A Study of the Prediction of Vibration-Induced 
Fretting Corrosion in Electrical Contacts 
  
by 
  
Chen Chen 
 
  
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Doctor of Philosophy 
    
Auburn, Alabama 
December 18, 2009 
 
 
 
 
Keywords:  electrical contacts, fretting corrosion,  
modeling, finite element analysis 
 
 
Copyright 2009 by Chen Chen 
 
 
Approved by 
 
George T. Flowers, Chair, Alumni Professor of Mechanical Engineering 
Jeffrey C. Suhling, Quina Distinguished Professor of Mechanical Engineering 
Robert L. Jackson, Associate Professor of Mechanical Engineering 
Michael J. Bozack, Professor of Physics Department 
 
 
          
        
 
 
 ii
Abstract  
 
 
It is generally recognized that fretting corrosion is one of the major failure 
mechanisms in electrical contacts. The negative effects of fretting corrosion were found 
in many areas such as aerospace, automobile, electrical packaging, etc. In recent years, 
much of the research work has focused on the causes of fretting corrosion, the 
mechanism of this phenomenon, and its prevention. However, nowadays, most evaluation 
of the connector fretting corrosion is conducted through exhaustive experiments, making 
the connector design and validation process time consuming and costly. Therefore, a new 
method using modeling and simulation techniques to predict the influence of various 
design factors on vibration-induced fretting propensity in electrical connectors would be 
very beneficial to the study of the fretting corrosion.  
In the author's work, a series of studies concerned with the modeling, analysis and 
experimental validation of vibration-induced fretting corrosion of electrical connector 
were conducted. A FEA based methodology was developed and optimized to predict and 
simulate the vibration-induced fretting corrosion on both typical single blade/receptacle 
connector pair. A series of corresponding experiments were then performed to evaluate 
its performance. Comparison between 2-D simplified and 3-D detailed modeling and 
analysis method were conducted. The 3-D detailed simulation was proved to be more 
accurate but requires larger computational cost. The influences of different connector 
design factors were investigated in both simulation and experiments. The relative motion
 iii
at contact interface was proved to be a great indicator for the threshold of fretting 
corrosion.  Finally, the simulation results were found to be in good agreement with 
experimental results. It is demonstrated that, this finite element modeling and analysis 
method have great potential in predicting of the vibration-induced fretting corrosion in 
electrical contacts. 
 iv
Acknowledgements 
 
 
            I would like to express my sincere thanks and deep appreciation to my advisor Dr. 
George T. Flowers for his guidance in the completion of this research work in Auburn 
University. His wise suggestions, his generous support and his whole-heartedly 
encouragement contributed immensely to the fulfillment of my study and lighted my path 
towards the magnificent science palace. 
           I also would like to thank the other advisory committee members, Dr. Jeffrey C. 
Suhling, Dr. Robert L. Jackson, and Dr. Michael J. Bozack for their academic instructions 
and assistance. I also thank Dr. John L. Evans for his valuable comments and corrections, 
and for his great help for being my outside reader. 
            Special thanks would be given to all my friends, especially Dr. Fei Xie and Dr. 
Alfonso Moreira, which without their constant support this ?journey? would have been 
very difficult to accomplish. 
 Finally, I would like to express my greatest gratitude and gratefulness to my 
parents, Zhaocai Chen and Aihua Liu, whose love, care and perpetual support have been 
invaluable for the completion of this degree (Doctor of Philosophy in Mechanical 
Engineering). 
 
 
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v 
Table of Contents 
 
 
List of Figures???. ....................................................................................................... ix?
List of Tables.???.. ..................................................................................................... xv?
Chapter 1? Introduction and Literature Review ............................................................ 1?
1.1 Fretting Corrosion ..................................................................................................... 2?
1.2 Finite Element Method ............................................................................................. 3?
1.3 Literature Review of Fretting Corrosion in Electrical Contacts ............................... 5?
Chapter 2? A Study of Vibration- Induced Fretting Corrosion in a Single 
Blade/Receptacle Connector Pair ............................................................. 14?
2.1 Introduction ............................................................................................................. 14?
2.2 Experimental Configuration .................................................................................... 15?
2.2.1 Experimental Samples ..................................................................................... 15?
2.2.2 Experimental Equipment ................................................................................. 17?
2.2.2.1 Keithley Model 2010 Multimeter ............................................................. 17?
2.2.2.2 Polytec Laser Vibrometer System ............................................................ 18?
2.2.2.3 HP 35665A Dynamic Signal Analyzer ..................................................... 19?
2.2.2.4 Vibration System ...................................................................................... 20?
2.2.3 Experimental Setup .......................................................................................... 23?
2.2.3.1 Transfer Function Measurement ............................................................... 23
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vi 
2.2.3.2 The Fretting Threshold Level Measurement ............................................. 26?
2.3 Finite Element Model ............................................................................................. 28?
2.3.1 Geometric Model ............................................................................................. 28?
2.3.2 Material Properties ........................................................................................... 31?
2.3.3 Boundary Conditions ....................................................................................... 31?
2.4 Vibration Process Simulation ................................................................................. 33?
2.5 Experiment and Simulation Results ........................................................................ 35?
2.5.1 Transfer Function Results ................................................................................ 35?
2.5.1 Fretting Threshold Results ............................................................................... 42?
2.6 Summary and Conclusions ..................................................................................... 53?
Chapter 3? Three Dimensional Modeling and Anlysis of a Blade/Receptacle 
Connector Pair for the Prediction of Vibration-Induced Fretting 
Degradation ............................................................................................... 55?
3.1 Introduction ............................................................................................................. 55?
3.2 Three Dimensional Detailed Finite Element Model Generation ............................ 56?
3.2.1 Geometric Model ............................................................................................. 56?
3.2.2 Mesh Control ................................................................................................... 58?
3.2.3 Parallel Execution ............................................................................................ 60?
3.2.4 Define Contact ................................................................................................. 62?
3.3 Simulation Methodology and Boundary Conditions .............................................. 63?
3.3.1 Mating Process Simulation .............................................................................. 63?
3.3.2 Boundary Conditions ....................................................................................... 67?
3.4 3-D Detailed Model Simulation Results ................................................................. 69?
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vii 
3.4.1 Transfer Functions ........................................................................................... 69?
3.4.2 Threshold Values ............................................................................................. 76?
3.5 Computational Cost ................................................................................................ 81?
3.5 Summary and Conclusions ..................................................................................... 82?
Chapter 4? The Application  of FEA Simulation Techniques to the Fretting 
Degradation of a Connector System ......................................................... 84?
4.1 Introduction ............................................................................................................. 84?
4.2 Experimental Configuration .................................................................................... 85?
4.2.1 Experimental Samples ..................................................................................... 85?
4.2.2 Experimental Equipment ................................................................................. 87?
4.2.3 Experimental Setup .......................................................................................... 92?
4.3 FEA Modeling ........................................................................................................ 94?
4.3.1 Detailed Three Dimensional Model ................................................................. 94?
4.3.2 Simplified Two Dimensional Model ............................................................... 95?
4.3.3 Comparison between 2-D and 3-D Model ....................................................... 97?
4.4 Experiment and Simulation Results ........................................................................ 98?
4.4.1 Transfer Function ............................................................................................. 98?
4.4.2 Fretting Rate ................................................................................................... 102?
4.5 Summary and Conclusions ................................................................................... 106?
Chapter 5? Conclusions and Recommandations ....................................................... 108?
References????? ................................................................................................... 111?
Appendix A     Ansys Log  File for the 2-D Simplified Finite Element Model ............. 119?
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viii 
Appendix B     MATLAB Code Example for Transfer Function and Relative Motion 
Calculation .............................................................................................. 146
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ix 
List of Figures 
 
