齿轮传动系统耦合单元整体传递矩阵的研究
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摘要
随着现代工业的发展,齿轮传动的旋转机械朝着高转速、大功率的趋势发展,应用范围也越来越广,车辆传动系是其中典型的具有复杂齿轮传动和分叉结构的多转子系统。由于齿轮的啮合作用,使得系统各转子之间的弯曲振动和扭转振动相互耦合,因而转子系统的动力学特性不能仅从单转子来考察,需要建立系统的弯扭耦合频率方程,对其动力学特性进行分析。
整体传递矩阵法是进行转子系统动力特性分析的新型方法,特别适用多轴转子链式系统。该方法在应用于求解包含齿轮啮合效应的多轴系统弯扭耦合振动的动力计算时,关键是要导出齿轮耦合单元的传递矩阵。本文给出了齿轮副啮合传动动力学表达式,建立了直齿轮、斜齿轮,锥齿轮、柱齿轮,平行轴、相交轴和交错轴等多种构造形式转子系统的耦合单元传递矩阵,准确地把整体传递矩阵法运用到齿轮啮合轴系振动分析问题中。
本文阐述了课题研究的产业和技术背景,总结了齿轮传动转子系统弯扭耦合振动问题的研究现状及主要的分析方法,介绍了多转子系统振动分析整体传递矩阵法理论。利用机械原理和机械设计中齿轮构造机理、理论力学的拉格朗日方程和达朗伯原理、材料力学的梁轴弯扭变形、振动力学的多自由度系统固有振动频率和模态分析、转子动力学的回转力矩等分析计算方法推导出平行轴圆柱齿轮啮合的广义动力学方程,并建立了对应于状态向量的传递矩阵。然后引入斜齿轮的螺旋角,考虑啮合力产生的轴向分量的影响,导出了弯扭耦合平行轴斜齿圆柱齿轮啮合耦合单元的传递矩阵,列入程序中进行计算。再对不同螺旋角组合情况下的交错轴斜齿圆柱齿轮的动力学特性进行研究,从该系统为点接触的啮合方式,分析啮合刚度的减小对系统临界转速的影响,总结交错轴的动力学特性。首次将整体传递矩阵法应用于解决相交轴锥齿轮啮合系统振动分析,并研究锥顶角不同对系统弯扭耦合临界转速的影响,对任意轴角斜齿锥齿轮进行动力学分析并建立耦合单元传递矩阵,计算分析不同轴角对系统弯扭耦合临界转速的影响。
For developing of modern industry, the rotary machine has a tendency of higher speed, higher power. Its structures become more complex contain multiple rotors. For gears meshing, bending vibration and torsion vibration are coupling in vehicle. Analysis on the dynamic character of rotors system is not limited in separated rotor. The frequency of coupling must be considered for the warning of loss of more important frequencies
The whole transfer matrix method is suitable to analyze dynamics property of multi-rotor system that linked in line. Dynamics equations of gear pair are deduced here, the coupling element transfer matrix of spur gear, helical gear; bevel gear, cylinder gear; parallel axis, intersecting axis, crossed-axis, and so on various style rotor system are founded.
The background of industry and technology of the topic in researching is explained, and the latest research state of lateral-bending vibration of vehicle gear-transmission system and the main analytic methods are synthesized. The dynamic equations are deduced based on the theories of gear construction in kinematics and dynamics of machinery, D'Alembert principle and Lagrange's equations in engineering mechanics, deformation of beams and shafts in applied strength of materials, analysis of vibration frequency and modal phase of multi-freedom system in vibration mechanics, attribute of gyratory torque in rotor dynamics. The helix angle of helical gear is introduced and the effects on the dynamic equations by the axial component of meshing force are considered, the coupling elements transfer matrix of spiral gear system and the crossed-axis rotor system's dynamic character of different helix angle helical gears is the main object to study, it takes point-connected style, the crossed-axis rotor system's dynamic character can be obtained. The transfer matrix of spur bevel gear meshing perpendicular transmission system and the effect of different cone-apex angle on coupling crisis speeds is analyzed. The transfer matrix of spiral bevel gear meshing intersecting axes transmission system and the effect of different axial angle on lateral and torsion coupling crisis speeds is analyze by calculation program.
