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mODIFIED
TORSIONAL MODEL DEVELOPMENT AND NATURAL CHARACTERISTICS ANALYSIS
OF 2K-H
EPICYCLIC GEARING
SONG Yimin XU Weidong ZHANG Ce
WANG Shiyu
(School
of Mechanical Engineering, Tianjin University, Tianjin 300072)
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Abstract: A
modified torsional model of planetary gear trains with equally-spaced
pinions is developed and used to identify unique properties of natural
frequencies and vibration modes. Compared with the purely torsional
model, tangential displacements and bearing stiffness of the pinions are
included in the governing equation of motion. On the basis of natural
characteristics analysis, vibration modes of the undamped system are
classified into three types, which are named rotational mode of the
central members, rotational mode of the pinions and translational mode
of the pinions, respectively. For each type of vibration modes the
associated reduced-order eigenvalue problems are derived and closed-form
analytical expressions of natural frequencies are presented for the
pinion modes. Natural frequency sensitivities to system parameters are
rigorously investigated, which reveals that pinion bearing stiffness
affects the first natural frequency of the system significantly. Through
a comparison of natural frequencies experimentally collected and
numerically computed, the modified torsional model is proved to be more
accurate than the purely torsional model and may be applied to dynamic
design of epicyclic gearing with equally-spaced pinions.
Key
words: Planetary
gear transmissions Dynamic model Natural characteristics Dynamic
design
CLC No: TH132.425
国家自然科学基金(50205019)和教育部博士点基金(20040056018)资助项目. Received 20050618,
received in revised form 20051130
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