膜片联轴器耦合的不对中转子—轴承系统动力学研究
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摘要
本文根据集总参数法建立了膜片联轴器耦合的不对中转子—轴承系统的动力学模型。基于线性振动理论分析了系统的固有特性、稳定性和不平衡响应。主要内容和结论如下：
首先分析了膜片组的静力学和动力学特性，导出了在工作状态下，膜片组应力和刚度的计算公式。然后对系统中的各典型部件分别进行了受力和运动学分析，同时考虑了转子的不对中和不平衡因素对系统动力学的影响，建立了膜片联轴器耦合的转子—轴承系统的动力学模型。
以膜片联轴器耦合的对称多跨转子—轴承系统为研究对象，分析了转子不对中量对轴承的动静特性、系统的固有特性和稳定性的影响。数值结果表明对于对称的转子—轴承系统，不对中对轴承的负荷分配和动静特性影响较大，而对系统的临界转速的影响较小。分析结果还表明不对中转子系统的模态与理想对中系统相比有较大的差别。在不对中量的作用下，系统的模态要发生改变，对于低阶模态一般以其中一跨转子的振动为主。另外不对中使膜片联轴器耦合的转子—轴承系统的稳定性有恶化的趋势。
研究了膜片联轴器耦合的转子—轴承系统的不平衡响应，重点分析了膜片联轴器的刚度和转子的不对中量对系统不平衡响应的影响。结果表明联轴器的转角刚度和径向刚度对转子系统不平衡响应的影响是不相同的，其中转角刚度对转子—轴承系统不平衡响应的影响较大，而径向刚度的影响较小。当转子系统在临界转速附近时，转子的不对中对系统的不平衡响应影响显著，而在其它转速处，这种影响较小。
The dynamic model of misaligned rotor-bearing system equipped with a flexible laminated membrane coupling was developed by using the method of lumped parameter in this dissertation, and the dynamic behavior, such as the nature characteristics, stability, steady state response of the system, etc. was analyzed based on the theory of linear vibration. The main contributions and conclusions of the work were summarized as follows:
Firstly, the static and dynamic characteristics of the laminated membrane were analyzed, and the computing formulas of it stress and stiffness was derived. After discussing the forces on the typical components of the system and their motions, the dynamic model of the flexible laminated membrane coupling-rotor-bearing system was developed, in which the effects of the misalignment and unbalance of the rotor system were considered.
The performance of the bearings, the nature characteristics and stability of a symmetric rotor-bearing system equipped with a flexible laminated membrane coupling were discussed duo to misalignment of rotors. The numerical results showed that the effects of the load distributions on bearings and their static and dynamic behavior of the symmetric rotor system by the misalignment were large, meanwhile that of the critical speeds of the system was small. The results also revealed that the modes of the misaligned rotor system were different from the aligned one. When considered the misalignment of rotors, the lowest modes were changed greatly, in which their vibrations of one rotor were fiercer than that of another one generally. Additionally, the misalignment of the system could make the stability have a tendency to deteriorate.
The unbalance responses of the rotor-bearing system with a flexible laminated membrane coupling were investigated, in which the effects of the stiffness of the coupling and the misalignment of the rotors were mainly taken into account, respectively. The results displayed that the influences of the responses were different to the angular stiffness of the coupling and the lateral one, that is, the former was large, and the latter small. When the rotating speed passed through the critical speed, the effect of the unbalance response of the system duo to the misalignment was remarkable, and at
the others its influence was not large.