整体传递矩阵法是进行转子系统动力特性分析的新型方法,特别适用多轴转子链式系统。该方法在应用于求解包含齿轮啮合效应的多轴系统弯扭耦合振动的动力计算时,关键是要导出齿轮耦合单元的传递矩阵。本文给出了齿轮副啮合传动动力学表达式,建立了直齿轮、斜齿轮,锥齿轮、柱齿轮,平行轴、相交轴和交错轴等多种构造形式转子系统的耦合单元传递矩阵,准确地把整体传递矩阵法运用到齿轮啮合轴系振动分析问题中。
本文阐述了课题研究的产业和技术背景,总结了齿轮传动转子系统弯扭耦合振动问题的研究现状及主要的分析方法,介绍了多转子系统振动分析整体传递矩阵法理论。利用机械原理和机械设计中齿轮构造机理、理论力学的拉格朗日方程和达朗伯原理、材料力学的梁轴弯扭变形、振动力学的多自由度系统固有振动频率和模态分析、转子动力学的回转力矩等分析计算方法推导出平行轴圆柱齿轮啮合的广义动力学方程,并建立了对应于状态向量的传递矩阵。然后引入斜齿轮的螺旋角,考虑啮合力产生的轴向分量的影响,导出了弯扭耦合平行轴斜齿圆柱齿轮啮合耦合单元的传递矩阵,列入程序中进行计算。再对不同螺旋角组合情况下的交错轴斜齿圆柱齿轮的动力学特性进行研究,从该系统为点接触的啮合方式,分析啮合刚度的减小对系统临界转速的影响,总结交错轴的动力学特性。首次将整体传递矩阵法应用于解决相交轴锥齿轮啮合系统振动分析,并研究锥顶角不同对系统弯扭耦合临界转速的影响,对任意轴角斜齿锥齿轮进行动力学分析并建立耦合单元传递矩阵,计算分析不同轴角对系统弯扭耦合临界转速的影响。
For developing of modern industry, the rotary machine has a tendency of higher speed, higher power. Its structures become more complex contain multiple rotors. For gears meshing, bending vibration and torsion vibration are coupling in vehicle. Analysis on the dynamic character of rotors system is not limited in separated rotor. The frequency of coupling must be considered for the warning of loss of more important frequencies
The whole transfer matrix method is suitable to analyze dynamics property of multi-rotor system that linked in line. Dynamics equations of gear pair are deduced here, the coupling element transfer matrix of spur gear, helical gear; bevel gear, cylinder gear; parallel axis, intersecting axis, crossed-axis, and so on various style rotor system are founded.
The background of industry and technology of the topic in researching is explained, and the latest research state of lateral-bending vibration of vehicle gear-transmission system and the main analytic methods are synthesized. The dynamic equations are deduced based on the theories of gear construction in kinematics and dynamics of machinery, D'Alembert principle and Lagrange's equations in engineering mechanics, deformation of beams and shafts in applied strength of materials, analysis of vibration frequency and modal phase of multi-freedom system in vibration mechanics, attribute of gyratory torque in rotor dynamics. The helix angle of helical gear is introduced and the effects on the dynamic equations by the axial component of meshing force are considered, the coupling elements transfer matrix of spiral gear system and the crossed-axis rotor system's dynamic character of different helix angle helical gears is the main object to study, it takes point-connected style, the crossed-axis rotor system's dynamic character can be obtained. The transfer matrix of spur bevel gear meshing perpendicular transmission system and the effect of different cone-apex angle on coupling crisis speeds is analyzed. The transfer matrix of spiral bevel gear meshing intersecting axes transmission system and the effect of different axial angle on lateral and torsion coupling crisis speeds is analyze by calculation program.
引文
[1]#12
[2]小林明.汽车工程手册[M].北京:机械工业出版社,1980.
[3]隋军,王学义,魏德永.传动系的弯曲振动及其对汽车飞轮壳强度影响的研究.汽车技术,1994(6):14-22.
