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RESEARCH PAPERS

A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs

[+] Author and Article Information
V. K. Tamminana

Department of Mechanical Engineering,  The Ohio State University, 206 W. 18th Avenue, Columbus, OH 43210

A. Kahraman1

Department of Mechanical Engineering,  The Ohio State University, 206 W. 18th Avenue, Columbus, OH 43210kahraman.1@osu.edu

S. Vijayakar

 Advanced Numerical Solutions, 3956 Brown Park Drive, Suite B, Hilliard, OH 43026

1

Corresponding author.

J. Mech. Des 129(1), 75-84 (Feb 12, 2006) (10 pages) doi:10.1115/1.2359470 History: Received June 10, 2005; Revised February 12, 2006

In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Deformable-body dynamic model of an example spur gear pair

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Figure 2

Discrete dynamic model a spur gear pair

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Figure 3

Gear dynamics test machine

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Figure 4

The test gear pairs used in this study: (a) δ=0, ICR=1.8; (b) δ=10μm, α=20.9deg, ICR=1.8; and (c) δ=0, ICR=1.4

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Figure 5

Time histories of (a) dynamic tooth force, (b) dynamic mesh force, and (c) dynamic max principal stress at 2kHz for a modified gear pair with δ=10μm, α=20.9deg, and ICR=1.8 at 340Nm using deformable body model

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Figure 6

Comparison of measured and predicted rms values of DTE for an unmodified gear pair with δ=0 and ICR=1.8 at 340Nm

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Figure 7

Comparison of measured and predicted rms values of DTE for a modified gear pair with δ=10μm, α=20.9deg, and ICR=1.8 at 340Nm

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Figure 8

Comparison of measured and predicted rms values of DTE for an unmodified gear pair with δ=0 and ICR=1.4 at 170Nm

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Figure 9

Comparison of the harmonic amplitudes of measured and predicted DTE for δ=10μm, α=20.9deg, and ICR=1.8 at 340Nm: (a) 1500Hz, (b) 2100Hz, and (c) 2900Hz

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Figure 10

Comparison of (DF)mf, (DF)tf, (DF)σ, and (DTE)rms for an unmodified gear pair with δ=0 and ICR=1.8 at 340Nm: (a) Deformable-body model and (b) discrete model

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Figure 11

Comparison of (DF)mf, (DF)tf, (DF)σ, and (DTE)rms for a modified gear pair with δ=10μm, α=20.9deg, and ICR=1.8 at 340Nm: (a) Deformable-body model and (b) discrete model

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Figure 12

Comparison of (DF)mf, (DF)tf, (DF)σ, and (DTE)rms for an unmodified gear pair with δ=0 and ICR=1.4 at 170Nm: (a) Deformable-body model and (b) discrete model

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Figure 13

Normalized values of (DMF)o‐p versus (DTE)o‐p for (a) δ=0, ICR=1.8, (b) δ=10μm, α=20.9deg, ICR=1.8, and (c) δ=0, ICR=1.4

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Figure 14

(DF)σ versus (DTE)max for (a) δ=0, ICR=1.8, (b) δ=10μm, α=20.9deg, ICR=1.8, and (c) δ=0, ICR=1.4

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