臺灣博碩士論文加值系統

滾珠型自動平衡機構在適當的工作條件下，可因應不同的偏心量，自動調整滾珠的平衡位置而大幅降低偏心振動，因此廣泛的應用於轉子系統上。然而，當轉速高於系統自然頻率時，滾珠有時無法定位於完全平衡位置上，而是繞著碟片作週期性的旋轉或是來回振盪運動，此時系統伴隨有劇烈的振動量。由於旋轉週期解無法由現有的數值方法直接求得，本文使用新發展的Modified Incremental Harmonic Balance法探討各種形式的週期解，求取週期解在Ω-η平面上的存在區域及其穩定性，並分析各參數的影響，最後進行實驗驗證。

Under proper working conditions, a ball-type automatic balancer can adjust the positions of its balls according to the imbalance of the rotor and significantly reduces the rotational vibrations. As a consequence, ball-type automatic balancers are widely applied to rotor systems. However, when the rotational speed is above the natural frequency of the system, the balls may not settle to the perfect balancing positions but keep circulating or oscillating around the disk and result in large vibrations. Moreover the rotary periodic motions can’t be determined by the existing numerical methods used for the detection of periodic solutions. In this study, we employed the modified incremental harmonic balance method to analyze all kind of periodic motions, obtain the existence regions in the η-Ω plane and determine the corresponding stability. Then a comprehensive parametric study was performed and the results were verified experimentally.

口試委員審定書...............................................I
誌謝......................................................II
中文摘要..................................................III
英文摘要...................................................IV
目錄.......................................................V
圖目錄....................................................VII
表目錄.....................................................XI


第一章 緒論................................................1
1-1 研究動機...........................................1
1-2 文獻回顧...........................................2
第二章 研究方法.............................................5
2-1 理論模型及運動方程式.................................6
2-1-1 二維碟片理論模型...............................7
2-1-2 運動方程式....................................7
2-2 Modified Incremental Harmonic Balance method.....10
2-3 週期解穩定性分析....................................18
第三章 數值結果及參數分析.....................................20
3-1 單滾珠平衡系統......................................20
3-2 Modified Incremental Harmonic Balance method驗證..21
3-3 旋轉週期解.........................................33
3-3-1 制振比的影響..................................33
3-3-2 支承阻尼的影響.................................36
3-3-3 軌道阻尼的影響........................................39
3-4 其它形式週期解......................................42
第四章 實驗驗證.............................................45
4-1 實驗設備與機台設計...................................45
4-1-1 實驗設備......................................45
4-1-2 機台設計......................................48
4-2 實驗流程...........................................49
4-3 單滾珠平衡系統......................................52
4-4 雙滾珠平衡系統..........................................55
4-4-1 制振能力驗證...................................55
4-4-2 旋轉週期解之振形及頻率比較.......................56
4-4-3 制振比對旋轉週期解的影響.........................60
4-4-4 雙穩態現象分析.................................63
4-4-5 制振比對旋轉週期解的影響.........................66
4-4-6 支承阻尼對旋轉週期解的影響.......................67
4-4-7 其它形式週期解.................................71
第五章 結論................................................78
參考文獻...................................................79

