Belisle Kathryn J

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EXPERIMENTAL AND FINITE ELEMENT ANALYSIS OF A

SIMPLIFIED AIRCRAFT WHEEL BOLTED JOINT MODEL

A Thesis

Presented in Partial Fulfillment of the Requirements for

the Degree Masters of Mechanical Engineering in the

Graduate School of The Ohio State University

By

Kathryn J. Belisle

*****

The Ohio State University

2009

Thesis Defense Committee: Approved by

Dr. Anthony Luscher, Adviser

_____________________________

Dr. Mark Walter Adviser

Graduate Program in Mechanical Engineering


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Copyright

by

Kathryn J. Belisle

2009


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ABSTRACT

The goal of this thesis is to establish a correlation between experimental and finite

element strains in key areas of an aircraft wheel bolted joint. The critical location in

fatigue is the rounded interface between the bolt-hole and mating face of the joint, called

the mating face radius. A previous study considered this area of a bolted joint but only

under the influence of bolt preload. The study presented here considered both preload

and an external bending moment.

This study used a more complete single bolted joint model incorporating the wheel

rim flange and the two main loads seen at the bolted joints; bolt preload and the external

load created by tire pressure on the wheel rim. A 2x3 full factorial DOE was used to

establish the joints response to various potential load combinations assuming two levels

of preload and three levels of external load. The model was analyzed both

experimentally and in finite element form. The strain results around the mating face

radius were compared between the two analyses. Several parameters were identified that

could affect the correlation between the results. The finite element model was modified

to incorporate each of these factors and the new results were compared against the

original finite element results and the experimental data. The best correlation was found

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when the finite element model preload was adjusted such that the mating face radius

strains under only preload matched those of the experimental results.

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This thesis is dedicated to my parents for always encouraging me, for listening when I

was frustrated, for picking me up when I was down, for helping me however they could,

and for taking pride in my triumphs.

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ACKNOWLEDGMENTS

I would like to thank Goodrich Aircraft Wheels and Brakes for allowing me the use

of their resources. I would particularly like to acknowledge Bud Runner of Goodrich

who was a constant source of expertise, advice, and support. I would like to thank all the

faculty and staff of the Ohio State University who helped me throughout the course of my

research. I would also like to recognize my fellow graduate students for their support and

help. Finally, I would like to acknowledge my family and friends for being constant

sources of support and encouragement.

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TABLE OF CONTENTS

Abstract ............................................................................................................................... ii

Acknowledgments............................................................................................................... v

List of Tables ................................................................................................................... viii

List of Figures .................................................................................................................... ix

CHAPTER 1: Introduction ................................................................................................ 1

CHAPTER 2: Background and Literature Review ............................................................ 5

2.1 Bolted Joint Models ................................................................................................ 5

2.2 Experimental Setup ................................................................................................. 7

2.3 Finite Element Modeling ........................................................................................ 8

2.4 Comparison of Experimental and Finite Element Results .................................... 10

2.5 Sensitivity Analysis Summary .............................................................................. 11

2.6 Torque Free Preload Experiment .......................................................................... 12

2.7 Literature Review.................................................................................................. 14

CHAPTER 3: Experimental Analysis .............................................................................. 16

3.1 Experimental Model Development ....................................................................... 16

3.2 Experimental Measurement and Data Acquisition System .................................. 21

3.3 Design of Experiment ........................................................................................... 28

3.4 Test Setup and Procedure...................................................................................... 29

CHAPTER 4: Experimental Results ................................................................................ 34

4.1 Statistical Analysis of Experimental Results ........................................................ 35

4.2 Design of Experiment Results .............................................................................. 38

4.3 Preload Variability Study ...................................................................................... 42

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4.4 Bolt Bending Results ............................................................................................ 44

4.5 Experimental Data for Finite Element Comparison.............................................. 45

CHAPTER 5: Finite Element Modeling .......................................................................... 47

5.1 Preliminary Model Setup ...................................................................................... 48

5.2 Preliminary Finite Element Analysis .................................................................... 53

5.3 Final Finite Element Model Setup ........................................................................ 56

CHAPTER 6: Finite Element Results .............................................................................. 63

6.1 Finite Element Results Acquisition ...................................................................... 63

6.2 Finite Element Convergence ................................................................................. 64

6.3 General Finite Element Results ............................................................................ 67

CHAPTER 7: Finite Element and Experimental Comparison ......................................... 69

CHAPTER 8: Summary and Conclusions ....................................................................... 91

List of references............................................................................................................... 98

APPENDICES .................................................................................................................. 99

APPENDIX A: Labview Block Diagrams and Setup .............................................. 100

APPENDIX B: Bolt Bending Calculations.............................................................. 105

APPENDIX C: Raw Experimental Data.................................................................. 108

APPENDIX D: Statistical Results of the DOE ........................................................ 112

APPENDIX E: Finite Element Data ........................................................................ 118

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LIST OF TABLES

Table 3.1: Strain Gage Location Descriptions (*MFR = Mating Face Radius) .............. 22

Table 3.2: Bolt Preload and External Load Values.......................................................... 29

Table 3.3: Loading Conditions ........................................................................................ 33

Table 4.1: Bolt Bending and Tensile Results................................................................... 45

Table 4.2: Results at Mating Face Radius Locations for Preload Only (microstrain) ..... 46

Table 4.3: Results at Mating Face Radius Locations (microstrain) ................................. 46Table 5.1: Material Properties .......................................................................................... 50

Table 5.2: Material Property Combinations ..................................................................... 60

Table 5.3: Adjusted External Loads ................................................................................. 61

Table 5.4: Adjusted Bolt Preloads ................................................................................... 61

Table B.1: Bolt Bending Calculation Spreadsheet ........................................................ 106

Table C.1: Experimental Principal Strains for 12:00 MF Radius Gages ....................... 109

Table C.2: Experimental Principal Strains for 3:00 MF Radius Gages ......................... 110

Table C.3: Experimental Principal Strains for 6:00 MF Radius Gages ......................... 111

Table D.1: Experimental Principal Strains for 6:00 MF Radius Gages ......................... 113

Table E.1: Descriptions of Models ................................................................................ 119Table E.2: Finite Element Mating Face Radius Data .................................................... 120

Table E.3: Finite Element Mating Face Radius Data for Preload Only......................... 121

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LIST OF FIGURES

Figure 1.1: Aircraft Wheel Assembly ................................................................................ 2

Figure 1.2: Bolted Joint Fillet ............................................................................................ 3

Figure 2.1: Circular Plate Experimental Model ................................................................. 6

Figure 2.2: Square Plate Experimental Model ................................................................... 6

Figure 2.3: Experimental Test Setup ................................................................................. 8

Figure 2.4: Circular Plate Finite Element Model ............................................................... 9Figure 2.5: Square Plate Finite Element Model ............................................................... 10

Figure 2.6: Exploded View of Bolted Joint for Torque Free Preload Experiment .......... 13

Figure 2.7: Torque Free Preload Experimental Setup ..................................................... 14

Figure 3.1: Diagram Comparing Actual Nose Wheel with General Model .................... 18

Figure 3.2: Diagram of the Final Experimental Model Design ....................................... 21

Figure 3.3: Strain Gage Locations ................................................................................... 22

Figure 3.4: Mating Face Radius Strain Gage Designations ............................................. 23

Figure 3.5: Strain Gages Applied to the Mating Face Radii ............................................ 25

Figure 3.6: Strain Gages Applied to the Rim Flange ....................................................... 26

Figure 3.7: National Instruments Strain Gage Conditioners ............................................ 27

Figure 3.8: National Instruments Bridge and Bridge Modules ........................................ 28Figure 3.9: Final Experimental Assembly ....................................................................... 31

