FINITE ELEMENT MODELS FOR SIMULATION OF WEAR IN ELECTRICAL CONTACTS Pradeep Lall(2), Darshan Shinde(2), Brett Rickett(1), Jeff Suhling(2) (2) Auburn University Dept of Mechanical Engineering and Center for Advanced Vehicle Electronics Auburn, AL 36849 (1) Molex, Inc., Lisle, IL 60532 Tele: (334) 844-3424 E-mail:
[email protected]
ABSTRACT Electrical 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 [1], unidirectional sliding of pin on disk [2], and wear mechanism maps for steelon-steel contacts [3]. 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 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 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. KEY WORDS: Electrical Contacts, Wear, Fretting, FiniteElement Models, Reliability, Contact Resistance.
H k H s P Pi Fi Ai
NOMENCLATURE Wear depth, mm Archard’s Wear Coefficient Hardness of Softer Material, N/mm2 Sliding Distance, mm Contact Pressure, MPa Contact Pressure at each node Contact Force on each node Contact area around each node
INTRODUCTION Wear involves loss of contact-surface material by contact and relative motion against another surface. Wear of the
component influences the contact resistance and reliability in the use application. Excessive wear may result in increased maintenance costs due to high wear rates or catastrophic failures. Wear simulation provides a convenient way of predicting wear in various electrical contact systems. Simulation techniques can help reduce costs and design cycle time, because it is often not feasible to test every contact configuration possible during product development. Previously, wear models have been used to simulate wear for dry unidirectional-sliding wear of a square-pin [1], unidirectional sliding of pin on disk [2], and wear mechanism maps for steel-on-steel contacts [3]. Prior researchers have used Archard’s wear model [1, 2, 4], mild oxidation wear law, severe oxidation wear law [3], to capture the wear process. Agelet [5] has used a nonlinear frictional contact formulation, derived from Laursen and Simo [6], where the frictional coefficient is a function of a wear related internal variable, frictional dissipation or slip amount. In prior models, the contact geometry is not continually updated during the wear process. Damage accumulation has been accounted for by using either Lagrangian or Eulerian descriptions of the model. The contact problem is solved at discrete intervals. Wear is computed and may be applied as a displacement boundary condition. In this paper, an arbitrary lagrangian-eulerian description of the contact surfaces, with adaptive re-meshing has been used to simulate the wear process. The modeling methodology simulates wear as a continuous process, with the contact surfaces updated continuously. The accrued wear has been computed and compared against experimental data. DEVELOPMENT OF NON-LINEAR FE MODEL GEOMETRY FOR VARIOUS END APPLICATIONS The finite element model developed in this paper targets a variety of end applications including RAM memory socket, SD-card sockets, micro-processor ZIF sockets, and fuzz button pressure contacts. Figure 1 shows a typical random-access memory module and its corresponding socket. The semicircular portion of the contact geometry in Figure 1 represents the receptacle in the socket and the flat-surface
978-1-4244-1701-8/08/$25.00 ©2008 IEEE
836
represents the contact pads on the memory module edge connector. Relative motion may be experienced due to vibration or thermo-mechanical loads during operation. Contact wear or edge connector pads may result from repetitive motion causing an increase in contact resistance and electrical failure. In the interest of computational efficiency, the near-field contact geometry has been captured for the wear simulation as shown in Figure 1.
thermo-mechanics caused due to external factors or internal sources like cooling systems. MICROPROCESSOR
ZIF SOCKET
MEMORY
0.5mm
0. 5m m
1m m
1mm
0.5mm
SOCKET
2.1mm
Figure 3: Simplification of Design for a Zero Insertion Force (ZIF) Socket. Figure 4 shows fuzz buttons made from gold plated beryllium copper wire compressed into a cylindrical shape. The spring characteristics of high tensile strength gold plated beryllium copper wire are excellent, which allows each fuzz button to compress 15% with virtually no compression set within the socket. Gold plated hard hats (miniature contact pins) are used to connect various IC packages such as LGA, PGA, BGA and gull wing to the Fuzz Buttons. A hard hat is shown in Figure 5, special shaped hard hats are used to minimize the damage to the solder ball or pins of the IC. Figure 6 shows the finite element model development for the fuzz-button assembly.
