摘要
旋转机械是机械系统的重要组成部分,在国防和国民经济众多领域中发挥着巨大作用。转子不平衡是旋转机械中的常见问题,也是诱发转子系统故障的主要原因之一。因此,开展动平衡技术研究具有重要的学术和工程应用价值。近年来,随着电子、计算机和测试等技术的迅猛发展,动平衡技术也得到了很大发展,其研究成果对推动旋转机械向高速、高效、高可靠方向发展起到了重要作用。目前,有关转子动平衡技术的研究主要集中在动平衡测试、非对称/非平面模态转子平衡、无试重平衡、自动平衡等技术领域。为了提高转子平衡精度与效率,论文从不平衡动态响应分析出发,围绕动平衡测试与自动平衡中的窄带跟踪滤波、自动平衡策略等关键技术问题展开深入研究。论文主要研究工作包括:
1、为了掌握转子系统振动响应与不平衡量及转子系统参数的关系,针对平面转子、刚性转子、挠性转子等典型转子系统,在总结、归纳已有研究成果的基础上,采用理论分析与数值仿真相结合的方法,深入研究了在恒加速条件下转子系统参数对转子瞬态不平衡响应的主要影响规律。研究结果表明:在恒加速条件下,转子同频振动分量与转子的转速、支承阻尼等因素密切相关,当角加速度较小且阻尼较大时,其瞬态响应对转速的波动不敏感;而当角加速度较大或阻尼较小时,恒加速过程不平衡响应与稳态响应在临界转速附近将产生明显的差异。
2、为了适应转速波动时高精度动平衡测试的需求,精确、快速地分离出不平衡响应中的同频振动分量,深入研究了两种新型模拟窄带跟踪滤波技术:(1)利用开关和电容可等效电阻的原理,导出了开关电容跟踪滤波方法,设计研制了一种新的开关电容模拟窄带跟踪滤波器;(2)利用互相关原理,导出了相关跟踪滤波方法,并采用乘法数模转换器(MDAC),设计研制了MDAC模拟窄带跟踪滤波器。
3、为了实现平衡头的快速、精确控制,针对初始状态未知的极坐标型平衡头,提出了两种各具特点的自动平衡策略和算法:(1)对单面坐标轮换寻优法进行了改进,提出了多轮坐标轮换寻优法,并将单面坐标轮换寻优法推广应用到双面转子的自动平衡,证明了该方法能得到全局最优解;(2)提出了基于影响系数法的快速自动平衡策略及其递推算法,快捷、有效地抑制了振动噪声、测量误差、控制误差等对平衡精度的影响。
4、为了快速、准确地掌握不平衡量在转子上的分布情况,针对信噪比低、工作转速范围宽、转速波动时的振动信号特点,深入研究了程控放大、程控积分、外触发等角度采样、不平衡量快速精确解算等信号处理技术;通过技术集成,研制了便携式高精度动平衡测试系统。为了避免转子系统离线平衡时的反复起、停车过程,及时补偿工作过程中出现的随机不平衡,提出了两种新型平衡头结构,其中,基于感应子式永磁步进电机原理的平衡头结构紧凑、精度高,而基于永磁式步进电机驱动的平衡头更容易实现;以此为基础,设计研制了基于红外控制信号传输的新型转子自动平衡系统。
5、对研制的动平衡测试系统进行了整机性能测试,并分别应用于低速鼓风机转子、高速陀螺转子以及特殊支承的磁悬浮转子的动平衡,均达到了较好的平衡效果,表明该测试系统在硬支承、软支承动平衡机以及现场动平衡测试时均能达到较高的平衡精度。应用坐标轮换寻优自动平衡策略和基于影响系数法的快速自动平衡策略对单面转子进行了自动平衡实验,结果表明,坐标轮换寻优法简单实用、操作安全,而基于影响系数法的快速自动平衡策略有较高的平衡精度和平衡效率。
综上,论文在深入分析典型转子系统不平衡动态响应特性的基础上,提出了两种模拟窄带跟踪滤波方法、两种各具特点的自动平衡控制策略和算法以及不平衡量的快速、精确解算方法,设计研制了便携式高精度动平衡测试系统,提出了两种新型平衡头结构,设计研制了基于红外控制信号传输的自动平衡系统,同时给出了进一步研究工作设想。
Rotating machine is an important part in mechanical system, which has a great significance in defensive and civil domain. Imbalance is a common problem for rotors, and also the principal reason of faults in rotor systems. The research of dynamic balancing technology has important scientific and engineering significance. With the rapid evolvement of electronics, computer, and measurement, dynamic balancing technology has been developed greatly in recent years, which helps to build up a trend of high-speed, high-efficiency, and high-reliability for rotor systems. At present, related researches are centering on dynamic balancing measurement, non-symmetrical/non-planar modal rotor balancing, balancing without trial weights, automatic balancing, and so on. Aimed to increase balancing precision and efficiency for rotors, this dissertation analyzes dynamic response of imbalance at first, discusses the related key technologies further in dynamic balancing measurement and automatic balancing such as narrowband tracking filtering, automatic balancing strategy, and so on. The main contents are as follows:
1. In order to interpret the relationship between vibration response and variables of imbalance together with parameters of system in typical rotor under constant acceleration, such as planar rotor, rigid rotor, and flexible rotor, the main influencing rules of system parameters on the transient imbalance response are studied deeply by theoretic analysis and numerical simulation on foundation of the existing research results summarized and concluded. The analysis results indicate that the vibration fractional factor with rotating frequency has a close relationship with both rotating speed of rotor and damping of bearing under constant acceleration. When rotating acceleration is small and damping is large, the transient response is not sensitive to the variation of rotating speed; otherwise the imbalance response with constant acceleration and the response in stable state will build up obvious differences near critical rotating speed.
