Abstract:The rotor dynamic balancing implementation process usually to start and stop several times to add trial weights. The Dynamic-balancing-method Without Trial-weights (DWT) avoids the risk of adding trial weights and has high implementation efficiency. Therefore, DWT has become the focus of research at home and abroad in recent years. In this paper, the development and shortcomings of traditional dynamic balancing methods are introduced firstly. Based on this, the basic concept and advantages of the DWT are put forward, and then, according to the implementation principle, the DWT are classified from six aspects: based on dynamic model, based on influence coefficient method, based on intelligent algorithm, the combination of dynamic model and influence coefficient method, the combination of dynamic model and intelligent algorithm, and the combination of influence coefficient method and intelligent algorithm. Secondly, on the basis of the above classification, the specific ideas of each type of DWT are summarized according to different specific implementation methods, and the identification mechanism and implementation effect are introduced in detail. Finally, the development trend of DWT is prospected.
Key words: dynamic balancing; without trial weights; dynamic model; intelligent algorithm; influence coefficient method
章云1,王晓宇1,梅雪松2. 高速转子无试重动平衡方法研究现状分析[J]. 振动与冲击, 2022, 41(21): 216-227.
ZHANG Yun1, WANG Xiaoyu1, MEI Xuesong2. Studying status review for high-speed rotor dynamic balancing method without trial weights. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(21): 216-227.
[1] 梅雪松, 章云, 杜喆. 机床主轴高精度动平衡技术[M]. 北京:科学出版社, 2015.
[2] 章云, 梅雪松. 高速主轴动平衡及其在线控制技术研究[J]. 机械工程学报, 2014(11):79.
ZHANG Yun, MEI Xuesong. Research on dynamic balance of high-speed spindle and its online control technology[J], 2014(11):79.
[3] 章云, 梅雪松. 面向航空制造的数控加工机床主轴单元及其发展趋势[J]. 航空制造技术, 2010(05):26-29.
ZHANG Yun, MEI Xuesong. Spindle unit of NC machine tool in aviation manufacturing and its development trend[J]. Aeronautical Manufacturing Technology, 2010(05):26-29.
[4] 章云, 梅雪松. 高速主轴动平衡及其在线控制技术[J]. 中国工程科学, 2013, 15(1):89-94.
ZHANG Yun, MEI Xuesong. Study of online balancing control technique for high-speed spindles[J]. Strategic Study of CAE, 2013, 15(1):89-94.
[5] FOILES W C, ALLAIRE P E, GUNTER E J. Review of rotor balancing[J]. Shock and Vibration, 1998, 5(5-6): 325- 336.
[6] DARLOW M S. Balancing of high-speed machinery[M]. New York: Springer-Verlag, 1989.
[7] KELLENBERGER W. Should a Flexible Rotor Be Balanced in N or (N plus 2) Planes[J]. Transactions of the ASME: Journal of Engineering for Industry, 1972,94(2):558-560.
[8] XU B G, Qu L S. A new practical modal method for rotor balancing[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2001, 215(2):179-189.
[9] DARLOW M S, SMALLEY A J. Application of the principle of reciprocity to flexible rotor balancing[J]. Journal of Mechanical Design, 1982, 104(2):27-31.
[10] MOHAMAD W S W, MAT ISA A A, ISMAIL M A. Analytical and Experimental Study on Balancing Using Influence Coefficient Method[J]. Applied Mechanics and Materials, 2013, 393:694-702.
[11] GNIELKA P. Modal balancing of flexible rotors without test runs: An experimental investigation[J]. Journal of Sound and Vibration, 1983, 90(2):157-172.
[12] Delgado E P, Bannister R H. Balancing of an experimental rotor without trial runs[J]. International Journal of Rotating Machinery, 2002, 2(8):99-108.
[13] 汪海良, 刘思汉. 柔性转子无试重动平衡法的实验研究[J]. 振动与冲击, 1992(03):57-65.
WANG Hailiang, LIU Sihan. Experimental study on dynamic balance method of flexible rotor without test weight[J]. Journal of Vibration and Shock, 1992(03):57-65.
[14] 李晓丰, 郑龙席, 刘振侠. 柔性转子无试重模态动平衡方法与试验[J]. 振动、测试与诊断, 2013, 33(04):565-570.
LI Xiaofeng, ZHENG Longxi, LIU Zhengxia. Theoretical and experimental research on balancing of flexible rotors without trial weights[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(04):565-570.
[15] 刘钢旗, 郑龙席, 梅庆, 等. 一种跨二阶柔性转子无试重模态平衡方法[J]. 航空学报, 2014, 35(04):1019-1025.
LIU Gangqi, ZHENG Longxi, MEI Qing, et al. Balancing method of flexible rotor across second order without trial weights[J]. Journal of Aeronautics, 2014, 35(04):1019-1025.
