ˇ FACTA UNIVERSITATIS (NI S) S ER .: E LEC . E NERG . vol. 23, no. 2, August 2010, 199-206.

Rotational Speed Measurement Using Induction Coil Sensor Inserted in the Magnetic Field of the Rotational Permanent Magnet Andreja S. Todorovi´c and Miroljub D. Jevti´c Abstract: In this paper the application of induction coil sensor, inserted into a mechanical rotational magnetic field of the rotational permanent magnet for the rotational speed measurements has been proposed and described. The sensor is simple, low-cost, and applicable for machine shafts speed measurements (spatially available and unavailable). On the shaft, whose rotational speed is measured, the rotational permanent magnet is fixed. From measured frequency value of induced voltage in the coil sensor the rotational speed value is given using PC with adequate software, interface for the analogue signal conditioning and AD converter. The rotational speed dependence on the induction coil sensor distance from the rotational permanent magnet has been given. The induced voltage dependence on the coil distance from the magnet has been obtained as well. The maximum distance for precise measurements of rotational speed has been determined from those relations. Keywords: Induction coil sensor, rotational speed measurements, rotational permanent magnet.

1 Introduction coil sensors are widely used. Their important advantages are: simplicity in operation and design, wide frequency bandwidth and large dynamics [1–3]. Special coil sensors kinds are [1]: Rogowski coil (current sensors and sensors used in the magnetic properties of materials measurements), gradient sensors, vibrating coil sensors, tangential field sensors, needle sensors and magnetic antennae (for the detection of metal objects). The induction coil sensor can be manufactured directly by the user and it is very simple, low-cost and precise.

I

NDUCTION

Manuscript received on February 17, 2010. The authors are with Faculty of Technical Sciences Kosovska Mitrovica, Kneza Miloˇsa 7, 38220 Kosovska Mitrovica, Serbia (e-mails: [andro50, jevticmir]@ptt.rs).

199

A. Todorovi´c and M. Jevti´c:

200

In this paper one novel application of induction coil sensor is proposed. It is the application for user-friendly rotational speed measurements of the motor driven system shafts. The rotational permanent magnet is fixed on the shaft and generates a mechanical rotational magnetic field. The induction coil sensor is fixed on a certain distance from the magnet in its rotational magnetic field. The induced voltage in a coil has a frequency proportional to the rotational speed. The frequency measurements are carried out by the system consisted of the interface for the analogue signal (induced voltage) conditioning, AD converter and PC with adequate software. From measured frequency value of induced voltage the rotational speed value is given. The frequency measurement accuracy is high and equal to the hardware module accuracy (0.024%) and conditioner accuracy (0.03%) [4]. Ferromagnetic core coil has higher sensitivity than air coil [1], but, the simpler, low-cost and very efficient air coil sensor for the rotational speed measurements, has been proposed and applied in this work. The precise rotational speed measurements by well established methods are often difficult to achieve, mainly because of the spatial unavailability of the industry shafts [5–7]. Application of induction coil sensor with rotational permanent magnet [5, 8] and system consisted of PC with hardware modules for the data acquisition, measurement, process control and graphic presentation enable this measurement. This method is also applicable for the indirect measurements of other mechanic characteristics given as a rotational speed functions [5, 8–10].

2 Sensor structure and basic operating principle The permanent magnet used for rotational speed measurements with the magnetic flux density of 0.1 T, is fixed at the available place on the machine shaft. Air coil sensor is fixed close to the rotational permanent magnet (figure 1). Design of the air coil sensor (figure 1) is in accordance with the design recommended in [1, 11]. Recommended relations for L/D and Di /D are L/D = 0.67 − 0.866 and Di /D ≤ 0.3. The number of turns, N, depends on the diameter, d, of the used wire, the packing factor k (k ≃ 0.85) and the dimensions of a coil [1, 2, 11]. The voltage V will be induced in an induction coil as a result of the fundamental Faradays induction law [1]: V = −N

dH dΦ = −µ0 N A dt dt

(1)

where Φ is the magnetic flux passing through a coil having an area A and a number of turns N, B is the magnetic flux density H is the magnetic field strength and µ0 is the core (air) permeability.

Rotational Speed Measurement Using Induction Coil Sensor ...

