一种高效的电主轴系统复频率计算方法
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摘要
针对电主轴各向异性轴承-转子系统的特点提出了一种高效的复频率计算方法。该方法用八个动力特性系数代替非线性油膜力,首先对Riccati传递矩阵法进行改进,修改了典型单元的状态向量,采用Riccati分块矩阵递推,直接获得了电主轴系统的特征多项式隐式表达。接着,针对实际工程中只关注系统共振区域中临界转速的现象,先采用幅角原理判定这一共振区域中特征多项式根的个数,再进行求解,求解时就只需求出工程中所关注共振区域内的根,从而提高了求解效率。然后,采用双种群进化策略对电主轴系统特征多项式的根进行求解,该方法避免了传统的抛物线法对初值选取的敏感,可以快速地求得电主轴系统的复频率,且可避免漏根现象。最后,作为算例,对一划分为8个轴段的电主轴系统的复频率作了计算,并与抛物线法进行对比,验证了该方法的高效性。
An efficient method for calculating complex frequency of a motorized spindle supported on anisotropic bearings was presented here. Aiming at the features of the motorized spindle rotor-bearing system,eight dynamic coefficients were used to describe nonlinear oil-film force. The state vector of a typical element was modified. Generally,the eigen-polynomial for a complex rotor-bearing system could be obtained by rearranging the calculations to be performed in an improved Riccati transfer matrix program. The complex frequency calculating problem was formulated as an optimization problem. Bi-group evolution strategy was used to search for the critical speed of a high-speed spindle with its eigen-polynomial. Finally,the presented method was applied to a typical motorized spindle with eight shaft elements. The first five complex frequencies were obtained and compared with those using Muller theoretical method. The results showed that the presented method has a higher efficiency than Muller theoretical method does.
An efficient method for calculating complex frequency of a motorized spindle supported on anisotropic bearings was presented here. Aiming at the features of the motorized spindle rotor-bearing system,eight dynamic coefficients were used to describe nonlinear oil-film force. The state vector of a typical element was modified. Generally,the eigen-polynomial for a complex rotor-bearing system could be obtained by rearranging the calculations to be performed in an improved Riccati transfer matrix program. The complex frequency calculating problem was formulated as an optimization problem. Bi-group evolution strategy was used to search for the critical speed of a high-speed spindle with its eigen-polynomial. Finally,the presented method was applied to a typical motorized spindle with eight shaft elements. The first five complex frequencies were obtained and compared with those using Muller theoretical method. The results showed that the presented method has a higher efficiency than Muller theoretical method does.
引文
[1]熊万里,阳雪兵,吕浪,等.液体动静压电主轴关键技术综述[J].机械工程学报,2009,45(9):2-18.XIONG Wan-li,YANG Xue-bing,LLang,et al.Review on key technology of hydrodynamic and hydrostatic highfrequency motor spindles[J].Journal of Mechanical Engineering,2009,45(9):2-18.
[2]孟杰,陈小安,合烨.高速电主轴电动机-主轴系统的机电耦合动力学建模[J].机械工程学报,2007,43(12):160-165.MENG Jie,CHEN Xiao-an,HE Ye.Electromechanical coupled dynamical modeling of high speed motorized spindle’s motor-spindle subsystems[J].Journal of Mechanical Engineering,2007,43(12):160-165.
[3]陈小安,单文桃,周进明,等.高速电主轴驱动控制技术研究综述[J].振动与冲击,2013,32(8):39-47.CHEN Xiao-an,SHAN Wen-tao,ZHOU Jin-ming,et al.A survey of drive and control technology for high-speed motorized spindle systems[J].Journal of vibration and shock,2013,32(8):39-47.
[4]Lund J W.The stability of an elastic rotor in journal bearing with flexible damped supports[J].ASME Journal of Applied Mechanics,1965,32(4):911-920.
[5]王正.Riccati传递矩阵法的奇点及其消除方法[J].振动与冲击,1987,(2):74-78.WANG Zheng.Singular point and elimination method of Riccati transfer matrix method[J].Journal of Vibration and Shock,1987,(2):74-78.
[6]Murphy B T,Vance J M.An improved method for calculating critical speeds and rotor dynamic stability of turbo machinery[C].Trans of ASME for Power,1983,(5):141-145.
[7]陆颂元.转子系统复频率的传递矩阵-多项式计算法[J].应用力学学报,1986,31(1):73-82.LU Song-yuan.A method for calculating damped critical speeds and stability of rotor-bearing systems[J].Journal of Applied Mechanics,1986,31(1):73-82.
[8]Zu J W,Ji Z.An improved transfer matrix method for steadystate analysis of nonlinear rotor-bearing systems[J].Transactions of the ASME,APRIL,2002(124):302-310.
[9]闻邦椿,顾家柳,夏松波,等.高等转子动力学[M].北京:机械工业出版社,2000.
[10]Beardon A F.Complex analysis[J].The Argument Principle in Analysis and Topology.Chichester,U.K.:Wiley,1979.