 
Figure 2-1: Photograph of the blade and receptacle parts ................................................. 16?
Figure 2-2: Mated blade/receptacle pair ........................................................................... 16?
Figure 2-3: Four-wire dry circuit resistance measurement ............................................... 18?
Figure 2-4: Photograph of the Polytec laser vibrometer system ....................................... 19?
Figure 2-5: Photograph of HP 35665A dynamic signal analyzer ..................................... 20?
Figure 2-6: PA 500L amplifier ......................................................................................... 21?
Figure 2-7: V408 shaker ................................................................................................... 22?
Figure 2-8: Typical vibration system ................................................................................ 22?
Figure 2-9: Experimental setup of the transfer function measurement ............................. 25?
Figure 2-10:  Detailed view of displacement measurement .............................................. 26?
Figure 2-11: Photograph of the fretting threshold levels experiment setup ...................... 27?
Figure 2-12: Photograph of the resistance measurement .................................................. 27?
Figure 2-13: Overall view of the 2-D geometric model ................................................... 29?
Figure 2-14: Close-up view of the 2-D geometric model ................................................. 29?
Figure 2-15:  Geometric model for the blade/receptacle configuration ............................ 32?
Figure 2-16: Sinusoidal vibration excitation with the load substeps ................................ 33?
Figure 2-17:  Full model motion at Time 1 during vibration ............................................ 34?
Figure 2-18:  Motion of the blade and the receptacle at time 1 ........................................ 34?
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Figure 2-19: Motion of the blade and the receptacle at time 2 ......................................... 35?
Figure 2-20: Node locations for the transfer function simulation ..................................... 36?
Figure 2-21: Transfer function results from experiment and 2-D model simulation for 
different friction coefficient .............................................................................................. 37?
Figure 2-22: Experimental results for different contact normal force levels .................... 38?
Figure 2-23: 2-D simulation results for different contact normal force levels ................. 38?
Figure 2-24: Experimental results showing the variation of transfer function with 
excitation amplitude for Specimen Type 1.a .................................................................... 40?
Figure 2-25: Experimental results showing the variation of transfer function with 
excitation amplitude for Specimen Type 2.a .................................................................... 40?
Figure 2-26: Simulation of relative motion transfer functions for various wire tie-off 
lengths (Specimen Type 1.a) ............................................................................................. 41?
Figure 2-27: Simulation of relative motion transfer functions for various levels of 
supplementary mass (Specimen Type 1.a) ........................................................................ 42?
Figure 2-28: Identification of the threshold displacement (or g-level) ............................. 44?
Figure 2-29: SEM picture of accumulation area ............................................................... 45?
Figure 2-30: Simulated X-axis relative motion at position 2 ............................................ 48?
Figure 2-31: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.a ................................................................................. 49?
Figure 2-32: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.b ................................................................................ 49?
Figure 2-33:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.c ................................................................................. 50?
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xi 
Figure 2-34: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.a ................................................................................. 50?
Figure 2-35: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.b ................................................................................ 51?
Figure 2-36: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.c ................................................................................. 51?
Figure 2-37: Comparison of fretting threshold displacements for Type 1 samples with 
different contact normal forces ......................................................................................... 52?
Figure 2-38: Comparison of fretting threshold displacements for Type 2 samples with 
different contact normal forces ......................................................................................... 53?
Figure 3-1: Overall view of the 3-D geometric model ..................................................... 57?
Figure 3-2: Close-up view (cross section) of the 3-D geometric model ........................... 57?
Figure 3-3: Partitions in the receptacle component .......................................................... 59?
Figure 3-4: Picture of the workstation for the 3-D simulation .......................................... 61?
Figure 3-5: Defined contact pair in 3-D model ................................................................. 63?
Figure 3-6: Unmated connector pair ................................................................................. 64?
Figure 3-7: Connector pair in mating process ................................................................... 65?
Figure 3-8: Mated connector pair ..................................................................................... 65?
Figure 3-9: Unmated receptacle part ................................................................................. 66?
Figure 3-10: Mated connector pair ................................................................................... 67?
Figure 3-11: Boundary conditions in the 3-D model ........................................................ 68?
Figure 3-12: Nodes location in the 3-D detailed model .................................................... 70?
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xii 
Figure 3-13: Experimental transfer function results for different contact normal force 
levels ................................................................................................................................. 71?
Figure 3-14: 2-D simulation transfer function results for different contact normal force 
levels ................................................................................................................................. 72?
Figure 3-15: 3-D simulation transfer function results for different contact normal force 
levels ................................................................................................................................. 72?
Figure 3-16: Comparison of experimentally determined transfer function and 2-D 
simulation model results ................................................................................................... 73?
Figure 3-17: Comparison of experimentally determined transfer function and 3D 
simulation model results ................................................................................................... 74?
Figure 3-18: Comparison between 2-D simulation and 3-D simulation of relative motion 
transfer functions for various tie-off lengths (Specimen Type 2.b) .................................. 75?
Figure 3-19: Comparison between 2-D simulation and 3-D simulation of relative motion 
transfer functions for various tie-off lengths (Specimen Type 2.b) .................................. 75?
Figure 3-20: Comparison between 3D simulation results and experimental results for 
scaled inverse relative motion transfer functions for Type 1 samples .............................. 76?
Figure 3-21: Comparison between 3D simulation results and experimental results for 
scaled inverse relative motion transfer functions for Type 2 samples .............................. 77?
Figure 3-22: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.a) ................... 78?
Figure 3-23: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.b) ................... 78?
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xiii 
Figure 3-24: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.c) ................... 79?
Figure 3-25: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.a) ................... 79?
Figure 3-26: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.b) ................... 80?
Figure 3-27: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.c) ................... 80?
Figure 4-1: Photograph of the connector system sample .................................................. 86?
Figure 4-2: Photograph of the connector system sample .................................................. 87?
Figure 4-3: Photograph of LDS V850 shaker with KISTLER accelerometer .................. 90?
Figure 4-4: DACTRON vibration control system and SPAK amplifier ........................... 90?
Figure 4-5: Diagram of LDS vibration test system ........................................................... 91?
Figure 4-6: Photograph of the experimental setup ............................................................ 92?
Figure 4-7: Photograph of transfer function measurement ............................................... 93?
Figure 4-8: Diagram of transfer function measurement configuration ............................. 94?
Figure 4-9: Picture of the 3-D detailed connector system model ..................................... 95?
Figure 4-10: Overall view of the 2-D connector system model ........................................ 96?
Figure 4-11: Detailed view of the 2-D connector system model ...................................... 96?
Figure 4-12: Comparison of computational cost for initial simulation between 2-D model 
and 3-D model ................................................................................................................... 98?
Figure 4-13: Comparison of experimentally determined transfer function and 2-D model 
simulation results .............................................................................................................. 99?
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xiv 
Figure 4-14: Experimental determined transfer function results for different contact 
normal force levels of specimen Type 1 ......................................................................... 100?
Figure 4-15: Simulation transfer function results for different contact normal force levels 
of specimen Type 1 ......................................................................................................... 101?
Figure 4-16: Experimental determined transfer function results for different contact 
normal force levels of specimen Type 2 ......................................................................... 101?
Figure 4-17: Simulation transfer function results for different contact normal force levels 
of specimen Type 2 ......................................................................................................... 102?
Figure 4-18: X-axis relative motion for different contact normal force levels for specimen 
Type 1 in simulation ....................................................................................................... 104?
Figure 4-19: X-axis relative motion for different contact normal force levels for specimen 
Type 2 in simulation ....................................................................................................... 104?
Figure 4-20: Rate of resistance change for Type 1 sample in experiment ...................... 105?
Figure 4-21: Rate of resistance change for Type 2 sample in experiment ...................... 105?
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List of Tables 
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Table 2-1: Different types of experimental samples ......................................................... 17?
Table 2-2: Displacement decoder specification of the laser vibrometer system .............. 19?
Table 2-3: Material and dimensional properties of the model components ...................... 30?
Table 2-4: Relationship analysis for type 1.a connector pair ............................................ 46?
Table 2-5: Relationship analysis for type 2.a connector pair ............................................ 47?
Table 3-1: Material properties for 3-D model components .............................................. 58?
Table 3-2: Mesh techniques and size control for different components ........................... 60?
Table 3-3: Specifications of the workstation .................................................................... 61?
Table 3-4: Corresponding circular frequency values in the 3-D simulation ..................... 69?
Table 4-1: Types of Experimental Samples ...................................................................... 86?
Table 4-2: G-levels and corresponding displacements at shaker head ........................... 103?
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1 
?
CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW  
 It is generally recognized that fretting corrosion is one of the major failure 
mechanisms in electrical contacts. In recent years, much of the research work was 
focused on the causes of fretting corrosion, the mechanism of this phenomenon and its 
prevention. However, most evaluation of the connector fretting propensity is conducted 
through exhaustive experiments, making the connector design and validation process 
time consuming and costly. Therefore, a method using modeling and simulation 
techniques to predict the influence of various design factors on the vibration-induced 
fretting corrosion in electrical connectors would be very beneficial.  
 In the author's work, a series of studies concerned with the modeling, analysis and 
experimental validation of vibration-induced fretting corrosion of electrical contacts were 
conducted. Based on these results, the dissertation is divided into five chapters. In chapter 
one, an introductory material as well as a comprehensive literature review about the 
vibration-induced fretting corrosion problem such as the meaning of fretting corrosion, 
the mechanism of this phenomenon, the history of related study, the present status of the 
research on this topic are stated. Chapter two describes a study of vibration-induced 
fretting corrosion in a single blade-receptacle connector pair. A research on the three-
dimensional modeling and analysis method on the prediction of vibration-induced fretting 
corrosion is discussed in Chapter three. Chapter four describes the application of FEA
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2 
techniques to the fretting degradation of a connector system. All the studies discussed in 
this dissertation are then summarized in chapter five and some recommendations for the 
necessary further work on this topic are also provided. 
 1.1 Fretting Corrosion 
            Fretting is one of the major contact failure mechanisms. It is a small amplitude 
contact movement between two contacting surfaces. Such micro motions (slip) may range 
from a few ?m to as much as 100 ?m in electronic connectors. This slip can be produced 
by external vibrations, changing temperatures, differential thermal expansion of the 
contacting metals, load relaxation, and junction heating as the power is switched on and 
off.  
 Fretting causes metal transfer and wear at the contact interface. This fretting 
damage serves to repeatedly expose fresh metal to atmospheric oxidation for non-
precious metal plated contact interfaces. This base-metal contact produces insulating 
oxide debris. The formation of metallic wear and oxidized debris is resulted from the 
adhesion, abrasion, and delamination wear progress in fretting. Catalytic materials such 
as palladium and other platinum group metals yield the insulting frictional polymers. The 
precursors to these polymers are absorbed organic air pollutants from the atmosphere. 
The accumulation of these insulating solids in the contact zone causes electrical 
resistance to increase. If these substances are inorganic solids, like oxides, the process is 
called "fretting corrosion"[1]. 
   It is widely know that fretting corrosion is a frequent cause of failure of 
suspension springs, bolt and rivet heads, king pins in auto steering mechanisms, jewel 
bearings, variable-pitch propellers, shrink fits, contacts of electrical relays, connecting 
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3 
rods, and other parts of vibrating machinery. It may also cause discoloration of stacked 
metal sheets during shipment. An early documented example of fretting corrosion was 
recognized when automobiles were being shipped some years ago by railroad from 
Detroit to the West Coast. By the reason of vibration, the ball-bearing races of the wheels 
became badly pitted by fretting corrosion. Therefore the automobiles were not operable 
on arrival. This damage was worse in winter than in summer, but could be avoided if the 
load on the wheels was relieved during shipment. 
            It is proven from laboratory experiments that fretting corrosion of steel against 
steel requires oxygen but not moisture. Moreover, damage is less in moist air compared 
to dry air and is markedly less in a nitrogen atmosphere. Damage increases as the 
temperature decreases, so the mechanism is clearly not electrochemical in nature. 
Increasing the load increases the damage. Fretting corrosion is also worsened by 
increased slip, provided the surface is not lubricated. Increases in frequency for the same 
number of cycles tend to decrease damage, but in nitrogen no frequency effect is 
observed [1]. 
1.2 Finite Element Method 
 The finite element method (FEM), sometimes named finite element analysis 
(FEA), is a computational technique which is used to obtain approximate solutions of 
boundary value problems in engineering. In simple, a boundary value problem is a 
mathematical problem in which one or more dependent variables must satisfy a 
differential equation everywhere within a known domain of independent variables and 
satisfy specific conditions on the boundary of domain [2]. FEM technology has been 
widely used in solving structural, mechanical, heat transfer, and fluid dynamics problems 
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4 
as well as problems of other disciplines. The advancement in computer technology 
enables us to solve an even larger system of equations, to formulate and assemble the 
discrete approximation, and to display the results quickly and conveniently. This has also 
helped the finite element method become a powerful tool.  
 From the early 1900s, Rayleigh [3], Ritz [4] used trail functions to approximate 
solutions of differential equations. Galerkin [5] used the same concept for solution and 
provided a very strong basis for the finite element method. However, the finite element 
method didn't have its real start until Courant [6] introduced the concept of piecewise-
continuous functions in a sub-domain in 1943. In the late 1940s, a matrix method of the 
force analysis was developed by certain aircraft engineers known as the flexibility 
method. In 1960, the term finite element was first used by Clough [7] in the context of 
plane stress analysis and has been in common usage since that time. From then on, the 
finite element method was extended to applications in shell bending, plate bending, 
pressure vessels, fluid flow, heat transfer [8][9], and general three-dimensional problems 
in elastic structural analysis. 
 The finite element method is computational intensive due to the complicated 
operation on very large matrices.Therefore, finite element software code was developed 
by taking advantage of the great computational capacity of modern computers. The first 
software code was NASTRAN [10] in conjunction with the space exploration program of 
the United States in 1960s. Since then, different commercial software packages have been 
introduced for finite element analysis, such as ANSYS [11], ALGOR [12], COSMOS [13] 
and ABAQUS [14]. Most of these packages can be used on desktop computers and 
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5 
workstations to solve large problems in many areas under today?s computational 
environment. 
1.3 Literature Review of Fretting Corrosion in Electrical Contacts 
 An understanding of the processes which contribute to connector degradation is 
necessary to facilitate the correct sections of contact materials and component designs 
and to establish the conditions in which they must be used so as to assure reliable 
performance. Fretting corrosion is known as a typical problem for many electrical and 
electronic equipments which could lead to huge cost in repair and replacement.  
Nevertheless, the negative effect of fretting corrosion was not generally recognized as a 
serious factor of electrical connector degradation problems until Bock and Whitley [15] 
clearly demonstrated its importance in 1974. 
            From then on, a series of systematic studies of the fretting corrosion phenomenon 
in electronic connectors were conducted [16][17][18][19][20]. In 1984, Antler [21] 
provided a comprehensive review of fretting corrosion problem. In his study, the 
mechanisms of this phenomenon were systematically discussed such as transfer, wear, 
oxidation, and frictional polymerization that apply to the fretting of contacts; the effect of 
operational parameters such as the cycle rate and force on contact resistance change; a 
survey of materials whose fretting behavior has been characterized; and an analysis of the 
different roles that lubricants play in controlling fretting according to the contact 
materials. It was also pointed out that the determination factors of whether contact 
materials will be satisfactory for a given application were the connector designs, the 
expected connector lifetimes, and their reliability requirements. Moreover, hardware tests 
such as shock and vibration were also suggested to be conducted before new contact 
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6 
designs and materials are incorporated in connectors. Antler concluded that contact 
resistance is determined by the composition of the interface and this composition may 
change during fretting with dissimilar metals due to transfer, wear, and film formation. 
The contact resistance for fretting corrosion and friction polymerizing systems generally 
becomes more unstable under longer wipe time. Contact resistance transients during 
fretting may be significantly higher than static contact resistance. Lubricants which may 
retard the rate of wear of thin noble metals on film-forming substrates by dispersing 
frictional polymers and thereby reducing the oxidation rate were proved to be able to 
stabilize the contact resistance. Finally, fretting process has been categorized into four 
regimes by Slade [1]: 
? Stick. Movement between the contact surfaces is accommodated by elastic 
deformation of the members in the near-surface regions. The asperities are joined, 
and there is no surface damage until the members are separated. The stick regime 
may occur for movements of about 1 ?m depending on the material, contact 
geometry, and on other factors. 
? Mixed Stick-Slip. There is a central stick area surrounded by an annular slip 
region where there may be crack formation, fretting fatigue, and wear debris. 
? Gross Slip. All asperity contacts are broken during each cycle. Asperities slide 
across several others of the opposing surface. Damage is extreme with 
delamination wear. Movements of 10-100 ?m are involved. 
? Reciprocating Sliding. With large displacements more than 100-200 ?m, there is 
sliding wear which may result in fretting.           
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7 
  Fretting corrosion exists in many application fields. One of the most critical 
fields is vehicle electronics. The automotive environment combines external vibrations 
with the strong environmental factors of temperature and humidity. Therefore, fretting 
corrosion can be a major problem on connector systems used in vehicle electronics. From 
1986, studies in this field were underway on automotive connector systems [22][23][24]. 
An early study on the fretting corrosion of tin-plated copper alloy used for a stepping 
motor/precision stage assembly was reported by Lee and Mamrick [23] in 1987. The 
purpose of their research is to explore the physical phenomena of electrical conduction 
using tin-plated contacts subjected to fretting corrosion and the influence of electric load 
on the fretting corrosion process. The rise in contact resistance of a tin-plated copper 
alloy under cyclical minute motion was studied a both dry circuit and then with electrical 
loads. It was found that in the range of circuit voltage and current investigated, the 
electrical conduction through slightly corroded contacts was shown not to be affected by 
the electrical load. For moderately corroded contacts, the resistance characteristic showed 
a sustained plateau near the melting voltage of Sn, and for severely corroded contacts, a 
plateau occurred in the resistance range corresponding to the voltage range of the 
melting, sublimation, and decomposition of the oxides and vaporization of tin. They 
summarized that the resistance plateaus were consistent with the view that the current 
passing through the contact constriction caused the contact spots to thermally run-away 
until melting of the tin occurred. With further corrosion giving higher resistance and 
more heating, the temperature could rise further up to the melting, sublimation, and 
decomposition of the oxides and even up to the vaporization of tin collectively forming 
the second contact resistance or voltage plateau. 
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8 
           In 2000, Swingler, Mcbride and Maul [25] proved the complexity of the fretting 
corrosion in vehicle environment. In this study, temperatures of automotive connectors, 
which were undergoing road testing, were being monitored to evaluate stress levels 
during real operation. An empirical model of temperature behavior for three types of 
connectors was presented based on real environmental data obtained from the tests. 
Furthermore, a number of micro-sensors embedded within a connector housing were then 
used to enhance this study. This for the first time allows real information about the events 
occurring at the connector interface. 
            Nevertheless, relatively few researchers have studied the vibration influence of 
fretting corrosion in electrical connectors. From 2002, Flowers and Xie [26] investigated 
the influence of accelerated vibration on fretting corrosion problems. An electrical 
measurement methodology by monitoring transfer functions and fretting thresholds was 
provided. The relationship between applied excitation levels and fretting rates was 
examined. The results of this study exhibited threshold behavior at each frequency for the 
onset of fretting degradation. Typically a plateau region was observed where similar g-
levels produced similar fretting rates. It was also found that outside the plateau region the 
g-levels varied according to the dynamic behavior of the mechanical system. In addition, 
a transfer matrix model was used to analyze these results. An empirical fit of the data 
correlated well with the model when damping was used. This analysis revealed the 
importance of the bending moment induced at the contact interface as a result of 
excitation levels and tie-off configurations. Consequently, it is concluded that dynamic 
response of the mechanical system under various g-levels and tie off configurations can 
greatly impact the performance of a connector system subjected to vibration stresses.          
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9 
             A different method for measuring the relative motion that causes fretting 
corrosion was reported recently. In 2005, Lam et.al [27] used a novel thick film sensor to 
measure the displacement at the connector interface to test for environmental influences 
on electrical contact fretting. The sensor was assembled into a connector sample, 
replacing the male component. When the interface experienced movement, the relative 
displacement of the contact point caused a corresponding linear change in the resistance 
measured across the male and female connection. The sensors were validated by a series 
of experiments and subsequently used in a field test to establish the relationships between 
the fretting effects and temperature, humidity and differential pressure. The group found 
that the variation in differential pressure dominated the movement behavior at the contact 
interface of the well-sealed connector sample, while temperature and humidity had 
negligible influences on the measured relative displacement. 
 Another similar work was conducted by N. Ben Jemaa and E. Carvou [28] in 
France in 2006. The purpose of this study was to examine conjointly the wear amount 
and electrical behavior of connector terminal under vibration and higher current stress. 
During this experiment, the spring lamellas were firmly attached to a fixed support under 
high number of vibrations (103 to 106). High frequency oscillation (100Hz) with 
amplitude of 50?m was used. The contact area was made with copper alloy and coated 
with 2ptm of tin. The contact was inserted in resistive circuit supplied by 20V and 3A 
and the contact voltage was then measured and observed in real time with a fast sampling 
oscilloscope. Finally, the main results showed that at low level of wear observed during 
the earlier stage of fretting corresponded to pure constriction voltage less than 20mV. 
However after this initiation period as the wear is increased, the contact voltage increased 
?
10 
and reached a few hundred milli-volts (melting and fritting voltage). In a later stage of 
degradation, an arcing voltage due to bounce phenomena was detected at about 12V. This 
short arc, observed for the first time in the fretting area under power could accentuate the 
wear and fretting degradation process on power connectors. 
Although many studies have been done for fretting corrosion based on exhausted 
experiments, it is a very difficult task to develop models to predict contact resistance 
behavior under fretting corrosion. In 1994, Bryant [29] developed a comprehensive 
model to predict the contact resistance during the nth fretting cycle and the ultimate 
usable lifetime of the contact. Different aspects such as contact wipe, fretting vibration 
amplitude and frequency, contaminant chemistry, material properties, plating thickness, 
asperity deformations, normal load, electrical load, and surface topography were 
considered in this model. It was based upon two corrosive fretting failure mechanisms: 
one involving the filling of surface valleys with wear debris generated by fretting while 
the other one involving the contamination of surface asperities by the corrosion product. 
Both showed estimates that were within an order of magnitude of the observed values for 
fretting tests and field failures. The model assumed that as fretting motions pull the 
exposed corroded asperities back together, a mismatch in size occurs and some of the 
corrosive products are scraped off and deposited in the valleys. Eventually, the valleys 
are filled and the a-spots are separated, resulting in ultimate failure. In contrast, a material 
balance between the amounts produced and scraped off was used to estimate the amount 
of corrosive product dragged into the contact. Shifting of molecules via plastic 
deformation mixes particles of corrosive product into the asperity metal. This model 
calculated the amount of corrosive product produced on the exposed surfaces during the 
?
11 
separation phase of a cycle of fretting. Assumptions that correlate mixing to plastic flow 
and the use of modern composite theory led to an estimate of the conductivity within the 
contaminated asperity. Integration over the asperity volume gave the asperity resistance, 
and then Greenwood?s theory was used to estimate the total contact resistance.  
            In the early 1990s, Malucci [30][31] refined and combined two previously 
developed models dealing with contact resistance and oxide build-up under fretting 
conditions respectively into a single analytical model. This model was then used to 
predict the average effects of contact force and fretting amplitude on contact degradation. 
The results from fretting tests on specially prepared tin plated contacts were explained 
within the framework of this model. This study found that decreasing contact force or 
increasing fretting amplitude produced increased degradation and this was explained in 
terms of an increase in oxide buildup due to either asperity deformation (lower forces) or 
an increase in the number of asperity deformations per cycle (longer fretting amplitude). 
In addition, the data from thermal shock experiments were analyzed to determine the 
relationship between the temperature swing (?T) and acceleration factor. He concluded 
that the assumed connection between the temperature swing and fretting amplitude was 
consistent with both the fretting probe data and the thermal shock tests. These results 
provided a basis for modeling the degradation rate in terms of fretting cycles and the 
temperature swing. Consequently, this model was developed sufficiently to estimate the 
acceleration factor for a given set of laboratory test parameters to simulate field 
degradation. 
             As mentioned in Chapter 1.2, the finite element method is widely used in 
engineering including fretting corrosion area.  For instance, in 1996 Villeneuve et.al [32] 
?
12 
from the Ford Motor Company used FEA to simulate the terminal crimping process for a 
vehicle connector. In this study, the terminal grip cross section, the punch tooling and the 
wire strands were modeled. The grip was forced into the punch while sitting on an anvil, 
mimicking the real life application. The results of the study showed that the friction 
between the grip surface and the punch surface is crucial to the formation of a ?good? 
crimp. The model also showed that the crimping process is a combination of both the 
plane stress and plane strain conditions. In 2005, Monnier et.al [33] used finite element 
analysis to simulate the behavior of a sphere-plane electrical contact when a high current 
flowed through it, taking into account the mechanical, electrical and thermal coupling 
involved. Several analytical expressions were used in the simulation and the model 
validity was confirmed by experimental results. The simulation also gave the contact 
terminal voltage, the contact resistance of the system and the solid temperature, which are 
impossible to measure experimentally.  
 In 2008, Jackson et.al [34] provided a multi-physics (structural, electrical and 
thermal) finite element model of the bulk region of an electrical connector. This model 
was developed based upon a multi-scale sinusoidal rough surface (MSRS) contact model 
using a MATLAB
TM
 code that communicates with ANSYS
TM
. The resulting coupled 
multi-physics connector model was then used to analyze the performance of the 
connector under certain current range. Finally, the result showed that there was a 
significant proportional rise in voltage drop and temperature across the bulk regions of 
the connector parts. Therefore, it is proved that this coupled multi-physics model together 
with the MSRS model had greater accuracy in the prediction of contact forces, electrical 
contact resistance (ECR) and thermal contact resistance (TCR).  
?
13 
             Currently, many universities and companies around the world are conducting 
important research on electrical contacts. These universities include Auburn University, 
Drexel University, Georgia Institute of Technology, Pennsylvania State University, 
University of Florida, University of North Carolina, University of Maryland (USA), 
Beijing University of Posts and Telecommunications, Beijing University of Technology, 
Harbin Institute of Technology, Huazhong University of Science&Technology, Xi?an 
Jiaotong University(China), the University of Manchester, the University of Southampton 
(England), Uppsala University, Linkoping University (Sweden), the University of Rennes 
(France), Vienna University of Technology (Austria), the University of Aarhus 
(Denmark), Nanyang Technology University (Singapore), Tver State University of 
Technology (Russia), the University of Tokyo, Keio University, Ishinomaki Senshu 
University, Keio University, Mie University, Nippon Institute of Technology, Shizuoka 
University (Japan), and so on. The large companies and research centers include Eaton 
Corporation, Molex Incorporated, AMI Doduco, Checon Corporation, Chugai USA, 
Rockwell Automation, MOOG Components Group, Delphi Research Labs, Sandia 
National Laboratories, and so on. The research fields covered include arc materials [35]  , 
arc interruption [36], power [37] connector fretting corrosion [38], modeling [39] MEMS 
in contacts [40], fundamental research [41], sliding [42], automotive contacts [43] and 
safety issues [44]. 
?
14 
CHAPTER 2 A STUDY OF VIBRATION-INDUCED FRETTING 
CORROSION IN A SINGLE BLADE/RECEPTACLE CONNECTOR PAIR 
2.1 Introduction  
 Fretting corrosion is generally recognized as one of the major failure mechanism 
for electrical connector systems. The importance, necessity, history and current status of 
fretting corrosion study have been introduced in chapter one. At present, most evaluations 
of the fretting propensity of particular connector designs and the influence of variations 
in those designs on fretting performance are conducted through exhaustive experimental 
testing, which requires a major commitment of time and resources. Thus, a simulation-
based method for a single blade-receptacle connector pair would therefore be of great 
value to those working on connector design and applications. In 2002, Flowers and Xie 
investigated a series of interesting behaviors on the topic of vibration-induced fretting 
degradation, especially a threshold vibration level for the onset of fretting and a strong 
relationship between vibration amplitude (beyond the threshold level) and the rate of 
resistance change[26][38][45]. The present study is the next step of this effort.  
 The main objective of this study is to develop and validate a methodology using 
modeling and simulation technology to predict the influence of various design factors on 
vibration-induced fretting propensity in electrical contacts. The procedure seeks to use 
finite element models for the connector system to relate the actual dynamics of the 
contact interface to the threshold vibration levels required for the onset of fretting and the 
?
15 
relative motion transfer function. Xie et.al [45] developed a two dimensional (2-D) model 
in ANSYS based on the typical single blade/receptacle connector pair configurations and 
the model was then adjusted and utilized for the evaluation of fretting propensity of this 
connector system by the author. A series of simulations of relative motion transfer 
functions and threshold levels were performed on this model as a function of excitation 
frequency, wire tie-off length, supplementary mass, interface friction coefficient and 
contact normal force. Corresponding experiments were also conducted to validate and 
test the simulation methodology. Finally, the results from the simulation are introduced 
and compared with the results from the experiment. All the details of this work are 
described in the sections below. 
2.2 Experimental Configuration 
2.2.1 Experimental Samples 
 A typical type of single blade/receptacle connector pair is used in this study. As 
shown in Figure 2-1, the sample basically consists of two parts: the blade part on the left 
and the receptacle part on the right. Inside the receptacle part, there is a spring component 
connected to the top front inner layer of the receptacle. A gap exists between the end of 
this spring and the inner layer of the bottom of part. When the blade is inserted into the 
receptacle as shown in Figure 2-2, because the height of this gap is less than that of the 
blade, the spring is forced to bend and generate the contact force, forming the contact pair.  
?
16 
 
 
 In order to investigate the influence of different friction coefficient and contact 
normal forces on the fretting propensity, six different types of samples were used in total. 
Table 2-1 summarizes the basic sample descriptions. Both finish type 1 and finish type 2 
were based upon tin deposits, with the type 2 finish having been modified to reduce the 
coefficient of friction (from 0.55 to 0.33) and the corresponding insertion force. In each 
finish type, three different gaps sizes (0.53mm, 0.48mm, 0.43mm) of the receptacle parts 
were used to represent different contact normal forces. 
?
Figure 2-2: Mated blade/receptacle pair 
?
Figure 2-1: Photograph of the blade and receptacle parts 
?
17 
 
2.2.2 Experimental Equipment 
 The experimental equipment used in this study include a Keithley Model 2010 
multimeter, which is used for the measurement of connector resistance values; Polytec 
laser vibrometers systems, which measures the displacements of the selected locations on 
connector samples; an HP 35665A dynamic signal analyzer, which could generate 
different types of excitation signals (such as random noise, sine wave, etc)  for the shaker 
and analyze the frequency response; a vibration system, which consists of a Dactron 
vibration control system, a PA500L Amplifier and a V408 Shaker. The details of these 
major components are described below. 
2.2.2.1 Keithley Model 2010 Multimeter 
 The Model 2010 is a 7
1
/
2
-digit high-performance digital multimeter. It has 
0.0018% 90-day basic DC voltage accuracy and 0.0032% 90-day basic resistance 
accuracy [46]. During the testing, the multimeter was working in four-wire mode with a 
resistance measurement range of 1u? to 120M?.  
 Moreover, the dry circuit method was introduced as shown in Figure 2-3. It is a 
typical type of low resistance measurement method which is made on contact devices 
Table 2-1: Different types of experimental samples 
Specimen Type Finish Gap Size 
(mm) 
Normal Force 
(N) 
Friction 
Coefficient 
1.a 1 0.53 4.7 0.55 
1.b 1 0.48 6.0 0.55
1.c 1 0.43 6.5 0.55 
2.a 2 0.53 4.3 0.33
2.b 2 0.48 5.3 0.33 
2.c 2 0.43 6.3 0.33
 
?
18 
such as switches and relay contacts. The purpose of this method is to determine whether 
oxidation has increased the resistance of the contacts. If the voltage across the contacts 
during the test is too high, the oxidation will be punctured and render the test meaningless. 
Therefore dry circuit testing limits the voltage across the DUT to 20mV or less. 
 
2.2.2.2 Polytec Laser Vibrometer System 
 As shown in Figure 2-4, the Polytec laser vibrometer system was used in the 
experiment for the non-contact displacement measurements [47]. The system consists of 
two Polytec OFV 353 sensor heads (lasers), two Manfrotto tripods to hold the lasers and 
two Polytec OFV 2610 controllers. The system provides the means for a displacement 
measurement according to the fringe counter principle. An analog voltage signal is 
available at its output that is proportional to the vibration amplitude of the measurement 
object. This signal can be visualized with an oscilloscope or can be entered into a data 
acquisition and processing system, such as the HP 35665A dynamic signal analyzer.  
Table 2-2 shows its displacement decoder specifications.  
?
Figure 2-3: Four-wire dry circuit resistance measurement 
?
19 
 
 
2.2.2.3 HP 35665A Dynamic Signal Analyzer 
 The picture of HP 35665A dynamic signal analyzer is shown in Figure 2-5. It is a 
two-channel fast Fourier transform (FFT) spectrum/network analyzer with a frequency 
range that extends from 0.19531 Hz to 102.4 kHz in the single channel mode and from 
0.097656 to 51.2 kHz in the two channel mode [48]. The analyzer has a built-in signal 
source providing random noise, burst random noise, periodic chirp, pink noise, and fixed 
sine. Measurements can be saved to an internal 3.5-inch flexible disk drive, or an external 
Table 2-2: Displacement decoder specification of the laser vibrometer system 
Measurement 
Range 
Full Scale Output 
(Peak-to-Peak) 
Resolution Max. 
Vibration 
Frequency
Max. 
Velocity 
Max. 
Acceleration
?m/V mm ?m kHz m/s g 
20 0.32 0.08 20 1.6 20,000 
80 1.3 0.32 20 1.6 20,000
320 5.2 1.3 20 1.6 20,000 
1280 20.5 5 20 1.6 20,000
5120 82 20 20 1.6 20,000 
?
Figure 2-4: Photograph of the Polytec laser vibrometer system 
?
20 
HP SS-80 disk drive, or can be directly printed out. The main characters of this analyzer 
used in this study are listed as below:  
 Input Noise Level: < -140 db 
 Full Span FFT Noise Floor: < -76 db (-85 db typical) 
 FFT Cross-Channel Gain Accuracy: ? 0.04 db (0.46%) 
 FFT Cross-Channel Phase Accuracy: ? 0.5 degree 
 Minimum Frequency Resolution: 122 ?Hz (Two Channel Mode) 
 
2.2.2.4 Vibration System 
 The vibration system used in this study consists of a PA500L Amplifier and a 
V408 Shaker, as shown in Figure 2-6 and Figure 2-7 respectively. The shaker is vibrating 
vertically and a set of fixtures are designed and attached on the shaker for the 
experimental setup.  
?
Figure 2-5: Photograph of HP 35665A dynamic signal analyzer 
?
21 
 The configuration of the vibration control system is shown in Figure 2-8. The 
vibration system generates time-domain signals that contain the required frequency-
domain characters or profile and sends them to the amplifier. The powerful amplified 
signal, with a larger current and voltage, then drives the shaker to vibrate. The 
accelerometer mounted on the payload senses the vibration on the shaker and converts it 
into an electrical signal, which is sent back to the vibration control system. The vibration 
control system deals with this time-domain signal and transfers into the frequency 
domain by FFT. The control system then compares the frequency-domain characteristics 
of this signal with the original setting. If they are different, the vibration control system 
will adjust its output signal accordingly. This process repeats until the frequency-domain 
characteristics of the signal on the shaker match the required characteristics specified by 
the original setting. 
 
