轉子動平衡最佳化方法及精度影響因數探討

本文探討影響係數法之轉子動平衡，藉由不同的量測點/平衡面之數目及位置的選擇，所建構的影響係數矩陣，基於線性系統理論，探討條件數對於轉子動平衡校正質量計算的影響。運用的最佳化方法，包括遺傳演算法及禁忌搜尋法，以最小化影響係數矩陣之條件數為目標函數，預先在平衡程序前決定量測點/平衡面之位置或數目，可提高動平衡效率及精度，降低成本，避免因矩陣病態而導致平衡失敗，甚至造成機組損傷。對於病態嚴重的影響係數矩陣，其條件數過大，微小的量測擾動，將導致傳統的最小平方法所求得之校正量大幅偏離精確值，使得動平衡完全失敗，因此，本文運用求解反問題的Tikhonov正則法，並且使用L曲線準則決定正則參數，使得病態影響係數矩陣之動平衡方程式求解，得到校正質量的精度，可有效改善。並且考量量測誤差之影響，比較最小平方法及正則法之動平衡效果，分析其校正量、平衡精度、條件數以及量測誤差之關係，以提昇平衡精度及抗誤差能力。本文使用有限元素法建立轉子-軸承系統之數值模型，分析其穩態響應，以實驗及數值分析方法驗證轉子之動平衡，包括單轉速以及雙轉速多平衡面影響係數法之動平衡程序。

關鍵字

遺傳演算法；禁忌搜尋法；量測誤差；最佳化； L曲線準則；條件數； Tikhonov正則法；轉子動平衡；最小平方法；影響係數法

並列摘要

In this dissertation, the rotor balancing is investigated by using the influence coefficient method. An influence coefficient (IC) matrix is constructed by various selections of numbers and locations of measurement sensors and/or balancing planes. The influences of condition number on the unbalance determinations are studied based on the linear system theorem. The minimization of condition number of influence coefficient matrix is served as an objective function for the reduction of computation and measurement errors in balancing procedure by using genetic algorithms and tabu search. Thus, credible locations and numbers of measurement sensors and/or balancing planes can be determined in advance. The balancing efficiency and accuracy will be improved as fulfilling the optimization methods. Moreover, the failure of rotor balancing could be avoided due to the wellness of influence coefficient matrix. For the illness of influence coefficient matrix, its condition number is large and the correction mass determined by least squares algorithm (LSA) will be away from the true value due to slight measurement errors. For this reason, the Tikhonov regularization is utilized to solve influence coefficient equations for the unbalances determination. Additionally, the L-curve criterion is adopted to search appropriate value of regularization parameter. The balancing accuracy and robustness against disturbance can be improved by using Tikhonov regularization (TR). Furthermore, the influences of measurement errors on the unbalances determination are considered in this dissertation. The capability of against perturbation is required for determination of correction mass. The relationships among balancing accuracies, correction mass, condition number, and measurement error are analyzed by adopting both LSA and TR. Also, the balancing results using TR are compared with those using LSA. The rotor-bearing systems are modelled based on finite element method for the analysis of steady-state responses. The balancing procedures are simulated and experimented by using a rotor kit, which include rigid and flexible rotor balancing with multi-planes.

並列關鍵字

Influence coefficient method ； Least squares algorithm ； Measurement error ； Condition number ； L-curve criterion ； Rotor balancing ； Optimization ； Genetic algorithm ； Tikhonov regularization ； Tabu search

參考文獻

[2] Goodman, T. P., “A Least-Squares Method for Computing Balance Corrections,” ASME Journal of Engineering for Industry, Vol. 86, No. 3, pp. 273-279, 1964.

[4] Lee, C.-W. and Kim, Y.-D., “Modal Balancing of Flexible Rotors During Operation: Design and Manual Operation of Balancing Head,” IMechE Part C: Journal of Mechanical Engineering Science, Vol. 201, pp. 349-355, 1987.

[5] Lee, C.-W., Joh, Y.-D., and Kim, Y. D., “Automatic Modal Balancing of Flexible Rotors During Operation: Computer Control Balancing Head,” IMechE Part C: Journal of Mechanical Engineering Science, Vol. 204, pp. 19-28, 1990.

[6] Van de Vegte, J. and Lake, R. T., “Balancing of Rotating Systems Operation,” Journal of Sound and Vibration, Vol. 57, No. 2, pp. 225-235, 1978.

[7] Lund, J. W. and Tonnesen, J. “Analysis and Experiments on Multi-Plane Balancing of a Flexible Rotor,” ASME Journal for Industry, Vol. 94, No. 1, pp. 233-242, 1972.

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轉子動平衡最佳化方法及精度影響因數探討

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