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Research Papers

Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications

[+] Author and Article Information
P. Velex1

INSA Lyon, LaMCoS, UMR CNRS 5259, Université de Lyon, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, Villeurbanne Cédex 69 621, Francephilippe.velex@insa-lyon.fr

J. Bruyère

INSA Lyon, LaMCoS, UMR CNRS 5259, Université de Lyon, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, Villeurbanne Cédex 69 621, Francejerome.bruyere@insa-lyon.fr

D. R. Houser

Department of Mechanical Engineering, Gear and Power Transmission Research Laboratory, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210houser.4@osu.edu

1

Corresponding author.

J. Mech. Des 133(3), 031010 (Mar 10, 2011) (11 pages) doi:10.1115/1.4003578 History: Received June 04, 2010; Revised January 31, 2011; Published March 10, 2011; Online March 10, 2011

Some theoretical developments are presented, which lead to approximate analytical results on quasi-static transmission errors valid for low and high contact ratio spur and helical gears. Based on a multidegree-of-freedom gear model, a unique scalar equation for transmission error is established. The role of profile relief is analyzed by using Fourier series and it is shown that transmission error fluctuations depend on a very limited number of parameters representative of gear geometry and profile relief definition. An original direct solution to the optimum relief minimizing transmission error fluctuations is presented, which is believed to be helpful for designers. The analytical results compare well with the numerical results provided by a variety of models and it is demonstrated that some general laws of evolution for transmission error fluctuations versus profile modifications can be established for spur and helical gears.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Generic gear model: schematic representation

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Figure 2

Simulation of mesh elasticity by a time-varying, nonlinear Wrinckler foundation

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Figure 3

Positions of contact lines on base plane

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Figure 4

Windowing functions

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Figure 5

Comparisons between analytical and numerical results (ISO mesh stiffness) for low and high contact ratio spur gears. Circle lines correspond to the optimum relief, as defined in Eq. 26 and Table 1: (a) εα=1.67: analytical results, (b) εα=1.67: numerical results, (c) εα=2.14: analytical results, and (d) εα=2.14: numerical results.

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Figure 6

Comparisons between analytical and numerical results (ISO mesh stiffness) for helical gears. Circle lines correspond to the optimum relief, as defined in Eq. 26 and Table 1: (a) εα=1.37, εβ=1.36: analytical results, (b) εα=1.37, εβ=1.36: numerical results, (c) εα=1.53, εβ=2.72: analytical results, and (d) εα=1.53, εβ=2.72: numerical results.

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Figure 7

Transmission error plots by using Weber, Banaschek, and Lundberg formulas. Circle lines correspond to the optimum relief, as defined in Eq. 26 and Table 1: (a) spur gear εα=1.67, (b) HCR spur gear εα=2.14, and (c) helical gear εα=1.37, εβ=1.75. Numerical results.

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Figure 8

Comparisons between the LDP results and the analytical results. Circle lines correspond to the optimum relief, as defined in Eq. 26 and Table 1. Contour plot of TEs peak-to-peak versus tip relief amplitude E and roll angle at the start of profile modification (a) LDP results (spur gear εα=1.67), (b) analytical results (spur gear εα=1.67), (c) LDP results (HCR spur gear εα=2.14), (d) analytical results (HCR spur gear εα=2.14), (e) LDP results (helical gear εα=1.35 and εβ=1.75, (f) analytical results (helical gear εα=1.35 and εβ=1.75.

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