frame or the SST are performed at a controlled sinusoidal voltage waveform of the secondary windings. The magnetic flux in the standard test specimens is assumed as sinusoidal. Why a sinusoidal magnetic flux or a sinusoidal induction B are employed in magnetic measurements? The major reason for using a sinusoidal controlled magnetic flux density is that in this way the experimental results of different measurements can be easily compared. As shown in Chapter 2, the actual working conditions in a machine or a transformer are far from the standard 1D conditions. The magnetic flux has a number of higher harmonics, which affect the magnetic properties and the energy loss in electrical steels. Moreover, due to clearly rotational behavior of magnetic flux in electrical steels, 2D magnetic measurements are required. The mechanical conditions of electrical steels can be included as well. Hence, novel measurement setups are required for an advanced magnetomechanical study. The art of advanced multidimensional magnetomechanical measurements has started from modifying conventional systems by introducing a second and even a third dimension into the measurement system [Zhu02]. A crucial choice in magnetic measurements is the choice of the dimensions of the sample. The Epstein frame uses 12 (or more) steel strips, having dimensions 30 mm x 300 mm. Its sample preparation is more complicated than the preparation for the SST. The latter uses the steel sample, having dimensions 500 mm x 500 mm, or smaller up to 30 mm for a miniature SSTs, as shown in Fig. 3.5. Despite so large difference, a majority of 2D measurement setups uses square or circle samples, having dimensions 60 to 100 mm [Sievert96]. In fact, these dimensions of the samples are considered the best in terms of measurement techniques and field strengths. Sometimes, different measurement techniques and different sensors could be successfully applied in a single measurement setup. According to [Sievert96], many European research centers, such as PTB, IWE, LEG, IEN, EBG, WCM, have developed various 2D measurement setups to investigate the rotational behavior of magnetic
Magnetic measurements under stress
71
flux in electrical steels. They all had an objective to develop a reliable and fairly accurate system of 2D magnetic measurements in electrical steels. However, each center has used different measurement techniques. Hereby, a brief study of 2D measurement setups, used in the above European research centers, as well as some centers in Japan, is presented. 3.2.1. 2D single sheet testers. For 2D magnetic measurements, two sets of B and H probes placed in the same area are required. The sets measure B and H in orthogonal directions. If it is possible to create uniform magnetic conditions in the area of the sample where the probes are, it can be assumed that the 2D magnetic measurements are relatively accurate. The first idea implemented in the 70s was an idea to use U-shape yokes, similar to the ones in the standard SST. It is a typical benchmark approach to use the proven SST technology and then calibrate it to the SST standards. Here, it is assumed that the two axes of the magnetic system are independent from each other. In this case, each axis can be considered separately. Thus, uniaxial results for each axis of magnetic excitation should correspond to the results obtained by equivalent SST measurements. The double yokes of the setup in Fig. 3.6 are used for each of the two axes, having a side of 300 mm or more. The yokes are laminated in U-shape from grain-oriented steel. The measurement area is defined as a result of a numerical analysis of the field distribution, and it corresponds to an 80 mm central square [Nencib96]. The sensors are positioned in the geometrical center of the system. The B coils are wound up through holes, drilled in the sample. The H coils are placed exactly above the area covered by the B coils. The double H coils method is used. The H coils are respectively 3 and 8 mm above the sheet surface. The magnetic field H at the surface of the specimen is obtained by linear extrapolating the values of H by the 3 mm and the 8 mm sensor [Nencib96]. The X and Y coils (XY plane = plane of the specimen) are separately wound crosswise on two 80 x 80 x 2 mm nonmagnetic formers, which are rigidly linked together. The system of sensors is then fixed to the yoke support in order to ensure a precise adjustment and good repeatability. The test specimen
72
Chapter 3.
can be placed easily without moving the H coils. The performance of the double yoke SST in Fig. 3.6 has been evaluated by making a comparison under an unidirectional field with a standard SST. Identical square samples of grain-oriented and nonoriented silicon steels were characterized with the new rotational single sheet tester (RSST) and the conventional SST. The experiments were carried out at 50 Hz along the rolling and transverse directions from 0.5 to 1.5 T. The maximum discrepancy between the two systems was within 5% in losses and 15% in field strength. This can be attributed to the fact that the SST field is measured with the magnetizing current method while the RSST uses the double H coils. An important part of the setup is the power and control system. The 300 mm RSST was supplied by a two-phase generator via two power amplifiers. A negative feedback technique was used for the two axes in order to control the rotating flux in the sheet. It was implemented taking into account different conditions, such as non- and grain-oriented electrical steels, and easy and hard direction excitations. Corrector components were added in order to avoid instabilities. The six signals (four H signals and two B signals) were measured using a Plug-In PC data acquisition card which offers an adaptable preamplification for each channel. The symmetry of the device was verified by rotating the sample 90 degrees. Besides rotational property measurements, the RSST performs an uniaxial excitation in any arbitrary direction. The upper and lower yokes of the RSSTs on the right in Fig. 3.6 have also the U shapes, similar to the construction of the standard SST. The laminated auxiliary yokes help to reduce the leakage fluxes [Nakata93]. The position of the exciting windings can be as near as possible to the test specimen in order to avoid leakage fluxes, as shown in Fig. 3.7. In this setup, a large square sample is used, having a size equal to 150 mm x 150 mm.
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73
Fig. 3.6. The large double yoke RSSTs: left -[Nencib96], right - [Nakata93] .
Fig. 3.7. An improvement of the double yoke RSST [Nakano99].
74
Chapter 3.
Fig. 3.8. Construction of the two-axis cross-wound H coils [Nakata93]. In order to determine the area for the B and H sensors, the uniformity of the magnetic field distribution in the specimen is measured and calculated. As a result of the analysis, the distribution of the magnetic field was found nearly uniform within a 40 mm square. The two H coils method is used to measure the magnetic field in the rolling and in the transverse direction. The H coils are wound on a single epoxy glass plate to eliminate the angle error between two H coils in the X and Y directions, see Fig. 3.8. The thickness of the epoxy glass plate is equal to 1 mm. This is considered as the best value for the H coils design [Pfutzner91]. 3.2.2. Shift to a horizontal rotational single sheet tester. The measurement setup of Fig. 3.7 was among the first in the world to use an advanced yoke design with the auxiliary yokes. A further shift from the SST-like U-shape design to an unconventionally flat design of a RSST seemed to be logical, see Fig. 3.9. Magnetising coils Core
Sample
Fig. 3.9. Shift from the SST-like (left) to a flat design (right) of the RSST.
Magnetic measurements under stress
75
Indeed, if the sample size is about 100 mm, then it is possible to construct a RSST for the sample in such a way that the whole design becomes flat and horizontal. With a sufficiently large cross section of the yokes, the magnetic fluxes from both X and Y excitations can coexist in a single core. Energy losses in the yokes can be neglected. The idea of a flat design for a RSST became so popular, that research centers created different types of these RSST. The one in EELAB is shown in Fig.3.10. When considering a two-phase system, the field homogeneity in the samples for different shapes and sizes should be studied in 3D. Due to the complexity of a 3D numerical model, 2D models were used for the magnetic field analysis of the setup in Fig. 3.10: a XY model and a XZ model. The XY model describes the field patterns in the sample at low and high inductions, see Fig. 3.11 and Fig. 3.12. The XZ model describes the flux lines passing from the yoke to the sample, see Fig. 3.13. The study reveals that, firstly, the square samples yield the most uniform field, and secondly, an increase of the air gap leads to a more uniform field distribution in the sample [Makaveev99]. y measurement coils sample yoke x magnetizing coils air gap
z
x
Fig. 3.10. Rotational single sheet tester with air gaps [Makaveev00].
76
Chapter 3.
Fig. 3.11. XY models of square and circle samples [Makaveev03].
Fig. 3.12. XY models of square sample at high induction [Makaveev03].
field lines
z
yoke
sample
x Fig. 3.13. XZ model for single sample and square yoke [Makaveev03]. Unfortunately, the magnetic field distribution in the XZ plane in Fig.
Magnetic measurements under stress
77
3.13 reveals some doubt about the accuracy of the magnetic field measurements by the H coil technique. The XZ model in Fig. 3.14 shows a substantial influence of stray fluxes on the field distribution above the sample, even in the central area, where the H coils usually perform the measurements. In order to measure a homogeneous magnetic field strength, a shielding method was applied, as shown in Fig. 3.14. Here, the samples have an 80 mm size square shape. When the H coil is shielded, i.e. laying between two similar samples, there are no stray fluxes in the XZ plane between the samples. When no shielding is applied as on the top of Fig. 3.14, the inhomogeneous field distribution leads to an incorrect interpretation of the signals of the H coils, resulting in different BH loop (Fig. 3.15). The method for a stray flux shielding was proven to be very effective in obtaining an accurate field strength measurements in the RSST [Makaveev00]. Thus, on the one hand, the shielding leads to the desired 2D homogeneous field pattern in almost the whole area of the samples. On the other hand, a single H coil method can be successfully applied instead of the double H coil method. Indeed, when the field is homogeneous between two samples, there is no need for two H coils to measure the magnetic field with sufficient accuracy.
Fig. 3.14. XZ model with and without shielding [Makaveev00]. Generally, the measurement of the magnetic field strength by the
78
Chapter 3.
H coil can only lead to a correct estimation of the field strength on the surface of the studied material, if the air-flux lines are parallel to the plane of the sample and thus do not penetrate the sample or the H coil in the Z direction. Thus, the double H coil method has a doubtful physical basis without shielding, as it does not remedy the 3D stray fluxes. To ensure that the magnetization in the shield and in the sample is approximately the same, the laminations should be made from the same material, which guarantees an uniform magnetic field strength H for the sample. Furthermore, the shielding laminations should be mounted with their RD parallel to the RD of the test specimen.
Fig. 3.15. BH loop with and without shielding [Makaveev00]. exciting coils air gap 0.1 B-coils
Y X unit : mm closer yoke
specimen
21 Y
H-coils
X 0.1
80
260
Fig. 3.16. A 3-phase RSST [Pfutzner96] and novel setup by [Sugimoto04]. In other words, it is crucial for the measurements to keep these two
Magnetic measurements under stress
79
samples under the same magnetic, thermal or mechanical conditions. There are some other designs of the RSST, each having its advantages and disadvantages. Fig. 3.16 depicts two other types of advanced RSSTs. These two have a higher limit for the magnetizing field and the induction in the sample. The one shown on the left in Fig. 3.16 obtains the power excitation from a conventional three-phase power supply [Pfutzner96]. The setup uses a hexagonal shape for the test specimen. Another setup (on the right in Fig. 3.16) has a square sample but a very complicated yoke design and a small air gap of 0.1 mm [Sugimoto04]. 3.2.3. Typical operational algorithms for magnetic measurements. The majority of modern 2D measurement setups use some kind of operational algorithm in order to control the magnetic flux density in the sample. This allows the intercomparison of the experimental results. Each measurement setup consists of two major parts: an excitation system enforcing a flux pattern to the test specimen and a set of measurement instruments. By changing the waveform of the excitation voltage it is possible to achieve the desired waveform of the magnetic flux density in the sample. Various control algorithms have been developed throughout the history of magnetic measurements. An up-to-date scheme of the measurement control and operations, as applied in the majority of modern measurement setups, is shown in Fig. 3.17. The upper part of the scheme in Fig. 3.17 represents the excitation, generated by the software and amplified by a power amplifier. Output Software
Waveform Control Input
Data Acquisition Card
Power Amplifier
Windings
Signal Amplifier
B and H probes
Fig. 3.17. Scheme of operational algorithm for magnetic measurements. Generally, that kind of excitation can supply multi-phase
80
Chapter 3.