Figure 4.1: General Time Series Plot and Statistics ........................................................ 36

Figure 4.2: Worst Case Time Series Plot and Statistics................................................... 37

Figure 4.3: Representative Normality Test ...................................................................... 38

Figure 4.4: Main Effect DOE Results .............................................................................. 40

Figure 4.5: Free Body Diagram of Model ....................................................................... 42

Figure 4.6: Results of the Preload Variability Study ....................................................... 43

Figure 5.1: General Preliminary Model ........................................................................... 49

Figure 5.2: General Finite Element Boundary Conditions and Loads ............................. 52

Figure 5.3: Internal Finite Element Boundary Conditions and Loads ............................. 53

Figure 5.4: Mesh Refinement Comparison ...................................................................... 58Figure 5.5: Model with Washers ...................................................................................... 62Figure 6.1: Finite Element Strain Measurements ............................................................ 64

Figure 6.2: Mesh Refinement Comparison ...................................................................... 66

Figure 6.3: Sample Finite Element Results (Six Load Cases) ......................................... 68

Figure 7.1: Zoomed Strain Flow Contour of Mating Face Radius .................................. 70

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x

Figure 7.2: Comparison of Baseline Experimental and Finite Element Results .............. 71

Figure 7.3: Effect of Mesh Refinement on Correlation ................................................... 73Figure 7.4: Effect of Bolt Material Stiffness ................................................................... 76

Figure 7.5: Zoomed Plot of Effect of Bolt Material Stiffness ......................................... 78

Figure 7.6: Effect of Bracket Material Stiffness .............................................................. 80

Figure 7.7: Zoomed Plot of Effect of Bracket Material Stiffness .................................... 82

Figure 7.8: Effect of Adjusted External Loads ................................................................ 84

Figure 7.9: Zoomed Plot of Effect of Adjusted External Loads ...................................... 86

Figure 7.10: Effect of Preload Modifications .................................................................. 88

Figure 7.11: Effect of Solid Washer ................................................................................ 90

Figure A.1: Bracket Gage Data Acquisition Block Diagram ........................................ 101

Figure A.2: Bolt Gage Data Acquisition and Averaging Block Diagram ..................... 102

Figure A.3: Data Acquisition Assistant Configuration .................................................. 103

Figure A.4: Filter Configuration .................................................................................... 104Figure D.1: Detailed Statistical Results for 12 Oclock Gage Location ........................ 115

Figure D.2: Detailed Statistical Results for 3 Oclock Gage Location .......................... 116

Figure D.3: Detailed Statistical Results for 6 Oclock Gage Location .......................... 117


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CHAPTER 1

INTRODUCTION

Goodrich Corporation has commissioned the research presented in this thesis to

improve the correlation of computer simulated bolted joint models to experimental data

as a tool for weight optimization of aircraft wheels, one of their key products. An

example of an aircraft wheel assembly is shown in Figure 1.1. The wheel of an aircraft is

designed to withstand high loads with minimal weight, so material is removed from the

unit wherever possible. Due to the stiffness and size of the tires used in aerospace

applications, the wheel must also be made in two halves. The halves are fitted into the

tire and then bolted together to form the wheel assembly. Typically, several different

tires are specified for a single wheel assembly, and each tire loads the wheel differently.

However, these variations in loading are difficult to know without testing. Thus, the

wheel must be designed to compensate for various potential load and pressure

distributions. This requirement, combined with the weight constraints and multiple

bolted joints, render the wheel assembly geometrically complex.

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Figure 1.1: Aircraft Wheel Assembly

The complexity of the wheel structure makes the design process extremely difficult.

Currently, the process is very reliant on experimentation and testing. This means that

new experimental models must be fabricated each time a design change is made to meet

weight or performance specifications. Fabrication and testing of multiple models can

become very costly and time consuming. Goodrich is interested in reducing the cost and

improving the speed of their design process. Computer-aided simulations, such as finite

element analyses, can significantly improve this speed and reduce expense. However, a

finite element analysis is only valuable if the results correlate to those obtained from

physical experimentation.

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A well-correlated finite element model has yet to be established for this particular

application. While the wheel structure can be modeled in finite element form, the results

do not match experimental results as closely as necessary. In particular, Goodrich has

demonstrated large differences between experimental and finite element strain

measurements taken in key areas around the wheels bolted joints. These discrepancies

are particularly prevalent around fillets around each bolt hole on the mating face of each

wheel half. Figure 1.2 shows the fillet around a single bolted joint on the mating face of

a wheel half.

MatingFace

Radius

Rim

MatingFace

Figure 1.2: Bolted Joint Fillet

Correction of these discrepancies depends on a thorough understanding of the wheel

system. The complexity of the system, particularly the multiple bolted joints, makes this

system especially difficult to study as a whole. Thus, the method adopted for this study

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was to simplify the system into a series of models that could be easily fabricated, tested,

and analyzed in finite element form. The study was completed in two phases.

Phase I, completed by Abhijit Dingare [1] of the Ohio State University, considered

several aspects of simplified bolted joint modeling. This phase is described more

thoroughly in Chapter 2. The study was based on two bolted joint models. The first was

an axisymmetric bolted joint with no extraneous geometric features. The second model

was a simplified version of the wheel face geometry found immediately surrounding each

bolt hole. Experimental and finite element analyses for both models were used to

establish the effect of several physical and virtual parameters on the strain in the mating

face fillet. Comparisons between experimental and finite element results were also used

to understand the correlation, or discrepancies, between testing and simulation.

The research presented in this thesis covers Phase II of the study of bolted joint

simulation. The goal of this project was to develop and study a new model that more

closely represented the actual loading seen in the bolted joints of the wheel structure.

Thus, a model was developed to introduce a load due to tire pressure into the bolted joint

where the tire pressure acts on the rim of the wheel. Experimental and finite element

analyses of this model were intended to shed light on the interactions between bolt

preload and external loads and their effect on the strain in the bolt and bolted joint.

Again, the correlation between experimental and finite element results was of particular

interest.

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CHAPTER 2

BACKGROUND AND LITERATURE REVIEW

In a previous study performed in majority by Abhijit Dingare [1], an aircraft wheel

single bolted joint was considered under only bolt preload. Two simplified joint models

were developed. These models were tested experimentally. Finite element models were

then developed for comparison against the experimental results. Based on the initial

results, a sensitivity study was performed to further characterize several finite element

and experimental parameters. A secondary experiment was also performed to establish

the effect of torque on the mating face radius strains. The results of this experiment were

compared against the original finite element results.

2.1Bolted Joint Models

Two models were developed to test the effect of bolt preload on an aircraft wheel

bolted joint. Both models were single bolted joints made up of two plates. The first

model, called the circular plate model, simplified the joint to a set of cylindrical,

axisymmetric plates with no face geometry. The second model, referred to as the square

plate model, was a pair of square plates. These plates incorporated some wheel face

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geometry into the mating faces of the plates. Both models had a round interface between

the plate mating faces and bolt holes referred to as the mating face radius. The circular

and square plates are shown in Figure 2.1 and Figure 2.2 respectively.

Figure 2.1: Circular Plate Experimental Model

Figure 2.2: Square Plate Experimental Model

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2.2Experimental Setup

The experiment was performed using a test setup housed at Goodrich Aircraft Wheels

and Brakes. The plates were fitted into a housing that would keep them from rotating. A

special bolt, called a Strainsert, was used for testing. A Strainsert is a hollowed bolt with

a strain gage applied internally. The Strainsert is calibrated for preload. The head of the

Strainsert was held with a wrench plate also made to fit in the housing. A torque tool was

then used to tighten the bolt to a specified preload. Strain gages were also applied to the

mating face radius of both plates to measure the effect of the preload on the strain in the

bolted joint. The strain gages were applied in both the hoop, called horizontal, and axial,

called vertical, directions. The symmetry of the two plates with respect to one another

was used to apply two gages of opposite orientations at a single location; one on each

plate. Figure 2.3 shows the test setup. An example of strain gages on the mating face

radius is included in Figure 2.1.

