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WEAR SIMULATION OF ELECTRICAL

1. 800 1000 1200 1400 1600 5 00E 04 1 00E 03 1 50E 03 Wear Depth mm 2 00E 03 2 50E 03 3 00E 03 Number of Fretting Cycles Figure 51 Simulated Wear Depth versus Number of Fretting Cycles at S 0 008mm 800 1000 1200 1400 1600 0 0005 0 001 0 0015 Wear Depth mm 0 002 0 0025 0 003 Number of Fretting Cycles Figure 52 Simulated Wear Depth versus Number of Fretting Cycles at S 0 008mm 96 0 00E 00 800 1000 1200 1400 1600 5 00E 04 1 00E 03 1 50E 03 S 0 020 Wear Depth mm 2 00E 03 2 50E 03 3 00E 03 Number of Fretting Cycles Figure 53 Simulated Wear Depth versus Number of Fretting Cycles at S 0 020mm D 800 1000 1200 1400 1600 0 0005 0 001 0 0015 0 002 Wear Depth mm 0 0025 0 003 0 0035 Cumulative Displacement mm Figure 54 Simulated Wear Depth versus Number of Fretting Cycles at S 0 020mm oF 0 00E 00 800 1000 1200 1400 1600 5 00E 04 1 00E 03 1 50E 03 2 00E 03 S 0 040 Wear Depth mm 2 50E 03 3 00E 03 3 50E 03 Number of Fretting Cycles Figure 55 Simulated Wear Depth versus Number of Fretting Cycles at S 0 040mm 800 1000 1200 1400 1600 0 0005 0 001 0 0015 0 002 0 0025 Wear Depth mm 0 003 0 0035 0 004 Cumulative Displacement mm Figure 56 Simulated Wea
2. Figure 69 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 107 0 00 0 04 0 03 0 02 0 01 0 00 0 01 0 02 e 003 0 04 N 60 0 50 n g e R 0 3234 z 1 00 l Ne D 7 Ne al 2 50 Displacement mm Figure 70 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 0 08 t 902 0 01 amp Displacement mm Pressure N mm 2 Figure 71 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 108 6 2 Model Validation The model was validated by comparing the wear rate for a particular contact system with the wear rate obtained from experimental results for the same contact system The experimental contact system selected was steel on steel contact system from Kato 1994 Kato has used two experimental data points and used a linear fit between them which is shown in Figure 74 Steel on steel contact system is a common electrical contact system used in battery contacts The wear coefficient for steel steel contact was assigned a value of 0 0150 Rabinowicz 1995 The hardness value of steel used was Hv 700 The wear rate was calculated as a function of the wear coefficient hardness sliding velocity and contact pressure using formula X p 25 gt e a The contact pressure was c
3. Figure 28 A standard 6 noded linear pie element 52 Figure 29 Top face of the slider consisting of two different elements on which load is applied 52 Figure 30 Von Mises stress shown at the neutral position of the slider at the start of a cycle 53 Figure 31 Von Mises stress plot with slider at the right extreme of the receptacle 54 Figure 32 Von Mises stress plot with slider at the left extreme of the receptacle 55 xii Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Von Mises stress plot of a worn out PCB after several wear cycles A circular model representing a fuzz button contacting a PCB 2D contact model with applied constraints 3D model with a fully constrained receptacle 3D Model with a partially constrained slider 3D Model with pressure load applied on the top face of the slider Node types used in the model Direction of motion of nodes which undergo wear Contacting surfaces used in the 2D contact model Elements with different orientations make up the loading surface Node to Surface contact discretization Loading surface Slidertopsurface The node set Slider used in BOUNDARY to define slider displacement Adaptive mesh domain defined using element set PCBcontact Lagrangian description of sliding co
4. metal transfer occurs if the contacting members are of different sizes There is a net metal transfer from the part with the larger surface involved in sliding to the smaller surface As shown in Figure 4 this is observed in a rider flat contact As sliding progresses a lump of severely work hardened metal the prow builds up and wears the flat by continuous plastic shearing or cutting The rider is not affected by wear Prows get detached from the rider by back transfer to the flat or as loose debris Theoretically if the rider always contacts virgin metal prow formation continues indefinitely When electrical contacts are made of dissimilar contacting metals prows are formed even when the flat 1s harder than the rider provided the hardness of the flat 1s not greater than the hardness of the rider by a factor of three The size of the prow formed is inversely related to the hardness Soft ductile metals like gold form large prows which can be seen by the naked eye Cocks 1962 explained the formation of prows with the following steps 13 1 Adhesion of metal at the point of contact 2 Plastic deformation of a volume of metal in the flat 3 Development of tensile stresses at the back of this deformed volume of metal 4 Rupture and separation of the deformed metal with transfer to the rider as a chip 5 Formation of multiple layers of chips on the rider 6 Loss of prow from the rider when it grows large and unstable by back transfer to the fla
5. tg B sin w t to In the first data line the first number corresponds to the number of terms in the fourier series in this case it s one The second term is the circular frequency in radians per time In this model a time period of 16 has been used The circular frequency is equal to 27 16 The third number corresponds to the starting time to In this case to 0 The fourth number corresponds to the constant term in the Fourier series Ao In this case Ao 0 In the second data line the first number A corresponds to the first coefficient of the cosine terms In this model a sinusoidal motion is required therefore the cosine term is eliminated by making A equal to zero B corresponds to the first coefficient of the sine terms In this model it is equal to the max amplitude of oscillation from the central position The max amplitude of oscillation from the central position is equal to 0 033868 The BOUNDARY option is used to prescribe boundary conditions at nodes In this model BOUNDARY controls the movement of the entire slider The AMPLITUDE parameter is set equal to the name of the amplitude curve defining the magnitude of the prescribed boundary conditions The amplitude curve is defined in AMPLITUDE The TYPE parameter is used in a stress or displacement analysis to specify whether the magnitude is in the form of a displacement history a velocity history or an acceleration history In this case the magnitude is specified in the
6. 0 5mm Figure 14 A 2D model representing a memory module and its corresponding socket based on DIMM Socket Manual Courtesy of DDK Sockets 36 An insertion force of 97N is required to insert these modules The semicircular part represents the connector in the socket The rectangular part represents a contact pin of the memory module 3 4 Zero Insertion Force Sockets Zero Insertion force Z I F sockets are Integrated Circuit 1 C sockets invented to avoid problems caused by applying force during insertion and extraction of microprocessors A normal IC socket requires the IC to be pushed into sprung contacts which then grip by friction In the case of microprocessors the IC has hundreds of pins therefore the total insertion force will be very large which might damage the IC or the PCB In case of a ZIF socket before the IC is inserted a lever or slider on the side of the socket is moved pushing all the sprung contacts apart so that the IC can be inserted with very little force The weight of the IC is sufficient and no external downward force 1s required The lever is then moved back allowing the contacts to close and grip the pins of the IC Large ZIF sockets are mounted on PC motherboards This assembly of ZIF socket and IC is subjected to vibrations Vibrations may arise from neighboring components like CD drives hard drives or cooling fans which are mounted above the IC to extract heat These vibrations may cause relative mo
7. D H And Kim B M Finite Element Analysis For The Wear Of T1 N Coated Punch In The Piercing Process Wear Vol 252 pp 859 869 2002 Lancaster J The Formation Of Surface Films At The Transition Between Mild And Severe Metallic Wear Proc Roy Soc A Vol 273 pp 466 83 1963 120 Laursen T A And J C Simo A Continuum Based Finite Element Formulation For The Implicit Solution Of Multi Body Large Deformation Frictional Contact Problems Int J Numer Methods Engg Vol 36 pp 3451 3485 1993 Lim S C And M F Ashby Wear Mechanism Maps Acta Metal Vol 35 Pp 1 24 1987 Lim S C M F Ashby And Brunton J H Wear Rate Transitions And Their Relationship To Wear Mechanisms Acta Metall Vol 35 pp 1343 1348 1987 Liu Y Asthana R And Rohatgi P A Map For Wear Mechanisms In Aluminum Alloys J Mater Sci Vol 26 pp 99 102 1991 Mccoll I R Ding J And Leen S Finite Element Simulation And Experimental Validation Of Fretting Wear Wear Vol 256 pp 1114 1127 2004 Molinari J F M Ortiz R Radovitzky And E A Repetto Finite Element Modeling Of Dry Sliding Wear In Metal Engineering Computations Vol 18 No 3 4 pp 592 609 2001 Nazem M And D Sheng Arbitrary Lagrangian Eulerian Method For Consolidation Problems In Geomechanics International Conference On Computational Plasticity Vol 8 2005 Oquist M Numerical Simulations Of Mild Wear Using Updated Geometry With Different Step Size Approaches Wear V
8. at a The left hand side of the equation is the wear rate h t s t is the sliding velocity This equation has been used in this model 5 1 User subroutine UMESHMOTION User subroutine UMESHMOTION is used in ABAQUS The wear model is integrated in this user subroutine UMESHMOTION is used to define the motion of nodes in an adaptive mesh domain The magnitude of movement of these nodes is controlled by the wear law UMESHMOTION is a fortran subroutine The subroutine used in this work is presented here Different parts of the code have been explained SUBROUTINE UMESHMOTION UREF ULOCAL NODE NNDOF LNODETYPE ALOCAL NDIM TIME DTIME PNEWDT KSTEP KINC KMESHSWEEP JMATYP JGVBLOCK All the words present inside the brackets are variables They can be classified into three types depending on their function variables which have to be defined variables that can be updated and variables that are passed in for information UREF 65 This is the value of the user specified velocity provided as part of the adaptive mesh constraint definition This value is updated based on any amplitude definitions used with the adaptive mesh constraint ULOCAL ULOCAL contains components of the mesh displacement or velocity of the adaptive mesh constraint node described in the coordinate system ALOCAL ULOCAL will be passed into the routine as values determined by the mesh smoothing algorithm In this model ULOCAL contains components of the nodal velocit
9. cause wear in different ways The first group was further classified into five subgroups Fretting Wear Erosive Wear Abrasive Wear Sliding Wear and Fatigue Wear Fretting Wear occurs when two contacting surfaces undergo small oscillatory motion Wear particles generated during this process can have a significant effect due to the high frequency of sliding and small contact area This type of wear 1s common in electrical contacts In case of noble metals fretting wear may cause the electrical contact resistance to change due to wearout of the surface finish resulting in exposure of the underlying base metal Figure 2 Fretting wear of a tin terminal Courtesy of Molex 10 Erosive wear occurs due to the impingement of solid particles on the wearing surface Large sub surface deformation crack nucleation and propagation take place during this wear This type of wear is observed in turbines and helicopter blades Figure 3 Erosion of a turbine blade subjected to 1500 micron particles Hamed 2005 Abrasive wear occurs when hard particles or asperities plow and cut the contacting surfaces during relative motion This type of wear is observed in earth moving equipment after prolonged use Sliding wear occurs when two materials slide against each other It results in plastic deformation crack nucleation and propagation in the subsurface This type of wear is observed in journal bearings gears and cams Fatigue wear occurs when the surf
10. different materials It also facilitates the treatment of materials with history dependent constitutive relations The main disadvantage of the Lagrangian representation of the model is its inability to follow large distortions of the computational domain without frequent re meshing In the Eulerian description the computational mesh is fixed and the continuum moves with respect to the grid As a result of this the interface definition and resolution of details are sacrificed Figure 48 shows the Eulerian description of the sliding contact 82 The mesh is shown in Figure 48 using the dotted lines and nodes Although the material deforms the mesh remains fixed Slider DN On ROA O A A A A Material Point Particle motion O Node 2 2 2 TTT Mesh motion Figure 46 Eulerian Description of the sliding contact ALE to a certain extent succeeds in combining the best features of both the Lagrangian and Eulerian approaches In the ALE description the nodes of the computational mesh may be moved with the continuum in normal Lagrangian fashion or be held fixed in Eulerian manner or as shown in be moved in some arbitrarily specified way Because of this freedom in moving the computational mesh offered by the ALE description greater distortions of the continuum can be handled than would be allowed by a purely Lagrangian method with more resolution than that afforded by a purely Eulerian approach 83 A Material Point Particle mot
11. e where each a d and b e are array declarators Each symbolic name a appearing in a DIMENSION statement declares a to be an array in that program unit d and e are dimension declarators The code used 1s DIMENSION ULOCAL NDIM JELEMLIST 50 DIMENSION ALOCAL NDIM TIME 2 DIMENSION JMATYP JGVBLOCK In this code the line DIMENSION ULOCAL NDIM declares an array ULOCAL of length NDIM In the 2D model NDIM 2 and in case of the 3D model NDIM 3 The CHARACTER type specification statement explicitly assigns the CHARACTER data type to symbolic names The command used here 1s CHARACTER 80 PARTNAME The name PARTNAME is defined as a type character and as 80 characters long The arrays ARRAY and VEL are defined using the commands DIMENSION ARRAY 3 DIMENSION VEL 6 86 The array ARRAY is used to store the nodal stress acting on the surface nodes of the receptacle The array VEL is used to store the sliding velocity of node 21 which is the bottom node of the slider The position of this node 1s shown in Node 21 Figure 48 Nodal sliding velocity of Node 21 used to calculate wear These values of pressures and velocities are used to calculate wear on the surface nodes The PARAMETER statement is used to define constants which appear many times in a program It is then often desirable to define them only once in the beginning of the program This is done using the PARAMETER sta
12. form of a displacement history The command used 1s BOUNDARY AMPLITUDE ampl TYPE DISPLACEMENT slider I 1 0 033868 79 The first entry in the data line indicates the node number or node set label Here slider refers to the nodeset which contains all the nodes which make up the slider This is shown in Figure 45 Node set Slider A Figure 43 The node set Slider used in BOUNDARY to define slider displacement The second entry in the data line refers to the first degree of freedom constrained The number 1 indicates that the slider is constrained to move in the x direction according to the boundary conditions specified The third entry refers to the last degree of freedom constrained In this model the last degree of constrained is still 1 The third entry refers to the actual magnitude of the displacement In this case it is 0 033868mm which is equal to the max amplitude of oscillation from the central position The ADAPTIVE MESH option is used to define an adaptive mesh domain and to specify the frequency and intensity of adaptive meshing for that domain The parameter 80 ELSET is set equal to the name of the element set that contains all the solid elements in the adaptive mesh domain In this model the element set PCBcontact contains all the elements of the receptacle The command used is ADAPTIVE MESH ELSET PCBcontact FREQ 1 MESH 5 The FREQ parameter is set equal to the frequency in increments at which adapt