windings of the measurement setup. The lower part of the scheme represents the measurement signals from the B and H probes, amplified by signal amplifiers and read by the data acquisition card. The software is responsible for all operations as well as for the waveform control to obtain the true waveform of B according to the desired waveform, e.g. a sinusoidal or distorted B. The data acquisition card converts analogue signals of the sensors into digital information for the software, and vice versa, from digital to analogue signals to the excitation windings. A typical algorithm generates an output to the excitation windings, and reads the B and H signals. The waveform control updates the output generation in a cycle until the magnetic induction waveform reaches the desired one. The accuracy of the complete scheme depends on the design of the setup and the choice of the measurement technique, as well as on the accuracy of the amplifiers, the parameters of the data acquisition, the features of the waveform control. Although the whole system looks complicated, a high accuracy can be achieved if every part of the system is designed and constructed at a high level. The waveform control plays a crucial role in the magnetic measurements. Generally, the waveform control depends on the physical property to be controlled: B or H, the design and physical parameters of the excitation windings, the design of the magnetic parts of the setup, the presence and value of the air gap in the magnetic path of the excitation flux, and so on. In case the flux density B is controlled [Makaveev03], the voltage V for the excitation windings reads for the X direction (analogously for the Y direction) :
V X = a X B X (t ) + b X
dB X (t ) dH X (t ) + c X H X (t ) + d X dt dt
(3.7)
Here, aX, bX, cX, dX are coefficients depending on the physical parameters of the setup. For 2D magnetic measurements, the variables BX(t) and HX(t) are projections of the corresponding vectors to the X axis. An analogous equation for the Y direction can be used, similar to eq. (3.7) with all the parameters and coefficients corresponding to the Y axis. In case B and H coils are used, the signals from the B and H sensors (search coils) are proportional to dB(t)/dt and dH(t)/dt, respectively, see Section 3.1.4.
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81
3.3. Magnetic measurements under stress. In order to perform magnetic measurements with the sample subjected to a mechanical load, it seems logical to start with the simplest case. A few research centers did the same job, taking a standard SST or its miniature copy and upgrading it with a mechanical system to apply tensile or compressive mechanical load. The first and most logical way to apply a tensile load is to use weight as shown in Fig. 3.18. Here, the specimen is gripped by two parts of the vertical system. The measurements are done by the SST. The system of Fig. 3.18 provides an ideal mechanical load, which is constant and uniaxial. Indeed, the uniaxial stress is proportional to the weight and inversely proportional to the cross section of the test specimen. The system is durable and simple, however, it has its limits. Only tensile load can be applied. Moreover, the load has a maximum value, limited not only by ultimate tensile strength of the material, but also by the safety norms. For example, it takes 2000 kg to create a sufficient load to start plastic deformation in non-oriented electrical steel with 0.5 mm thickness and having a width of 80 mm. That kind of load is difficult to provide in non-industrial working space.
Sample
B-coil
H-coil primary winding
SST
yokes (U-shape)
Weight
Fig. 3.18. Vertical SST under uniaxial stress due to weight [Hubert04].
82
Chapter 3.
In addition to mechanical limits, there are some limits related to magnetic measurements. To use the U-shape yokes of the SST, it takes an extra frame to hold these yokes vertically. The accuracy of the magnetic measurements will depend on the air gap between the SST yokes and the sample, which must be controlled by an extra supporting frame. Here, the dimensions are very important. The standard SST of 500 mm is not as convenient as a small SST, calibrated to the standard SST.
Fig. 3.19. Horizontal small SST under uniaxial stress ±50 MPa [DeWulf02].
Fig. 3.20. Horizontal measurement setup with uniaxial stress [Delage97].
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Using a miniature SST, it is also possible to introduce uniaxial stress to a small sample, as shown in Fig. 3.19. The mechanical load is applied horizontally by a manual limb (on the right) and measured by a load cell installed on the shaft (on the left). The sample dimensions are 30 mm width and 90 mm length. The SST has a length of 60 mm. When a weight system is used, as in Fig. 3.18, a compressive stress is impossible to apply to the steel sample. A miniature system in Fig. 3.19 allows applying uniaxial stresses, both tensile and compressive, up to 50 MPa. A higher tensile stress is also feasible to achieve. Another example of how to apply an external mechanical load to a larger sheet of electrical steel is shown in Fig. 3.20. Translating the mass along the lever arm creates a moment, amplified by the toothed wheel work around the axis A. This creates a tangential force to the cylinder C, normal to the axis A, transmitted to the specimen via a steel strip and the pivot linking. The maximal applied force is 15 kN [Delage97]. Typical dimensions for the sample used in this setup are a width of 100 mm and a length of 400 mm. When considering a steel sheet of 0.35 mm thickness, the mechanical system is capable of externally applied tensile stress up to 425 MPa, which generally corresponds to the elastic limits of fully processed electrical steels. Higher thickness, however, would lead to lower externally applied tensile stress. Plastic deformation of steel sheet is possible but unlikely. An external compression is not possible. The magnetic part of that 2D measurement setup consists of two independent axes. Despite the first impression that the magnetic system in Fig. 3.20 is similar to the SST in Fig. 3.2, it is not, actually. There are two yokes in the considered system, a longitudinal and a transversal. Each yoke in Fig. 3.20 is equipped with an excitation winding, responsible for the magnetic excitation in the X or the Y directions. There is no symmetry present in the system in Fig. 3.20 compared to the standard SST in Fig. 3.2. The absence of a symmetrical yoke above the longitudinal one or below the transversal one leads to a drastic error, if using the same method as in the SST. Assuming the field being proportional to the current in the excitation winding, the single yoke system can give a systematic error up to 20% due to additional dynamic losses in the sample [Pfutzner91]. A miniature air gap between the steel sheet and a yoke results in drastic changes of the measured permeability as in Fig. 3.15, causing the method to be unsuitable [Nakata86]. Therefore, other techniques than the SST method must be used.
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Both B and H magnetic measurements can be performed locally in the geometrical center of the system, as in Fig. 3.20. It seems that two reliable measurement techniques could give very accurate results. However, two questions remain: how to measure and what to measure. The question how is mainly about the accuracy of local magnetic measurements. However, the main question is what to measure, i.e. a question of uniformity of the field in the steel sheet. According to the analysis of the magnetic field distribution [Delage97], the magnetic field is uniform only in a central area in Fig. 3.20. Moreover, the air gap between the steel sheet and the yokes has a major effect on an uniform area. At constant exciting level, an increase of the air gap extends the size of the area with the uniform field. With increasing exciting level, the size of the area with the uniform field gradually decreases. Despite the nonlinearity of the sample, a 3 mm optimal air gap leads to a 4 cm2 central area, where the magnetic field is uniform. A set of two crossed H coils is used close to the sample in order to determine the magnetic field components, one for each direction. The H-coil measurements are useful when the H-coil and B-coil are covering exactly the same area with the uniform field [Pfutzner91]. Normally, in order to measure B, it is possible to drill small holes in a sample, wound the B-coil locally through the holes and apply the principle of eq. (3.3). However, for an externally applied mechanical load, it is impossible to make holes in the sheet without introducing a disturbing stress field. Therefore, nondestructive B sensors are required to measure the components of the flux density. Thus, two pairs of special needles are applied perpendicularly to the sample, see Fig. 3.21.
Fig. 3.21. Magnetic sensors: H coils and B needles [Delage97].
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Fig. 3.22. Needle probe methods with 2 needles at points 1 and 2. Needle probes have proved to be very effective to measure the magnetic flux density B. In fact, the needle probe method was first proposed by Werner in 1949. Since then the method was critically assessed a few times by Japanese and European scientists. The needle probe method makes it possible to measure the local flux, as shown in Fig. 3.22. Generally, the needles can be used as shown in Fig. 3.22. Faraday's law (1.1) for the loop 1-2-3-4-1 in the XY plane gives
dB ⋅ 1Z dS dt S/2
∫ E ⋅ dl = ∫
1− 2 −3− 4 −1
(3.8)
In general case of the path 1-2-3-4-1, eq. (3.8) is given by
dB ⋅ 1Z dS dt S/2
∫ E ⋅ dl + ∫ E ⋅ dl + ∫ E ⋅ dl + ∫ E ⋅ dl = ∫
12
23
34
41
(3.9)
Here, S/2 is the cross section 1-2-3-4. If the induced eddy currents are parallel to the surface of the sheet in the area 1-2-3-4, then the path 3-4 gives zero as well as the two paths 2-3 and 4-1. Indeed, the E23 ┴ dl and E41 ┴ dl which gives zero when integrating (3.9). Thus, the path 1-2 is the only path remains non-zero in the left part of eq. (3.9). If the needle probe method is used at a distance from the edge, more or equal to three times the thickness of the steel sheet then the assumption above is acceptable [Loisos01], and consequently, the two-needle probe method can be easily used for the measurements. The induced Vsensor in the needle probe circuit is equal to
Vsensor =
dB dH ⋅ 1Z dS + ∫ µ 0 ⋅ 1Z dS Air dt dt S/2 S Air
∫
(3.10)
Here, the second term of the induced Vsensor in eq. (3.11) corresponds with the loop formed by the surface of the specimen and the lead wires
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connecting probes to the measuring instruments. This error can be large in case of large distance between the sheet surface and the closing wire. Therefore, to ensure a high quality measurements, the wire between the needle probes must be placed as close as possible to the surface of the studied sample. In addition, the technique to reduce the second term is the twisting of the wires to reduce the area SAir. It is essential to use the needle probes in the middle of the sample to avoid arising errors due to using two needles at the edge [Loisos01]. If the magnetic measurements are performed at the edge of the steel sheet, then the general 4 needle probe method should be used to reduce a possible error [Loisos01], [DeWulf02], [Pulnikov03]. An experimental study of using different distances between needles in different electrical steels shows that for the measurements over distances greater than 10 mm two needle probes technique can give fairly accurate results [Loisos01]. At distances greater than 25 mm the two needle probe method can give accurate results both for non-oriented and grain-oriented steels, without any damage due to drilling holes for a search coils in the sample. The latter is particularly important in case of applying tensile or compressive stress to the sample of electrical steel. 3.4. 2D magnetic measurement system under stress. Based on the presented overview of different magnetic measurement systems, the following conclusions can be drawn. The target of a novel measurement setup is to carry out various 2D magnetic measurements in a steel sample under externally applied mechanical stress. Because of the interest in both compressive and tensile stresses, a measurement setup should be capable of creating either compressive or tensile mechanical load. An extra opportunity to apply a mechanical load above the elastic limit is preferable in order to study the effect of plastic deformation, or a plastic strain, on the 2D magnetic properties of various electrical steels. The 2D magnetic measurement system should resemble the proved design of the RSST. The horizontal flat design of the symmetrical RSST is preferable. It allows a waveform control of various 2D conditions of alternating and rotational magnetic fluxes.