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Figure 2.3: Experimental Test Setup

2.3Finite Element Modeling

Finite element models were developed based on the dimensions of the experimental

models. Figure 2.4 shows the finite element model of the circular plates. Axisymmetry

was used to reduce the model to a 2D model. Symmetry between the plates also served

to reduce the model. Figure 2.5 shows the finite element model of the square plates.

Symmetry across the yz-plane was used to reduce the model as shown. This model was

analyzed in 3D. In both cases, the model was fixed as required by symmetry conditions.

The preload was applied as a displacement on the split end (or ends) of the bolt with the

displacement being iterated until the desired preload was achieved.

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Figure 2.4: Circular Plate Finite Element Model

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Figure 2.5: Square Plate Finite Element Model

2.4Comparison of Experimental and Finite Element Results

In both cases, the experimental results showed low individual and overall

repeatability. Both finite element models tended to under-predict the experimental

strains. For the circular plate model, the correlation between finite element and

experimental results was reasonable for most gages with strain gage three being an

exception. However, this was not considered particularly problematic since this gage was

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measuring in the low strain, or hoop, direction. The correlation was unacceptable, in

most cases, for the square plate model.

2.5Sensitivity Analysis Summary

After comparing the initial experimental and finite element results, several potential

sources of variation were identified. The parameters that would affect these variations

were included in a sensitivity study to see their effect on the joint strains. The finite

element parameters included mesh refinement, dimensionality, material modeling, and

bolt alignment. Several experimental factors included torque rate, preload control

method, and dwell.

The first finite element parameter analyzed was mesh refinement. The mesh

refinement was increased until the results were no longer affected by the change. It was

found that the increased mesh refinement had a significant effect on the results, but at a

very high computational expense. Dimensionality was a concern for the circular plate

model. A comparison of 2D and 3D models revealed that the 2D axisymmetric model

was acceptable. Material property modeling was the next parameter considered. Three

material models were available, isotropic, orthotropic, and hypoelastic. The comparison

showed that the hypoelastic properties resulted in the best correlation to experimental

data. The differences between the three models, however, were minimal, so any model

should be acceptable. Finally, the alignment of the bolt within the bolt hole was studied.

It was found that a misalignment of the bolt could reduce the overall joint stiffness, thus

increasing the strains in all mating face radius locations slightly.

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Several parameters were also tested experimentally. The rate at which torque was

applied to the bolt during preloading was tested first. Increasing the torque rate from one

to five rpm significantly improved the experimental repeatability. Two methods of

controlling the preload were also considered; control of the amount of torque applied and

control of the strain in the bolt shaft. The torque control method was found to be more

repeatable than the strain control method. Finally, the effect of dwell on the strain output

was considered. In the worst case, a 20 microstrain drift was seen over the first 30

seconds of data acquisition. The data tended to stabilize after approximately 30 seconds.

2.6Torque Free Preload Experiment

The application of torque during experimental preloading was identified as a big

discrepancy between the experimental and finite element models. A secondary

experiment was designed to remove torque from the preload process. To accomplish this,

the bolt was cut in two through the bolt shaft. A dowel was used to align the two halves

without passing any axial load between them. Figure 2.6 shows the circular plate model

with the cut bolt. A similar setup was used for the square plate model. An Instron type

testing machine was used to apply the required preload force to the ends of the bolt.

Figure 2.7 shows the square plate model setup on the Instron machine.

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Figure 2.6: Exploded View of Bolted Joint for Torque Free Preload Experiment

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Figure 2.7: Torque Free Preload Experimental Setup

The original experimental results were generally under-predicted by the finite element

models for both the square and circular plates. The results from the torque free

experiment were typically over-predicted by the finite element analyses. The correlation

between finite element and experimental results worsened when torque was removed

from the experiment. One possible reason for this was misalignment of the Instrons test

frame. Based on the reduced correlation to finite element results as well as time

constraints, this line of research was not pursued further.

2.7Literature Review

A study performed by Jeong Kim, et al. [2] considered four methods of modeling a

bolted joint in finite element form. These included a solid bolt preloaded thermally, a

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beam element coupled to nodes on the gripped bodies preloaded by an initial strain on the

beam element, a beam element connected to the gripped bodies with 3D element spiders

also preloaded by an initial strain on the beam element, and finally a preload pressure

applied directly to the contacted bodies with no bolt represented. It was found that the

solid bolt model gave the best correlation to experimental results. However, the coupled

bolt model significantly improved the computational efficiency of the model.

Another study, performed by Gang Shit, et al. [3], incorporated end-plate bolt preload

into a finite element model of a beam-to-column connection. The finite element model

was compared against an experimental model. The finite element results correlated well

to experimental results and gave a more detailed view of the joint response based on

results not easily measured during experimentation.

Slippage in bolted joint of transmission towers was simulated by finite element

analysis in a study by R. Rajapakse, et al. [4]. Bolted joint slippage was found to have a

significant, negative effect on the load bearing capacity and displacement of the tower

trusses. However, the correlation between finite element analysis and actual results

improved when slippage was accounted for under a specific case called frost-heaving.

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CHAPTER 3

EXPERIMENTAL ANALYSIS

The first step towards achieving a well correlated finite element model of a bolted

joint was the establishment of a baseline for comparison. For this purpose, an

experimental analysis was developed. Several criteria were considered in the design of

the experimental model and procedure. First, the experiment required the application of

two main forces; bolt preload and an external shear load generated by tire pressure on the

wheel rim. The model had to allow for the application of both forces with minimal

interference to the actual bolted joint. Next, a system was required to measure the effect

of these forces at key locations in and around the bolted joint. Third, an experimental

design was needed to incorporate the various loading conditions of an aircraft wheel

bolted joint. Finally, a test setup and procedure were necessary that would allow for

repeatable force application and data acquisition.

3.1Experimental Model Development

An experimental model of an aircraft wheel bolted joint was developed. The model

needed to incorporate the two main load sources of an aircraft wheel bolted joint; bolt

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preload and tire pressure on the wheel rim. The model also needed to incorporate the

geometry of the aircraft wheel surrounding the joint in order to approximate the

appropriate load paths. Boundary conditions were created which allowed the application

of simulated loads with minimal interference to the key areas of interest in and around the

bolted joint.

The first goal of the model design was to simulate the basic geometry of an aircraft

wheel bolted joint. The design method adopted was to select an aircraft wheel with

certain desirable features and simplify the bolted joint geometry to a feasible set of test

brackets. A small wheel was desirable as the proportions of the geometry would be

easier to simulate. A wheel with a lower tire pressure rating would reduce the forces

required for testing. Symmetry between the joint halves was also desired as this would

simplify both the experimental setup and the finite element model. Based on these

criteria, the nose wheel of a DeHavilland (DHC-8-400) aircraft was chosen as the basis of

the experimental model. This wheel assembly used an eight bolt pattern of 5/16 in. bolts.

The bolts were rated for individual bolt torque of 255 in-lbs, which was equivalent to a

preload of 6,825 lbs. The rated tire pressure for this wheel was 85 psi. The nose wheel

was made of 2014-T6 aluminum. Figure 3.1 shows the cross sectional geometry of a

single nose wheel bolted joint (in red) overlaid with the simplified geometry of the

experimental model (in green).

