外文翻译--行星齿轮固有频率.doc

附录 附录1 英文原文 NATURAL FREQUENCY VEERING IN PLANETARY GEARS ABSTRACT To achieve noise and vibration reduction in planetary gear applications, key design parameters are often varied to avoid resonances,optimize load distribution, and reduce weight. In the plots of natural frequencies versus planetary gear parameters,veering phenomena occur when two eigenvalue loci approach each other, but then abruptly veer away. The importance of veering is manifested in the dramatic changes in the vibration modes of the veering natural frequencies and the consequent impact on response.This work analytically characterizes the rules of eigenvalue veering in planetary gears.The coupling factors between two close eigenvalue loci are approximated by perturbation analysis. Special veering patterns were obtained using the unique properties of planetary gear vibration modes.The results are illustrated by an example. Key design parameters were investigated, and generalized guidance is provided for tuning planetary gear natural frequencies. I. INTRODUCTION Noise and vibration reduction are critical concerns in planetary gear applications. During the design process, system parameters are varied to evaluate alternative design choices,avoid resonances,optimize load distribution,and reduce weight. It is important to characterize the effects of parameter variations on the natural frequencies and vibration modes for effective vibration tuning. In planetary gear dynamic models (Fig. 1), the key design parameters include the mesh stiffnesses, support/bearing stiffnesses, component masses, and moments of inertia. Some plots of natural frequencies versus planetary gear parameters are presented by Cunliffe et al. [1], Botman [2], Kahraman [3,4], and Saada and Velex [5]. Natural frequency plots in these studies, especially Ref. 3, show natural frequency veering phenomena when two eigenvalue loci approach each other as a parameter is varied, but then abru