[4]高云凯,吕振华,李卓森.汽车动力总成弯曲振动试验模态分析中的非线性特性.吉林工业大学学报,1996,26(4):6-9.
[5]刘辉,项昌乐,郑慕侨.车辆动力传动系通用扭振模型的研究.中国机械工程,2003,14(15):1282-1285.
[6]Centea D,Rahnejat H,Menday M T.Non-linear multi-body dynamic analysis for the study of clutch torsional vibrations(judder).Applied Mathematical Modeling,25(2001):177-192.
[7]Zou C P,Chen D S,Hua H X.Torsional vibration analysis of complicated multi-brached shafting systems by modal synthesis method.Journal of Vibration and Acoustics,Transaction of ASME,125(2003):317-323.
[8]Crowther A,Zhang N.Torsional finite elements and nonlinear numerical modeling in vehicle powertrain dynamics.Journal of Sound and Vibration,284(2005):825-849.
[9]Crowther A,Zhang N,Liu D Jeyakumaran J M.Analysis and simulation of clutch engagement judder and stick-slip in automotive powertrain systems.Proceedings of the Institution of Mechanical engineers Part D:Journal of Automobile Engineering,218(2004):1427-1446.
[10]http://www.noveri.com.cn
[11]Iannuzzeui R.J.,Elward R.M.Torsional-lateral coupling geared rotors.ASME Paper.1984,71-84
[12]石守红,韩玉强,等.齿轮耦合的转子-轴承系统的研究现状.机械科学与技术,2002,21(5):703-706
[13]伍良生,陈卫福.弯扭耦合齿轮传动系统固有频率与振型计算的传递矩阵法.北京工业大学学报,1999,25(1):94-98
[14]韩玉强,石守红,等.齿轮耦合对转子-轴承系统固有特性的影响.机械科 与技术,2003,22(1):66-70
[15]张辉,朱梓根,等.齿轮驱动的转子系统弯扭耦合振动.全国第二界转子动力学学术讨论会文集[C].青岛,1992
[16]夏伯乾,虞烈,等.齿轮-转子-轴承系统弯扭耦合振动模型研究.西安交通大学学报,1997,31(12):93-99
[17]朱勤,谢友柏,等.多根平行轴齿轮转子系统的弯曲耦合振动分析.振动与冲击,1996,15(4):43-47
[18]朱勤.齿轮连接多平行轴系的扭转耦合振动分析.动力工程,1996,16(1):14-17
[19]余光伟.多平行轴齿轮-轴承-转子系统耦合振动的有限元分析.博士学位论文[D].上海大学,1999
[20]余光伟.多平行轴齿轮-轴承-转子系统耦合振动的有限元分析.上海:上海大学出版社,2000
[21]http://www.arla-online.com.
[22]鲁统利.汽车动力传动系扭转振动与整车纵向振动、垂直振动耦合的研究[硕士学位论文].长春:吉林工业大学,1990.
[23]#12
[24]#12
[25]Qin Q H,Mao C X.Coupled torsional-flexural vibration of shaft systems in mechanical engineering-I:finite element model.Computers and Structures,58(1996):835-843.
[26]Mohiuddin M A,Khulief Y A.Coupled bending torsional vibration of rotors using finite element,Journal of Sound and Vibration,223(1999):297-316.
[27]Rao J S,Shiau T N,Chang J R.Theoretical analysis of lateral response due to torsional excitation of geared rotors.Mechanism and Machine Theory,33(1998):761-783.
[28]Li M,Yu L.Analysis of the coupled lateral torsional vibration of a rotor-bearing system with a misaligned gear coupling.Journal of sound and vibration,2001,243(2):283-300.
[29]于百胜,郑钢铁,杜华军.分叉结构系统传递矩阵计算方法.振动与冲击,2003,22(1):93-95.
[30]杨建刚,高亹.改进传递矩阵法计算转子系统不平衡响应和灵敏度.机械工程学报,2001,37(6):109-112.
[31]黄太平.多转子系统振动的子系统分析方法-阻抗耦合法与分振型综合法.振动工程学报,1988,3(1):30-39.