 
?
Figure 2-6: PA 500L amplifier 
?
22 
 
 
 
?
Figure 2-8: Typical vibration system 
?
Figure 2-7: V408 shaker 
?
23 
2.2.3 Experimental Setup 
 Two different types of experiments were conducted in this study. One is the 
transfer function measurement and the other one is the fretting threshold (resistance 
change) measurement. Details of the two experimental setups are described in the 
following sections. 
2.2.3.1 Transfer Function Measurement 
 It is generally agreed that relative motion between contacting terminals is the root 
cause of fretting corrosion. Flowers, et.al.[38][45][51][52] provides a description of the 
electrical measurement methods and test procedures for determining fretting thresholds 
and transfer functions. The transfer function for each sample is determined by comparing 
the output vibration response at the connector interface to the input excitation at the 
vibratory shaker head. The ratio of the steady-state output amplitude to the input 
amplitude for a given excitation frequency is the magnitude of the transfer function at 
that frequency.  The phase difference between the steady-state output and input responses 
for a given frequency is the phase of the transfer function at that frequency.  
 From a dynamic modeling perspective, a transfer function is a functional 
relationship, in the frequency domain, between the magnitude (M) and phase (?) of an 
input motion and the corresponding output motion. For example, a transfer function 
magnitude of 1 and zero phase shift indicates that there is no relative motion between the 
respective input and output measurement points. Similarly, a transfer function with a 
magnitude of 2 and a 45?phase indicates that the output motion is twice as large as that of 
the input and that it lags the input response by 45?.  For most dynamic systems, there is a 
peak magnitude for input excitations at one or more of the resonant frequencies. 
?
24 
Typically, the phase shift is small for low frequency excitations and increases 
dramatically as the driving frequency approaches and exceeds the primary resonance 
value. Another way of thinking of the transfer function is in terms of a complex number 
where the real part is M cos (?) and the imaginary part is M sin (?). Therefore, the 
transfer function can be expressed by the following equation: 
 Transfer Function = M*cos(?) + i*M*sin(?) or M? ?                                          (1) 
 Based on the above transfer function, the relative motion between the two-half 
interfaces is defined by: 
                                     
22
)]sin([)]cos(1[ ?? MMZ
F
+?=                                            (2) 
where Z
F 
is the relative motion, and M cos (?) and M sin (?) are the real part and 
imaginary part of the transfer functions, respectively. 
 Figure 2-9 shows the basic setup of the transfer function measurement for the 
blade/receptacle connector pair. Because the front-half connecter interface is fixed at the 
shaker head, its input displacement is the same as for the shaker head. Therefore the 
reflector for the input measurement was taped on the top of blade right next to the 
receptacle after mated while the output reflector was taped on the top of the receptacle, as 
shown in Figure 2-10. A wire leads 230mm in length was attached to the receptacle 
samples those were to be tested. A group of three steel balls was attached to the wire lead 
by using the heat shrink tube to serve as a supplementary mass to lower the natural 
frequency and increase the fretting propensity of the system. Without the addition of the 
supplementary mass, it was very difficult to impart sufficient energy to the system to 
produce fretting. These small diameter (2.5mm diameter) steel balls were attached to the 
wiring lead 13.0mm from the junction with the receptacle. The blade to be tested was 
?
25 
firmly attached to the shaker head with a clamp, as shown, while the receptacle was 
mated to the blade, with the other end of the wire lead clamped to a fixed (non-vibrating) 
table. Vertical driven motion (random noise) was input to the shaker head. The 
displacement of the blade and receptacle were then measured using the non-contacting 
laser displacement measurement system as described in the previous section.   
                                                                        
  
Figure 2-9: Experimental setup of the transfer function measurement 
?
26 
 
2.2.3.2 The Fretting Threshold Level Measurement 
 The setup of the fretting threshold level measurement is shown in Figure 2-11 and 
Figure 2-12. The blade and receptacle are clamped the same way to the shaker table as in 
the previous transfer function testing. In order to measure the resistance of the connector 
pair and minimize the effect of magnetic field, the electrical wire in the receptacle part 
was clamped in the fixture while the other wire connected in the blade part was bent and 
secured to the top of the fixture the shaker table. Another reason of putting the both ends 
of the electrical wire close is because the four gator connectors and measuring wires of 
the multimeter should be placed closer so that the wires could be plaited together to 
minimize the circuit loops. Sinusoidal signals were generated from the control system, 
and the real-time resistance change was then observed and recorded by a computer 
system with a Labview program.                    
 
Figure 2-10:  Detailed view of displacement measurement 
?
27 
 
 
Figure 2-12: Photograph of the resistance measurement 
?
Figure 2-11: Photograph of the fretting threshold levels experiment setup 
?
?
28 
2.3 Finite Element Model 
 An ANSYS [11] finite element simulation model was developed based on the 
same samples and experimental configurations as those introduced in the previous part of 
this chapter. A two-dimensional (2-D) simplified model was used in order to reduce the 
number of elements and increase simulation speed. The geometric model was generated 
according to the detailed CAD drawings of the single blade/receptacle connector pair 
with proper material properties which were first measured from the real experiment and 
then adjusted according to the 2-D geometry. Different mesh controls for mesh 
convergence and simulation precision were assigned to the different parts of the model 
depending on its geometry and importance. Two simulation method, harmonic and 
transient simulation, were utilized to simulate the transfer function and fretting process 
respectively. Details of the modeling study are described in the sections below. 
2.3.1 Geometric Model 
 The 2-D model was generated to simulate the real single blade/receptacle 
connector pair configuration in the experiment. The dimensions of the geometric model 
followed those of the real blade/receptacle sample, wire and balls used. Figure 2-13 and 
2-14 show the overall view and a close-up view of the 2-D model, respectively. In Figure 
2-13, the blue part on the left represents is the blade; the cyan part on the right represents 
is the receptacle and its leading wire; the yellow parts on top of the wire are the 
supplementary balls. Detailed geometry of each part is shown in Figure 2-14. The 2-D 
model consists of seven parts in total: blade, U-bend, cantilever beam spring, receptacle 
(outer structure), crimp, supplementary mass and wire. 
?
29 
 
 
 As just mentioned before, most of these geometric parts are used exactly the same 
dimensions as the real components besides the outer structure of the receptacle. The real 
outer structure of the 3D receptacle was composed of four metal pieces and served as a 
?box? for the blade to be inserted into. Both the annulus and the spring component are 
inside the box. Obviously, the metal pieces on the two sides of the receptacle can restrict 
the displacement of the upper and bottom pieces in the reality. However, for the 
limitation of 2-D plane model, these two pieces on both sides cannot be included. 
Therefore, the stiffness of the outer structure of the receptacle was adjusted to be 
 
Figure 2-14: Close-up view of the 2-D geometric model 
?
X
Y
Z
Figure 2-13: Overall view of the 2-D geometric model 
?
30 
significantly high in order to fix the two sides as that of real situation. Therefore the 
Young?s modulus of the outer structure was set to a very large value. 
 As shown in Table 2-3, most thickness values of the components in the geometric 
model are the same as those of the real parts. However, 1.12mm was not the real 
thickness of the wire. This is because when the thickness value was applied to the wire, it 
would generally extrude according to the thickness value and thus the cross section of the 
wire would be a rectangle instead of a circle. Due to this geometric change, it is important 
to make sure that the I
equivalent
 * E
equivalent
 for the 2-D wire model was equal to the I
real
 * 
E
real
 for the real wire, where I is the wire?s inertia moment (a function of its dimensions) 
and E is its Young?s modulus. This requirement resulted in the 2D wire being assigned a 
thickness of 1.12mm. 
 
 
Table 2-3: Material and dimensional properties of the model components 
Components Thickness Density Modulus of
Elasticity 
Blade (portion inside the 
receptacle) 
1.5 mm 8910 kg/m3 130 GPa 
Blade (portion 
outside the receptacle) 
1.5 mm 6974 kg/m3 130 GPa 
U-bend portion of the 
cantilever beam 
1.9 mm 8910 kg/m3 130 GPa 
Cantilever beam spring in 
the receptacle 
1.5 mm 8910 kg/m3 130 GPa 
Receptacle (excluding spring 
member) and 
part of wire under the crimp 
2.6 mm 8794 kg/m3 130 GPa 
Wire portion outside the 
crimp 
1.1 mm 4564 kg/m3 96.5 GPa 
Supplementary mass (balls) 2.6 mm 12,876 kg/m3 195 GPa 
?
?
31 
 2.3.2 Material Properties 
 The values of material properties used in the 2-D model are also shown in Table 
2-3. Due to the changes of dimensions of thickness of certain parts, the material 
properties of each component were adjusted to the corresponding values from the real 
connector samples to ensure the correct functioning of the model. The density of the 
blade, receptacle and balls remained the same as the real values because that they has the 
same weights as their real world counterparts. The weights and the volume of some other 
components had also changed, particularly the outer structure of the receptacle and the 
wire. Hence, their densities also had to be adjusted to match the weights of the original 
samples in experiments.  
 As mentioned in the previous section, the Young?s modulus for the outer structure 
of the receptacle was set to a very large value to constrain this structure (excluding the 
annulus and spring inside the receptacle) from deforming when the blade was being 
inserted into the receptacle. A series of initial simulations have been performed to select 
the necessary Young?s modulus value. The results revealed that this value had to be 
increased to 1000 times larger than the original value to obtain the same function. 
2.3.3 Boundary Conditions 
 The boundary conditions applied to the 2-D model were set up to match the real 
conditions with respect to the experimental configuration and vibration. As shown in 
Figure 2-11, the blade was clamped on the shaker head and the end of the wire (which 
was attached with the receptacle) was also clamped onto the fixture. During the vibration, 
the blade and the shaker head moved back and forth vertically (along the y-axis in the 2-
D model) as a sinusoidal driven motion. Consequently, in the 2-D model, the end of the 
?
32 
wire was fixed in all degree of freedom while the end of the blade was constrained in x-
axis and z-rotation to vibrate only in the y-axis. A sinusoidal function was utilized to the 
y-axis motion to simulate the real vibration process. Each vibration cycle was evenly 
divided into forty small substeps to ensure the accuracy of the simulation analysis. 
Moreover, the small substep intervals made it easier to obtain the solving convergence. 
No restraint was needed on the receptacle in both experiment and simulation. Figure 2-14 
and Figure 2-15 show all the boundary conditions assigned to the 2-D model and the 
profile of the sinusoidal vibration excitation with the load substeps respectively. 
 
1
X
Y
Z
                                                                                
AUG 29 2006
13:22:56
ELEMENTS
U
?
Figure 2-15:  Geometric model for the blade/receptacle configuration 
?
?
33 
 
2.4 Vibration Process Simulation  
 As shown in Figure 2-17, the excitation of the sinusoidal vibration at the blade 
produced motion in the wires and the supplementary mass (balls). In turn, that motion 
caused motion of the receptacle and at the connector interface. Figure 2-18 and Figure 2-
19 show the motion of the receptacle, which clearly indicates that the receptacle rocks 
(rotates), rather than simply sliding along with the blade. Therefore, rocking was found to 
be the main mode for the receptacle?s motion. 
0 0.005 0.01 0.015 0.02
-1.5
-1
-0.5
0
0.5
1
1.5
           Time (sec)    f=50Hz
Am
pl
i
t
ude (
m
m
)
 
Figure 2-16: Sinusoidal vibration excitation with the load substeps 
?
34 
 
 
 
1
X
Y
Z
                                                                                
SEP 21 2006
12:19:57
DISPLACEMENT
STEP=1
SUB =38
TIME=.02375
DMX =.003159
?
Figure 2-18:  Motion of the blade and the receptacle at time 1 
1
X
Y
Z
                                                                                
SEP 21 2006
12:09:44
DISPLACEMENT
STEP=1
SUB =52
TIME=.0325
DMX =.003558
?
Figure 2-17:  Full model motion at Time 1 during vibration 
?
?
35 
 
2.5 Experiment and Simulation Results 
 Based on the experimental configuration and 2-D model generation described 
above, concurrent simulation and experimental studies were performed to evaluate the 
dynamic response and the threshold vibration levels as a function of excitation frequency, 
interface friction coefficient, contact normal force, supplementary mass and wire tie-off 
length. Detailed analysis of the results is discussed in the sections below. 
2.5.1 Transfer Function Results 
 As described in section 2.2.3.1, the relative motion between the contacting 
sections is generally agreed to be the basic inducement of fretting degradations. 
Therefore the transfer function in a certain frequency domain which is recognized as the 
indicator of dynamic response of the system and the relative motion between contacting 
terminals is observed in both of the experimental and simulation studies instance. In the 
1
X
Y
Z
                                                                                
SEP 21 2006
12:21:54
DISPLACEMENT
STEP=1
SUB =52
TIME=.0325
DMX =.003558
?
Figure 2-19:  Motion of the blade and the receptacle at time 2 
?
?
36 
transfer function simulation, the input and output measurement locations remained the 
same as the locations of the transfer function measurements in the experiment. In this 
particular model, the input location was on the node 124 (input node) and the output 
location was on node 743(output node), as shown in Figure 2-19. These two nodes 
corresponded to the two locations where the laser spots measured the transfer function in 
the experiment. 
 
 Example transfer functions of the Type 1.a and Type 2.a configurations for 
different friction coefficient (0.55 and 0.33 respectively), obtained both experimentally 
and using the simulation model, are shown and compared in Figure 2-21. The transfer 
functions generated by the 2-D model for the Type 1 and Type 2 connector finishes were 
very similar to each other and they generally matched the experimental measured values 
well, particularly for the lower frequency range (around the first resonant peak).  The 
reason why these two types of finish contact pairs had a similar transfer function was due 
to the main motion mode, in other word, the first vibration mode of the receptacle being 
the rocking mode. This rocking motion mode minimized the effect of differences in the 
?
Figure 2-20: Node locations for the transfer function simulation  
?
37 
friction coefficient at the contact interface due to the different surface finishes on the 
connectors. During the author?s study, it was also observed that this mode minimized the 
effect of differences in the contact normal forces between the blade and the spring. As 
shown in Figure 2-22 and Figure 2-23, both experiment and simulation results show that 
the differences of overall shape and resonant peak of the transfer functions for different 
contact normal forces are very similar. However, it is still could be observed that the 
simulation results show less variation comparing with experiment results. This is because 
of the adjusted high stiffness of the outer structure as described in section 2.3.1. 
 
20 30 40 50 60 70 80
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
an
s
f
er
 F
unc
t
i
on
 
 
Type1--from experiment
Type2--from experiment
Type1--from simulation
Type2--from simulation
?
Figure 2-21: Transfer function results from experiment and 2-D model simulation for 
different friction coefficient 
 
?
38 
 
 A series of experiment testing was performed to study the ?slippage? effect of the 
friction at the contact interface in the experiment. Figures 2-24 and 2-25 show the 
transfer functions that were obtained for selected vibration amplitudes for the Type 1 and 
Type 2 samples, respectively. For the Type 1 samples with a higher friction coefficient, 
20 25 30 35 40 45 50 55 60 65 70
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
an
s
f
e
r
 F
u
nc
t
i
o
n
 
 
Type a
Type b
Type c
 
Figure 2-23: 2-D simulation results for different contact normal force levels 
20 25 30 35 40 45 50 55 60 65 70
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
an
s
f
e
r
F
u
nc
t
i
on
 
 
Type a
Type b
Type c
?
Figure 2-22: Experimental results for different contact normal force levels  
?
39 
the effect of increasing the input amplitude is clearly observable but does not tend to 
greatly alter the overall shape of the transfer function. The peak of the first resonant 
frequency did shift to the left as the increment of vibration displacement. The difference 
between the lowest and the highest peak amplitudes of transfer functions is about 10%.  
This is due to the slippage at the contact interface, which results in a somewhat longer 
cable length and a lower cable tension. However, for the Type 2 samples, the effect of 
different vibration displacements is much more dramatic as shown in Figure 2-24. These 
samples have a much lower contact friction coefficient compared to the Type 1 samples. 
The peak of the first nature frequency has a significantly larger shift than the Type 1 
results. Moreover, the difference between the lowest and the highest peak amplitudes of 
transfer functions is about 25%. It should also be noted that, for both sample types, 
decreasing the amplitude below the smallest value shown (0.082 mm) did not result in 
any observable shifting of the resonant peak. Therefore, as one could intuitively expect, 
the ?slippage? effect at the contact interface was generally reduced for the higher friction 
finish (Type 1).   
?
40 
 
 
 As mentioned in previous sections, several simulation studies were performed 
with the goal of understanding the predicted effects of wire length and supplementary 
20 30 40 50 60 70 80
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
T
r
a
n
s
f
er F
unc
t
i
o
n
Frequency(Hz)
 
 
0.082mm
0.100mm
0.180mm
0.326mm
?
Figure 2-25: Experimental results showing the variation of transfer function with 
excitation amplitude for Specimen Type 2.a 
 
?
20 30 40 50 60 70 80
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
a
n
s
f
er F
unc
t
i
o
n
 
 
0.082mm
0.100mm
0.180mm
0.326mm
?
Figure 2-24: Experimental results showing the variation of transfer function with 
excitation amplitude for Specimen Type 1.a 
?
?
41 
mass on the behavior of the transfer function.  The results are presented as relative 
motion transfer functions. The definition of the relative motion transfer function was 
discussed in section 2.2.3.1. 
 Figure 2-25 shows the effect of changing cable tie-off length. As the tie-off length 
is decreased, the resonant peak shifts to the right and tends to becomes somewhat higher 
in amplitude.  This effect is due to a relative decrease in system internal damping, which 
comes primarily from the wiring. 
 
 Figure 2-26 shows the simulation results of predicted effects of supplementary 
mass on the relative motion transfer function. As the supplementary mass is increased, 
the resonant frequency shifts to the left and the amplitude of the resonant peak increase 
dramatically. This trend provides an explanation for the difficulty in obtaining fretting for 
samples without supplementary mass. That is, the relative motion in the frequency and 
amplitude range of interest is too small to produce significant fretting degradation.  
20 30 40 50 60 70
0
0.05
0.1
0.15
0.2
0.25
Frequency(Hz)
R
e
l
a
t
i
v
e
 
M
o
t
i
on T
r
ans
f
e
r F
u
nt
i
o
n
 
 
Wire Length =126mm
Wire Length =156mm
Wire Length =186mm
Wire Length =216mm
?
Figure 2-26: Simulation of relative motion transfer functions for various wire tie-off 
lengths (Specimen Type 1.a) 
?
?
42 
Substantial additional vibration energy would have to be put into that sample 
configuration in order to exceed the threshold levels required for the onset of fretting, as 
discussed by Malucci [53]. 
 
2.5.1 Fretting Threshold Results 
 The threshold fretting level for a given configuration and vibration frequency is 
determined by exposing samples to differing amplitudes of vibration and measuring the 
resistance for two minutes. For all electrical resistance measurements, the four-wire 
configuration was used as described in section 2.2.2.1.  The resulting time trace is then 
visually inspected.  If there is no net increase in resistance over the time period of the test, 
the sample is deemed to have not fretted. A fresh sample was then tested, with the 
vibration amplitude increased by an increment of 0.1mm and the inspection process 
repeated until a net increase in the resistance of greater than 5x10
-6
ohm/sec is observed. 
The lowest vibration amplitude for which such a net increase in resistance is observed is 
20 30 40 50 60 70
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Frequency(Hz)
R
e
l
a
t
i
v
e
 
M
o
t
i
o
n
 T
r
a
n
s
f
er F
unc
t
i
on
 
 
Supplementary mass=0g
Supplementary mass=1.5g
Supplementary mass=3g
Supplementary mass=6g
 
Figure 2-27: Simulation of relative motion transfer functions for various levels of 
supplementary mass (Specimen Type 1.a) 
?
43 
designated as the threshold g-level for that sample. For each configuration and frequency, 
a minimum of 5 samples are tested and the threshold g-levels averaged to obtain the 
nominal threshold g-level for that configuration and frequency.  
 By using the method described above, a series of fretting threshold experiments 
have been performed on all six different types of connector samples. Figure 2-28 shows 
an example of how the threshold displacement value was determined using the change in 
resistance curves. In this example, the Type 1.a samples were tested under different 
vibration amplitude at the frequency of 45Hz. It could be observed that below 0.8mmpk, 
which signifies a vibration amplitude of 0.8mm peak-to-peak at the shaker head, the 
trends of the resistance change curves are generally flat. Once the displacement reached 
0.8mmpk, however, the trend began to rise and after 0.8mmpk, the trends continued to 
increase. Consequently, 0.8mmpk was determined to be the threshold displacement at the 
shaker head for the type1 connector with a 0.53mm gap at 45Hz. The other contact pairs 
were also characterized in the same way.  The reason of the increase is the accumulation 
of Sn oxidations as described in Chapter 1.  
?
44 
 One interesting phenomenon observed in the fretting threshold experiments was 
that even for the flat resistance curves, such as curves for vibration amplitudes smaller 
than 0.8mm peak-to-peak, the resistance values still varied periodically like a repeated 
half sine wave (first 180 degrees phase).  For example, for the curve Type1-45Hz-
0.6mmpk, the entire trend is flat with a resistance changes in a period of roughly 10 
seconds. Obviously this is not due to the changing amplitudes of vibration because the 
frequency of vibration is 45Hz, which is a period of about 0.022 second. Part of the 
reason of this phenomenon is the effects of magnetic field from the shaker. Besides that, 
Another possible guess to explain this phenomenon is the ?build-up? and ?break-down? 
process of the insulating Sn oxidations. According to the surface analysis, the Sn board 
finish is generally a combination of SnO, SnO2, Sn (elemental), and Sn-OHx[57]. As the 
vibration process started, the Sn oxidations start to be worn away from the contact 
surfaces and accumulated at the edge. As shown in Figure 2-29, the marked spot is one 
accumulation area. As more and more insulating debris stacked together, the height and 
0 20 40 60 80 100 120
0.0135
0.014
0.0145
0.015
0.0155
0.016
0.0165
0.017
0.0175
0.018
0.0185
           Time (sec)   Sine test 
R
e
si
st
ance (
O
hm
)
Type1-45Hz-0.4mmpk-1.64g
Type1-45Hz-0.5mmpk-2.05g
Type1-45Hz-0.6mmpk-2.46g
Type1-45Hz-0.7mmpk-2.87g
Type1-45Hz-0.8mmpk-3.28g
Type1-45Hz-0.9mmpk-3.68g
Type1-45Hz-1.0mmpk-4.09g
Type1-45Hz-1.1mmpk-4.50g
Type1-45Hz-1.2mmpk-4.91g
 
Figure 2-28:  Identification of the threshold displacement (or g-level) 
 
?
45 
volume of the accumulation generally increased which resulted in the increment of the 
contact resistance. This is the ?build-up? process, roughly first 5 seconds of each period. 
However, this higher ?stack? also resulted in higher contact normal forces and 
corresponding higher shear stress due to the sliding effect. Therefore, as the value of the 
shear stress reached certain critical value, the stack started to ?break down? and the 
resistance decreased. This explains the second half of the resistance decrease period. 
Further study might be needed to prove this hypothesis. 
 