[16] 贾胜锡, 郑龙席, 邓旺群, 等. 柔性转子无试重模态动平衡测试系统[J]. 振动、测试与诊断, 2018, 38(06):1108-1113.
JIA Shengxi, ZHENG Longxi, DENG Wangqun, et al. Development of modal balancing system without trail weights for high speed flexible rotors[J]. Journal of Vibration, Measurement & Diagnosis, 2018, 38(06):1108-1113.
[17] 傅超, 任兴民, 杨永锋, 等. 基于加速不平衡响应的柔性转子无试重动平衡[J]. 西北工业大学学报, 2017, 35(05):898-904.
FU Chao, REN Xingmin, YANG Yongfeng, et al. Balancing of flexible rotors based on accelerating unbalance response without trial weights[J]. Journal of Northwestern Polytechnical University, 2017, 35(05):898-904.
[18] ZHAO S B, REN X M, DENG W Q, et al. A transient characteristic-based balancing method of rotor system without trail weights[J]. Mechanical Systems and Signal Processing, 2021, 148:107117.
[19] DENG W Q, TONG M Y, ZHENG Q Y, et al. Investigation on transient dynamic balancing of the power turbine rotor and its application[J]. Advances in Mechanical Engineering, 2021, 13(4):1-12.
[20] KHULIEF Y A, MOHIUDDIN M A, EL-GEBEILY M. A new method for field-balancing of high-speed flexible rotors without trial weights[J]. International Journal of Rotating Machinery, 2014, 2014:1-11.
[21] 蒋瑞祥, 廖与禾, 李帅,等. 结合阶次跟踪与动刚度分析的无试重全息动平衡方法[J]. 中国科技论文, 2016, 11(16):1797-1801.
JIANG Ruixiang, LIAO Yuhe, LI Shuai, et al. Order-tracking technique and dynamic stiffness analysis intergrated non-trial holobalancing method[J]. China Sciencepaper, 2016, 11(16):1797-1801.
[22] 章云, 梅雪松, 邹冬林, 等. 应用模态分析及傅里叶变换的柔性转子无试重动平衡方法[J]. 振动与冲击, 2012, 31(11):7-10.
ZHANG Yun, MEI Xuesong, ZOU Donglin, et al. A field balancing method of a flexible rotors based on modal analysis and fourier transformation[J]. Journal of Vibration and Shock, 2012, 31(11):7-10.
[23] ZHANG Y, LI M, YAO H Z, et al. A modal-based balancing method for a high-speed rotor without trial weights[J]. Mechanical Sciences, 2021, 12(1):85-96.
[24] 章云, 梅雪松, 邹冬林, 等. 应用动力学模型的高速主轴无试重动平衡方法[J]. 西安交通大学学报, 2011, 45(7):39-42.
ZHANG Yun, MEI Xuesong, ZOU Donglin, et al. Model-based balancing method for high-speed machine tool spindle without trial weights[J]. Journal of Xi’an Jiaotong University, 2011, 45(7):39-42.
[25] 章云, 梅雪松. 机床柔性主轴转子低速无试重动平衡方法研究[J]. 西安交通大学学报, 2016, 50(04):89-93.
ZHANG Yun, MEI Xuesong. A low-speed balancing method for the flexible rotor of machine tool spindles without trial weights[J]. Journal of Xi’an Jiaotong University, 2016, 50(04):89-93.
[26] 温广瑞, 刘石, 张西宁, 等. 基于多传感信息的转子无试重现场动平衡方法研究[C]// 2011年全国机械动力学学术大会暨中国振动工程学会机械动力学学会成立30周年庆祝会议. 中国浙江杭州, 2011.
[27] 屈梁生, 邱海, 徐光华. 全息动平衡技术:原理与实践[J]. 中国机械工程, 1998, 9(1):60-63.
QU Liangsheng, QIU Hai, XU Guanghua. Rotor balancing based on holospectrum analysis: principle and practice[J]. China Mechanical Engineering, 1998, 9(1):60-63.
[28] 胡谢努. 旋转机械不平衡校正:影响系数法与全息平衡法[D]. 武汉: 华中科技大学, 2009.
[29] LIAO Y H, LANG G F, WU F J, et al. An improvement to holospectrum based field balancing method by reselection of balancing object[J]. Journal of Vibration and Acoustics, Transactions of the ASME, 2009: 131(3).
[30] ZHANG Y, MEI X S, SHAO M P, et al. An improved holospectrum-based balancing method for rotor systems with anisotropic stiffness[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012, 227(2):246-260.
[31] XIE D M, YANG Y, LIU Z H, et al. A balance method without trial mass based on lag phase[C]// ASME International Mechanical Engineering Congress & Exposition. San Diego, California, United states, 2013.