2. In order to adapt to the requirements of high-precision dynamic balancing measurement with rotating speed variation and to isolate the vibration fractional factor with rotating frequency from imbalance response precisely and quickly, two new types of analog tracking filtering technologies are deeply studied: (1) the tracking filtering method using switched-capacitor is deduced from the equivalent principle between switch & capacitor and resistance, and a new narrow-brand tracking filter using switched-capacitor is designed accordingly; (2) the correlative tracking filtering method is deduced from the correlation principle, and an analog narrow-brand tracking filter using Multiplying Digital-to-Analog Converter (MDAC) is designed accordingly.
3. In order to realize fast and precise control of balancing head, two special types of automatic balancing strategies with the corresponding algorithms are brought forward for balancing head in polar coordinates: (1) an alternate-coordinate optimization method with multiple circulations is built up to improve alternate-coordinate optimization method for single plane in existence, and widens its application to automatic balancing for double planes which proves to be able to gain global optimal solution;(2) a fast automatic balancing strategy and its recursive algorithm are presented based on the influence coefficient method, which restrains the influences on balancing precision from vibration noises, measurement errors, and control errors rapidly and effectively.
4. In order to gain the distributing condition of imbalance on rotor quickly and precisely, the signal processing technologies such as programmed amplifying, programmed integrating, equal -angle sampling with outer triggering, and precise imbalance solving are studied deeply, and a portable high-precision dynamic balancing measurement system is developed. To avoid multiple on/off process when balancing off-line and to compensate the random imbalance in running timely, two new types of balancing head structures are advanced, of which the balancing head based on the principle of permanent-magnetic-induction stepping motor has a compact structure and a high precision and the balancing head driven by permanent-magnetic stepping motor is easier to realize; and an automatic balancing system based on infrared control signal transmission is designed and developed accordingly.
5. The performances of the developed dynamic balancing measurement system are tested, and then the system is applied to dynamic balancing of low-speed fan rotor, high-speed gyro rotor, and magnetic-suspended rotor respectively. The balancing effects are satisfactory, which indicate that the system has high measurement precision when applied to both dynamic balancer with hard/soft bearing and field dynamic balancing. The automatic balancing strategy based on alternate-coordinate optimization method and the rapid automatic balancing strategy based on the influence coefficient method are applied to the automatic balancing experiment of rotor with single plane, which reveals that alternate-coordinate optimization method is easy to use and safe to operate, and that the rapid automatic balancing strategy based on the influence coefficient method has high balancing precision and balancing efficiency.