As observed in previous studies [45][51][52], the inverse relative motion transfer 
function is proved to be a good predictor of the variation in the threshold values with 
excitation frequency. The excitation frequencies, amplitudes of the relative motion, 
threshold displacement at the shaker head, and their product values are listed in Table 2-4 
and Table 2-5 for type 1.a and type 2.a connectors, respectively. It could be observed that 
the products of the threshold displacement at the shaker head and the relative motion for 
each type of connector pairs remained generally constant. This relationship provided a 
 
Figure 2-29:  SEM picture of accumulation area 
Accumulation 
Area 
?
46 
solid theoretical base for looking for a consistent indicator of the fretting threshold value 
simulation.  
 For current FEA simulation technology, it is still impossible to simulate the real-
time resistance changes. Therefore, a key task in the prediction of threshold values using 
a simulation model is to select a relative motion indicator. In the simulation model, there 
will always be some relative motion at the contact interface for any input vibration level. 
In order to make a selection, the interface motion was examined in detail. Because of the 
rocking motion mode of the receptacle, three points of contact were of particular interest, 
as shown in Figure 2-20. Position 1 was the point of contact between the blade and the 
end of the spring during the vibration, Position 2 was the point of contact between the 
blade and the left inner bottom surface of the receptacle during the rocking motion, and 
Position 3 was the point of contact between the blade and the right inner bottom surface 
of the receptacle during the rocking motion. 
 
Table 2-4: Relationship analysis for type 1.a connector pair 
                    
Frequency 
                   
Relative Motion 
(RM) 
Threshold 
displacement at 
shaker head (peak) 
                   
Product of RM and 
Displacement 
30Hz 0.0321 3.0mm 0.0963mm 
35Hz 0.0696 1.4mm 0.0974mm 
40Hz 0.1355 0.6mm 0.0813mm 
45Hz 0.1273 0.8mm 0.1019mm 
50Hz 0.1004 0.9mm 0.0904mm 
?
47 
 
 Initially, the threshold displacements at the shaker head at different frequencies 
obtained from the experiment were used as the input excitation displacement for the real-
time vibration simulation. At all position 1, 2 and 3, the x-axis relative motions for these 
different frequencies were very similar while the y-axis relative motions were quite 
different. This reflected that the fretting was only related to the x-axis (not y-axis) 
relative motion between the contact interfaces, as expected. Moreover, the x-axis relative 
motion at position 2 is larger than those at position 1 and position 3. This means the x-
axis relative motion at position 2 made the largest contribution to the fretting. As shown 
in Figure 2-30, the x-axis relative motion vibration amplitude at position 2 was 
approximately 1.5 ?m peak-to-peak.  This value is in reasonably good agreement with the 
work of Hamman, et. al.[54], who reported that ?Almost any slip (>1 ?m) resulted in an 
increased contact resistance in the performed experiments,? for the particular system that 
was considered. It should be noted that the threshold level for a given connector system 
depends upon the contact material and will generally be different for different plating 
materials, so a somewhat different value to that reported by Hamman, et. al. [54] is not 
unexpected.     
Table 2-5: Relationship analysis for type 2.a connector pair 
                    
Frequency 
                  
Relative Motion 
(RM) 
Threshold 
displacement at 
shaker head (peak) 
Product of RM and 
Displacement 
30Hz 0.0371 2.9mm 0.1076mm 
35Hz 0.0826 1.2mm 0.0991mm
40Hz 0.1645 0.6mm 0.0987mm 
45Hz 0.1221 1.0mm 0.1221mm
50Hz 0.0696 1.45mm 0.1009mm 
?
48 
 
 Based on the fundamentals described above, the input excitation amplitude at a 
particular frequency was adjusted until the x-axis relative motion at position 2 reached 
the value of 1.5 ?m peak-to-peak.  The resulting amplitude was taken to be the threshold 
input level at that frequency. Both fretting threshold value experiments and simulation 
were conducted for different input excitation levels and the frequencies of 30Hz, 35Hz, 
40Hz, 45Hz and 50Hz. The reason of choosing these frequencies is because the first 
resonant peak of the relative motion transfer function is around 40Hz, thus the differences 
between relative motions at different frequencies are more significant. Figure 2-31 to 
Figure 2-36 show the simulation and experiment threshold results as well as the inverse 
relative motion transfer functions. As expected, the inverse relative motion transfer 
function is a good predictor of the variation in the threshold values with excitation 
frequency. The threshold displacements at the frequency with lower relative motion 
transfer function values (roughly 40Hz to 50Hz) are somewhat lower than others. The 
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.0125
-0.01
-0.0075
-0.005
-0.0025
0
0.0025
0.005
0.0075
0.01
0.0125
Time (second)
X
-
ax
i
s
 rel
a
t
i
v
e
 m
o
t
i
on at
 P
o
s
i
t
i
on
 2(m
m
)
 
 
30Hz-2p9mmpk
35Hz-2p0mmpk
40Hz-1p3mmpk
45Hz-0p8mmpk
50Hz-1p2mmpk
 
Figure 2-30:  Simulated X-axis relative motion at position 2 
?
49 
overall simulation threshold results generally correlated well with experiment results for 
all six types of connector samples. 
 
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 1.a Scaled Inv. Rel. Motion Tran.Fun.
Type 1.a Threshold Value from Experiment
Type 1.a Threshold Value from 2D Simulation
 
Figure 2-31:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.a 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
res
hol
d D
i
s
p
l
a
c
e
m
ent
 
at
 t
he S
hak
er H
ead (m
m
)
 
 
Type 1.b Scaled Inv. Rel. Motion Tran.Fun.
Type 1.b Threshold Value from Experiment
Type 1.b Threshold Value from 2D Simulation
 
Figure 2-32:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.b 
?
50 
 
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.a Scaled Inv. Rel. Motion Tran.Fun.
Type 2.a Threshold Value from Experiment
Type 2.a Threshold Value from 2D Simulation
 
Figure 2-34: Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.a 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 1.c Scaled Inv. Rel. Motion Tran.Fun.
Type 1.c Threshold Value from Experiment
Type 1.c Threshold Value from 2D Simulation
 
Figure 2-33:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 1.c 
?
51 
 
 
 One purpose of this fretting threshold study is to evaluate the influence of various 
design factors on vibration-induced fretting degradation. Figure 2-37 and Figure 2-38 
show the differences of fretting threshold displacements for Type1 and Type 2 connector 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.c Scaled Inv. Rel. Motion Tran.Fun.
Type 2.c Threshold Value from Experiment
Type 2.c Threshold Value from 2D Simulation
 
Figure 2-36:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.c 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.b Scaled Inv. Rel. Motion Tran.Fun.
Type 2.b Threshold Value from Experiment
Type 2.b Threshold Value from 2D Simulation
 
Figure 2-35:  Comparison between experimental and simulation results for fretting 
threshold displacements of Type 2.b 
?
52 
samples with different contact normal forces, respectively. As the contact normal forces 
increased from Type a to Type c, the threshold values generally increased. The higher 
contact normal force at the contact interfaces leads to smaller relative motion between the 
blade and the receptacle and then reduces the insulating oxidation accumulation process 
at contact terminals. Therefore, higher contact normal force inhibited the fretting process 
and resulted in higher fretting threshold values. In additional, the fretting threshold 
displacements of Type 1 and Type 2 samples with different friction coefficient at contact 
terminals are similar. This result is with the same trend of transfer function results. Each 
is due to the minimized effect of ?rocking mode? as described in previous sections.  
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
ol
d
 D
i
s
p
l
a
c
e
m
ent
 a
t
 t
h
e
 S
h
ak
er H
e
ad 
(
m
m
)
 
 
Type 1.a Scaled Inv. Rel. Motion Tran.Fun.
Type 1.b Scaled Inv. Rel. Motion Tran.Fun.
Type 1.c Scaled Inv. Rel. Motion Tran.Fun.
Type 1.a Threshold Value from 2D Simulation
Type 1.b Threshold Value from 2D Simulation
Type 1.c Threshold Value from 2D Simulation
 
Figure 2-37:  Comparison of fretting threshold displacements for Type 1 samples 
with different contact normal forces  
?
53 
 
2.6 Summary and Conclusions  
 A study of the vibration induced fretting degradation of a single blade-receptacle 
pair was presented.  A series of blade/receptacle connector pair configurations were 
analyzed both experimentally and with an FEA model. Two variations of finish type were 
considered, with each finish type having three different contact normal force levels. 
Three supplementary steel balls served as an artificial loading condition were attached to 
the wires of each receptacle sample to make the system susceptible to fretting. The 
transfer functions and the fretting threshold displacement for a series of frequencies were 
measured in the experiment. The relative motion transfer function was proved to be a 
good indicator of the tendency of such systems to fret. The geometric dimensions, 
material properties and boundary conditions of the FEA model were generated based on 
the experimental values. The same x-axis relative motion at the contact interfaces was 
observed when the experimental threshold displacements were used as the input vibration 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
ol
d D
i
s
p
l
a
c
e
m
e
n
t
 at
 
t
h
e S
h
a
k
er 
H
e
ad
 
(
m
m
)
 
 
Type 2.a Scaled Inv. Rel. Motion Tran.Fun.
Type 2.b Scaled Inv. Rel. Motion Tran.Fun.
Type 2.c Scaled Inv. Rel. Motion Tran.Fun.
Type 2.a Threshold Value from 2D simulation
Type 2.b Threshold Value from 2D simulation
Type 2.c Threshold Value from 2D simulation
 
Figure 2-38:  Comparison of fretting threshold displacements for Type 2 samples 
with different contact normal forces  
?
54 
levels for this single blade/receptacle pair system. Finally, the results from the simulation 
were compared with the results from the experiment and generally found to be in good 
agreement. It was demonstrated that, for this limited system, finite element modeling and 
analysis methodology is a potentially valuable tool for the evaluation of the influence of 
design variations on the fretting behavior of connector. This study?s findings can be 
summarized and concluded as follows: 
? Transfer functions and threshold fretting displacements at the shaker head at 
different frequencies for the single blade/receptacle pair were observed in both 
experiments and simulation. 
? The relationship between the relative motion function and the threshold fretting 
displacement at the shaker head for this contact pair system was proven. 
? The x-axis relative motion at the contact interface was indicated to be the main 
source of fretting. 
? The results from the simulation generally correlated well with those obtained 
from the experiment. 
? Finite element modeling and analysis method has great potential for evaluating 
the influence of design variations on fretting behaviors. 
?
55 
CHAPTER 3 THREE DIMENSIONAL MODELING AND ANALYSIS OF 
A BLADE/RECEPTACLE CONNECTOR PAIR FOR THE PREDICTION 
OF VIBRATION-INDUCED FRETTING DEGRADATION 
3.1 Introduction  
 Vibration-induced fretting can be a major problem for connector systems used in 
vehicle electronics. At present, most of the evaluations of fretting propensity for 
particular connector designs and the influence of variations in those designs on fretting 
performance are conducted through exhaustive experimental testing.  A simulation-based 
method would be of great value to those responsible for connector design and application. 
As mentioned in Chapter 2, an earlier initial study was conducted in which a simplified 
finite element model was developed and experimentally validated for a blade/receptacle 
pair. However, due to the restrict assumptions and the geometric limitation of two-
dimensional planar finite element analysis, the 2-D simplified model might not be 
accurate enough to completely represent the influences of the design factors, for example, 
the dynamic response of different contact normal forces. Moreover, considering of the 
fast development of computational capacity of computers, it is practical to perform 
simulations of a more complicated model in an acceptable time period on a better 
platform.   
 Based on the reasons above, in this study, a highly detailed 3-D finite element 
simulation model was developed in ABAQUS [14] according to true dimensions and
?
56 
boundary conditions of the blade-receptacle connector pair configuration in experiments. 
A workstation with better computational capability (2 Quad Core Xeon Proc 5320, 16GB 
ddr2 memory, 640GB hard drive) as well as the parallel execution technology in ABQUS 
was utilized to reduce the computational time. The 3-D detailed model was then 
optimized and analyzed to evaluate the threshold vibration levels as a function of 
excitation frequency, wire tie-off length, supplementary mass, interface friction 
coefficient, and normal force. Finally, the results from the simulation were introduced 
and compared with the results from the 2-D simplified model simulation and the 
experiment. The content in this chapter describes all the details of this work. 
3.2 Three Dimensional Detailed Finite Element Model Generation 
 An ABAQUS [14] detailed finite element model in three dimension (3-D) was 
developed from the CAD drawings for the sample experimental configuration as 
described in Chapter 2. This is a complicated but accurate model with all the real 
boundary conditions and material properties. This model is expected to have enough 
potential to precisely simulate most of the influences of different design factors of this 
blade/receptacle connector configuration. 
3.2.1 Geometric Model  
 Figure 3-1 and Figure 3-2 show the overall view and cross-section view of the 3-
D connector model to represent both the outside and inside structure. The connector 
model basically consists of four parts: wire, which is the electrical lead for electrical 
power transfer; supplementary mass, which serves to provide enough fretting damage for 
?
57 
the system; receptacle, including an out frame and an inside spring; blade, mated with the 
receptacle part with contacts with the spring and bottom inner layer. 
 
?
Figure 3-2: Close-up view (cross section) of the 3-D geometric model 
?
Figure 3-1: Overall view of the 3-D geometric model 
?
58 
 The material properties of each model component are listed in Table 3-1. There 
are two sets of material properties for the two different plating finishes. Basically, the 
plating is expected to dictate the coefficient of friction. However almost all the other 
mechanical responses of the system are related to the copper alloy base materials used, 
which resulted in somewhat different for the two sample types.  The material properties 
for the wire leads and auxiliary mass remain the same in simulations for all types of 
specimens. 
  
3.2.2 Mesh Control  
 3D standard stress elements were utilized for all components in this 3-D detailed 
model. According to the calculation strategy of finite element method, the hex elements 
with cuboids structure would result in more accurate results. Therefore, all parts in the 3-
D model were meshed by structure technique into hex elements except the three 
supplementary balls. Proper partitions were assigned to the model to ensure the execution 
of the structure mesh especially for the receptacle part which includes complicated 
geometry. Figure 3-3 shows the details of partitions in the receptacle (without spring). 
The supplementary balls and wire were meshed separately by sweep technique. This is 
Table 3-1: Material properties for 3-D model components 
Components Friction 
Coefficient 
Density Young?s Modulus 
Plating Type 1 
(blade/receptacle section) 
0.55 8910 kg/m
3
 129.7 GPa 
Plating Type 2 
(blade/receptacle section) 
0.33 8910 kg/m
3
 120.6 GPa 
Wire portion - 3423 kg/m3 96.5 GPa 
Supplementary mass(balls) - 7793kg/m3 195 GPa 
?
59 
because the circular structure can only be meshed with sweep or free mesh, and sweep 
technique is considered to be more precise in this situation.  
 
 In consideration of the complexity as well as the resulting computational cost, 
different mesh size controls were assigned to different parts based on its importance. As 
shown in Figure 3-2, the blade was finely meshed to elements of approximately 
0.4mm*0.375mm*0.4mm (length*width*height). It is basically a nonlinear contact 
process between spring and the upper surface of the spring, which would significantly 
affects the convergence . Therefore, mesh convergence and adjusted step increment was 
utilized in this model. Moreover, as one could easily expected, after mated together, the 
spring part inside the receptacle had very large deformation and high bending stress. 
Therefore, the mesh size on the spring was adjusted to be very small, at a size of 
0.15mm*0.15mm*0.15mm.  After optimized mesh, the 3-D details model contains 3442 
elements and 6150 nodes.  Table 3-2 lists the element types, mesh techniques and sizes 
for all parts in the model. 
?
Figure 3-3: Partitions in the receptacle component 
?
60 
  
3.2.3 Parallel Execution 
 The accurate 3-D model contains a large number of elements which could result 
in long computational time (four to six hours in many cases) for a single simulation run 
on a single-processor workstation. Dell Precision 690 workstation was utilized for the 3D 
simulation, as shown in Figure 3-4. This is an ultra-high-performance workstation that is 
designed to maximize performance and scalability in an innovative, customer-driven 
workstation with great computational capability. Table 3-3 lists the specifications of the 
system.  Moreover, the Linux Operating System was installed in this computer to 
enhance the computational speed of ABAQUS especially for complicated models. 
Parallel execution technology in ABAQUS was utilized to increase the computational 
speed. This technology allows the computer to run the complex model in multiple 
processors (8 processors on this workstation) at the same time and dramatically reduce 
the computational cost. 
Table 3-2: Mesh techniques and size control for different components 
                
Components 
                  
Mesh Technique 
                           
Mesh Size (mm) 
Blade Structure 0.4*0.375*0.4 
Receptacle Frame Structure 0.35*0.35*0.35 
Spring Structure 0.15*0.15*0.15 
Supplementary Mass  Sweep 1.5 (Global Size) 
Wire Sweep 2.0 (Global Size) 
?
61 
 
 
?
Figure 3-4: Picture of the workstation for the 3-D simulation 
Table 3-3: Specifications of the workstation 
Type  Dell Precision 690n Mini-Tower  
Processor Quad Core Xeon Proc E5320 1.86GHz, 2 X 4MB L2 Cache  
Memory 16GB, DDR2 ECC SDRAM Memory 667MHz, 4X4GB 
Video Card nVidia, Quadro FX 3500, 256MB PCIe x16, dual VGA or DVI 
Graphics Card 
Hard Drive 4*?160GB Serial ATA, 10K RPM Hard drive with 16MB Data 
Burst Cache 
Operating System Red Hat Enterprise Linux WS v4Intel EM64T 64bit 
 
?
62 
3.2.4 Define Contact 
 Contact is a crucial problem in the 3-D modeling and simulation. In section 2.4, 
the vibration process simulation in 2-D simplified model indicated that the main motion 
of the receptacle is a ?rock motion?. Therefore a complicated process in combination of 
impact, slippage and sliding would be expected to exist in the contact. Figure 3-5 shows 
the defined node-to-surface contact pair in the model. The pink surfaces are the slave 
surfaces including bottom surface of the spring and upper side of bottom inner layer of 
the receptacle with smaller mesh size. The red surfaces are the master surfaces including 
bottom and upper surfaces of the blade with larger mesh size. One reason of the different 
mesh sizes is during the calculation of contact in ABAQUS, the slave surface is not 
allowed to penetrate into the master but the penetration of master nodes to slave surface 
is acceptable. Thus, if the mesh size of the master surface is smaller than slave surface, 
more nodes will penetrate into the slave surface and more intersection will exists in the 
contact pair which might lead to inaccurate results and difficulties in convergence.  
?
63 
 
3.3 Simulation Methodology and Boundary Conditions 
 In order to evaluate the fretting behavior of the connector systems, two different 
simulation: the harmonic analysis in frequency domain to determine the transfer 
functions and the vibration process simulation in real time domain to observe the relative 
motion at the contact terminals were conducted 
3.3.1 Mating Process Simulation 
 One challenging aspect in this simulation is to ensure the stiffness value of the 
spring as well as the generated contact normal force to be as close as possible to the real 
values. In the production process, the spring part was pushed up with different forces to 
generate different distances between the right bottom surface of the spring and upper side 
of the inner layer of the receptacle. These different distances of ?gaps? were utilized to 
?
Figure 3-5: Defined contact pair in 3-D model 
?
64 
reflect different spring stiffness and contact normal forces. One example for the ?gap? is 
shown in the unmated connector pair in Figure 3-8. Therefore, in order to assure the same 
effect, a ?mating? step was created in both harmonic and vibration simulation. In this step, 
the blade was located close to the spring at the beginning, then inserted in and finished 
entire mating process. The insert-in distance is determined as the same distance in the 
experiments. Figure 3-9 and Figure 3-10 show the pictures of details of the mating 
process in 3-D simulation. 
 
?
Figure 3-6: Unmated connector pair  
Gap 
?
65 
 
 
 Epoxide solidification experiments were performed to study the mated process 
especially the inside structure geometry for mated and unmated connector pairs. The 
?
Figure 3-8: Mated connector pair 
?
Figure 3-7: Connector pair in mating process 
?
66 
connector samples were first epoxided in a rubber cup and solidified for about 24 hours. 
Then the side part of the connectors were polished away to expose the inside structure. 
The unmated receptacle part and the mated connector pair are shown in Figure 3-9 and 3-
10, respectively. It could be observed that the 3-D mating process simulation generally 
represented the real situation. Thus the stiffness and contact normal force values in the 3-
D detailed model should be very close to the real values in the experiments. 
  
?
Figure 3-9: Unmated receptacle part 
?
67 
 
3.3.2 Boundary Conditions 
 Figure 3-11 shows the boundary conditions utilized in harmonic and fretting 
simulation of the 3-D detailed model. These conditions were determined the same as 
those in the experiment setup. The end of the electrical wire from the receptacle part was 
constrained in all degrees of freedoms while the left end of the blade was fixed in 
horizontal axis (z-axis in the model)  to reflect that it was clamped firmly at the shaker 
head and only vertical motions (y-axis in the model) were allowed in the experiment. In 
order to simulate the vibration motions, the periodic motion function was used to define 
the amplitude.  The function is defined as below: 
                                              (1) 
?
Figure 3-10: Mated connector pair 
?
68 
where A
0
 is the initial amplitude, A
n
 and B
n
 are the constants, w is the circular frequency 
defined as: 
                                                          w=2?*f                                                                  (2) 
where f is the frequency value from the experiments. The corresponding circular 
frequency values for frequencies tested in the experiment are shown in Table 3-4. 
According to the fretting threshold experiments, sinusoidal motion was generated from 
the shaker head for different frequency. Therefore in this particular circumstance, A
0
= 0, 
n=1, A
1
=0, B
1
=1 n=1. The refined function is as below: 
                         
This function could correctly reflect the different vibration motions in fretting threshold 
experiments. For harmonic, simulation, a random noise from 20Hz to 70Hz was utilized 
in transfer function experiments.  
 