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Figure 3.1: Diagram Comparing Actual Nose Wheel with General Model

The actual bolted joint was nearly symmetrical, so the major features could be

approximated as such. For the experimental model, the overall thickness of material

immediately surrounding the bolted joint was equivalent to that of the actual joint. The

geometry in this region was simplified to remove any asymmetry. This was intended to

reduce the complexity of the experimental and finite element analyses. The modeled rim

flange thickness approximated the thickness of the portion of the actual rim immediately

connected to the bolted joint. This was chosen to allow the experimental model to more

closely simulate the load path of the aircraft wheel. The width of the experimental model

was chosen to be four times the diameter of the bolt plus a quarter inch to insure that no

yielding would occur in the rim flange during external load application. See Figure 3.1

for this equation for model width.

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While several dimensions were taken directly from the wheel dimensions, certain

dimensions were modified for various purposes. One modification was needed to

eliminate a potential source of interference to the desired load path in the rim flange

resulting from the method of external load application. In the aircraft wheel, the external

load, generated by tire pressure against the rim of the wheel, would be very even along

the rim. Thus, an even load distribution across the width of the modeled flange was

required. The anticipated loading method for experimentation would not necessarily

result in an evenly distributed load at the flange interface to the bolted joint. To remedy

this, the flange length of each bracket was extended by three inches. This allowed room

to connect the flange to a load source with enough space between the connector and the

bolted joint for the load path to spread across the width of the flange. The four holes

passing through the rim flanges, shown in Figure 3.2, were designed for the purpose of

connecting the brackets to a load source.

Another modification to the bolted joint was needed for the measurement system

selected for the characterization of the load effects. Strain gages were chosen for

measurement. A strain gage would have no effect on the solid material surrounding the

bolted joint; however, the wiring required for data acquisition could be problematic given

a tight space tolerance. This was recognized as a potential issue inside the bolted joint

where key areas of interest included both the bracket mating face radii and the bolt shaft.

The diameter of the bolt hole was increased by 0.1 in. and the mating face radius was

opened to 0.25 in. to resolve this problem.

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Figure 3.2 shows the final design for the body of the experimental model of the bolted

joint. One feature was not included in this diagram; a small runner used to pass strain

gage wires out of the bolted joint. The runner was made up of adjoining slots machined

into each brackets mating face to a width of approximately 0.075 in. and a depth of

approximately one half of the width. The slots opened into the mating face radius

between the six and three (or nine) oclock positions to avoid interference with the key

areas of interest; twelve, three, and six oclock. The wires passed out near a corner of the

bolted joint body opposite the rim flange so as to avoid interfering with the joint loading.

These runners were considered inconsequential to the stress in the areas of interest in and

around the bolted joint. Figure 3.5 shows the wires passing through the slots on the

mating faces of both brackets. Based on typical Goodrich practice, the wires running

from the strain gages on the bolt shaft were passed through a slot in a special washer,

called a shouldered washer. The shouldered washer had a flat face in contact with the

bracket face, as would a normal washer. It also incorporated a shoulder that dropped into

the bolt-hole. This shoulder served to center both the washer and the bolt which kept the

strain gages on the bolt shaft from coming in contact with the sides of the bolt-hole.

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Figure 3.2: Diagram of the Final Experimental Model Design

3.2Experimental Measurement and Data Acquisition System

In order to fully characterize the reaction of the bolted joint to the applied loads, a

measurement system was required. Strain gages were chosen as the applicable

measurement device. There were three main areas of interest in the bolted joint model.

The first was the radius interfacing the bolt-hole and the mating face of each bracket;

called the mating face radius. The second was the shaft of the bolt. The third was the

rim flange. Figure 3.3 depicts the strain gage locations on the brackets and the bolt shaft.

Table 3.1 describes the location intended for each strain gage number ofFigure 3.3.

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Figure 3.3: Strain Gage Locations

Gage # Body/Region Position Description1 Bracket 1/Rim Flange Upper surface near load source2 Bracket 1/Rim Flange Lower surface tangent to fillet3 Bracket 1/MFR* 12 oclock4 Bracket 1/MFR* 3 oclock5 Bracket 1/MFR* 6 oclock6 Bracket 2/MFR* 12 oclock7 Bracket 2/MFR* 3 oclock8 Bracket 2/MFR* 6 oclock

9/10/11 Bolt/Shaft 120o

apart

Table 3.1: Strain Gage Location Descriptions (*MFR = Mating Face Radius)

The mating face radius was the primary area of interest for this experiment. This area

has been particularly problematic in Goodrichs past attempts to correlate finite element

and experimental data. A good correlation in this region is essential to a valuable finite

element model. More specifically, three locations were designated on this radius at

intervals around the bolt-hole. These locations were defined as twelve, three, and six

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oclock where twelve oclock was closest to the rim flange (see Figure 3.4). There were

also two strain gages placed at each of these locations; one on each bracket. Since the

brackets were symmetrical, the stresses around the mating face radii were expected to be

equivalent. The gage on one bracket at each location was aligned with the curvature of

the radius. These strain gages were referred to as axial gages because they approximately

aligned with the axis of the bolt shaft. The second gage at each location, on the opposing

bracket, was aligned with the curvature of the bolt-hole. These were referred to as hoop

gages because they followed the radius of the bolt-hole, the hoop direction. In future,

gage alignments may be shortened to A for axial gages and H for hoop gages. Refer

to strain gage numbers three through eight in Figure 3.3 and Table 3.1 for the mating face

radius strain gage locations and descriptions.

Figure 3.4: Mating Face Radius Strain Gage Designations

The bolt shaft was also of interest for two reasons. First, a strain reading on the bolt

shaft was directly proportional to the preload being applied by the bolt. Thus, a strain

gage on the bolt shaft would allow the operator to apply the required bolt preload based

on a direct measurement, as opposed to a less precise torque reading, during testing. This

also eliminated test equipment as no torque measurements were required during bolt

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preloading. Furthermore, a strain gage would readily provide information about the

change in preload after external load application. Apart from preload measurements, an

interest was expressed by Goodrich in the bending of the bolt due to the external loading.

For this purpose, a set of three strain gages were placed at 120 degree increments around

the center of the bolt shaft. This triad of strain gages could be used to establish bolt

bending regardless of the gages orientations with respect to the bending axis. Reference

gages nine through eleven in Figure 3.3 and Table 3.1 for the bolt shaft strain gage

locations and descriptions.

The final area of interest for experimental characterization was the rim flange. The

bending in this region was of particular interest. For this purpose, two strain gages were

placed on the rim flange (the rim flange is the end pieces of the wheel. We dont have

these modeled.); one on the upper surface and one on the lower surface. Both strain

gages were placed in the center of the flange width and were aligned to the loading axis.

One gage was located tangent to the fillet interfacing the flange to the bolted joint. The

second gage was placed on the upper flange surface approximately 2.5 in. from the

mating face to capture bending closer to the point of loading. Reference gages one and

two in Figure 3.3 and Table 3.1 for the rim flange strain gage locations and descriptions.

A total of eleven strain gages were applied to the bolted joint model. All of the gages

were Nickel Chromium, 120 ohm, foil strain gages with a gage length of 0.015 in.

Amongst these eleven gages, two different Vishay Micro-Measurements strain gages

were used: EA-13-015EH-120 and EA-13-015DJ-120. However, the only difference

between them was the location of the solder pads with respect to the gage grid; all other

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features were equivalent. The strain gages were applied using M-Bond 610, the

recommended bonding agent of the strain gage supplier. Figure 3.5 shows the strain

gages on the mating face radii of the brackets. Figure 3.6 shows the strain gages on the

rim flange.