In sum, this dissertation analyzes the characteristics of imbalance response in typical rotors deeply at first, and brings forward two types of analog narrow-band tracking filtering methods and two special types of automatic balancing control strategies with the corresponding algorithms, then develops a portable high-precision dynamic balancing measurement system, and then presents two new types of balancing head structures, and develops an automatic balancing system based on infrared control signal transmission afterwards, and gives out further imagination for future research in the end.
引文
[1] Parkinson A G.Balancing of Rotating Machinery.Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science,1991,205(1):53-66
[2] Zhou S,Shi J.Active Balancing and Vibration Control of Rotating Machinery: A Survey.Shock and Vibration Digest,2001,33(5):361-371
[3] 徐宾刚.转子平衡的信息原理与实践:[博士学位论文].西安:西安交通大学,2000
[4] 三轮修三,下村玄.旋转机械的平衡.北京:机械工业出版社,1992
[5] Bishop R E D,Gladwell G M L.The Vibration and Balancing of an Unbalanced Flexible Rotor.Journal of Mechanical Engineering Science,1959,1(1): 66-77
[6] Bishop R E D,Parkinson A G.On the Use of Balancing Machines for Flexible Rotors.ASME Transactions, Journal of Engineering for Industry,1972,94:561-576
[7] Parkinson A G,Darlow M S,Smalley A J.An Introduction to a Unified Approach to Flexible Rotor Balancing.The Gas Turbine Conference and Exhibit and Solar Energy Conference,1979:1-14
[8] Parkinson A G,Darlow M S,Smalley A J.A Theoretical Introduction to the Development of a Unified Approach to Flexible Rotor Balancing.Jounal of Sound and Vibration,1980,68:489-506
[9] Van de Vegte J.Continuous Automatic Balancing of Rotating Systems.Journal of Mechanical Engineering Science,1964,6(3):264-269
[10] Van de Vegte J,Lake R T.Balancing of Rotating Systems During Operation.Journal of Sound and Vibration,1978,57(2):225-235
[11] Van de Vegte J.Balancing of Flexible Rotors During Operation.Journal of Mechanical Engineering Science,1981,23(5):257-261
[12] Gnielka P.Modal Balancing of Flexible Rotors without Test Runs: An Experimental Investigation.Journal of Sound and Vibration,1983,90(2):157-172
[13] Morton P G.Modal Balancing of Flexible Shafts without Trial Weights.Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science,1985,199(1):157-172
[14] Gosiewski Z . Automatic Balancing of Flexible Rotors, Part I: Theoretical Background.Journal of Sound and Vibration,1985,100(4):551-567
[15] Beale S,Shafai B,LaRocca P.Adaptive Forced Balancing for Magnetic Bearing Control Systems.Proceedings of the 31st Conference on Decision & Control,1992:3535-3539
[16] Zeng S,Wang X X.The Electromagnetic Balancing Regulator and the Automatic Balancing System.Journal of Sound and Vibration,1998,209(1):5-13
[17] Dyer S W,Ni J.Adaptive Influence Coefficient Control of Single-Plane Active Balancing Systems for Rotating Machinery . American Society of Mechanical Engineers, Manufacturing Engineering Division,1999,10:747-775
[18] Dyer S W,Ni J,Zhuang Z.Auto-Tuning Adaptive Supervisory Control of Single-Plane Active Balancing Systems.Society of Manufacturing Engineers,2000(5):1-6
[19] Dyer S W,Ni J,Shi J.Robust Optimal Influence-Coefficient Control of Multiple-Plane Active Rotor Balancing Systems.Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME,2002,124(1):41-46
[20] Foiles W C,Allaire P E,Gunter E J.Min-Max Optimum Flexible Rotor Balancing Compared to Weighted Least Squares. The 7th International Conference on Vibrations in Rotating Machinery,2000:141-148