?
Figure 3-11: Boundary conditions in the 3-D model 
                                                     a = Sinw (t-t
0
)                                                          (3) 
?
69 
 
3.4 3-D Detailed Model Simulation Results 
 Based upon the system configuration above, simulation studies of the 3-D detailed 
model were performed to evaluate the dynamic behavior of the system including the 
harmonic (transfer functions) and fretting thresholds simulations. The results were then 
compared and validated with 2-D simplified model simulation and experiments results. 
Details are described in sections below. 
3.4.1 Transfer Functions 
 As described in Chapter 2, relative motion between the contacting terminals is 
proved to be the basic inducement and a significant indicator of the fretting degradations.      
In the previous study, transfer functions were observed in both the experiments and the 2-
D simplified model simulation in ANSYS. For this 3-D detailed model simulation, the 
input location was on node Blade-296 and the output location was on node Female-2124 
as shown in Figure 3-12. Both nodes were selected as the same positions as those in the 
experiments and the 2-D simulation.  
Table 3-4: Corresponding circular frequency values in the 3-D simulation 
Frequency 
tested in 
experiments  
Corresponding 
circular frequency in 
the 3-D simulation  
30Hz 188.4 
35Hz 219.8 
40Hz 251.2 
45Hz 282.6 
50Hz 314.0 
?
70 
 
 Figure 3-13, Figure 3-14 and Figure 3-15 show the transfer functions which were 
obtained from experimental testing, the 2-D simplified model simulation, and the 3-D 
detailed model simulation for different contact normal force levels respectively. It can be 
observed from Figure 3-13 that there were significant variations between the transfer 
functions for the various normal forces in the experiment, especially the first resonant 
peak. The frequency where the first resonant peak occurs for Type b is lower than Type a, 
while the frequency for Type c is larger than Type a. This behavior cannot be obtained 
from the 2-D simplified model in Figure 3-14. However, in the 3-D detailed model 
simulation, as shown in Figure 3-15, this trend was observed again. A possible reason of 
the better fit of the 3-D simulation results is that the 3-D detailed model could reflect all 
the same geometry and boundary conditions as in experiments, no stringent assumptions 
needed. Moreover, as described in Section 2.3, due to the limitation of the 2-D plane 
?
Figure 3-12: Nodes location in the 3-D detailed model 
?
71 
model, the elasticity of the outer structure of the receptacle was adjusted to be much 
higher than real value in order to fix the two sides as that of the experimental 
configuration. This assumption would result in over constrains on the spring and the 
upper side of receptacle, which could minimize the different effects of different contact 
normal forces levels as well as the correlated transfer function results. 
 
20 25 30 35 40 45 50 55 60 65 70
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
an
s
f
e
r
F
u
nc
t
i
on
 
 
Type a
Type b
Type c
?
Figure 3-13: Experimental transfer function results for different contact normal force 
levels  
?
72 
 
 
 Figure 3-16 and 3-17 show the comparison of experimental data to the 2-D model 
simulation results and the 3-D model simulation results for different friction coefficient 
(Type1 and Type 2). It could be observed from Figure 3-16 that the transfer function 
20 25 30 35 40 45 50 55 60 65 70
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Frequency(Hz)
T
r
an
s
f
e
r
 F
u
nc
t
i
on
 
 
Type a
Type b
Type c
 
Figure 3-15: 3-D simulation transfer function results for different contact normal 
force levels 
20 25 30 35 40 45 50 55 60 65 70
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
a
n
s
f
er F
unc
t
i
o
n
 
 
Type a
Type b
Type c
 
Figure 3-14: 2-D simulation transfer function results for different contact normal 
force levels 
?
73 
results generated from 2-D model simulation matched the experimentally measured 
values well particularly for the lower frequency. However, this result did not fit the 
experimental results in the entire frequency range. Moreover, in consideration of the first 
resonant peak, the magnitude of the transfer function from the 2-D model simulation is 
approximately 5% lower. In comparison, the 3-D model simulation result generally 
matched the experimental result well and the magnitude of the first resonant peak is only 
about 1.7% lower. The overall shape of the 3-D model simulation result also matched the 
experimental result much better than 2-D model simulation. Especially from 45Hz to 
55Hz, the experimental result trace and the 3-D simulation result trace almost superposed 
each other while there?s an significant difference for the 2-D model simulation result. 
Thus, the detailed 3-D model simulation shows a much better potential in the prediction 
of transfer functions than the 2-D simplified model. 
 
20 30 40 50 60 70 80
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
ans
f
e
r
 F
unc
t
i
on
 
 
Type1--from experiment
Type2--from experiment
Type1--from 2-D simulation
Type2--from 2-D simulation
?
Figure 3-16: Comparison of experimentally determined transfer function and 2-D 
simulation model results 
?
74 
 
 The comparison of the predicted influences of different the wire tie-off lengths on 
relative motion transfer functions between 2-D simplified model simulation and 3-D 
detailed model simulation are shown in Figure 3-18.  It is observed from both simulations 
that as the tie-off length is decreased, the resonant peak shifts to the right and tends to 
become somewhat higher in amplitude.  This effect is due to a relative increase of the 
system stiffness which would result in an increment in the nature frequency. The shorter 
wire tire-off length also leads to a decrease in system internal damping, which comes 
primarily from the wiring and result in the increment of amplitude. Figure 3-19 shows the 
comparison of predicted effects of different auxiliary mass on the relative motion transfer 
functions between the 2D simplified model simulation and the 3D detailed model 
simulation. Similarly, both 2D and 3D simulations shows that as the auxiliary mass is 
increased, the resonant frequency decreases and the amplitude of the resonant peak 
increases dramatically. This trend provides an explanation for the difficulty in obtaining 
fretting for samples without auxiliary mass. That is, the relative motion in the frequency 
20 25 30 35 40 45 50 55 60 65 70
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Frequency(Hz)
T
r
an
s
f
e
r
 F
u
nc
t
i
on
 
 
Type1--from experiment
Type2--from experiment
Type1--from 3-D simulation
Type2--from 3-D simulation
?
Figure 3-17: Comparison of experimentally determined transfer function and 3D 
simulation model results 
?
75 
and amplitude range of interest is too small to produce significant fretting degradation.  
Substantial additional vibration energy would have to be put into that sample 
configuration in order to exceed the threshold levels required for the onset of fretting. 
 
20 30 40 50 60 70
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Frequency(Hz)
R
e
l
a
t
i
v
e
 M
o
t
i
on
 T
r
ans
f
e
r
 
F
unc
t
i
on
 
 
2-D Simulation
Wire Length=116mm
2-D Simulation
Wire Length=136mm
2-D Simulation
Wire Length=156mm
3-D Simulation
Wire Length=116mm
3-D Simulation
Wire Length=136mm
3-D Simulation
Wire Length=156mm
?
Figure 3-18: Comparison between 2-D simulation and 3-D simulation of relative 
motion transfer functions for various tie-off lengths (Specimen Type 2.b) 
20 30 40 50 60 70
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Frequency(Hz)
R
e
l
a
t
i
v
e
 M
o
t
i
on T
r
ans
f
e
r
 
F
u
nc
t
i
on
 
 
2-D Simulation
Auxiliary Mass=0g
2-D Simulation
Auxiliary Mass=3g
2-D Simulation
Auxiliary Mass=4.5gg
3-D Simulation
Auxiliary Mass=0g
3-D Simulation
Auxiliary Mass=3g
3-D Simulation
Auxiliary Mass=4.5g
?
Figure 3-19: Comparison between 2-D simulation and 3-D simulation of relative 
motion transfer functions for various tie-off lengths (Specimen Type 2.b) 
?
76 
3.4.2 Threshold Values 
 As described in Chapter 2, the inverse relative motion transfer function is 
demonstrated to be a good predictor of the variation in the threshold values with 
excitation frequency. It was also observed that the x-axis relative motion at the position 1 
where the blade and the left inner bottom surface contact during the rock motion, as 
shown in Figure 3-12, is the indicator  of the threshold values in the modeling simulation.    
Figure 3-20 and Figure 3-21 show the threshold values from the 3-D detailed model 
simulation results and experimental inverse relative motion transfer functions. The 3-D 
simulation results generally match the experimental inverse relative motion transfer 
function quite well. The same trend, that is the fretting threshold value generally 
increased as the increment of the contact normal force levels (from Type a to Type c), 
was also predicted. 
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 1.a Scaled Inv. Rel. Motion Tran.Fun.
Type 1.b Scaled Inv. Rel. Motion Tran.Fun.
Type 1.c Scaled Inv. Rel. Motion Tran.Fun.
Type 1.a Threshold Value from 3D Simulation
Type 1.b Threshold Value from 3D Simulation
Type 1.c Threshold Value from 3D Simulation
?
Figure 3-20: Comparison between 3D simulation results and experimental results for 
scaled inverse relative motion transfer functions for Type 1 samples 
 
?
?
77 
 
 Figure 3-22 to Figure 3-27 show the comparison of the threshold value from 
experiments, the 2-D simulation and the 3-D simulation. It could be observed that the 3-D 
detailed model simulation matches the experimental results slightly better than the 2-D 
model especially in the higher frequency range (for example at 50Hz). The better fit in 
the 3-D results especially at higher frequency is in good match with the transfer function 
results observed in the 2-D simplified model simulation as mentioned in previous 
sections.      
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.a Scaled Inv. Rel. Motion Tran.Fun.
Type 2.b Scaled Inv. Rel. Motion Tran.Fun.
Type 2.c Scaled Inv. Rel. Motion Tran.Fun.
Type 2.a Threshold Value from 3D simulation
Type 2.b Threshold Value from 3D simulation
Type 2.c Threshold Value from 3D simulation
?
Figure 3-21: Comparison between 3D simulation results and experimental results for 
scaled inverse relative motion transfer functions for Type 2 samples 
?
78 
 
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 1.b Scaled Inv. Rel. Motion Tran.Fun.
Type 1.b Threshold Value from Experiment
Type 1.b Threshold Value from 2D Simulation
Type 1.b Threshold Value from 3D Simulation
?
Figure 3-23: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.b) 
 
?
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 1.a Scaled Inv. Rel. Motion Tran.Fun.
Type 1.a Threshold Value from Experiment
Type 1.a Threshold Value from 2D Simulation
Type 1.a Threshold Value from 3D Simulation
?
Figure 3-22: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.a) 
?
79 
 
 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.a Scaled Inv. Rel. Motion Tran.Fun.
Type 2.a Threshold Value from Experiment
Type 2.a Threshold Value from 2D Simulation
Type 2.a Threshold Value from 3D Simulation
?
Figure 3-25: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.a) 
 
?
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
hol
d D
i
s
p
l
a
c
e
m
e
nt
 at
 
t
he S
h
ak
e
r
 
H
e
a
d
 
(
m
m
)
 
 
Type 1.c Scaled Inv. Rel. Motion Tran.Fun.
Type 1.c Threshold Value from Experiment
Type 1.c Threshold Value from 2D Simulation
Type 1.c Threshold Value from 3D Simulation
?
Figure 3-24: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 1.c) 
 
 
?
80 
 
 
 A comparison of fretting threshold results for different wire tire-off lengths was 
performed on both 2-D and 3-D model simulations. As shown in Figure 3-28, both 2-D 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d D
i
s
p
l
a
c
e
m
e
nt
 at
 t
h
e
 
S
h
ak
e
r
 
H
e
ad
 
(
m
m
)
 
 
Type 2.c Scaled Inv. Rel. Motion Tran.Fun.
Type 2.c Threshold Value from Experiment
Type 2.c Threshold Value from 2D Simulation
Type 2.c Threshold Value from 3D Simulation
?
Figure 3-27: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.c) 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
o
l
d 
D
i
s
p
l
a
c
e
m
e
nt
 
at
 
t
h
e
 S
h
ak
e
r
 H
e
ad
 (
m
m
)
 
 
Type 2.b Scaled Inv. Rel. Motion Tran.Fun.
Type 2.b Threshold Value from Experiment
Type 2.b Threshold Value from 2D Simulation
Type 2.b Threshold Value from 3D Simulation
?
Figure 3-26: Comparison of 2-D simulation, 3-D simulation and experimental results 
with scaled inverse relative motion transfer functions (Specimen Type 2.b) 
 
 
?
81 
and 3-D simulation results showed the same trend. As the tie-off length is decreased, the 
lowest threshold displacement at the shaker head shifts to the right. This result generally 
matches the first resonant peak shifting in the transfer function simulation. 
 
3.5 Computational Cost 
 Computational cost is always a crucial issue in simulation. In three-dimensional 
simulation in ABAQUS/Standard, considering the cubic mesh, if the size of each element 
is reduced to half, the total computational cost will increase 2*2*2 times for three 
dimensions. Moreover, due to the size change of the smallest elements in this model; the 
cost will increase another 2 times. Therefore, the total computational cost will increase to 
2
4 
or 16 times. This explains the complicity of the 3-D detailed model and the importance 
of the optimization to balance the mesh size and the accuracy of the results.   
 Figure 3-30 shows the comparison of computational time of single threshold 
simulation between 2-D and 3-D models. It could be observed that the time of 3-D 
25 30 35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
T
h
r
e
s
h
ol
d D
i
s
p
l
a
c
e
m
e
nt
 
at
 
t
he S
h
a
k
e
r
 H
e
a
d
(m
m
)
 
 
Wire Length=116mm
Wire Length=136mm
Wire Length=136mm
?
Figure 3-28: 3D detailed model simulation of threshold values for various tie-off 
lengths (Specimen Type 2.b) 
?
?
82 
detailed model is about 45 minutes while that of the 2-D simplified model simplified 
model is about 4 minutes. Although the 3-D model takes about 11 times longer than 2-D 
model, a 45 minutes run is still acceptable for repeated simulation studies. Therefore, for 
this particular configuration, the 3-D model is practical and more accurate while the 2-D 
simplified model simulation is more time-efficient and less accurate. However, if for a 
more complicated system, the 2-D model might be more practical. 
 
3.5 Summary and Conclusions 
 In this study, a highly detailed 3-D finite element model in ABAQUS for a single 
tin-plated blade/receptacle connector pair was developed and analyzed to evaluate the 
threshold vibration levels. Specimens with different normal forces and finish Type have 
been considered. The geometric dimensions, material properties and boundary conditions 
of the FEA model were generally the same as the real experimental values. Simulations 
of the 3D detailed model have been performed to determine the transfer functions and 
?
Figure 3-30: Comparison of single threshold simulation running time between 2D 
simplified model and 3D detailed model 
?
83 
threshold fretting levels for various excitation frequencies, wire tie-off lengths, 
supplementary mass, interface friction coefficients, and normal force values. 
 Finally, the 3-D detailed model simulation results were compared with the 2-D 
simplified model simulation results and with the physical experiments. The 3-D detailed 
model simulation results were found to be in good agreement with the experiment and 
proved to be more adaptable than the 2-D simulation which requires constraining 
assumptions and corresponding model components. It was proven that, the present finite 
element modeling and analysis methodology has demonstrated potential for evaluating 
the influence of design variations on fretting behavior of the single blade/receptacle 
connector pair. This study?s findings can be summarized and concluded as follows: 
? A 3-D detailed finite element model was developed and optimized in ABAQUS. 
? Harmonic simulation and fretting threshold simulation studies were performed on 
this 3-D model for all different types of connector samples. 
? Consistent relationships between the relative motion function and threshold 
displacement at the shaker head were once again proven. 
? Results from the 3-D simulation results generally matched those from the 
corresponding experiments quite well. 
? The 3-D simulation is more adaptable to the analysis of practical connector 
designs than 2-D simulation, which requires constraining assumptions and 
corresponding model components. 
? The present finite element modeling and analysis have demonstrated potential for 
evaluating the influence of design variations on fretting behavior. 
?
84 
CHAPTER 4 THE APPLICATION OF FEA SIMULATION TECHNIQUES 
TO THE FRETTING DEGRADATION OF A CONNECTOR SYSTEM 
4.1 Introduction  
 Fretting degradation can be a major problem in vehicle connectors. At present, 
much of the evaluation of fretting propensity for particular connector designs and the 
influence of variations in those designs on fretting performance is conducted through 
exhaustive experimental testing, which requires a major commitment of time and 
resources. Therefore, a simulation-based method would be of great value to those 
working on connector design and applications. 
 In the author?s previous work, a simplified two dimensional finite element model 
and a highly detailed three dimensional finite element model were developed and 
experimentally validated for a single blade/receptacle pair connector system, as described 
in previous chapters. The 3-D detailed model simulation results were then compared with 
the 2-D simplified model simulation results and with the physical experiments in many 
aspects. The 3-D simulation results show a slight advantage than 2-D simulation in 
predicting overall shape of the transfer function but requires more computational cost. 
Both the 2-D simplified model and 3-D detailed model simulations were generally found 
to be in good agreement with the experiments. This finding demonstrated the great 
potential of the finite element analysis techniques in predicting the vibration-induced 
fretting corrosion in single blade/receptacle connector pair configuration. 
?
85 
 However, in the industry application of the connector system in vehicles, not 
single but sixteen pin connector pairs are sealed together in a housing part and serve as 
one entire system. Therefore, it would be of great value to apply the FEA techniques to 
develop and analyze a connector system model in order to provide a reliable tool to the 
designers to evaluate the fretting characteristics of different connector designs. Based on 
this purpose, a two dimensional simplified model and a three dimensional detailed model 
were developed and compared for the connector system in this study. A series of 
simulations were performed on the selected 2-D model. Corresponding experiments were 
conducted to validate and test the performance of the system. 
4.2 Experimental Configuration 
4.2.1 Experimental Samples 
 A series of samples were fabricated based upon a commercially available 
automotive connector design, as shown in Figure 4-1. Both receptacle and blade part 
have two rows of connectors with each row consists of 8 single tin-plated 
blade/receptacle connector pairs. After mating, all the connector pairs are sealed in the 
plastic housing and leads with two 230 mm long wires at both ends. Similar to the single 
connector pair samples, the connector system samples also have two different plating 
finish / base metal configurations and three contact normal force levels. Table 4-1 
summarizes the sample types. Both finishes were based upon a pure tin system, although 
the type 2 finish structure had been modified to produce a coefficient of friction 
approximately half of the coefficient for the type 1 finish. The thicknesses of the metal 
strips used to fabricate the terminals were the same, and the elastic modulus of the 
samples were very similar.  
?
86 
 
 
 
 As described in previous chapters, the relative motion transfer function was 
proved to be a great indicator for vibration-induced fretting degradation in vehicle 
connectors. In previous experimental study, the transfer functions were determined by the 
non-contact displacement measurements using the Polytec laser vibrometer systems. 
However, because all the connector pairs are sealed in the plastic housing, the laser beam 
 
Table 4-1: Types of Experimental Samples 
 
Specimen Type Finish Gap Size 
(mm) 
Normal Force 
(N) 
Friction 
Coefficient 
1.a 1 0.53 4.7 0.55 
1.b 1 0.48 6.0 0.55
1.c 1 0.43 6.5 0.55 
2.a 2 0.53 4.3 0.33
2.b 2 0.48 5.3 0.33 
2.c 2 0.43 6.3 0.33
 
?
Figure 4-1: Photograph of the connector system sample 
?
87 
cannot reach the measurement location on the connector pairs. According to Flowers and 
Xie?s previous study on this topic [38][52], viewing slots were machined on the housing 
system, as shown in Figure 4-2. These slots allow the laser beams to go through the 
plastic housing and direct access to the mating terminal pairs in each half of the 
connector. The slots were positioned carefully at the locations which not only could 
reflect the right motions for the transfer function testing but also not to alter any features 
of the housing that constrained terminal motions.  
 
