0
Research Papers: Design Automation

Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration

[+] Author and Article Information
Gang Liu

Department of Mechanical Engineering, The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210liu.442@osu.edu

Robert G. Parker

Department of Mechanical Engineering, The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210parker.242@osu.edu

J. Mech. Des 130(12), 121402 (Oct 21, 2008) (13 pages) doi:10.1115/1.2976803 History: Received October 14, 2007; Revised June 25, 2008; Published October 21, 2008

This work studies the effects of tooth profile modification on multimesh gearset vibration. The nonlinear analytical model considers the dynamic load distribution between the individual gear teeth and the influence of variable mesh stiffnesses, profile modifications, and contact loss. The proposed model yields better agreement than two existing models when compared against nonlinear gear dynamics from a finite element/contact mechanics benchmark. These comparisons are made for different loads, profile modifications, and bearing stiffness conditions. This model captures the total and partial contact losses demonstrated by finite element. Perturbation analysis based on the proposed model finds approximate frequency response solutions for the case of no total contact loss due to the optimized system parameters. The closed-form solution is compared with numerical integration and provides guidance for optimizing mesh phasing, contact ratios, and profile modification magnitude and length.

Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Translational-rotational model of idler gearsets

Grahic Jump Location
Figure 2

Mesh stiffnesses of the pinion-idler mesh for system parameters in Table 1 and no profile modifications

Grahic Jump Location
Figure 3

Gap constraints and finite element NLTE of the pinion-idler mesh with system parameters and tooth profile modifications in Table 1

Grahic Jump Location
Figure 4

Finite element model of the example idler gearset in Table 1

Grahic Jump Location
Figure 5

Comparison of dynamic transmission error (with mean removed) from Model 1 and finite element for multiple torques, no tooth modification, and other system parameters in Table 1

Grahic Jump Location
Figure 6

Comparison of dynamic transmission error (with mean removed) from Model 2 and finite element for multiple torques, no tooth modification, and other system parameters in Table 1

Grahic Jump Location
Figure 7

Comparison of dynamic transmission error (with mean removed) from Model 3 and finite element for multiple torques, no tooth modification, and other system parameters in Table 1

Grahic Jump Location
Figure 8

Comparison of dynamic transmission error from Model 1 and AUTO for input torque of 100 N m, no tooth modification, and other system parameters in Table 1 ((—) stable AUTO solution; (- ⋅ -) unstable AUTO solution; (●) numerical up-sweep; (◯) numerical down-sweep).

Grahic Jump Location
Figure 9

Comparison of dynamic transmission error (with mean removed) from the three analytical models and FE for modification A, input torque of 100 N m, and other system parameters in Table 1 ((- ⋅ -) FE; (⋅ ⋅ ⋅) Model 1; (—) Model 2; (- - -) Model 3)

Grahic Jump Location
Figure 10

Comparison of RMS of dynamic transmission error (with mean removed) from the three analytical models and FE with modification B, an input torque of 100 N m, and other system parameters in Table 1 ((- ⋅ -) FE; (⋅ ⋅ ⋅) Model 1; (—) Model 2; (- - -) Model 3)

Grahic Jump Location
Figure 11

Comparison of idler line-of-action translation from Model 1 and FE with system parameters in Table 1 and an input torque of 100 N m ((- ⋅ -) FE no profile modification; (⋅ ⋅ ⋅) Model 1 no profile modification; (- - -) FE profile modification A; (—) Model 1 profile modification A).

Grahic Jump Location
Figure 12

Dynamic mesh forces for mesh 1 for two mesh frequencies near jump-down for an input torque of 100 N m, no tooth modification, and other system parameters in Table 1 ((—) Model 1; (– –) FE): (a) Mesh frequency f=2470 Hz for lower branch; (b) Mesh frequency f=2490 Hz for upper branch

Grahic Jump Location
Figure 13

Profile modification, DTE from Model 1, and tooth contact from FE over one mesh cycle for system parameters in Table 1: (a) Mesh frequency of 2750 Hz for a torque of 100 N m and tooth modification B ((- - -) profile modification; (⋅ ⋅ ⋅) DTE; (—) mesh force); (b) Mesh frequency of 1400 Hz for a 50 N m torque and tooth modification A ((- - -) profile modification; (⋅ ⋅ ⋅) DTE; (—) tooth number)

Grahic Jump Location
Figure 14

Comparison of DTE between perturbation and numerical simulation for c1=1.4, c2=1.6, ϕ=0, ρ1=10 μm, ρ2=12 μm, and gear 1 torque of 100 N m ((—) perturbation; (- - -) numerical integration)

Grahic Jump Location
Figure 15

Contour plot of the DTE amplitudes varying with the two tip relief magnitudes for ω=ω1, c1=1.4, c2=1.6, ξn=cn−1, and ϕ=0 ((—) analytical solution; (- - -) numerical integration): (a) z1 and (b) z2

Grahic Jump Location
Figure 16

Contour plot of the response amplitude z2 varying with two tip relief magnitudes for ω=ω1, c1=1.4, c2=1.6, ξn=cn−1, and ϕ=π

Grahic Jump Location
Figure 17

Contour plot of z2 amplitude varying with two contact ratios for ω=ω1, ρ1=10 μm, ρ2=12 μm, ξn=cn−1, and ϕ=0: (a) analytical solution and (b) numerical integration

Grahic Jump Location
Figure 18

Contour plot of z2 amplitude varying with two modification lengths for ω=ω2, c1=1.4, c2=1.6, ρ1=10 μm, ρ2=12 μm, and ϕ=0

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In