201

(a)

(b) Fig. 1. Induction coil position referring to the rotational magnet in the rotational speed measurements: (a) - the coil axis matches the shaft axis; (b) - coil axis is perpendicular to the shaft axis. The marks on the figure are: RM - the rotational (round) permanent magnet; IL - insulation layer between shaft and the rotational magnet; DRM - the rotational magnet diameter, δ - thickness of the rotational magnet; N - North pole of the magnet, S - South pole of the magnet; SH - shaft, DI1 and DI2 - inner and outer diameter of the insulation layer between shaft and the magnet; IC - induction coil; IN - insulation roller; Di and D - innner and outer diameter of a coil; δ1 - insulation roller thickness; lc - the distance between induction coil and the rotational magnet; L- length of an induction coil. The geometrical parameters of an induction coil are: Number of turns, N = 13778; Di = 21 mm; D = 24.84 mm; L = 43 mm; Diameter of a conductor d = 0.1 mm.

The mechanical rotational magnetic field frequency can be expressed by known formula: fmech =

pm n 60

(2)

A. Todorovi´c and M. Jevti´c:

202

Fig. 2. The wave-form of induction voltage in a coil.

where fmech is the rotational magnetic field frequency, n is the machine shaft rotational speed (rotational speed of the rotational magnetic field), and pm is a poles pairs number of the rotational magnet, that is pm = 1. The rotational speed n can be expressed from (2): n = 60 fmech

(3)

The induced voltage frequency f in a coil is equal to the frequency fmech ( f = fmech ), thus equation (3) can be rewritten in a form: n = 60 f

(4)

From the equation (4) follows that rotational speed n value can be determined after the induced voltage frequency f is obtained. In this work, the value of f (and consequently, the value of n) is obtained in the following manner. The actual values of induced voltages are measured by hardware consisted of PC, AD converter and external interface for the analogue signal conditioning [4]. The induced voltage wave-form in a coil, has been sinusoidal in this work (figure 2), however can be distorted in general. The software measurement platform is the R

LabVIEW package, which is regarded as a high standard software platform in the area of modern virtual instruments. By further processing, e.g. by application of the R

MATLAB program, the obtained time dependent voltage function is transformed in terms of the harmonics of Fourier order. The obtained harmonics are processed R

in the MATLAB program, to calculate: the effective values of induced voltage V , period T and a frequency f of the dominant harmonic. These values are determined from the formulas:

Rotational Speed Measurement Using Induction Coil Sensor ...

q V = V02 +V12 + · · · +Vk2 f=

1 T

203

(5) (6)

where V1 , V2 , . . ., Vk are effective values of voltage harmonics, k is a number of harmonics.

3 Experimental results The rotational speed measurements have been carried out on a three-speed electric motor of type MVU 10B - 8/6/4T, “Rade Koncar”, with nameplate data: 700/1000/1410 rpm, 380 V, 40/100/120 W, 50 Hz. The measurements have been done by the procedure described in a chapter 2. The measurements have been performed for several different induction coil distances from the rotational magnet, where two cases have been considered: (i) the induction coil axis matches the shaft axis; (ii) the induction coil axis is perpendicular to the shaft axis. Measured distances lc of the induction coil from the rotational magnet, are marked in figure1. The corresponding effective values of the magnetic flux Φ passing through a coil, which caused the voltage to be induced in an induction coil, are determined as well. The magnetic flux effective values have been calculated from the induced voltage effective values, according to the relation: Φ=

V 2π f N

(7)

where N is a number of induction coil turns. The obtained values of Φ can be used to calculate corresponding values of the magnetic flux density by using the well-known relation: B=

Φ A

(8)

Twenty measurements have been performed for every measured distance and average values of effective voltages, frequencies, magnetic fluxes and magnetic flux densities have been calculated. The dependencies of average values obtained for V and n on the distance have been presented on graphs in figure 3 and figure 4. The graphs Φ(lc ) and B(lc ) have the same shape as the graph V (lc ) because of their proportionality and they are not shown in this paper. It can be seen, from Figure 3, that induced voltage values decrease with the increasing of distance lc , and the curve V (lc ) decreases to zero. The dependence

A. Todorovi´c and M. Jevti´c:

204

(a) (b) Fig. 3. Dependence of the induced voltage average values V in respect to distance lc from the rotational magnet to induction coil, for two cases: (a) - an induction coil axis matches the shaft axis, (b) - the induction coil axis is perpendicular to the shaft axis. Curves 1, 2 and 3 are given for different rotational speeds of the shaft.