4.2.2 Experimental Equipment 
 During this study, most experimental equipments used were the same as those in 
the previous studies. Details of the equipments including the Keithley Model 2010 
multimeter, the HP 35665A Dynamic Signal Analyzer, and the POLYTEC laser 
vibrometer were all described in Chapter 2. However, in order to meet the requirement of 
?
Figure 4-2: Photograph of the connector system sample 
?
?
88 
the larger g-level in the experiments, a more capable vibration system which consists of a 
bigger shaker and an enhanced amplifier was utilized.  
 The vibration system consists of the equipment below: LDS V850 shaker [55], 
LDS SPAK amplifier, KISTLER 8720 accelerometer, DACTRON LASER vibration 
control system with DAQ card and a cooling system [56]. Figure 4-3 and Figure 4-4 
show photographs of these facilities. In general, this is a close-loop system and the details 
of its constructions are shown in Figure 4-5. During its working process, the controller 
first sends the output signals which have been pre-defined in the profile to the amplifier 
and then to the shaker. When the shaker starts vibrating, the feedback signal is generated 
from the accelerometer attached to the sliding table and then received by the control 
system through the DAQ card. The control system would compare the feedback signal 
with the pre-defined profile to identify if it runs properly and make proper adjustments to 
the output. This close-loop would keep running to ensure the shaker is vibrating properly 
according to the pre-defined profile. Specifications of the all these equipments are listed 
as below. 
LDS 350 vibratory shaker: 
? Useful frequency range: DC~3000Hz 
? Velocity, sine, peak: 2.0 m/s (78.7 in/s) 
? Acceleration, sine, peak: 5888.4 m/s
2
 (60.0 g
n
) 
? Displacement peak-peak: 50.8 mm (2.0 in) 
LDS SPAK Amplifier: 
? Power range: 5-50 kVA in 5 kVA increments 
?
89 
? Rated output voltage: 100 V rms 
            An amplifier?s self-protection capability is very important for safety reasons 
during vibration tests. The amplifier system is protected by the following interlocks: 
? Output over-voltage 
? Amplifier over-temperature 
? Vibrator over-travel 
? Slip Table over-travel 
? Vibrator cooling system failure 
? Input overdrive 
? Power module failure 
KISTLER 8702B50 accelerometer,: 
? Measuring Range: -50 g~50 g 
? Sensitivity: 99.5 mV/g 
? Transverse Sensitivity: 0.3 % 
? Resonant Frequency: 54.0 kHz 
? Temperature: -54 ? 100 (  
DACTRON LASER Vibration control system: 
? Frequency range: Up to 42 kHz analysis frequency. 
? Frequency accuracy: Within 0.01% 
? Dynamic range: 120 dBfs. 
?
90 
 
 
\ 
 
?
Figure 4-3: Photograph of LDS V850 shaker with KISTLER accelerometer  
?
Figure 4-4: DACTRON vibration control system and SPAK amplifier 
?
91 
 
 
Figure 4-5: Diagram of LDS vibration test system 
?
92 
4.2.3 Experimental Setup 
 A photograph showing the basic connector system experiment configuration is 
shown in Figure 4-6. This is the same setup as in Flowers and Xie?s previous work [38]. 
As described in previous section, the connector system consists of 16 pin connector pairs 
for both the male and female terminals. Thus 16 wires were attached at each end of the 
connector and the other ends were clamped in the fixture. The blade terminal housing 
part was also clamped at the fixture to serve as an input of the system. In order to insure 
consistent fretting degradation in the frequency and amplitude ranges provided by the 
available laboratory shaker system, the supplementary inertial mass was clamped to the 
wire leads close to the connector housing, with a 2 mm gap between the connector 
housing and the mass. This inertial mass consisted of three plates, with one plate 
positioned between the two rows of wire leads and the other two plates on the outside of 
each row, with the resulting assembly clamped together with bolts. 
 
 The typical transfer function testing setup is shown in Figure 4-7. This setup is 
based on the same methodology used in the transfer function measurements in Chapter 2. 
 
Figure 4-6: Photograph of the experimental setup 
?
93 
Figure 4-8 shows a schematic diagram of the detailed test setup. The entire assembly was 
bolted to a horizontal slip table, which was driven by a vibratory shaker. The transfer 
function for each sample was then determined by comparing the output vibration 
response at the connector interface to the input excitation at the vibratory shaker head. 
Both are measured using Polytec non-contacting laser displacement measuring systems. 
The ratio of the steady-state output amplitude to the input amplitude for a given 
excitation frequency is the magnitude of the transfer function at that frequency. The 
phase difference between the steady-state output and input responses for a given 
frequency is the phase of the transfer function at that frequency. 
 
 
Figure 4-7: Photograph of transfer function measurement 
?
?
94 
 
4.3 FEA Modeling 
 ABAQUS [14] finite element simulation models were developed based on the 
experimental configuration described above. A simplified two dimensional (2-D) and a 
detailed three dimensional (3-D) model were developed and compared. The workstation 
with multiple processors was utilized to reduce the computational time.  
4.3.1 Detailed Three Dimensional Model 
Figure 4-9 show the picture of the detailed 3-D model. This is a complicated 
model including most details of the experimental configuration. Sixteen blade/receptacle 
connector pairs were developed and sealed in a housing part. All the dimensions and 
material properties are the real value from the experiments. One crucial problem for the 
3-D model is the optimization of the mesh size. In consideration of the convergence 
problem in the highly non-linear contact in this model, the springs and the contact pairs in 
 
Figure 4-8: Diagram of transfer function measurement configuration 
?
?
95 
have to be finely meshed. Also the elements connected to these finely meshed elements 
cannot be meshed too course to insure the accuracy of the entire system. Based on these 
considerations, this model contains a very large volume of elements (92780 elements and 
139267 nodes) and is expected to result in huge computational cost. 
           
 
4.3.2 Simplified Two Dimensional Model 
In comparison, a simplified two dimensional model of the connector system was 
developed in ABAQUS. Figure 4-10 and Figure 4-11 show the overall view and detailed 
view of the 2-D model respectively. This model is basically a cross-section view of the 
connector system. The material properties and dimensions were adjusted similar to the 2-
D model for single blade/receptacle connector pair described in Chapter 2. The wires in 
the blade part have been ignored because that the input location of the connector system 
in the experiment is at the blade-housing part, therefore the absence of these wires will 
 
Figure 4-9: Picture of the 3-D detailed connector system model 
?
96 
not have significant effect the dynamic response of the system. Three plates were also 
added on the wire to serve as the supplementary mass. 
 
All elements in this model were meshed to hex elements by structure mesh 
technique. The spring part was especially finely meshed in consideration of contact 
convergence. Tie constrains were utilized for the connection between the supplementary 
 
Figure 4-11: Detailed view of the 2-D connector system model 
 
Figure 4-10: Overall view of the 2-D connector system model 
?
97 
mass and wires, the housing part and connector pairs, etc. After optimization, this 2-D 
simplified model has only 1270 elements and 1916 nodes. Compared with the 92780 
elements and 139267 nodes in 3-D detailed model, this 2-D simplified model is expected 
to be more practical and could significantly reduce the computational time. 
4.3.3 Comparison between 2-D and 3-D Model  
An initial mating-process simulation (move the blade part into receptacle part to 
connect the entire system) was performed on both 3-D and 2-D models to compare the 
computational cost. As shown in Figure 4-11, it takes about 3154 minutes to finish for the 
3-D model while takes only 0.5 minute for the 2-D model, which is approximately more 
than 6000 times. As expected, the large volume of elements required for this detailed 3-D 
model and more defined constrains and contact areas tend to result in much more 
computational cost. The present computational capacity could not meet the requirement 
of this complicated model. Therefore, the 2-D simplified model is proved to be a more 
practical tool to investigate the fretting characteristics of this connector system. 
?
98 
 
4.4 Experiment and Simulation Results 
 Based upon the system configuration described above, a series of simulation 
studies were performed to evaluate the fretting behavior. Corresponding experiments 
were conducted to validate it. 
4.4.1 Transfer Function  
 Transfer functions were proved to be the great indicator of the fretting behavior, 
as described in previous chapters. The input and output measurement locations for both 
the simulation and experiments were selected to be the same.  The specific positions are 
shown as input and output node in the 2-D model in Figure 4-11. Example transfer 
functions for Type 1.b and Type 2.b obtained from both experimentally and using the 
simulation model, are shown and compared in Figure 4-12. It can be observed form the 
comparison that the simulation results generally matches overall shape of the 
 
Figure 4-12: Comparison of computational cost for initial simulation between 2-D 
model and 3-D model 
?
99 
experimentally measured results very well. The frequency where the highest peak occurs 
appears to be very similar between experiment and simulation results. For Type1, the 
frequency value generated from simulation is 125.1Hz compared with 124Hz from 
experiment; for Type2, the value decreased to 121.6Hz and 123Hz. The magnitudes of 
the first resonant peak from the simulation results are only about 2.76% and 6.21% higher 
than those from the experiment for Type 1 and Type 2 respectively. Please note that 
there?s a significant difference in magnitude between two different types.  
 
 Figure 4-14, Figure 4-15, Figure 4-16 and Figure 4-17 show the transfer function 
results which were obtained from experimental testing and 2-D model simulation for 
different finish/base metal type and contact normal force levels respectively. As observed 
from the experiment results in Figure 4-14 and Figure 4-16, the magnitude of the first 
resonant peak of Type 1 samples is about 20% higher than the Type 2 samples. So it 
appears that the resonant frequency and the associated amplitude peak for the higher 
friction finish (Type 1) were somewhat higher. Moreover, as the normal force level is 
20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
2
2.5
Frequency(hz)
T
r
a
n
s
f
er F
u
nc
t
i
on
 
 
Type1--from Experiment
Type2--from Experiment
Type1--from Simulation
Type2--from Simulation
 
Figure 4-13: Comparison of experimentally determined transfer function and 2-D model 
simulation results 
?
100 
increased, the magnitude of the first resonant peak of transfer function tends to be 
correspondingly increased. As shown in Figure 4-15 and Figure 4-17, the same 
phenomenon could be predicted by the 2-D model simulation very well. It could be 
observed from the simulation results that for both type of finish, the magnitude of Type c 
with the highest contact normal force is larger than Type b, while that of Type b is larger 
than Type a, which has the lowest contact normal force. 
 
20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
2
2.5
Frequency(Hz)
T
r
a
n
s
f
er F
u
nc
t
i
on
 
 
Type 1a
Type 1b
Type 1c
 
Figure 4-14: Experimental determined transfer function results for different contact 
normal force levels of specimen Type 1 
?
101 
 
 
20 40 60 80 100 120 140 160 180 200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Frequency(Hz)
T
r
a
n
s
f
er F
u
nc
t
i
on
 
 
Type 2a
Type 2b
Type 2c
 
Figure 4-16: Experimental determined transfer function results for different contact 
normal force levels of specimen Type 2 
20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
2
2.5
Frequency(Hz)
T
r
an
s
f
er F
u
n
c
t
i
on
 
 
Type 1a
Type 1b
Type 1c
 
Figure 4-15: Simulation transfer function results for different contact normal force 
levels of specimen Type 1 
?
102 
 
4.4.2 Fretting Rate  
Fretting rate experiments were performed for each type of samples at 90Hz by 
Flowers and Xie [38].The different g-levels (acceleration of the shaker head) used in the 
experiments were calculated and transferred to be the input excitation displacement in the 
vibration simulation. Table 4-3 shows g-levels and corresponding displacements. The x-
axis relative motion at position 1 was selected as a great indicator for the fretting 
corrosion in simulation. In this particular 2-D connector system model, position 1 was the 
point of the contact between the blade and the left inner bottom surface of the receptacle 
during the rocking motion as shown in Figure 4-11.  
 
20 40 60 80 100 120 140 160 180 200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency(Hz)
T
r
an
s
f
e
r
 F
u
nc
t
i
o
n
 
 
Type 2a
Type 2b
Type 2c
 
Figure 4-17: Simulation transfer function results for different contact normal force 
levels of specimen Type 2 
?
103 
 
From Figure 4-18 and Figure 4-19, it could be observed that for each sample type, 
as the increment of contact normal force, the x-axis relative motion at position 1 
generally increased. In another word, the x-axis relative motion amplitude of Type c is 
larger than that of Type b, while Type b is larger than Type a. Moreover, the comparison 
of the results of the two finish types showed the significant differences between the 
relative motions, with the higher friction finish having markedly higher x-axis relative 
motion amplitude. These results show a great agreement with the Flowers and Xie?s 
previous work [38] of fretting rate in experiments in Figure 4-20 and Figure 4-21. The 
experimental results indicated that as the increase of the contact normal force, the fretting 
rate (rate of resistance changes) generally increased (expect type 2b) too. Meanwhile, the 
fretting rate results for Type 1 with higher friction finish is larger than Type 2, with the 
slopes of the linear regression line are approximately 0.12 and 0.06 respectively. This 
phenomenon is generally in good agreement with the transfer function results. The 
magnitude of the transfer function is increased as the increase of the contact normal force 
and the magnitude of Type 1 is larger than Type 2. 
Table 4-2: G-levels and corresponding displacements at shaker head 
G-level Peak-to-peak displacement at shaker head 
2g 0.06135mm 
4g 0.12265
6g 0.18400mm 
 
?
104 
 
 
1 2 3 4 5 6 7
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
G-Value of Sine Test at f=90Hz
R
e
l
a
ti
v
e
 M
o
ti
o
n
 a
t
 Po
s
i
ti
o
n
 
1
(
n
m
)
 
 
Type 2.a
Type 2.a
Type 2.b
Type 2.b
Type 2.c
Type 2.c
 
Figure 4-19: X-axis relative motion for different contact normal force levels for 
specimen Type 2 in simulation 
1 2 3 4 5 6 7
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
G-Value of Sine Test at f=90Hz
R
e
l
a
t
u
i
v
e M
o
t
i
on at
 
P
o
s
i
t
i
on
 
1(
n
m
)
 
 
Type 1.a
Type 1.a
Type 1.b
Type 1.b
Type 1.c
Type 1.c
 
Figure 4-18: X-axis relative motion for different contact normal force levels for 
specimen Type 1 in simulation 
?
105 
 
 
Both results from experiment and simulation tend to follow the basic theory which 
was developed as part of earlier work on this topic [38]. In that work, it was observed that 
the fretting degradation rate satisfied the relationship: 
0 1 2 3 4 5 6 7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10
-4
g-value (peak) of sine test at f=90Hz
R
a
t
e
 of
 
r
e
si
st
a
n
ce c
h
an
ges (
O
hm
/
s
)
 
 
type 2a
type 2b
type 2c
type 2a
type 2b
type 2c
 
Figure 4-21: Rate of resistance change for Type 2 sample in experiment 
 
0 1 2 3 4 5 6 7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10
-4
g-value (peak) of sine test at f=90Hz
R
a
t
e
 of
 
r
e
si
st
a
n
ce c
h
an
ges (
O
hm
/
s
)
 
 
type 1a
type 1b
type 1c
type 1a
type 1b
type 1c
 
Figure 4-20: Rate of resistance change for Type 1 sample in experiment 
?
106 
where Z
F
 is the magnitude of the transfer function relating the relative motion between 
mating terminals (nominally equivalent to the motion of the ?output? terminal relative to 
the ?input? shaker head), G
f
 is the G-level acceleration of the shaker head, G threshold is 
the threshold vibration of the shaker head before the onset of fretting, f is the frequency 
of vibration, and E is a scaling factor. It is obviously from the relationship that as the 
increase of relative motion between mating terminals (E.g. position 1 in Figure 4-11 in 
simulation), the fretting rate should (rate of resistance changes) correspondingly increase. 
This relationship was proved by the trend shown in both simulation and experiment 
results. This value is in building a reasonable and consistent relationship between the 
experiment and simulation results. 
4.5 Summary and Conclusions  
 A study of the application of FEA simulation techniques to vibration-induced 
fretting degradation of a connector system was presented. Two variations of surface 
finish types of connector systems were considered, with each type having three different 
contact normal force levels. The transfer functions and the fretting rate at certain 
frequency were measured in the experiment. A detailed 3-D model and a simplified 2-D 
model were developed and compared using ABAQUS for the connector system. The 
geometric dimensions, material properties and boundary conditions of both models were 
generated based on the experimental values. The 2-D finite element model was selected 
to be a better simulation tool especially in consideration of the computational cost. A 
series of simulations were performed on the 2-D housing connector model and 
??????????????????????????????????????? ??????????????????????????????????    (1)?
?
107 
corresponding experiments were conducted to validate and test the performance of the 
system. Finally, the results from the simulation were compared with the results from the 
experiment and generally found to be in good agreement. It was demonstrated that, for 
this connector system, finite element modeling and analysis has enough potential to 
evaluate of the influence of design variations on the fretting behavior. This study?s 
findings can be summarized and concluded as follows: 
? Fretting rate and transfer function results were measured for all six types of 
samples in both experiment and simulation. 
? The 2-D simplified model was proved to be a better tool than 3-D detailed model, 
especially in consideration of the computational cost. 
? The relationship between the relative motion function and the fretting rate for this 
connector system was found in good agreement with the fretting degradation 
relationship concluded in previous study. 
? The results from the simulation generally correlated well with that obtained from 
the experiment. 
? Finite element modeling and analysis methodology has great potential for 
evaluating the influence of design variations on fretting behavior of the connector 
system.
?
108 
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 
 A study of the prediction of vibration-induced fretting corrosion in electrical 
contacts has been described in this dissertation. Simulation-based modeling and analysis 
method accompany with corresponding experimental validations were conducted to 
evaluate the influences of different connector design factors on fretting behaviors of 
connectors. The dissertation consists of three chapters. 
 First of all, a research on vibration-induced fretting corrosion in a single 
blade/receptacle connector pair is introduced. A two dimensional (2-D) simplified finite 
element model was developed in ANSYS [11] based on the typical experimental 
configurations. The model was then optimized, simulated and experimentally validated. 
The relative motion transfer function was proved to be a good indicator of the tendency 
of such systems to fret. The same x-axis relative motion at the contact interfaces was 
observed when the experimental threshold displacements were used as the input vibration 
levels for this single blade/receptacle pair system. The results from the simulation were 
finally compared with the results from the experiment and generally found to be in good 
agreement. This finding proved that for this limited system, finite element modeling and 
analysis methodology is a potentially tool for the evaluation of the influence of design 
variations on the fretting behavior of connector.  
 In the second part, a three-dimensional modeling and analysis method for the 
same connector configuration was studied. A highly detailed 3-D finite element model 
?
109 
was developed in ABAQUS [14] according to true dimensions and boundary conditions 
of the blade/receptacle connector pair configuration in the experiments. A high-
performance workstation as well as the parallel execution technology was utilized to 
increase the computational speed. The 3-D detailed model was then optimized and 
analyzed to evaluate the threshold vibration levels as a function of excitation frequency, 
wire tie-off length, supplementary mass, interface friction coefficient, and normal force. 
The 3-D simulation results were compared with the results from the 2-D simplified model 
simulation and the experimental results. The 3-D simulation correlated very well with the 
experiment and was proved to be practical and more adaptable than the 2-D simulation 
for this connector pair configuration.  
 The third study presented a study of the application of FEA simulation techniques 
to vibration-induced fretting degradation of a connector system. The connector system 
consists of 16 blade/receptacle connector pairs and the housing part. A detailed 3-D FEA 
model and a simplified 2-D FEA model were developed and compared using ABAQUS. 
The 2-D finite element model was proved to be a better tool in consideration of the 
computational cost. A series of simulations were performed on the 2-D housing 
connector model and corresponding experiments were conducted to validate and test the 
performance of the system. After comparison, the simulation results from the 2-D 
housing model generally match the experiments very well. It was demonstrated that, for 
this connector system configuration, finite element modeling and analysis has enough 
potential to evaluate of the influence of design variations on the fretting behavior.  
?
110 
 There is certainly a great deal of fertile ground for further investigations on the 
topic of vibration-induced fretting corrosion. Some suggestions for future work in this 
area are:  
? Investigation and prediction of the effects of contaminants on vibration-induced 
fretting degradation in electrical connectors. 
? Detailed experimental and simulation analysis of surface profile and material 
composition at the contact interfaces to study the fretting mechanism. 
? Study of the wear effect in connector systems. 
? Optimization and simplification of the three-dimensional finite element model of 
the connector system to make it practical. 
? Simplified computational mechanics model for connector systems in Matlab or 
C++ for industry applications. 
 
