A Finite Element Analysis Based Approach to Determining the Nut Factor by Andrew Biehl An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the degree of Master of Engineering Major Subject: Mechanical Engineering

Approved: _________________________________________ Dr. Ernesto Gutierrez Miravete, Project Adviser

Rensselaer Polytechnic Institute Hartford, CT December 2015

© Copyright 2015 by Andrew Biehl All Rights Reserved

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CONTENTS LIST OF TABLES ............................................................................................................ iv LIST OF FIGURES ........................................................................................................... v ACKNOWLEDGMENT .................................................................................................. vi ABSTRACT .................................................................................................................... vii 1. Introduction/Background ............................................................................................. 1 1.1

The Nut Factor ................................................................................................... 1

1.2

Obtaining the Nut Factor .................................................................................... 1 1.2.1

Published Nut Factor Data ..................................................................... 1

1.2.2

Representative Torque-Tension Testing ................................................ 3

1.2.3

Analytical Approach to the Nut Factor .................................................. 6

2. Methodology ................................................................................................................ 7 3. Single-Fastener Bolted Joint Testing and Analysis ..................................................... 8 3.1

Single-Fastener Bolted Joint Test Data .............................................................. 8

3.2

Single-Fastener Bolted Joint Finite Element Analysis ...................................... 9 3.2.1

Model Geometry .................................................................................... 9

3.2.2

Mesh and Boundary Conditions ........................................................... 10

3.2.3

Finite Element Analysis Results .......................................................... 15

4. Multi-Fastener Bolted Joint Analysis ........................................................................ 20 4.1

Finite Element Analysis ................................................................................... 20 4.1.1

Model Geometry .................................................................................. 20

4.1.2

Mesh and Boundary Conditions ........................................................... 21

4.1.3

Finite Element Analysis Results .......................................................... 22

5. Conclusion ................................................................................................................. 26 6. List of References ...................................................................................................... 27

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LIST OF TABLES Table 1.1 Nut Factor Data for an Array of Joint Characteristics ....................................... 2 Table 3.1 Nut Factor and Coefficient of Friction Data ..................................................... 9 Table 3.2 Nut Factor and Shank Stress Convergence Analysis Results .......................... 18 Table 4.1 Comparison of Torque, Preload and Nut Factor Data ..................................... 25

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LIST OF FIGURES Figure 1.1 Fastener Torque-Tension Test Set-Up [4] ........................................................ 4 Figure 1.2 Torque-Tension Relationship for a M12 X 1.75 Property Class 8.8 Flanged Headed Bolt [5].................................................................................................................. 4 Figure 1.3. Torque-Tension Testing of a Six Bolt Wheel Hub [7] .................................... 5 Figure 3.1. Plots of Torque vs Tension for Five Tests of an M12 Fastener, Nut and Washer Assembly Coated in Lubrisilk Grease [8] ............................................................ 8 Figure 3.2 Comparison Betw. Tested Joint Config. and Modeled Joint Config. ............ 10 Figure 3.3 Single-Fastener Bolted Joint Finite Element Model ..................................... 11 Figure 3.4 Single-Fastener Bolted Joint Tie Constraints and Contact Interfaces ........... 13 Figure 3.5 Single-Fastener Bolted Joint Boundary Conditions and MPCs .................... 15 Figure 3.6 VM Stress Distribution Through Single-Fastener Model Cross-Section ....... 16 Figure 3.7 Contact Stress Under Fastener and Washer ................................................... 17 Figure 3.8 Single-Fastener Bolted Joint Torque-Tension Relationship .......................... 18 Figure 3.9 Convergence of Shank Stress and Nut Factor ................................................ 19 Figure 4.1 Significant Dimensions and GD&T of Flat Faced Flange ............................. 20 Figure 4.2 Part Imperfections Added to the Multi-Fastener Model ................................ 21 Figure 4.3 Multi-Fastener Bolted Joint Finite Element Model........................................ 22 Figure 4.4 VM Stress Distribution Through Multi-Fastener Model Cross-Section ........ 23 Figure 4.5 Multi-Fastener Bolted Joint Torque-Tension Relationship ............................ 24

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ACKNOWLEDGMENT Somewhat ironically, I am typing this acknowledgement on Thanksgiving Day. In light of that fact, it is difficult to be brief in listing those in my life for whom I am thankful and who deserve special thanks. For the sake of the reader though, I will limit the list to Professor Ernesto Gutierrez-Miravete who guided me through this project, my parents who have given so much more to me than I will ever be able to give back to them, and my wife who means more to me than anyone.

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ABSTRACT The objective of this study is to present a finite element analysis (FEA) based approach to determining the nut factor. The approach is first validated by comparison of single-fastener bolted joint test results with FEA predictions. FEA predictions are within 5% of the test results. The approach is then demonstrated on a multi-fastener bolted joint. Part imperfections are introduced to the multi-fastener joint in order to simulate the statistical scatter that is seen in experimental nut factor results.