[32] 邱海, 屈梁生, 张海军, 等. 神经网络在转子动平衡中应用的几个关键问题[J]. 机械工程学报, 2001, 37(01):88-91.
QIU Hai, QU Liangsheng, ZHANG Haijun, et al. Some key problems of the neural network applied in rotor balancing[J]. Chinese Journal of Mechanical Engineering, 2001, 37(01):88-91.
[33] WALKER R B, VAYANAT R, PERINPANAYAGAM S, et al. Unbalance localization through machine nonlinearities using an artificial neural network approach[J]. Mechanism and Machine Theory, 2014, 75:54-66.
[34] LIU S, A new balancing method for flexible rotors based on neuro-fuzzy system and information fusion[J]. International Conference on Fuzzy Systems and Knowledge Discovery, 2005, 34(5):507-511.
[35] MORTON P G. Modal balancing of flexible shafts without trial weights[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1985, 199(1):71-77.
[36] EDWARDS S, LEES A W, FRISWELL M I. Experimental identification of excitation and support parameters of a flexible rotor-bearings-foundation system from a single run-down[J]. Journal of Sound and Vibration, 2000, 232(5):963-992.
[37] SINHA J K, FRISWELL M I, LEES A W. The identification of the unbalance and the foundation model of a flexible rotat form a single run-down[J]. Mechanical Systems and Signal Processing, 2002, 16(2-3):255-271.
[38] SINHA J K, LEES A W, FRISWELL M I. Estimating unbalance and misalignment of a flexible rotating machine from a single run-down[J]. Journal of Sound and Vibration, 2004, 272(3-5):967-989.
[39] RAMLAU R, NIEBSCH J. Imbalance estimation without test masses for wind turbines[J]. Journal of Solar Energy Engineering, 2009, 131(1):110101-110107.
[40] YUN X L , MEI X S , JIANG G D , et al. Investigation on a no trial weight spray online dynamic balancer[J]. Shock and Vibration, 2018, 7021215:1-15.
[41] 运侠伦, 梅雪松, 姜歌东, 等. 辨识主轴转子系统能量传递特性的矢量匹配平衡方法研究[J]. 振动与冲击, 2019, 38(10):143-147+173.
YUN Xialun, MEI Xuesong, JIANG Gedong, et al. Vector matching balance method for identifying the energy transfer characteristics of a spindle rotors system[J]. Journal of Vibration and Shock, 2019, 38(10):143-147+173.
[42] DEEPTHIKUMAR M B, SEKHAR A S, SRIKANTHAN M R. Balancing of flexible rotor with bow using transfer matrix method[J]. Journal of Vibration and Control, 2012, 20(2):225-240.
[43] ZHANG Y , MEI X S , ZOU D L , et al. A new field unbalance estimation method for flexible rotors[C]// Asme International Mechanical Engineering Congress & Exposition. Denver, Colorado, United states, 2012.
[44] ZHANG Y, WEI Q, ZOU D L, et al. Study on the relationship between the imbalance status and its vibration response in balancing method of rotors[C]// International Institute of Acoustics and Vibrations, Athens, Greece, 2016.
[45] 章云, 胡振邦, 梅雪松. 高速转子分布式不平衡量无试重识别方法[J]. 振动与冲击, 2017, 36(04):28-31.
ZHANG Yun, HU Zhenbang, MEI Xuesong. An identification method of distributed imbalance without trial weights for high speed rotors[J] Journal of Vibration and Shock, 2017, 36(04):28-31.
[46] 章云, 孙虎, 胡振邦, 等. 高速主轴不平衡振动行为分析与抑制策略[J]. 西安交通大学学报, 2019, 53(05):24-29.
ZHANG Yun, SUN Hun, HU Zhenbang, et al. Behavior analysis and suppression strategy for unbalabnced vibration in high-speed spindle system[J] Journal of Xi’an Jiaotong University, 2019, 53(05):24-29.
[47] 王维民, 高金吉, 江志农, 等. 旋转机械无试重现场动平衡原理与应用[J]. 振动与冲击, 2010, 29(02):221-224.
WANG Weiming, GAO Jinji, JIANG Zhinong, et al. Principle and application of no trial weight field balancing for a rotating machinert[J]. Journal of Vibration and Shock, 2010, 29(02):221-224.
[48] WANG Y G, FANG J C, ZHENG S Q. A field balancing technique based on virtual trial-weights method for a magnetically levitated flexible rotor[J]. Journal of Engineering for Gas Turbines and Power, 2014, 136(9). 92501-92502.
[49] 周瑾, 王玉龙, 郭勤涛. 基于动平衡机有限元模型的无试重动平衡方法[J]. 江苏大学学报(自然科学版), 2013, 34(01):72-75.