V (lc ) is best approximated by using the function of the exponential type (Figure 3): V = C(1 − e−A lc )

(9)

where the values of parameters C and A for measured speeds of the shaft (curves 1,2 and 3 of Figure 3) are given in Table 1. Table 1. Values of parameters C and A, relation (9), for three measured speeds of the shaft and for two positions of a coil. Position of a coil The coil axis is perpendicular to the shaft axis The coil axis matches the shaft axis

Speed 1 of the shaft C A

Speed 2 of the shaft C A

Speed 3 of the shaft C A

0.4481

37.6991

0.8409

48.2487

0.5508

42.2907

1.7602

65.2335

1.9394

66.2654

1.0331

60.7935

Figure 3 (and values of C and A in Table 1) shows that the induced voltage effective values are higher in a case when the induction coil axis matches the shaft axis than in a case when the induction coil axis is perpendicular to the shaft axis, due to the higher flux values for the coil position in a first case. However, induction voltage decreases faster with lc values in a first case, rather than in a second case. From Figure 4 it can be observed that the coil distances for the rotational speed values n are not scattered significantly (the deviation is in ±2 rpm limits), are lc = 10-70 mm, if the induction coil axis is perpendicular to the shaft axis and lc = 2060 mm, if the induction coil axis matches the shaft axis. It is obvious that the first

Rotational Speed Measurement Using Induction Coil Sensor ...

205

position has the advantage, because of the larger limit of distances between coil and the magnet. The dependencies n(lc ), for above distance values, are best approximated by the flat lines (figure 4). Obtained rotational speed values are verified by the Laser digital tachometer, Sinometer DT-6234C.

(a) (b) Fig. 4. Dependence of the rotational speed average values n in respect to the distance lc from the rotational magnet to induction coil, for two cases: (a) - an induction coil axis matches the shaft axis, (b) - the induction coil axis is perpendicular to the shaft axis. Curves 1, 2 and 3 are given for different rotational speeds of the shaft.

The obtained dependencies can be used for the further processing and for obtaining other mechanical parameters as torque and the machine efficiency [5, 7, 9, 10]. Acknowledgment The work in this paper was partially funded by the Ministry of Science of Republic of Serbia, project No. TR-18001A ”Research of 16 micro hydropower plants constructed in catchment area of Timok, for increasing of their energy efficiency”.

4 Conclusions Rotational speed measuring method, proposed in this work, offers high accuracy results. Measuring system contains: the rotational permanent magnet fixed at the machine shaft, induction coil sensor inserted into the magnetic field of the rotational magnet, where the voltage of adequate frequency is induced, hardware consisted of PC, AD converter and external interface for the analogue signal conditioning. The R

software platform for measurements is the LabVIEW package. The limited distances of induction coil from the rotational magnet for accurate measured value of rotational speed have been given. The position when the induction coil axis is perpendicular to the shaft axis has advantage in comparison to the position when the

A. Todorovi´c and M. Jevti´c:

206

induction coil axis matches the shaft axis, because of the larger limited distances. This new application of induction coil sensor for rotational speed measurement is very suitable for user-friendly rotational speed measurements of spatially unavailable shafts.

References [1] S. Tumanski, “Induction coil sensors a review,” Meas. Sci. Technol., no. 3, pp. R31 – R46, 2007. [2] G. Dehmel, Magnetic field sensors: induction coil (search coil) sensors, sensors a comprehensive survey ed. New York: VCH, 1989, vol. 5, ch. 6, pp. 205–54. [3] P. Ripka, Induction sensors, Magnetic Sensors and Magnetometers. Boston, MA: Artech House, 2001. R

[4] National instruments, LabVIEW development guidelines, NI Corporation, 2006. [5] A. Todorovi´c and M. Jevti´c, “Device for measurement of rotation speed, sleep, torque, mechanical power and efficiency of cage induction machines, in operating conditions,” Serbian Patent MP-2008/0084, 2008. [6] N. V. Kirianaki, S. Yurish, and S. N. O., “New processing methods for microcontrollers compatible sensors with frequency output,” in Proc. 12th European Conference on Solid-State Transducers and the 9th UK Conference on Sensors and their Applications, Southampton, UK, 1998, pp. 883–886. [7] A. T. De Almeida and F. T. E. Ferreira, “User-friendly high-precision electric motor testing system,” in Proc. 4th Int.Conf. Energy Efficiency in motor Driven System, Heidelberg, Germany, 2005, pp. 149–157. [8] A. Todorovi´c and M. Jevti´c, “Device for determination of equivalent circuit parameters of cage induction motors, in operating conditions,” Serbian Patent MP2008/0085, 2008. [9] Standard test procedure for Polyphase Induction Motors and Generators, Std. IEEE 112, 2004. [10] Method for determining losses and Efficiency of Three-Phase Cage Induction Motors, Std. IEC 61 972, 2002, 1st Edition. [11] H. Zijlstra, Experimental Methods in Magnetism. Amsterdam: North-Holand, 1967.