一种高效的电主轴系统复频率计算方法

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (19) : 164-168.

论文

一种高效的电主轴系统复频率计算方法

毛文贵1, 2 刘桂萍1 韩旭1 郭维祺1 林禄生1

作者信息 +

A High Efficient Method for Calculating Complex Frequency of the Motorized Spindle

MAO Wengui 1, 2 LIU Guiping 1 HAN Xu 1 GUO Weiqi 1 LIN Lusheng 1

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文章历史 +

摘要

本文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，验证了本文方法的高效性。

Abstract

This paper presents a high efficient method for calculating complex frequency of the motorized spindle supported on anisotropic bearings. Directed against the special structure of the motorized spindle, the eight dynamic coefficients are used to describe the nonlinear oil- film force. The status vector of typical unit was modified．Generally, the characteristic polynomial for a complex rotor-bearing system can be obtained by rearranging the calculations performed in an improved Riccati transfer matrix program. This can derive the characteristic polynomial for a complex rotor-bearing system. The modeling procedures are identical for the rotor and bearing, including the effects of gyroscopic, damping, and any or all destabilizing influences which are linearized in the usual manner. Complex frequency can be estimated and stability predicted by argument principle with greater efficiency and without missing any modes. The complex frequency calculating problem is formulated as an optimization problem. Bi-group evolution strategy is used to search for the critical speed of the high-speed spindle with the characteristic polynomial. Finally, the present method is applied to a typical motorized spindle with eight main shaft elements. The lowest five complex frequency are obtained and compared with Muller theoretical method. The results show that the present method has higher efficiency than Muller theoretical method.

导出引用

毛文贵; 刘桂萍韩旭郭维祺林禄生. 一种高效的电主轴系统复频率计算方法[J]. 振动与冲击, 2014, 33(19): 164-168

MAO Wengui; LIU Guiping HAN Xu GUO Weiqi LIN Lusheng . A High Efficient Method for Calculating Complex Frequency of the Motorized Spindle [J]. Journal of Vibration and Shock, 2014, 33(19): 164-168