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RESEARCH PAPERS

Inclusion of Sliding Friction in Contact Dynamics Model for Helical Gears

[+] Author and Article Information
Song He

Acoustics and Dynamics Laboratory, Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210he.81@osu.edu

Rajendra Gunda

Advanced Numerical Solutions, Hilliard, OH 43026gunda.2@osu.edu

Rajendra Singh1

Acoustics and Dynamics Laboratory, Department of Mechanical Engineering and The Center for Automotive Research, The Ohio State University, Columbus, OH 43210singh.3@osu.edu

1

Corresponding author

J. Mech. Des 129(1), 48-57 (Apr 29, 2006) (10 pages) doi:10.1115/1.2359474 History: Received December 26, 2005; Revised April 29, 2006

Abstract

This paper proposes a new analytical model for helical gears that characterizes the contact plane dynamics and captures the velocity reversal at the pitch line due to sliding friction. First, the tooth stiffness density function along the contact lines is calculated by using a finite element code. Analytical formulations are then derived for the multidimensional mesh forces and moments. Contact zones for multiple tooth pairs in contact are identified, and the associated integration algorithms are derived. A new 12-degree-of-freedom, linear time-varying model with sliding friction is then developed. It includes rotational and translational motions along the line-of-action, off-line-of-action, and axial directions. The methodology is also illustrated by predicting time and frequency domain results for several values of the coefficient of friction.

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Figures

Figure 7

Time and frequency domain responses of pinion bearing forces FSB,xp, FSB,yp, and FSB,zp at Tp=2000lb∕in and Ωp=1000rpm. All forces are normalized with respect to 1lbf. Key: blue solid line μ=0.01, red dotted line μ=0.1.

Figure 8

Time and frequency domain responses of composite displacements δx, δy, δz, and velocity δ̇z at Tp=2000lbf∕in. and Ωp=1000rpm. All motions are normalized with respect to 39.37μin.(1μm) or 39.37μin.∕s(1μm∕s). Key: blue solid line μ=0.01, red dotted line μ=0.1.

Figure 1

Schematic of the helical gear pair system

Figure 2

Tooth stiffness function calculated using Eq. 1 based on the FE/CM code (11). Key: red dotted line, tooth pair 0; green solid line, tooth pair 1; blue dashed-dotted line, tooth pair 2; thick solid line, combined tooth pair stiffness.

Figure 3

Contact zones at the beginning of a mesh cycle: (a) in the helical gear pair and (b) contact zones within contact plane. Key: PP′ is the pitch line; AA′ is the face width W; AD is the length of contact zone Z.

Figure 4

Predicted tooth stiffness functions. Predicted tooth stiffness functions. Key: blue dashed-dotted line, tooth pair 0; green solid line, tooth pair 1; red dotted line, tooth pair 2; thick solid line, combined tooth pair stiffness.

Figure 5

Schematic of the bearing-shaft model. Here, the shaft and bearing stiffness elements are assumed to be in series to each other. Only pure rotational or translational stiffness elements are shown. Coupling stiffness terms Kxθy, Kxθx are not shown.

Figure 6

Time and frequency domain responses of translational pinion displacements uxp, uyp, uzp at Tp=2000lb∕in. and Ωp=1000rpm. All displacements are normalized with respect to 39.37μin.(1μm). Key: blue solid line μ=0.01, red dotted line μ=0.1.

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