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The measurement technique can be chosen freely from standard methods, due to the absence of a standard on 2D magnetic measurements. The accuracy of every single measurement technique is crucial to ensure the overall accuracy of the novel measurement system. Calibration of each axis to the standard results is advisory but not an obligation due to the different magnetic circuits and measurement methods applied. A local magnetic measurement technique by means of B needles and H coils is preferable due to its high accuracy and sound physical ground. If proper designed and then placed in the same area with uniform conditions, they can provide a high degree of accuracy and repeatability. In case of B needles, the non-destructive method of two needle probes allows avoiding drilling holes in the samples. A shielding applied to achieve uniform magnetic flux distribution is considered the best technique to use the H coils for the X and the Y axis. A double H coil technique is unnecessary in that case. The area of magnetic measurements and the sample dimensions should be chosen wisely. One of the features of electrical steels is the grain size, see Chapter 1. In order to obtain macroscopic properties of electrical steel under applied stress, the area of magnetic measurements should be large enough to measure statistical data based on a large number of grains. Furthermore, taking into account the minimal distances to use B and H probes, described in Section 3.3, the measurement area covered by the probes should be at least a square with a width of 25 mm, situated in the center of the sample. The dimensions of the sample can be chosen as usual to the range of the RSST, e.g. an 80 mm square sample. A further 2D or 3D analysis of the magnetic flux distribution is required to ensure that the central area has uniform magnetic conditions. The main question remains: how to combine all of the above into a single measurement system? Focusing on stress dependence of the magnetic properties, the choice of the mechanical system is the main question. The mechanical setup should be able to apply a tensile or a compressive mechanical load to a square sample of 80 mm size up to 1 mm thickness.
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A vertical mechanical system is unable to create compressive stress. Furthermore, it requires an extensive weight capacity for the building. Instead, a horizontal mechanical system can be used, comprising enough strength, a possibility to create either compressive or tensile load as well as a high accuracy of the design, which should ensure that the mechanical load is applied in a single direction only. One of the drawbacks of the horizontal mechanical system is a slight instability of the mechanical load due to a horizontal mechanical load. The shaft of such a system has some degree of an overall elastic capacity. In other words, once the load is applied by the manual winch, the load does not remain constant but slightly decreases in time. Another drawback is the need to hold the sample and to pull or to compress it. That requires nonmagnetic grips with abrasive layers to hold the sample. Thus, the shaft should also be a part of the magnetic system, i.e. the part of the magnetic core of the RSST. The following solution was created in EELAB to comply with the above choices. A horizontal mechanical subsystem consists of a solid frame to carry a load, a manually driven shaft, and a combined system of grips, parts of the magnetic core, placed on brass rolls, see Fig. 3.23. In fact, only sample and core parts are magnetic. At one side of the shaft a transducer is installed to measure the applied mechanical load. The magnetic subsystem is horizontal but asymmetrical in comparison with other RSSTs. The non-symmetry comes from the mechanical subsystem, having the core parts as a part of the shaft, see Fig. 3.23. Those parts are movable, and furthermore, they create a magnetic flux in the longitudinal axis of the setup. The rest of the RSST consists of two similar parts, having an Eshape, to provide the magnetic flux in the transverse axis by means of the middle leg of the E-shape design, as shown in Fig. 3.24.
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manual winch
grips abrasive samples core parts
Fig. 3.23. Horizontal mechanical subsystem to apply uniaxial load to the samples of steels up to 2 mm thick.
Fig. 3.24. Horizontal non-symmetrical magnetic subsystem, an analogue of flat RSST with an extension to apply mechanical load.
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3.4.1. The mechanical subsystem of the 2D setup. The scheme of the mechanical subsystem is shown in Fig. 3.23 and Fig. 3.25. Its frame is 1.2 m long. The sample is held by means of brass grips in order to apply uniaxial mechanical load. To increase the traction force of the grips, special abrasive pieces have been used to hold the sample under very high loads. The chosen design has been proved to be very effective for a wide range of materials up to very high uniaxial loads. Due to the high strength of the grips required to hold the sample, an extra space is used to place the bolts, which contract two grips together, as shown in Fig. 3.26. Therefore, a sufficiently large space of the sample is used for holding the sample by means of grips, abrasive and bolts under compression up to 40 kN. Moreover, a large air gap is used between the sample and the core parts of the magnetic subsystem, which are simultaneously the parts of the mechanical subsystem. The following dimensions are used: - 10 mm on each side is the air gap due to bolts, - 20 mm on each side is the grips for clamping a sample, - at least 40 mm is enough to use the B and H sensors. Taking these dimensions into account, a minimal length of the sample can be 100 mm.
Fig. 3.25. The mechanical subsystem: a) top view, b) front views.
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Fig. 3.26. Holding a sample in a non-symmetrical magnetic subsystem. The mechanical subsystem allows to create either a compression or a tension. In order to achieve a compression, the left part of the mechanical subsystem in Fig. 3.25 is fixed to the frame from the inside, as shown in Fig. 3.27. The part with the winch moves towards the center of the setup by means of non-fixed aluminum bars, as shown in Fig. 3.28. The value of the applied compression is limited by the possible buckling of the sample of the laminated steel. Thus, the limit of the compressive stress is up to 100 MPa for a sample of 1 mm thickness. Tension can be applied by means of fixing the part of Fig. 3.27 from outside the frame, while the part of Fig. 3.28 is movable outwards the center of the setup by means of the manual winch. The tensile stress can be applied manually in steps up to the elastic limit, and even further up to destruction. In our experiments the sample is always destructed in the middle between the grips, as shown in Fig. 3.29. transducer
to fix from the outside
to fix from the inside
Fig. 3.27. The part, which can be fixed either from inside or outside.
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manual winch
removable aluminum bars (used for compression)
Fig. 3.28. The part, which is movable either towards or outwards the center.
Fig. 3.29. Plastically destroyed samples of different electrical steels. 3.4.2. The magnetic subsystem of the 2D setup. To create a magnetic core of the flat horizontal RSST type taking into account the non-symmetry, a three phase transformer core was used with suitable E-shape laminations, having a width of 80 mm. The same 80 mm strips of the same steel were used to create two movable parts, which are the components of the mechanical subsystem. Four excitation windings provide the excitation in the longitudinal direction, parallel to the direction of externally applied mechanical load, according to the scheme of Fig. 3.24. Only two excitation windings provide the excitation in the transverse direction, perpendicular to the direction of the applied mechanical load, as shown in Fig. 3.24 and 3.30.
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Fig. 3.30. The magnetic subsystem with two switchboards of excitation windings, having each 5 sections for interconnections. A significant question for all RSSTs is the overall value of the air gap, and consequently, the field distribution in the sample. Due to the nonsymmetry of the setup, and consequently, different field distributions along the two excitation axes, the air gap and the dimensions of the sample are the parameters to choose in order to achieve an uniform field distribution in the center of the sample, where the B and H probes are placed. Basically, the choice of the dimensions is one of the crucial points to ensure that the magnetic measurements are accurate and repeatable. The air gap in the longitudinal direction of the setup is equal to 20 mm as stated above. Its value is constant, however the length of the sample may vary from 100 to 200 mm. In fact, the variation of the sample length would result in the change of the magnetic field distribution. The air gap in the transverse direction is equal to 10 mm, i.e. 5 mm on each side of the sample. However, the width of the sample can be reduced to enlarge the air gap in the transverse direction if necessary. The width of the sample equals 80 mm or less, whereas the length of the sample equals 100 mm or more. Thus, the working dimensions of the sample were chosen as 80 mm x 120 mm. These dimensions allow the largest width of the sample and the minimal length, taking into account the parts of the sample under grips and the required space of the sensors. To define the area for the magnetic measurements, many calculations have been done. The field distribution was first analyzed in 2D: in the XY plane and in the XZ plane. An extra 2D analysis was
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performed for the application of shielding, which is used to reduce the stray fluxes, as was shown before in Fig. 3.14 and 3.15. Some numerical results of the 2D model of the setup considering the XY and XZ planes are shown in Fig. 3.31 – 3.32. a)
b)
Fig. 3.31. XY models of the magnetic flux in different directions: a) in the X axis direction, b) in the 60 degree direction.
Fig. 3.32. XZ model of the magnetic flux in the air with a single sample.
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The doubt about the presence of a proper magnetic flux distribution arises from the XZ model. An extra study was performed to compare the magnetic flux distribution in the case that a single sample is used with the case of two samples, as shown in Fig. 3.33. The shielding should lead to an uniform magnetic flux distribution between two samples, as shown in Section 3.2.2. An extra study of magnetic flux patterns in the XZ plane has been performed in the central area of the sample, where the H coils will measure the magnetic field, as shown in Fig. 3.34 and Fig. 3.35. When the single H coil is placed on top of a single sample, the stray fluxes are measured by the H coil, as shown in Fig. 3.34. This leads to the above described error. When the single H coil is placed between two samples, the stray fluxes are shielded by the samples. The single H coil measures the horizontal flux only, as shown in Fig. 3.35.
Fig. 3.33. Principle of application of shielding for accurate H measurements.
Fig. 3.34. XZ model of the flux in the H coil, placed on top of a single sample.
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Fig. 3.35. XZ model of the flux in the H coil, placed between two samples.
Fig. 3.36. The flux density in ¼ of sample for the Y excitation [Pulnikov03].
Fig. 3.37. The flux density in ¼ of sample for the X excitation [Pulnikov03].
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The flux density distribution under the excitation in the longitudinal direction Y is uniform in almost the whole sample area, see Fig. 3.36. However, in the transverse direction X the picture is completely different. The flux density distribution under the excitation in the X direction is highly non-uniform in the majority of the sample. Only a central area can be considered as having uniform flux density distribution, see Fig. 3.37. Thus, the magnetic measurements uniaxial with the applied stress can be performed with a high degree of accuracy considering the uniform area of the flux density in the sample. As for the second axis, perpendicular to the applied stress, some extra means are required to ensure uniform magnetic flux distribution in the central area of the sample. This can be achieved, for example, by adding removable magnetic pole shoes installed in the X direction. Basically, the application of the pole shoes reduces the non-symmetry of the magnetic subsystem and improves the flux density distribution as shown in Fig. 3.37. Taking into account the 2D analysis of the magnetic field distribution with the application of the shielding, the following conclusions can be drawn. To achieve accurate magnetic measurements, it is recommended to use two samples and to place the H coils between the two samples in the geometrical center of the sample, see Fig. 3.31. When two samples are used, both of them should be placed under the same externally applied mechanical load to provide compressive or tensile stress simultaneously to both samples. Similar mechanical conditions applied to both samples ensure accurate magnetic measurements in the center by the H coils. A single sample is possible to use under uniaxial stress and magnetization in the longitudinal direction only, because of a large uniform area and a large air gap. To avoid drilling holes, a non-destructive method of two needle probes can be used to measure the flux density in the sample. For a shielding solution, it is impossible to use B coils or B needles between two samples. Therefore, the only way to measure B in the two sample solution is to place B needles on top of the upper sample in the center of the samples. Moreover, due to the movable shaft, the samples should always be placed in the geometrical center of the magnetic subsystem. Based on the above recommendations, the magnetomechanical setup was created and tested in EELAB, as shown in Fig. 3.38.
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Chapter 3.
The setup was first presented orally at the 15th Soft Magnetic Materials Conference in Bilbao, Spain in 2001 by V. Permiakov.
Fig. 3.38. Novel 2D magnetic measurement setup with 1D mechanical stress. 3.4.3. Magnetic measurement technique. The choice of the magnetic measurement technique has already been discussed in the preceding sections. However, there are a few aspects to be discussed separately. When it comes to the accuracy of the measurements, the design
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and calibration of the sensors are crucial. In the current study, a pair of H coils was constructed manually. According to recommendations in [Pfutzner91], the thickness of the epoxy layer in the middle of the H coil is taken equal to 1 mm. The number of turns for each H coil is about 1200 turns. A 0.1 mm thick isolated copper wire was used to wind the H coils. Thus, the dimensions of the H coils are: inside thickness of 1 mm, outside thickness of 2 mm, width of 10 mm, and length of 15 mm. Each H coil was calibrated by means of the Helmholtz coils shown in Fig. 3.3. As a result of the calibration, accurate values of the cross sections NS were obtained. The design of the B needle probes is also important. Commercially available needles GKS079, produced by INGUN and shown in Fig. 3.39, were applied. The needle is a special multi-alloy sensor with golden plating, having a spring force of 1.3 N and a stroke of 1.2 mm. This construction ensures an excellent electrical contact, even if there is a strong coating on a steel sheet. A pair of needles is sufficient to measure B in one direction accurately, if the distance between the needles is sufficiently large and the needles are not too close to the edge of the sheet, see Section 3.3.