0.2mm
2.9mm
1.4mm
Figure 1: Simplification of Design for a Memory Module and Socket System. Figure 2 shows the contact system for an SD-card socket. Memory cards are used by several electronic devices like cell phones, cameras and gaming consoles. Repetitive sliding contact may be encountered in these contact systems 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 Figure 2, the memory card is represented by the rectangular receptacle and the socket contact is represented by the semicircular slider
0.8mm
Figure 4: Magnified View of a Fuzz Button [7]
0.4mm
Figure 2: Simplification of Design for a Memory Card and Socket. Figure 3 shows a contact-system between a microprocessor and a zero insertion force socket. Once a microprocessor is assembled into the system, the assembly may be subjected to vibrations. Motion may result from shock, vibration, and
837
Figure 5: Hard Hats (Courtesy of Tecknit, Inc.)
and resolution of details are sacrificed in the Eulerian description because the computational mesh is fixed and the continuum moves with respect to the grid
SECTION LINE SOCKET FUZZ BUTTON PCB
Figure 6: Model for fuzz-button to PCB Pad Contact. NON-LINEAR FINITE ELEMENT MODEL Figure 7 shows the semicircular spring-contact along with the flat contact surface. This semicircular spring-contact undergoes a reciprocating motion on the contact surface, therefore the semicircular spring-contact is constrained such that it’s free to move only parallel to the contact surface. The bottom face of the rectangular contact-pad is fixed. During the reciprocating fretting motion, a vertical pressure-load is applied on the top face of the slider to simulate the contact force. The contact force varies with application simulated.
Figure 8: Lagrangian Description of Sliding Contact
Figure 9: Eulerian Description of Sliding Contact
Figure 7: Contact Model With Boundary Conditions and applied Pressure Loads. Figure 7 shows the loaded slider at the start of a fretting cycle. The slider starts from the central position shown in Figure 7, moves to the right extreme of the receptacle, reverses direction and moves to the left extreme of the receptacle and finally returns to the initial starting position. A complete reversal of the slider represents one fretting cycle. Arbitrary lagrangianeulerian (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. Each individual node of the computational mesh follows the associated material particle during motion in the Lagrangian representation (Figure 8) of the model resulting in the inability to follow large distortions of the computational domain without frequent re-meshing The interface definition
Figure 10: 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 (Figure 10). The nodes of the computational mesh may be moved with the continuum in lagrangian fashion, or be 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 [8, 9, 10]. ALE adaptive meshing enables the maintenance of a high-quality mesh throughout an analysis,
838
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 obtained by solving the governing equations. In the Eulerian step, a new mesh is 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. WEAR MODEL FOR DAMAGE ACCUMULATION Several wear models are available in literature to model the phenomena of wear. Broadly the wear models can be categorized based on the type of relative motion between the bodies undergoing wear [11Hammitt 1980], the wear mechanism during wear [12], the severity of wear on wearing surfaces [13, 14] and mechanisms by which particles get detached during wear [15]. The most frequently used equation in wear modeling is the linear wear equation, Q=(K)(p), where Q is the volume wear rate, p is the normal pressure and K is a wear constant. Archard’s wear model [1956], which is defined in terms of wear depth can be represented as follows,
V A s h
K F H A
§K· ¨ ¸ s P ©H¹
h i is the total wear up to the ith wear step, h i 1 is the total
wear up to the (i-1)th wear step and 'h i is the wear occurring during the ith step The nodes on the top surface of the contact surface which undergo wear, are moved into the material, to simulate wear, depending on the calculated wear depth h. MODEL PREDICTIONS The simulation has been run for over 2000 fretting cycles. Wear accrues on the contact-surface of the connector with the increase in the fretting cycles. Figure 11 shows the change in the surface profile and the stress distribution in the pristine contact and the contact-system after 1600 cycles of fretting wear. The accrued wear has been plotted versus fretting cycles in Figure 12. 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. Figure 13 shows the pressure variation versus number of cycles accrued after the pristine state of the contact system and the differences in the accrued wear because of difference in the instantaneous velocity at various parts of a harmonic fretting wear cycle. t=0 Pristine Surface
t = t0+'t Contacting Surfaces with Wear after 1600 Cycles.
(1)
Where V is the wear volume, s is the sliding distance, K is the wear coefficient, H is the hardness, A is the Area, F is the Contact force, H is hardness of softer material, h is the wear depth and P is the contact pressure. Archard’s model has been used previously by several researchers, for representing electrical contact systems. Cantizano [3], Molinari [1], Podra [2] and Hegadekatte [4] have used Archard’s wear model due to it’s ability to predict mild wear accurately. In this paper, Archard’s wear model has been used in conjunction with the ALE finite element formulation to model fretting wear. The amount of material worn out, depends primarily on the stress field in the contact and the relative sliding distance between the contacting surfaces. In the simulation, Archard’s model is discretized with respect to the sliding distance as,
§K· ¨ ¸P ©H¹
0.00E+00
Wear Depth (mm)
dh ds
Figure 11: Accrued Wear on Contact Surface due to Fretting.
(2)
-2.00E-05 0
500
1000
1500
2000
-4.00E-05 -6.00E-05 -8.00E-05 -1.00E-04 -1.20E-04
An Euler integration scheme has been used to integrate the wear model over the sliding distance. (3) h i h i 1 'h i
Number of Fretting Cycles Figure 12: Simulated Wear Depth versus Number of Fretting Cycles..