A

A

H

H

A

H

Figure 3.5: Strain Gages Applied to the Mating Face Radii

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(Left: Near Load Application; Right: Fillet Tangency)

Figure 3.6: Strain Gages Applied to the Rim Flange

A new National Instruments (NI) Compact DAQ series system was selected for

acquiring data from the strain gages. The system consisted of four main elements. Each

strain gage was connected to a 120 ohm, quarter-bridge strain gage conditioner (part # NI

9944), see Figure 3.7. The conditioners adapted the strain gage wire input to an RJ50

cable output and passed the signal to the channels of a bridge module. Each 24-bit

simultaneous bridge module (part # NI 9237) had four channels. The bridge modules

connected directly to an NI Compact DAQ chassis (part # 9172) [5]. The bridge could

accept up to eight modules, however only three were required in this case. Figure 3.8

shows bridge modules connected to the bridge.

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Labview software was used to acquire and process data retrieved from the NI data

acquisition system. This software was used to filter the signal, convert the voltage to a

strain output, and write the data to a separate file. Labview was also used in real time to

provide feedback for the bolt preload application. The two Labview block diagrams and

the associated codes used for the experiment are provided in Appendix A.

Figure 3.7: National Instruments Strain Gage Conditioners

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Figure 3.8: National Instruments Bridge and Bridge Modules

3.3Design of Experiment

To properly characterize the bolted joint response to bolt preload and tire pressure, a

range of possible load conditions must be considered. For this purpose, a design of

experiment (DOE) was proposed. A two by three full factorial DOE was chosen. This

design would incorporate two preload values, high and low, and three external loads,

high, mid, and low. The actual preload value of the nose wheel bolts for the DeHavilland

aircraft was 6,825 lbs. However, this load would produce yielding under the washer in

the experimental model. This would make the experiment unrepeatable and the finite

element modeling very difficult. Thus, the high preload value was calculated such that

no yielding would occur under the washer. The low preload value was chosen to be 10

percent lower than the high preload. The mid value of the external load was calculated

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based on rated tire pressure of the nose wheel and the width of the model. The low and

high external loads were 50 percent low and 50 percent high respectively. The

calculations were completed and the final values provided by Goodrich. Table 3.2 gives

the values of bolt preload and external load for the DOE.

DOE Level Preload (lbs) External Load(lbs)

Low 3240 900Mid -- 1800High 3600 2700

Table 3.2: Bolt Preload and External Load Values

3.4Test Setup and Procedure

The final step in the experimental process was the development of the test setup and

procedure. Several portions of the test setup have already been discussed, including the

experimental model and the measurement system. The external load application method

was the final piece of this design.

A servo-hydraulic Instron machine (model # 8511) was used as the mechanism for

external load application as it was capable of applying varied loads with high

repeatability. However, there were several options for connecting the model brackets to

the Instron. For example, an extension, such as that seen on the actual wheel rim, could

be added to the models flange and the Instron could apply force to the side of that

extension. The more desirable approach was to clamp the ends of the brackets and

connect the clamp to the Instron. But again, there were several methods by which to

accomplish this goal. In order to conserve the symmetry of the model, it was decided that

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the connecting clamps for the two bracket halves should also be symmetrical. The

simplest symmetrical design was found to be a double lap joint. Based on the yield

strength of the bracket material, the thickness of the rim flange, and the maximum

loading conditions, two bolt-holes were added to the experimental model for attaching

the lap joint to the rim flange. This bolt pattern was copied on the flange of a steel block

threaded to connect to the Instron. The straps of the lap joint were made of aluminum to

reduce the rigidity added to the rim flange by the double lap joint. The thickness of the

straps was chosen to be equal to the thickness of the rim flange and was verified based on

yield parameters. Figure 3.9 shows the model brackets assembled and connected to the

Instron machine.

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Figure 3.9: Final Experimental Assembly

There were two main aspects of the experimental procedure, loading and data

acquisition. Based on the loading cycle of the aircraft wheel, the preload was applied

first followed by the external load. Data was acquired at several times during a single

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loading condition to insure a complete understanding of the effect of loading on the joint.

A single loading condition referred to a pair of preload and external load values, so there

were six loading conditions required by the design of the experiment. Prior to testing,

however, the test setup had to be prepared. First, to insure proper alignment, the brackets

were clamped on the two sides of the bolted joint. The bolt was then tightened until the

joint closed producing an obvious increase in strain in the bolt shaft as shown by the

measurement system. The four bolts of the Instron connectors, kept loose to this point,

were then tightened and the clamps on the bolted joint were removed. The model was

ready for testing.

Preload was applied first based on the real time strain feedback from the bolt shaft.

Once the appropriate preload value was achieved, two Labview programs were run; one

to save 30 seconds of data from the three bolt strain gages and another to save 30 seconds

of data from the eight strain gages on the bracket. With the preload data saved, the

Instron was used to apply the desired external force for the loading condition being

tested. Once the appropriate force was reached, the Labview programs were run again to

save data as before. The external load was then reduced to zero and the programs were

run a third time to acquire data to show the difference in preload after external loading.

Once the data was acquired, the joint was ready for the next loading condition. The order

of loading conditions for a full test is given in Table 3.3. The test was repeated seven

times to provide enough data for statistical analysis.

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Condition # Preload External Load1 Low Low2 Low Mid3 Low High4 High Low

5 High Mid6 High High

Table 3.3: Loading Conditions

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CHAPTER 4

EXPERIMENTAL RESULTS

Prior to generating a finite element model of the bolted joint, the experimental data

was analyzed. A statistical analysis was performed to verify that the experiment was

repeatable and that the results were statistically significant. A design of experiment

(DOE) analysis was used to establish an understanding of the bolted joint response to

loading. A supplemental analysis was performed to show that the method of bolt

preloading was repeatable. The bolt bending stress was analyzed to further highlight the

joints response to the various loading conditions. Finally, the experimental results were

compiled into a baseline data set for comparison against the finite element results.

Initially, the test was only replicated three times. Analysis of this data revealed an

anomaly where the third set of data was drastically different from the first two. The test

was then repeated four more times to establish the validity of the results. A review of the

seven data sets revealed that the first two data sets were different from the last five.

Several potential causes of this discrepancy were considered including yielding under the

washer, misalignment of the bolt or washers, stretching in the bolt, and the orientation of

the bolt strain gages with respect to the bracket flange. The discrepancy could also have

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been caused by slight modifications made as the operator became more familiar with the

test setup, equipment, and method. Regardless, the first two runs were considered joint

conditioning and were removed from the final data set. This decision was supported by

the agreement between the last five data sets.

4.1Statistical Analysis of Experimental Results

The five final data sets were statistically analyzed to verify their validity. The time

series stability and the normality of the data signals were validated. Figure 4.1 and

Figure 4.2 show representative plots of the general and worst case time series

respectively. The maximum, minimum, and mean values are shown by the horizontal

lines on each plot with the data values shown on the right axis. The standard deviations

are printed on the plots as well.

The range of the strain measurement was less than six microstrains for every case.

This was considered acceptable since the range was several orders of magnitude smaller

than the measured values. In most cases, represented by the general plot, there was little

drift in the strain measurement over 40 seconds of data acquisition. Thus, the mean in

these cases was readily acceptable. At certain locations under higher loading conditions,

more drift was seen as in Figure 4.2. This could have been caused by the method of load

application utilized. The ideal method would have used the Instron to directly control the

applied load. Due to constraints created by the test setup, a position control method was

implemented instead. This control method resulted in a slight downward drift in load

over time, which may have translated to the strain results at more sensitive locations.

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Another possible source of drift was relaxation in the bolt or in the joint over time. Given

that the overall data range remained within six microstrains, the mean strains were again

considered acceptable.