Fig. 3.39. The holder (left) and the needle (right) geometry. Source: Ingun.com. X and Y pairs of B needles
Fig. 3.40. The 4 needles in the holder to measure B in X and Y directions.
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The distance between the needles, placed in the holder shown in Fig. 3.40, is 42 and 30 mm for the X and the Y directions, respectively. According to [Loisos01], these distances are sufficiently large to measure the magnetic flux density accurately both in grain-oriented and in non-oriented electrical steels. Thus, the total set of measurement instruments consists of two H coils and two pairs of B needles. The central area of 40 mm x 40 mm can be assumed to be sufficiently uniform to perform accurate local magnetic measurements. The signals from the B and H probes are amplified by signal amplifiers as shown in Fig. 3.41. The accuracy of the signal amplifiers affects the total accuracy of the magnetic measurements [Pfutzner91]. To reduce a possible error, an already proven design of signal amplifiers [Makaveev03], equipped with operational amplifiers at variable gain (1 to 10000), are used. The excitation windings shown in Fig. 3.38 are supplied by bipolar power amplifiers. The excitation voltage is controlled by the software developed in EELAB. A stack of KEPCO bipolar power amplifiers, each having 400 W power, is shown in Fig. 3.42. As many as four KEPCO amplifiers have been used in the present study, connected in series to increase the total gain factor from 3.6 to as much as 10.
DAC contacts
B and H signal amplifiers in X and Y directions
Fig. 3.41. The 4 signal amplifiers and the board of data acquisition card (DAC).
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Fig. 3.42. A stack of KEPCO power amplifiers for the excitation windings. 3.4.4. Waveform control. As was mentioned in Section 3.1, it is crucial to ensure a sinusoidal waveform of the magnetic flux density B in order to permit comparison of different measurements. Generally, there are two target approaches for the waveform control: to control B or to control H. Consequently, the results, i.e. the energy loss and the permeability, will depend on that choice. When a closed magnetic circuit is used, for example, in a SST, the current method is applied to obtain the magnetic field H. Of course, in that case it is logical to operate with H. Although H is controlled in many SSTs, the main criterion for the control remains a sinusoidal B, as was discussed before. When an air gap is present in the magnetic circuit, or when B and H are measured locally by the test probes, then it is better to control the magnetic flux density B in the sample. Indeed, by controlling B almost any kind of flux density waveform can be created. The two axes of the
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measurement setup are considered independent and so is the waveform control. The ability to create any kind of magnetic flux density in each axis of the sample is an advantage as virtually any mode of alternating or rotational magnetization can be studied. Various techniques for flux density waveform control have been used by different researchers. To control B in the present study, the technique of [Makaveev01] was applied. It works very well in the measurement system having an air gap. High induction is difficult to achieve due to high power requirements. The control is based on an iteration procedure. The output voltage to the excitation windings are created from the signals of the B and H probes. The control modifies the next output voltage to achieve B sinusoidal. A new voltage is generally calculated according to eq. (3.7). Parameters of the equation (3.7) depend on the following: - resistance and inductance of the excitation winding, - number of turns and connections of the excitation windings, - the overall air gap, or the equivalent air gap [Makaveev01], - the number of the highest harmonic used in the algorithm, etc. As a result of the waveform control, the magnetic flux density becomes sinusoidal with an error as low as 1%. At the same time, the output voltage V to the excitation windings changes gradually from the primary sinusoidal to the distorted one as shown in Fig. 3.43. 0.2
Before a waveform control
After a waveform control
0.15 0.1
Voltage, V
0.05 0 0
50
100
150
200
-0.05 -0.1 -0.15 -0.2 time, msec
Fig. 3.43. Output voltage V to the excitation windings before and after control in order to obtain a sinusoidal B, measured locally by the B needles.
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3.5. Magnetic measurement procedure. Operational software. Except the application of the mechanical load, which is done manually, everything else is controlled by means of the operational software, developed for this study. The software consists of several modules, each responsible for one specific operation. The following main modules are used in the software: - a Global Setup Database module that includes all parameters for measurements (Fig. 3.44), - a user defined module, i.e. a choice of the automatic range of measurements, - an initialization module, an excitation algorithm based on the primary data, - an output generation module, the control of the two output channels of the DAC, - a data acquisition module, the main control of the measurements (Fig. 3.45), - an update module for the waveform control iterations (Fig. 3.46). The Global Setup Database allows all data to be collected at one place, and to be achieved easily from any module of the developed software. The main clusters of data collected in the Global Setup Database shown in Fig. 3.44 are: - setup files, including data about samples, sensors, acquisition, amplifiers, - sensors, including data about NS values of B and H probes for X and Y axes, - signal and power amplifiers, including gains of B and H for X and Y axes, - acquisition, including input and output channels, scan/update rates, buffer size, - control, including signal type, frequency, amplitude, phase, axis ratio, etc. Other modules in the package are responsible for partial operations: - a module for DC offset compensation that eliminates the DC offset in the signals, - a demagnetization module that demagnetize a sample with a predefined waveform, - a storage module that is responsible for storage of all data obtained during the measurements.
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Fig. 3.44. Global Setup Database of the developed software package.
Fig. 3.45. Modules of the data acquisition and experimental results.
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Fig. 3.48. Update module, responsible for iterations of the waveform control. 3.6. Sample preparation. It is crucial to prepare the samples for the study in a proper way. The steel sheet has to be clean and flat, without any damages of the sheet surface. Any damage or loss of quality of the sheet can affect the results of the magnetic measurements. The typical sample is cut along the rolling or any given arbitrary direction, having 120 mm length and 80 mm width. When two samples are used simultaneously, these should be cut from the same sheet with the same direction along the longest size of the steel sample. 3.7. Conclusions. Chapter 1 has introduced to the reader the subject of this study. Chapter 2 has described 2D magnetic and mechanical working conditions of various electrical steels used in different electrical machines, both from theoretical and experimental point of view. This chapter has described various measurement methods, applied worldwide for characterization of electrical steels. The measurement setup along with a suitable measurement technique has been chosen to meet the objectives of this study. The setup was specially designed, constructed, tested and upgraded in EELAB.
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Chapter 3.
The following features for the magnetomechanical measurements can be used: - manually applied uniaxial compressive load, - manually controlled uniaxial tensile load up to elastic strength, - various tensile plastic deformations up to destruction, - alternating magnetization in arbitrary directions in the plane of the sample, - rotational magnetization up to circular rotation of the magnetic flux density vector, - sinusoidal (or distorted) controlled magnetic flux density, - high accuracy due to the chosen measurement technique, - fully automatic operations of the magnetic measurements. The combination of the above features is quite unique. It allows to create novel magnetomechanical conditions. The following chapters present actual 1D and 2D magnetic measurements in various electrical steels under uniaxial mechanical stress.
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An expert is a person who has made all the mistakes that can be made in a very narrow field. Niels Bohr (1885 - 1962) CHAPTER 4. 1D MAGNETIC MEASUREMENTS UNDER STRESS. The main instrument of the present research is the magnetic measurement system for 2D magnetomechanical conditions. Hence, the study is based on experimental observation, followed by a physically sound explanation. As with any research instrument, the novel 2D measurement system must first be extensively tested up to its limits. Having a little experience with magnetic measurements, it is crucial to gain the measurement skills, i.e. to make "all the mistakes that can be made in a very narrow field". To narrow the field of the measurements, a primary investigation is done for the simplest case of uniaxial magnetization under uniaxial applied stress. This allows us to make a comparison between our results and the already known stress dependences of magnetic properties for electrical steels. A comparison of the experimental results with the known tendency from literature can give an idea about how the novel measurement setup is operating under uniaxial conditions. Thanks to uniform magnetic conditions for uniaxial magnetic measurements in the longitudinal direction of the setup (see Chapter 3), a number of uniaxial magnetic measurements under stress can be carried out for a single sample of electrical steel with a high accuracy. The externally applied mechanical load can be either compressive or tensile, applied in the longitudinal axis of the setup, see Fig. 4.1. As shown in Chapter 2, the uniaxial case is of interest to both grain-oriented and non-oriented electrical steels. In grain-oriented steels, an uniaxial compression and tension occurs in the transformer cores due to assembling. In non-oriented steels, an uniaxial magnetization under stress occurs in the tooth region of the laminations. Hence, an uniaxial magnetization under stress is useful to study from both experimental and theoretical point of view. Different measurement techniques, described in the previous chapters, are put into practice in the 1D case. To explain the experimental results, different theoretical approaches are presented. Based on the study of Chapter 2, the actual magnetic working conditions are included as well. A number of electrical steels have been studied under complex uniaxial conditions.
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Fig. 4.1. The magnetomechanical setup to apply uniaxial stresses. 4.1. Uniaxial measurements in electrical steels. Based on the analysis presented in Chapters 2 and 3, a single sample of electrical steel is used for uniaxial (1D) magnetomechanical measurements. The procedure for the 1D magnetic measurements includes all the limits of the components of the measurement system, developed in EELAB for 1D and 2D magnetic measurements under mechanical stress, including hardware and software modules. According to Fig. 3.17, the detailed procedure within the limits is as follows: - a digital generation of an output voltage V to supply the excitation windings, - a data-acquisition of the voltage V in the range of ±10 V, - an amplification of the voltage by a gain factor 3.6 or 5, - a measurement of B and H signals by local probes, - an analog amplification of the signals by a factor 1 to 1065, - a data-acquisition of the signals in the range of ±10 V, - a digital integration of the signals to obtain B and H waveforms, - a construction of the BH loop, a calculation of energy loss. In order to achieve the sinusoidal (or distorted) flux density in a sample, the B waveform is compared to the desired sinusoidal (or distorted) waveform. The primary mechanism is to update the amplitude of the voltage V to increase or decrease the amplitude of B. This mechanism has proved to be very fast and effective up to high inductions, but the
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form correction is also required. Hence, the second mechanism is a form update. This was described in section 3.4.4. An "elementary cycle" of strictly controlled magnetic measurements consists of the above procedure, followed by a construction of the update to ensure the desired sinusoidal B. The elementary cycle is terminated when the required condition is met, in this case, when the error between the desired and the obtained B waveform in the sample is less than 1%. The elementary cycle was developed to be fully automatic, controlled by a user-defined operational algorithm. When the externally applied stress is considered, the elementary cycle has to be repeated each time a new stress is applied as follows: - a new mechanical load is applied manually, shown by a digital indicator, - the parameters for the magnetic measurements are defined, - the elementary cycle is applied automatically, controlled by the software, - the experimental results are saved automatically into a specific data file, - the demagnetization module of the software is applied after each regime of magnetic measurements. The following range of working parameters for the uniaxial magnetic measurements can be obtained: - the amplitude of the induction B is between 0.2 and 1.5 T, - the frequency of magnetization ranges from 2 to 200 Hz. If the magnetic measurements are performed under a range of inductions or a range of frequencies, the operational algorithm for magnetic measurements is the one as shown in Fig. 4.2.
