Proposed Solution Methodology for the Dynamically Coupled Nonlinear Geared Rotor Mechanics Equations

[+] Author and Article Information
L. D. Mitchell, J. W. David

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

J. Vib., Acoust., Stress, and Reliab 107(1), 112-116 (Jan 01, 1985) (5 pages) doi:10.1115/1.3274700 History: Received June 20, 1983; Online December 08, 2009


The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Copyright © 1985 by ASME
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