[21] Kang Y,Liu C P,Sheen G J.A Modified Influence Coefficient Method for Balancing Unsymmetrical Rotor-Bearing Systems.Jounal of Sound and Vibration,1996,194:199-218
[22] Kang Y,Chang Y P,Tseng M H.Modified Approach Based on Influence Coefficient Method for Balancing Crank-Shafts.Journal of Sound and Vibration,2000,234(2):277-296
[23] Xu B,Qu L.A New Practical Modal Method for Rotor Balancing.Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,2001,215(2):179-190
[24] Foiles W C,Allaire P E,Gunter E J.Review: Rotor balancing.Shock and Vibration,1998,5(5-6):323-336
[25] Gutierrez-Wing E S,Aguirre-Romano J E.Rotor Balancing Using Vibration Data from Fast Run-Ups and Coast-Downs.Proceedings of the International Modal AnalysisConference - IMAC,1999,2:1669-1673
[26] Preciado E,Bannister R H.On the Balancing of Flexible Rotors without Trial Runs.7th International Conference on Vibration in Rotating Machinery,2000:121-130
[27] Zhou S , Shi J . Supervisory Adaptive Balancing of Rigid Rotors During Acceleration. Transactions of the North American Manufacturing Research Institution of SME,2000,28:425-430.
[28] Zhou S,Dyer S W,Shin K-K.Extended Influence Coefficient Method for Rotor Active Balancing During Acceleration.Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME,2004,126(1):219-223
[29] El-Shafei A,El-Kabbany A S,Younan A A.Rotor Balancing without Trial Weights.Jounal of Engineering for Gas Turbines and Power,2004,126(3):604-609
[30] 汪希萱,曾胜.电磁式在线自动平衡系统及其动平衡方法研究.热能动力工程,2003,18(1):53-57
[31] 张志新,金志江,贺世正.同轴式微速差双转子系统整机动平衡方法研究.机械工程学报,2004,40(8):40-44
[32] 王晓升,姜建东.应用载荷识别技术的一种转子动平衡方法.振动工程学报,1997,10(2):198-202
[33] 朱晓东.新型动平衡方法研究:[博士学位论文].杭州:浙江大学,1996
[34] 顾晃,杨建明,任浩仁.减少转子动平衡启动次数的优化方法.电力技术,1985(4):38-47
[35] 曾胜,汪希萱.电磁式在线自动平衡调节器的原理及其实验.流体工程,1997,25(5):11-14
[36] 屈梁生,邱海.全息动平衡技术:原理与实践.中国机械工程,1998,9(1):60-63
[37] 叶能安,余汝生.动平衡原理与动平衡机.武汉:华中工学院出版社,1985
[38] 邱海.动平衡中的信息原理:[博士学位论文].西安:西安交通大学,1999
[39] 胡正荣.平衡机的设计与应用.北京:国防工业出版社,1988
[40] 谭青,唐任仲.风机自动平衡应用技术研究.浙江大学学报:自然科学版,1998,32(4):473-479
[41] 陶利民.转轴系统自动平衡研究:[硕士学位论文].长沙:国防科学技术大学,1987
[42] 佟德纯,黄文振.转子动平衡技术(上).机电一体化,2002,8(2):63-66
[43] 佟德纯,黄文振.转子动平衡技术(下).机电一体化,2002,8(3):77-80
[44] 王晓升.考虑平衡质量受限时最小二乘影响系数法的改进.西安交通大学学报,1998,32(11):76-80
[45] 夏松波,刘永光.旋转机械自动平衡综述.中国机械工程,1999,10(4):458-461
[46] 钟一谔,何衍宗,王正.转子动力学.北京:清华大学出版社,1987
[47] 王忠谦,王梅英.300,600MW 高中压转子室温动平衡和超速试验的研究.汽轮机技术,1996,38(3):175-180
[48] 张柏林.125MW 机组轴系现场动平衡.湖南电力,1999,19(3):26-28
[49] 陈岩,高运达.200MW 汽轮发电机组转子高速动平衡.邵阳学院学报:自然科学版,2004,1(1):56-58
[50] 赵彤军,黄懋丁.600MW 汽轮发电机组的振动特性和现场平衡.汽轮机技术,1997,39(1):47-52
[51] 黄迪南,黄雅罗.300MW 汽轮机高中压转子中间平面加重现场动平衡技术.上海汽轮机,1996(2):9-13
[52] 李生泉,史庆宗,索继红.200MW 汽轮机转子快速动平衡——谐分量—影响系数法的应用.黑龙江电力,2003,25(3):214-216
[53] 金文鹏,丛培田.IMB—Ⅱ智能化多功能动平衡测试仪的设计与研制.沈阳工业学院学报,1998,17(2):101-105
[54] 郑建彬,黎明发,等.超微型转子动平衡测试机不平衡量提取.中国机械工程,2003,14(6):464-466,540
[55] 王杰,范剑波.车轮动平衡机的原理与应用.信息技术(哈尔滨),2002(6):49-49
[56] 鲁统利,刘贵森.大型回转件动平衡测试系统研究.汽车工艺与材料,2000(7):25-28
[57] 顾乾坤.电机转子动平衡测试系统.微电机,1996,29(1):35-37
[58] 崔亚辉.动平衡 APPLE—Ⅱ微机测试系统的研制.机械与电子,1994(1):9-10
[59] 朱志刚,李铁在,天玲.计算机辅助平衡测试系统.机械工程师,1996(3):44
[60] 李顺利,房振勇.精密离心机动平衡测试信号的研究.机械研究与应用,2000,13(1):6-8,11
[61] 郭新华,杨书华.汽车发电机转子动平衡测试仪.汽车技术,1999(7):20-21
[62] 刘振国,杨晓荣.汽轮机转子低速动平衡测试仪的设计与研制.山西电力技术,1994,14(4):6-8
[63] 唐一科,林可,等.嵌入式智能动平衡测试系统及其滤波器设计.重庆大学学报:自然科学版,2003,26(3):5-7
[64] 唐一科,顾乾坤.软支承动平衡机的 CAB 技术研究.中国机械工程,1994,5(6):63-64
[65] 邱宁,孙大川.瞬态动平衡仪.四川电力技术,1997,20(5):37-39
[66] 薛剑平,崔海鳌.我国试验通信卫星的静、动平衡测试..航空工艺技术,1993(6):1-5
[67] 高兴海,刘训涛.现场转子动平衡测试方法.黑龙江科技学院学报,2002,12(4):13-15
[68] 陈文勇,王秋晓,王世耕.一种动平衡测试系统测试方法的研究.机械研究与应用,2003,16(2):36-38
