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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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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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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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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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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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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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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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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