滾珠軸承剛度估測與驗證

Estimation and Verification of Stiffness Coefficients for Ball Bearings

黃志清(Chih-Ching Huang)

指導教授 ： 張永鵬 ； 康 淵

中原大學/工學院/機械工程研究所/博士(2006年)

https://doi.org/10.6840/cycu200600108

摘要

雖然設計者和工程人員廣泛使用Jones-Harris方法(JHM)，計算滾珠軸承靜剛度，然而，非線性的聯立方程組迭代求解過程，對設計者和工程人員而言，是困難且耗時的。
由於同一型式之滾珠軸承，在幾何、力學及結構上具有相同的特徵。本研究將剛度與軸承幾何、尺寸、操作狀態間的關係的複雜及高階偶合變數的函數關係，以少許滾珠軸承做為樣本，經由倒傳遞類神經網路(BPNN)學習後建立剛度估測器，對設計者而言，只需輸入軸承需要資料，就可準確且快速估算。
以JHM方法所計算之靜剛度，由於未考慮實際操作狀況，在使用於實際轉子軸承系統的動態行為之預測，會造成誤差。將系統輸入與輸出信號關係，以系統鑑別技術，鑑别未知的軸承動參數，較可符合實際狀況。所以，本研究亦提出一套撓性轉子系統之軸承動態參數鑑別方法。
為克服位移感測器安裝的限制及提昇估測精度，在鑑別過程中取鄰近待估測軸承處的兩節點量測之響應，基於機械阻抗技術，估算軸承位置處的響應，再者，以錘擊法獲得之系統頻率響應函數，與系統估測模型所預測之結果做比較，以驗證本估測方法是有效的，另外，以SKF6001深溝滾珠軸承為例，探討動態參數與頻率之相關性。

關鍵字

系統鑑别 ； 軸承剛度係數 ； 最小平方法 ； 倒傳遞類神經網路

並列摘要

The Jones-Harris methods (JHM) is widely and generally used by designers and engineers to determine stiffness coefficients for ball bearings. The JHM, however, involves the determination of coupled and non-linear, simultaneous equations with complex inputs and iterative calculations. This causes the method to be difficult and time-consuming for designers and engineers.
All ball bearings have the similar features in geometry, mechanism, and structure. The stiffness of this type of bearings can be related to geometry, dimension, and operating conditions by a very complex function. This study presents this stiffness function for all ball bearings by a back-propagation neural network method (BPNN), which is trained by using several (not all) samples. When this BPNN is utilized by a bearing designer, few input data are requested and a determination result can be accurately obtained with very short time.
The JHM didn’t consider the actual mounting and operating condition of bearings in rotor bearing systems. The dynamic analysis of system would lead to the discrepancy between measurements and predictions. The technique of parameter identification is used to estimate bearing dynamic coefficients from input-output measurements of the system. The estimated results would satisfy the actual condition for the analysis and design of rotor machinery. This study also presents that a simple identified algorithm of bearing dynamic coefficients is developed in flexible rotor systems.
In practical operation, the sensor of unbalance responses cannot be mounted at bearing position in systems. On basis of mechanical impedance technique, the measured unbalance responses on two nodes of shaft at adjacent bearing position are employed to determine the unbalance responses on the node of shaft at bearings position. It would overcome the limitation of sensors mounting and reduce the estimated error. Moreover, the experimental accuracy of bearing dynamic coefficients is also verified by the comparison between rotor kit and estimated system model of the frequency response functions. Additionally, the characteristic of dynamic parameters of ball bearing with frequency is also discussed by the case of SKF 6001 deep-groove ball bearing.

並列關鍵字

BPNN ； the least square method ； system identification ； bearing stiffness coefficients

參考文獻

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