[69] 刘亚彬,王秋晓,王世耕.智能动平衡机电测系统研究.四川大学学报:工程科学版,2003,35(2):100-103
[70] 赖世有.智能化动平衡机测试系统.风机技术,2001(1):28-30
[71] 杨健,贺世正.自主式虚拟现场整机动平衡仪研究.仪器仪表学报,2002,23(3):236-240
[72] 张志新.微速差双转子系统智能化整机动平衡仪的开发与研究:[博士学位论文].杭州:浙江大学,2001
[73] Xu B,Qu L,Sun R.Optimization Technique-Based Balancing of Flexible Rotors without Test Runs.Journal of Sound and Vibration,2000,238(5):877-892
[74] 楼向明,郑水英.旋转机械转子不平衡在线识别方法的实验研究.汽轮机技术,1998,40(4):222-226
[75] 邱海,张海军,等.遗传算法在柔性转子动平衡中的应用.中国机械工程,2002,13(5):413-416
[76] 饶柱石,周海亭.多跨转子不平衡载荷在线识别的一种新方法.上海交通大学学报,1994,28(4):26-30
[77] 汪海良,刘思汉.柔性转子无试重动平衡法的实验研究.振动与冲击,1992(3):57-65
[78] 王群峰,汪希萱.慢时变参数转子系统动平衡校正量的确定.振动工程学报,1995,8(1):86-89
[79] 徐宾刚,屈梁生.基于影响系数法的柔性转子无试重平衡法研究.西安交通大学学报,2000,34(7):63-67
[80] 应光耀,郑水英,刘淑莲.遗传算法在转子-轴承系统参数识别中的应用.机械强度,2004,26(1):6-9
[81] 应光耀,郑水英,马振飞.基于遗传算法的挠性转子系统的参数识别.机械,2003,30(5):13-15
[82] Watkins J,Lee K,Hernandez C.Adaptive Auto-Balancing Control of Magnetic Bearings for an Optical Chopper.Proceedings of the American Control Conference,2001,2:1298-1303
[83] Woo K C,Rodger A A,Neilson R D.Application of the Harmonic Balance Method to Ground Moling Machines Operating in Periodic Regimes.Chaos, Solitons and Fractals,2000,11(15):2515-2525
[84] Bovik P,Hogfors C.Auto-Balancing of Rotors.Journal of Sound and Vibration,1986,111(3):429-440
[85] Gosiewski Z . Automatic Balancing of Flexible Rotors, Part Ⅱ : Synthesis of System.Journal of Sound and Vibration,1987,114(1):103-119
[86] Rajalingham C,Bhat R B,Rakheja S.Automatic Balancing of Flexible Vertical Rotors Using a Guided Ball.International Journal of Mechanical Sciences,1998,40(9):825-834
[87] Chung J,Jang I.Dynamic Response and Stability Analysis of an Automatic Ball Balancer for a Flexible Rotor.Journal of Sound and Vibration,2003,259(1):31-43
[88] Pashkov E N,Nesterenko V P,Pashkova T V.Transients of Rotation System with Autobalancer Filled with Liquid.7th International Scientific and Practical Conference of Students, Post-graduates and Young ,2001:77-78
[89] 李长河,原所先,修世超.超高速磨削中的砂轮自动平衡技术.新技术新工艺,2004(5):29-31
[90] 欧阳红兵,赵永彬,等.电磁式自动平衡头在线动平衡实验及应用研究.振动与冲击,2002,21(1):24-26
[91] 刘永光,夏松波.非线性转子系统自动平衡方法研究.哈尔滨工业大学学报,1999,31(3):77-79,83
[92] 李勇,须根发.高速转子电动平衡头的设计与技术措施.哈尔滨工业大学学报,1998,30(3):1-3
[93] 孙宝东.高速转子自动平衡技术的研究:[博士学位论文].哈尔滨:哈尔滨工业大学,1995
[94] 李顺利.精密离心机在线自动平衡方法研究.哈尔滨工业大学学报,2002,34(5):636-638
[95] 苏健,贺向阳,等.砂轮自动平衡系统的原理及应用.轴承,2003(1):29-31
[96] 陶利民,葛哲学,温熙森.刚性转子自动平衡控制策略.机械科学与技术,2004,23(2):140-142
[97] 谭青.风机故障诊断与自动平衡技术研究:[博士学位论文].长沙:中南大学,1996
[98] 曾胜.电磁式旋转机械在线自动平衡系统研究:[博士学位论文].杭州:浙江大学,1997
[99] 顾家柳,丁奎元,刘启洲.转子动力学.北京:国防工业出版社,1985
[100] Zhou S.Modeling, Estimation, and Active Balancing of Speed Varying Rotor System:[Ph.D. dissertation]:Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA,2001
[101] 伽西,菲茨耐.转子动力学导论.北京:机械工业出版社,1986
[102] 孟光.转子动力学研究的回顾与展望.振动工程学报,2002,15(1):1-9
[103] Ruhl R L,Booker J F.Finite Element Model for Distributed Parameter Turborotor Systems.Transactions of ASME, Journal of Engineering for Industry,1972,94(1):126-132
[104] Lund J W.Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings.ASME Transactions, Journal of Engineering for Industry,1974,96(2):509-517
[105] Lund J W,Orcutt F K.Calculations and Experiments on the Unbalance Response of a Flexible Rotor.ASME Transactions, Journal of Engineering for Industry,1967(11):785-796
[106] Shen F A.Transient Flexible- Rotor Dynamics Analysis Part 1-Theory.ASME Transactions, Journal of Engineering for Industry,1972(5):531-538