13. is made of brick and pie elements It is important to apply pressure on that face of the element which 1s pointing upwards to ensure correct load application C3D6 elements C3D8 elements Figure 27 Top face of the slider consisting of two different elements on which load is applied 52 In the 3D model the slider oscillates over the receptacle and causes fretting wear Figure 30 shows the neutral position of the slider with load applied Mises CEIC Fos 000e 00 000e 00 000e 00 00 e 00 2 ODB cu odb LBAQUS STANDARD Version 6 5 1 ay step Step 1 nerement O Step Tine 0 000 3 rimary Yar 5 Mises Deformed war U Deformation Scale Factor 1 000e 00 Figure 28 Von Mises stress shown at the neutral position of the slider at the start of a cycle 53 This happens at the beginning of each cycle The slider first moves to the right extreme of the PCB with load applied on the top face of the slider This position is shown in Figure 31 re le 0l ODE Cu odb ABAQUS STANDARD Version 6 5 1 aylight Time 2007 Step Step 1 nerenent 10 Step Time 5 000 3 rimary Var 5 Mises Deformed Var U Deformation Scale Factor 1 000e 00 Figure 29 Von Mises stress plot with slider at the right extreme of the receptacle After this the slider reverses direction and travels to the left extreme of the PCB This is shown in Figure 32 The slider again reverses direction and heads back to the neutral po
14. model was constructed the simulation was allowed to run for 1600 cycles Figure 67 shows the change in the surface profile and stress distribution in the pristine contact and the contact system after 1600 cycles in the new 2D model S Mises Ave Crit 75 Pristine Surface S Nises Ave Crit 75 Worn Surface ERR Figure 65 Von Mises stress plot showing wear on the contact surface due to fretting as seen in the 2D model 104 The 3D model was allowed to run for 1600 cycles shows the change in the surface profile and stress distribution in the pristine contact and the contact system after 1600 cycles in the 3D model 4a ai on Al al S 0058 SAGAS Fy His 0 g k H a 0 0 r 3 HO 0 PERENNER Pristine Surface 2 OPB Cu cdi ABLOUS STANDARD Version 6 5 1 Sj See Step 1 O Step Time 0 000 3 goera E risary Ver 3 Hises Deiormed Var ir Deformation Scale Factor 1 0008 00 3 Hises Worn Surface ABAQIS STANDARD Versi f nae 2 ODE Cu od A Step 1 ACE Gent 14 Step Time 60 00 3 Trimcy var S Hises betormed Var Deformation Scale Fagtor 1 000e 0 Figure 66 Von Mises stress plot of wear on the contact surface due to fretting as seen in the 3D model 105 As wear progresses the contact pressure at the nodes varies because of changing surface profile Thus the wear rate fluctuates continuously as wear progresses This is
15. number JTYP is set equal to 0 to look up a node number or 1 to look up an element number PARTNAME is the name of the part instance that contains NODE LOCNUM is the part local node number corresponding to NODE JRCD returns a code zero if there is an error and one 1f there s no error Utility routine GETNODETOELEMCONN is called from user subroutine UMESHMOTION to retrieve a list of elements connected to a specified node The code used 1s CALL GETNODETOELEMCONN NODE NELEMS JELEMLIST JELEMTYPE JRCD JGVBLOCK 89 NODE corresponds to the user node number in this case PCB NELEMS is the maximum allowable length of JELEMLIST JELEMLIST returns an array of element numbers for elements connected to NODE The list will contain elements only in adaptive mesh domains active in the step as well as any contact elements associated with the domain JELEMTYPE contains an array describing the element types for each element entry in JELEMLIST The number 1 in the array indicates a solid element The number 2 in the array indicates a contact element JRCD is a return code which is returned as 0 when no error is present or when there exists an output request error or all components of the output request are zero JGVBLOCK is a variable that must be passed into the GETNODETOELEMCONN utility routine Contact pressure at each node is calculated using GETVRMAVGATNODE Utility routine GETVRMAVGATNODE is called from user subroutine UMESHMOTION to access materi
16. presented analysis is applicable to wide variety of contact systems found in consumer and defense applications including RAM memory card sockets SD card sockets microprocessor ZIF sockets and fuzz button contacts ACKNOWLEDGEMENTS I would like express my sincere gratitude to my advisor Dr Pradeep Lall for letting me work on this challenging project I have benefited both professionally and personally from the many interactions I have had with him Without his guidance patience and constant encouragement completion of the thesis would not have been possible It has been a real pleasure to work with and learn from him I also wish to extend my gratitude to Dr Robert Jackson Dr Barton Prorok and Dr Jeff Suhling for serving on my thesis committee and examining my thesis I would like to thank Dr Suhling for agreeing to be on my committee at a short moment s notice I would also like to thank all my friends especially Chandan Robert Bhushan Shirish Prashant Amit Ganesh Sandeep and all other colleagues and friends whose names are not mentioned for their priceless love and support Finally many thanks go to my family for their unwavering encouragement and love vi Style manual or journal used Graduate School Guide to Preparation and Submission of Theses and Dissertations Computer software used Microsoft Office 2003 Abaqus V6 5 Hypermesh V7 0 Compaq Visual Fortran V6 0 Vil TABLE OF CONTENTS ETS TOE FIGURE
17. pressure becomes important while testing Micro Electronic Packages They have high test point density result in high pressures per square inch Gold plated hard hats are used to connect Integrated circuits like BGA s LGA s PGA s and gull wing to Fuzz Buttons These are miniature contact pins These help minimize the damage to solder balls or pins of the IC Typical hardhats are shown in Figure 8 28 Figure 8 Hard Hats Courtesy of Tecknit Interconnection Products The skin effect is the tendency of an Alternating Electric Current AC to distribute itself within a conductor such that the current density near the surface of the conductor is greater than that at its core The electric current tends to flow at the skin of the conductor There is less surface area to pass the signal The skin effect causes the effective resistance of the conductor to increase with the frequency of the current Skin effect is due to eddy currents set up by the AC current The random orientation of the wires within fuzz buttons negates the skin effect to a large extent In case of fuzz buttons the small diameter of the wire also helps reduce skin effect 3 1 2 Modeling a fuzz button contact To represent the contact between a fuzz button and the PCB a two dimensional finite element model is constructed as shown in Figure 9 29 SECTION LINE POCKET FUZZ BUTTON WIRE Figure 9 2D modeling of a fuzz button and PCB contact As shown
18. shown in Figure 69 004 0 03 0 0 0 50 01 l l 04 Pressure N mm 2 Displacement mm Figure 67 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles In Figure 69 the pressure variation is almost flat as the surface is not degraded and the contact pressure at all nodes on the receptacle is almost the same As the number of fretting cycles increase the surface gets degraded and the contact pressure exerted at various nodes changes This variation is clearly shown in the pressure versus displacement plots The X axis represents the vibration amplitude with the origin representing the neutral position The Y axis represents the pressure variation as the slider slides over the receptacle The Y axis has negative values since the pressure is compressive Several pressure plots have been plotted to show the change in pressure 106 values as the simulation progresses N represents the cycle number for which the pressure plot has been plotted 0104 0 660 Oe 0 01 04 Pressure N mm 2 Displacement mm Figure 68 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles I I 0 00 I I I 0 04 0 02 0 01 0 00 0 01 0 02 0 03 0 04 A E N 40 Z 9 2 5 R 0 3669 D 1 50 d 2 gt A Pe e o 2 00 2 50 Displacement mm
19. this stage the wear rate became independent of the apparent area of contact Kapoor and Franklin 2000 have used Archard s wear model to simulate delamination wear Sarkar 1980 has proposed a wear model that relates the friction coefficient and the volume of the material removed This model is an extension of Archard s wear model and is given by V F gt k 1 3 9 7 u 9 V is the volume of material removed s is the sliding distance k is a dimensionless wear coefficient Fn is the normal load H is the hardness and u is the friction coefficient Str mberg 1999 developed a finite element formulation for thermoelastic wear based on Signorini contact and Archard s wear model de Saracibar amp Chiumenti 1999 developed a numerical model for simulating the frictional wear behavior within a fully nonlinear kinematical setting including large slip and finite deformations This model was implemented into a finite element program where the wear was computed using Archard s wear model quist 2001 Ko et al 2002 McColl et al 2004 Ding et al 2004 Gonzalez et al 2005 and K nya et al 2005 developed wear models based on Archard s wear model and implemented them in finite element post processing Sui et al 1999 and Hoffmann et al 2005 implemented re meshing to update the geometry of 16 the model after wear Kim et al 2005 developed a three dimensional finite element model and a re meshing techniqu
20. to apply pressure on this surface slidertopsurface Figure 42 Loading surface Slidertopsurface a Dsload SLIDERTOPSURF ACE P 10 The first word in the data line represents the surface on which load is applied in this case it is slidertopsurface P stands for the distributed load type label in this case pressure The number 10 stands for the actual magnitude of the pressure applied AMPLITUDE allows arbitrary time or frequency variations of load displacement and other prescribed variable magnitudes to be given throughout a step The command used 1S AMPLITUDE NAME ampl TIME STEP TIME DEFINITION PERIODIC VALUE ABSOLUTE 1 0 3927 0 0 0 0 033868 The parameter NAME is set equal to a label that will be used to refer to the amplitude curve For AMPLITUDE an amplitude curve must be defined In this model an amplitude curve is defined which allows arbitrary time variations of displacement to be given throughout a step The amplitude curve is defined as a mathematical function as a sinusoidal variation TIME STEP TIME indicates that the amplitude is defined as a function of step time VALUE ABSOLUTE indicates that absolute magnitudes are specified for the amplitude curve DEFINITION PERIODIC defines the amplitude as a fourier series a Ag tA cosnolt to B sinna t to 23 78 In this model only the first term of the fourier series is used 1 e till n 1 The amplitude equation becomes a Ag Ay cos a t
21. AL ALOCAL is defined as the local coordinate system aligned with the tangent to the adaptive mesh domain at the node If the node is on the interior of the adaptive mesh domain ALOCAL is set to the identity matrix In case of the 2D model NDIM 2 the 2 direction 1s normal to the surface Wear occurs along this direction Figure 40 shows the wear direction in the 2D model and 3D model The nodes are moved in the direction shown in Figure 40 to simulate wear The magnitude of motion is determined from 68 ULOCAL In case of the 3D model NDIM 3 the 2 direction also lies in the plane of a flat surface or is arbitrary if the node is on an edge When NDIM 3 the 3 direction is normal to the surface Wear occurs along this direction Slavenodes Nodes undergoing wear Direction of motion of slavenodes 2 in the 2D model and 3 in the 3D model Figure 38 Direction of motion of nodes which undergo wear TIME TIME indicates the current value of the timestep DTIME DTIME indicates the time increment used in the code This is defined in STATIC in the input file KSTEP Each simulation is divided into steps KSTEP defines which Step number is progressing in the simulation KINC KINC indicates the Increment number 69 KMESHSWEEP KMESHSWEEP indicates the mesh sweep number JMATYP JMATYP is the variable that must be passed into the GETVRMAVGATNODE utility routine to access local results at the node JGVBLOCK JGVBLOCK is the vari
22. CB was modeled as a rectangular block whose length was equal to the length of the fuzz button The cylinder oscillated over the rectangular block causing wear on the PCB surface Due to the length of this model it proved computationally expensive to simulate wear using this model To reduce the running time of the simulation the model was constructed with 50 a reduced length The slider was modeled having a length equal to the width of two elements This length was equal to 0 01058mm The PCB was modeled with a length equal to the length of the slider This model is shown in Figure 27 Fuzz Button wire Length of slider equal to the width of 2 elements Figure 25 Modified 3D Model with model length equal to the width of two elements The fuzz button is made of brick and pie elements namely brick elements C3D8 and pie element C3D6 The pie element is a solid continuum element It is a 6 node linear triangular prism Figure 28 shows a pie element The brick element is a solid continuum element It is an 8 noded linear brick element This element supports adaptive meshing The PCB is entirely made up of brick elements The 3D model aims to replicate the contact conditions in the actual contact 51 Figure 26 A standard 6 noded linear pie element Load is applied on the top face of the fuzz button The face numbers of brick are important while applying load on the top face of the fuzz button wire The top face of the fuzz button
23. E 0 000025761 VELOCITY CPRESS The wear rate is in turn governed by the VELOCITY and CPRESS VELOCITY indicates the velocity of node 21 Node 21 is located on the bottom of the slider Therefore VELOCITY indicates the velocity of the slider The velocity of the slider is continuously varying It s maximum at the central position and zero at the extremes this is Shown in Figure 51 As the surface of the PCB degrades the contact pressure keeps varying The contact pressure is continuously updated using CPRESS to maintain the accuracy of the results All these factors result in an uneven wear rate 94 0 Vmax 0 Figure 49 Velocity variation of the slider affecting wear rate The accrued wear has been plotted versus fretting cycles as shown in Figure 52 S is defined as the distance of nodes from the neutral position Starting from the neutral position left side is negative and the right side is assigned positive values Several such plots have been prepared to include nodes spanning across the top face of the receptacle This plot is prepared by plotting the nodal displacement of a node located on the top face of the PCB As the number of fretting cycles increase the node moves 0 00E 00 800 1000 1200 1400 5 00E 04 1 00E 03 1 50E 03 Wear Depth mm 2 00E 03 2 50E 03 3 00E 03 Number of Fretting Cycles Figure 50 Simulated Wear Depth versus Number of Fretting Cycles at S 0 95 0 00E 00
24. Forming Annals Of The Cirp Vol 54 pp 217 220 2005 Holm R Electric Contacts Berlin Springer Verlag 1946 Hsu S M Shen M C amp Ru A W Wear Prediction For Metals Tribology International Vol 30 pp 377 383 1997 Jiang J And Arnell R D On The Running In Behaviour Of Diamond Like Carbon Coatings Under The Ball On Disk Contact Geometry Wear Vol 217 pp 190 199 1998 119 Kalin M amp Vizintin J Use Of Equations For Wear Volume Determination In Fretting Experiments Wear Vol 237 pp 39 48 2000 Kapoor A And Franklin F J Tribological Layers And The Wear Of Ductile Materials Wear Vol 245 pp 204 215 2000 Kapoor A Williams J A And Johnson K L The Steady State Sliding Of Rough Surfaces Wear Vol 175 pp 81 92 1994 Kim N H Won D Burris D Holtkamp B Gessel G Swanson P And Sawyer W G Finite Element Analysis And Experiments Of Metal Metal Wear In Oscillatory Contacts Wear Vol 258 pp 1787 1793 2005 Kato H T S Eyre And B Ralph Wear Mechanism Map Of Nitrided Steel Acta Metal Mater Vol 42 No 5 pp 1703 1713 1994 Kato K And Hokkirigawa K Abrasive Wear Diagram Proc Eurotrib Vol 4 Section 5 3 pp 1 5 Elsevier Amsterdam 1985 Konya L Varadi K And Friedrich K Finite Element Modeling Of Wear Process Of A Peek Steel Sliding Pair At Elevated Temperature Periodica Polytechnica Mechanical Engineering Vol 49 pp 25 38 2005 Ko D C Kim
25. S sea EE ENE 1X LISTOFTABLES coreenii en O Garewenaducaweadera oe eseusue ete XVI CHAPTER INTRODUCTION ales wasters tebe E tee eat nda AEA l ol selection or Wear Mechas essi 3 TZ Selecion or Wear Mode Poriioninne a a a a E N 4 CHAPTER2 LITERATURE REVIEW cripriimiurnrintn n EET 9 CHAPTER 3 FINITE ELEMENT REPRESENTATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRA HONS wv ccoccennsstrtienwoncnniebinwcwetente i iiecaonceveioets CME irra WIPE E aTe AE EA E TEES E EEN E 3 1 1 Construction of Fuzz Buttons ccccccccccccccccccccccessccccesscccceessccccessecesessesesecsuseeseaes 3 1 2 Modeline atuzz b ttom conta toane e EET DZ MEMO C AdS onee E O E R i 3 2 1 Construction of Memory Cards S D Cards ccccccccesseesesseeeeeeeeeeeeees 3 2 2 Modeling a memory Card CONtACT ecserin a i S25 Memory NMOGWIES eria n eas a E E AA 3 4 Zero Insertion Force Sockets cccecceccsceecacceccsceccsccsccecsccsccceccscscacuscacens 37 CHAPTER 4 MODELING OF ELECTRICAL CONTACTS ee eeeeeeeeeneeneneees 40 4 1 Two Dimensional Model First Model With Coarse Mesh cccccseseeeeeeeeees 40 4 2 Two Dimensional Model Second Model with a Finer Mesh 0000085 43 4 3 Three Dimensional Mode lienrssinisriuaran a a ANE 49 AA Boundary CondilonS aers a E AAE 58 CHAPTER 5 IMPLEMENTATION OF THE WEAR LAW IN THE FINITE ELEMENT MODE Conese a a a TT EN ene Cer er 64 5 1 User subroutine UMESHMOTION creierii tate asea