Fig. 4.2. The algorithm of uniaxial magnetic measurements under stress.
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The typical operations for the magnetic measurements consist of the following steps: - making a choice of the electrical steel and the preparation of the sample, - making a choice of the parameters for measurements according to Fig. 4.2, - conducting magnetic measurements under stress for the chosen parameters, - analyzing the experimental results, such as BH loops and energy losses. When the experimental results are analyzed, the next step is a comparison with the knowledge, obtained by other measurements setups which are limited either to small stresses, or to uniaxial magnetization under tension only, or to magnetization at plastic deformation only. Eventually, the present study should either confirm the previous results, or bring a certain novelty into the subject of the target research. This is the first evaluation of the EELAB measurement setup for the 1D case, followed by the 2D magnetic measurements under mechanical stress. 4.1.1. Uniaxial magnetization in grain-oriented steels. Grain-oriented steels are known for their large grain sizes and the orientation of an easy axis of the crystals close to the rolling direction of the steel sheet. In the present study for grain-oriented materials, the mechanical stress is applied in the rolling direction. A 0.30 mm thick grain-oriented steel sample has been cut along the rolling direction, having a length of 120 mm and a width of 80 mm. The measurement procedure described above has been applied for a controlled sinusoidal B, within a range of peak inductions of 0.25, 0.5, 0.75, 1.0, 1.25 T at the power frequency. A higher induction level was not possible to achieve due to the limitations of the excitation power because of the large air gaps of the measurement setup. As a result of the magnetic measurements, BH loops are obtained for every peak induction level. Fig. 4.3 depicts the experimental BH loops at peak induction of 0.5 T under a range of applied stresses from compression of 10 MPa to elastic tension of 100 MPa. The BH loops are the basic data about the magnetic properties of steel. Many other
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magnetic properties can be obtained from these loops. For example, the energy loss is equal to the area of the BH loop as in (1.7) [Sievert84]. Fig. 4.4 depicts the experimental energy losses under stresses.
Fig. 4.3. The BH loops under a range of uniaxial stresses at 50 Hz.
Fig. 4.4. The energy losses under a range of uniaxial stresses at 0.25 to 1.25 T.
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The application of a tensile stress in the rolling direction of a grainoriented steel leads to a considerable improvement of the magnetic properties in this direction. Indeed, the area of BH loops under tension is reduced in comparison with the stress-free condition. In fact, a further increase of the tensile stress up to 100 MPa results in a very little change of the BH loops, see Fig. 4.3. On the contrary, a compressive stress of 10 MPa leads to a drastic deterioration of the magnetic properties of grain-oriented steel. The area of the BH loop at compression of 10 MPa is much larger than the area at the stress-free condition. A similar tendency was observed for other peak induction levels up to 1.25 T. In fact, the improvement of energy losses under uniaxial stress in the rolling direction of grain-oriented steels has been well-documented before. Fig. 4.5 depicts the experimental data on the effect of applied tensile stress on energy loss at 1.5 T at 50 Hz in different grain-oriented steels having different average grain diameter [Shilling74]. As shown in Fig. 4.5, the largest loss reduction with an increasing tensile stress occurs in a single crystal. A conventional grain-oriented electrical steel with an average grain size of around 10 mm exhibits a weaker improvement under tensile stress. Below a certain optimum grain size (about 7 mm, according to [Shilling74]), the energy loss increases with decreasing grain size after a certain tensile stress, as shown in Fig. 4.5. The cause for the increase of energy loss under large tensile stress is an increasing amount of domain wall pinning due to a larger magnetostatic energy at the grain boundaries [Shilling74]. Thus, in grain-oriented steels the tensile stress applied in the rolling direction can reduce the energy loss. The effect of tensile stress has been successfully exploited by the use of stress inducing coatings for grain-oriented steels. The effect of different surface coatings on domain structure and energy loss was studied e.g. in [Fukuda81].
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Fig. 4.5. The effect of applied tensile stress on energy loss [Shilling74].
Fig. 4.6. The effect of compressive (negative) and tensile (positive) stress on energy loss in various grain-oriented steels [Moses80].
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In another experimental study [Moses80], several grades of grainoriented steels have been tested at 1.5 T and 50 Hz. Fig. 4.6 depicts an experimental comparison between the mean measured losses in several steel grades. In fact, the right part of Fig. 4.6, i.e. the loss at tensile stress, has a good correspondence with Fig. 4.5 by [Shilling74] and the experimental results of the present study, as shown in Fig. 4.4. The left part of Fig. 4.6, i.e. the energy loss at compressive stress, has a very good correspondence with the experimental results of the present study at 10 MPa, as shown in Fig. 4.4. Unfortunately, it was difficult to obtain high compressive stress in the present setup due to buckling of the very thin sample of the considered grain-oriented steel. It is worth mentioning here that a compressive stress higher than 10 MPa is not likely to happen in actual devices such as power transformers, as shown in Chapter 2. A similar sharp increase of the energy loss under a small compressive stress up to 10 MPa can be observed in the past experimental results [Moses80]. 4.1.2. Uniaxial magnetization in non-oriented steels. Due to the orientation of the grains, grain-oriented steel is presented first. As a matter of fact, the present research of 1D magnetization under uniaxial stress had started from the non-oriented steels, and this was for at least two reasons. Non-oriented electrical steels are the most common magnetic materials, so is the interest in the properties. Furthermore, to gain the skills in special magnetic measurements, it is much easier to deal with a "simple" high-loss material such as non-oriented steel than with a "fine" low-loss grain-oriented steel. Hence, the trial measurements were performed on non-oriented electrical steels. The thickness of non-oriented electrical steels ranges from 0.35 mm up to 1.0 mm, which results in much larger eddy current loss in the laminations. Moreover, due to the higher thickness, magnetic measurements are feasible at larger compressive stress without bending of a steel sample, as occurs in grain-oriented steels. As shown in Chapter 2, there can be very large compressive stresses (above 50 MPa) in the stator and rotor cores of rotating machines. Furthermore, the difference in magnetic properties between arbitrary directions of non-oriented steels is much smaller than in the case of grain-oriented steels. The mechanical stress can be applied in any arbitrary direction of the steel sheet with a little difference in
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magnetomechanical properties between directions. By default, the mechanical load is applied in the rolling direction (RD) of the steel samples of the considered non-oriented electrical steels. Samples of several fully-processed non-oriented electrical steels with thickness of 0.50 mm and 0.65 mm have been used during the present research. The above measurement procedure has been applied for a controlled sinusoidal B, having a peak induction between 0.2 and 1.4 T. Only a selection of the experimental results is presented here. One of the parameters of the operational control shown in Fig. 4.2 is stress. Three areas of applied mechanical stress are considered: small elastic stresses including compression and tension, all elastic stresses up to the elastic limit, and plastic strains. The typical range of small compressive and tensile stresses is ±50 MPa. This is also the range of stresses considered in most electrical steel research. A further increase of tensile stress can be achieved up to the elastic limit, followed by plastic deformation up to the destruction of the sample. As a result of a series of magnetic measurements on 0.65 mm steel, BH loops can be drawn for every considered peak induction. Fig.4.7 depicts the experimental BH loops at peak induction of 1.0 T under applied stresses ranging from compression under 60 MPa to tension up to 150 MPa. Fig. 4.8 depicts the experimental BH loops at peak induction of 1.4 T under a similar range of applied elastic stresses. The application of tensile stress in the rolling direction of the non-oriented steel leads to some improvement of the magnetic properties in this direction. Indeed, the area enclosed by the BH loops under small tension is reduced in comparison with the stress-free condition. On the contrary, the application of compressive stresses leads to a drastic deterioration of the magnetic properties of the considered non-oriented steel. The area of the BH loop at compression of 60 MPa is much larger than the area under the stress-free condition. A similar tendency was observed for peak inductions up to 1.4 T. Fig. 4.9 depicts the experimental energy losses under a range of compressive (20, 40, 60 MPa) and tensile (30, 70, 100, 150 MPa) stresses at several peak inductions up to 1.4 T. Fig. 4.10 depicts the relative permeability changes under the same range of applied stresses at peak inductions of 1.0 T and 1.4 T. The relative permeability was determined in correspondence with the maximum flux density for every BH loop.
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Fig. 4.7. The BH loops under compression and tension at 1.0 T and 50 Hz.
Fig. 4.8. The BH loops under compression and tension at 1.4 T and 50 Hz.
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Fig. 4.9. The energy losses under a range of uniaxial stresses at 0.7 to 1.4 T.
Fig. 4.10. The relative permeability under a range of stresses at 1.0 and 1.4 T.
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Considering magnetic properties versus stress, it is possible to establish the value of a tensile stress corresponding to the minimum energy loss (see Fig. 4.9) or to the maximum permeability (see Fig. 4.10). This stress is called here a "critical stress", where the applied uniaxial tension results in the best magnetic properties in the same direction. The range where the critical stress is located can be observed at 20 to 60 MPa, depending on the material. The critical stress phenomenon was found in various grain-oriented and non-oriented steels in the present study. In fact, the improvement of energy losses under uniaxial stress in non-oriented steels has been experimentally studied very recently. Fig. 4.11 depicts the energy loss per cycle W under a range of uniaxial stresses σ from compression of 50 MPa to tension of 75 MPa [LoBue00]. Here, the open symbols correspond to non-oriented steel with an average grain size of 50 µm and the closed symbols correspond to nonoriented steel with an average grain size of 270 µm, see Fig. 4.11. Both kinds of materials show a drastic increase of the energy loss under compression and a moderate change under tension. The critical stress can be observed at about 30 MPa for the material with a small grain size. The non-oriented steel with larger grains shows a lower sensitivity to the applied tension but a higher sensitivity to the applied uniaxial compression.
Fig. 4.11. The energy loss per cycle under uniaxial stresses at 0.5, 1.0 and 1.5 T. Grain size: open symbols - 50µm, closed symbols - 270µm [LoBue00].
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4.1.3. Uniaxial magnetization at tensile plastic deformation. The condition of tensile plastic deformation requires a separate attention. According to Chapter 2, the production process for rotating machines consists of the inevitable procedure of punching or cutting of the sheet to produce the tooth-and-slot structure of the laminations. A complex plastic deformation occurs due to cutting. The simplest way to study the plastic deformation is to apply uniaxial strain to the sample, using the same measurement setup as for applying uniaxial compressive and tensile elastic stresses. Indeed, the setup created in EELAB allows to apply tensile plastic deformation up to the destruction of the sample, see Chapter 3. The experimental procedure in case of plastic deformation is different from the one used for elastic stress. When elastic stress is studied, a mechanical load is applied and the measurements are performed according to Fig. 4.2. Then the sample is unloaded to the stress-free conditions. The fact that the physical and magnetic properties of the unloaded sample are the same as before the applied mechanical load ensures that the stress was indeed elastic. When the tensile plastic deformation starts after the yield stress σy (see Fig. 4.12), the application of a larger stress σf leads to a plastic strain εf, depicted by the point A in Fig. 4.12. When the load is released after point A, the material will not return to the unloaded "zero" strain, but instead a residual strain εr occurs. The experimental procedure to study the effect of tensile plastic deformation on the magnetic properties of non-oriented electrical steels consists of the following steps, as shown in Fig. 4.12.
Fig. 4.12. Applied experimental procedure 1-2-3-4 at a strain curve [Sablik04].
