系统参数对DWX型单体液压支柱动力稳定性的影响

Effect of System Parameters on Dynamic Stability of DWX Single Hydraulic Prop

建立了DWX型单体液压支柱的动力学模型,利用Hamilton原理导出了分段表示的运动微分方程.采用有限差分法对微分方程中的空间变量进行离散,得到仅含有时间变量的微分方程组,引入状态变量,得到一阶周期系数状态方程,采用隐式2级4阶Runge-Kutta法求解,根据Floquet理论确定了支柱的动力不稳定区域和稳定性区域.以缸径为100 mm的DWX35型的单体液压支柱为例,讨论了系统参数对支柱动力稳定性的影响.

A dynamic model of DWX single hydraulic prop is established. Differential equations of motion for each part of the hydraulic prop are derived based on the Hamilton＇ s principle. Using the finite difference method and by discretization of spatial variables, differential equations with only time variable are obtained. By introducing state vector, the first order state equations with periodic coefficients is solved by the implicit second class fourth order Runge-Kutta method. Based on the Floquet theory, the principal dynamic instability regions and dynamic stability regions for the hydraulic prop are determined. As an example of DWX35 single hydraulic prop with a cylinder of 100 mm diameter, effects of the system parameters on dynamic stability of the hydraulic prop are discussed.