 
 
 
 
 
?
111 
REFERENCES 
 
 
[1] Ed P. Slade, ?Electrical Contacts: Principles and Applications", Chapter 6, 
1990. 
[2] D.V. Hutton, "Fundamentals of Finite Element Analysis", 2004. 
[3] L. Rayleigh, "On the Theory of Resonance", Transactions of the Royal 
Society (London), A161 (1870). 
[4] W. Ritz, "Uber eine neue Methode zur Losung gewissen Variations-Probleme 
der mathematischen Physik", J.Reine Angew.Math., 135(1909). 
[5] B.G. Galerkin, "Series Solution of Some Problems of Elastic Equilibrium and 
Rods and Plates?, Vestn.Inzh.Tekh, 19(1915). 
[6] R. Courant, ?Variational Methods for the Solution of Problems of 
Equilibrium and Vibrations?, Bulletin of the American Mathematical Society, 
49(1943). 
[7] R.W. Clough, ?The Finite Element Method in Plane Stress Analysis?, 
Proceedings, American Society of Civil Engineering, Second Conference on 
Electronic Computation, Pittsburgh, 1960. 
[8] H,C, Martin, ?Finite Element Analysis of Fluid Flows?, Proceedings of the 
Second Conference on Matrix Methods in Structural Mechanics, Wight-
Patterson Air Force Base, Kilborn, Ohio, Oct. 1968.
?
112 
[9] E.L. Wilson and R.E. Nickell, ?Application of the Finite Element Method to 
Heat Conduction Analysis?, Nuclear Engineering Design, 4(1966). 
[10] MSC/NASTRAN. Lowell, MA: MacNeal-Schwindler Corp. 
[11] ANSYS. Houston, PA: Swanson Analysis Systems. Inc. 
[12] ALGOR. Pittsburgh: Algor Interactive Systems. 
[13] COSMOS/M. Los Angeles: Structural Research and Analysis Corp. 
[14] ABAQUS, Providence, RI: Dassault Systemes Simulia Corp. 
[15] E.M. Bock and J.H. Whitley, ?Fretting Corrosion in Electric Contacts?, 
Electric Contacts -1974, Chicago, 1974, p.128. 
[16] S. Krumbein, ?Contact Properties of Tin Plates?, Electric Contacts -1974, 
Chicago, 1974, p.38. 
[17] M. Antler, W.F. Graddick and H.G. Tompkins, ?Base Metal Contacts: An 
Exploratory Study of Separable Connection To Tin-Lead?, Electric Contacts -
1975, Chicago, 1975, p.25. 
[18] J.H. Whitley, ?Investigation of Fretting Corrosion Phenomena in Electric 
Contacts?, Proc. 8
th
 Int. Conf. Electrical Contact Phenomena, Tokyo, 1976, 
pp.659-665. 
[19] M. Antler, and E.S. Sproles, ?Effect of Fretting on the Contact Resistance of 
Palladium?, IEEE Trans. CHMT, V.5, N.1, 1982, p.158. 
[20] J.M. Hooyer and K. Peekstok, ?The Influence of Practical Contact Parameters 
on Fretting Corrosion of Tin-Base Low-Level Connector Contacts?, Electric 
Contacts -1987, IEEE - HOLM, Chicago, 1987, p.43. 
?
113 
[21] M. Antler, ?Survey of Contact Fretting in Electrical Contacts?, Proceedings 
of the Twenty Ninth IEEE Holm Conference on Electrical Contacts, 1984, 
pp.3-22. 
[22] A. Lee and M.S. Mamrick, ?Fretting Corrosion of Tin with Electrical Load?, 
Proc. 13 International Conference On Electric Contacts, Lausanne, 
Switzerland, 1986, p.476. 
[23] A. Lee and M.S. Mamrick, ?Fretting Corrosion of Tin-Plated Copper Alloy?, 
IEEE Trans. CHMT ? 10, 1987, p.63. 
[24] A.Lee and M.S.Mamrick ?Fretting Corrosion of Tin at Elevated 
Temperatures? Proceedings of the Thirty Fourth IEEE Holm Conference on 
Electrical Contacts, 1988, p. 87-91. 
[25] J. Swingler, J.W. McBride, and C. Maul, ?The Degradation of Road Tested 
Automotive Connectors?, IEEE Transactions on Components and Packaging 
Technologies (CPMT), 2000, 23(1), p. 157-164. 
[26] G. T. Flowers, F. Xie, M. Bozack, and R.D. Malucci, "Vibration Thresholds 
for Fretting Corrosion in Electrical Connectors," Proceedings of the 48th 
IEEE Holm Conference on Electrical Connectors, October 21-23, 2002, 
pp.133-139. 
[27] L. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, ?Displacement 
Measurements at the Connector Contact Interface Employing a Novel Thick 
Film Sensor?, Electrical Contacts, 2005. Proceedings of the Fifty-First IEEE 
Holm Conference on 26-28 Sept. 2005, pp. 89 ? 96. 
?
114 
[28] N. Ben Jemaa, E. Carvou, ?Electrical contact behavior of power connector 
during fretting vibration?, Proceedings of the 52nd IEEE Holm Conference on 
Electrical Connectors, 25-27 Sept. 2006, pp. 263 ? 266. 
[29] M.D. Bryant, ?Resistance Buildup in Electrical Connectors Due To Fretting 
Corrosion of Rough Surfaces?, IEEE Transactions on Components Packaging 
and Manufacturing Technology, V.17, N.1, March 1994, pp. 86-95. 
[30] R. D. Malucci, ?Multispot Model of Contacts Based on Surface Features?, 
Electric Contacts -1990, IEEE - HOLM, Montreal, 1990, p. 625. 
[31]  R. D. Malucci, ?Impact of Fretting Parameters on Contact Degradation?, 
Proceedings of the 42nd IEEE Holm Conference on Electrical Contacts, 1996, 
pp. 395-403. 
[32] G. Villeneuve, D. Kulkarni, P. Bastnagel, and D. Berry, ?Dynamic Finite 
Element Analysis Simulation of the Terminal Crimping Process?, Electrical 
Contacts, 1996., Proceedings of the Forty-Second IEEE Holm Conference 
Joint with the 18th International Conference on Electrical Contacts, Sept. 
1996 pp. 156-172. 
[33] A. Monnier, B. Froidurot, C. Jarrige, R. Meyer, and P. Teste, ?A Mechanical, 
Electrical, Thermal Coupled-field Simulation of a Sphere-plane Electrical 
Contact?,  Proceedings of the 51st IEEE Holm Conference on electrical 
Contacts, 26-28 Sept. 2005 pp. 224-231. 
[34] S.V. Angadi, W.E.  Wilson, R.L. Jackson, Flowers, G.T. and B.I. Rickett, ?A 
Multi-Physics Finite Element Model of an Electrical Connector Considering 
?
115 
Rough Surface Contact?, Proceedings of the 54th IEEE Holm Conference on 
electrical Contacts, 27-29 Oct. 2008 pp. 168-177. 
[35] C. Leung, E. Streicher, D. Fitzgerald, and J. Cook, ?Contact Erosion of 
Ag/SnO
2
/In
2
O
3
 Made by Internal Oxidation and Powder Metallurgy?, 
Electrical Contacts, 2005. Proceedings of the Fifty-First IEEE Holm 
Conference on 26-28 Sept. 2005 Page(s):22 ? 27. 
[36] E. D. Taylor; ?Cathode Spot Behavior on Tungsten-Copper Contacts in 
Vacuum and the Effect on Erosion?, Electrical Contacts, 2005. Proceedings 
of the Fifty-First IEEE Holm Conference on 26-28 Sept. 2005 Page(s):135 ? 
138. 
[37] A. Gunatilake, S. Rowland, Z. Wang, and N. Allen, ?Modeling and 
Management of Microshocks under High Voltage Transmission Lines?, 
Electrical Contacts, 2005. Proceedings of the Fifty-First IEEE Holm 
Conference on 26-28 Sept. 2005 Page(s):63 ? 68. 
[38] G. Flowers, F. Xie, M. Bozack, B. Rickett, and R. Malucci, ?The Influence of 
Contact Interface Characteristics on Vibration-Induced Fretting Degradation?, 
Electrical Contacts, 2005. Proceedings of the Fifty-First IEEE Holm 
Conference on 26-28 Sept. 2005 Page(s):82 ? 88. 
[39] M. Braunovic, V. Izmailov, and M. Novoselova, ?A Model for Life Time 
Evaluation of Closed Electrical Contacts?, Electrical Contacts, 2005. 
Proceedings of the Fifty-First IEEE Holm Conference on 26-28 Sept. 2005 
Page(s):217 ? 223. 
?
116 
[40] D. J. Dickrell; M. T. Dugger, ?The Effects of Surface Contamination on 
Resistance Degradation of Hot-Switched Low-Force MEMS 
Electrical .Contacts?, Electrical Contacts, 2005. Proceedings of the Fifty-First 
IEEE Holm Conference on 26-28 Sept. 2005 Page(s):255 ? 258. 
[41] E. Takano, ?Equivalent Constriction Resistance Measured with the Low Dc 
Voltage Method under the Influence of Fretting Phenomena?, Electrical 
Contacts, 2005. Proceedings of the Fifty-First IEEE Holm Conference on 26-
28 Sept. 2005 Page(s):284 ? 290. 
[42] T. Ueno, and N. Morita, ?Influence of Surface Roughness on Contact Voltage 
Drop of Sliding Contacts?, Electrical Contacts, 2005. Proceedings of the 
Fifty-First IEEE Holm Conference on 26-28 Sept. 2005 Page(s):324 ? 328. 
[43] D. Sallais, N. Jemaa, E. Carou, C. Bourda, and D. Jeannot, ?An Arc Study at 
High DC Current Levels in Automotive Applications?, Electrical Contacts, 
2005. Proceedings of the Fifty-First IEEE Holm Conference on 26-28 Sept. 
2005 Page(s):329 ? 334. 
[44] J. Aronstein, ?Performance Classification for Electrical Connection Using 
ASTM B868?, Electrical Contacts, 2005. Proceedings of the Fifty-First IEEE 
Holm Conference on 26-28 Sept. 2005 Page(s):162 ? 166. 
[45] F. Xie, , G. Flowers, , C. Chen, M. Bozack,  J. Suhling, B. Rickett, R. 
Malucci, C. Manlapaz,  "Analysis and Prediction of Vibration-Induced 
Fretting Motion in a Blade/Receptacle Connector Pair," Proceedings of 53rd 
IEEE HOLM Conference on Electrical Contacts, pp. 222-228, PITTSBURGH, 
PA, Sept 16-19, 2007. 
?
117 
[46] Model 2010 Multimeter User?s Manual, Keithley Instruments, Inc., USA, 
1999 
[47] Laser Vibrometer User Manual, Controller OFV-2610/2620, Sensor Head 
OFV-353, POLYTEC Co., Germany 
[48] HP 35665A Dynamic Signal Analyzer Installation and Verification Guide, 
Hewlett-Packard Company, USA, 1991 
[49] Installation and Operating Manual PA 500/1000L-CE Amplifiers, LDS 
Company, USA 
[50] Installation and Operating Manual V400 Series Vibrators, LDS Company, 
USA  
[51] G. T. Flowers, F. Xie,  M. Bozack, R. Horvath, R. D. Malucci,, and B. 
Rickett., ?Vibration Testing of Fretting Corrosion in Electrical Connectors 
Subjected to Multi-Frequency and Random Spectral Profiles,? Proceedings of 
the 49th IEEE Holm Conference on Electrical Contacts,  pp. 45-50, 
Washington, DC, September 8-10, 2003. 
[52] G. T. Flowers, F. Xie, M. Bozack, X. Hai,  B. Rickett and R. D. Malucci, ?A 
Study of the Physical Characteristics of Vibration Induced Fretting 
Corrosion,? Proceedings of the 50th IEEE Holm Conference on Electrical 
Contacts, pp. 312-319, Washington, DC, September 20-23, 2004. 
[53] B. Malucci, ?Fretting Corrosion Degradation, Threshold Behavior and 
Contact Instability?, Ragnar Holm Scientific Achievement Award Address, 
Proceedings of the 49th IEEE Holm Conference on Electrical Contacts, pp. 1-
15, Washington, D.C., September 8-10, 2003. 
?
118 
[54] Hammam, Tag, Kassman-Rudolphi, Asa, and Lundstrom, Per,  ?Vibration-
induced deterioration of in-coated connectors studied by using a force 
controlled fretting bench-test,?  Proceedings of the Fifty-First IEEE Holm 
Conference on Electrical Contacts, 2005, p 97-106, Sep 26-28 2005. 
[55] V850 Vibration Testing Systems Manual, LDS Company, USA 
[56] Laser Shaker Control System Guide, Dactron Incorporated, Milpitas, 
CA95035 
[57] Unpublished data, Professor M. J. Bozack, Surface Science Laboratory, 
Department of Physics, Auburn Univ
?
119 
APPENDIX A     ANSYS LOG FILE FOR THE 2-D SIMPLIFIED FINITE 
ELEMENT MODEL 
 
 
!* Modeling generation   
 
/PREP7   
!*   
!*set element type as plane42 with thickness*! 
ET,1,PLANE42 
!*   
KEYOPT,1,1,0 
KEYOPT,1,2,0 
KEYOPT,1,3,3 
KEYOPT,1,5,0 
KEYOPT,1,6,0 
!*   
!*thickness set1=2.55e-3 for receptacle*!   
R,1,2.55e-3, 
!*   
!*thickness set2=1.90e-3 for partial annulus*!     
R,2,0.0019,  
!*   
!*thickness set3=1.50e-3 for blade and spring*!     
R,3,0.0015,  
!*   
R,4,0.00112, 
!*   
  
!*set material properties*!   
 
!*type1-C19025-Star: blade,annulus*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,1,,1.29742e11   
MPDATA,PRXY,1,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,1,,8910 
?
120 
MPTEMP,,,,,,,,   
MPTEMP,1,0 
MPDATA,MU,1,,0.33 
 
!*type2-star: spring*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,2,,1.29742e11   
MPDATA,PRXY,2,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,2,,8910  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,MU,2,,0.33    
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DAMP,2,,0.000 
 
!*type3: wire for 2D model*!  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,3,,1.35e9 
MPDATA,PRXY,3,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,3,,4564  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DAMP,3,,0.0005 
 
!*type4: Balls for 2D model*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,4,,1.95e11 
MPDATA,PRXY,4,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,4,,12876.3 
 
 
!*type5-C19025-Star-equivalent: receptacle*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,5,,1.29742e14  
MPDATA,PRXY,5,,0.3   
?
121 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,5,,8794  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,MU,5,,0.33    
 
!*type6-klf5-Reflow-equivqlent*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,6,,1.20622e14   
MPDATA,PRXY,6,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,6,,3210  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,MU,6,,0.44    
 
!*type7: blade rear part*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,7,,1.29742e11   
MPDATA,PRXY,7,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,7,,6974.3  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,MU,7,,0.33 
!!MPTEMP,,,,,,,,   
!!MPTEMP,1,0   
!!MPDATA,DAMP,7,,0.001    
 
!*type8:  end rectangle of spring*! 
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,EX,8,,1.29742e11   
MPDATA,PRXY,8,,0.3   
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,DENS,8,,8910  
MPTEMP,,,,,,,,   
MPTEMP,1,0   
MPDATA,MU,8,,0.33    
 
?
122 
!*generate blade*! 
K,1,0,0,,    
K,2,0,0.8e-3,,  
K,3,7.85e-3,0.8e-3,,   
K,4,7.85e-3,0,,   
K,5,8.85e-3,0.2e-3,,  
K,6,8.85e-3,0.6e-3,,  
K,7,-9.0e-3,0,,  
K,8,-9.0e-3,0.8e-3,,  
 
FLST,2,4,3   
FITEM,2,1    
FITEM,2,2    
FITEM,2,3    
FITEM,2,4    
A,P51X   
 
FLST,2,4,3   
FITEM,2,3    
FITEM,2,4    
FITEM,2,5    
FITEM,2,6    
A,P51X   
 
FLST,2,4,3   
FITEM,2,1    
FITEM,2,2    
FITEM,2,8    
FITEM,2,7    
A,P51X   
 
!*generate receptacle--front part*! 
RECTNG,0,1.0e-3,-0.6e-3,-0.3e-3,  
 
!!RECTNG,2.0e-3,2.15e-3,-0.3e-3,0, 
RECTNG,1.6e-3,2.15e-3,-0.3e-3,0, 
RECTNG,2.15e-3,5.45e-3,-0.3e-3,0, 
!!RECTNG,5.45e-3,5.6e-3,-0.3e-3,0,  
RECTNG,5.45e-3,6.2e-3,-0.3e-3,0, 
 
RECTNG,2.15e-3,5.45e-3,-0.6e-3,-0.3e-3,  
 
RECTNG,6.80e-3,9.65e-3,-0.6e-3,-0.3e-3, 
RECTNG,9.65e-3,9.95e-3,-0.6e-3,-0.3e-3, 
 
FLST,2,4,3   
?
123 
FITEM,2,11   
FITEM,2,10   
FITEM,2,13   
FITEM,2,16   
A,P51X   
FLST,2,4,3   
FITEM,2,22   
FITEM,2,29   
FITEM,2,32   
FITEM,2,23   
A,P51X   
 
CYL4,0.63e-3,1.70e-3,0.2e-3,90,0.5e-3,257    
RECTNG,3.37e-3,3.67e-3,0.48e-3,0.78e-3,  
 
FLST,2,4,3   
FITEM,2,39   
FITEM,2,38   
FITEM,2,41   
FITEM,2,44   
A,P51X   
 
RECTNG,0.63e-3,9.65e-3,1.90e-3,2.20e-3,  
RECTNG,9.65e-3,9.95e-3,1.90e-3,2.20e-3,  
 
RECTNG,9.65e-3,9.95e-3,-0.30e-3,0.8e-3, 
RECTNG,9.65e-3,9.95e-3,0.80e-3,1.10e-3, 
RECTNG,9.65e-3,9.95e-3,1.10e-3,1.90e-3, 
 
!*generate receptacle--rear part*! 
RECTNG,9.95e-3,12.80e-3,1.90e-3,2.20e-3,  
 
RECTNG,12.80e-3,13.10e-3,1.90e-3,2.20e-3,  
RECTNG,12.80e-3,13.10e-3,1.55e-3,1.90e-3, 
RECTNG,12.80e-3,13.10e-3,1.25e-3,1.55e-3, 
RECTNG,12.80e-3,13.10e-3,1.10e-3,1.25e-3, 
 
FLST,2,4,3   
FITEM,2,59   
FITEM,2,55   
FITEM,2,77   
FITEM,2,73   
A,P51X   
 
RECTNG,13.10e-3,16.70e-3,1.90e-3,2.20e-3,  
RECTNG,13.10e-3,16.70e-3,1.55e-3,1.90e-3,  
?
124 
RECTNG,13.10e-3,16.70e-3,1.25e-3,1.55e-3,  
RECTNG,13.10e-3,16.70e-3,1.10e-3,1.25e-3,  
 
RECTNG,18.45e-3,20.45e-3,2.20e-3,2.50e-3,  
RECTNG,18.45e-3,20.45e-3,1.40e-3,2.20e-3,  
RECTNG,18.45e-3,20.45e-3,1.10e-3,1.40e-3,  
RECTNG,18.45e-3,20.45e-3,0.60e-3,1.10e-3,  
 
FLST,2,4,3   
FITEM,2,87   
FITEM,2,86   
FITEM,2,101  
FITEM,2,104  
A,P51X   
FLST,2,4,3   
FITEM,2,86   
FITEM,2,90   
FITEM,2,105  
FITEM,2,101  
A,P51X   
FLST,2,4,3   
FITEM,2,90   
FITEM,2,94   
FITEM,2,109  
FITEM,2,105  
A,P51X   
 
!*generate wire and balls*! 
RECTNG,20.45e-3,34.00e-3,2.20e-3,2.50e-3,  
RECTNG,20.45e-3,34.00e-3,1.40e-3,2.20e-3,  
RECTNG,20.45e-3,34.00e-3,1.10e-3,1.40e-3,  
RECTNG,20.45e-3,34.00e-3,0.60e-3,1.10e-3, 
 
!*three balls*! 
CYL4,35.00e-3,5.5e-3,3.16e-3    
CYL4,41.32e-3,5.5e-3,3.16e-3 
CYL4,47.64e-3,5.5e-3,3.16e-3 
 
RECTNG,34.00e-3,36.00e-3,2.20e-3,2.50e-3, 
RECTNG,34.00e-3,36.00e-3,1.40e-3,2.20e-3,  
RECTNG,34.00e-3,36.00e-3,1.10e-3,1.40e-3,  
RECTNG,34.00e-3,36.00e-3,0.60e-3,1.10e-3, 
 
RECTNG,36.00e-3,40.32e-3,2.20e-3,2.50e-3,  
RECTNG,36.00e-3,40.32e-3,1.40e-3,2.20e-3,  
RECTNG,36.00e-3,40.32e-3,1.10e-3,1.40e-3,  
?
125 
RECTNG,36.00e-3,40.32e-3,0.60e-3,1.10e-3, 
 
RECTNG,40.32e-3,42.32e-3,2.20e-3,2.50e-3,  
RECTNG,40.32e-3,42.32e-3,1.40e-3,2.20e-3,  
RECTNG,40.32e-3,42.32e-3,1.10e-3,1.40e-3,  
RECTNG,40.32e-3,42.32e-3,0.60e-3,1.10e-3, 
 
RECTNG,42.32e-3,46.64e-3,2.20e-3,2.50e-3,  
RECTNG,42.32e-3,46.64e-3,1.40e-3,2.20e-3,  
RECTNG,42.32e-3,46.64e-3,1.10e-3,1.40e-3,  
RECTNG,42.32e-3,46.64e-3,0.60e-3,1.10e-3, 
 
RECTNG,46.64e-3,48.64e-3,2.20e-3,2.50e-3,  
RECTNG,46.64e-3,48.64e-3,1.40e-3,2.20e-3,  
RECTNG,46.64e-3,48.64e-3,1.10e-3,1.40e-3,  
RECTNG,46.64e-3,48.64e-3,0.60e-3,1.10e-3, 
 
RECTNG,48.64e-3,156.00e-3,2.20e-3,2.50e-3,  
RECTNG,48.64e-3,156.00e-3,1.40e-3,2.20e-3,  
RECTNG,48.64e-3,156.00e-3,1.10e-3,1.40e-3,  
RECTNG,48.64e-3,156.00e-3,0.60e-3,1.10e-3, 
 
!*substract three rectangles from three balls*! 
RECTNG,34.00e-3,36.00e-3,2.20e-3,2.50e-3, 
RECTNG,40.32e-3,42.32e-3,2.20e-3,2.50e-3, 
RECTNG,46.64e-3,48.64e-3,2.20e-3,2.50e-3, 
 
!*firstly, change the booleans tolerance to 0.3e-3*! 
BOPTN,KEEP,0 
BOPTN,NWARN,0    
BOPTN,VERS,RV52  
BTOL,3e-004, 
!*   
 
ASBA,      44,      71   
ASBA,      43,      70   
ASBA,      42,      69   
 
!*change the Booleans tolerance back to 1e-5*! 
BOPTN,KEEP,0 
BOPTN,NWARN,0    
BOPTN,VERS,RV52  
BTOL,1e-005, 
!*   
 
!*glue*! 
?
126 
FLST,2,3,5,ORDE,2    
FITEM,2,1    
FITEM,2,-3   
AGLUE,P51X   
 
FLST,2,65,5,ORDE,5   
FITEM,2,4    
FITEM,2,-41  
FITEM,2,43   
FITEM,2,-68  
FITEM,2,72   
AGLUE,P51X   
 
!*compress number for areas*! 
NUMCMP,AREA  
NUMMRG,KP, , , ,LOW  
APLOT  
 
!*named blade*! 
ALLSEL,ALL  
FLST,5,3,5,ORDE,2    
FITEM,5,1    
FITEM,5,-3   
ASEL,R, , ,P51X  
CM,blade,AREA    
 
!*named receptacle*! 
ALLSEL,ALL   
FLST,5,25,5,ORDE,4   
FITEM,5,4    
FITEM,5,-14  
FITEM,5,17   
FITEM,5,-30  
ASEL,R, , ,P51X  
/MREP,EPLOT  
CM,receptacle,AREA   
 
!*named balls*! 
ALLSEL,ALL  
FLST,5,3,5,ORDE,2    
FITEM,5,66   
FITEM,5,-68  
ASEL,R, , ,P51X  
CM,balls,AREA    
 
!*named wire*! 
?
127 
ALLSEL,ALL  
FLST,5,37,5,ORDE,4   
FITEM,5,15   
FITEM,5,-16  
FITEM,5,31   
FITEM,5,-65  
ASEL,R, , ,P51X  
CM,wire,AREA 
 
!*color the blade, receptacle, balls and wire*! 
ALLSEL,ALL   
APLOT    
/COLOR,CM,ORAN,BALLS 
/REPLOT  
!*   
/COLOR,CM,BLUE,BLADE 
/REPLOT  
!*   
/COLOR,CM,RED,RECEPTACLE 
/REPLOT  
!*   
/COLOR,CM,CYAN,WIRE  
/REPLOT  
!*   
 