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Magnetisation, T
Step 1 as shown by the arrow 1 in Fig. 4.12 corresponds to a tensile strain εf2 , i.e. from the point A (strain εf) to the point B (strain εf2). At the point B, a series of magnetic measurements, called here "under stress", is performed according to Fig. 4.2. Step 2 as shown by the arrow 2 in Fig. 4.12 corresponds to a residual strain εr2 , i.e. from the point B (a loaded condition, or under stress σf2) to the point C (an unloaded condition, or after the stress release). At the point C, a series of magnetic measurements, called here "after release", is performed according to Fig. 4.2. Step 3 as shown by the arrow 3 in Fig. 4.12 corresponds to the area of elastic stresses applied to the plastically deformed material having a stress-free condition in the point C, i.e. at a plastic strain εr2 . Step 3 can consists of a number of applied tensile elastic stresses from the point C to the point B in Fig. 4.12. Step 4 repeats Step 1, resulting in a new level of tensile plastic deformation. Fig. 4.13 depicts the evolution of BH loops under tensile elastic stresses and tensile plastic deformation. In fact, the BH loops shown in Fig. 4.13 were the first published experimental results obtained by means of the novel magnetomechanical setup at EELAB. The yield stress for this non-oriented steel with a thickness of 0.65 mm is equal to 430 MPa. So, the tensile plastic deformation is presented here by the two largest BH loops, depicted by the dotted lines. 1.2 1 0.8 0.6 0.4 0.2 0 -250
0 -0.2
250
500
750
1000
1250
1500
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Magnetic Field, A/m
-0.4 -0.6 -0.8
No tensile stress, 20, 40, 60, 80, 100, 130, 165, 200, 250, 300, 350, 400 Mpa (-----) and 450, 500 Mpa ( - - - )
-1 -1.2
Fig. 4.13. The BH loops at tensile stresses up to 400 MPa and two plastic strains, depicted as two curves at 450 and 500 MPa.
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Fig. 4.13 includes another interesting information about the BH loops behaviour. All BH loops at elastic stresses have two cross points in the second and the fourth quadrants, very close to the remanence points. The two largest BH loops (see Fig. 4.13) of plastic deformations are not in the common cross point of all the others BH loops for tensile elastic stresses.
Fig. 4.14. The BH loops at two plastic strains under stress and after release.
Fig. 4.15. The energy losses at plastic strains under stress and after release.
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Fig. 4.16. The relative permeability changes at plastic strains. Fig. 4.14 depicts the BH loops obtained according to the experimental procedure as shown in Fig. 4.12. Fig. 4.15 depicts the energy loss "under stress" and "after release" according to the experimental procedure. The application of tensile plastic deformation leads to a very fast deterioration of the magnetic properties at plastic strains less than 10% and a steady deterioration at higher plastic strains up to destruction, which occurs at 35% for the considered steel. The energy loss under stress is considerably lower than the loss after release. The material "after release" can be considered as a newly deformed material. When a tensile elastic stress is applied "after release" (see arrow 3 in Fig. 4.12), the magnetic properties can be improved. A physical interpretation of this observation will be given later on. Fig. 4.16 depicts the change of the relative permeability at the same plastic strains as in Fig. 4.15. 4.1.4. Uniaxial magnetization in semi-processed and annealed steels. Semi-processed non-oriented electrical steels are widely used in the USA and Japan. The idea to use semi-processed steels in rotating machine laminations is simple. The cutting of steel is performed to a low-quality material, which is annealed later to achieve the best magnetic properties, comparable with the ones of the available fully-processed steels.
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To study the effect of uniaxial stress on semi-processed steels, a 0.65 mm thick semi-processed steel was used to produce two kinds of samples: an ordinary semi-processed sample and the one annealed according to EN10126. The magnetic measurements under stress were performed and the stress effect was compared with a 0.65 mm fully-processed steel. Fig. 4.17 depicts the stress-free BH loops for samples of fully-processed (FP), semi-processed (SP) and annealed semi-processed (SPA).
Fig. 4.17. The stress-free BH loops of FP, SP, and SPA steels.
FP
SP
SPA
Fig. 4.18. The energy losses of FP, SP, and SPA steels under elastic stresses.
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Fig. 4.19. The energy loss of FP (triangle), SP (circle), and SPA (square) steels at plastic strains. Open symbols: under stress. Closed symbols: after release.
FP
SP
SPA
Fig. 4.20. The relative permeability of FP, SP, and SPA at a range of stresses.
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FP
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SP
SPA
Fig. 4.21. The coercive force of FP, SP, and SPA steels at a range of stresses.
FP
SP
SPA
Fig. 4.22. The remanence of FP, SP, and SPA steels at a range of stresses.
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Fig. 4.18 to Fig. 4.22 depict various magnetic properties of the three compared steels under uniaxial stress and plastic deformation. This work was presented by V. Permiakov at 2DM'2002. Although a similar tendency can be observed for all materials in comparison with the previous experimental results presented above, the sensitivity of semi-processed steel to the applied stress and the tensile plastic deformation is very low in comparison with the behaviour of the same material after the annealing and with the one of the fullyprocessed steel. The annealed steel shows the best magnetic properties and the largest dependence of the applied compressive and tensile stress. A critical stress can be observed at uniaxial tension of 20 to 60 MPa, similar to the one observed above. 4.1.5. Uniaxial distorted magnetization under stress. According to Chapter 2, the actual magnetic flux waveforms in machines are distorted (non-sinusoidal) in most cases. Although all magnetic measurements are usually performed at sinusoidal flux density in the sample, a study of distorted magnetization under stress can be easily performed in the novel magnetomechanical system. The waveform control of the system allows to achieve virtually any form of magnetic flux density in the material. A study of the stress effect on the magnetic properties under actual distorted magnetization has been performed for the experimental flux patterns at rated load shown in Fig. 2.5, see Chapter 2. Fig. 4.23 depicts the BH loops under a distorted flux versus a sinusoidal flux of the same peak induction level at compressive stresses [Permiakov03]. Fig. 4.24 depicts the BH loops under a distorted flux versus a sinusoidal flux under plastic deformation [Permiakov03]. Fig. 4.25 depicts the distorted BH loops under a complete range of applied stresses. Fig. 4.26 depicts the energy loss under distorted and sinusoidal fluxes and "after release" [Permiakov03].
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Fig. 4.23. The BH loops at compressive stresses: sinusoidal vs. distorted.
Fig. 4.24. The BH loops at plastic deformations: sinusoidal vs. distorted.
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Fig. 4.25. The BH loops at a range of applied stresses under distorted flux.
Fig. 4.26. The energy loss at a range of stresses and plastic deformations. Closed symbols: under stress. Open symbols: after release. S: sinusoidal. D: distorted.
1D magnetic measurements under stress 4.1.6. Experimental tendencies.
results
of
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129 measurements:
preliminary
Based on a large number of experiments for different electrical steels, of which only a part was presented above, the following preliminary conclusions can be drawn for grain-oriented and non-oriented electrical steels under sinusoidal and distorted uniaxial magnetization: - a compressive stress leads to a drastic deterioration of the magnetic properties, - grain-oriented steel is strongly sensitive to even a small compressive stress, - a tensile stress improves the magnetic properties in the direction of the stress, - a "cross point" can be observed for BH loops at tension in two quadrants, - the "critical tensile stress" of 20-60 MPa corresponds to the best magnetic properties, - grain-oriented steel is barely sensitive to tensile stress above the critical tensile stress, - semi-processed steel is less sensitive to stress than fullyprocessed steel, - annealing of semi-processed steel leads to a higher sensitivity to the applied stress, - a tensile plastic deformation deteriorates the magnetic properties of all steels, - a tensile plastic elongation of less than 10% leads to a very fast tendency for the deterioration, - an elongation larger than 10% leads to a steady deterioration up to destruction, - a deformed steel has poorer properties "after release" than "under stress", - a distorted magnetization exhibits a similar stress effect as a sinusoidal one, - a plastically deformed material is less sensitive to a distorted magnetization, - uniaxial compression and plastic deformation are the worst conditions, resulting in a large increase of energy loss and a large decrease of permeability.
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4.2. The magnetomechanical effect: theoretical approach. The previous section presents a broad range of experimental results obtained by means of the novel magnetomechanical system under uniaxial stress and magnetization. For every aspect of the above tendencies there must be a physically sound explanation. To explain the experimental results, it is better to start with grainoriented steel. One of the features of grain-oriented steel is the orientation of the [001] crystallographic direction of the (110) crystal plane along the rolling direction of the material. Furthermore, due to large grains, it is easy to obtain an experimental observation of the domain structure for grain-oriented steels. 4.2.1. Energy theory and domain structures. Domain theory is indeed a suitable tool for a physically sound explanation of the stress effect in grain-oriented steels. Fig. 4.27 depicts the domain structure at tension in the rolling direction (RD) of 0.30 mm 3%-Si steel without coating [Fukuda81]. A clear GOSS texture can be observed in Fig. 4.27, when the [001] crystallographic direction of the grains is close to the RD of the sheet. For this grain-oriented steel, the (110) crystallographic plane is parallel to the RD of the sheet. Several grains can be observed as well in Fig. 4.27. A stress-free condition can be described by a small number of fairly large domains oriented inside each grain close to the rolling direction. The application of tensile stress parallel to the RD of grain-oriented steel leads to an increase of the number of domains in every grain with a clearly observed decrease of the width of each domain. The effect is described as if a stress-free domain is split into a few longitudinal domains. Moreover, in Fig. 4.27 the material is not magnetized.
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Fig. 4.27. Domain structures due to tensile stress in the RD [Fukuda81].
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Fig. 4.28. (a) ideal domain structure, (b) effect of compression [Moses80]. Indeed, the application of tensile stress refines the wall spacing of "main domains" and removes "supplementary structure", resulting in almost an ideally oriented domain structure [Shilling74]. The stress effect can then be easily understood based on the fact that the supplementary structure consists mainly of transverse domains, oriented perpendicular to main domains in the plane of the sheet. In other words, when a tensile stress is applied in the RD of grain-oriented steel, there is at least a partial elimination of transverse domains and a structural refinement, or a "splitting", of main domains that are oriented parallel to the applied tensile stress, see Fig. 4.27. Indeed, due to the orientation of grains and the domains in the direction parallel to the applied mechanical load, tensile stress seems to improve the domain structure. Compression on the other hand leads to completely different results in a demagnetized state. Fig. 4.28 depicts the effect of compression on (110) [001] oriented electrical steel in the RD. Consequently, when a magnetic field is applied in the rolling direction of grain-oriented steel under tension or compression, the stress effect is completely different. An uniaxial tension is favourable for the uniaxial magnetization, resulting in smaller BH loops, see Fig. 4.3, and smaller energy loss, see Fig. 4.4. On the contrary, an uniaxial compression is unfavourable for the uniaxial magnetization, resulting in much larger BH loops and a higher energy loss, see Fig. 4.3 and Fig. 4.4. When magnetization is applied in the rolling direction parallel to the direction of applied stress, the domain theory should be considered. An introduction into the domain theory has been given in section 1.2.2. Here, a more detailed explanation is required. The ferromagnetic domains are magnetically ordered regions
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within which the magnetization is equal to the saturation magnetization. The overall magnetization of the material is the vector sum of the magnetization within all domains. When a magnetic field is applied to a magnetic material, changes occur in the domain structure which produce changes in the overall magnetization. Changes in the domain structure can occur by two means. The primary mechanism is the domain wall movement, i.e. when the boundary between two domains moves. The second mechanism is the domain rotation, i.e. when the magnetization within a domain rotates to another direction, e.g. parallel to the applied field.
