一种高效的电主轴系统复频率计算方法  

An efficient method for calculating complex frequency of a motorized spindle

作　　者：毛文贵[1,2] 刘桂萍[1] 韩旭[1] 郭维祺[1] 林禄生 

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]湖南工程学院机械工程学院,湘潭411101

出　　处：《振动与冲击》2014年第19期164-168,174,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金11202073;高等学校博士学科点专项科研基金(20130161130001);科技重大专项2012(2012ZX04002-091)

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.

关 键 词：电主轴 复频率 改进的Riccati传递矩阵法 幅角原理 双种群进化策略 

分 类 号：TH113.1[机械工程—机械设计及理论]