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TECHNICAL PAPERS

Strategies for Modeling Friction in Gear Dynamics

[+] Author and Article Information
Manish Vaishya, Rajendra Singh

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210-1107

J. Mech. Des 125(2), 383-393 (Jun 11, 2003) (11 pages) doi:10.1115/1.1564063 History: Received March 01, 2001; Revised September 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

Martin,  K. F., 1978, “A Review of Friction Predictions in Gear Teeth,” Wear, 49, pp. 201–238.
Kelley,  B. W., and Lemanski,  A. J., 1967, “Lubrication of Involute Gearing,” Proc. Inst. Mech. Eng., 182(3A), pp. 173–184.
Radzimovsky,  E., and Mirarefi,  A., 1974, “Dynamic Behavior of Gear Systems and Variation of Coefficient of Friction and Efficiency during the Engagement Cycle,” ASME J. Eng. Ind., 74-DET-86, pp. 1–7.
Iida,  H., Tamura,  A., and Yamada,  Y., 1985, “Vibrational Characteristics of Friction between Gear Teeth,” Bull. JSME, 28(241), pp. 1512–1519.
Borner, J., and Houser, D. R., 1996, “Friction and Bending Moments as Gear Noise Excitations,” Society of Automotive Engineers Technical Paper Series, 961816, pp. 1–8.
Velex, P., and Cahouet, V., 2000, “Experimental and Numerical Investigations on the Influence of Tooth Friction in Spur and Helical Gear Dynamics,” Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/PTG-14430, pp. 1–10.
Vaishya, M., and Houser, D. R., 2000, “Modeling and Analysis of Sliding Friction in Gear Dynamics,” Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/PTG-14431, pp. 1–10.
Vaishya,  M., and Singh,  R., 2000, “Analysis of Periodically Varying Gear Mesh Systems with Coulomb Friction using Floquet Theory,” J. Sound Vib., 243(3), pp. 525–545.
Ozguven,  H. N., and Houser,  D. R., 1988, “Mathematical Models used in Gear Dynamics—a Review,” J. Sound Vib., 121(3), pp. 383–411.
Blankenship, G. W., and Singh, R., 1992, “A Comparative Study of Selected Gear Mesh Force Interface Dynamic Models,” Proceedings of the 6th ASME International Power Transmission and Gearing Conference, Vol. DE-43-1, pp. 137–146.
Padmanabhan,  C., and Singh,  R., 1996, “Analysis of Periodically Forced Nonlinear Hill’s Oscillator with Application to a Geared System,” J. Acoust. Soc. Am., 99(1), pp. 324–334.
Blankenship,  G. W., and Singh,  R., 1995, “Analytical Solution for Modulation Sidebands Associated with a Class of Mechanical Oscillators,” J. Sound Vib., 179(1), pp. 13–36.
Ozguven,  H. N., and Houser,  D. R., 1988, “Dynamic Analysis of High Speed Gears by using Loaded Static Transmission Error,” J. Sound Vib., 125(1), pp. 71–83.
Benton,  M., and Seireg,  A., 1978, “Simulation of Resonances and Instability Conditions in Pinion-Gear Systems,” ASME J. Mech. Des., 100, pp. 26–32.
Vaishya,  M., and Singh,  R., 2000, “Sliding Friction Induced Non-linearity and Parametric Effects in Gear Dynamics,” J. Sound Vib., 248(4), pp. 671–694.
Conry,  T. F., and Seireg,  A., 1973, “A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems,” ASME J. Eng. Ind., pp. 1115–1122.
Oh, S., Grosh, K., and Barber, J. R., 1998, “Dynamic Behavior of Interacting Spur Gears: Energy Conservation,” Proceedings of the National Conference on Noise Control Engineering, Institute of Noise Control Engineering, pp. 145–150.
Richards, J. A., 1983, Analysis of Periodically Time-Varying Systems, Springer-Verlag, New York.
Padmanabhan,  C., Barlow,  R. C., Rook,  T. E., and Singh,  R., 1995, “Computational Issues Associated with Gear Rattle Analysis,” ASME J. Mech. Des., 117, pp. 185–192.
Oberhettinger, F., 1973, Fourier Expansions A Collection of Formulas, Academic Press, Inc., New York.

Figures

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Simulated mesh and friction forces on the two teeth when static and dynamic mesh forces are considered at Γ=1.532, μ=0.1, ζ=0.01, Ωp=2400 rpm (non-resonant condition). (a) Mesh load using N; (b) Mesh load using Fmesh; (c) Ff using N; (d) Ff using Fmesh. Key: [[dashed_line]] 1st tooth in mesh, – 2nd tooth in mesh (2 mesh cycles shown).
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Spectra of total friction force on when static and dynamic mesh forces are considered at Γ=1.532, μ=0.1 and ζ=0.01. (a) Ff calculated using N, at Ωp=2400 rpm (nonresonant condition); (b) Ff using Fmesh, at Ωp=2400 rpm; (c) Ff using N, at Ωp=2300 rpm (resonant condition); (d) Ff using Fmesh, at Ωp=2300 rpm.
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Variation in coefficient of friction for different models at Ωp=100 rpm, μ=0.1, Γ=1.590, ζ=0.01. (a) No friction; (b) Assumed variation corresponding to Fig. 7(b); (c) Actual variation corresponding to Fig. 7c.
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Sample response for δ due to individual and combined excitations. (a) All excitations combined; (b) Only friction excitation Tf(t).
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Dynamic response for the three friction models in terms of δ, at Ωp=200 rpm, ζ=0.05. (a) LTV system with μ0=0; (b) LTV system with μ0=0.1; (c) NLTV system with μ0=0.1.
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Effect of Coulomb friction on instability zone, (–) with friction, ([[dashed_line]]) without friction (area enclosed within the curves is the unstable zone)
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Torsional model of gear pair with friction force
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Typical variation in μ over the entire surface of a spur gear tooth
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Measured pinion deflection in traction (ξ) and sliding (η) direction for Tp=102 Nmp=1000 rpm. (a) Low η0 lubricant, ξ-direction; (b) Low η0 lubricant, η-direction; (c) High η0 lubricant, ξ-direction; (d) High η0 lubricant, η-direction.
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Dynamic response δ(t) for 2000 rpm, ζ=.05, Γ=1.473, μ=0.1, k/kb=5×105 (a) Semi-positive definite system: time response; (b) Semi-positive definite system: frequency spectrum; (c) Positive definite system with extra spring: time response; (d) Positive definite system with extra spring: frequency spectrum.
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Variation of sliding speed for the three friction models. (a) VS for quasistatic case; (b) Vs for LTV model; (c) Vs with nonlinear friction. Key: – 1st tooth, [[dashed_line]] 2nd tooth.
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Input power to the geared system. (a) With constant output and input torques, mean power=0; (b) With constant input torque and spring attached to output gear, mean power=629 Watts (equivalent to energy loss due to friction).
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Dynamic response δ(t) with LTV analysis, near resonance conditions for ζ=0.001, μ=0.1, Ωp=1490 rpm, Γ=1.473. (a) LTV system; (b) NLTV system.

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