首先分析了膜片组的静力学和动力学特性，导出了在工作状态下，膜片组应力和刚度的计算公式。然后对系统中的各典型部件分别进行了受力和运动学分析，同时考虑了转子的不对中和不平衡因素对系统动力学的影响，建立了膜片联轴器耦合的转子—轴承系统的动力学模型。
以膜片联轴器耦合的对称多跨转子—轴承系统为研究对象，分析了转子不对中量对轴承的动静特性、系统的固有特性和稳定性的影响。数值结果表明对于对称的转子—轴承系统，不对中对轴承的负荷分配和动静特性影响较大，而对系统的临界转速的影响较小。分析结果还表明不对中转子系统的模态与理想对中系统相比有较大的差别。在不对中量的作用下，系统的模态要发生改变，对于低阶模态一般以其中一跨转子的振动为主。另外不对中使膜片联轴器耦合的转子—轴承系统的稳定性有恶化的趋势。
研究了膜片联轴器耦合的转子—轴承系统的不平衡响应，重点分析了膜片联轴器的刚度和转子的不对中量对系统不平衡响应的影响。结果表明联轴器的转角刚度和径向刚度对转子系统不平衡响应的影响是不相同的，其中转角刚度对转子—轴承系统不平衡响应的影响较大，而径向刚度的影响较小。当转子系统在临界转速附近时，转子的不对中对系统的不平衡响应影响显著，而在其它转速处，这种影响较小。
The dynamic model of misaligned rotor-bearing system equipped with a flexible laminated membrane coupling was developed by using the method of lumped parameter in this dissertation, and the dynamic behavior, such as the nature characteristics, stability, steady state response of the system, etc. was analyzed based on the theory of linear vibration. The main contributions and conclusions of the work were summarized as follows:
Firstly, the static and dynamic characteristics of the laminated membrane were analyzed, and the computing formulas of it stress and stiffness was derived. After discussing the forces on the typical components of the system and their motions, the dynamic model of the flexible laminated membrane coupling-rotor-bearing system was developed, in which the effects of the misalignment and unbalance of the rotor system were considered.
The performance of the bearings, the nature characteristics and stability of a symmetric rotor-bearing system equipped with a flexible laminated membrane coupling were discussed duo to misalignment of rotors. The numerical results showed that the effects of the load distributions on bearings and their static and dynamic behavior of the symmetric rotor system by the misalignment were large, meanwhile that of the critical speeds of the system was small. The results also revealed that the modes of the misaligned rotor system were different from the aligned one. When considered the misalignment of rotors, the lowest modes were changed greatly, in which their vibrations of one rotor were fiercer than that of another one generally. Additionally, the misalignment of the system could make the stability have a tendency to deteriorate.
The unbalance responses of the rotor-bearing system with a flexible laminated membrane coupling were investigated, in which the effects of the stiffness of the coupling and the misalignment of the rotors were mainly taken into account, respectively. The results displayed that the influences of the responses were different to the angular stiffness of the coupling and the lateral one, that is, the former was large, and the latter small. When the rotating speed passed through the critical speed, the effect of the unbalance response of the system duo to the misalignment was remarkable, and at
the others its influence was not large.
引文
[1] 陈大禧，朱铁光．大型回转机械诊断现场实用技术．北京：机械工业出版社，2002
[2] 虞烈，刘恒．轴承—转子系统动力学．西安：西安交通大学出版社，2001
[3] R．迦西，H．菲茨耐．转子动力学导论．北京：机械工业出版社，1986
[4] 倪振华．振动力学．西安：西安交通大学出版社，1986
[5] 郑兆昌．机械振动(上)．北京：机械工业出版社，1980
[6] 刘习军，贾启芬，张文德．工程振动与测试技术．天津：天津大学出版社，1999
[7] 钟一谔，何衍宗，王正，等．转子动力学．北京：清华大学出版社，1986
[8] J. W, Lund. Stability and damped critical speeds of a flexible rotor in fluid film bearings. J. of Eng. for Indus, trans. ASME, 1974, 96 (2): 509～517