[107] Childs D W.Simulation Models for Flexible Spinning Bodies.Simulation,1969(6):291-296
[108] Childs D W.Simulation Model for Flexible Rotating Equipment.ASME Transactions, Journal of Engineering for Industry,1972:201-209
[109] Subbiah R,Rieger N F.On the Transient Analysis of Rotor-Bearing Systems.Journal ofVibration, Acoustics, Stress, and Reliability in Design,1988,110(4):515-520
[110] 黄文虎,武新华,等.非线性转子动力学研究综述.振动工程学报,2000,13(4):497-509
[111] 克利宗(苏),等.转子动力学:弹性支承.北京:科学出版社,1987
[112] 闻邦椿,等.高等转于动力学-理论、技术与应用.北京:机械工业出版社,2000
[113] 胡茑庆.转子碰摩非线性行为与故障辨识的研究:[博士学位论文].长沙:国防科学技术大学,2001
[114] 杨光,程胜文.高速转子的动力学研究.武汉理工大学学报:信息与管理工程版,2002,24(2):119-121
[115] 刘耀宗.碰摩转子混沌振动分析与控制:[博士学位论文].长沙:国防科学技术大学,2001
[116] 朱晓龙.国产平衡机的现状与发展预测.试验技术与试验机,1997,37(3-4):10-20
[117] 监督哨.平衡机总体质量较好 .中国技术监督杂志,1997(11):21
[118] 王树蕉.ETB—SIA 微机电测系统在闪光式动平衡机上的应用.航空制造工程,1996(8):34-34
[119] 何川,毛乐山,等.一种快速跟踪带通滤波器的实现.振动.测试与诊断,2002,22(3):212-216
[120] 胡毓涛.动平衡测量中的滤波技术.电脑与信息技术,1997,5(4):33-35
[121] 刘健,潘双夏,杨克己.动平衡测量数字滤波方法研究.机械强度,2005,27(1):38-43
[122] 赵午云,郭维强.动平衡测试技术方法浅析.机械工程师,2004(4):15-18
[123] 姚富光,肖沙里,丘柳东.动平衡实时监测及分析系统.计算机测量与控制,2004,12(7):623-625,634
[124] 李顺利.多传感器信息融合在精密离心机动平衡测试系统中的应用.机械工程学报,2002,38(6):115-118
[125] 郑建彬.基于 DWT 和 DFT 的动平衡机不平衡量提取原理及实现.系统工程与电子技术,2003,25(4):501-504
[126] 郑建彬,田春仿.基于离散小波变换的动平衡机不平衡量提取算法研究.测控技术,2002,21(8):21-23,26
[127] 段红.基于虚拟仪器的动平衡仪设计与测试方法研究.传感技术学报,2005,18(1):82-85
[128] 臧渭贤.汽车动平衡单片机测试系统.机械与电子,1998(3):42-43
[129] 岳明君.曲轴的高精度动平衡.内燃机,1998(2):27-29
[130] 余先涛.软支撑刚性转子动平衡测试系统设计.机械与电子,2000(3):44-46
[131] 姜淑娟,丛培田.双单片机控制动平衡测试系统.沈阳工业学院学报,2004,23(3):32-35
[132] 张剀,赵雷,等.新一代智能动平衡仪软件平台的方案选择.振动.测试与诊断,2003,23(1):54-57
[133] 刘健,潘双夏,杨克己.整系数数字滤波器在动平衡机测量系统中的应用研究.机床与液压,2005(2):119-120,140
[134] Sinha J K,Lees A W,Friswell M I.Estimating Unbalance and Misalignment of a Flexible Rotating Machine from a Single Run-Down.Journal of Sound and Vibration,2004,272(3-5):967-989
[135] Bustamante L G , Soderstrand M A . High-Range Switched-Capacitor Tracking Filter.Proceedings - IEEE International Symposium on Circuits and Systems,1999,2:65-68
[136] 王晓升.大型转子系统动平衡技术研究:[博士学位论文].西安:西安交通大学,1997
[137] 徐宾刚,屈梁生.非对称转子的全息动平衡技术.西安交通大学学报,2000,34(3):60-65
[138] 付大鹏,陈向伟.刚性外悬转子平衡方法的研究.华北电力技术,1999(5):35-36
[139] 曹树谦,张延安,等.高速转子动平衡的传递函数法.机械强度,2002,24(4):500-504
[140] 杨建刚,谢东建,等.基于多传感器数据融合的动平衡方法研究.动力工程,2003,23(2):2275-2278
[141] 耿炎,贺尔铭.基于遗传算法的多级轮盘主动平衡法.航天制造技术,2004(1):23-26
[142] Abduljabbar Z,ElMadany M M,AlAbdulwahab A A.Active Vibration Control of a Flexible Rotor.Computers and Structures,1996,58(3):499-511
[143] Ahmed J,Bernstein D S.Adaptive Force Balancing of an Unbalanced Rotor.Proceedings of the IEEE Conference on Decision and Control,1999,1:773-778
[144] Chakraborty A.Dynamic Balancing in NMR Double Rotor System.Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy,2000,56(14):2725-2727
[145] Chen P Y P,Feng N,Hahn E J.Flexible Rotor Balancing Taking Bearing Non-Linearity into Accountt.Proceedings of the ASME Design Engineering Technical Conference,2001,6 A:683-689
[146] Dyer S W.Adaptive Optimal Control of Active Balancing Systems for High-Speed Rotating Machinery : [Ph.D. dissertation] : Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA,1999
[147] Fan Y-H,Chen S-T,Lee A-C.Active Control of an Asymmetrical Rigid Rotor Supported by Magnetic Bearings.Journal of the Franklin Institute,1992,329(6):1153-1178
[148] Fritzen C P,Gans P,Wiese D.A Model-Based Method for Balancing of Flexible Rotors Mounted On Oil-Film Bearings Without Trial Weight.Proceedings of Design Engineering Technical Conference 17th Biennal Conference on Mechanical Vibration and Noise,1999:1027-1036