Fig. 4.29. Demagnetized domain structures in: a) isotropic material, b) single crystal, c) grain-oriented steel, d) grain-oriented steel at tension [Shilling74]. In electrical steels, domain rearrangement occurs to a major extent by wall movement between neighbouring domains. Domain rotation occurs only at large applied magnetic fields. Due to the complex domain structures in electrical steels, a prediction of the domain structure by means of a minimization of crystal energy is a large scientific challenge. So far, nobody succeeded in doing this. Instead, an adaptation of domain structures and an approximation of the total energy are usually used. In Fe-Si alloys such as electrical steels, the major energy components are: - the magnetostatic energy, - the magnetocrystalline anisotropy energy, - the magnetoelastic energy, - the exchange energy, - the energy of the domains in the presence of an applied field. The magnetostatic energy is the energy of a sample in its own field. In order to minimize this energy, a convenient multidomain structure is usually introduced, as shown in Fig. 1.5b. The magnetostatic energy without a domain structure (se Fig. 4.29a) is very large. For a domain structure shown in Fig. 4.29b, i.e. a "two-two" structure of two main and two transverse domains, the magnetostatic energy in Fe-Si steels
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corresponds to a minimum energy state in a demagnetized material. The magnetic moments of the atoms have preferable directions in the crystal structure. The magnetocrystalline anisotropy describes a minimum energy for domains located parallel to certain crystallographic directions, called "easy directions of magnetization." The same atomic moment interactions giving rise to magnetism and magnetic anisotropy produce forces between atoms, which tend to strain the material lattice anisotropically. The magnetic energy associated with these lattice strains is called the magnetoelastic energy, usually characterized by two parameters λ100 and λ111. These parameters are defined experimentally as the strains in the [100] and [111] directions, when the magnetization is in the [100] and [111] directions, respectively. Because of the dependence of magnetoelastic energy on lattice strain, a strong interaction exists between the orientation of domains and applied stress. For example, if an uniform tensile stress is applied parallel to the [100] easy direction of grain-oriented steel, the magnetoelastic energy proportional to the applied stress reaches its minimum state for the domains which lie parallel to the externally applied tensile stress. However, if tensile stress is applied at some angle with respect to the cube edges, domains can be expected to lie along the closest easy direction to the tensile stress, but not parallel to it. Residual stresses can also introduce a magnetoelastic energy component into the total energy. There are two wall types in Fe-Si electrical steels: the 180-degree walls and the 90-degree walls. A 180-degree wall reverses the flux by 180º and a 90-degree wall reverses the flux by 90º, as shown in Fig. 4.29b. How can the total energy be minimized? The magnetostatic energy can be reduced to zero by using four 90-degree walls and one 180-degree wall, see Fig. 4.29b. The anisotropy energy is equal to zero for the domains oriented in easy directions. The wall energy (exchange, anisotropy, magnetoelastic energy within the wall region) can be neglected. Thus, the magnetoelastic energy in the domains is the largest component existing in the considered domain structure. In fact, the magnetoelastic energy is proportional to the volume of the closure domains [Shilling74]. Therefore, by reducing the volume of the supplementary structure, the magnetoelastic energy can be reduced to some optimal value. When tension is applied, this optimal value can be achieved, as shown in Fig. 4.29d. From theory to practice, in order to explain the experimentally
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observed domain structures under tension shown in Fig. 4.27, the energy behaviour is crucial. The magnetoelastic energy of the main domains decreases if tensile stress is applied parallel to the rolling direction (i.e. an easy direction) or increases if compressive stress is applied instead. The magnetoelastic energy of transverse domains does the opposite. Hence, based only on magnetoelastic energy the assumption can be made that the supplementary structure of closure domains tends to disappear under tension. However, the removal of the supplementary structure by tensile stress increases the magnetostatic energy. Hence, a simultaneous refinement of the wall spacing of main domains occurs (see Fig. 4.29c,d) to reduce the magnetostatic energy [Shilling74]. When a magnetic field is applied to the material, domain wall movement occurs, see Fig. 1.5. In Fe-Si steels, magnetization occurs by the motion of 180º and 90º domain walls until the net force of all walls is zero. During magnetization under tensile stress, the supplementary structure of transverse domains that disappears under stress in demagnetized state reappears again to support the magnetization process [Shilling74]. This occurs when movement of the 180° walls separating main domains has increased the magnetostatic energy to the point where the sum of the magnetostatic energy and magnetoelastic energy is reduced by the formation of a supplementary structure. Thus, there is in fact an "energy balance" of domain structures, depending on many parameters, such as grain size, impurities and other pinning centers, residual stresses, and of course, the externally applied stress and the magnetic field. 4.2.2. Applied stress and domain theory. As shown in Fig. 4.3, the application of tensile stress at medium magnetization has an useful effect on macroscopic energy loss due to the reduction of the magnetoelastic energy of the domains. A further increase of the tensile stress seems to have a moderate effect on energy loss of the considered grain-oriented steel as shown in Fig. 4.4. Applied tensile stress does not indefinitely refine the wall spacing due to the reappearance of supplementary structure during magnetization. The more stress is applied reducing the magnetoelastic energy, the more supplementary structure is required for uniaxial magnetization. Furthermore, pinning of domain walls by grain
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boundaries can occur, although high-quality grain-oriented steel has large grains and a limited number of pinning centers. In fact, in grainoriented materials with a smaller grain size, the stress dependence of energy loss is different, see Fig. 4.5. Here, the increase of energy loss after a certain tensile stress can be explained by an increasing number of pinning centers at grain boundaries, resulted in the build-up of a larger magnetostatic energy at higher stress. At compressive stress in the direction of the magnetization, the domain structure makes a transition from an ideal one shown in Fig. 4.28a to the compressed structure shown in Fig. 4.28b. Here, in order to magnetize the domain structure modified by compression, a considerably large domain rotation must occur [Moses80]. The domain walls must move further and faster than in the stress-free state. The amount of domain wall movement can be very large due to a large volume of the closure domains, which are unfavourable to the uniaxial magnetization in the rolling direction of grain-oriented steel. A similar dependence can be observed in nonoriented steels under compression.
Fig. 4.30. Schematic of spin rotation in a 180-degree domain wall [Bulte02].
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A further increase of compressive stress, however, leads to a smaller rate of deterioration of the magnetic properties, as shown in Fig. 4.6. Once all the grains in the material have the stress pattern, further increase of stress reduces the domain spacing. The difference in energy loss at higher compressive stress becomes smaller, although more domains must rotate at a higher stress. The amount of domain wall movement is not greatly different since the volume of the closure domains is very small at a high stress. The domains in different grains switch at different stresses so the energy loss increases up to very high stresses. The tendency for grain-oriented steels in Fig. 4.6 can be observed at large compression in non-oriented steels, as shown in Fig. 4.9 and 4.11. 4.2.3. Levels of understanding: microscopic, domain, macroscopic. A general difficulty to plot a reliable theoretical explanation of the stress effect is derived from the fact that electrical steels are complex polycrystalline soft magnetic materials. Different levels of physically sound explanations can be applied: - a macroscopic level, where the sample dimensions are considered, - a domain structure level, where domains in the grains are considered, - a microscopic level, where the atomic spins and the micromagnetic energies are considered. Generally, there is a range of different types and orientations of grains in non-oriented electrical steels. Therefore, only a statistical approach on a macroscopic level can be considered as a reliable method for research. For example, if the average grain size is equal to 20 µm and the distance between two needle probes is 40 mm, the magnetic behaviour of a couple of thousand of grains is considered in an average way during each magnetic measurement. Although the grains in non-oriented steel have random orientation, resulting in a little anisotropy in the plane of the sheet, the magnetization processes are basically the same as in grain-oriented steels. These include both the domain structure changes under stress as well as the domain wall movement and the domain rotation. Apparently, a physically sound explanation of the stress effect in non-oriented steels can be approached from a microscopic level, and in particular, by considering domain walls and spin rotations in detail, as
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shown in Fig. 4.30 [Bulte02]. In a 90-degree wall, none of the spins within the wall will lie in one of the easy directions. In a 180-degree wall, the center of the wall will lie in an easy direction but the rest of the wall spins will all be in non-easy directions, as shown in Fig. 4.30 [Bulte02]. The interactions on a microscopic level in the domain walls are very complex. The key relationships are the spin-spin interaction, which defines the exchange energy, and the interaction between the spin and the magnetocrystalline preferable directions. In fact, the total energy per unit wall area is a sum of the exchange energy and the anisotropy energy. In a wall of thickness δ (see Fig. 4.30), the angle between neighboring spins is proportional to the distance between the neighboring atoms and inversely proportional to the thickness δ. Hence, the exchange energy per unit wall area is inversely proportional to the wall thickness and the distance between atoms [Bozorth51]. Moreover, the anisotropy energy is proportional to the thickness of the wall. Hence, the thickness of the wall is defined by the above energy balance. When the anisotropy is modified by an externally applied strain, the corresponding magnetoelastic energy is added to the anisotropy energy. The magnetoelastic energy is proportional to the applied stress. Thus, the thickness of the domain wall is modified according to a new minimum for the wall energy. The latter is now the sum of the exchange energy, the magnetocrystalline anisotropy energy and the stress-induced anisotropy energy. In a single crystal, the externally applied stress distorts the crystal lattice, and consequently, the cubic directions will no longer be perpendicular to each other [Bozorth51]. Depending on the orientation of the lattice with regards to the applied stress, the angles between the easy directions will increase or decrease. Any spins which are not aligned with one of the easy directions will be affected by these lattice distortions. When the easy axes and the atomic spins move relative to each other, the induced changes in the anisotropy energy and the exchange energy will modify the total energy, which is required to keep the moments pointing in any given direction. A new "energy balance" must be found to minimize the total energy of the wall. As domain walls are groups of magnetic moments, not aligned with any easy direction, the walls will be affected by externally applied stresses. A wall movement will occur for 90-degree walls as a result of the applied stress. The 90-degree wall will experience an "effective
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pressure" as a response to the stress [Bulte02]. For example, if the tension is applied along the [100] easy axis, and the orientation of the spins of a 90-degree starts from the [100] direction and ends at the [010] direction, the magnetic moments of the wall will tend to align with the [100] direction in order to decrease the magnetoelastic energy of the 90-degree domain wall. This results in 90-degree wall movement "out" of the main domain that is oriented parallel to the tension. A 180-degree wall may be regarded as composed of two 90-degree walls. Therefore, the pressure on 180-degree walls will be on both sides of the wall but in opposite directions. Hence, the wall thickness will change slightly, but the wall position will not be affected. In the demagnetized state, due to this process alone the net magnetization will remain zero. When a magnetic field is applied, uniaxial stress will affect the magnetization as it will reduce (compression) or increase (tension) the size of favourable domains by means of the movement of 90-degree domain walls. Thus, making a step up from a microscopic level to a domain level, the growth of the main domains under tension occurs due to an "effective pressure" on 90-degree walls. A single 180-degree wall in a "two-two" minimum energy domain structure remains stress unaffected. The four 90-degree walls are "pressed out" of the main domains and the area of these walls shrinks, so does the volume of transverse domains. At compression, the four 90-degree walls are "pressed into" the main domains, forcing the apparent domain rotation to the direction transverse to the applied compression. The magnetomechanical effect is virtually the same for all Fe-Si steel, although its contribution is different. Thus, to simplify the uniaxial magnetomechanical effect, an external stress "presses" the 90-degree walls "in" or "out" of the favourable domains under externally applied uniaxial mechanical load. Other effects, which have been observed experimentally, can be explained as well. The presented domain theory and the domain wall movement approach can be used to explain a "critical" stress, a sensitivity, an effect at plastic deformation, and other conclusions drawn in Section 4.1.6. 4.2.4. Explanation of various effects: the cross points in two quadrants. The behaviour of the BH loops, shown in Fig. 4.3, 4.7, 4.8, and 4.13, can be explained as follows, starting from Fig. 4.13.