[9] Nelson H D, McVaugh J M. The dynamics of rotor-bearing system using finite element. J of Enf. for Industry, 1976, 98(2): 593～601
[10] 闻邦椿，顾家柳，夏松波，等．高等转子动力学——理论、技术与应用．北京：机械工业出版社，2000
[11] Johnstone, Norman. J. What is a flexible coupling?. Power Transmission Design, 1977,19(5): 37～40
[12] Wireman, Terry. Fitness Plan For Flexible Couplings. Power Transmission Design, 1983, 25(4): 20～22
[13] Dewell, D. L. Mitchell, L. D. Detection Of A Misaligned Disk Coupling Using Spectrum Analysis. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1984, 106 (1): 9～16
[14] Anon. Design Evaluation Of The Metastream Coupling. Engineering Materials and Design, 1978, (22) 452～458
[15] 王昭甫．膜片联轴器的使用特性及其中国应用的十年．热能动力工程，1992，7(4)：173～178
[16] 王金才．连续环式叠层结构膜片联轴器．风机技术，1994，(3)：19～24
[17] 吕万铭，赵保宇．金属叠层膜片联轴器应用技术研究．现代机械，1993，(2)：5～8
[18] 王玉良，郭会．金属叠层膜片联轴器．机械科学与技术，1991，(3)：45～49
[19] 李友萍，张仲毅，陈晓岑，等．新型膜片联轴器中膜片应力与刚度的计算．武
汉汽车工业大学学报，1996，18(2)：11～14
[20] 徐伟，冯桂军，周开勤，等．膜片联轴器的强度与刚度分析．机械设计，1992，(5)：21～25
[21] 花家寿．新型联轴器和离合器．上海：上海科学技术出版社，1986
[22] 王心丰，方鸿慧．挠性膜片联轴器优化设计．南京航空航天大学学报，1993，25(5)：618～623
[23] 华军，许庆余，张亚红．膜片联轴器应力计算及疲劳寿命分析．机械科学与技术，2000，19(2)：203～205
[24] 华军，许庆余，张亚红．应用局部应力—应变法计算联轴器膜片疲劳寿命．工程力学，2000，17(4)：132～137
[25] 申屠留芳，汤洪涛，王成轩，等．轴不对中对叠片膜片联轴器应力的影响．机械强度，1999，21(2)：112～114
[26] 申屠留芳，汤洪涛，王成轩，等．链板式叠片联轴器强度分析．机械科学与技术，1998，17(6)：944～946
[27] 史建波．金属叠片式挠性联轴器联结的多跨转子—轴承系统的振动特性研究：[学位论文]．西安：西安交通大学，1996
[28] 李明，张勇，姜培林，等．转子—齿轮联轴器系统的弯扭耦合振动研究．航空动力学报，1999，14(1)：60～66
[29] 李明．轴承—转子—齿轮联轴器耦合系统的动力学研究：[学位论文]．西安：西安交通大学，1999
[30] 李明，张金玉，虞烈．不对中齿轮联轴器转子系统的振动特征研究．西安矿业学院学报，1998，18(1)：240～243
[31] Chaika. V. Steady state response of a system of rotors with various types of flexible couplings. Journal of Sound and Vibration, 1994,77(4): 521～537
[32] Xu.M, Marangoni, R. D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance part Ⅰ: theoretical model and analysis. Journal of Sound and Vibration, 1994, 176(5):663～679
[33] Xu.M, Marangoni, R. D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance part Ⅱ: experimental validation. Journal of Sound and Vibration, 1994, 176(5): 681～691
[34] Jackon C. Successful Shaft hot-alignment. Hydrocarbon Processing, 1969,48(6): 28～40
[35] 夏松波，张新江，刘占生，等．旋转机械不对中故障研究综述．振动、测试与诊断，1998，18(3)：157～161
[36] 魏伟．转子不对中故障机理与诊断．石油化工设备，1997，27(4)：48～50
[37] 陈进．机械设备振动监测与故障诊断．上海：上海交通大学出版社，1999
[38] M. Li, L. Yu. Analysis of the Coupled Lateral Torsional Vibration of Rotor-bearing System with a Misaligned Gear Coupling. Journal of Sound and Vibration, 2001, 243(2): 283～300
[39] Jackson, Charles. Techniques for Alignment of Rotating Equipment. Hydrocarbon Processing, 1976, 55(1): 81～86
[40] 宋秋生．改齿式联轴器为膜片联轴器．大氮肥，1999，22(5)：347～349
[41] 周明衡．联轴器选用手册．北京：化学工业出版社，2001
[42] 施高义，唐金松，喻怀正，等．联轴器．北京：机械工业出版社，1988
[43] Feng. N. S, Hahn, E. J. Effects of misalignment on the stability and unbalance response of statically indeterminate rotating machinery. Rotordynamic instability Problem in High Performance Turbormachinery, NASA Conference Publication on 3344, 1996, 163～175
[44] Hu. W, Miah. H., Feng. N. S., Hahn, E. J. A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings. Tribology International, 2000, 33:197～204
[45] Nikolajsen J. L. Effect of misalignment on rotor vibrations. ASME Journal of Engineering for Gas Turbines and Power, 1998,120: 635～670.