26. Theoretical Results 112 CHAPTER 7 SUMMARY AND FUTURE SCOPE FOR WORK 7 1 Summary In this work a methodology for simulation of fretting wear in electrical contacts has been presented Electrical contacts are subjected to relative motion due to vibrations or thermo mechanical loads during operation The finite element model developed in this paper targets a variety of end applications including RAM memory sockets SD card sockets micro processor ZIF sockets and fuzz button pressure contacts In RAM memory sockets relative motion may be experienced due to vibration or thermo mechanical loads during operation This results in edge connector pads wear causing an increase in contact resistance and electrical failure In SD card sockets repetitive sliding contact may be encountered due to shock drop thermo mechanical loads key pad actuation battery insertion and removal or during removal of the memory cards for data transfer In micro processor ZIF sockets relative motion may be caused due to vibrations resulting from internal sources like cooling systems It is critical to simulate the wear in these electrical contacts to predict product life The model has been constructed in Hypermesh Wear is calculated using Archard s Wear Law This wear is applied to the surface of the wearing 113 surface in the form of nodal displacements The nodes are moved in the direction of wear by a magnitude calculated using Archard s Law This nodal mo
27. These sockets are slightly larger than the diameter of the fuzz button The amplitude of vibration of the fuzz button depends on the size of these sockets The PCB is 0 08467mm long and its length is selected by taking into consideration the amplitude of oscillation during vibrations As shown in Figure 7 a hard hat presses down on a fuzz button The IC rests on the hard hat The contact force required to ensure proper contact 44 of fuzz buttons with the PCB is specified by fuzz button manufacturers For the size of the fuzz button used in this model a contact force of 0 834N is used The magnitude of force required is given by the manufacturer Tecknit Co This force is applied on an annular area whose width is equal to the diameter of the wire Figure 20 Loading applied on the top face of the slider The contact pressure was found by dividing the contact force by the contact area It was found to be 51 71 MPa Since the hard hat transmits the contact pressure to the fuzz button this pressure is applied on the top face of the slider This is shown in Figure 21 As the slider slides over the PCB the pressure is continuously applied on the slider 45 The slider slides over the PCB for a large number of cycles At the start of the cycle the slider is positioned at the centre of the PCB as shown in Figure 22 0 000e 00 0 000e 00 Pristine Surface e roan Figure 21 Von Mises stress plot with the position of the sli
28. WEAR SIMULATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRATIONS Except where reference is made to the work of others the work described in this thesis is my own or was done in collaboration with my advisory committee This thesis does not include proprietary or classified information Darshan U Shinde Certificate of Approval Bart Prorok Pradeep Lall Chair Assistant Professor Thomas Walter Professor Materials Engineering Mechanical Engineering Robert L Jackson Jeffrey C Suhling Assistant Professor Quina Distinguished Professor Mechanical Engineering Mechanical Engineering Joe F Pittman Interim Dean Graduate School WEAR SIMULATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRATIONS Darshan U Shinde A Thesis Submitted to the Graduate Faculty of Auburn University in Partial Fulfillment of the Requirement for the Degree of Master of Science Auburn Alabama August 9 2008 WEAR SIMULATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRATIONS Darshan Shinde Permission is granted to Auburn University to make copies of this thesis at its discretion upon the request of individuals or institutions at their expense The author reserves all publication rights Signature of Author Date of Graduation il THESIS ABSTRACT WEAR SIMULATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRATIONS Darshan Shinde Master of Science August 9 2008 B E Pune University VIT 2003 139 Typed Pages Directed by Pradeep Lall E
29. a mesh adaptation strategy based on local error indicators for non linear dynamic problems developed by Radovitzky and Ortiz 1999 has been used This meshing algorithm automatically generates unstructured tetrahedral meshes The finite element model was validated against experimental observations of Lancaster 1963 The contact system used was a 60 40 brass pin set against a rotating steel disk Podra 1999 used a finite element model to model wear for a pin on disc contact system The contact problem was solved with the area of contact between the bodies not known in advance making the analysis non linear Special subroutines were developed to generate the finite element model and define the loads and constraints automatically The model was meshed with a fixed static mesh A finer mesh was used in the areas expecting higher stress This provided accurate results at the cost of computation time The contact 20 pressure distribution in the contact area was calculated from the nodal stresses of the nodes in the contact region Damage accumulation caused due to wear was accounted for by using the Euler integration scheme hjn j i n ADjn 14 Ah n is the wear increment n is the node number and j is the step number To prevent the simulation results from becoming erratic due to excessively large wear increments a predetermined maximum wear increment limiter was defined Ahj A two dimensional half symmetry model was constructed Th
30. able that must be passed into the GETVRN GETNODETOELEMCONN and GETVRMAVGATNODE utility routines to access local results at the node PNEWDT PNEWDT is the ratio of suggested new time increment to the time increment currently being used 5 2 Defining model properties and slider sliding frequency All material properties are defined in the input file Steel on steel contact is modeled in both 2D and 3D model Material properties for steel are entered in the input file using MATERIAL This option is used to indicate the start of a material definition The slider 1s made of steel The code used in the input file 1s defined here MATERIAL NAME fuzzbutton DENSITY 7 8SE 09 ELASTIC TYPE ISOTROPIC 70 200000 0 0 29 The first line defines the name under which the material properties defined will be stored NAME is a required parameter and its set equal to a label in this case fuzzbutton that will be used to refer to the material in element property options The slider is made of steel DENSITY assigns the density to the material The slider is assigned a density of 7 85E 09 tonnes mm The material is assumed to be isotropic This is defined in ELASTIC ELASTIC is used to define linear elastic modules The modulus of elasticity of steel is defined as 200000 MPa The Poisson s ratio is defined as 0 29 Using MATERIAL the material properties of the receptacle which represents the PCB are also defined The slider needs t
31. ace is subjected to cyclic loading After several cycles fatigue cracks appear which propagate perpendicular to the surface This type of wear is observed in ball bearings and roller bearings The second group Chemical wear was 11 further classified into four subgroups Oxidative Wear Corrosive Wear Solution Wear and Diffusive Wear Oxidation Wear occurs when oxide films are formed on the surface during high sliding velocities As the thickness of the oxide film increases frictional heating causes it to flow plastically or melt Corrosive wear occurs when surfaces slide against each other in a corrosive atmosphere This results in the formation of pits Solution wear occurs when a solution is formed between the materials in contact decreasing the free energy This is an atomic level wear process in which new compounds are formed at high temperatures This type of wear is observed in carbide tools during high speed cutting Diffusive Wear occurs when there is a diffusion of elements across the interface It is observed in high speed tool steels In most practical cases materials wear out due to the combination of the above mentioned mechanisms In spite of this in order to solve the wear problem a primary mechanism is identified Ragnar Holm 1938 stated that when two surfaces were brought together they touched at their asperities and the area of contact was related to the load divided by the yield pressure of the material This contact resu
32. al integration point information averaged at a node The results variables available from GETVRMAVGATNODE are nearly the same as those available from GETVRM Since it will average results GETVRMAVGATNODE will operate only on real valued results The command used is CALL GETVRMAVGATNODE NODE CSTRESS ARRAY JRCD JELEMLIST NELEMS JMATYP JGVBLOCK NODE refers to the node number in this case nodeset PCB which contains all the nodes on the top face of the receptacle Pressure is extracted from these nodes The second input in the data line corresponds to the output variable key This key is selected from the Abaqus Standard output variable identifiers table This key is listed in the output table as 90 being available for results file output at the element integration points The key used in this model is CSTRESS This output variable CSTRESS contains three components CPRESS which indicates the contact pressure CSHEARI which indicates contact traction in the local 1 direction and CSHEAR2 which indicates contact traction in the local 2 direction The third component is returned only in the 3D model ARRAY is a real valued array containing individual components of the output variable ARRAY contains 3 components CPRESS CSHEARI and CSHEAR2 JRCD is a return code which is returned as 0 when no error is present or 1 when there exists an output request error or all components of the output request are zero JELEMLIST is an array of elemen
33. ameter of the CONTACT PAIR option The FRICTION option is used to introduce friction properties into a mechanical surface interaction model governing the interaction of contact surfaces The command used 1s FRICTION 0 78 A friction coefficient value of 0 78 is used for steel on steel contact Dieter 1986 FRICTION must be used in conjunction with SURFACE INTERACTION 75 CONTACT DAMPING is used to define viscous damping between two interacting surfaces It must be used in conjunction with SURFACE INTERACTION The command used 1s CONTACT DAMPING DEFINITION DAMPING COEFFICIENT 1 0 0 02 In the data line 1 refers to the damping coefficient and 0 02 is the clearance at which the damping coefficient is zero In Abaqus this option is primarily used to damp relative motions of the surfaces during approach or separation STEP option is used to begin each step definition It must be followed by a procedure definition option The command used 1s STEP nlgeom yes inc 1000000 NLGEOM YES 1s used to indicate that geometric nonlinearity should be accounted for during the stress analysis Once the NLGEOM option has been switched on it will be active during all subsequent steps in the analysis INC is set equal to the maximum number of increments in a step This value is only an upper bound In this analysis the maximum number of increments is set at 1000000 STATIC is used to indicate that the step should be analyzed as a static loa
34. ard s Law W ka F 13 ka is the Archard s wear coefficient A two dimensional model was constructed for a pin on disk configuration with the pin modeled as a square pin for the sake of simplicity Molinari 2000 developed a finite element model to show dry sliding wear in metals Adaptive meshing was used in the model to remove deformation induced element distortions While using Adaptive meshing a Lagrangian formulation was used to move nodes to their new position 19 Archard s law was used for damage computation To model the transition of wear rates with increase in sliding speeds Archard s law was generalized by allowing the hardness of the material to change with temperature The change in hardness affects the wear rate when used in Archard s Law According to Lancaster 1963 the transition of wear rates was a direct result of the presence of oxide layer At higher sliding speeds higher contact temperatures exist which increases the oxidation rate The protective oxide layer gets regenerated faster than it is removed by wear The dependence of hardness on temperature H T takes into account the effects of oxidation The Newmark algorithm was used to enforce the impenetrability constraint in the contact which is used to calculate the frictional forces and the contact pressure used in Archard s Law Frictional forces are used to calculate heat generated which change the hardness of the material During adaptive meshing
35. ard s coefficients for some common contact systems are given in Table 5 Zinc on zinc 0 0530 Copper on copper 0 0110 Platinum on platinum 0 0130 Mild steel on mild steel 0 0150 Stainless steel on stainless 0 0070 steel Copper on mild steel 0 0005 Mild steel on copper 0 00017 Table 5 Archard s Wear Coefficients Table Rabinowicz 1995 The value of Hardness used for steel 1s 424MPa The formula used is 92 WEARRATE 0 000035377 VELOCITY CPRESS If a copper on copper contact system is used Archard s coefficient for copper is 0 0110 The hardness value used for copper is 427MPa The formula used is WEARRATE 0 000025761 VELOCITY CPRESS Once the wear rate is calculated the wear occurring at the nodes is calculated using the formula ULOCAL NDIM ULOCAL NDIM WEARRATE ULOCAL contains components of the mesh velocity of the adaptive mesh constraint node Wear rate is subtracted from ULOCAL to simulate ablation The nodes undergoing wear move in a direction normal to the surface with a velocity equal to ULOCAL 93 CHAPTER 6 MODEL PREDICTIONS AND MODEL VALIDATION 6 1 Model Predictions The simulation was allowed to run for 2000 fretting cycles Wear accrues on the contact surface of the connector with increase in fretting cycles As the simulation progresses the nodes at the surface of the receptacle move in a direction shown in Figure 40 The velocity at which these nodes move is governed by the formula WEARRAT
36. are used in several electronic devices like cell phones cameras and gaming consoles Amongst memory cards SD card is a very popular configuration Very often in these devices the memory card must be removed for data transfer and reinserted Typically an insertion force of 40N is required for these cards After several insertions and removals the contacts of the sockets will wear off These cards are used in several portable devices During their usage these devices may be subjected to drops or shocks or vibrations generated due to neighboring components which might result in fretting wear 31 3 2 1 Construction of Memory Cards S D Cards A Secure Digital card is compact with dimensions 24mm 32mm 2 1mm It was jointly developed by Panasonic SanDisk and Toshiba The Secure Digital Card is a flash based memory card that is specifically designed to meet the security capacity performance and environmental requirements required in newly emerging audio and video consumer electronic devices An SD card includes a copyright protection mechanism It uses a nine pin interface for communication These pins are subjected to fretting wear and eventually will get damaged resulting in card failure Figure 10 shows an SD card with nine contact pins Write protect tab 24 l al yp Figure 10 A typical SD Card construction 32 Each pin has a specific function These pins perform the following functions pin for clock 1 pin for command 4
37. ation of nodes in UMESHMOTION ccccccccccccceeceeeeeeeeeeeeeeeeeees 67 Table 5 Archard s Wear Coefficients Table Rabinowicz 1995 ceecee 92 XVI CHAPTER 1 INTRODUCTION Microelectronic Technology has evolved at a fast rate resulting in the shrinking of the size of electronic components As devices become portable they also become more susceptible to vibrations during usage and transportation Electronic components are subjected to vibrations during the operational life of the component The vibrations are transmitted inside the body of the component There exist several electrical contacts in a component When these contacts are subjected to repetitive vibrations fretting wear occurs Fretting wear is defined as the repeated cyclical rubbing between two surfaces which over a period of time will remove material from one or both surfaces in contact Fretting wear can reduce the life of components Wear is a very complex phenomenon Based on the failure mechanism wear can be defined in many ways a few of which are listed below Wear can be categorized into several categories adhesive wear abrasive wear surface fatigue and corrosion Adhesive wear occurs when asperities interact leading to transfer of metal from one surface to another This occurs at high speeds and temperatures Scuffing is a severe form of adhesive wear In Scuffing material 1s removed from the hotter surface and deposited on the cooler surface Abrasive w