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As the magnetization of the material moves along the loop from the tip of the loop in the first quadrant to the remanence and further to the second quadrant, the magnetic field is first reduced to zero, which corresponds to the remanence. The remanence is a result of positive internal field sufficient to maintain a reversible rotation of magnetic moments. When a negative field of a larger amplitude is applied, the point is reached where the field is insufficient to maintain reversible rotation. The overall magnetization of the material is still positive due to the fact that it is a sum of the internal and the applied fields. However, no magnetic moments are experiencing a sufficient field strength to overcome the stress-induced anisotropy. Thus, all moments are aligned in the easy directions which are closest to the direction of the original field. Consequently, no domain walls will exist within the grains. At this point, there are no more non-easy-aligned spins. Thus, the magnetization can be independent of the applied tensile stress in the "cross points" in the second and the forth quadrants, see Fig. 4.13. The magnetization remains dependent on the history, the applied field and the temperature. Hence, all BH loops of that sample with the same history, temperature and field strength will coincide at that cross point, no matter which tensile stresses are applied to the sample. The stress applies an effective pressure on 90-degree domain walls. If a domain wall is considered as a series of non-easy-aligned magnetic moments, then it is assumed that applied stress can only affect non-easyaligned spins. Hence, no 90-degree walls are present at the cross points. At compression or plastic deformation, the cross point slips away either because a domain rotation take place, or respectively, a plastically deformed material with a higher dislocation density is considered in comparison with the one at elastic tension. A further study is advised. 4.2.5. Explanation of various effects: the critical tensile stress. Another visible effect from the experimental results is the "critical" tensile stress, which corresponds to the best magnetic properties at uniaxial case of stress and magnetization. Why do the losses increase after the critical stress? From the above theoretical explanations, the critical tensile stress corresponds to the macroscopic "energy balance", where all energies are reduced to its minimized states. The "effective pressure" on 90-degree domain walls leads to partial elimination of the transverse domains, which "helps" to
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magnetize the material in the direction parallel to the applied tension. This positive effect of uniaxial tension is limited by microstructure of electrical steels. A larger tension results in an increase of the magnetostatic energy at a larger number of pinning centers at the grain boundaries. All considered non-oriented steels seem to have the critical stress around 20 to 60 MPa. For the considered grain-oriented steel, a large tensile stress does not lead to a loss increase (see Fig. 4.4) in comparison with the nonoriented steels. However, other researchers have found that tension above the critical stress does increase the loss in a grain-oriented steel with smaller grains, as shown in Fig. 4.5 [Moses80]. 4.2.6. Explanation of various effects: the plastic deformation. The energy losses are generally associated with the various rearrangements of main and supplementary domain structures. Considering the rearrangement of the main structure, the 180-degree domain wall movement is the major mechanism. The domain wall movement can be characterized by the velocity and the distance of this movement. For a 180-degree domain wall movement, not influenced by neighbouring walls, the energy loss will be proportional to the square of the wall velocity. The wall velocity is proportional to the spacing 2L between neighbouring 180-degree domain walls. When a system of finely spaced walls is considered, the eddy currents from the neighbouring walls interact. Generally, the impurities, grain size, grain orientation and stress might have a similar impact to the domain wall movement. If the motion of an individual wall is interrupted, by pinning for example, the wall will move slower than the average wall velocity when it is pinned and faster than the average wall velocity for a short period of time after it becomes unpinned. This process will result in an increase of losses compared to uniform wall motion due to a square dependence of losses on the wall velocity. Therefore, the presence of pinning centers is indeed undesirable. The pinning centers can be impurities or grain boundaries as well as any kind of dislocations in the lattice. At elastic stress, the dislocation density remains unchanged. However, the grain boundaries can be very effective pinning centers. Two variables mainly affect the wall spacing: applied tensile stress and grain size.
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The wall velocity should decrease if the wall spacing 2L is reduced, followed by a reduction of losses. When tensile stress is applied, the 180-degree walls become more closely spaced. The decrease of loss is observed up to the "critical" stress, when the domain wall movement becomes harder, taking into account smaller wall spacing and the interaction between domain walls. To explain the behaviour of the magnetic properties under plastic deformation, an increase of the dislocation density must be considered due to the fact that dislocations of crystal lattice are the major pinning centers for domain wall movement. Indeed, the main cause for a hindered domain wall movement at plastic strain is a linear increase of dislocation density and a formation of blocks of dislocations. A hindered domain wall movement results in a large increase of energy loss at plastic strains, as shown in Fig. 4.15 and 4.26. Amazingly, the increase of loss at smaller strains is rapid in comparison with a steady increase at larger strains, see Fig. 4.15. A possible reason for the non-linearity is the fact that the deformation is non-uniform, especially at small strains, when different parts of the material are deformed at different rate. At larger strains, when necking of the sample occurs, a more uniform deformation in the center of the sample might be a reason for a gradual increase of energy loss at high strains. In fact, dislocations or irregularities in the crystal lattice exist in vast amounts in semi-processed steel. Therefore, the dependence of energy loss in semi-processed steel is less "sensitive" to applied stress. Here, the sensitivity to applied stress is somewhat similar to the sensitivity at a highly strained material, see Fig. 4.16. When a semi-processed steel is annealed, the dislocations disappear, which results in a larger sensitivity of the material properties to an applied mechanical stress, see Fig. 4.20 and 4.21. The fact that the energy loss "after release" is larger than "under stress" is simply because of the presence of residual stresses in the deformed material. After the dislocation density, the residual stress is the second major reason for worse properties. A separate study of the residual stresses was performed in [Pulnikov04], see Chapter 5. Briefly, when a tension is removed at pre-strained material, the residual stresses caused by tensile strain must be transverse to the applied tension. The amount of residual stresses can be evaluated indirectly. Generally, the application of tensile elastic stress to the material with residual stresses leads to a biaxial redistribution of internal stresses.
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Another effect is generally known as a frequency dependence. Indeed, the main domain spacing varies with the excitation frequency. As was mentioned above, the domain wall movement is not smooth and continuous in electrical steels. One of the views on this subject assumes that domain wall movement in Fe-Si steels is limited due to eddy currents [Shilling74]. When the excitation frequency increases, the wall cannot move fast enough to keep the local fields ahead of the wall below the level required to nucleate a new domain. If the velocity of a 180degree domain wall is increased by increasing the magnetizing frequency, the applied field must also increase in order to move the wall to reach the same peak induction level. Thus, if the frequency of magnetization is increased, the magnetic field must increase, which at some point can lead to nucleation of new domains. This happens when the activation energy for nucleation is exceeded and the pinned wall becomes unpinned and starts to move. Furthermore, skin-effect can be observed at higher frequencies. More about these effects can be found in [Shilling74] and [Bertotti98]. To conclude the theoretical approach, different physical levels, from a microscopic to domain to macroscopic, can be considered to explain the behaviour of magnetic properties in electrical steels under stress. 4.3. Statistical theory of energy losses. A common practice for the energy loss evaluation in electrical steels has been the separation of losses [Bertotti98]. According to this theory, the average energy loss per unit volume P of soft magnetic material consists of the sum of both a hysteresis and a dynamic contribution, given by (4.1) [Bertotti88]:
P = P ( hyst ) + P ( dyn )
(4.1)
Both hysteresis and dynamic losses are investigated in a separate way. The physical reason for such a decomposition is that P(hyst) originates from the discontinuous character of the magnetization process at a microscopic level (Barkhausen jumps), whereas P(dyn) is associated with the macroscopic dynamic behaviour of the domain structure. It is generally assumed that the effects of these two levels do not overlap [Bertotti98]. The interpretation of the dynamic loss P(dyn) is usually based on the induced electrical currents around the moving domain walls,
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without taking into account microscopic behaviour of the domain wall. The classical dynamic loss model does not take into account the domains at all, but assumes that a magnetization process is perfectly homogeneous in space. Neglecting skin effects at the range of low magnetizing frequencies, the classical dynamic loss model for a lamination having a thickness d predicts [Bertotti88]:
P ( dyn ) ≡ P ( class ) = π 2 ⋅ σ ⋅ d 2 ⋅ Bm2 ⋅ f 2 / 6
(4.2)
Here, σ is the electrical conductivity of the material, Bm is the amplitude of the sinusoidal magnetic flux density, and f is the magnetizing frequency. The simplification of the dynamic loss to only a classical loss component gives a known error. As a consequence of domain effects, the dynamic loss P(dyn) is generally found to be larger than the classical loss P(class). The difference between them is called the excess loss P(exc), which can be much larger than the classical loss, for example, in case of grainoriented materials. Thus, the total energy loss is given by:
P = P ( hyst ) + P ( class ) + P ( exc )
(4.3)
Each component of total energy loss is discussed further in details. 4.3.1. Classical loss. The classical loss can be considered as a side effect of magnetization. This is in fact the dynamic eddy current loss obtained from the Maxwell's equations (see Chapter 1), assuming that there are no magnetic domains present. A general expression for the classical loss in conductive laminations is given by [Bertotti98]:
P ( class ) = (σ ⋅ d 2 / 12)(dB / dt ) 2
(4.4)
Under a sinusoidal magnetic flux, when B(t) = Bmsin(2πft), the classical loss is given by (4.2). Thus, the classical loss generally depends on: - the electrical conductivity σ of the considered electrical steel, - the square of the thickness d of the lamination, - the square of the amplitude Bm of the magnetic flux density, - the square of the magnetizing frequency f. For every considered frequency and peak induction level, an electrical steel with a smaller thickness (the square dependence!) or a smaller resistivity (i.e. a higher Si content) has a smaller classical loss.
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4.3.2. Hysteresis loss. The hysteresis loss P(hyst) can be obtained from the area of the quasi-static hysteresis BH loop times the power frequency f :
P ( hyst ) = Wh ( Bm ) ⋅ f
(4.5)
Here, Wh(Bm) is a hysteresis energy related to the microstructure of the material and defined by the quasi-static BH loop. Thus, the hysteresis loss depends on: - the magnetization frequency f, - the material parameter Wh depending on the peak magnetic flux density Bm. The hysteresis loss can be obtained experimentally at a sufficiently low frequency, such as below 0.1 Hz, when the dynamic effects are negligible. Other methods can be applied to define the hysteresis energy as well, see section 4.3.4. 4.3.3. Excess loss. The excess loss P(exc) is given by the difference of the total loss and the two other loss components (classical loss and hysteresis loss) derived from eq. (4.3). The understanding of the origin and the properties of the excess loss P(exc) has been a challenge for many years. The primary idea was that excess losses are the consequence of the existence of magnetic domains. The guideline in the interpretation of excess losses has been, for a long time, the model proposed by Pry and Bean [Bertotti88]. In this model, only 180-degree domain walls perpendicular to the plane of the sheet are considered. In the demagnetized state of the material, the width of each domain is equal to 2L. The dynamic loss P(dyn) of an infinite lamination of thickness d and containing a periodic array of domains is calculated from Maxwell's equations. This model indicates that the main parameter controlling excess losses is the ratio 2L/d between the domain size and the lamination thickness, and predicts the following: when P ( exc ) 1
(4.7)
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Unfortunately, this model of (4.6) and (4.7) is very idealized. On the one hand, excess losses have been found non-negligible to classical loss at 2L/d