[46] 宋曦，赵荣珍．转子——轴承系统固有频率对设计参数的灵敏度．甘肃工业大学学报，1999，25(2)：37～40
[47] 李明，虞烈，沈润杰．齿轮联轴器对轴承—转子系统失稳转速的影响．发电设备，2000，(3)：26～28．
[48] 郑铁生，蔡则彪．非对称矩阵结构系统固有值分析的广义逆迭代法．振动工程学报，1990，3(2)：79～84
[49] Lee A C, Shih Y P. Identification of the unbalance distribution and dynamic characteristics of bearings in flexible rotors. Journal of Mechanical Engineering Science, 1996, 210 (5): 409～428.
[50] 李志荣，候洪海，曾亚洪．转子不平衡的故障特征．洛阳工学院学报，1999，20(1)：54～57
[51] 石守红，韩玉强，张锁怀，等．参数对齿轮耦合的转子—轴承系统响应的影响．机械科学与技术，2001，20(4)：584～587
[2] 虞烈，刘恒．轴承—转子系统动力学．西安：西安交通大学出版社，2001
[3] R．迦西，H．菲茨耐．转子动力学导论．北京：机械工业出版社，1986
[4] 倪振华．振动力学．西安：西安交通大学出版社，1986
[5] 郑兆昌．机械振动(上)．北京：机械工业出版社，1980
[6] 刘习军，贾启芬，张文德．工程振动与测试技术．天津：天津大学出版社，1999
[7] 钟一谔，何衍宗，王正，等．转子动力学．北京：清华大学出版社，1986
[8] J. W, Lund. Stability and damped critical speeds of a flexible rotor in fluid film bearings. J. of Eng. for Indus, trans. ASME, 1974, 96 (2): 509～517
[9] Nelson H D, McVaugh J M. The dynamics of rotor-bearing system using finite element. J of Enf. for Industry, 1976, 98(2): 593～601
[10] 闻邦椿，顾家柳，夏松波，等．高等转子动力学——理论、技术与应用．北京：机械工业出版社，2000
[11] Johnstone, Norman. J. What is a flexible coupling?. Power Transmission Design, 1977,19(5): 37～40
[12] Wireman, Terry. Fitness Plan For Flexible Couplings. Power Transmission Design, 1983, 25(4): 20～22
[13] Dewell, D. L. Mitchell, L. D. Detection Of A Misaligned Disk Coupling Using Spectrum Analysis. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1984, 106 (1): 9～16
[14] Anon. Design Evaluation Of The Metastream Coupling. Engineering Materials and Design, 1978, (22) 452～458
[15] 王昭甫．膜片联轴器的使用特性及其中国应用的十年．热能动力工程，1992，7(4)：173～178
[16] 王金才．连续环式叠层结构膜片联轴器．风机技术，1994，(3)：19～24
[17] 吕万铭，赵保宇．金属叠层膜片联轴器应用技术研究．现代机械，1993，(2)：5～8
[18] 王玉良，郭会．金属叠层膜片联轴器．机械科学与技术，1991，(3)：45～49
[19] 李友萍，张仲毅，陈晓岑，等．新型膜片联轴器中膜片应力与刚度的计算．武
汉汽车工业大学学报，1996，18(2)：11～14
[20] 徐伟，冯桂军，周开勤，等．膜片联轴器的强度与刚度分析．机械设计，1992，(5)：21～25
[21] 花家寿．新型联轴器和离合器．上海：上海科学技术出版社，1986
[22] 王心丰，方鸿慧．挠性膜片联轴器优化设计．南京航空航天大学学报，1993，25(5)：618～623
[23] 华军，许庆余，张亚红．膜片联轴器应力计算及疲劳寿命分析．机械科学与技术，2000，19(2)：203～205
[24] 华军，许庆余，张亚红．应用局部应力—应变法计算联轴器膜片疲劳寿命．工程力学，2000，17(4)：132～137
