An analytical solution to the dynamic transmission error of a helical gear pair is developed by using a single-degree-of-freedom model with piecewise stiffness functions that characterize the contact plane dynamics and capture the velocity reversal at the pitch line. By assuming a constant mesh stiffness density along the contact lines, a linear time-varying model (with parametric excitations) is obtained, where the effect of sliding friction is quantified by an effective mesh stiffness term. The Floquet theory is then used to obtain closed-form solutions to the dynamic transmission error, and responses are derived to both initial conditions and the forced periodic function under a nominal preload. Analytical models are validated by comparing predictions with numerical simulations, and the effect of viscous damping is examined. Stability analysis is also briefly conducted by using the state transition matrix. Overall, the sliding friction has a marginal effect on the dynamic transmission error of helical gears, as compared with spur gears, in the context of the torsional model.
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Research Papers
Dynamic Transmission Error Prediction of Helical Gear Pair Under Sliding Friction Using Floquet Theory
Song He,
Song He
Acoustics and Dynamics Laboratory, Department of Mechanical Engineering,
e-mail: he.81@osu.edu
The Ohio State University
, Columbus, OH 43210
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Rajendra Singh
Rajendra Singh
Fellow ASME
Acoustics and Dynamics Laboratory, Department of Mechanical Engineering,
e-mail: singh.3@osu.edu
The Ohio State University
, Columbus, OH 43210
Search for other works by this author on:
Song He
Acoustics and Dynamics Laboratory, Department of Mechanical Engineering,
The Ohio State University
, Columbus, OH 43210e-mail: he.81@osu.edu
Rajendra Singh
Fellow ASME
Acoustics and Dynamics Laboratory, Department of Mechanical Engineering,
The Ohio State University
, Columbus, OH 43210e-mail: singh.3@osu.edu
J. Mech. Des. May 2008, 130(5): 052603 (9 pages)
Published Online: April 1, 2008
Article history
Received:
May 6, 2007
Revised:
August 17, 2007
Published:
April 1, 2008
Citation
He, S., and Singh, R. (April 1, 2008). "Dynamic Transmission Error Prediction of Helical Gear Pair Under Sliding Friction Using Floquet Theory." ASME. J. Mech. Des. May 2008; 130(5): 052603. https://doi.org/10.1115/1.2890115
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