Dynamics of high-speed precision geared rotor systems

Gears are one of the most widely applied precision machine elements in power transmission systems employed in automotive, aerospace, marine, rail and industrial applications because of their reliability, precision, efficiency and versatility. Fundamentally, gears provide a very practical mechanism to transmit motion and mechanical power between two rotating shafts. However, their performance and accuracy are often hampered by tooth failure, vibrations and whine noise. This is most acute in high-speed, high power density geared rotor systems, which is the primary scope of this paper. The present study focuses on the development of a gear pair mathematical model for use to analyze the dynamics of power transmission systems. The theory includes the gear mesh representation derived from results of the quasi-static tooth contact analysis. This proposed gear mesh theory comprising of transmission error, mesh point, mesh stiffness and line-of-action nonlinear, time-varying parameters can be easily incorporated into a variety of transmission system models ranging from the lumped parameter type to detailed finite element representation. The gear dynamic analysis performed led to the discovery of the out-of-phase gear pair torsion modes that are responsible for much of the mechanical problems seen in gearing applications. The paper concludes with a discussion on effectual design approaches to minimize the influence of gear dynamics and to mitigate gear failure in practical power transmission systems.