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Research Papers

A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

[+] Author and Article Information
Christopher G. Cooley

 The Ohio State University, Columbus, OH 43210

Robert G. Parker1

 The Ohio State University, Columbus, OH 43210; Distinguished Professor Chair, State Key Laboratory for Mechanical Systems and Vibration, University of Michigan–Shanghai Jiao Tong University Joint Institute, 200240, Shanghai, Chinaparker.242@osu.edu

Sandeep M. Vijayakar

 Advanced Numerical Solutions, LLC, Hilliard, OH 43026

1

Corresponding author.

J. Vib. Acoust 133(4), 041004 (Apr 06, 2011) (9 pages) doi:10.1115/1.4003399 History: Received January 01, 2010; Revised September 27, 2010; Published April 06, 2011; Online April 06, 2011

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides an accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 10

Time and frequency domain finite element calculations of natural frequency for profile ICR 1.37 gear pairs with unity ratio at 170 N m torque with varying helix angle. The time domain calculation of natural frequency is shown by (○). The frequency domain calculation is shown by a solid line.

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Figure 11

Contour plot of frequency domain finite element calculation of RMS of oscillating DTE for 5–30 deg helix angles over a range of mesh frequencies. The gear pair is a unity ratio (50 teeth) profile ICR1.37 gear pair loaded to 170 N m torque.

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Figure 12

Contour plot of frequency domain finite element calculation of RMS of oscillating DTE for varying profile ICRs over a range of mesh frequencies. The gear pair is a unity ratio (50 teeth) pair with 1.0 face contact ratio loaded to 170 N m torque.

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Figure 8

Finite element calculation of static transmission error (upper) and spectra (mean removed) (lower) for a three-dimensional profile ICR 1.37 helical gear pair with 30 deg helix angle for 85 N m (○), 170 N m (◇), and 340 N m (△)

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Figure 1

Finite element model of a spur gear pair

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Figure 2

Time domain finite element calculation of RMS of oscillating dynamic transmission error of a three-dimensional spur gear pair with ICR 1.37 at 170 N m torque (△) compared with experimental data from Ref. 13 (○)

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Figure 3

Finite element calculation of static transmission error and spectra (mean removed) for three-dimensional ICR 1.37 ((a) and (c)) and ICR 1.77 ((b) and (d)) spur gear pairs for 340 N m (△), 170 N m (◇), and 85 N m (○) torques

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Figure 4

Frequency domain finite element calculation of RMS of dynamic transmission error for a three-dimensional ICR 1.37 spur gear pair (solid) compared with experimental data from Ref. 13 (○) at (a) 85 N m, (b) 170 N m, and (c) 340 N m torques. The gear pair natural frequencies are given in Table 1.

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Figure 5

Frequency domain finite element calculation of RMS of dynamic transmission error for a three-dimensional ICR 1.77 spur gear pair (solid) compared with experimental data from Ref. 13 (○) at (a) 85 N m, (b) 170 N m, and (c) 340 N m torques. The gear pair natural frequencies are given in Table 1.

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Figure 6

Finite element calculation of RMS of dynamic transmission error for a three-dimensional profile ICR 1.37 helical gear pair with 30 deg helix angle at 170 N m torque using the time domain solution (○) and frequency domain solution (solid)

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Figure 7

Finite element calculation of RMS of dynamic transmission error for a three-dimensional profile ICR 1.37 helical gear pair with 15 deg helix angle at 170 N m torque using the time domain solution (○) and frequency domain solution (solid)

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Figure 9

Finite element calculation of RMS of dynamic transmission error for a three-dimensional profile ICR 1.37 helical gear pair with 30 deg helix angle at 85 N m using the time domain method (○) and frequency domain method (dashed) and at 340 N m using the time domain method (△) and frequency domain method (solid)

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