[25] 申屠留芳，汤洪涛，王成轩，等．轴不对中对叠片膜片联轴器应力的影响．机械强度，1999，21(2)：112～114
[26] 申屠留芳，汤洪涛，王成轩，等．链板式叠片联轴器强度分析．机械科学与技术，1998，17(6)：944～946
[27] 史建波．金属叠片式挠性联轴器联结的多跨转子—轴承系统的振动特性研究：[学位论文]．西安：西安交通大学，1996
[28] 李明，张勇，姜培林，等．转子—齿轮联轴器系统的弯扭耦合振动研究．航空动力学报，1999，14(1)：60～66
[29] 李明．轴承—转子—齿轮联轴器耦合系统的动力学研究：[学位论文]．西安：西安交通大学，1999
[30] 李明，张金玉，虞烈．不对中齿轮联轴器转子系统的振动特征研究．西安矿业学院学报，1998，18(1)：240～243
[31] Chaika. V. Steady state response of a system of rotors with various types of flexible couplings. Journal of Sound and Vibration, 1994,77(4): 521～537
[32] Xu.M, Marangoni, R. D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance part Ⅰ: theoretical model and analysis. Journal of Sound and Vibration, 1994, 176(5):663～679
[33] Xu.M, Marangoni, R. D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance part Ⅱ: experimental validation. Journal of Sound and Vibration, 1994, 176(5): 681～691
[34] Jackon C. Successful Shaft hot-alignment. Hydrocarbon Processing, 1969,48(6): 28～40
[35] 夏松波，张新江，刘占生，等．旋转机械不对中故障研究综述．振动、测试与诊断，1998，18(3)：157～161
[36] 魏伟．转子不对中故障机理与诊断．石油化工设备，1997，27(4)：48～50
[37] 陈进．机械设备振动监测与故障诊断．上海：上海交通大学出版社，1999
[38] M. Li, L. Yu. Analysis of the Coupled Lateral Torsional Vibration of Rotor-bearing System with a Misaligned Gear Coupling. Journal of Sound and Vibration, 2001, 243(2): 283～300
[39] Jackson, Charles. Techniques for Alignment of Rotating Equipment. Hydrocarbon Processing, 1976, 55(1): 81～86
[40] 宋秋生．改齿式联轴器为膜片联轴器．大氮肥，1999，22(5)：347～349
[41] 周明衡．联轴器选用手册．北京：化学工业出版社，2001
[42] 施高义，唐金松，喻怀正，等．联轴器．北京：机械工业出版社，1988
[43] Feng. N. S, Hahn, E. J. Effects of misalignment on the stability and unbalance response of statically indeterminate rotating machinery. Rotordynamic instability Problem in High Performance Turbormachinery, NASA Conference Publication on 3344, 1996, 163～175
[44] Hu. W, Miah. H., Feng. N. S., Hahn, E. J. A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings. Tribology International, 2000, 33:197～204
[45] Nikolajsen J. L. Effect of misalignment on rotor vibrations. ASME Journal of Engineering for Gas Turbines and Power, 1998,120: 635～670.
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