38. card Courtesy of Panasonic 34 Figure 12 2D Modeling of a Memory card and a memory card connector contact based on SD Card Product Manual Courtesy of Hirose Connectors 34 Figure13 A Typical Dual In line Memory Module Courtesy of Kingston Technology 35 Figure 14 A Typical Memory Socket Courtesy of Kingston Technology 36 Xi Figure 15 A 2D model representing a memory module and its corresponding socket based on DIMM Socket Manual Courtesy of DDK Sockets 36 Figure 16 2D model representing a ZIF socket and IC pin contact based on Lin 2003 38 Figure 17 2D Model Representation of Fuzz Button contacting the PCB 41 Figure 18 A standard Constant Strain Triangle 3 noded linear plane strain element 42 Figure 19 A standard Q4 4 noded bilinear plane strain element 43 Figure 20 2D Model with a finer mesh representing the fuzz button and PCB 44 Figure 21 Loading applied on the top face of the slider 45 Figure 22 Von Mises stress with the position of the slider at the start of a cycle 46 Figure 23 Von Mises stress at the rightmost position of slider after completion of one quarter of a cycle 47 Figure 24 Von Mises stress at the leftmost position of the slider after completion of 3 4th of the cycle 48 Figure 25 Von Mises stress on a worn out PCB surface after several cycles 49 Figure 26 3D model representing a fuzz button contact on a PCB 50 Figure 27 Modified 3D Model with model length equal to the width of two elements 51
39. cheme used explained in Equation 14 is used to integrate the wear law over the sliding process The surface nodes in the contact region are shifted in the direction of the inward surface normal depending on the amount of wear at that particular node To allow this motion the surface elements would have to be meshed such that they have enough height to accommodate this wear resulting in a coarse mesh in the contact region This problem was eliminated in this model by using Adaptive Remeshing The element mesh in the contact region is re meshed which corrects the deformed mesh at the surface The nodes are shifted towards the interior of the model depending on the amount of wear This refines the mesh and reduces the size of the elements To apply the calculated wear the model is fixed in space at its geometrical boundaries except at the surface nodes At the surface nodes the computed wear is applied as a displacement boundary condition which moves the surface nodes inside the 22 material These new nodal coordinates form the reference configuration for the next wear step Dry sliding contact has been simulated in this model Wear occurring due to the rotation of a hemispherical Brass ring on flat steel ring has been simulated Load is applied on the top surface of the brass ring as it rotates on the steel ring whose position 1s fixed The contact is initially non conformal contact which conforms with sliding due to wear Hegadekatte s model
40. d Degrees of freedom corresponding to that number a X Displacement O l Y Displacement 3 Z Displacement Rotation about the x axis in radians Rotation about the y axis in radians ia Rotation about the z axis in radians Table 3 Numbers corresponding to dof used in Abaqus 58 Once the motion of the slider was constrained it was necessary to fix the position of the PCB which acts as the receptacle This was achieved by using the command BOUNDARY in the inp file The command used was BOUNDARY PCBbotnodes ENCASTRE A nodeset PCBbotnodes was defined which contained all the nodes on the bottom face of the PCB The ENCASTRE command makes dof to 6 zero 1 e all dof are zero The PCB is not allowed to displace or rotate in any direction All the Boundary Conditions applied to the slider and the receptacle are shown in Figure 35 Nodeset slidertopsurfnodes Nodeset pcbbotnodes Figure 33 2D contact model with applied constraints 59 In case of the 3D model similar boundary conditions are enforced The slider is constrained to displace only in the X and Y directions All rotational degrees of freedom are constrained This was enforced by using the command BOUNDARY The command used was BOUNDARY topnodes 3 6 A nodeset topnodes is defined which contains all the nodes on the top surface of the slider The numbers 3 6 indicate that dof from 3 to 6 are constrained In ABAQUS each number stands for a specific do
41. d step The command used 1s STATIC 05 3 0 000000005 0 5 In the data line the first number 0 5 indicates the initial time increment This value will be modified as required if the automatic time stepping scheme is used In this model automatic time stepping scheme is used The second number 3 indicates the time period of the step If this entry is zero or is not specified a default value of 1 is assumed The 76 third number 0 00000005 is the minimum time increment allowed in the automatic time increment If ABAQUS finds it needs a smaller time increment than this value the analysis is terminated A small value is selected for the minimum time increment to prevent the analysis from getting terminated If this entry is zero a default value of the smaller of the suggested initial time increment or 10 times the total time period is assumed The last number 0 5 is the maximum time increment allowed A very high value of increment may cause the simulation to fail CONTACT CONTROLS is used to provide additional optional solution controls for models involving contact between bodies The command used 1s CONTACT CONTROLS FRICTION ONSET IMMEDIATE FRICTION ONSET IMMEDIATE instructs the model to include friction in the increment when contact occurs DSLOAD is used to prescribe distributed surface loading A surface slidertopsurface is defined at the top face of the slider This surface is shown in Figure 44 DSLOAD is used
42. depending on the sliding velocity At moderate sliding velocities flash temperatures are reached and iron oxide is formed as wear debris The oxide film formed on the surface is cold and brittle which causes this film to split off This is called mild oxidation wear The amount of wear is given by 2 CA wala OO exp _ Qo JE 11 Z a RTp v 18 W is the normalized wear rate C is a constant Ao is the Arrhenius constant for oxidation ro is the radius of the pin Ze is the critical thickness of the oxide film a is the thermal diffusivity Qo is the activation energy for oxidation R is the molar gas constant T is the flash temperature F is the normalized load and v is the sliding velocity As the sliding velocities increase the interface temperatures increase resulting in the formation of a thicker continuous and a more plastic oxide film This is called severe oxidation wear The amount of wear is given by f K Tp A nae aq ox m b Ar 12 le A fm 1s the volume fraction of molten material removed during sliding a is the heat distribution coefficient q is the rate of heat input per unit area Kox is the thermal conductivity of the oxide T is the melting temperature of the oxide Tp is the bulk temperature l is the diffusion distance for flash heating A is the real area of contact A is the nominal area of contact At very low sliding speeds surface heating is negligible Wear rate was calculated using Arch
43. der at the start of a cycle After this the slider moves to the right extreme of the PCB The magnitude of this movement is decided by the size of the PCB The dimensions of the PCB depend on the amplitude of vibration Figure 23 shows the slider in the rightmost position During this motion pressure is continuously applied on the top face of the slider At this position one quarter of the cycle is complete 46 Mises Time 2006 Figure 22 Von Mises stress at the rightmost position of slider after completion of one quarter of a cycle At the position shown in Figure 23 the slider reverses direction and heads back towards the central position Once it reaches the centre one half of the cycle gets completed The slider continues to move leftward till it reaches the position shown in Figure 24 This position marks the completion of 3 4 of the cycle 47 5S Mises Pave CEIC 8032 02 ODB cu odb LBAOUS ST Figure 23 Von Mises stress at the leftmost position of the slider after completion of 3 4th of the cycle During this entire motion pressure 1s applied on the top face of the slider As the slider moves from the rightmost position shown in Figure 23 to the leftmost position shown in Figure 24 the PCB surface gets damaged These are the first signs of wear on the PCB surface At this position the slider reverses direction and heads back to the central position This marks the completion of one cycle The slider is al
44. doesn t take into consideration the changes in the model as wear progresses The results obtained at individual nodes do not take into consideration the history of the loading at those nodes Thompson 2006 proposed a wear model which calculated wear in the solution process instead of calculating it in the post processor to eliminate the drawbacks of Hegadekatte s model A modified Archard s equation was used in this model W K 8 7 R amp 18 W is the change in volume K C2 C3 are constants which account for the materials in contact S is the stress created by the contacting pairs and R is the number of repetitions of the load A quantity known as wear strain was defined by dividing Equation 18 by the original volume Cy C1 S RO 19 wr 1s the wear strain C1 is equal to K divided by the original volume Unlike other strains wear strain represents material that is removed from the system Wear strain used in this model differs from wear as proposed by Archard In Archard s equation the applied loading is assumed to be distributed over the entire loading area hence wear is expected to occur uniformly over the entire surface The 23 Wear strain proposed in this model is a function of stress and load repetitions Only those regions of the surface which are loaded experience wear Wear strain permits wear to be different at different locations of the surface depending on the loading condition This model uses a wear
45. e for simulating wear on a block contacting a rotating ring Podra amp Andersson 1997 Jiang amp Arnell 1998 and Dickrell amp Sawyer 2004 used the elastic foundation method for the computation of contact pressure The elastic foundation method for contact pressure computation did not take into consideration the effects of shear deformation or lateral interactions in the contact In these models wear was calculated using Archard s wear model Yan et al 2002 proposed a computational approach for simulating wear on coatings in a pin on disc contact system Agelet 1999 developed a numerical model for the simulation of frictional wear behavior He used a nonlinear kinematic setting which included large slip and finite deformation The model uses a fully nonlinear frictional contact formulation Wear occurring in tools is predicted by using a wear estimate derived from Archard s Law Hot forging and sheet metal forming are the two processes considered for which wear is calculated Hot forging dies get worn off due to Abrasive Wear Hard scale particles embedded in the surface of the work piece cause the die to wear In sheet metal forming process abrasive and adhesive wear are the two main mechanisms which cause die failure During the process when the sheets are pressed together the real area of contact is much smaller than the apparent one due to the presence of asperities and surface roughness The high pressures involved causes plast
46. e model was verified by performing experiments involving a spherical steel pin sliding on a steel disc Hegadekatte 2005 has created a finite element model which simulates wear between steel and brass contact system Archard s wear law has been used for damage computation Two dimensional and three dimensional models have been constructed to simulate wear Wear is computed on both the interacting surfaces In wear simulation the maximum amount of wear possible is limited by the surface element height To overcome this limitation adaptive re meshing has been used in this model A wear simulation tool has been developed which solves the contact problem a number of times at different stages of the sliding process Contact pressure is calculated at the surface nodes which are involved in wear The contact pressure is calculated at the surface nodes from the normal vector and the stress tensor calculated at each surface node t O 0 15 Se Ea P t nj 2i tj is the traction vector oj 1s the stress tensor nj is the inward surface normal at the corresponding surface node and P is the contact pressure Archard s wear model is used to calculate wear at each of the surface nodes kp P 16 h is the nodal wear s is the sliding distance kp is the dimensional wear coefficient and P is the contact pressure at each surface node This wear law is discretized with respect to the sliding distance as ee P 17 ds An Euler integration s
47. ear occurs when a surface is damaged by the introduction of a harder material This harder material could exist in the form of particles which enter the contact system externally or they can be internally generated by oxidation or other chemical processes Surface fatigue is a form of wear which is predominant in rolling contact bearings These bearings are subjected to repeated intense loadings Hertzian stress 1s distributed in such a way such that the max shearing stress occurs within the surface As a result of this failure commences below the surface This finally results in pitting failure Hirst 1957 classified wear depending on it s intensity into mild and severe wear Lancaster 1963 suggested a theory for the transition of wear from mild wear to severe wear When two surfaces contact resulting in wear there exists two opposing dynamic processes the first one being the rate of formation of fresh metal surfaces as a result of wear the other being the rate of formation of a surface film as a result of the reaction with atmosphere These surface films are generally oxide films which remain protective as long as they bond to the parent surface and are rapidly renewed In the absence of these films surfaces in contact tend to seize resulting in extremely high friction and surface damage Scuffing wear is defined as surface damage characterized by the formation of local welds between sliding surfaces In scuffing there is a tendency for ma
48. ection The fuzz button was allowed to 56 oscillate on the PCB which resulted in ring on ring contact This model is shown in Figure 34 Fuzz Button Figure 32 A circular model representing a fuzz button contacting a PCB The bottom face of the PCB ring was fixed It was found that modeling wear in this model was computationally expensive To run the wear simulation using this model for a large number of cycles was computationally expensive and the running time was 7 days As a result this model was abandoned and the 3D model shown in Figure 33 was used 3 4 4 Boundary Conditions Boundary conditions were enforced both in the 2D model and 3D model to constrain the motion of the fuzz button wire In the 2D model the slider which represents the fuzz button was constrained to move only in the X and Y direction Only the displacement dof was active Rotation of the slider about the X and Y axis was not permitted It was not allowed to move in the Z direction or rotate about the Z direction This was enforced using the command BOUNDARY in the input file The command used was BOUNDARY slidertopsurfnodes 3 6 A nodeset slidertopsurfnodes is defined which contains all the nodes on the top surface of the slider In Abaqus each number corresponds to a specific dof This is shown in Table 3 The number 3 defines the first dof constrained The number 6 defines the last dof constrained This meant that dof 3 4 5 and 6 are constraine
49. ed to the projection point This is shown in Figure 43 Master Surface ie 1 a yo Slave Surface Figure 41 Node to Surface contact discretization In node to surface discretization the slave nodes are constrained not to penetrate into the master surface The contact discretization is based on the normal of the master surface 74 Abaqus enforces the following rules related to the assignment of master and slave surfaces A rigid element based surface must always be a master surface A node based surface can act only as a slave surface Slave surfaces must be attached to deformable bodies The INTERACTION parameter is set equal to the name of the SURFACE INTERACTION property definition associated with the contact pair being defined The first surface in the data line SURFACE 1s the slave surface The second surface in the data line SURF ACE2 is the master surface The master surface is an elemental surface and the slave surface is a nodal surface Since the PCB is supposed to wear off it is assigned to be the slave surface SURFACE INTERACTION is an option used to create a surface interaction property definition The surface interaction properties will govern any contact interactions that reference this surface interaction The command used 1s SURFACE INTERACTION NAME fricbhv The parameter NAME is set equal to a label that will be used to refer to this surface interaction property This label is used in the INTERACTION par
