Belisle Kathryn J
Transcript of Belisle Kathryn J
-
8/4/2019 Belisle Kathryn J
1/132
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
-
8/4/2019 Belisle Kathryn J
2/132
Copyright
by
Kathryn J. Belisle
2009
-
8/4/2019 Belisle Kathryn J
3/132
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
ii
-
8/4/2019 Belisle Kathryn J
4/132
when the finite element model preload was adjusted such that the mating face radius
strains under only preload matched those of the experimental results.
iii
-
8/4/2019 Belisle Kathryn J
5/132
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.
iv
-
8/4/2019 Belisle Kathryn J
6/132
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.
v
-
8/4/2019 Belisle Kathryn J
7/132
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
vi
-
8/4/2019 Belisle Kathryn J
8/132
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
vii
-
8/4/2019 Belisle Kathryn J
9/132
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
viii
-
8/4/2019 Belisle Kathryn J
10/132
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
ix
-
8/4/2019 Belisle Kathryn J
11/132
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
-
8/4/2019 Belisle Kathryn J
12/132
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.
1
-
8/4/2019 Belisle Kathryn J
13/132
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.
2
-
8/4/2019 Belisle Kathryn J
14/132
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
3
-
8/4/2019 Belisle Kathryn J
15/132
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.
4
-
8/4/2019 Belisle Kathryn J
16/132
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
5
-
8/4/2019 Belisle Kathryn J
17/132
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
6
-
8/4/2019 Belisle Kathryn J
18/132
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.
7
-
8/4/2019 Belisle Kathryn J
19/132
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.
8
-
8/4/2019 Belisle Kathryn J
20/132
Figure 2.4: Circular Plate Finite Element Model
9
-
8/4/2019 Belisle Kathryn J
21/132
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
10
-
8/4/2019 Belisle Kathryn J
22/132
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.
11
-
8/4/2019 Belisle Kathryn J
23/132
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.
12
-
8/4/2019 Belisle Kathryn J
24/132
Figure 2.6: Exploded View of Bolted Joint for Torque Free Preload Experiment
13
-
8/4/2019 Belisle Kathryn J
25/132
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
14
-
8/4/2019 Belisle Kathryn J
26/132
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.
15
-
8/4/2019 Belisle Kathryn J
27/132
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
16
-
8/4/2019 Belisle Kathryn J
28/132
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).
17
-
8/4/2019 Belisle Kathryn J
29/132
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.
18
-
8/4/2019 Belisle Kathryn J
30/132
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.
19
-
8/4/2019 Belisle Kathryn J
31/132
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.
20
-
8/4/2019 Belisle Kathryn J
32/132
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.
21
-
8/4/2019 Belisle Kathryn J
33/132
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
22
-
8/4/2019 Belisle Kathryn J
34/132
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
23
-
8/4/2019 Belisle Kathryn J
35/132
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
24
-
8/4/2019 Belisle Kathryn J
36/132
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
25
-
8/4/2019 Belisle Kathryn J
37/132
(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.
26
-
8/4/2019 Belisle Kathryn J
38/132
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
27
-
8/4/2019 Belisle Kathryn J
39/132
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
28
-
8/4/2019 Belisle Kathryn J
40/132
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
29
-
8/4/2019 Belisle Kathryn J
41/132
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.
30
-
8/4/2019 Belisle Kathryn J
42/132
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
31
-
8/4/2019 Belisle Kathryn J
43/132
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.
32
-
8/4/2019 Belisle Kathryn J
44/132
Condition # Preload External Load1 Low Low2 Low Mid3 Low High4 High Low
5 High Mid6 High High
Table 3.3: Loading Conditions
33
-
8/4/2019 Belisle Kathryn J
45/132
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
34
-
8/4/2019 Belisle Kathryn J
46/132
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.
35
-
8/4/2019 Belisle Kathryn J
47/132
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
36
-
8/4/2019 Belisle Kathryn J
48/132
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.
37
-
8/4/2019 Belisle Kathryn J
49/132
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
38
-
8/4/2019 Belisle Kathryn J
50/132
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.
39
-
8/4/2019 Belisle Kathryn J
51/132
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
40
-
8/4/2019 Belisle Kathryn J
52/132
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
41
-
8/4/2019 Belisle Kathryn J
53/132
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
42
-
8/4/2019 Belisle Kathryn J
54/132
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
-
8/4/2019 Belisle Kathryn J
55/132
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.
44
-
8/4/2019 Belisle Kathryn J
56/132
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
45
-
8/4/2019 Belisle Kathryn J
57/132
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)
46
-
8/4/2019 Belisle Kathryn J
58/132
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.
47
-
8/4/2019 Belisle Kathryn J
59/132
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.
-
8/4/2019 Belisle Kathryn J
60/132
Figure 5.1: General Preliminary Model
49
49
-
8/4/2019 Belisle Kathryn J
61/132
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
50
-
8/4/2019 Belisle Kathryn J
62/132
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
area on each bracket.
-
8/4/2019 Belisle Kathryn J
63/132
Figure 5.2: General Finite Element Boundary Conditions and Lo
52
52
-
8/4/2019 Belisle Kathryn J
64/132
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
53
-
8/4/2019 Belisle Kathryn J
65/132
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.
54
-
8/4/2019 Belisle Kathryn J
66/132
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
55
-
8/4/2019 Belisle Kathryn J
67/132
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.
56
-
8/4/2019 Belisle Kathryn J
68/132
57
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.
-
8/4/2019 Belisle Kathryn J
69/132
Unrefined
Figure 5.4: Mesh Refinement Comparison
58
58
-
8/4/2019 Belisle Kathryn J
70/132
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.
59
-
8/4/2019 Belisle Kathryn J
71/132
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.
60
-
8/4/2019 Belisle Kathryn J
72/132
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.
61
-
8/4/2019 Belisle Kathryn J
73/132
Figure 5.5: Model with Washers
62
-
8/4/2019 Belisle Kathryn J
74/132
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.
63
-
8/4/2019 Belisle Kathryn J
75/132
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
64
-
8/4/2019 Belisle Kathryn J
76/132
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