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1. Introduction/Background 1.1 The Nut Factor The torque-tension equation, Equation 1, is used to calculate the installation torque, , necessary to achieve the desired tension in a fastener, , also known as the fastener preload. Preload is often utilized in order to protect a fastener from fatigue failure, when it is known that the joint will be subjected to cyclic loading. The installation torque is calculated by multiplying the desired preload by the nominal diameter of the fastener, , and the nut factor, . (1) The torque-tension equation typically provides sufficient accuracy to be useful in the selection of the appropriate fastener installation torque, but it is too great of a simplification to be considered an accurate representation of the torque-tension relationship for any given joint. The uncertainty in the equation resides in the nut factor. The nut factor is not a mathematically derived term. Rather, it is an experimentally determined fudge factor representing all of the variables that affect preload. These variables include the coefficient of friction between the head of the fastener and the clamped member, the coefficient of friction between the threads of the fastener and of the nut or external hole, in addition to many other variables related to the geometry of the fastener and the hole.

In one study, over 76 statistically significant variables

affecting the nut factor were found [1].

1.2 Obtaining the Nut Factor 1.2.1

Published Nut Factor Data

Because the nut factor cannot be mathematically derived and depends on many variables, it is common practice to store nut factor data in reference tables. There nut factors are organized according to basic joint characteristics, such as fastener material, clamped member material, lubrication choice and fastener condition.

Engineering

organizations often develop nut factor reference tables based on the specific subset of materials and joint conditions that they specialize in. Nut factor data can also be found in reference books. An excerpt from Table 7.1 of “An Introduction to the Design and

1

Behavior of Bolted Joints” is reproduced below in Table 1.1, as an example [2]. Lubricant manufacturers also occasionally provide nut factor data for an array of fastener materials and joint characteristics. Table 1.1 Nut Factor Data for an Array of Joint Characteristics

Pure aluminum coating on AISI 8740 alloy steel Electroplated aluminum coating on AISI 8740 alloy steel As-received, mild or alloy steel on steel As-received, stainless steel on mild or alloy steel As-received, 1 in. dia. A-490 Very rusty With Johnson 140 stick wax Black oxided 7/8 A325 and A490, slightly rusty Black oxide Cadmium plate (dry) Vacuum cadmium + chromate Copper-based antiseize Cadmium plate (waxed) Cadmium-plated A286 nuts and bolts Cadmium plate plus cetyl alcohol on A286 nuts and bolts Cadmium-plated nuts used with MP35N bolts Dag (graphite + binder) Dicronite (tungsten carbide in lamellar form) Emralon (PTFE + resin)

Reported Nut Factors Min. Mean Max. 0.42 0.52 0.62 --0.52 --0.158 0.2 0.267 --0.3 ----0.179 ----0.389 ----0.275 --0.15 --0.22 0.109 0.179 0.279 0.106 0.2 0.328 --0.21 --0.08 0.132 0.23 0.17 0.187 0.198 0.15 --0.23 0.11 --0.16 0.18 --0.29 0.16 --0.28 0.045 --0.075 0.10 --0.15

Everlube 810 (MoS2/graphite in silicone binder)

0.09

---

0.115

Everlube 811 (MoS2/graphite in silicone binder) Everlube 6108 (PTFE in phenolic binder) Everlube 6109 (PTFE in epoxy binder) Everlube 6122 Fel-Pro C54 Fel-Pro C-670 Fel-Pro N 5000 (paste)

0.09 0.105 0.115 0.069 0.08 0.08 0.13

------0.086 0.132 0.095 0.15

0.115 0.13 0.14 0.103 0.23 0.15 0.27

Fastener Materials and Coatings

The convenience of reference tables makes them a common approach to obtaining nut factor data. However, while nut factor data may be available, it is not always clear under what specific conditions the data can be applied with confidence.

The

characteristics of the original tested joint are not always well-documented – reference

2

tables rarely take into account more than a few of the major factors which affect the nut factor (e.g., see Table 1.1). For this reason, it is typically recommended to only use reference table nut factors when approximate preload is sufficient for the design [3]. In these cases, both the minimum and maximum nut factor should be considered when calculating the installation torque value. For a specific installation torque value, a low nut factor results in a higher preload, putting the bolt closer to its yield strength. A high nut factor lowers the preload, reducing the capacity of the joint to resist external loads. The possible range of preload values should be calculated and deemed acceptable for the design. 1.2.2

Representative Torque-Tension Testing

While many joints may be tolerant of a relatively high preload variation resulting from nut factor variation, there are certainly cases where this is not acceptable. If a high level of preload is required (e.g. 75% of the fastener’s yield strength) in order to protect the fastener from high cyclic loading, uncertainty in the nut factor may result in inadvertently specifying an installation torque which has the potential to cause yielding in the fastener. In such a case, the relationship between the installation torque and the preload must be determined more accurately. This is usually accomplished through testing. Representative testing of a single-fastener joint may be performed if the clamped member materials, material finishes, fastener material and the desired lubrication of the joint being designed are known and are replicated in the test. Figure 1.1, depicts a typical single-fastener torque-tension test. A drive motor provides the applied torque, which is measured by a torque transducer. The load in the fastener is measured by a load cell. The nut factor is then calculated from the test data using Equation 1. A plot of sample torque-tension test data is shown in Figure 1.2.