50. elected to reduce the simulation running time at the cost of accuracy of results Once it was established that the analysis was running successfully a new 2D model was constructed with a finer mesh This resulted in the increase of computation time but at the same time better results would be obtained 4 2 Two Dimensional Model Second Model with a Finer Mesh A new 2D model was constructed in HYPERMESH using a finer mesh Material properties were assigned to the model The slider which represents the fuzz button was assigned the properties of BeCu namely the density modulus of elasticity and poisson s ratio The top surface of the PCB where the fuzz button contacts is made of copper The receptacle which represents the PCB was assigned the material properties of copper The semicircular slider was modeled using Q4 quad elements and some CST triangular 43 elements Q4 is a solid 4 node bilinear plane strain element CST is a 3 node linear plane strain element The rectangular PCB was modeled using Q4 quad elements Figure 20 shows the fine mesh model 0 0508 La FUZZ BUTTON amp cv0 0 0 08467 Figure 19 2D Model with a finer mesh representing the fuzz button and PCB The dimensions of the model are selected to represent the actual size of the electrical contact As shown in Figure 20 the fuzz button wire has a diameter of 0 0508mm This wire is subjected to vibrations The fuzz buttons are mounted inside sockets
51. equation that is similar to creep equations Creep is used to simulate wear The strain hardening creep equation used 1s given by Leo C1 stress 7 pa exp C4 T 20 C1 C2 C3 C4 are user defined constants Incremental creep strain is calculated using Equation 20 The incremental creep strain is multiplied by the incremental time and added to the previous creep strain The same procedure is used to calculate the wear strain For each load step the incremental wear strain is calculated multiplied by the load step time and added to the previous wear strain 24 CHAPTER 3 FINITE ELEMENT REPRESENTATION OF ELECTRICAL CONTACTS SUBJECTED TO VIBRATIONS The wear simulation tool developed here can be used to simulate wear between electrical contacts subjected to vibrations In today s electronic devices there exist thousands of electrical contacts In this work four different electrical contact systems have been studied namely Fuzz Buttons SD Cards Memory Cards and Zero Insertion Force Z I F sockets A finite element representation of each of these electrical contacts has been presented here 3 1 Fuzz Buttons Fuzz buttons are special interconnects used to connect an Integrated Circuit I C to a Printed Circuit Board P C B Fuzz button interconnections have several advantages over traditional interconnections like soldering socketing and plug in connectors due to their simple design good performance and long
52. ese vibrations are transmitted inside the electronic components to the contacts This causes repeated cyclical rubbing between the contact surfaces resulting in fretting wear This can lead to sudden and premature failure of the component Experimental techniques and simulations are used to predict wear rates for different contact systems This has resulted in a better understanding of the wear processes leading to accurate life predictions Wear is a complex phenomenon Wear modeling has been a subject of extensive research in the past There exist several theories and equations that try to explain wear and measure it Due to its complex nature there exists no universal law that can explain wear A thorough study of the literature published on wear is necessary to understand the various methodologies used to predict wear and how various wear models are used in wear simulations to predict wear rates Wear is a process which occurs when the surfaces of engineering components are loaded together and subjected to sliding or rolling motion Archard 1980 There are many major mechanisms that are involved in wear Burwell 1957 was the first to attempt a classification of these wear mechanisms Wear mechanisms were classified by Suh 1986 into two groups The first group consisted of mechanisms which were governed by mechanical behavior of solids The second group consisted of mechanisms which were governed by the chemical behavior of materials Solids can
53. f This list is given in Table 3 The receptacle which represents the PCB needs to be fixed 1 e all dof s must be constrained This is achieved by using the command ENCASTRE ENCASTRE makes dof 1 through 6 zero As a result of this all displacement dof and all rotational dof are zero The command used was BOUNDARY _PickedSet16 ENCASTRE _PickedSet16 is a nodeset which contains all the node on the bottom surface of the PCB The fixed receptacle is shown in Figure 36 60 Fixed PCB Nodeset PickedSet16 Figure 34 3D model with a fully P receptacle The receptacle is fully constrained using the command ENCASTRE The PCB is fixed as the fuzz button oscillates on the PCB The slider is allowed to slide in the X and Y directions Displacement degree of freedom in the z direction and all rotational degrees of freedoms are constrained This is shown in Figure 37 6l Sliding fuzz button wire Slider constrained to slide in the X and Y directions _ gt Figure 35 3D Model with a partially constrained slider As the slider slides on the receptacle load is applied on the top face of the slider The loaded slider is shown in Figure 38 The top face of the slider consists of brick and pie elements While applying load it is important to ensure that load is applied on the correct element face This element face number may vary depending on the orientation of the element This is done by picking the faces of the elements manual
54. f prow by back transfer to flat e Newly formed prow f Prow consisting of overlapping thin layers of metal The Arrow indicates the direction of movement of flat Slade 1999 wear rates wear was determined by measuring the wear scar on the pin For higher wear rates wear was measured by weighing the pin The apparent area of contact was minimum at the start of the experiment and increased with an increase in the dimension of the wear scar It was found for metals light loads resulted in mild wear As the load was increased after a period of mild wear severe wear was initiated as a patch of heavy damage This creates the conditions for the continuance of severe wear and the rough patch spreads to cover the entire contacting surface It was found that mild wear involved the slow removal of the tips of the higher asperities and severe wear involved the welding and plucking of surfaces Unlike mild wear severe wear also resulted in subsurface 15 damage In severe wear the crystal structure of the surface layers becomes heavily distorted and these deformations extended below the surface It was concluded that the transition from mild to severe wear was associated with a change in depth of deformation Hirst and Lancaster 1956 found during the early stages of rubbing wear rate changes but after an initial period of running the wear rate becomes constant This occurred when the two contacting surfaces attained their equilibrium condition At
55. fretting cycles 103 Figure 66 Nodal Displacement plot in the receptacle at 800 cycles 103 Figure 67 Von Mises stress plot showing wear on the contact surface due to fretting as seen in the 2D model 104 Figure 68 Von Mises stress plot of wear on the contact surface due to fretting as seen in the 3D model 105 Figure 69 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 106 Figure 70 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 107 Figure 71 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 107 X1V Figure 72 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 108 Figure 73 Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles 108 Figure74 Comparison of Predicted Wear Rates Versus Experimental Results 110 Figure75 Comparison of Predicted Wear Rates versus Theoretical Results 112 Figure76 A typical vibration experimental setup 115 XV LIST OF TABLES Table 1 Classification of Wear Mechanisms ccccscsseesssesesseseesseeeseeseesseeeeeeeeeeeeeees 3 Table 2 SD Card pins and their functions ccccccccccccccccceeeseseeeccceeeecaaseseeececeeeeeaaaeeeees 33 Table 3 Numbers corresponding to dof used in AbDaquy cccccccccccececeeeeeeeeeeeeeeseeeees 58 Table 4 Classific
56. ic deformation of these asperities At the same time the metal sheet slides over the tool surface generating heat due to frictional dissipation High pressures combined with heat generation leads to welding of the asperities of the two contacting surfaces The break off of these welded asperities 17 scratches the tool surface and causes wear For constant friction coefficient wear is calculated using the formula z Sweat g 10 HoH where Z is the wear volume per unit area K wear 1S a wear constant which is determined experimentally uois the constant friction coefficient H is the hardness of the material and a is the frictional dissipation force per unit length or the slip amount A two dimensional model of the roller die was constructed to study the effects of wear on the die Time integration of the wear rate estimate is carried out which gives an estimate of the accumulated tool wear over a large number of cycles Cantizano 2002 used a microthermomechanical approach in his model In this model depending on the operating conditions normal force and sliding velocity the predominant wear mechanism is selected In order to reproduce the behavior of the contact interface between two rough surfaces a plastic law for the behavior of the asperities in contact based on statistical characterization of the surfaces has been implemented Steel on steel contact has been modeled Cantizano calculated wear using three different wear equations
57. in Figure 7 fuzz buttons are mounted in sockets As mentioned earlier fuzz buttons are used in applications involving severe vibrations There exists a slight clearance between fuzz buttons and their respective sockets The diameters of the sockets are slightly bigger than the diameters of fuzz buttons to facilitate easy removal of fuzz buttons during repair When this assembly is subjected to external vibrations the fuzz buttons oscillate at a high frequency inside sockets After several oscillations the surface 30 of the PCB wears off due to fretting wear This might result in the loss of an electrical connection leading to failure of component When fuzz buttons are used in test sockets they deform slightly when the test socket 1s loaded with a component This might cause the fuzz button wire to slide against the PCB resulting in fretting wear The contact between a fuzz button and PCB is simplified to enable modeling The bottom of the fuzz button 1s assumed to be a complete circle of wire A model is constructed which represents the cross section of a circular wire on a flat PCB Since the bottom of the wire is contacting the PCB only the lower semicircular half of the wire is modeled This semicircular slider oscillates on the rectangular receptacle resulting in fretting wear The wear model presented here will help predict the wear rate of the PCB which will help to predict the life of the component 3 2 Memory Cards Memory Cards
58. ing portion of the electrical contact contacts the fixed portion which is represented by the rectangular receptacle 4 1 Two Dimensional Model First Model with Coarse Mesh A two dimensional model is constructed to represent the contact between a fuzz button and PCB To simplify the model a single wire from the fuzz button which contacts the PCB has been modeled Instead of modeling the entire wire a circular cross section of the wire has been modeled During contact only the bottom half of the wire will contact the PCB To simplify the model further only the bottom half of the wire is modeled 1 e a semicircular cross section representing the bottom half of the wire has been constructed which slides on the PCB 40 Since the amplitude of oscillation of the wire on the PCB is very small instead of modeling the entire PCB only a small rectangular section of the PCB has been modeled The semicircular slider representing the wire oscillates on the rectangular receptacle representing the PCB After several oscillations the surface of the PCB wears off due to fretting wear Figure 17 shows the two dimensional model representing the contact system SLIDER REPRESENTING RECEPTACLE THE FUZZ BUTTON REPRESENTING WIRE THE PCB Figure 16 2D Model Representation of Fuzz Button contacting the PCB This two dimensional model is constructed in HYPERMESH Material properties are assigned to the model The fuzz button is made of Bery
59. inst a copper receptacle The wear coefficient for copper copper contact was assigned a value of 0 0110 Rabinowicz 1995 The hardness value of copper used was Hv 130 A clean and dry contact surface was assumed with a coefficient of friction equal to 1 21 The contact pressure was continuously extracted from the model and updated depending on the location of the node on the receptacle and the position of the upper pin The analytical data was calculated from Archard s law using the formula 110 h ae s P 26 H Upon substituting the values this relation was found to be h 0 00025761 s The Archard s law plot was plotted using this relation Wear depth of the slider in mm was plotted on the Y axis and the cumulative sliding distance in mm was plotted on the X axis Simulation results were extracted from the model and plotted on the same x and y axis Simulation plots were plotted for several nodes on the top face of the receptacle The slopes which indicate wear rates were compared for the theoretical Archard s Law plot and the simulation plot as shown in Figure 75 Similar wear rates were found indicating that the model had been validated 111 Model Predictions Archard s Law 0 0016 0 0014 T 0 0012 0 001 na _ oz gt 0 0008 O t 0 0006 0 0004 0 0002 0 2 4 6 8 Cumulative Displacement mm Figure73 Comparison of Predicted Wear Rates versus
60. ion O Node aaan Mesh motion Figure 47 Arbitrary Lagrangian Eulerian description of the model The use of ALE in the sliding contact wear problem allows a topologically similar mesh throughout the analysis without creating or destroying elements allowing the mesh to move independently of the material ALE adaptive meshing enables the maintenance of a high quality mesh throughout an analysis even when the contact surface gets worn out by allowing the contact surface mesh to move independently of the material The topology and connectivity of the elements is not altered Abaqus applies the user specified spatial mesh constraint without regard to the current material displacement at the node This behavior allows a mesh displacement that differs from the current material displacement at the free surface of the adaptive mesh domain effectively eroding material at the boundary The analysis is performed in two steps a Lagrangian step followed by an Eulerian step In the Lagrangian step material displacements are 84 obtained by solving the governing equations In the Eulerian step a new mesh 1s generated for the deformed domain All kinematic and static variables are then transferred from the distorted mesh to the new mesh The mapping is performed using a first order expansion of Taylor s series which is also known as the convection equation in the ALE literature The ADAPTIVE MESH CONSTRAINT option is used to prescribe independent me
61. ion Bearings Gears where stresses gt Scuffing Sliding with the formation of local welds exceed the endurance limit of the material Adhesive Wear Relative motion Bronze Bush wear wear of with interaction of shafts asperities Impact Wear One body impacts Presses Punches hammers fo the other rain erosion Corrosive Wear No motion Metal parts like chains necessary subjected to harsh Deterioration of the environments material due to reaction with the environment Cavitation Collapse of vapor Water pipes water pumps bubbles in liquid due to pressure fluctuations From the above discussion it can be inferred that when relative motion exists between two surfaces the surfaces can be attacked by a variety of wear modes they can be damaged in different ways depending on various factors like the thermal and chemical environment at the point of contact and materials of the mating surfaces and surface 4 properties In most cases wear can result due to the combination of wear modes described above and it 1s impossible to predict which mode is dominant It is possible however to select the dominant wear mode based on the type of system the nature of relative motion between the contacting surfaces and the application In this work wear between electrical contacts subjected to vibrations has been simulated Based on the application and the nature of relative motion fretting wear is the dominant wear mode Table 1 show