!*define material property, real constant, element type*! 
!*blade_front part: MP=1, RC=3 thickness(1.5mm), ET=1*! 
FLST,5,2,5,ORDE,2    
FITEM,5,1    
FITEM,5,-2   
CM,_Y,AREA   
ASEL, , , ,P51X  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       1,       3,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*blade_rear part: MP=7, RC=1 thickness(2.55mm), ET=1*! 
CM,_Y,AREA   
ASEL, , , ,       3  
CM,_Y1,AREA  
?
128 
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       7,       1,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*spring: MP=2, RC=3 thickness(1.5mm), ET=1*! 
CM,_Y,AREA   
ASEL, , , ,       11  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       2,       3,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*end of the spring: MP=8, RC=2 thickness(1.9mm), ET=1*! 
CM,_Y,AREA   
ASEL, , , ,       10  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       8,       2,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*annulus: MP=1, RC=2 thickness(1.9mm), ET=1*! 
CM,_Y,AREA   
ASEL, , , ,       9  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       1,       2,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
?
129 
!*receptacle: MP=5(equivalent MP), RC=1 thickness(2.55mm), ET=1*! 
FLST,5,31,5,ORDE,7   
FITEM,5,4    
FITEM,5,-8   
FITEM,5,12   
FITEM,5,-32  
FITEM,5,34   
FITEM,5,-37  
FITEM,5,43   
CM,_Y,AREA   
ASEL, , , ,P51X  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       5,       1,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*balls: MP=4, RC=1 thickness(2.55mm), ET=1*! 
FLST,5,3,5,ORDE,2    
FITEM,5,66   
FITEM,5,-68  
CM,_Y,AREA   
ASEL, , , ,P51X  
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       4,       1,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
!*   
 
!*wire: MP=3, RC=4 thickness(1.12mm), ET=1*! 
FLST,5,28,5,ORDE,5   
FITEM,5,33   
FITEM,5,38   
FITEM,5,-42  
FITEM,5,44   
FITEM,5,-65  
CM,_Y,AREA   
ASEL, , , ,P51X  
?
130 
CM,_Y1,AREA  
CMSEL,S,_Y   
!*   
CMSEL,S,_Y1  
AATT,       3,       4,   1,       0,    
CMSEL,S,_Y   
CMDELE,_Y    
CMDELE,_Y1   
   
!*mesh size control*! 
!*manual mesh size for blade*! 
!*thickness of blade into 4 divisions*! 
FLST,5,4,4,ORDE,4    
FITEM,5,1    
FITEM,5,3    
FITEM,5,6    
FITEM,5,9    
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
!*length of bladehead into 3 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,5    
FITEM,5,7    
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,3, , , , ,1   
!*   
!*length of bladebody into 20 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,2    
FITEM,5,4    
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,20, , , , ,1  
?
131 
!*   
 
!*length of blade back part into 20 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,8    
FITEM,5,10   
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,20, , , , ,1   
!*   
 
!*manual mesh size for receptacle*! 
!*thickness into 3 divisions*! 
FLST,5,36,4,ORDE,35  
FITEM,5,12   
FITEM,5,14   
FITEM,5,16   
FITEM,5,18   
FITEM,5,20   
FITEM,5,24   
FITEM,5,32   
FITEM,5,34   
FITEM,5,36   
FITEM,5,44   
FITEM,5,46   
FITEM,5,48   
FITEM,5,50   
FITEM,5,54   
FITEM,5,58   
FITEM,5,63   
FITEM,5,67   
FITEM,5,74   
FITEM,5,78   
FITEM,5,81   
FITEM,5,85   
FITEM,5,93   
FITEM,5,95   
FITEM,5,98   
FITEM,5,114  
FITEM,5,116  
FITEM,5,264  
FITEM,5,-266 
FITEM,5,268  
?
132 
FITEM,5,272  
FITEM,5,275  
FITEM,5,278  
FITEM,5,283  
FITEM,5,-284 
FITEM,5,287  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,3, , , , ,1   
!*   
 
!*length of samll rectangles into 4 divisions*! 
FLST,5,14,4,ORDE,10  
FITEM,5,11   
FITEM,5,13   
FITEM,5,15   
FITEM,5,17   
FITEM,5,39   
FITEM,5,-42  
FITEM,5,261  
FITEM,5,-262 
FITEM,5,279  
FITEM,5,-282 
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
!*length of springend rectangle into 2 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,47   
FITEM,5,49   
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,2, , , , ,1   
!*   
 
?
133 
!*length of median rectangles into 10 divisions*! 
FLST,5,11,4,ORDE,11  
FITEM,5,27   
FITEM,5,31   
FITEM,5,33   
FITEM,5,94   
FITEM,5,96   
FITEM,5,155  
FITEM,5,-156 
FITEM,5,276  
FITEM,5,-277 
FITEM,5,285  
FITEM,5,-286 
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,10, , , , ,1  
!*   
 
!*length of spring into 20 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,51   
FITEM,5,-52  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,20, , , , ,1  
!*   
 
!*curves of partial circle into 20 divisions*! 
FLST,5,2,4,ORDE,2    
FITEM,5,43   
FITEM,5,45   
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,20, , , , ,1  
!*   
 
!*length of large rectangle into 18 divisions*! 
?
134 
FLST,5,2,4,ORDE,2    
FITEM,5,269  
FITEM,5,-270 
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,18, , , , ,1  
!*   
 
!*length of rectangle-rear part into 4 divisions*! 
FLST,5,4,4,ORDE,4    
FITEM,5,113  
FITEM,5,115  
FITEM,5,129  
FITEM,5,-130 
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
!*manual mesh size control for cable*! 
!*tiny thickness into 1 division*! 
FLST,5,3,4,ORDE,3    
FITEM,5,290  
FITEM,5,-291 
FITEM,5,313  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,1, , , , ,1   
!*   
 
!*continue the previous: thickness into 3*! 
FLST,5,3,4,ORDE,3    
FITEM,5,134  
FITEM,5,136  
FITEM,5,295  
CM,_Y,LINE   
LSEL, , , ,P51X  
?
135 
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,3, , , , ,1   
!*   
 
!*continue the previous: length of median rectangle into 10*! 
FLST,5,3,4,ORDE,3    
FITEM,5,298  
FITEM,5,-299 
FITEM,5,312  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,10, , , , ,1  
!*   
 
!*continue the previous: length of small rectangle into 4*! 
FLST,5,5,4,ORDE,5    
FITEM,5,117  
FITEM,5,121  
FITEM,5,125  
FITEM,5,132  
FITEM,5,135  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
!*thickness of median rectangle into 4*! 
FLST,5,5,4,ORDE,5    
FITEM,5,131  
FITEM,5,133  
FITEM,5,288  
FITEM,5,-289 
FITEM,5,292  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
?
136 
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
FLST,5,2,4,ORDE,2    
FITEM,5,296  
FITEM,5,-297 
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,2, , , , ,1   
!*   
 
!*continue the previous: thickness into 3*! 
FLST,5,14,4,ORDE,14  
FITEM,5,138  
FITEM,5,214  
FITEM,5,230  
FITEM,5,246  
FITEM,5,302  
FITEM,5,306  
FITEM,5,311  
FITEM,5,317  
FITEM,5,323  
FITEM,5,331  
FITEM,5,337  
FITEM,5,343  
FITEM,5,349  
FITEM,5,355  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,3, , , , ,1   
!*   
 
!*continue the previous: thickness of median rectangle into 4*! 
FLST,5,7,4,ORDE,7    
FITEM,5,315  
FITEM,5,321  
FITEM,5,328  
FITEM,5,335  
FITEM,5,341  
FITEM,5,347  
?
137 
FITEM,5,353  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,4, , , , ,1   
!*   
 
!*continue the previous: thickness of median rectangle into 2*! 
FLST,5,7,4,ORDE,7    
FITEM,5,319  
FITEM,5,325  
FITEM,5,333  
FITEM,5,339  
FITEM,5,345  
FITEM,5,351  
FITEM,5,357  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,2, , , , ,1   
!*   
 
!*length of median rectangles into 20 divisions*! 
FLST,5,5,4,ORDE,5    
FITEM,5,293  
FITEM,5,-294 
FITEM,5,314  
FITEM,5,316  
FITEM,5,318  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,20, , , , ,1  
!*   
 
!*joint lines between cable and balls into 2 divisions*! 
FLST,5,15,4,ORDE,15  
FITEM,5,267  
FITEM,5,300  
FITEM,5,-301 
?
138 
FITEM,5,303  
FITEM,5,-304 
FITEM,5,310  
FITEM,5,320  
FITEM,5,322  
FITEM,5,324  
FITEM,5,334  
FITEM,5,336  
FITEM,5,338  
FITEM,5,346  
FITEM,5,348  
FITEM,5,350  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,2, , , , ,1   
!*   
 
!*lines between balls into 8 divisions*! 
FLST,5,10,4,ORDE,10  
FITEM,5,305  
FITEM,5,307  
FITEM,5,326  
FITEM,5,-327 
FITEM,5,329  
FITEM,5,-330 
FITEM,5,332  
FITEM,5,340  
FITEM,5,342  
FITEM,5,344  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,8, , , , ,1   
!*   
 
!*longest length of cable into 100 divisions*! 
FLST,5,5,4,ORDE,5    
FITEM,5,308  
FITEM,5,-309 
FITEM,5,352  
FITEM,5,354  
?
139 
FITEM,5,356  
CM,_Y,LINE   
LSEL, , , ,P51X  
CM,_Y1,LINE  
CMSEL,,_Y    
!*   
LESIZE,_Y1, , ,100, , , , ,1 
!*   
 
!*mesh blade, receptacle, and cable*! 
FLST,5,65,5,ORDE,2   
FITEM,5,1    
FITEM,5,-65  
CM,_Y,AREA   
ASEL, , , ,P51X  
CM,_Y1,AREA  
CHKMSH,'AREA'    
CMSEL,S,_Y   
!*   
MSHKEY,1 
AMESH,_Y1    
MSHKEY,0 
!*   
CMDELE,_Y    
CMDELE,_Y1   
CMDELE,_Y2   
!*   
 
!*mesh balls*!   
SMRTSIZE,6   
 
MSHKEY,0 
FLST,5,3,5,ORDE,2    
FITEM,5,66   
FITEM,5,-68  
CM,_Y,AREA   
ASEL, , , ,P51X  
CM,_Y1,AREA  
CHKMSH,'AREA'    
CMSEL,S,_Y   
!*   
AMESH,_Y1    
!*   
CMDELE,_Y    
CMDELE,_Y1   
CMDELE,_Y2   
?
140 
!*   
 
!*generate contact pair*!   
!* 
/COM, CONTACT PAIR CREATION - START  
CM,_NODECM,NODE  
CM,_ELEMCM,ELEM  
CM,_KPCM,KP  
CM,_LINECM,LINE  
CM,_AREACM,AREA  
CM,_VOLUCM,VOLU  
/GSAV,cwz,gsav,,temp 
MP,MU,1,0.33 
MAT,1    
MP,EMIS,1,7.88860905221e-031 
R,5  
REAL,5   
ET,2,169 
ET,3,172 
R,5,,,0.01,0.1,0,    
RMORE,,,1.0E20,0.0,1.0,  
RMORE,0.0,0,1.0,,1.0,0.5 
RMORE,0,1.0,1.0,0.0,,1.0 
KEYOPT,3,3,0 
KEYOPT,3,4,0 
KEYOPT,3,5,0 
KEYOPT,3,7,0 
KEYOPT,3,8,0 
KEYOPT,3,9,0 
KEYOPT,3,10,1    
KEYOPT,3,11,0    
KEYOPT,3,12,0    
KEYOPT,3,2,0 
! Generate the target surface    
LSEL,S,,,2   
LSEL,A,,,4   
LSEL,A,,,5   
LSEL,A,,,6   
LSEL,A,,,7   
CM,_TARGET,LINE  
TYPE,2   
NSLL,S,1 
ESLN,S,0 
ESURF    
CMSEL,S,_ELEMCM  
! Generate the contact surface   
?
141 
LSEL,S,,,13  
LSEL,A,,,17  
LSEL,A,,,33  
LSEL,A,,,40  
LSEL,A,,,42  
LSEL,A,,,43  
LSEL,A,,,47  
LSEL,A,,,51  
LSEL,A,,,156 
LSEL,A,,,262 
CM,_CONTACT,LINE 
TYPE,3   
NSLL,S,1 
ESLN,S,0 
ESURF    
ALLSEL   
ESEL,ALL 
ESEL,S,TYPE,,2   
ESEL,A,TYPE,,3   
ESEL,R,REAL,,5   
/PSYMB,ESYS,1    
/PNUM,TYPE,1 
/NUM,1   
EPLOT    
ESEL,ALL 
ESEL,S,TYPE,,2   
ESEL,A,TYPE,,3   
ESEL,R,REAL,,5   
CMSEL,A,_NODECM  
CMDEL,_NODECM    
CMSEL,A,_ELEMCM  
CMDEL,_ELEMCM    
CMSEL,S,_KPCM    
CMDEL,_KPCM  
CMSEL,S,_LINECM  
CMDEL,_LINECM    
CMSEL,S,_AREACM  
CMDEL,_AREACM    
CMSEL,S,_VOLUCM  
CMDEL,_VOLUCM    
/GRES,cwz,gsav   
CMDEL,_TARGET    
CMDEL,_CONTACT   
/COM, CONTACT PAIR CREATION - END    
/MREP,EPLOT  
 
?
142 
EPLOT 
 
SAVE,'model_LongBlade_static_LowE_step3_48Gap','db','C:\ansyscc\'  
 
! Harmonic Analysis   
 
/CWD,'C:\ansyscc' 
RESUME, 'model_LongBlade_static_LowE_step3_48Gap','db','C:\ansyscc',0,0 
 
/SOLU    
!*   
ANTYPE,3 
!*   
!*   
HROPT,FULL   
HROUT,ON 
LUMPM,0  
!*   
EQSLV,FRONT,1e-008,  
PSTRES,0 
!*   
HARFRQ,0.05,200,    
NSUBST,200,   
KBC,1    
!*   
ALPHAD,0,  
BETAD,0, 
DMPRAT,0,    
!*   
 
FLST,2,3,1,ORDE,3    
FITEM,2,1286 
FITEM,2,2112 
FITEM,2,2710 
!*   
/GO  
D,P51X, ,0,0, , ,ALL, , , , ,    
 
FLST,2,3,1,ORDE,3    
FITEM,2,121  
FITEM,2,141  
FITEM,2,143  
!*   
/GO  
D,P51X, ,0,0, , ,UX, , , , , 
 
?
143 
FLST,2,3,1,ORDE,3    
FITEM,2,121  
FITEM,2,141  
FITEM,2,143  
!*   
/GO  
D,P51X, ,0.0005,0, , ,UY, , , , ,    
 
/STATUS,SOLU 
SOLVE    
 
 
!* Transient analysis   
 
/CWD,'C:\ansyscc\' 
RESUME,'model_LongBlade_static_LowE_step3','db','C:\ansyscc\',0,0 
 
EPLOT 
 
!*   
FINISH   
/SOL 
 
!*define loads*! 
!*The end of wire is fixed*! 
FLST,2,3,1,ORDE,3    
FITEM,2,1286 
FITEM,2,2112 
FITEM,2,2710 
!*   
/GO  
D,P51X, ,0, , , ,ALL, , , , ,    
   
!*read sine_static_xxHz_0p3mm function*! 
*DEL,_FNCNAME    
*DEL,_FNCMTID    
*DEL,_FNCCSYS    
*SET,_FNCNAME,'SS0p3_40' 
*SET,_FNCCSYS,0  
! /INPUT,sine_static_40Hz_0p3mm.func 
*DIM,%_FNCNAME%,TABLE,6,6,1,,,,%_FNCCSYS%    
!    
! Begin of equation: 0.0003*sin(251.2*{TIME}) 
*SET,%_FNCNAME%(0,0,1), 0.0, -999    
*SET,%_FNCNAME%(2,0,1), 0.0  
*SET,%_FNCNAME%(3,0,1), 0.0  
?
144 
*SET,%_FNCNAME%(4,0,1), 0.0  
*SET,%_FNCNAME%(5,0,1), 0.0  
*SET,%_FNCNAME%(6,0,1), 0.0  
*SET,%_FNCNAME%(0,1,1), 1.0, -1, 0, 251.2, 0, 0, 1    
*SET,%_FNCNAME%(0,2,1), 0.0, -2, 0, 1, -1, 3, 1  
*SET,%_FNCNAME%(0,3,1),   0, -1, 9, 1, -2, 0, 0  
*SET,%_FNCNAME%(0,4,1), 0.0, -2, 0, 0.0003, 0, 0, -1 
*SET,%_FNCNAME%(0,5,1), 0.0, -3, 0, 1, -2, 3, -1 
*SET,%_FNCNAME%(0,6,1), 0.0, 99, 0, 1, -3, 0, 0  
! End of equation: 0.0003*sin(251.2*{TIME})   
!--> 
 
!*define displacement of blade at x-axis as 0*!  
FLST,2,3,1,ORDE,3    
FITEM,2,121  
FITEM,2,141  
FITEM,2,143  
!*   
/GO  
D,P51X, ,0, , , ,UX, , , , , 
 
!*define displacement of blade at y-axis as sine_static_xxHz_0p3mm function*!  
FLST,2,3,1,ORDE,3    
FITEM,2,121  
FITEM,2,141  
FITEM,2,143  
!*   
/GO  
D,P51X, , %SS0p3_40% , , , ,UY, , , , ,   
 
!*solution control*! 
!*analysis type: transient*! 
!*   
ANTYPE,4 
!*   
TRNOPT,FULL  
LUMPM,0  
!*   
ANTYPE,4 
NLGEOM,1 
NSUBST,480,480,480 
OUTRES,ERASE 
OUTRES,ALL,ALL   
TIME,0.3    
 
NEQIT,50 
?
145 
!*solve*! 
/STATUS,SOLU 
/nerr,100,100,off 
 
SOLVE   
?
146 
APPENDIX B     MATLAB CODE EXAMPLE FOR TRANSFER FUNCTION 
AND RELATIVE MOTION CALCULATION 
 
 
?Transfer_functions_star_reflow_type_c.m? 
 
load Reflow_43gap_50mV_1.TXT  
  
load Reflow_43gap_50mV_2.TXT  
  
load Reflow_43gap_50mV_3.TXT  
 
load Star_43gap_40mV_1.TXT  
  
load Star_43gap_40mV_2.TXT  
  
load Star_43gap_40mV_3.TXT  
 
load Star_43gap_40mV_3.TXT  
 
hold on 
 
plot((Reflow_43gap_50mV_1(21:141,1)+Reflow_43gap_50mV_2(21:141,1)+Reflow
_43gap_50mV_3(21:141,1))/3,(Reflow_43gap_50mV_1(21:141,2)+Reflow_43gap_5
0mV_2(21:141,2)+Reflow_43gap_50mV_3(21:141,2))/3) 
  
plot((Star_43gap_40mV_1(1:121,1)+Star_43gap_40mV_2(1:121,1)+Star_43gap_40
mV_3(1:121,1)+Star_43gap_40mV_4(1:121,1))/4,(Star_43gap_40mV_1(1:121,2)+St
ar_43gap_40mV_2(1:121,2)+Star_43gap_40mV_3(1:121,2)+Star_43gap_40mV_4(1:
121,2))/4,'g') 
 
?Relativemotion_Type2_all.m? 
clear all 
close all  
M=10; 
N=75; 
load Star_43gap_40mV_1.TXT  
  
load Star_48gap_40mV_1.TXT  
?
147 
 
load Star_53gap_40mV_1.TXT  
  
s43=Star_43gap_40mV_1; 
s48=Star_43gap_40mV_1; 
s53=Star_43gap_40mV_1; 
  
f=s43(:,1); 
  
[n,m]=size(s43); 
  
for i=1:n, 
     
    mags43(i)=sqrt((1-s43(i,2))^2+s43(i,3)^2); 
    imags43(i)=1/mags43(i); 
     mags48(i)=sqrt((1-s48(i,2))^2+s48(i,3)^2); 
    imags48(i)=1/mags48(i); 
     mags53(i)=sqrt((1-s53(i,2))^2+s53(i,3)^2); 
    imags53(i)=1/mags53(i); 
end 
  
  
figure; 
   
f2=[30,35,40,45,50]; 
  
fs48=[4.4,2.5,.85,1.2,1.4];  
fs43=[5.25,2.6,1.5,0.9,1.2]; 
  
fs53=[2.9,1.45,0.6,1.,1.3]*1; 
fs53sim=[2.8,1.6,1.2,0.7,0.8]*1; 
  
fs48sim=[4.2,2.4,1.3,1.0,1.0]*1;  
fs43sim=[5.1,2.7,1.8,1.05,1.0]*1; 
sc1=fs43(1)/imags43(21); 
sc2=fs48(1)/imags48(21); 
sc3=fs53(1)/imags53(21);  
  
plot(f(M:N),sc3*imags53(M:N),'k--',f(M:N),sc2*imags48(M:N),'k-
.',f(M:N),sc1*imags43(M:N),'k-') 
  
hold 
  
plot(f2,fs53sim,'k*') 
plot(f2,fs48sim,'kd') 
plot(f2,fs43sim,'ks') 
?
148 
  
legend('Type 2.a Scaled Inv. Rel. Motion Tran.Fun.', 'Type 2.b Scaled Inv. Rel. 
Motion Tran.Fun.', 'Type 2.c Scaled Inv. Rel. Motion Tran.Fun.', 'Type 2.a Threshold 
Value from 3D simulation', 'Type 2.b Threshold Value from 3D simulation', 'Type 2.c 
Threshold Value from 3D simulation') 
  
hold off 
  
xlabel('Frequency (Hz)') 
ylabel('Threshold Displacement at the Shaker Head (mm)') 
axis([25,55,0,10]);