[32]Prohl M A.A general method for calculating critical speeds of flexible rotors.Journal of Applied Mechanics,12(1945):142-148.
[33]Johnson D.C.Modes and frequencies of shafts coupled by straight spur gears.Journal of Mechanical Engineering Science,1962,4:241-250
[34]Fukuma H.,Furukawa T.Fundamental research on gear noise and vibration.Bulletin of JSME,1973,16:1094-1107
[35]Lund J.W.Critical speeds,stability and response of a geared train of rotor.ASME Journal of Mechanical Design,1978,100(3):535-538
[36]D.J.哈特.振动分析的矩阵计算方法.北京:机械工业出版社,1982
[37]晏砺堂,朱梓根,李其汉等.高速旋转机械振动.北京:国防工业出版社.1994:9-12
[38]闻邦椿,顾家柳,夏松波,王正.高等转子动力学--理论、技术与应用.北京:机械工业出版社,1998:20-26
[39]黄太平.转子动力学中传递矩阵阻抗耦合法.航空动力学报,1988,3(4):315-318
[40]蒋书运,陈照波.用整体传递矩阵法计算航空发动机整机临界转速特性.哈尔滨工业大学学报,1998,30(1):32-35.
[41]Horner G C,Pilkey W D.The Riccati transfer matrix method.Journal of Mechanics,100(1978):297-302.
[42]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems.Journal of Sound and Vibration,289(2006):294-333.
[43]Choi S T,Mau S Y.Dynamic analysis of geared rotor-bearing systems by the transfer matrix method.Journal of Mechanical Design,Transactions of the ASME,123(2001):562-568.
[44]李润方,王建军.齿轮系统动力学[M].科学出版社,18-35
[45]Kahraman·A.Dynamic analysis of geared rotors by finite elements·Journal of Mechanical Design[J].Transmissions of ASME,1992,11(4):507-514
[2]小林明.汽车工程手册[M].北京:机械工业出版社,1980.
[3]隋军,王学义,魏德永.传动系的弯曲振动及其对汽车飞轮壳强度影响的研究.汽车技术,1994(6):14-22.
[4]高云凯,吕振华,李卓森.汽车动力总成弯曲振动试验模态分析中的非线性特性.吉林工业大学学报,1996,26(4):6-9.
[5]刘辉,项昌乐,郑慕侨.车辆动力传动系通用扭振模型的研究.中国机械工程,2003,14(15):1282-1285.
[6]Centea D,Rahnejat H,Menday M T.Non-linear multi-body dynamic analysis for the study of clutch torsional vibrations(judder).Applied Mathematical Modeling,25(2001):177-192.
[7]Zou C P,Chen D S,Hua H X.Torsional vibration analysis of complicated multi-brached shafting systems by modal synthesis method.Journal of Vibration and Acoustics,Transaction of ASME,125(2003):317-323.
[8]Crowther A,Zhang N.Torsional finite elements and nonlinear numerical modeling in vehicle powertrain dynamics.Journal of Sound and Vibration,284(2005):825-849.
[9]Crowther A,Zhang N,Liu D Jeyakumaran J M.Analysis and simulation of clutch engagement judder and stick-slip in automotive powertrain systems.Proceedings of the Institution of Mechanical engineers Part D:Journal of Automobile Engineering,218(2004):1427-1446.