Time (secon ds)

Strain(m

icrostrains)

4035302520151050

1387.5

1387.0

1386.5

1386.0

1385.5

1385.0

1384.5

1384.0

1385.8

1384.3

1387.1

Mating Face Radius 6 O'clock Location

St. Dev. = 0.416

Figure 4.1: General Time Series Plot and Statistics

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Time (seconds)

Strain(microstrains

)

4035302520151050

3817

3816

3815

3814

3813

3812

3811

3810

3813.5

3810.8

3816.6

Mating Face Radius 3 O'clock Location

St. Dev. = 1.29

Figure 4.2: Worst Case Time Series Plot and Statistics

The strain results were also checked for normality. In general, the strain results were

found to be normal, as shown in the representative normality plot ofFigure 4.3. The

normality test used was the Anderson-Darling method. Thus, a p-value greater than 0.05

was indicative of a normal distribution. There were a couple of cases where the strain

results were found to be non-normal. However, the abnormalities were associated with

the previously described drift and were considered inconsequential.

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Strain (microstrains)

Percent

1387.51387.01386.51386.01385.51385.01384.51384.0

99.99

99

95

80

50

20

5

1

0.01

Mean

0.363

1386

StDev 0.4172N 6

AD 0.399

P-Value

Probability Plot of Mating Face Radius 6 O'clock LocationNormal

69

Figure 4.3: Representative Normality Test

4.2Design of Experiment Results

A DOE was performed based on the results of the experiment. The intent of the DOE

was to provide a statistically based understanding of the bolted joint response to the

various loading conditions. The two main factors were preload and external load.

External load, applied by an Instron machine, was easily adjusted. The preload level,

however, was statistically difficult to adjust as the method required the operator to

manually adjust the load using a wrench while monitoring the real time output of the bolt

shaft strain gages. Thus, a split plot DOE was applied. The preload level was set and the

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three external loads were tested. The preload level was then adjusted and the three

external loads were tested again. This was repeated for a total of five tests.

It was expected that the DOE would indicate preload and external load both as

main effects at each gage location. It was also expected that preload would have a more

drastic effect on the bolted joint. The external load, being of a lower magnitude, was

expected to have a lesser effect. Some interaction was expected between preload and

external load as well.

Figure 4.4 shows the main effect and interaction plots for the three gage locations on

the mating face radius. The term column referred to the effect or interaction of effects

being considered in that row, while the charts next to the term columns illustrated the

magnitudes of the effects. Any effect whose bar fell outside the blue boundary lines was

considered statistically meaningful. The magnitude of each effect or interaction is

indicated by the contrast value. The individual p-values indicated whether or not a term

could be considered a main effect. A low p-value corresponded to a main effect while a

high p-value indicated that the term was statistically insignificant. The main effects are

highlighted in black in the term column. See Appendix D for more outputs of the DOE

analysis.

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Figure 4.4: Main Effect DOE Results

As expected, preload, external load, and the interaction between the two were found

to be main effects at most gage locations. However, the greater magnitude of the external

load effect, indicated by the squared main effect (external load*external load), was not

expected. The magnitude of both preloads by comparison to the high external load led to

the expectation that the preload would have a greater effect on the bolted joint. Further

inspection revealed that the effect of the external load was magnified by the mechanical

advantage generated by the lever arm between the rim flange and the bolted joint. The

bending moment generated by this lever arm resulted in bending across the three oclock

strain gage location. This allowed the external load to overcome the preload, which was

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seen during the experiment in the separation of the joint between the rim flanges. Thus,

the statistical insignificance of preload at the three oclock location was caused by the

overwhelming effect of this bending moment across the three oclock location.

The moment passing through the three oclock location explained the increased

strains at this gage location as well as the reduced effect of the preload on those strains.

The increased strains spread into the twelve oclock gage location as well, particularly

under higher external load conditions. However, the external load did not completely

overwhelm the effect of preload at this location. Preload was also a main effect at the six

oclock gage location where the external load had the least effect. This was explained by

analyzing the joint in terms of the bending moment. The six oclock location was closer

to the fulcrum of the bending moment. Thus, the strains in this location were not as

drastically affected by the external load as were the other locations.

This was supported by the free body diagram of the system shown in Figure 4.5.

Looking at the left bracket in the diagram, there were three forces acting on the model:

external load, preload, and the reaction force generated by the second bracket. Assuming

the three loads were equally spaced from one another at a distance of L, the resulting

force and moment equations are shown in the bottom left of the figure. The calculations

indicated that the preload could be equated to two times the external load and that the

reaction force was equivalent to the external load. The mating face was then viewed as a

simply supported beam, shown at the bottom right of the figure. The beam was found to

be supported by the external load and the reaction force with the equivalent preload

acting at the center. The center load of two times the external load resulted in a moment

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on the beam that was greatest at the location of preload application. Looking back at the

free body diagram showed this center location corresponding to the three oclock strain

gage location with six oclock being closer to the pin-joint, or fulcrum, and twelve

oclock being further from the fulcrum. Thus, the highest strain in the mating face radius

was expected to occur at the three oclock location. The twelve and six oclock strains

were also expected to be comparable to one another.

Figure 4.5: Free Body Diagram of Model

4.3Preload Variability Study

During testing, some variability was noticed in the preload application. The method

for preloading the bolt was to torque the bolt with a ratchet. The bolt was tightened until

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the average strain in the bolt shaft reached the strain necessary to produce the desired

load. This method was potentially inexact. Thus a study was needed to insure that the

variation was within acceptable limits.

A very simple method was used for the study. The same basic test setup was used as

in the actual experiment, though no external force was applied. The bolt was preloaded

to each of the two levels of interest. The preload was applied via the same method as in

the actual experiment. Strain measurements were taken at each preload level. The test

was repeated three times. Figure 4.6 shows the average equivalent Von Mises strain, in

microstrains, for the low and high preload values. All three replicates were included to

show the repeatability. The data was also separated by the three bolt shaft strain gages to

show any variations between them. The replicates were indicated by colors and the

different gages were indicated by symbol shape.

43

Figure 4.6: Results of the Preload Variability Study


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The maximum range across the three replicates for any of the gage locations was only

about 30 microstrains. The difference between the averages of the two levels was 106

microstrains. Dividing the variance of the group means (106 microstrains) by the mean

of the within-group variances (30 microstrains) resulted in an F-value of approximately

3.5. A higher F-value indicates better statistical repeatability. The F-value of 3.5

indicated that the repeatability was adequate, however improvements to the preload

application method would be desirable if the testing were repeated. Thus, the results

validated the method of preload application.

4.4Bolt Bending Results

The bending stress in the bolt was calculated from the average strain results of the

three gages on the bolt shaft for each load condition. See Appendix B for the spreadsheet

setup and equations used for the calculation of bolt bending based on three strain gages

positioned 120o

apart around the bolt shaft. Table 4.1 shows the bolt bending strain for

each of the six loading conditions. The tensile and total strains are included as well. The

last row shows the percent of bolt bending strain over total strain.

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Preload Low High

External Load Low Mid High Low Mid High

Strain (bend) 131 328 805 140 255 736

Strain (tensile) 1,460 1,954 2,715 1,617 2,024 2,756

Strain (total) 1,591 2,282 3,520 1,757 2,279 3,492

% Bend/Total 8% 14% 23% 8% 11% 21%

Table 4.1: Bolt Bending and Tensile Results

The trend across the load cases was expected. The bending increased as the external

load increased. This supported the conclusion that the lever arm between the bolted joint

and rim flange magnified the effect of the external load on the bolted joint. At the mid

and high external loads, the bolt bending stress was greater for the low preload cases.