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Head of Fastener Nut (not shown)

Torque Transducer

Socket

Drive Motor Load Cell Figure 1.1 Fastener Torque-Tension Test Set-Up [4]

Figure 1.2 Torque-Tension Relationship for a M12 X 1.75 Property Class 8.8 Flanged Headed Bolt [5]

Multiple tests are typically performed, in order to determine the variation in the nut factor inherent to the combination of materials, lubrication, etc that characterize the joint. Variations of approximately 10% have been found when repeated testing of a single-bolt test joint is performed and all variables are reasonably controlled [6]. This degree of variation is usually not cause for concern. For real world, multi-fastener joints, however, the number of variables affecting the torque-tension relationship and the extent of their impact is sometimes greater than can 4

be adequately represented in a single-fastener test. The effect on the nut factor of part deviations (e.g. wavy mating surfaces, varying surface roughness, varying through hole diameters, etc) can be magnified by the increased area in contact and quantity of fasteners in a multi-fastener joint. In addition, assembly related variables (speed of torquing, pattern of torquing, etc) can contribute to nut factor variations. In cases where even greater accuracy is needed, testing of an exact replica of the multi-fastener design joint is necessary in order to determine the average nut factor of the joint and its distribution about the mean [6]. Figure 1.3 illustrates a torque-tension test of a six bolt wheel hub. Preload can also be controlled with more direct methods than the use of the torquetension relationship to calculate an installation torque. Other methods include the use of strain gauges installed directly on the fastener shank to determine average shank stress, ultrasonic sensing equipment to measure bolt elongation, or hydraulic bolt tensioners to directly apply a specified preload [2]. However, these methods are typically more time consuming, more expensive, and can provide more opportunity for operator error.

Figure 1.3. Torque-Tension Testing of a Six Bolt Wheel Hub [7]

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1.2.3

Analytical Approach to the Nut Factor

Where an accurate preload is required, but nut factor testing and other preload control methods are too expensive, it is proposed in this study that analysis of the joint is a viable alternative. Although the large quantity of variables which affect the nut factor cannot be captured in a mathematical equation or set of equations, it is shown in this study that a sufficiently detailed finite element model can be used to accurately simulate the torque-tension behavior of a bolted joint. In addition to potential cost savings, this approach provides the potential for isolating the effects of design changes on the nut factor. As design variables of the joint change during the course of the design process (clamped member materials, fastener sizes, even mechanical tolerances), finite element analysis can be used to determine the effects of the changes on the nut factor. A survey of published literature relating to the analysis of bolted joints has not produced any studies which attempted to determine the nut factor using finite element analysis. It is expected that this is due to both the size of the finite element model required to represent the detail necessary to accurately capture joint behavior, and to the sheer number of variables affecting the nut factor.

However, steady advances in

computing power have resulted in ever increasing limits of finite element model size. Also, while there are a large number of known variables which affect the nut factor, it is not practical to control many of them during testing. Only the most significant variables are controlled. Therefore, like finite element analysis, testing is an approximation. Furthermore, many of the variables that are typically controlled during testing are included in the coefficient of friction of the threads and the coefficient of friction under the fastener head (which are therefore only fudge factors themselves), and these coefficients can be specified in a finite element model. Therefore, it is proposed in this study that finite element analysis can be used to accurately determine the nut factor of a bolted joint.

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2. Methodology The approach of this study is two-fold. First, the use of finite element analysis to determine the nut factor is validated by comparison of single-fastener torque-tension test results with FEA predictions. Second, the approach is demonstrated on a multi-fastener bolted joint. Part imperfections are introduced to the multi-fastener joint in order to simulate the statistical scatter that is seen in experimental nut factor results.

This

approach is broken into the following steps: 1. Obtain torque-tension test data from the test of a single-fastener joint. 2. Build and analyze a finite element model of the single-fastener test joint. 3. Compare single-fastener joint FEA nut factor results with test results. 4. Build and analyze a finite element model of a multi-fastener bolted joint, assuming the same joint characteristics as the single-fastener test joint (materials, fastener size, lubrication, etc). 5. Add part imperfections to the multi-fastener joint and determine the effects of the imperfections on the nut factor. 6. Compare the multi-fastener joint FEA results with both the test data and the single-fastener joint FEA results. Further validation of the use of FEA to determine the nut factor should include an attempt to analytically determine the statistical distribution of the nut factor for a given joint and correlate FEA results with test results. This would require knowledge of the actual variation in the tested joint of all significant factors which affect the nut factor, so that these variations could be modeled. Using FEA to reproduce the actual statistical distribution of the nut factor was not attempted in this study because of the lack of this data. Instead, variations in several joint variables were assumed and were modeled along with the known variation in the friction coefficient, in order to simulate the statistical scatter that is typically seen in experimental nut factor results. The intent was to demonstrate the feasibility of using FEA to determine the statistical distribution of the nut factor in a future study.