[1]黃仕軒, 2005, “懸吊機構對滾珠自動平衡裝置之影響,” 台灣大學碩士論文
[2]洪嘉興, 2006, “多滾珠自動平衡系統之動態特性, ” 台灣大學碩士論文
[3]K.Green, A. R. Champneys, and N. J. Lieven, 2006, “Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors,” Journal of Sound and Vibration, Vol 291, pp.861-881.
[4]J. D. Alwxander, 1964, “An automatic dynamic balancer,” Proceedings for the Second Southeastern Conference, Vol. 2, pp. 415-426.
[5]J. W. Cade, 1965, “Self-compensating balancing in rotating mechanism,” Design News, pp. 234-239.
[6]T. Majewski, 1988, “Position errors occurrence in self balancers used on rigid rotors of rotating machinery,” Mechanism and Machine Theory, Vol. 23, pp. 71-77.
[7]J. Lee, 1995, “An analytical study of self-compensating dynamic balancer with damping fluid and ball,” Shock and Vibration, Vol. 2, pp. 59-67.
[8]J. Lee and W. K. Van Moorhen, 1996, “Analytical and experimental analysis of a self-compensating dynamic balancer in a rotating mechanism,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 118, pp. 468-475.
[9]C. Rajalingham and S. Rakheja, 1998, “Whirl suppression in hand-held power tool rotors using guided rolling balancers,” Journal of Sound and Vibration, Vol.217, pp. 453-466.
[10]R. Silin, V. Royzman, A. Malygin, I. Borko, and R. Tholovsky, 1999, “The research into automatic balancing processing of rotors with vertical axis of rotation,” Tenth World Congress on the Theory of Machine and Mechanisms, Oulu, Finland, June 20-24, pp. 1734-1739.
[11]J. Chung and D. S. Ro, 1999, “Dynamic analysis of an automatic dynamic balancer for rotating mechanisms,” Journal of Sound and Vibration, Vol. 228, pp. 1035-1056.
[12]C. Hwang and J. Chung, 1999, “Dynamic analysis of an automatic ball balancer with double races,” JSME International Journal, Vol. 42, No.2, pp. 265-272.
[13]J.-R. Kang, C.-P. Chao, C.-L. Huang, and C.-K. Sung, 2001, “The dynamics of a ball-type balancer system equipped with a pair of free-moving balancing masses,” ASME Journal of Vibration and Acoustics, Vol. 123, pp. 456-465.
[14]W.-Y. Huang, C.-P. Chao, J.-R. Kang, and C.-K. Sung, 2002, “The application of ball-type balancers for radial vibration reduction of high-speed optic disk drives,” Journal of Sound and Vibration, Vol. 250, pp. 415-430.
[15]C.-P. Chao, C.-K. Sung, and H.-C. Leu, 2005, ”Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives,”ASME Journal of Tribology, Vol. 127, pp. 845-856.
[16]C.-J. Lu, 2006, “Stability Analysis of a Single-Ball Automatic Balancer,” ASME Journal of Vibration and Acoustics, 128, No. 1, pp. 122-125. ( NSC -93- 2212-E-002-066)
[17]C.-J. Lu and C.H. Hung, 2008, “Stability Analysis of a Three-Ball Automatic Balancer,” ASME Journal of Vibration and Acoustics, 130, pp. 051008-1 - 051008-7 (NSC94-2212-E-002-033)
[18]W. Kim, D.-J. Lee, and J. Chung, 2005, ”Three-dimensional modeling and dynamic analysis of an automatic ball balancer in an optical disk drive,” Journal of Sound and Vibration, Vol. 285, pp. 547-569.
[19]C.-P. Chao, C.-K. Sung, and C.-C. Wang, 2005, “Dynamic Analysis of the Optical Disk Drives Equipped with an Automatic Ball Balancer with Consideration of Torsional Motions,” ASME Journal of Applied Mechanics, Vol.172, pp. 826-842.
[20]C.-J. Lu, M.-C. Wang, and S.-H. Huang, 2009, “Analytical Study of the Stability of a Two-Ball Automatic Balancer,” Mechanical System and Signal Processing, 23(3), pp. 884-896. (NSC96-2221-E-002-216)
[21]A. H. Nayfeh and B. Balachandran, 1995, Applied nonlinear dynamics： analytical, computational, and experimental methods, New York：Wiley- Interscience.
[22]C.-J. Lu and Y.-M. Lin, 2010, “A Modified Incremental Harmonic Balance Method for Rotary Periodic Motions,” Nonlinear Dynamics (in press).
[23]S. L. Lau, and S. W. Yuen, 1993, “Solution Diagram of Non-Linear Dynamic Systems by the IHB method,” Journal of Sound and Vibration, Vol. 167(2), pp. 303-316.
[24]Ogata, K., 1970, Modern Control Engineering, Prentice-Hall, Inc., New Jersey, U.S.A.