[11]夏慧明,梁华,周永权.用双种群进化策略算法求解复函数方程的根[J].计算机工程与应用,2008,44(7):78-81.XIA Hum-ming,LIANG Hua,ZHOU Yong-quan.Novel bigroup evolution strategy algorithm for solving complex functional equation[J].Computer Engineering and Applications,2008,44(7):78-81.
[12]张才稳,瞿红春,陆颂元.转子系统复频率算法中数值溢出问题的研究[J].振动、测试与诊断,1998,18(3):206-210.ZHANG Cai-wen,QU Hong-chun,LU Song-yuan.Research on the problem of overflow in calculating the damped critical speeds of rotor-bearing systems[J].Journal of Vibration,Measurement&Diagnosis,1998,18(3):206-210.
[13]Rusu C,Astola J.Note on argument principle[J].Ieee Signal Processing Letters,2004,11(10):817-820.
[14]Lee Wei-ping,Chien Wan-jou.A novel differential evolution with co-evolution[J].Journal of Computers,2011,6(3):594-602.
[15]熊万里,侯志泉,吕浪,等.基于动网格模型的液体动静压轴承刚度阻尼计算方法[J].机械工程学报,2012,48(23):118-126.XIONG Wan-li,HOU Zhi-quan,LLang,et al.Method for calculating stiffness and damping coefficients of hybrid bearings based on dynamic mesh model[J].Journal of Mechanical Engineering,2012,48(23):118-126.
[2]孟杰,陈小安,合烨.高速电主轴电动机-主轴系统的机电耦合动力学建模[J].机械工程学报,2007,43(12):160-165.MENG Jie,CHEN Xiao-an,HE Ye.Electromechanical coupled dynamical modeling of high speed motorized spindle’s motor-spindle subsystems[J].Journal of Mechanical Engineering,2007,43(12):160-165.
[3]陈小安,单文桃,周进明,等.高速电主轴驱动控制技术研究综述[J].振动与冲击,2013,32(8):39-47.CHEN Xiao-an,SHAN Wen-tao,ZHOU Jin-ming,et al.A survey of drive and control technology for high-speed motorized spindle systems[J].Journal of vibration and shock,2013,32(8):39-47.
[4]Lund J W.The stability of an elastic rotor in journal bearing with flexible damped supports[J].ASME Journal of Applied Mechanics,1965,32(4):911-920.
[5]王正.Riccati传递矩阵法的奇点及其消除方法[J].振动与冲击,1987,(2):74-78.WANG Zheng.Singular point and elimination method of Riccati transfer matrix method[J].Journal of Vibration and Shock,1987,(2):74-78.
[6]Murphy B T,Vance J M.An improved method for calculating critical speeds and rotor dynamic stability of turbo machinery[C].Trans of ASME for Power,1983,(5):141-145.
[7]陆颂元.转子系统复频率的传递矩阵-多项式计算法[J].应用力学学报,1986,31(1):73-82.LU Song-yuan.A method for calculating damped critical speeds and stability of rotor-bearing systems[J].Journal of Applied Mechanics,1986,31(1):73-82.
[8]Zu J W,Ji Z.An improved transfer matrix method for steadystate analysis of nonlinear rotor-bearing systems[J].Transactions of the ASME,APRIL,2002(124):302-310.
[9]闻邦椿,顾家柳,夏松波,等.高等转子动力学[M].北京:机械工业出版社,2000.
[10]Beardon A F.Complex analysis[J].The Argument Principle in Analysis and Topology.Chichester,U.K.:Wiley,1979.
[11]夏慧明,梁华,周永权.用双种群进化策略算法求解复函数方程的根[J].计算机工程与应用,2008,44(7):78-81.XIA Hum-ming,LIANG Hua,ZHOU Yong-quan.Novel bigroup evolution strategy algorithm for solving complex functional equation[J].Computer Engineering and Applications,2008,44(7):78-81.
[12]张才稳,瞿红春,陆颂元.转子系统复频率算法中数值溢出问题的研究[J].振动、测试与诊断,1998,18(3):206-210.ZHANG Cai-wen,QU Hong-chun,LU Song-yuan.Research on the problem of overflow in calculating the damped critical speeds of rotor-bearing systems[J].Journal of Vibration,Measurement&Diagnosis,1998,18(3):206-210.
[13]Rusu C,Astola J.Note on argument principle[J].Ieee Signal Processing Letters,2004,11(10):817-820.
[14]Lee Wei-ping,Chien Wan-jou.A novel differential evolution with co-evolution[J].Journal of Computers,2011,6(3):594-602.
[15]熊万里,侯志泉,吕浪,等.基于动网格模型的液体动静压轴承刚度阻尼计算方法[J].机械工程学报,2012,48(23):118-126.XIONG Wan-li,HOU Zhi-quan,LLang,et al.Method for calculating stiffness and damping coefficients of hybrid bearings based on dynamic mesh model[J].Journal of Mechanical Engineering,2012,48(23):118-126.