多齿轮耦合复杂转子系统的振动特性分析
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摘要
探讨了多对齿轮耦合对齿轮转子系统动力学特性的影响程度,以压缩机转子系统为例,对整个耦合系统进行了安全校核。首先,基于有限元法,建立了通用的弯-扭-轴-摆斜齿轮耦合动力学分析模型,此模型中考虑了啮合刚度、方位角、啮合角、螺旋角以及主动轴转动方向对齿轮啮合刚度矩阵的影响;接着,对系统进行了固有特性分析,得到了系统的临界转速和安全裕度表;然后,基于模态叠加法,对系统进行了不平衡响应分析,对比了考虑齿轮啮合前后系统各位置处的不平衡响应变化曲线。研究结果表明,对于多对齿轮啮合的系统,齿轮间的耦合使系统之间的振动强烈,必须考虑齿轮耦合的影响,并且要结合固有特性以及瞬态响应分析来判断临界转速和振动峰值的大小。
A compressor rotor system was taken for example,the effect of coupled multi-gear meshing on the dynamic characteristics of the rotor system was studied and a safety check for the overall coupled system was conducted.Firstly,based on FEM,a general dynamic lateral-torsional-axial-swinging coupled model for helical gear meshing considering the effect of mesh stiffness,gear position angle,transverse pressure angle,helical angle and the rotating direction of the driving shaft on the gearing mesh stiffness matrix was established.Then,the critical speeds of the system and its safety margin tables were obtained as a result of the analysis of the natural vibration characteristics of the system.Next,the unbalance response of the system was analyzed based on MSM(the mode superposition method).Unbalanced response curves for every gear mesh point were compared before and after meshing.The results demonstrated that the effect of gear couplings must be considered in a multi-gear meshing system because the vibration of the system becomes so strong that its critical speeds and vibration peaks must be judged with the combination between its natural vibration characteristics and transient response analysis.
A compressor rotor system was taken for example,the effect of coupled multi-gear meshing on the dynamic characteristics of the rotor system was studied and a safety check for the overall coupled system was conducted.Firstly,based on FEM,a general dynamic lateral-torsional-axial-swinging coupled model for helical gear meshing considering the effect of mesh stiffness,gear position angle,transverse pressure angle,helical angle and the rotating direction of the driving shaft on the gearing mesh stiffness matrix was established.Then,the critical speeds of the system and its safety margin tables were obtained as a result of the analysis of the natural vibration characteristics of the system.Next,the unbalance response of the system was analyzed based on MSM(the mode superposition method).Unbalanced response curves for every gear mesh point were compared before and after meshing.The results demonstrated that the effect of gear couplings must be considered in a multi-gear meshing system because the vibration of the system becomes so strong that its critical speeds and vibration peaks must be judged with the combination between its natural vibration characteristics and transient response analysis.
引文
[1]Kahraman A,Ozguven H N,Houser D R,et al.Dynamic analysis of geared rotors by finite elements[J].Journal of Mechanical Design,1992,114(3):507-514.
[2]Rao J S,Shiau T N,Chang J R.Theoretical analysis of lateral response due to tensional excitation of geared rotors[J].Mech.Mach.Theory,1998,33(6):761-783.
[3]Lee A S,Ha J W,Choi D H.Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system[J].Journal of Sound and Vibration,2003,263:725-742.
[4]宋雪萍,于涛,李国平等.齿轮轴系弯扭耦合振动特性[J].东北大学学报(自然科学版),2005,26(10):990-993.SONG Xue-ping,YU Tao,LI Guo-ping,et al.Characteris-tics of bending-torsional coupled vibrations of gear shafting[J].Journal of Northeastern University(Natural Science),2005,26(10):990-993.
[5]蒋庆磊,吴大传,谭善光,等.齿轮传动多转子耦合系统振动特性研究[J].振动工程学报,2010,23(3):254-259.JIANG Qing-lei,WU Da-chuan,TAN Shan-guang,et al.Development and application of a model for coupling geared rotors system[J].Journal of Vibration Engineering,2010,23(3):254-259.
[6]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击,2007,26(6):21-25.PANG Hui,FANG Zong-de,OU Wei-lin.Analysis on lateral-torsional coupling vibration characteristics of multi-parallel gear-rotor system[J].Journal of Vibration and Shock,2007,26(6):21-25.
[7]Kahraman A.Dynamic analysis of multi-mesh helical gear train[J].Journal of Mechanical Design,1994,116:706-711.
[8]Kubur M,Kahraman A,Zini D M,et al.Dynamic analysis of a multi-shaft helical gear transmission by finite elements:model and experiment[J].Transactions of the ASME,2004,126:398-406.
[9]Viktor S,Marijonas B.Vehicle gearbox dynamics:center distance influence on mesh stiffness and spur gear dynamics[J].Transport,2010,25(3):278-286.
[10]Cai C,Zheng H,Khan M S,et al.Modeling of material damping properties in ANSYS[A].2002CADFEM Users’Meeting&ANSYS Conference,Germany,2002.
[11]钟一谔,何衍宗,王正,等.转子动力学[M],北京:清华大学出版社,1987.
[2]Rao J S,Shiau T N,Chang J R.Theoretical analysis of lateral response due to tensional excitation of geared rotors[J].Mech.Mach.Theory,1998,33(6):761-783.
[3]Lee A S,Ha J W,Choi D H.Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system[J].Journal of Sound and Vibration,2003,263:725-742.
[4]宋雪萍,于涛,李国平等.齿轮轴系弯扭耦合振动特性[J].东北大学学报(自然科学版),2005,26(10):990-993.SONG Xue-ping,YU Tao,LI Guo-ping,et al.Characteris-tics of bending-torsional coupled vibrations of gear shafting[J].Journal of Northeastern University(Natural Science),2005,26(10):990-993.
[5]蒋庆磊,吴大传,谭善光,等.齿轮传动多转子耦合系统振动特性研究[J].振动工程学报,2010,23(3):254-259.JIANG Qing-lei,WU Da-chuan,TAN Shan-guang,et al.Development and application of a model for coupling geared rotors system[J].Journal of Vibration Engineering,2010,23(3):254-259.
[6]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击,2007,26(6):21-25.PANG Hui,FANG Zong-de,OU Wei-lin.Analysis on lateral-torsional coupling vibration characteristics of multi-parallel gear-rotor system[J].Journal of Vibration and Shock,2007,26(6):21-25.
[7]Kahraman A.Dynamic analysis of multi-mesh helical gear train[J].Journal of Mechanical Design,1994,116:706-711.
[8]Kubur M,Kahraman A,Zini D M,et al.Dynamic analysis of a multi-shaft helical gear transmission by finite elements:model and experiment[J].Transactions of the ASME,2004,126:398-406.
[9]Viktor S,Marijonas B.Vehicle gearbox dynamics:center distance influence on mesh stiffness and spur gear dynamics[J].Transport,2010,25(3):278-286.
[10]Cai C,Zheng H,Khan M S,et al.Modeling of material damping properties in ANSYS[A].2002CADFEM Users’Meeting&ANSYS Conference,Germany,2002.
[11]钟一谔,何衍宗,王正,等.转子动力学[M],北京:清华大学出版社,1987.