本文研究滾珠軸承轉子系統的內外環含表面波紋之非線性動態分析。系統由一內外環含表面波紋及間隙之滾珠軸承支撐一水平轉軸，並且滾珠軸承受一恆定的垂直徑向預壓，而系統的轉軸假設為剛體，且轉軸與內環緊密連接無滑動。非線性現象來自於軸承滾珠與內外環之間的赫茲接觸、內外環表面波紋與徑向間隙。本文利用Lagrange’s equation描述系統之動態行為，之後採用Newmark-β法解非線性聯立方程組。透過頻譜圖、龐加萊截面及瀑布圖，探討內外環之波紋數及轉子轉速對於系統動態行為的影響。由數值結果顯示波紋數越大，產生諧振的頻率越大，且內外環的諧振頻率數值皆有一定的規律。

Nonlinear dynamic behavior of rotor-ball bearing system due to surface waviness of inner and outer races is studied. The system consists of a horizontal shaft which is supported by a ball bearing with a constant vertical radial preload and surface waviness of inner and outer races. The rotor is considered to be rigid and shaft is tied to the inner ring without slipping. The non-linearity is due to surface waviness and the Hertzian contact between the races and the balls. The governing differential equations of motion are obtained by using Lagrange’s equations. The numerical integration method used in the present analysis is based on the Newmark-β method. Through the spectrograms, Poincaré maps, and waterfall plots, effects of number of waves and rotational speed on dynamic behavior of the system are studied. Numerical results show that, as the waviness order increases, the peak amplitude of vibration will appear at higher frequency. Also, there is a certain regulation within the waviness order of inner and outer races and vibration frequency.

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