[149] Bishop R E D.The Vibration of Rotating Shafts.Journal of Mechanical Engineering Science,1959,1(1):50-65
[150] Kellenberger W.Should a Flexible Rotor Be Balanced in N or (N plus 2) Planes.ASME Transactions, Journal of Engineering for Industry,1972,94(2):548-560
[151] Saito S,Azuma T.Balancing of Flexible Rotors by the Complex Modal Method.ASME Transactions, Journal of Vibration, Acoustics, Stress, and Reliability in Design,1983,105(1):94-100
[152] 邱海,屈梁生.力偶分解法在全息关平衡面问题.化工机械,1999,26(2):82-85
[153] 邱海,屈梁生.全息谱力、力偶分解法在全息动平衡中的应用.中国机械工程,1998,9(3):44-46
[154] 徐宾刚,屈梁生,等.柔性弯曲转子的特征识别与诊断.西安交通大学学报,2001,35(3):288-291
[155] Goodman T P.A Least-Squares Method for Computing Balance Corrections.ASME Transactions, Journal of Engineering for Industry,1964(8):273-279
[156] Lund J W,Tonneson J.Analysis and Experiments in Multi-plane Balancing of Flexible Rotors.ASME Transactions, Journal of Engineering for Industry,1972,94:233-242
[157] Pilkey W D,Bailey J,Smith P D.Computational Technique for Optimizing Correction Weights and Axial Location of Balance Planes of Rotating Shafts.ASME Transactions,Journal of Vibration, Acoustics, Stress, and Reliability in Design,1983,105(1):90-93
[158] Li G,Lin Z,Untaroiu C.Balancing of High-Speed Rotating Machinery Using Convex Optimization.Proceedings of the IEEE Conference on Decision and Control,2003,4:4351-4356
[159] 康凯宁,王培俊.挠性转子动平衡时最大残余振动的极小化研究.机械强度,1996,18(3):1-5
[160] 朱向阳,钟秉林.具有上界约束的挠性转子最优平衡质量计算.机械工程学报,1999,35(3):34-36,50
[161] 勾新刚,张大卫,曾子平.遗传算法在转子影响系数平衡法中的应用.机械设计,2002,19(7):32-34
[162] 章璟璇,唐云冰,罗贵火.最小二乘影响系数法的优化改进.南京航空航天大学学报,2005,37(1):110-113
[163] 贺尔铭,陈新海.非对称转子系统主动平衡型抑振控制.航空动力学报,1996,11(2):138-140
[164] 刘占生,黄文虎,等.非对称柔性转子系统的动力特性分析.振动工程学报,2002,15(2):210-214
[165] 曹树谦. 高维复杂转子系统非线性动力学的若干现代问题研究:[博士学位论文].天津:天津大学,2003
[166] 谭青.多盘转子不平衡状态的系统辨识方法.中南工业大学学报,1998,29(3):266-269
[167] 谭青,李仲阳.离心鼓风机转子不平衡响应计算的实践.风机技术,1997(4):20-23
[168] 杨东波,潘丽,刘永光.球式自动平衡装置的理论研究.汽轮机技术,2000,42(3):162-165
[169] 葛哲学.刚性转子自动平衡系统研究:[硕士学位论文].长沙:国防科学技术大学,2002
[170] 徐志强,耿秋军,刘希杰.LIB-1 精密陀螺转子激光智能动平衡系统研制总结.中国惯性技术学报,1996,4(1):46-50,60
[171] 欧阳红兵,曾胜,汪希萱.转子系统在线动平衡综述及展望.机械强度,1997,19(4):20-24
[172] 马世骧,冀清发.微机控制砂轮在线液体自动平衡系统的研究.吉林工学院学报:自然科学版,1997,18(4):4-7
[173] 贺世正.释放液体式自动平衡头的研究.浙江大学学报(工学版),2001,35(4):418-422
[174] Kim Y D,Lee C W.Determination of the Optimal Balancing Head Location on Flexible Rotors Using a Structural Dynamics Modification Algorithm.Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science,1985,199(1):19-25
[175] 孙宝东,须根法.转子自动平衡技术的试验研究.中国电机工程学报,1995,15(5):317-322
[176] 李勇.遥控平衡头的单盘转子自动平衡实验研究.振动工程学报,1998,11(2):220-223
[177] 李勇.自动平衡头供电特性研究.汽轮机技术,1998,40(2):104-106
[178] 李勇,刘亚光.自动平衡头中的步进电动机红外遥控驱动系统.微特电机,1997,25(2):14-15
[179] 李勇,陆永平.采用永磁频差电动机的自动平衡头.微特电机,1998,26(5):31-33
[180] 李勇,陆永平.永磁差频电动平衡头的振动控制实验研究.振动工程学报,2000,13(2):302-306
[181] 李勇,王靖,陆永平.高速转子自动平衡头的研究现状及发展趋势展望.振动、测试与诊断,1998,18(4):273-276,307
[182] 曾胜,汪希萱.旋转机械在线自动平衡系统的研究——电磁式动平衡调节器在线试重平衡法研究.机械强度,1998,20(1):14-18
[183] 欧阳红兵.电磁式在线自动平衡系统的特性研究:[博士学位论文].杭州:浙江大学,1998
[184] 欧阳红兵,汪希萱.两种新型电磁式在线自动平衡头.机械制造,2002,40(7):47-48
[185] 欧阳红兵,汪希萱.新型电磁式自动平衡头控制决策研究.制造技术与机床,1998(1):20-22
[186] 欧阳红兵,汪希萱.新型自动平衡头的特性研究:磁化曲线的解析算法.中国机械工程,2000,11(7):820-822
[187] Zhou S , Shi J . The Analytical Imbalance Response of Jeffcott Rotor During Acceleration.Journal of Manufacturing Science and Engineering,2001,123:299-302