ZHOU Jin, WANG Yulong, GUO Qintao. Dynamic balance method without trial weight based on finite element model of dynamic balancer[J], Journal of Jiangsu University (Natural Science Edition), 2013, 34(01):72_75.
[50] 宾光富, 姚剑飞, 江志农, 等. 基于有限元模型的转子动平衡影响系数求解法[J]. 振动、测试与诊断, 2013, 33(06):998-1002.
BIN Guangfu, YAO Jianfei, JIANG Zhinong, et al. Solving method of influence coefficient for rotor dynamic balancing based on finite elemeng model[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(06):998-1002.
[51] BIN G F, LI X J, WU J G, et al. Virtual dynamic balancing method without trial weights for multi-rotor series shafting based on finite element model analysis[J]. Journal of Renewable and Sustainable Energy, 2014, 6(4):130-136.
[52] 宾光富, 李学军, 沈意平, 等. 基于动力学有限元模型的多跨转子轴系无试重整机动平衡研究[J]. 机械工程学报, 2016, 52(21):78-86.
BIN Guangfu, LI Xuejun, SHEN Yiping, et al. Whole-machine dynamic balancing method without trial weights for multi-span rotor shafting based on dynamic finite element model[J]. Journal of Mechanical Engineering, 2016, 52(21):78-86.
[53] 李志炜, 何立东, 张俎琛, 等. 虑及双转速双平面无试重虚拟动平衡研究[J]. 机电工程, 2019, 36(9):969-974.
LI Zhiwei, HE Dongli, ZHANG Zuchen, et al. Test-free virtual dynamic balance in consideration of double-rotation double-plane[J]. Journal of Mechanical & Electrical Engineering, 2019, 36(9):969-974.
[54] DE CASTRO H F, CAVALCA K L, DE CAMARGO L W F, et al. Identification of unbalance forces by metaheuristic search algorithms[J]. Mechanical Systems and Signal Processing, 2010(6):1785-1798.
[55] SALDARRIAGA M V, STEFFEN V, HAGOPIAN J D, et al. On the balancing of flexible rotating machines by using an inverse problem approach[J]. Journal of Vibration and Control, 2010, 17(7):1021-1033.
[56] FANG J C, WANG Y G, HAN B C, et al. Field balancing of magnetically levitated rotors without trial weights[J]. Sensors, 2013, 13(12):16000-16022.
[57] LIU C, LIU G. Field dynamic balancing for rigid rotor-AMB system in a magnetically suspended flywheel[J]. IEEE/ASME Transactions on Mechatronics, 2016, 21(2):1140-1150.
[58] 刘淑莲, 郑水英. 应用遗传算法的非线性转子-轴承系统参数辨识[J]. 动力工程, 2006, 26(04):479-482.
LIU Shulian, ZHENG Shuiying. Parameter identification of rotor-bearing systems with non-linear behavior by using gengtic algorithm[J], Journal of Power Engineering, 2006, 26(04):479-482.
[59] 邱海, 张海军, 屈梁生, 等. 遗传算法在柔性转子动平衡中的应用[J]. 中国机械工程, 2002, 13(05):60-63.
QIU Hai, ZHANG Haijun, QU Liangsheng, et al. The application of genetic algorithm in flexible rotor dynamic balancing[J]. China Mechanical Engineering, 2002, 13(05):60-63.
[60] CHATZISAVVAS I, DOHNAL F. Unbalance identification using the least angle regression technique[J]. Mechanical Systems and Signal Processing, 2015, 50-51:706-717.
[61] OKE W A, ABIDO M A, ASAFA T B. Balancing of flexible rotors based on evolutionary algorithms[J]. Mechanics & Industry, 2015, 16(4):406
[62] ZHANG Y, LI M, HU Y. Model-based balancing method of rotors using differential evolution algorithm[J]. IOP conference series. Materials Science and Engineering, 2020, 751(1):12046.
[63] TAPLAK H, ERKAYA S, UZMAY İ. Passive balancing of a rotating mechanical system using genetic algorithm[J]. Scientia Iranica, 2012, 19(6):1502-1510.
[64] 徐宾刚, 屈梁生, 孙瑞祥. 基于影响系数法的柔性转子无试重平衡法研究[J], 西安交通大学学报, 2000, 35(07):63-67.
XU Binggang, QU Liangsheng, SUN Ruixiang. Balancing of flexible rotors without test weights[J]. Journal of Xi’an Jiaotong University, 2000, 35(07):63-67.
[65] 瞿红春, 崔秀峰. 基于遗传算法的动平衡优化方法研究[J]. 中国民航大学学报, 2013, 31(05):24-26.
QU Hongchun, CUI Xiufeng. Optimizing dynamic balancing of aeroengine based on genetic algorithm[J]. Journal of Civil Aviation University of China, 2013, 31(05):24-26.