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3. Single-Fastener Bolted Joint Testing and Analysis 3.1 Single-Fastener Bolted Joint Test Data Data was obtained from the torque-tension testing of an M12 fastener, nut and washer lubricated with Lubrisilk synthetic grease [8]. Thirty-three total tests were performed under varying conditions. Five tests were performed with a new fastener, nut and washer used for each test, under constant conditions, and with grease applied to the fasteners just prior to the test. The torque-tension relationship for each of the five tests for which conditions were constant is shown in Figure 3.1. Nut factor and coefficient of friction data from the five torque-tension tests are reproduced below in Table 3.1. Average values are also shown. The average coefficient of friction is used in the finite element model, and the finite element analysis nut factor results are compared with the average test results (See Section 3.2.3.2).

Figure 3.1. Plots of Torque vs Tension for Five Tests of an M12 Fastener, Nut and Washer Assembly Coated in Lubrisilk Grease [8]

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Table 3.1 Nut Factor and Coefficient of Friction Data

Test No.1

Coefficient of Friction

Nut Factor K

20

0.052

0.083

21

0.063

0.095

22

0.05

0.108

23

0.062

0.095

24

0.06

0.092

Average

0.057

0.089

1

Note that 33 tests were performed with varying conditions. For

tests 20-24, the grease was applied just prior to the test and a new fastener, bolt and washer was used for each test.

3.2 Single-Fastener Bolted Joint Finite Element Analysis 3.2.1

Model Geometry

The finite element model of the single-fastener bolted joint was built and analyzed in Abaqus/Standard version 6.13. Figure 3.2 compares the configuration of the as-tested bolted joint with the configuration of the modeled bolted joint. All of the clamped members are consolidated into a single rectangular block in the modeled joint. This reduction in the number of contact interfaces simplifies the model. The modification is not expected to affect the results, since the interfaces between the clamped components are small in area and likely exceptionally smooth (no surface irregularities to stack up and affect the seating of the bolt). Also, no relative movement would be expected between these members, since the only load applied is transverse to their contact interfaces.

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Figure 3.2 Comparison Between Tested Bolted Joint Configuration and Modeled Bolted Joint Configuration

Dimensions for the M12 fastener, nut and washer were obtained from References [9], [10] and Error! Reference source not found.. In most cases, minimum and aximum dimensions are provided by the relevant specification. Average dimensions were used in the finite element model, since the intent is to determine the average nut factor of the joint for comparison with the test data. 3.2.2

Mesh and Boundary Conditions

The single-fastener bolted joint finite element model is shown in Figure 3.3 below. All components were meshed with 8-noded linear brick elements with reduced integration and hourglass control (Abaqus C3D8R elements). The mesh is significantly refined in the threads, as this is the region of the most complex contact behavior. The mesh is also moderately refined in the regions of contact between the fastener head and clamped plate, and between the washer, and the clamped plate and nut. Far from these regions of contact, the mesh is coarsened to conserve elements. As detailed in Section 3.2.3.3, a convergence analysis was performed in order to ensure that mesh refinement is satisfactory.

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Figure 3.3 Single-Fastener Bolted Joint Finite Element Model

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The fastener and the nut are each separated into several components connected via tie constraints, as shown in Figure 3.4. Tie constraints allow regions with disparate meshes to be connected, without requiring nodal conformity. In the case of the fastener and the nut, a fine mesh is used in the area of the threads and a coarse mesh is used elsewhere. The resulting abrupt changes in mesh refinement greatly reduce the number of elements required in the model. Tie constraints are also used to connect the fastener head to the shank, and the unthreaded shank to the threaded shank. Contact is specified in both the normal and tangential directions between all applicable surfaces, as illustrated in Figure 3.4. A penalty contact formulation is used for each of the contact pairs in both the normal and tangential directions. The average coefficient of friction from the test results, 0.057, is applied in the tangential direction for each contact pair. The Abaqus option “Surface Smoothing” is applied to the thread contact interaction.

This geometric correction greatly improves the contact stress

accuracy and solution convergence for cylindrical shapes in contact, which otherwise would be represented by faceted surfaces with discontinuous surface normals [12].

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Tie: Fastener Head to Shank

Contact: Fastener Head and Clamped Plate

Contact: Washer and Clamped Plate

Tie: Fastener Unthreaded Shank to Threaded Shank

Contact: Washer and Nut Tie: Nut OD to Nut Threads

Tie: Fastener Threads to Fastener Threads ID

Contact: Nut Threads to Fastener Threads

Figure 3.4 Single-Fastener Bolted Joint Tie Constraints and Contact Interfaces

A fixed boundary condition (x=0, y=0, z=0) is applied to a section of one side of the clamped plate, as shown in Figure 3.5, representing the fixed support in the test joint (see Figure 3.2). A roller boundary condition (x=0, z=0) is applied to the OD of the fastener head. The fastener head is allowed to move in the y-direction (along axis of fastener), as the head would be expected to translate in the negative y-direction as the nut is tightened and the plate is compressed. A multi-point constraint (MPC) is used to control rotation and prevent lateral translation (θy = θ1, x=0, z=0) of the nut. The MPC is located at the center of the nut, 13

and is connected to each of the nodes around the outer diameter of the nut. A prescribed rotation is applied to the MPC. A prescribed rotation is used instead of an applied moment, because prescribed rotations/displacements are inherently more stable than applied moments/loads for nonlinear analyses. The magnitude of the prescribed rotation was iterated until a maximum torque of 50,100 Nmm was achieved, which is within the range of the maximum torque values achieved in the tests (50,100 Nmm – 54,000 Nmm). For information, a rotation of 27.3 degrees was applied in order to achieve the analysis torque. An MPC is also used to prevent initial lateral translation of the washer and rotation about the y-axis (x=0, z=0, θy = 0), until about 10% of the final torque is applied. At this point, the MPC connected to the washer is deactivated.

