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TECHNICAL PAPERS

Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics

[+] Author and Article Information
Yuping Cheng

Ford Motor Company, Livonia, MI 48150

Teik C. Lim

Department of Mechanical, Industrial & Nuclear Engineering, The University of Cincinnati, Cincinnati, OH 45221-0072

J. Mech. Des 125(2), 373-382 (Jun 11, 2003) (10 pages) doi:10.1115/1.1564064 History: Received July 01, 2001; Revised July 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

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Figures

Grahic Jump Location
Illustrations of (a) hypoid gear setup, (b) contact cells and three coordinate systems denoted by S0,S1 and S2, and (c) load distributions on the tooth surface for a specific gear angular position
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A multi-degree-of-freedom lumped parameter model of a hypoid geared rotor system
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Flowchart of the proposed computational approach
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Loaded transmission error and corresponding Fourier coefficients for two different pinion torques: (a) effect of load; (b) 113 Nm; and (c) 509 Nm
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Effect of mean pinion torque load on averaged mesh stiffness
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Quasi-static multi-tooth contact analysis results of (a) load sharing characteristic within one mesh cycle at 509 Nm pinion input torque; and (b) load distributions for two different mesh positions
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Predicted dynamic mesh loads for one mesh cycle at the resonant frequency of 340 Hz for the case of time-varying (TV) and time-invariant (TI) mesh vectors at 509 Nm of applied pinion torque load (friction coefficient μ=0)
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Mesh load FFT spectra of the time response shown in Fig. 8
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Comparison of the frequency response functions of the non-linear time-varying (NLTV) and time invariant (NLTI) cases for 509 Nm of pinion torque. Note that the linear time-invariant response (LTI) is also plotted (friction coefficient μ=0)
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Effect of applied pinion torque load on the dynamic mesh force assuming the same mesh stiffness of 3×108N/m for all 3 cases shown (friction coefficient μ=0)
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Effect of applied pinion torque load on dynamic mesh force with load-dependent averaged mesh stiffness (no friction effect)
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Effect of applied pinion torque load on the pinion bearing force with load-dependent averaged mesh stiffness (no friction effect)
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Time-history response of the dynamic mesh force near the jump frequency under light load condition (113 Nm)
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Dynamic mesh force and pinion bearing force due to the fundamental harmonic of LTE compared to that of the first three harmonics of LTE. These cases assume 509 Nm of pinion torque, time-varying mesh vector, time-invariant mesh stiffness, and no friction effect.
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Dynamic transmission error for 2 different pinion torque loads assuming constant mesh stiffness with time-varying mesh vector and no friction effect. The corresponding linear time-invariant solutions are also shown. The super-harmonics indicated are due to the 3rd harmonic of the LTE excitation.
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Frequency spectrum of DTE (μm) at operating frequency of 580 Hz for the case of 226 Nm of input pinion torque
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Waterfall plots of the dynamic response at 509 Nm of input pinion torque. (a) Pinion bearing force; (b) Dynamic mesh force

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