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TECHNICAL PAPERS

Nonlinear Transient Behavior of a Sliding System With Frictionally Excited Thermoelastic Instability

[+] Author and Article Information
P. Zagrodzki

Raytech Composites, Inc., Crawfordsville, IN 47933

K. B. Lam, E. Al Bahkali, J. R. Barber

University of Michigan, Ann Arbor, MI 48109

J. Tribol 123(4), 699-708 (Jan 04, 2001) (10 pages) doi:10.1115/1.1353180 History: Received August 17, 2000; Revised January 04, 2001
Copyright © 2001 by ASME
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References

Inoue, H., 1986, “Analysis of Brake Judder Caused by Thermal Deformation of Brake Disk Rotors,” SAE Paper 865131.
Dow,  T. A., and Burton,  R. A., 1972, “Thermoelastic Instability of Sliding Contact in the Absence of Wear,” Wear, 19, pp. 315–328.
Burton,  R. A., Nerlikar,  V., and Kilaparti,  S. R., 1973, “Thermoelastic Instability in a Seal-like Configuration,” Wear, 24, pp. 177–188.
Lee,  K., and Barber,  J. R., 1993, “Frictionally-Excited Thermoelastic Instability in Automotive Disk Brakes,” ASME J. Tribol., 115, pp. 607–614.
Yi,  Y.-B., Du,  S., Barber,  J. R., and Fash,  J. W., 1999, “Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches,” ASME J. Tribol., 121, pp. 661–666.
Barber,  J. R., 1976, “Some Thermoelastic Contact Problems Involving Frictional Heating,” Q. J. Mech. Appl. Math., 29, pp. 1–13.
Lee, K., and Dinwiddie, R. B., 1998, “Conditions of Frictional Contact in Disk Brakes and Their Effects on Brake Judder,” SAE Paper 980598.
Kennedy,  F. E., and Ling,  F. F., 1974, “A Thermal, Thermoelastic, and Wear Simulation of a High-Energy Sliding Contact Problem,” ASME J. Lubr. Technol., 97, pp. 497–508.
Azarkhin,  A., and Barber,  J. R., 1985, “Transient Thermoelastic Contact Problem of Two Sliding Half-planes,” Wear, 102, pp. 1–13.
Azarkhin,  A., and Barber,  J. R., 1986, “Thermoelastic Instability for the Transient Contact Problem of Two Sliding Half-Planes,” ASME J. Appl. Mech., 53, pp. 565–572.
Zagrodzki,  P., 1990, “Analysis of Thermomechanical Phenomena in Multidisk Clutches and Brakes,” Wear, 140, pp. 291–308.
Heinrich,  J. C., Huyakorn,  P. S., Zienkiewicz,  O. C., and Mitchell,  A. R., 1977, “An “Upwind” Finite Element Scheme for Two-Dimensional Convective Transport Equation,” Int. J. Numer. Methods Eng., 11, pp. 131–143.
Yu,  C.-C., and Heinrich,  J. C., 1986, “Petrov-Galerkin Methods for the Time-Dependent Convective Transport Equation,” Int. J. Numer. Methods Eng., 23, pp. 883–901.
Yu,  C.-C., and Heinrich,  J. C., 1987, “Petrov-Galerkin Method for Multidimensional, Time-Dependent, Convective-Diffusion Equations,” Int. J. Numer. Methods Eng., 24, pp. 2201–2215.
ABAQUS, 1998, Theory Manual, Version 5.8, HKS.
Craslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Clarendon Press, Oxford.
Banaszek,  J., 1993, “Fourier Mode Analysis in Error Estimation for Finite-Element Solution to Convective-Diffusive Phenomena,” Arch. Thermodyn., 14, pp. 67–92.
Lee,  K., and Barber,  J. R., 1993, “The Effect of Shear Tractions on Frictionally-Excited Thermoelastic Instability,” Wear, 160, pp. 237–242.
Anderson,  A. E., and Knapp,  R. A., 1990, “Hot Spotting in Automotive Friction Systems,” Wear, 135, pp. 319–337.
Yi,  Y.-B., Barber,  J. R., and Zagrodzki,  P., 2000, “Eigenvalue Solution of Thermoelastic Instability Problems Using Fourier Reduction,” Proc. R. Soc. London, Ser. A, 456, No. 2003, pp. 2799–2821.

Figures

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Schematic of sliding system
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Character of temperature distribution in a skin layer of poor conductor
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Detail of finite element mesh
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Contact pressure distribution at a series of instants during the stage with full contact
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Change in amplitude and location of pressure perturbation: pa—amplitude of pressure perturbation; pm—mean pressure; x0—location of maximum pressure along x-axis
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Temperature distribution representing dominant eigenmode
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Dimensionless critical speed determined by Lee and Barber’s analytical model and estimated by finite element model
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Dimensionless migration speed determined by Lee and Barber’s analytical model and estimated by finite element model
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Contact pressure distribution at a series of instants during the stage with contact separation
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Temperature contours at different instants
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Temperature distribution along contact surfaces at different instants
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Maximum contact pressure, contact length and migration speed: pmax,pm—maximum and mean contact pressure, respectively; Lc—contact length; L—length of the interface; cs—migration speed; c—migration speed in the full contact phase.
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Maximum contact pressure, contact length and migration speed: pmax,pm—maximum and mean contact pressure, respectively; Lc—contact length; L—length of the interface; cs—migration speed; c—migration speed in the full contact phase
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Contact pressure distribution in the transient stage with contact separation and in the quasi-steady state
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Dimensionless critical speed determined by Lee and Barber’s analytical model: V1, V2, and V3—sliding speeds used in simulations
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Contact pressure distribution at a series of instants from simulation with two unstable modes

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