This initial restriction on

movement of the washer was necessary to provide initial stability to the model, and is analogous to someone using their hand to initially center a washer, while tightening a nut.

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Roller BC: ux , uz = 0

MPC1: ux , uz = 0

Y

Fixed BC: ux , uy , uz = 0

X

MPC: ux , uz = 0, θy = 27.3°

1MPC

deactivated after 10% of final torque is applied

Figure 3.5 Single-Fastener Bolted Joint Boundary Conditions and MPCs

3.2.3

Finite Element Analysis Results

3.2.3.1 General Model Behavior Analysis Results Figure 3.6 and Figure 3.7 illustrate the general behavior of the single-fastener bolted joint due to the torquing of the nut. Both figures represent the condition of the joint after the full torque is applied. Figure 3.6 shows the von Mises stress distribution through a cross-section of the model. The peak stresses in the nut and in the fastener occur in the thread root, which is consistent with References [13] and [14].

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Figure 3.6 Von Mises Stress Distribution Through Single-Fastener Model Cross-Section

Figure 3.7 shows the contact stress distribution on the clamped plate under the head of the fastener and under the washer. Consistent with tests of contact stress distributions under the head of fasteners and washers, [15], the stress is greatest at the edge of the hole and quickly decreases in the radial direction.

It is also evident that the washer

effectively spreads out the load such that the peak stress at the edge of the hole is significantly lower under the washer than under the head of the fastener (31% lower).

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Peak Contact Stress = 541.7 MPa

Peak Contact Stress = 372.7 MPa

Contact Stress Under Fastener Head

Contact Stress Under Washer

Figure 3.7 Contact Stress Under Fastener and Washer

3.2.3.2 Torque-Tension Relationship Analysis Results Torque-tension results from the analysis are shown in Figure 3.8. The relationship between applied torque and fastener tension is highly linear with an R-squared value of 1.000. The torque-tension relationship exhibited in the test results, however, is initially non-linear (see Figure 3.1). This is because the coefficient of friction is initially variable during the test as the nut, washer, clamped member and fastener settle into one another. This phenomenon is not represented in the analysis, where the coefficient of friction is a constant. However, this phenomenon does not influence the nut factors produced from the test data, as the torque and tension data from 0% to 40% of the maximum preload are excluded from the average nut factor calculation [8]. Only the linear portion of the data is included in the test nut factor calculation. The analysis nut factor is calculated with Equation 1, using the final torque and tension values.

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There is a 4.5% difference between the single-fastener bolted joint nut factor analysis results and the test results. This is within one standard deviation of the mean of the test data. It is concluded that the analysis accurately represents the torque-tension behavior of the tested single-fastener joint. 60

Bolt Torque (Nm)

50 40 30 20 10 0 0

10

20

30

40

50

Bolt Preload (kN)

Figure 3.8 Single-Fastener Bolted Joint Torque-Tension Relationship

3.2.3.3 Convergence Analysis A convergence analysis was performed to ensure mesh adequacy. Four analyses of the single-fastener model were completed with successively refined meshes. Table 3.2 displays the nut factor and the average stress in the fastener shank for each analysis. The nut factor and shank stress are plotted against the number of elements in the model in Figure 3.9. Table 3.2 Nut Factor and Shank Stress Convergence Analysis Results

Number of Nodes 165223 235085 365027 569510

Number of Elements 129556 188400 300259 469627

Average Shank Stress 530.0 530.3 531.4 532.5

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Percent Change

Nut Factor

Percent Change

--0.07 0.20 0.20

0.09315 0.09310 0.09310 0.09310

--0.05 0.00 0.00

0.09316 0.09315

Shank Stress

537.0

Nut Factor

0.09314

535.0

0.09313

533.0 531.0

0.09312

529.0

0.09311

527.0

0.09310

525.0 0

100000

200000

300000

400000

Nut Factor

Average Shank Stress (MPa)

539.0

0.09309 500000

Number of Elements Figure 3.9 Convergence of Shank Stress and Nut Factor

The nut factor converges to 0.09310 with a mesh of 188,400 elements. The shank stress also appears to have converged, or nearly converged (change of only 0.47% with an increase in number of elements of 262%). Shank stress results, however, are only reported for information. The nut factor is the variable of interest and a converged shank stress is unnecessary for convergence of the nut factor. Also, convergence of the nut factor prior to convergence of the shank stress is expected. The nut factor is based on nodal displacements/rotations, which converge prior to element stresses.

