本論文研究的主題為轉子-滑動軸承系統中碰摩故障現象分析、以偶應力流體為潤滑劑之軸承-轉子動態分析、以微極流體為潤滑劑之軸承-轉子動態分析、軸承-轉子系統在紊流流場之動態分析、多孔性擠壓油膜阻尼器支撐之油膜軸承-轉子動態分析，同時皆考慮比較接近實際物理系統的非線性支撐之撓性轉子，並且藉由Runge-Kutta法之數值模擬得到系統基本之動態軌跡，再進一步利用頻譜圖、龐卡來映射圖以及分岔圖分析系統的動態特性，最後再藉由李雅普諾夫指數之運算對系統是否進入混沌運動作更進一步的佐證。
軸承中心與轉子中心在轉子質量偏心的不平衡力與非線性油膜力的作用下產生同步振動、分諧振、準週期振動與混沌振動等複雜性響應。經由不同轉速比下的數值模擬的結果我們也發現了在非線性因素作用下，軸承中心與軸頸中心的動態方程式是互相耦合，在大部分轉速比下，軸承中心與轉子中心運動軌跡呈現不規則混亂運動時。碰摩轉子系統之動態響應不論在長軸承或短軸承的假設下都具有相當豐富的非週期特性。系統運作初期出現低頻的現象，但是隨著碰摩的發展，會出現高頻分量的情形，顯示碰摩越來越嚴重，不論轉子中心或軸承中心的動態軌跡與頻譜圖都呈現相當紊亂與不規則的非週期振動情形。
在偶應力潤滑劑之軸承-轉子動態分析方面，結果顯示隨著 值越大，代表偶應力流體的效應越強，軸承與轉子中心也相對的較穩定而且由分岔圖可看出， 值越大，分岔圖中的週期運動區域越大。在微極流體潤滑劑之軸承-轉子動態分析方面，在不同 下軸承中心與轉子中心的分岔圖， 表示為牛頓流體；而 愈大表示微極流體的的效應愈強。結果顯示隨著 的值愈大，不管軸承或轉子中心的運動軌跡並不會較穩定而是愈紊亂，也印證了雖然預期 的值愈大，負載愈大；但是其摩擦力亦相對增加，導致系統的振動愈來愈不穩定。在紊流潤滑油軸承-轉子動態分析方面，在不同轉速比下，軸承中心或轉子中心顯示相當豐富的動態特性，包括：週期、2T週期、3T週期、準週期與混沌運動等等的振動。在多孔性擠壓油膜阻尼器支撐之油膜軸承-轉子動態分析方面，軸承中心與轉子中心在不同轉速比下顯示週期、2T週期與混沌運動等等的情形。根據分析結果亦得知， 與 值越大，軸承與轉子中心的動態軌跡愈穩定，亦即非線性振動的區域相對減少，故可知多孔性擠壓油膜阻尼器的確有助於改善系統整體的穩定性。

The dynamic analysis of the rotor-bearing system is studied under different cases of rub-impact rotor, couple stress fluid film bearing, micropolar fluid film bearing, turbulent lubrication flow and porous squeeze film damper with couple stress fluid in this paper under nonlinear suspension. The numerical analysis is carried out by using the Runge-Kutta method. Dynamic trajectories, power spectra, Poincaré Map, Bifurcation diagrams and Lyapunov exponent are applied to analyze the dynamic conditions.
An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed for more precise analysis of rotor- bearing systems. The periodic, quasi-periodic, sub-harmonic and chaotic motion are demonstrated in this study. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. According to the dynamic analysis of a rotor supported by two couple stress fluid film journal bearings with nonlinear suspension, it is found that periodic, quasi-periodic, sub-harmonic and chaotic motion are demonstrated in this study. The results also confirm that the stability of the system varies with the non-dimensional speed ratios, the non-dimensional unbalance parameters and the dimensionless parameter of . The result of the dynamic analysis of a rotor supported by two micropolar fluid film journal bearings with nonlinear suspension demonstrates that the stability of the system varies with the non-dimensional speed ratios, but doesn’t vary with the non-dimensional parameter N2. The dynamic analysis of a rotor supported by two turbulent model journal bearings with nonlinear suspension has found that the dynamic behaviors of the system include 3T-periodic, jump phenomena and chaotic motions. It is also found that more nonlinear dynamic behaviors occur under turbulent flow assumption than laminar flow model. A dynamic analysis of a flexible rotor supported by two porous squeeze couple stress fluid film journal bearings with nonlinear suspension has found that the stability of the system varies with the non-dimensional speed ratios, the non-dimensional parameter and the permeability .
The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems can be more precise.

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