[188] Zhou S,Shi J. Imbalance Estimation for Speed-Varying Rigid Rotors Using Time-Varying Observer.Journal of Dynamic Systems, Measurement, and Control,2001,123:637-644
[189] Zhou S , Shi J . Optimal One-Plane Active Balancing of a Rigid Rotor During Acceleration.Journal of Sound and Vibration,2002,249(1):196-205
[190] Mohamed A M,Busch-Vishniac I.Imbalance Compensation and Automation Balancing in Magnetic Bearing Systems Using the Q-Parameterization Theory.IEEE Transactions on Control Systems Technology,1995,3(2):202-211
[191] Maslen E H , Beilk J R. A Stability Model for Flexible Rotors with Magnetic Bearings.Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME,1992,114(1):172-175
[192] Knospe C R,Tamer S M,Fedigan S J.Robustness of Adaptive Rotor Vibration Control to Structured Uncertainty.ASME Transactions, Journal of Dynamic Systems, Measurement, and Control,1997,119:243-250
[193] Ulsoy A G.Vibration Control in Rotating or Translating Elastic Systems.ASME Transactions, Journal of Dynamic Systems, Measurement, and Control,1984,106(1):6-14
[194] Markert R,Skricka N,Zhang X.Unbalance Compensation on Fexible Rotors by Magnetic Bearings Using Transfer Functions.8th International Symposium on Magnetic Bearing,2002:417-422
[195] Kim J-S,Lee S-H.The Stability of Active Balancing Control Using Influence Coefficients for a Variable Rotor System . International Journal of Advanced Manufacturing Technology,2003,22(7-8):562-567
[196] Hredzak B,Guo G.Investigation of the Feasibility of Active Balancing of Hard Disk Drives.Mechatronics,2004,14(7):853-859
[197] 李勇,陆永平.采用磁力平衡方法的在线动平衡机技术研究(Ⅰ):基本原理和结构.微特电机,1999,27(1):3-5
[198] 李勇,王靖.采用旋转电磁力的在线动平衡机技术研究(Ⅱ)结构参数与电流波形优化.微特电机,1999,27(6):13-15,19
[199] 李勇,王靖.采用旋转电磁力的在线动平衡机技术研究(Ⅲ):运行特性分析与实验验证.微特电机,2000,28(4):18-20
[200] 楼向明.运转状态下的不平衡识别方法的研究:[博士学位论文].杭州:浙江大学,1998
[201] 黄晓蔚.数控磁轴承-转子系统的研究:[博士学位论文].北京:北京工业大学,1999
[202] 刘永光,李勇.柔性转子自动动平衡的寻优控制.振动工程学报,1999,12(4):558-564
[203] 李伟华,华达勋.CIMT2001 数控外圆磨床展品评述.精密制造与自动化,2001(3):3-5
[204] Lalanne M,Ferraris G.Rotordynamics Prediction in Engineering.New York:John Wiley & Sons,1998
[205] 邓重一.滤波技术的发展现状.中国仪器仪表,2004(2):1-4
[206] 张筱华,林莘.滤波技术.北京:人民邮电出版社,1994
[207] 费树铮.CMOS 开关电容滤波器电路.电子技术,1987(2):32-35
[208] 温熙森,陈循,徐永成.机械系统建模与动态分析.北京:科学出版社,2004
[209] 孙向东,王秀方.用开关电容电路技术实现的七阶椭圆函数滤波器.郑州轻工业学院学报,1998,13(1):45-49
[210] 黄金法.开关电容滤波器 IC 发展概况.振动、测试与诊断,1991,11(2):53-62
[211] 陈照章.跟踪滤波器的设计及其应用.仪器仪表学报,2001(6):244-246
[212] 陈怀超,丛培田.基于开关电容的自动跟踪滤波器的设计及研究.仪表技术与传感器,2003(10):38-39
[213] 江驹,沈勇璋,汪旭旦.智能化动平衡测量仪的研制.数据采集与处理,2000,15(4):476-480
[214] 温熙森,陈循,唐丙阳.机械系统动态分析理论与应用.长沙:国防科技大学出版社,1998
[215] 约翰逊 D E,约翰逊 J R,穆尔 H P.有源滤波器精确设计手册.北京:电子工业出版社,1984
[216] 欧海涛,张飞虎.基于 98 单片机红外遥控通信的智能化砂轮自动平衡系统.测控技术,2000,19(3):51-53
[217] 李德,钱颂迪.运筹学.北京:清华大学出版社,1982
[218] 谢政,李建平,汤泽滢.非线性最优化.长沙:国防科技大学出版社,2003
[219] 刘金环,任玉田.机械工程测试技术.北京:北京理工大学出版社,1990
[220] 陶利民,沈国际,陈仲生.直升机齿轮箱振动信号的角度估计.第 19 届全国直升机年会,哈尔滨,2003,8
[221] 沈国际,陶利民,温熙森.基于 Wigner 分布的齿轮箱振动信号相位估计.机械工程学报,2004,40(9):185-189
[222] 陈清山,陈燕科.最新世界集成模数和数模转换器及接口器手册.长沙:中南工业大学出版社,1990
[223] 程佩青.数字滤波与快速傅里叶变换.北京:清华大学出版社,1990
[224] 邵朝,阴亚芳,卢光跃.数字信号处理.北京:北京邮电大学出版社,2004
[225] Sperling L,Ryzhik B,Linz C.Simulation of Two-Plane Automatic Balancing of a Rigid Rotor.Mathematics and Computers in Simulation,2002,58(4-6):351-365
[226] 顾乾坤,唐一科.转子自动平衡理论及应用研究.重庆大学学报:自然科学版,1995,18(6):124-128
[227] 卢奂采,汪希萱.转子在线自动平衡研究.机械工程学报,1998,34(3):33-38
[228] 上海微电机研究所著.微特电机.上海:上海科学技术出版社,1982
[229] 国家标准.通用卧式平衡机检验法(GB4201-84).北京:中国标准出版社,1984
[230] 黄晓蔚,唐钟麟.数控有源磁力轴承对转子不平衡振动抑制的一种新方法.机械科学与技术,1999,18(5):721-724