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4. Multi-Fastener Bolted Joint Analysis 4.1 Finite Element Analysis A finite element analysis of the preloading of a four bolt flanged joint was performed in order to demonstrate an FEA approach to determining the nut factor of a multi-fastener bolted joint. The joint was first analyzed without any part imperfections included, and second assuming variations in hole sizes, hole locations, the flatness of the flange surfaces, and in the friction coefficient. The torque-tension relationship was plotted and the nut factor was calculated for each of the four bolts. The results from the multi-fastener bolted joint analysis are compared with the single-fastener bolted joint analysis results and with the test data. 4.1.1

Model Geometry

As with the single-fastener model, the multi-fastener model was built and analyzed in Abaqus/Standard version 6.13. The multi-fastener bolted joint is comprised of two flat-faced flanges. Significant dimensions and geometric dimensioning and tolerancing (GD&T) are specified in Figure 4.1.

Figure 4.1 Significant Dimensions and GD&T of Flat Faced Flange

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Part imperfections within manufacturing tolerances were introduced in the second model, as shown in Figure 4.2 below. Hole size was varied from 13.75 mm to 14.25 mm. Hole true position was varied from the basic condition by +/- 0.125 in different directions. The flatness control on the flange mating face is very tight (typical), and so a deviation in this feature was not modeled. Instead, the surface on which the bolts seat was varied as shown in Figure 4.2.

Figure 4.2 Part Imperfections Added to the Multi-Fastener Model

4.1.2

Mesh and Boundary Conditions

The multi-fastener bolted joint finite element model is shown in Figure 4.3. All constraints, boundary conditions and contact conditions are identical to those in the single-fastener model, except for two additions: contact was added between the flange faces, and fixed boundary conditions were added to the top of the neck of each flange where the flange would be welded to a pipe. The single-fastener bolted joint mesh convergence results were assumed to apply to the multi-fastener model (see Section 3.2.3.3).

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Figure 4.3 Multi-Fastener Bolted Joint Finite Element Model

4.1.3

Finite Element Analysis Results

4.1.3.1 General Model Behavior Analysis Results The von Mises stress acting through a cross-section of the assembly is shown in Figure 4.4.

The stress distribution in and around each fastener is nearly identical to the

distribution for the single-fastener model (Figure 3.6).

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Figure 4.4 Von Mises Stress Distribution Through Multi-Fastener Model Cross-Section

4.1.3.2 Torque-Tension Relationship Analysis Results Torque-tension analysis results are shown in Figure 4.5. Unexpectedly, nut factor results did not significantly vary from bolt to bolt within the multi-fastener bolted joint without part imperfections. As the fasteners were individually torqued, it was expected that enough asymmetries would develop in the model to cause nut factor variations. The lack of variation may be due to factors such as the thickness of the flange, the low number of fasteners and their large spacing (approximately 5D). Regardless, it is shown that nut factor variations from bolt to bolt do develop as part imperfections are introduced.

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35

30

Bolt Torque (Nm)

25

20

15

10

5

Imperfections - Bolt 1

Imperfections - Bolt 2

Imperfections - Bolt 3

Imperfections - Bolt 4

No Imperfections 0

0

5

10

15

20

Bolt Preload (kN)

Figure 4.5 Multi-Fastener Bolted Joint Torque-Tension Relationship

24

25

30

A nut factor for each of the bolts is calculated with Equation 1 using the final torque and tension values. Multi-fastener analysis results are shown in Table 4.1, along with the test results and single-fastener analysis results. Maximum torque and preload values are included in the table in addition to the nut factor. The nut factor for the multi-fastener model without part imperfections is nearly identical to the nut factor for the single-fastener model. The average nut factor for the model with part imperfections is 0.088, which is within 6% of the nut factor for the single-fastener analysis and 1.8% of the average nut factor from the test data. The four nut factors for the model with part imperfections vary from the average by +5% to -8%. It is observed that adding part imperfections to the model results in significantly lower bolt torques and preloads with the same prescribed rotation applied to the nut. The four bolts in the multi-fastener model without part imperfections registered torques of approximately 54.9 Nm.

The four bolts in the model with part imperfections

registered bolt torques of 26.5-29.2 Nm, approximately 50% lower.

This is likely

because the imperfections cause the initial contact between surfaces to be poor, whereas in the model without imperfections, all surfaces start in perfect contact. The poor initial contact results in a lower initial resistance to the torquing of the nut, and correspondingly a lower initial preload. Table 4.1 Comparison of Torque, Preload and Nut Factor Data

Average Test Data Single-Fast. Analysis Multi-Fast. Analysis, No Imperfections Multi-Fast. Analysis, No Imperfections, Bolt 1 Multi-Fast. Analysis, No Imperfections, Bolt 2 Multi-Fast. Analysis, No Imperfections, Bolt 3 Multi-Fast. Analysis, No Imperfections, Bolt 4

Maximum Torque (Nm) 50.8 50.1

Maximum Preload (kN) 43.9 44.9

Nut Factor 0.089 0.093

54.9

49.0

0.093

26.5

27.3

0.081

28.8

28.0

0.086

29.2

28.3

0.086

31.5

28.4

0.092

25

5. Conclusion It is shown in this study that finite element analysis is a viable method for determining the nut factor of a bolted joint. Nut factor data from a single-fastener torque-tension test was obtained. A finite element analysis of the test was performed. FEA predictions of the nut factor are within 5% of the test results. The finite element analysis approach to the nut factor was then demonstrated on a four bolt flanged joint. The multi-fastener joint was analyzed with and without part imperfections. Without imperfections, the nut factors for the four bolts were uniform, and were equivalent to the nut factor of the single-fastener joint. When imperfections were added, the nut factors varied from the average nut factor by +5% to -8%.