839
Pressure (N/mm^2)
0 -0.04
-0.02
-0.5
0
0.02
-1
N=60 N=40
plot and the simulation plots as shown in Figure 14. Similar wear rates were found, indicating that the model had been validated.
0.04
N=20 N=2
-1.5 -2 -2.5
Displacement (mm) Figure 13: Contact Pressure Variation across Vibration Amplitude with Wear Evolution due to Fretting Cycles (N) 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 [16]. Steel-on-steel contact system is a common electrical contact system used in battery contacts. The wear coefficient value of 0.0150 for steel-steel contact from experimental data was used in the model predictions [17]. The hardness value of steel used was Hv 700. The wearrate was calculated as a function of the wear coefficient, hardness, sliding velocity and contact pressure using formula,
§ K ·§ s · ¨ ¸¨ ¸ P © H ¹© t ¹
h t
Wear Depth (mm)
0.0025
Model Predictions Experimental Data
0.0020 0.0015 0.0010 0.0005 0.0000 0
50000
100000 150000 200000 250000 30000
Cummulative Displacement (mm) Figure 14: Comparison of Predicted Wear Rates Versus Experimental Results. 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. 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
SUMMARY AND CONCLUSIONS In this paper, a methodology for simulation of fretting wear in electrical contacts has been presented. The modeling methodology based on ALE formulation adaptive meshing extends the state-of-art by enabling the continuous wear evolution of the contact surfaces through computation of accrued wear. The model has been validated with published experimental data on an electrical contact system. The modeling results show good correlation with experimental data. The model geometry analyzed has been shown have wide applicability to random access memory sockets, securedigital memory card sockets, microprocessor sockets and fuzz button pressure contacts. 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. ACKNOWLEDGMENTS The research presented in this paper has been supported by the National Science Foundation and the Members of NSF Center for Advanced Vehicle Electronics (CAVE) at Auburn University. REFERENCES 1. 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. 2. Podra, P., Soren Andersson, Simulating Sliding Wear With Finite Element Method, Tribology International, Vol. 32, pp.71-81, 1999. 3. Cantizano A, A. Carnicero a, G. Zavarise, Numerical Simulation of Wear-Mechanism Maps, Computational Materials Science, Vol. 25, pp. 54–60, 2002. 4. 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. 5. Agelet de Saracibar C., M. Chiumenti, On the Numerical Modeling of Frictional Wear Phenomena, Comput. Methods Appl. Mech. Engineering, Vol.177, pp.401-426, 1999. 6. Laursen T.A. and J.C. Simo, A Continuum-Based Finite Element Formulation For the Implicit Solution of MultiBody, Large Deformation Frictional Contact Problems, Int. J. Numer. Methods Engg. Vol. 36, pp. 3451–3485, 1993. 7. Carter, D., Fuzz Buttonapos; Interconnects at Microwave and mm-Wave Frequencies, Packaging and Interconnects at Microwave and MM-Wave Frequencies, IEE Seminar, Volume , Issue , pp. 3/1 - 3/6, 2000. 8. 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. 9. Donea J., Antonio Huerta, J.-Ph. Ponthot and A. Rodrguez-Ferran, Arbitrary Lagrangian–Eulerian
840
Methods, Encyclopedia of Computational Mechanics. Volume 1:Fundamentals, 2004. 10. Nazem M. and D. Sheng, Arbitrary Lagrangian-Eulerian Method For Consolidation Problems in Geomechanics, International Conference on Computational Plasticity, Vol. 8, 2005. 11. R.T. Knapp, J.W. Daily, F.G. G Hammitt, Cavitation, McGraw-Hill, New York, 1970. 12. Peterson, M. B., Winer, W. O., eds., Wear Control Handbook. NY: Am. Soc. Mech. Eng., 1358 pp., 1980. 13. Archard J. F., Contact and Rubbing of Flat Surfaces, J. Appl. Phys., Vol. 24, No. 8, pp. 981-8, 1953 14. Archard J. F., Single Contacts and Multiple Encounters, J. Appl. Phys., vol. 32, no. 8, pp. 1420-5, 1961. 15. Lancaster, J.K., A review of the influence of environmental humidity and water on friction, lubrication and wear, Tribology International, Vol. 23, No. 6, pp. 371–389, 1990. 16. Kato H., T.S. Eyre and B. Ralph, Wear Mechanism Map of Nitrided Steel, Acta metal. Mater., vol. 42, no. 5, pp. 17031713, 1994. 17. Rabinowicz, Friction and Wear of Materials, Edition 2, Table 6.2, pp. 159, 1995
841