62. it Interconnection Products 26 Fuzz buttons are available in diameters ranging from 0 010 to 0 125 Their lengths may vary from 2X to 10X their diameter Fuzz buttons are tiny Figure 6 gives a general idea of the size of fuzz buttons Figure 6 Small size of fuzz buttons enabling high contact density Courtesy of Tecknit Interconnection Products Fuzz buttons provide a low inductance value and a short signal path resulting in a distortion free connection Fuzz buttons are also currently used in test sockets for various chip packages like Ball Grid Arrays Pin Grid Arrays and Land Grid Arrays Figure 7 shows the assembly of a fuzz button in a test socket 27 BGA HARD HAT FUZZ BUTTON SOLDER BALL PCB Figure 7 Fuzz button assembly Spring characteristics of the fuzz button contacts are excellent as they are made from high tensile strength gold plated BeCu wire This ensures long life of the contacts Each fuzz button is designed to compress 15 with no compression set within the socket When fuzz buttons are used in test sockets more than 500 000 insertions are possible on a single test socket before the fuzz buttons have to be replaced In test sockets a single fuzz button can also be removed to isolate a connection to aid testing and fault finding on a particular chip package The contact pressure required to use fuzz buttons is minimal enabling them to be used with most delicate of packages This reduction in
63. ive meshing is to be performed In this model the frequency is set to 1 This ensures that adaptive meshing is performed frequently and the model geometry is updated as the simulation progresses The MESH parameter is set equal to the number of mesh sweeps to be performed in each adaptive mesh increment This number cannot be set to a very high number as this would increase computation time Only those elements which are specified in the adaptive mesh domain will be allowed to undergo wear Figure 46 shows the adaptive mesh domain used in this model defined by element set PCB contact Adaptive mesh domain element set pcbcontact Figure 44 Adaptive mesh domain defined using element set PCBcontact Arbitrary lagrangian eulerian ALE formulation with adaptive meshing has been used to simulate wear in this model ALE has been used to combine the advantages of the 81 Lagrangian and Eulerian descriptions In the Lagrangian representation of the model each individual node of the computational mesh follows the associated material particle during motion This is shown in Figure 47 The material points represented by triangles overlap the nodes The particle motion solid lines overlap the mesh dashed lines Slider Receptacle A Material Point Particle motion O Node TRF FFT rrr Mesh motion Figure 45 Lagrangian description of sliding contact Lagrangian description allows an easy tracking of free surfaces and interfaces between
64. lectrical contacts may be subjected to wear because of shock vibration and thermo mechanical stresses resulting in fretting increase in contact resistance and eventual failure over the lifetime of the product Previously models have been constructed for various applications to simulate wear for dry unidirectional sliding wear of a square pin unidirectional sliding of pin on disk and wear mechanism maps for steel on steel contacts In this paper a wear simulation model for fretting of reciprocating curved spring loaded contacts has been proposed based on instantaneous estimation of wear rate which is time integrated over a larger number of cycles with continual update of the contact geometry during the simulation process Arbitrary Lagrangian Eulerian adaptive meshing has been used to simulate the wear phenomena Model predictions of wear have been compared to experimental data plots available from existing literature to 1V validate both the 2D and 3D models A large number of wear cycles have been simulated for common contact geometries and the wear accrued computed in conjunction with the wear surface updates The modeling methodology extends the state of art by enabling the continuous wear evolution of the contact surfaces through computation of accrued wear The proposed methodology is intended for reducing the number of design iterations in deployment and selection of electrical contact systems in consumer and defense electronics The
65. life Fuzz buttons provide a reliable and a cost effective interconnection for new chips which run at very high clock speeds and have very high package densities Traditional interconnects like sockets require expensive plated through holes and fabrication Plug connectors use metal fingers or prongs to make contacts which are prone to bending or breaking The size of these connectors also limits 25 their density Solder connections can be expensive and operations such as disassembling replacing and repairing are cumbersome Fuzz button interconnects were invented by Tecknit Co They were first used in static dissipation pads for computer chassis Fuzz buttons were later used in radar and space applications They were also used in ARM missiles as an interconnect between ring shaped PCB s Fuzz buttons were able to cope with very severe vibrations without being damaged while maintaining a good connection which made them ideal for the above mentioned applications 3 1 1 Construction of Fuzz Buttons Fuzz buttons are constructed from a large quantity of gold plated Beryllium Copper BeCu wire This wire is compressed into a cylindrical shape by a purpose built machine The wire used for manufacturing fuzz buttons is extremely thin Standard fuzz buttons are manufactured from a single strand of 0 002 inch gold plated BeCu wire Figure 5 shows a standard fuzz button Figure 5 Magnified view of a standard fuzz button Courtesy of Teckn
66. llium Copper wires The slider which represents the fuzz button 1s assigned the properties of BeCu namely the density modulus of elasticity and poisson s ratio The top surface of the PCB is made of copper 41 The receptacle which represents the PCB is assigned the material properties of copper The entire model is made of plain strain elements The semicircular slider 1s modeled using CPE4 which is a Q4 quad element and some CPE3 linear constant strain triangular CST elements Q4 is a solid 4 node bilinear plane strain element CST is a 3 node linear plane strain element The rectangular PCB is modeled using Q4 elements Figure 18 shows a CST element Face 3 Face 2 1 Face 1 2 Figure 17 A standard Constant Strain Triangle 3 noded linear plane strain element Figure 19 shows a standard Q4 element The face numbers of these elements are important while applying load on the top face of the fuzz button wire The top face of the fuzz button is made of Q4 elements It is important to apply pressure on that face of the element which is pointing upwards to ensure correct load application 42 Face 3 3 Face 4 iene 4 Face 1 2 Figure 18 A standard Q4 4 noded bilinear plane strain element These elements support adaptive meshing hence they are used in this model Load is applied on the top surface of the semicircular slider as it oscillates on the receptacle A coarse mesh was used in this model A coarse mesh was initially s
67. lowed to slide over the PCB for several number of cycles The PCB surface gets worn out which causes a change in the electrical resistance This is shown in Figure 25 When the PCB surface gets worn the surface elements get severely distorted A method had to be devised to 48 remesh these elements in order for the simulation to continue running for a large number of cycles Adaptive meshing has been used to remesh the elements of the PCB so they would be able to show severe damage accumulation 5S Mises ave Crit IOF 069e 02 o00e 00 Figure 24 Von Mises stress on a worn out PCB surface after several cycles 4 3 Three Dimensional Model Once the 2D model ran successfully a 3D model was constructed to simulate wear Initially two different 3D models were constructed In the first model the fuzz button wire which represents the slider was modeled as a cylinder The PCB which represents the receptacle was modeled as a rectangular block Since the bottom half of the 49 fuzz button wire contacts the PCB the wire is modeled as a half cylinder To simulate wear this entire half cylinder slides on the rectangular block Figure 25 shows the three dimensional model Fuzz Button Wire PCB Figure 25 3D model representing a fuzz button contact on a PCB Initially the fuzz button was modeled as a half cylinder having length equal to the outer circumference of a fuzz button This length was equal to 3 192mm The P
68. lted in cold welding of the asperities particularly if the contact surfaces were clean The force required to separate these members resulted in the shearing of asperities This was the beginning of adhesion theory of friction which was subsequently developed by Bowden and Tabor 1950 The first quantitative statement of wear was also given by Holm 1946 Ps H a W is the wear volume s is the sliding distance P is the load H is the yield pressure of the metal and Z is a dimensionless number P H was called the real area of contact 12 The serious deficiency in Holm s analysis was Holm believed that asperity encounters and wear occurred at an atomic level when in they start at an atomic level but are active at a much larger scale Wear in electrical contacts usually occurs due to the loss of material from contacting surfaces in the form of particles Adhesive wear occurs in electrical contacts when bonds formed between touching asperities are stronger than the cohesive strength of the metal In electrical contacts the transition from mild to severe wear occurs due to the loss of a protective oxide layer Most electrical contacts are made up of noble metals Noble metals are oxide free Any sliding results in noble metals results in severe wear due to the absence of an oxide film Many electrical contacts wear by a severe adhesive process called prow formation Slade 1999 When two surfaces which are made up of the same material contact
69. ly in ABAQUS Figure 38 shows the slider with the load applied 62 Load applied on the top _face of the slider Figure 36 3D Model with pressure load applied on the top face of the slider 63 CHAPTER 5 IMPLEMENTATION OF THE WEAR LAW IN THE FINITE ELEMENT MODEL Archard s model predicts wear with a sufficient degree of accuracy while predicting mild wear in metal contacts Archard s model has been used by Molinari 2000 Podra 1999 Cantizano 2002 Agelet 1999 Hegadekatte 2005 to predict wear Archard s wear law has been used in the model to predict wear Archard s wear model is given by V _k F A s H A This law can also be expressed in terms of wear depth as k h s P 21 7 21 h is the wear depth k is Archard s wear coefficient H 1s the hardness of the softer material s 1s the sliding distance P is the contact pressure Archard s wear coefficient has been interpreted in various ways It is the fraction of asperities yielding wear particles ratio of volume worn to volume deformed a factor inversely proportional to critical number of load cycles number of repeated asperity 64 encounters for producing ruptures as a factor reflecting the inefficiencies associated with the various processes involved in generating wear particles Rigney 1994 This wear law is integrated in the model in the form of wear rate Both sides of Equation 21 are divided by time Pp 22 gt
70. n Wear Mechanism derived from Suh 1973 The most common wear model used to model sliding wear is Archard s wear model Archard s model has been used by Molinari 2000 Podra 1999 Cantizano 2002 Agelet 1999 Hegadekatte 2005 In this wear simulation Archard s wear model has been selected to simulate fretting wear occurring in electrical contacts The Arbitrary Lagrangian Eulerian ALE adaptive meshing technique has been used in this model ALE was developed to combine the advantages of the Lagrangian and Eulerian descriptions while minimizing their respective drawbacks as far as possible Archard s wear law is integrated into a Fortran code and used in the Abaqus user subroutine UMESHMOTION To take into account damage accumulation caused by surface wear adaptive meshing is employed As the surface wears the elements in the components get distorted This will eventually cause the simulation to fail Adaptive meshing remeshes the components at a regular frequency to take into account the damage accumulation CHAPTER 2 LITERATURE REVIEW All complex electronic products used today have thousands of electrical contacts New advances in electronic packaging technology have shrunk the size of electronic components resulting in the reduction in size of electronic devices This in turn has resulted in the increased density of electrical contacts in electronic devices These devices are subjected to vibrations during their operation Th
71. nodes with rotational degrees of freedom There are a total of 6 components 3 translational and 3 rotational Out of the 3 translational components only the first component which represents sliding along the X direction is required VEL is a real array containing individual components of the output variable JRCD is a return code which is returned as 0 when no error is present or 1 when there exists an output request error or all components of the output request are zero 88 JGVBLOCK is a variable that must be passed into the GETVRN utility routine LTRN is a variable indicating the coordinate system the nodal quantity is to be returned in A value of zero specifies that the results are to be returned in the global coordinate system regardless of any transformation applied at the node A value of one specifies that the results are to be returned in the local transformed system In this model all results are returned in the global coordinate system Once the sliding velocity is obtained at node 21 the next step is to find the pressures at the surface nodes of the PCB Pressure is not calculated at node 21 and this is ensured using the ELSE statement The command used 1S ELSE CALL GETPARTINFO NODE 0 PARTNAME LOCNUM JRCD Getpartinfo 1s used to obtain part instance information from the global node number NODE is the internal node number to be looked up The second entry is JTYP which is an integer flag indicating whether NODE is a node or element
72. ntact Eulerian Description of the sliding contact Arbitrary Lagrangian Eulerian description of the model Nodal sliding velocity of Node 21 used to calculate wear Velocity variation of the slider affecting wear rate Simulated Wear Depth versus Number of Fretting Cycles at S 0 Simulated Wear Depth versus Number of Fretting Cycles at S 0 008 Simulated Wear Depth versus Number of Fretting Cycles at S 0 008 Simulated Wear Depth versus Number of Fretting Cycles at S 0 020 xili 56 57 59 6l 62 63 68 69 12 73 74 Te 80 81 82 83 84 87 95 95 96 96 97 Figure 56 Simulated Wear Depth versus Number of Fretting Cycles at S 0 020 97 Figure 57 Simulated Wear Depth versus Number of Fretting Cycles at S 0 040 98 Figure 58 Simulated Wear Depth versus Number of Fretting Cycles at S 0 040 98 Figure 59 Simulated wear depth versus Number of fretting cycles for 7 nodes spanning across the receptacle surface from S 0 040 to S 0 040 99 Figure 60 Zero Displacement plot on the receptacle at the start of the simulation 100 Figure 61 Nodal Displacement plot in the receptacle at 150 fretting cycles 101 Figure 62 Nodal Displacement plot in the receptacle at 240 fretting cycles 101 Figure 63 Nodal Displacement plot in the receptacle at 360 fretting cycles 102 Figure 64 Nodal Displacement plot in the receptacle at 480 fretting cycles 102 Figure 65 Nodal Displacement plot in the receptacle at 585
73. ntacts And Multiple Encounters J Apl Phys Vol 32 No 8 pp 1420 5 1961 Armero F And Love E An Arbitrary Lagrangian Eulerian Finite Element Method For Finite Strain Plasticity Int J Numer Methods Eng Vol 57 pp 471 508 2003 Ashby M F And Lim S C Wear Mechanism Maps Scripta Metall Vol 24 pp 805 810 1990 Barwell F T Wear Of Machine Elements In N P Suh N Saka Eds Fundamentals Of Tribology The Mit Press pp 401 441 1978 Bayer R G Mechanical Wear Prediction And Prevention Marcel Dekker 1994 Bowden F P And D Tabor Friction Lubrication And Wear A Survey Of Work During The Last Decade Br J Appl Phys Vol 17 pp 1521 1544 1966 117 Burwell Jt Strang Cd On The Empirical Law Of Adhesive Wear Journal Of Applied Physics Vol 23 pp 18 28 1952 Cantizano A A Carnicero A G Zavarise Numerical Simulation Of Wear Mechanism Maps Computational Materials Science Vol 25 pp 54 60 2002 Challen J M And P L B Oxley An Explanation Of The Different Regions Of Friction And Wear Using Asperity Deformation Models Wear Vol 53 pp 229 243 1979 Chen H amp Alpas A T Sliding Wear Map For The Magnesium Alloy Mg 9al 0 9 Zn Az91 Wear Vol 246 pp 106 116 2000 Childs T H C The Sliding Wear Mechanisms Of Metals Mainly Steels Tribology International Vol 13 pp 285 293 1980 Childs T H C The Mapping Of Metallic Sliding Wear Proc I Mech E Vol 202 pp 379 395 1988 Cocks M I