26

6. List of References [1]

Stewart, Richard. Torque-Tension Variables. A List Prepared by WrightPatterson Air Force Base, Dayton, OH, April 16, 1973.

[2]

Bickford, John H. “An Introduction to the Design and Behavior of Bolted Joints.” Third Ed., Revised and Expanded. Marcel Dekker, Inc., New York, 1995.

[3]

Shigley, J. E., C. R. Mischke, and T. H. Brown, Jr. “Standard Handbook of Machine Design,” 7th Ed., McGraw-Hill Book Company, NY 2004.

[4]

IPitch Fastener Test System. Micro Control Inc. www.mcrts.com.

[5]

Torque-Force Fastener Tests. Bolt Science. http://www.boltscience.com/ pages/ torque-force-graph.htm.

[6]

Archer, David. Dissecting the Nut Factor. Machine Design. Dated 20 August 2009.

[7]

Fastener Testing. PCB Load & Torque, a PCB Piezotronics Division. Dated 2014. www.pcb.com.

[8]

Eccles, William. “Report on Torque-Tension Tests on Fasteners Coated with Lubrisilk Synthetic Grease.” Bolt Sciences Limited, dated February 18, 2008.

[9]

“Hexagon Head Bolts – Product Grades A and B.” ISO 4014.

[10] “Hexagon Regular Nuts (Style 1) – Product Grades A and B.” ISO 4032. [11] “Plain Washers – Normal Series – Product Grade A.” ISO 7089. [12] Abaqus Version 6.13, “Abaqus Documentation,” Dassault Systèmes, Providence, RI. [13] Rafatpanah, Ramin M. Finite Element Analysis of a Three-Dimensional Threaded Structural Fastener. An Engineering Project Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in Mechanical Engineering. Dated May 2013. [14] Fukuoka, Toshimichi & Nomura, Masataka. “Proposition of Helical Thread Modeling with Accurate Geometry and Finite Element Analysis.” Journal of Pressure Vessel Technology, Vol. 130, February 2008. [15] Archer, David. “Use of Washers and Flange Heads.” American Fastener Journal, Vol. 26 No. 5, September 2010. 27

7. Appendix Select sections from the input file used in the analysis of the multi-fastener model are provided below:

*Heading ** Job name: M12_assem_test4 Model name: Model-1 ** Generated by: Abaqus/CAE 6.13-2 *Preprint, echo=NO, model=NO, history=NO, contact=NO ** MATERIALS ** *Material, name=Steel *Density 0.0076, *Elastic 200000., 0.3 ** ** INTERACTION PROPERTIES ** *Surface Interaction, name="Hard Contact" 1., *Friction, slip tolerance=0.005 0.057, *Surface Behavior, pressure-overclosure=HARD ** BOUNDARY CONDITIONS ** ** Name: Fixed head Type: Displacement/Rotation *Boundary Set-34, 1, 1 Set-34, 2, 2 Set-34, 3, 3 ** Name: Fixed head2 Type: Displacement/Rotation 28

*Boundary Set-35, 1, 1 Set-35, 2, 2 Set-35, 3, 3 ** Name: Fixed head3 Type: Displacement/Rotation *Boundary Set-36, 1, 1 Set-36, 2, 2 Set-36, 3, 3 ** Name: Fixed head4 Type: Displacement/Rotation *Boundary Set-37, 1, 1 Set-37, 2, 2 Set-37, 3, 3 ** Name: Fixed pipe ends Type: Displacement/Rotation *Boundary Set-13, 1, 1 Set-13, 2, 2 Set-13, 3, 3 ** ** INTERACTIONS ** ** Interaction: Bolt head *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-115, m_Surf-115 ** Interaction: Bolt head2 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-109, m_Surf-109 ** Interaction: Bolt head3 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-111, m_Surf-111

29

** Interaction: Bolt head4 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-113, m_Surf-113 ** Interaction: Flange_contact *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE Upper_flange, Lower_flange ** Interaction: Threads *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE, geometric correction=Threads s_Surf-118, m_Surf-117 ** Interaction: Threads2 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE, geometric correction=Threads2 s_Surf-119, m_Surf-119 ** Interaction: Threads3 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE, geometric correction=Threads3 s_Surf-121, m_Surf-121 ** Interaction: Threads4 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE, geometric correction=Threads4 s_Surf-123, m_Surf-123 ** Interaction: Washer_and_Nut *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-125, m_Surf-125 ** Interaction: Washer_and_Nut2 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-127, m_Surf-127 ** Interaction: Washer_and_Nut3 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-129, m_Surf-129

