Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equationsThe 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.
Document ID
19840046327
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Mitchell, L. D. (Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
David, J. W. (Virginia Polytechnic Institute and State University Blacksburg, VA, United States)