74. nteraction Of Sliding Metal Surface J Appl Phys Vol 33 pp 2152 2101 1962 Dickrell D J And Sawyer W G Evolution Of Wear In A Two Dimensional Bushing Tribology Transactions Vol 47 pp 257 262 2004 Ding J Leen S B And Mccoll I The Effect Of Slip Regime On Fretting Wear Induced Stress Evolution International Journal Of Fatigue Vol 26 pp 521 531 2004 Donea J Antonio Huerta J Ph Ponthot And A Rodriguez Ferran Arbitrary Lagrangian Eulerian Methods Encyclopedia Of Computational Mechanics Volume 1 Fundamentals 2004 118 Eden E M W N Rose And F L Cunningham The Endurance Of Metals Inst Mech Eng pp 875 1911 Franklin F J Widiyarta I Kapoor A Computer Simulation Of Wear And Rolling Contact Fatigue Wear Vol 251 pp 949 955 2001 Gonzalez C Martin A Garrido M A Gomez M T Rico A And Rodriguez J Numerical Analysis Of Pin On Disc Tests On AI L1i Sic Composites Wear Vol 259 pp 609 612 2005 Hamed A W Tabakoff Rb Rivir K Das P Arora Turbine Blade Surface Deterioration By Erosion Journal Of Turbomachinery Vol 127 Issue 3 pp 445 452 July 2005 Hegadekatte V N Huber And O Kraft Finite Element Based Simulation Of Dry Sliding Wear Modelling Simul Mater Sci Eng Vol 13 pp 57 75 2005 Hirst W Wear Of Unlubricated Metals Proc Conf Lubr Wear Ime London Pp 674 681 1957 Hoffmann H Hwang C And Ersoy K Advanced Wear Simulation In Sheet Metal
75. nto the dominant wear mechanism it can be used fairly accurately and conveniently to model mild wear Archard s law is not applicable for any specific mechanism It is generally used to model Adhesive and Abrasive wear Quinn 1971 proposed a wear mechanism based on oxidation This model was based on Archard s wear model Quinn s model is based on the assumption that a volume of material near the region of contact gets heated up due to sliding force and an oxide film grows on the surface After the thickness of the oxide film reaches a critical value it will separate from the surface as wear debris d A A He Q RT 7 E2 p axe 9 Where A is Arrhenius constant Q is the activation energy for oxidation R is the gas constant To is the temperature of oxidation Suh 1973 proposed the delamination theory to explain the production of flake debris on worn surfaces According to this model crystal lattices dislocations under the influence of a sliding force meet together form a crack and propagate parallel to the surface to produce flake debris Cracks become nucleated below the surface and join resulting in the loosening of thin sheets of metals forming wear debris Challen and Oxley 1979 applied slip line field analysis to describe the deformation of a soft asperity by a hard one and derived equations for wear rate 7 Rider Rider Motion L PT o Q i Elongated holes Small holes Figurel Delaminatio
76. o contact the receptacle A surface to surface contact is defined in the model Initially a surface is defined on the slider using the SURFACE command SURFACE is used to define surfaces for contact simulations The command is defined as SURFACE NAME SURFACE2 TYPE ELEMENT slidersurface The NAME parameter is set equal to a label that will be used to refer to that surface in this case SURFACE2 Set TYPE ELEMENT defines a free surface automatically for the elements specified It can also be used to define a surface on the elements by using element face identifiers An element number or element set name is specified as the first entry of each data line In this model an element set slidersurface is defined which contains all the elements which make up the slider surface A second surface is defined which represents the top face of the PCB SURFACE NAME SURFACE TYPE NODE 71 PCB 1 TYPE NODE defines a surface by specifying a list of nodes or node set labels In this model a node set PCB is defined at the top face of the receptacle The surface formed from the node set PCB is called SURFACE1 The contacting surfaces SURFACE and SURFACE2 are shown in Figure 41 ELEMENT SURFACE 2 NODAL SURFACE 1 Figure 39 Contacting surfaces used in the 2D contact model A third surface called slidertopsurface is defined SURFACE NAME SLIDERTOPSURFACE TYPE ELEMENT slidertopsurfelem_s2 S2 slidertopsurfelem_s3 S3 12 This
77. ol 249 pp 6 11 2001 Podra Priit Soren Andersson Simulating Sliding Wear With Finite Element Method Tribology International Vol 32 pp 71 81 1999 Rabinowicz Friction And Wear Of Materials Edition 2 Table 6 2 pp 159 1995 Rhee S K L Halberstadt J A Mansfield Wear Of Materials Asme pp 560 568 1977 121 Rigney D A The Role Of Hardness In The Sliding Behavior Of Materials Wear Vol 175 pp 63 69 1994 Rigney D A Comments On The Sliding Wear Of Metals Tribology International Vol 30 pp 361 367 1997 Slade P Electrical Contacts Principles And Applications New York Marcel Dekker Inc 1999 Suh N P The Delamination Theory Of Wear Wear Vol 25 pp 111 124 1973 Sui H Pohl H Schomburg U Upper G And Heine S Wear And Friction Of Ptfe Seals Wear Vol 224 pp 175 182 1999 Sandisk Secure Digital Card Product Manual Version 1 9 2003 Sarkar A D Friction And Wear Academic Press 1980 Sarkar A D Wear Of Metals Pergamon Press International Series On Materials Science And Technology Vol 18 1977 Scott D Treatise On Materials Science And Technology Wear Vol 13 Academic Press 1979 Stromberg N Finite Element Treatment Of Two Dimensional Thermoelastic Wear Problems Computational Methods For Applied Mechanical Engineering Vol 177 pp 441 455 1998 Thompson J M And Thompson M K A Proposal For The Calculation Of Wear Proceedings Of The 2006 International Ansys Users C
78. onference amp Exhibition Pittsburgh Pa 2006 Tomlinson A Philos Mag 7 pp 905 911 1927 122 Yan W O dowd N P And Busso E P Numerical Study Of Sliding Wear Caused By A Loaded Pin On A Rotating Disc J Mech Phys Sol Vol 50 pp 449 470 2002 123
79. ontinuously extracted from the model and updated depending on the location of the node on the receptacle and the position of the upper pin Figure 74 shows a plot of model predictions and experimental data Wear of contact in mm was plotted on the Y axis and the sliding distance in mm was plotted on the X axis The experimental wear rate was found by calculating the slope of this plot Simulation results were extracted from the model and plotted on the same x and y axis Simulation plots were plotted for several nodes on the top face of the receptacle The slopes which indicate wear rates were compared for the experimental plot and the simulation plots Similar wear rates were found indicating the model has been validated 109 Experimental Data Model Predictions z lt par Q nA i Q s 50000 100000 150000 200000 250000 300000 350000 Cumulative Displacement mm Figure72 Comparison of Predicted Wear Rates Versus Experimental Results The model was also validated for a copper on copper contact system The model was validated by comparing the wear rate for a copper on copper contact system with the wear rate obtained from Archard s wear law for the same contact system Copper on copper contact system is a very common electrical contact system used in electrical contacts A 10MPa pressure load was applied on the top face of a slider as shown in Figure 21 This copper slider reciprocated aga
80. pins for data and 3 pins for power Table 2 shows the pin numbers names their type and their specific functions PIN PIN PIN TYPE FUNCTION NAME DAT3 Input Output I O Card Detect Data Line Bit3 2 CMD I O using push Command Response pull drivers Input Clock Power Supply Supply Voltage i Vss2 Power Supply Ground DATO Input Output I O Data Line Bit0 DATI Input Output 1 0 Data Line Bit1 DAT2 Input Output 1 0 Data Line Bit2 Table 2 SD Card pins and their functions These SD cards are inserted into special SD card connectors When fully inserted the contact pins on the SD card touch the connector Figure 11 shows a typical SD card connector 33 Figure 10 SD card connector with card Courtesy of Panasonic 3 2 2 Modeling a memory card contact To represent the contact between an SD card and its respective connector a two dimensional finite element model is constructed as shown in Figure 12 2 9mm 0 4mm Figure 11 2D Modeling of a Memory card and a memory card connector contact based on SD Card Product Manual Courtesy of Hirose Connectors 34 When this assembly is subjected to vibrations the card will vibrate in its socket This will cause the pins of the card to oscillate rapidly with respect to the connector which will result in fretting wear This model can be used to predict the wear rate and hence the life of the component 3 3 Memory Modules Memor
81. r Depth versus Number of Fretting Cycles at S 0 040mm 98 0 00E 00 800 1000 1200 5 00E 04 1 00E 03 1 50E 03 2 00E 03 2 50E 03 Wear Depth mm 3 00E 03 3 50E 03 4 00E 03 Number of Fretting Cycles 1400 1600 S 0 020 S 0 04 Figure 57 Simulated wear depth versus Number of fretting cycles for 7 nodes spanning across the receptacle surface from S 0 040 to 0 040mm inside the material due to wear occurring at the surface As seen from Figure 52 the plot is not smooth The uneven wear rates are because of the changes in the surface profile contact pressure and instantaneous relative velocity with the evolution of the wear process It can be concluded from Figure 59 that the maximum wear rate was present at the right and left extremes of the receptacle Through show the displacement of nodes in the receptacle as wear progresses The legend in these figures indicates the magnitude of displacement Blue color indicates minimal nodal displacement and red color indicates maximum nodal displacement Figure 60 shows the displacement on nodes at the start of the simulation The uniform blue color indicates zero displacement of the nodes at the start of the simulation 99 v2 Figure 58 Displacement plot showing Zero Displacement on the receptacle at the start of the simulation As the simulation progresses the nodes at the receptacle surface mo
82. ration system can be used to generate vibrations in the slider Vibrating Slider Clamped Receptacle Bruel and Kjaer shaker Figure74 A typical vibration experimental setup 115 A vibration setup typically consists of a shaker fixture with clamps to fix the specimen generator of input signal that excites shaker software and hardware that may be used to control vibrations and take measurements Przemystaw 2005 The receptacle would be clamped down and the slider would be connected to a shaker as shown in Figure 76 When the shaker is excited the slider will oscillate on the receptacle resulting in fretting wear A profilometer can be used to measure the wear depth at regular intervals A plot of wear depth versus the sliding distance can be plotted The slope of this plot will predict the wear rate This experimental wear rate can than be compared to the wear rate predicted by this model By changing the material of the slider and the receptacle various contact systems can be tested using this experimental setup 116 BIBLIOGRAPHY Antoniou R And Subramanian C Wear Mechanism Map For Aluminum Alloys Scripta Metall Vol 22 pp 809 814 1988 Agelet De Saracibar C M Chiumenti On The Numerical Modeling Of Frictional Wear Phenomena Comput Methods Apl Mech Engineering Vol 177 pp 401 426 1999 Archard J F Contact And Rubbing Of Flat Surfaces J Apl Phys Vol 24 No 8 pp 981 8 1953 Archard J F Single Co
83. relative velocity with the evolution of the wear process The model was validated by comparing the wear rate for a steel on steel contact system with the wear rate obtained from experimental results for the same contact system The contact pressure was continuously extracted from the model and updated depending on the location of the 114 node on the receptacle and the position of the upper pin Wear of contact in mm was plotted on the Y axis and the sliding distance in mm was plotted on the X axis The experimental wear rate was found by calculating the slope of this plot Simulation results were extracted from the model and plotted on the same x and y axis Simulation plots were plotted for several nodes on the top face of the receptacle The slopes which indicate wear rates were compared for the experimental plot and the simulation plot Similar wear rates were found indicating that the model had been validated The model was also validated by comparing the wear rate for a copper on copper contact system with the wear rate obtained from Archard s Law for the same contact system 7 2 Scope for future work The wear model can be validated for several other contact systems like gold on gold steel on copper and gold on copper More complex 2D and 3D models can be constructed depending on the specific contact being simulated An experimental setup can be created to simulate fretting wear for various contact systems A Bruel and Kjaer vib
84. rewiaestnwees 65 5 2 Defining model properties and slider sliding frequency cccceeeeeeeeeeeees 70 5 3 Calculation of wear in user subroutine UMESHMOTION cece cee eees 86 CHAPTER 6 MODEL PREDICTIONS AND MODEL VALIDATION 0 ee 94 GP MIOGe k Prodi MONS 4 052356 asece a s eats aa Geese eds te ee 94 602 Mod l VY anal OU sesecsue secioxsdssecsursacsesresacnisem A aa 109 CHAPTER 7 SUMMARY AND FUTURE SCOPE FOR WORK eee 113 SMS SIDA AMEN sty eters hala ata tethers he laa dea ence ted years tated ieee eeee 113 7 2 Scope for BIBLIOGRAPHY future work anesnenenenenesesesseseseseseseeresoseseseeserososeseesesesosososresesoseseses LIST OF FIGURES Figure 1 Delamination Wear Mechanism derived from Suh 1973 8 Figure 2 Fretting wear of a tin terminal Courtesy of Molex 10 Figure 3 Erosion of a turbine blade subjected to 1500 micron particles Hamed 2005 11 Figure 4 Prow formation mechanism for a rider on a flat Gold on gold contact Slade 1999 15 Figure 5 Magnified view of a standard fuzz button Courtesy of Tecknit Interconnection Products 26 Figure 6 Small size of fuzz buttons enabling high contact density Courtesy of Tecknit Interconnection Products 27 Figure 7 Fuzz button assembly 28 Figure 8 Hard Hats Courtesy of Tecknit Interconnection Products 29 Figure 9 2D modeling of a fuzz button and PCB contact 30 Figure 10 A typical SD Card construction 32 Figure 11 SD card connector with
85. s classification of wear mechanisms with typical examples where the corresponding form of wear is most likely to be found Once the wear mechanism is identified a suitable wear model needs to be selected which will accurately represent the wear mechanism 1 2 Selection of Wear Model There exist hundreds of wear models in wear literature A suitable wear model must be selected depending on the wear mechanism which is being simulated Some wear models are empirical equations involving material properties and working conditions These models are constructed by manipulating experimental data and they are valid within a tested range Some of these wear models are listed below Barwell 1958 suggested a wear model which consists of three empirical equations P ohr wa i e 1 W at 2 W B 3 Where V is the Volume loss B is a constant is some characteristic of the initial surfaces t is the time and e is natural logarithm Rhee 1970 suggested another empirical wear equation where wear was a function of 5 The load F speed V and time t AW KF v t 4 Where AW is the weight loss of a friction material and K a b c are empirical constants Some models were developed to identify the main mechanism of material loss from surfaces These models were based on explanations consistent with observed wear behavior Wear maps were developed for specific materials Lim amp Ashby 1987 developed a wear map for steel Hs
86. sh motion for nodes in an adaptive mesh domain or to define nodes that must follow the material It can be used only in conjunction with the ADAPTIVE MESH option The command used is ADAPTIVE MESH CONSTRAINT CONSTRAINT TYPE SPATIAL TYPE VELOCITY USER PCB 1 1 0 0004657 The parameter CONSTRAINT TYPE SPATIAL is used to prescribe mesh motions that are independent of the underlying material The parameter TYPE VELOCITY is used to prescribe mesh velocity to the nodes in an adaptive mesh domain The USER parameter is used if the mesh motion is to be defined in user subroutine UMESHMOTION This parameter cannot be used when CONSTRAINT TYPE LAGRANGIAN The first entry in the data line indicates the node number or node set label in this case it is the node set PCB The second entry indicates the first degree of freedom constrained The third entry indicates the last degree of freedom constrained The last entry indicates the actual magnitude of mesh motion This command allows transfer of control from the input file to the fortran code written as a part of user subroutine UMESHMOTION 85 5 3 Calculation of wear in user subroutine UMESHMOTION In the fortran code the first step is to define all the arrays which are going to be used in the code This is done using the dimension statement A DIMENSION statement is used to specify the symbolic names and dimension specifications of arrays The form of a DIMENSION statement is DIMENSION a d b
