固体火箭发动机药柱整形装备机电耦联动力学建模与计算

Dynamical Modeling and Computation on Electromechanical Coupling System of Grain Reshaping Machine Tool for Solid Propellant Rocket Motor

机电耦联系统动力学系统是典型的多输入、多输出、非线性、强耦合、不确定性系统。机电耦联系统动力学的建模与计算对于深入研究机电一体化装备整机动力学性能,改善控制精度等方面具有重要意义。据此,针对固体火箭药柱整形装备主轴部件2自由度机电耦联系统,运用Park变换推导该系统基于伺服电动机dq0坐标系的拉格朗日-麦克斯韦方程,建立包括机构、伺服电动机和控制器的系统微分方程组。该机电耦联动力学建模方法不需测量电动机的磁路尺寸。只要测量电动机dq0坐标系绕组电感和永磁体磁链的幅值就可直接列出微分方程,推导简洁高效,便于应用。动力学微分方程求解采用稳定性较好、数值精度较高的Hamming方法实现方程组高效的求解。仿真结果证明动力学微分方程推导正确,求解高效。

Electromechanical coupling dynamical system is representative multi-input, multi-output, non-linear, tight coupling, and uncertain system. Dynamical modeling and calculation of eleetromechanical coupling system play an important role in the deep exploration of dynamical-performance and improvement of control accuracy for complete electromechanical equipment. Thus, Lagrange-Maxwell equations have been deduced based on 2-DOF electromechanical coupling system and spindle unit of grain refitted machine tool for solid propellant rocket motor by using Park transform in dq0 coordinate system of servomotor. In this dynamical modeling method of electromechanical coupling system, to establish dynamical differential equations, it is needed to measure amplitude of the flux induced by the permanent magnets and the winding＇s inductance in dq0 reference of the motor but not to measure the size of magnetic circuit. The equations deduction is terse, efficient, and the equations are easy to use. System differential equations have been established that include mechanism, servomotor and controller, which could be solved efficiently by Hamming method with high numerical accuracy and stability. The results of computer simulation prove the preciseness of formulation deduced and efficiency of differential equations solved.