This was expected because the external load had less force to overcome at the lower

preload level. At the low external load, the bolt bending stress was greater for the high

preload case, which indicated that the low external load did not overcome the bolt

preload as overwhelmingly as the higher external loads. This trend was supported by the

fact that the low external load did not visibly separate the bolted joint during testing.

4.5Experimental Data for Finite Element Comparison

Table 4.2 presents the average strain results, in microstrains, for the various gage

locations around the mating face radius when only preload was applied to the bolted

joint. The preload conditions were included in the rows of the table and the external load

conditions were included in the columns. Table 4.3 presents the final set of data taken for

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the six loading conditions at each mating face radius strain gage location. Both data sets

were taken from the average of the last five replicates. The values of each replicate were

assumed to be the mean of all data points taken during the appropriate run. The values

presented here were used as the baseline for comparison against the finite element

analyses. See Appendix C for tables of raw experimental data.

Table 4.2: Results at Mating Face Radius Locations for Preload Only (microstrain)

Table 4.3: Results at Mating Face Radius Locations (microstrain)

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CHAPTER 5

FINITE ELEMENT MODELING

Once the experimental baseline was established, a finite element model was needed

for comparison. A preliminary model was developed based on the experimental design.

An iterative process was used to establish the effect of various parameters on the results.

The parameters included contact area, mesh symmetry, contact friction, boundary

conditions, and rigid body elements (RBE). The model was then updated to incorporate

the knowledge gained from the preliminary analysis as well as more accurate geometry.

The updated geometry was based on the dimensions of the actual experimental brackets

which were not exactly the same as those defined by the design. The model was then

used to investigate the effects of other parameters on the bolted joint finite element

results. These included mesh refinement, material properties, load accuracy, and the

inclusion of washers in the assembly.

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48

5.1Preliminary Model Setup

Initially, MSC.Patran and MSC.Marc were used to mesh and analyze the bolted joint

with HEX8 isoparametric (brick) elements. However, the meshing method and

computation time required for even the simple single bolted joint made this model

infeasible. The results of research with this model would not have been readily related to

Goodrichs more complex models either, as the modeling method and software were

drastically different from Goodrichs methods. A new approach was needed to improve

the relationship between the FE model of the single bolted joint and the actual multi-joint

models required by Goodrich. Thus, the preliminary model was developed in UG NX

5.0, the FE package employed by Goodrich. This model was meshed with ten node

tetrahedral elements as the geometry of an actual wheel model would require.

Figure 5.1 shows the general model and mesh used in the preliminary finite element

analysis. Both brackets were included in the model; however the rim flanges were

shortened to exclude the Instron connectors. The assumption was made that the stiffness

of these connectors could be adequately modeled by boundary conditions such as fixed

surfaces or sliders. The washers and bolt were also excluded from the preliminary model

to simplify the development process. The simplified model was used to understand and

verify boundary conditions, contact application, and other finite element parameters with

a readily modifiable model and a low computation time.


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Figure 5.1: General Preliminary Model

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As previously mentioned, the model was meshed with 10-noded tetrahedral elements.

A 1D beam element was used to represent the bolt because a bolt preloading tool was

available in UG NX for use on this element type. The beam element, centered on the axis

of the bolt shaft, was connected to the bracket body using an array of 1D rigid body

elements of class three (RBE3s). These elements were connected to every node within

the projected washer contact area on the surface of the bracket. Table 5.1 gives the

material properties applied to the brackets and to the bolt element. 0D spring elements

with unit stiffness in all six degrees of freedom, called c-bush spring-to-ground elements,

were applied to four nodes on each rim flange. These elements were intended to prevent

potential unconstrained rigid body modes.

Part MaterialYoungs

Modulus (psi)Poissons

RatioDensity(lbm/in

3)

Bracket Aluminum 10.2e6 0.33 0.000253

Bolt Steel 29e6 0.29 0.000732

Washer Steel 29e6 0.29 0.000732

Table 5.1: Material Properties

Once the mesh was generated, boundary conditions and loads were applied to

simulate the conditions of the experimental setup as shown in Table 5.2. To remove the

potential for rigid body motion, the end of one rim flange was fixed in the three

translational degrees of freedom (shown in bright green). The external force was applied

evenly to the end of the other bracket (shown in orange) under the assumption that the

law of equal and opposite reaction would supply the load on the fixed bracket. Rigid

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51

sliders were applied to the sides of the unfixed rim flange to simulate the motion

constraints of the Instron in testing (shown in bright pink).

Figure 5.3 illustrates the mating face contact area and the bolt preload. Contact was

applied between the mating faces of the two brackets (shown in blue). Though the

contact is shown by spots in the figure, the actual contact is made evenly across the entire

surface area. The initial model utilized linear contact with an arbitrary friction coefficient

of 0.05. The bolt preload (shown in red) was applied to the beam element (shown in

yellow) via the bolt preload tool in UG NX. This tool applied the preload before the

external load during the analysis process. Rigid body element spiders (shown in deep

green) were used to connect the ends of the bolt beam to every node in the washer contact

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Figure 5.2: General Finite Element Boundary Conditions and Lo

52

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Figure 5.3: Internal Finite Element Boundary Conditions and Loads

5.2Preliminary Finite Element Analysis

An iterative process was then used to establish the effect of certain finite element

model parameters on the preliminary analysis. The first parameter considered was the

contact area at the mating face. The initial model included both the flat surface of the

mating faces and a portion of the mating face radii. The principal maximum strain results

were analyzed at the strain gage locations around the mating face radius of each bracket.

A comparison of the results for the two brackets showed an interesting phenomenon.

While results for the bracket with the force applied to it were on the same order as the

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experimental strains, the results taken from the bracket with the fixed end were

drastically lower. An investigation of the cause of this issue revealed that the contact

area was at fault. When the contact area was reduced to include only the flat surfaces of

the mating faces, the results were found to be much more closely related.

Though the modified contact area resolved the drastic differences between the two

brackets, slight discrepancies were still found in the results. Differences between the

strains at the three and nine oclock mating face radius gage locations for a single bracket

were of particular interest. Since the boundary conditions and loads were applied

symmetrically to the system, the results should have been equivalent. The results at a

single gage location for both plates demonstrated a similar error. It was found that

asymmetry in the mesh, though minor, would affect the symmetry of the results. The

asymmetry resulted from the meshing method which used a 2D paved surface mesh to

seed, or enforce a mesh distribution, in the 3D mesh. The order in which surfaces were

paved, the number of surfaces paved, and the built-in paving tool used could affect the

symmetry of the resulting 3D mesh. This issue was resolved by improving the symmetry

of the 2D seed meshes.

Using the model with the improved contact area and mesh symmetry, the effect of

changing the coefficient of contact friction was analyzed. The initial coefficient of 0.05

was chosen arbitrarily to minimize friction. The modified friction coefficient was chosen

based on the aluminum-to-aluminum contact to be 1.05. The model was analyzed with

this value and the results were equivalent to those of the initial model. Friction

coefficient did not affect the response of the bolted joint.

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The next adjustments to the model focused on the boundary conditions. First, the

fixed constraint was moved from the end surface of the rim flange to the upper and lower

surfaces of the end partition. Refer to Figure 5.2 for visual definition of the end partition.

This change did not affect the results. Next, the length of the flange included in the slider

constraint was considered. Both longer and shorter sliders were used with the initial

slider being of a middle length. Figure 5.2 shows the three slider lengths along the edge

of one flange. It was found that increasing the slider length increased the bending in the

rim flange unrealistically and reduced the correlation to the experimental results.

However, the shorter slider had no appreciable effect on the results. Thus, it was

concluded that the slider length in the initial model, the mid length, was acceptable.