[10]http://www.noveri.com.cn
[11]Iannuzzeui R.J.,Elward R.M.Torsional-lateral coupling geared rotors.ASME Paper.1984,71-84
[12]石守红,韩玉强,等.齿轮耦合的转子-轴承系统的研究现状.机械科学与技术,2002,21(5):703-706
[13]伍良生,陈卫福.弯扭耦合齿轮传动系统固有频率与振型计算的传递矩阵法.北京工业大学学报,1999,25(1):94-98
[14]韩玉强,石守红,等.齿轮耦合对转子-轴承系统固有特性的影响.机械科 与技术,2003,22(1):66-70
[15]张辉,朱梓根,等.齿轮驱动的转子系统弯扭耦合振动.全国第二界转子动力学学术讨论会文集[C].青岛,1992
[16]夏伯乾,虞烈,等.齿轮-转子-轴承系统弯扭耦合振动模型研究.西安交通大学学报,1997,31(12):93-99
[17]朱勤,谢友柏,等.多根平行轴齿轮转子系统的弯曲耦合振动分析.振动与冲击,1996,15(4):43-47
[18]朱勤.齿轮连接多平行轴系的扭转耦合振动分析.动力工程,1996,16(1):14-17
[19]余光伟.多平行轴齿轮-轴承-转子系统耦合振动的有限元分析.博士学位论文[D].上海大学,1999
[20]余光伟.多平行轴齿轮-轴承-转子系统耦合振动的有限元分析.上海:上海大学出版社,2000
[21]http://www.arla-online.com.
[22]鲁统利.汽车动力传动系扭转振动与整车纵向振动、垂直振动耦合的研究[硕士学位论文].长春:吉林工业大学,1990.
[23]#12
[24]#12
[25]Qin Q H,Mao C X.Coupled torsional-flexural vibration of shaft systems in mechanical engineering-I:finite element model.Computers and Structures,58(1996):835-843.
[26]Mohiuddin M A,Khulief Y A.Coupled bending torsional vibration of rotors using finite element,Journal of Sound and Vibration,223(1999):297-316.
[27]Rao J S,Shiau T N,Chang J R.Theoretical analysis of lateral response due to torsional excitation of geared rotors.Mechanism and Machine Theory,33(1998):761-783.
[28]Li M,Yu L.Analysis of the coupled lateral torsional vibration of a rotor-bearing system with a misaligned gear coupling.Journal of sound and vibration,2001,243(2):283-300.
[29]于百胜,郑钢铁,杜华军.分叉结构系统传递矩阵计算方法.振动与冲击,2003,22(1):93-95.
[30]杨建刚,高亹.改进传递矩阵法计算转子系统不平衡响应和灵敏度.机械工程学报,2001,37(6):109-112.
[31]黄太平.多转子系统振动的子系统分析方法-阻抗耦合法与分振型综合法.振动工程学报,1988,3(1):30-39.
[32]Prohl M A.A general method for calculating critical speeds of flexible rotors.Journal of Applied Mechanics,12(1945):142-148.
[33]Johnson D.C.Modes and frequencies of shafts coupled by straight spur gears.Journal of Mechanical Engineering Science,1962,4:241-250
[34]Fukuma H.,Furukawa T.Fundamental research on gear noise and vibration.Bulletin of JSME,1973,16:1094-1107
[35]Lund J.W.Critical speeds,stability and response of a geared train of rotor.ASME Journal of Mechanical Design,1978,100(3):535-538
[36]D.J.哈特.振动分析的矩阵计算方法.北京:机械工业出版社,1982
[37]晏砺堂,朱梓根,李其汉等.高速旋转机械振动.北京:国防工业出版社.1994:9-12
[38]闻邦椿,顾家柳,夏松波,王正.高等转子动力学--理论、技术与应用.北京:机械工业出版社,1998:20-26
[39]黄太平.转子动力学中传递矩阵阻抗耦合法.航空动力学报,1988,3(4):315-318
[40]蒋书运,陈照波.用整体传递矩阵法计算航空发动机整机临界转速特性.哈尔滨工业大学学报,1998,30(1):32-35.
[41]Horner G C,Pilkey W D.The Riccati transfer matrix method.Journal of Mechanics,100(1978):297-302.
[42]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems.Journal of Sound and Vibration,289(2006):294-333.
[43]Choi S T,Mau S Y.Dynamic analysis of geared rotor-bearing systems by the transfer matrix method.Journal of Mechanical Design,Transactions of the ASME,123(2001):562-568.
[44]李润方,王建军.齿轮系统动力学[M].科学出版社,18-35
[45]Kahraman·A.Dynamic analysis of geared rotors by finite elements·Journal of Mechanical Design[J].Transmissions of ASME,1992,11(4):507-514