87. sition This marks the completion of one cycle 54 Mises CriE i ras 960e 035 647e 035 4535e 035 220e 03 UO07 e 05 1 o3e 03 2 2o0e 05 36re 03 153e 03 400e 02 26 e 0e Lla3e 0e2 000e 02 2 a4te 00 2 OLB Cu odb ABAQUS STANDAPD Version 6 5 1 Er otep Step 1 nerement 2a atep Tine 11 00 3 rimary Yar 5 Mises TNieFoarmearn Wer TT TNieaetormerion Seala Tartar LA DN e L Figure 30 Von Mises stress plot with slider at the left extreme of the receptacle After several such cycles the PCB surface gets worn out as shown in Figure 33 It is easy to understand the effects of fretting wear in electrical contacts by looking at the results of the 3D model The worn out PCB surface may cause failure of the electrical contact resulting in failure of the component 55 a Mises CELIC i foo S63e64 03 900e 03 o2e4 03 6836403 o 5e 05 4676405 355e64 03 200eE 03 1426405 O33e4 03 200eE4 02 16 e 02 083e 02 000e 02 S60e 01 ODE cu odh ABLGUS STANDARD Versi aoe atep Step l1 ne Eerme nt 160 Step Time 60 00 3 rimary Var 5 Mises Deformed Var U Deformation Scale Factor 1 000E Figure 31 Von Mises stress plot of a worn out PCB after several wear cycles A second three dimensional model was constructed In this model the PCB was modeled as a circular ring with a rectangular cross section The fuzz button was modeled as a circular ring having a semi circular cross s
88. surface consists of two element sets The first element set slidertopsurfelem_s2 consists of elements with their face 2 pointing upwards The second element set slidertopsurfelem_s3 consists of elements with their face 3 pointing upwards When slidertopsurface is defined all the top element faces are selected S2 represents face 2 of all elements in element set slidertopsurfelem_s2 S3 represents face 3 of all elements in the element set slidertopsurfelem_s3 Both these element sets are shown in Figure 42 Element set Face 2 slidertopsurfelem_s2 Element set Slidertopsurfelem_s3 Figure 40 Elements with different orientations make up the loading surface 73 After defining the surfaces a contact is defined between the two contacting surfaces This is done using the command CONTACT PAIR This option is used to define pairs of surfaces or pairs of node sets and surfaces that may contact or interact with each other during the analysis The code used 1s CONTACT PAIR INTERACTION fricbhv SURFACE1 SURFACE2 Contact is defined using the node to surface discretization With node to surface discretization the contact conditions are established such that each slave node on one side of a contact interface effectively interacts with a point of projection on the master surface on the opposite side of the contact interface Thus each contact condition involves a single slave node and a group of nearby master nodes from which values are interpolat
89. t On many electrical contacts fretting wear occurs where the rider repeatedly traverses the same path resulting in rider wear Prow formation stops after a certain number of cycles The back transfer prows from the rider accumulate on the flat increasing its hardness at all places due to work hardening When the hardness of the flat reaches the hardness of the prows the rider begins to wear This rider wear has been modeled in this work Burwell and Strang 1952 measured the wear of steels and other metals at slow speeds using cetane as the lubricant The relationship between wear rate pressure and load was determined It was found that wear rate 1s proportional to the load and independent of pressure until the point where the surface stress exceeds a value equal to one third the hardness of the material Krushchov and Babichev 1953 measured the wear of metals when rubbing against emery cloth and concluded that the wear rate of different metals was inversely proportional to their hardness with the exception of heat treated steels Archard 1956 conducted experiments and found that the wear rate was independent of the apparent area of contact A pin on ring contact was used during these experiments 14 The ring was rotated and a pin was pressed against the circumference of the ring For low Figure 4 Prow formation mechanism for a rider on a flat Gold on gold contact a Start of run b Well developed prow c and d Loss of portion o
90. t numbers for elements connected to NODE for which you want material point quantities considered in the average result Results from each element in the list that contain the node will be extrapolated to that node and averaged JELEMLIST can be obtained from utility routine GETNODETOELEMCONN NELEMS is the maximum allowable length of JELEMLIST JMATYP and JGVBLOCK are variables that must be passed into the GETVRMAVGATNODE utility routine An array CPRESS is defined The first variable from ARRAY is stored in CPRESS The command used is CPRESS ARRAY 1 The contact pressure on the nodes which are located on the top face of the PCB is stored in CPRESS The sliding velocity of node 21 in the X1 direction which is located on the slider is used to calculate wear Six components of velocity are stored in the array VEL Out of these just the 1 component is required The command used is VELOCITY VEL 1 9 The sliding velocity of node 21 is stored in VELOCITY Once the sliding velocity and contact pressure are obtained the wear rate is calculated using formula X an p 24 R t S o Nn e s t is the sliding velocity P is the contact pressure k is the Archard s coefficient H is the hardness of the softer material and h t is the wear rate In this model the formula used varies with the contact system used If a steel on steel contact system is used Archard s coefficient for steel is 0 0150 Rabinowicz 1995 Arch
91. tement The command used is PARAMETER CPRESS 0 0D0 VELOCITY 0 0D0 CPRESS is the pressure component of the array ARRAY VELOCITY is the sliding velocity component of the array VEL They are initially set to zero at the start of the program 87 A nodeset NODE is passed into the subroutine This nodeset contains node 21 and all the surface nodes of the PCB which undergo wear The IF ELSE statement helps to differentiate node 21 from the other nodes Nodal velocity of node 21 is required to calculate wear at the surface nodes shown in Figure 40 It is essential that velocity is extracted just at node 21 This is ensured using the 1f then statement The command used 1S IF NODE 21 THEN ULOCAL NDIM 0 When the node number is 21 there is no need to find out the mesh velocity in ULOCAL since its not a part of the PCB and will not undergo wear Therefore for node 21 ULOCAL NDIM is set to zero The sliding velocity at node 21 is extracted using GETVRN Utility routine GETVRN is called from user subroutine UMESHMOTION to access node point information The command used is CALL GETVRN NODE V VEL JRCD JGVBLOCK LTRN Node refers to the node number from which the node point information is extracted V is the output variable key selected from the table in Abaqus Standard output variable identifiers of the Abaqus analysis user s manual The variable V includes all velocity components including rotational velocities at
92. terial to be removed from a slower surface and deposited on the faster surface Fretting was first recorded by Eden et al 1911 Tomlinson 1927 first defined fretting wear as wear which occurs as a result of very small oscillatory displacement between surfaces consisting of interactions among several forms of wear initiated by adhesion amplified by corrosion and having it s major effect by abrasion or fatigue Fretting occurs when two loaded surfaces in contact undergo relative oscillatory tangential motion known as slip as a result of vibrations or cyclic stressing The 2 amplitude of relative motion is very small As fretting proceeds the area over which slip is occurring usually increases due to the incursion of debris The amount of debris produced depends on the mechanical properties of the material and it s chemical reactivity This debris produced by fretting is mainly the oxide of the metal involved This oxide occupies a greater volume than the volume of metal destroyed If space is confined this will lead to seizure of the contact 1 1 Selection of Wear Mechanism Table 1 Classification of Wear Mechanisms Wear Mechanism Motion Typical Occurrences of the Mechanism Fretting Wear Reciprocating Electrical Contacts Fasteners inl subjected to vibrations Abrasion Particle sliding Abrasive sand papers files ial _ Surface Fatigue Relative motion Bearings with repeated intense loadings Pitting Relative mot
93. tion between the sprung contacts and the IC pins After several cycles the sprung contacts wear out due to fretting wear This will result in failure of the electric contact and the component Figure 16 shows a 2D model representation of ZIF socket and pin contact 37 ICROPROCESSOR ZIF SOCKET Figure 15 2D model representing a ZIF socket and IC pin contact based on Lin 2003 All these applications prove that the model developed in this study can be used to predict the wear rate of various electrical contacts For each case considered the material properties of the contacting surfaces are inputted the dimensions are changed and load 1s applied depending upon the contact force in the system considered The model helps predict the wear rate which in turn can predict the rate of degradation of the contacting surface Once the surface of the electrical contact wears off it ceases to function resulting 38 in failure of the component This model can therefore be used for life prediction of components 39 CHAPTER 4 MODELING OF ELECTRICAL CONTACTS As shown in Figure 12 Figure 15 and Figure 16 electrical contact between various electrical systems can be modeled using a two dimensional model of a slider which slides on a receptacle Two dimensional and three dimensional models have been constructed to model electrical contacts The slider represents the part which undergoes repetitive motion when subjected to vibrations This slid
94. u amp Shen 1996 developed a wear map for ceramics Chen amp Alpas 2000 developed a wear map for magnesium alloy These wear maps helped in the selection of the dominant wear mechanism depending on a particular set of operating conditions Archard 1961 proposed a wear model to model sliding wear According to Archard s model the amount of wear depends on the stress field in the contact and the relative sliding distance between the contacting surfaces W s A s x 5 T a gt This equation can be rewritten in terms of wear depth h s p 6 H where W is the wear volume A is the area of contact k is the wear coefficient F is the contact force H is the hardness of the softer material s is the sliding distance h is the wear depth and P is the contact pressure Measuring wear volume is difficult because wear volume boundaries are established subjectively Kalin and Vizintin 2000 This makes predicting wear depth an important step Archard s wear coefficient has been interpreted in various ways It is the fraction of asperities yielding wear particles ratio of volume worn to volume deformed a factor inversely proportional to critical number of load cycles number of repeated asperity encounters for producing ruptures as a factor reflecting the inefficiencies associated with the various processes involved in generating wear particles Rigney 1994 Even though Archard s wear model gives little insight i
95. ve downwards inside the material to simulate wear This can be seen in Figure 61 where the light blue band just below the receptacle surface represents nodal displacement Figure 62 shows the nodes have displaced further indicating that the wear depth increases with an increase in the number of fretting cycles Figure 63 shows the nodes keep displacing inwards as the simulation progresses Since the entire receptacle has been defined as an adaptive mesh domain the nodes deep inside the receptacle also undergo downward movement This can be seen by the light blue band in Figure 63 100 U2 1 309e 06 1 427e 03 1 557e 03 Figure 59 Nodal Displacement plot in the receptacle at 150 fretting cycles U2 1 309e 06 ABER AER RES eRe eBABL Bae ee RRR REARS AR H E Figure 60 Nodal Displacement plot in the receptacle at 240 fretting cycles 101 Figure 61 Nodal Displacement plot in the receptacle at 360 fretting cycles OOH en 557e 03 Figure 62 Nodal Displacement plot in the receptacle at 480 fretting cycles 102 The yellow band in Figure 64 indicates wear is continuously occurring as the simulation progresses 557e 03 Figure 63 Nodal Displacement plot in the receptacle at 585 fretting cycles 309e 06 557e 03 Figure 64 Nodal Displacement plot in the receptacle at 800 cycles 103 The red regions in Figure 66 indicate the areas of maximum wear Once the new
96. vement causes the mesh elements to distort severely To ensure continuation of the wear simulation for a large number of cycles the wearing surface is remeshed using Adaptive Meshing Arbitrary lagrangian eulerian ALE formulation with adaptive meshing has been used to simulate wear in this model ALE has been used to combine the advantages of the Lagrangian and Eulerian descriptions The use of ALE in this model allows a topologically similar mesh throughout the analysis without creating or destroying elements allowing the mesh to move independently of the material The nodes of the computational mesh may be moved with the continuum in lagrangian fashion or held fixed in eulerian manner or may be moved in an arbitrary way This freedom of moving the computational mesh allows greater distortions of the continuum to be handled than would be allowed by a purely lagrangian method with more resolution than the eulerian method ALE adaptive meshing enables the maintenance of a high quality mesh throughout an analysis even when the contact surface gets worn out by allowing the contact surface mesh to move independently of the material The topology and connectivity of the elements is not altered The simulation has been run for over 2000 fretting cycles Wear accrues on the contact surface of the connector with increase in the fretting cycles The wear rate is uneven because of the changes in the surface profile contact pressure and the instantaneous
97. y This value of nodal velocity is controlled by the wear rate NODE NODE contains the node numbers which are passed in UMESHMOTION from ABAQUS NNDOF NNDOF determines the number of degrees of freedom at each node LNODETYPE LNODETYPE defines the node type flag Nodes are classified depending on their position constraints and their grouping into master or slave nodes Table 4 shows all node types with their explanation LNODETYPE 1 This indicates that the node is on the interior of the adaptive mesh region LNODETY PE 2 This indicates that the node is involved in a tied constraint LNODETYPE 3 This indicates that the node is at the 66 LNODETYPE 4 LNODETYPE 5 LNODETYPE 6 LNODETYPE 7 corner of the boundary of an adaptive mesh region This indicates that the node lies on the edge of a boundary of an adaptive mesh region This indicates that the node lies on a flat surface on a boundary of the adaptive mesh region This indicates that the node participates in a constraint as a master node This indicates that the node participates in a constraint as a slave node Table 4 Classification of nodes in UMESHMOTION The different nodetypes present in this model are shown in Figure 39 67 lt SS ee eS LNODETYPE 5 jests LNODETYPE 3 gt A LNODETYPE 7 LNODETYPE 2 A VV Vey VN Figure 37 Node types used in the model NDIM NDIM is equal to the number of coordinate dimensions ALOC
98. y modules are used in many electronic devices like servers laptops and printers They are mounted in special sockets which are mounted on the PCB Portable devices like laptops may be subjected to external vibrations during usage Devices like servers are run for extended periods of time Vibrations generated by various components like cooling fans and hard drives are transmitted throughout the system When these vibrations reach memory module sockets they might cause the memory modules to vibrate in their respective sockets resulting in fretting wear Figure 13 shows a typical dual in line memory module DIMM manh faites s m Fi sa 2 ite i nAn Pritts Se aa r F aana A oY A ai A ay ii AnA AANA AAA NANANAAdNANANANAAN gt gt gt DA 4 t we i T A vw KA ingsta wenom MARDANA AAMRARANANAAAAN AANA NAN TETT iN Y nR Figure 12 A Typical Dual In line Memory Module Courtesy of Kingston Technology Figure 14 shows a memory socket As shown in Figure 14 the contact pins which enter the socket are at the bottom of the memory module Fretting wear will degrade these contacts causing the component to fail 35 Figure 13 A Typical Memory Socket Courtesy of Kingston Technology To represent the contact between a DIMM memory module and its socket a two dimensional finite element model is constructed as shown in MEMORY 580mm 6 60mm SOCKET

WEAR SIMULATION OF ELECTRICAL

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