本文研究滾珠軸承轉子系統的非線性動態特性。系統由一含間隙之滾珠軸承支撐一水平轉軸，並且有一恆定的垂直徑向預壓，其中轉軸為剛體且與內環緊密相連無滑動。非線性是由於軸承中滾珠與環之間的赫茲接觸、內部徑向間隙以及軸 承的變剛度。本文透過分岔圖、瀑布圖、頻譜圖、吸引子及龐加萊映射，探討軸承間隙、垂直徑向預壓以及滾珠數量，對於系統動態行為的影響。由數值結果顯示，在軸承的間隙增加至系統出現不穩定的響應之後，隨著間隙的增加，系統不穩定區域的範圍會越大。軸承預壓的增加，系統不穩定區域會往高轉速的方向偏移。軸承的滾珠數量越多，系統不穩定區域的範圍會越小，且系統不穩定區域會往低轉速方向偏移。

Nonlinear dynamic behavior of rotor-ball bearing systems is studied. The system consists of a horizontal shaft which is supported by a ball bearing with clearance and a constant vertical radial preload. The shaft is considered to be rigid and is tied to the inner ring without slipping. The non-linearity is due to the radial internal clearance and the Hertzian contact between the ring and the balls; there is also a parametric effect because of the varying compliance of the bearing. Through the bifurcation diagrams, waterfall plots, spectrograms, attractors and Poincaré maps, effects of bearing parameters, such as, clearance, vertical radial preload, number of balls on dynamic behavior of the system are studied. Numerical results show that, after when unstable response has occurred, the range of unstable region will become bigger as the bearing clearance increases. When the bearing preload increases, unstable region of the system will shift to the higher speed range. The higher the number of balls of bearings, the range of unstable region of the system will be smaller, and unstable region of the system will shift to the lower speed range.

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