Finally, the model was analyzed with the sliders and external force applied on both rim

flanges instead of fixing one end. This version resulted in equivalent strains to those of

the initial model.

The last parameter changed in the preliminary analysis was the class of the rigid body

elements (RBEs) used to connect the bolt beam to the washer contact area. The two

available classes were RBE2 and RBE3. Both element types can be used to distribute a

load between two bodies. The RBE2s are typically applied to mitigate solution errors

caused by large discrepancies between the stiffness of two adjoining bodies. While this

might be necessary in some cases, it ultimately adds stiffness to the overall model.

RBE3s are not intended to mitigate stiffness differences, and thus do not add stiffness to

the model. The RBE3s were chosen for the initial model because these elements would

not affect the overall model stiffness as would the RBE2s. No large variations in

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stiffness were expected between bodies, so RBE2s were not necessary. It was also

expected that the less rigid RBE3s would more realistically simulate the interaction

between the bolt, washer, and bracket. It was found that the class 2 elements reduced the

correlation between the finite element and experimental models significantly. The

reduced correlation coupled with the expectation that the class 3 RBEs would better

represent the actual stiffness of the bolt led to the decision to use RBE3s in the final

model.

5.3Final Finite Element Model Setup

Upon completion of the preliminary analysis, the assembly parts were updated to

incorporate the exact geometry of the experimental brackets still excluding the Instron

connectors. While the majority of the bracket dimensions matched the design, the grip

length of the brackets, the width of material through which the bolt passes in the bolted

joint, had been shortened in the actual unit do to a machining error.

With the updated geometry, the finite element model was developed to incorporate

some of the lessons learned from the preliminary analysis. Specifically, the model was

developed with attention to the mesh symmetry around the bolt hole and between the two

brackets. The contact area between the brackets included only the flat surfaces and the

coefficient of friction was held at 0.05. The boundary conditions included the external

force and sliders on both rim flanges to improve the symmetry of the model. Finally, the

class 3 rigid body elements were used to connect the bolt to the brackets as these seemed

to more closely simulate an actual bolt.

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Once the final model was developed, it was used to test the effect of several

parameters on the correlation to the experimental baseline. The first of these was the

refinement of the mesh. Specifically, the mesh refinement was only considered

potentially significant in the contact area and where measurements were needed. Thus,

the mesh was refined at the mating faces and around the mating face radii. The mesh

remained less refined throughout the remainder of the model to improve the

computational efficiency. The initial mating face and mating face radius meshes were

based on an element size of 0.1 in. To achieve a relatively refined mesh, the element size

in these areas was decreased to approximately 0.05 in. Figure 5.4 illustrates the

difference between the refined and unrefined meshes at the mating face and mating face

radius.


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Unrefined

Figure 5.4: Mesh Refinement Comparison

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Next, several potential discrepancies were identified in the material properties,

specifically the modulus of elasticity, of both the bracket and bolt materials. First, the

modulus of elasticity of the bracket aluminum (7050-T7351) was called into question. It

was discovered that the manufacturers specification of 10.3e6 psi differed from the

specification typically used by Goodrich, 10.2e6 psi. A value of 10.0e6 psi was also

chosen arbitrarily to further the understanding of this parameter.

The modulus of elasticity of the bolt was also varied based on a different concept. It

was recommended that the reduced bolt length due to the exclusion of the bolt head, the

nut, and the washers could affect the resulting stiffness of the bolt in the model. The

inclusion of threads in the loaded section of the bolt shaft could also serve to reduce the

stiffness of the bolt. Based on the knowledge of Goodrichs bolt structures expert, the

modulus of elasticity was reduced by four percent, to a value of 27.9e6 psi, as a way to

counter the effect of threads in the loaded portion of the bolt shaft. The model was also

analyzed with the bolt modulus reduced by 40 percent. This represented the worst case

scenario; taking into account the difference in bolt length, the exclusion of stiffening

material in the bolt head and nut, and the inclusion of threads in the loaded section of the

shaft. The resulting worst case modulus of elasticity was 17.4e6 psi. Table 5.2 shows the

various combinations of material properties used to characterize the effect of varying the

modulus of elasticity of the bracket and of the bolt on the resulting mating face radius

strains.

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Modulus of Elasticity (psi)Bracket Bolt10.2e6 17.4e610.2e6 27.9e610.2e6 29.0e6

10.3e6 29.0e610.0e6 29.0e6

Table 5.2: Material Property Combinations

Another potential source of error between the finite element and experimental models

was the accuracy of the loads applied during experimentation. This possible inaccuracy

applied to both the external load and bolt preload. To characterize this parameter, the

external load was first increased and then decreased by 50 lbs for each load case. The

preload values were maintained for these analyses. The new external load values are

given in Table 5.3. The preload values also offered some potential discrepancies. First,

it was recognized that the experimental preload was slightly decreased after the external

load was removed. The average experimental bolt preloads were calculated for the high

and low preloads after the external load had been applied and removed. These values

were then used in the six load cases with the original external loads. It was also noted

that the original preloads applied in the finite element model resulted in significantly

lower strains than the experiment at the mating face radius strain gage locations. The

preloads were increased until the mating face radius finite element results matched the

average results from the experiment within one percent. The six load cases were repeated

with the increased preloads and the original external loads. Table 5.4 provides the new

preload values analyzed.

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ModelCase

External Load (lbs)

Low Mid High

Original 900 1800 2700

+50 lbs 950 1850 2750-50 lbs 850 1750 2650

Table 5.3: Adjusted External Loads

Model Case

Bolt Preload

(lbs)

Low High

Original 3240 3600

Post-External Load 3133 3522Matching Experimental MFR 4200 4600

Table 5.4: Adjusted Bolt Preloads

The final step was to analyze the model with washers incorporated into the assembly.

To accomplish this, the model was regenerated from scratch with two shouldered

washers, one on each side of the bolted joint. The bolt beam and RBE3s were adjusted

such that the bolt length included the washers and the RBE3s connected the bolt to the

faces of the washers instead of to the bracket. Contact was applied between the washer

and the bracket face as well as between the shoulder of the washer and the inside of the

bolt hole. The friction coefficient of 0.05 was used in this case as well. Figure 5.5

illustrates the meshed model with the washers.

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Figure 5.5: Model with Washers

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CHAPTER 6

FINITE ELEMENT RESULTS

6.1Finite Element Results Acquisition

Strain results were extracted from the finite element models at the three experimental

strain gage locations around the mating face radius; twelve, three, and six oclock. These

locations are identified in Figure 6.1. Two methods were available for extracting strain

data. The first was to take the value of the single node corresponding to the center of the

experimental strain gage. This is shown at the top ofFigure 6.1. The second method was

to take an average of the strains for several nodes immediately surrounding the center of

the strain gage location. This method was tested using a refined mesh such that the area

covered by the averaged nodes would more closely represent the dimensions of the strain

gage. See the bottom ofFigure 6.1 for a representation of the averaging method.

Ultimately, it was found that the results of both methods were comparable. Thus, the

single node method was used to simplify the data acquisition process. The single node

results for each gage location were averaged between the two brackets to obtain the final

data values. See Appendix E for data values for all strain gage locations and models.

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12:00

3:00

6:00

Figure 6.1: Finite Element Strain Measurements

6.2Finite Element Convergence

A brief study was performed to verify that the selected mesh refinement represented a

fully converged solution. The initial mesh is illustrated at the top ofFigure 6.3 while a

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doubly refined mesh is shown at the bottom. Both meshes show the principal maximum

strain contours. The general trends in the strain results were found to be comparable

between the two meshes. The less refined mesh did not appear to disrupt the flow of the

strain distribution. Individual nodal results showed a slight, one to two percent, variation

in strain between the

Belisle Kathryn J

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