30

** Interaction: Washer_and_Nut4 *Contact Pair, interaction="Hard Contact", type=SURFACE TO SURFACE s_Surf-131, m_Surf-131 ** ---------------------------------------------------------------** ** STEP: Torque1 ** *Step, name=Torque1, nlgeom=YES, inc=10000000 *Static 0.0001, 1., 1e-20, 0.1 ** ** BOUNDARY CONDITIONS ** ** Name: Ang_rot_nut Type: Displacement/Rotation *Boundary, op=NEW Set-26, 1, 1 Set-26, 3, 3 Set-26, 5, 5, -0.477 ** Name: Ang_rot_nut2 Type: Displacement/Rotation *Boundary, op=NEW Set-27, 1, 1 Set-27, 3, 3 Set-27, 5, 5 ** Name: Ang_rot_nut3 Type: Displacement/Rotation *Boundary, op=NEW Set-28, 1, 1 Set-28, 3, 3 Set-28, 5, 5 ** Name: Ang_rot_nut4 Type: Displacement/Rotation *Boundary, op=NEW Set-29, 1, 1

31

Set-29, 3, 3 Set-29, 5, 5 ** Name: Fixed head Type: Displacement/Rotation *Boundary, op=NEW Set-34, 1, 1 Set-34, 3, 3 ** Name: Fixed head2 Type: Displacement/Rotation *Boundary, op=NEW Set-35, 1, 1 Set-35, 3, 3 ** Name: Fixed head3 Type: Displacement/Rotation *Boundary, op=NEW Set-36, 1, 1 Set-36, 3, 3 ** Name: Fixed head4 Type: Displacement/Rotation *Boundary, op=NEW Set-37, 1, 1 Set-37, 3, 3 ** Name: Fixed pipe ends Type: Displacement/Rotation *Boundary, op=NEW Set-13, 1, 1 Set-13, 2, 2 Set-13, 3, 3 ** Name: Restrict_washer_cntrl_pt Type: Displacement/Rotation *Boundary, op=NEW Washer_cntrl_pt, 1, 1 Washer_cntrl_pt, 3, 3 Washer_cntrl_pt, 5, 5 ** Name: Restrict_washer_cntrl_pt2 Type: Displacement/Rotation *Boundary, op=NEW Set-30, 1, 1

32

Set-30, 3, 3 Set-30, 5, 5 ** Name: Restrict_washer_cntrl_pt3 Type: Displacement/Rotation *Boundary, op=NEW Set-31, 1, 1 Set-31, 3, 3 Set-31, 5, 5 ** Name: Restrict_washer_cntrl_pt4 Type: Displacement/Rotation *Boundary, op=NEW Set-32, 1, 1 Set-32, 3, 3 Set-32, 5, 5 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** *Output, field, time interval=0.1, time marks=NO *Node Output CF, RF, RM, TF, U *Element Output, directions=YES LE, NFORC, PE, PEEQ, PEMAG, S *Contact Output CDISP, CSTRESS ** ** HISTORY OUTPUT: H-Output-1 ** *Output, history, variable=PRESELECT, time interval=0.1, time marks=NO *End Step

33

** ---------------------------------------------------------------** ** STEP: Torque2 ** *Step, name=Torque2, nlgeom=YES, inc=10000000 *Static 0.0001, 1., 1e-20, 0.1 ** ** BOUNDARY CONDITIONS ** ** Name: Ang_rot_nut3 Type: Displacement/Rotation *Boundary Set-28, 5, 5, -0.477 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** *Output, field, time interval=0.1, time marks=NO *Node Output CF, RF, RM, TF, U *Element Output, directions=YES LE, NFORC, PE, PEEQ, PEMAG, S *Contact Output CDISP, CSTRESS ** ** HISTORY OUTPUT: H-Output-1 ** *Output, history, variable=PRESELECT, time interval=0.1, time marks=NO

34

*End Step ** ---------------------------------------------------------------** ** STEP: Torque3 ** *Step, name=Torque3, nlgeom=YES, inc=10000000 *Static 0.0001, 1., 1e-20, 0.1 ** ** BOUNDARY CONDITIONS ** ** Name: Ang_rot_nut2 Type: Displacement/Rotation *Boundary Set-27, 5, 5, -0.477 ** Name: Ang_rot_nut3 Type: Displacement/Rotation *Boundary Set-28, 5, 5, -0.477 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** *Output, field, time interval=0.1, time marks=NO *Node Output CF, RF, RM, TF, U *Element Output, directions=YES LE, NFORC, PE, PEEQ, PEMAG, S *Contact Output CDISP, CSTRESS

35

** ** HISTORY OUTPUT: H-Output-1 ** *Output, history, variable=PRESELECT, time interval=0.1, time marks=NO *End Step ** ---------------------------------------------------------------** ** STEP: Torque4 ** *Step, name=Torque4, nlgeom=YES, inc=10000000 *Static 0.0001, 1., 1e-20, 0.1 ** ** BOUNDARY CONDITIONS ** ** Name: Ang_rot_nut4 Type: Displacement/Rotation *Boundary Set-29, 5, 5, -0.477 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** *Output, field, time interval=0.1, time marks=NO *Node Output CF, RF, RM, TF, U *Element Output, directions=YES LE, NFORC, PE, PEEQ, PEMAG, S *Contact Output

36

CDISP, CSTRESS ** ** HISTORY OUTPUT: H-Output-1 ** *Output, history, variable=PRESELECT, time interval=0.1, time marks=NO *End Step

37