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TECHNICAL PAPERS

Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems

[+] Author and Article Information
Jian Lin

John Deere Product Engineering Center, Waterloo, IA 50704-8000

Robert G. Parker

Department of Mechanical Engineering, The Ohio State University, 206 W. 18th Ave, Columbus, OH 43210e-mail: parker.242@osu.edu

J. Vib. Acoust 124(1), 68-76 (Sep 01, 2001) (9 pages) doi:10.1115/1.1424889 History: Received August 01, 2000; Revised September 01, 2001
Copyright © 2002 by ASME
Topics: Gears , Stiffness
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References

Figures

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Two-stage gear system with (a) four gears and (b) three gears. kL1,kL2 denote mesh stiffnesses and Z2,Z4 denote number of gear teeth. kL0 is the torsional stiffness of the anchored shaft.
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Modeling of mesh stiffnesses ki(t)=kgi+kvi(t).ci are contact ratios, kgi are average mesh stiffnesses, and piTi are phasing angles.
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Instabilities regions when Ω12=Ω,ε12=ε; — analytical solution;* * * numerical solution. The parameters are from Table 1 and c1=c2=1.5,h=0.
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Vibration modes for the time-invariant system with parameters in Table 1
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Comparison of instability regions for various contact ratios and mesh phasing. The parameters are in Table 1. ---c1=c2=1.5,h=0.5; —c1=1.1,c2=1.9,h=0.9; -⋅-⋅-⋅- c1=c2=1.5,h=0.
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Instabilities regions when Ω1=RΩ212=ε. (a) R=3/5, (b) R=1/2. The parameters are in Table 1 and c1=c2=1.5,h=0.* * * denotes numerical solutions.
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Instabilities regions when Ω12. (a) Ω1 versus ε1 and ε2=C=0.3. (b) Ω1 versus ε12 and the solid line indicates vanishing of the combination instability. The parameters are in Table 1 and c1=c2=1.5,h=0.
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Comparison of instability regions from different analyses. The parameters are from Table 1, c1=1.47,c2=1.57, and phasing (a) h=0, (b) h=0.4. —Perturbation method;* * * Numerical method; ---Tordion and Gauvin (1977); ⋅⋅⋅ Benton and Seireg (1980).
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Free responses for Ω=4.2,ka=ε=0.3 (point A in Fig. 8) and the parameters of (a) Fig. 8(a) and (b) Fig. 8(b). The initial conditions are x1=x2=x3=0.1,ẋ1=ẋ2=ẋ3=0.

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