海上柔性并联平台空间动力学建模与分析

Space Dynamic Modelling and Analysis of Offshore HUS Flexible Parallel Platform

针对某海上螺旋副-虎克铰-球铰(HUS)柔性并联平台由快速稳定和大负载引起的支撑连杆弹性变形和负载瞄准位置偏差问题,进行了空间弹性动力学建模。采用模态函数和空间等截面梁单元模型对弹性连杆进行空间建模,基于虎克铰和球铰连接的连杆为两自由度空间运动,推导了空间单元坐标与系统坐标的两自由度转换矩阵,利用平台的运动学和动力学约束条件建立了HUS柔性并联平台的空间弹性动力学方程;运用Newmark方法对弹性动力学方程进行离散求解,分析了平台的弹性动力学响应和支撑连杆的最大动应力,并进行了动力学测试实验;进一步分析了弹性变形对负载瞄准精度的影响。研究结果表明:由弹性变形引起的支撑点最大位移为2.45 mm,且x轴明显大于y轴和z轴;由弹性角位移引起最大位置偏差为1.35 m.实验结果与仿真结果一致,验证了数值建模的有效性。

The space elastic dynamic modelling of parallel platform is created for the elastic deformation and the load pointing displacement error of support link due to the rapid stabilization and large load of offshore HUS flexible parallel platform. Space elastic link is modelled by modal function and space equal section beam element model. The link based on hook joint and ball joint has two degrees of freedom space movement. The transformation matrix of two degrees of freedom between space element coordinate and system coordinate is derived. The kinematic and dynamic constraints of platform are used to establish the space elastic dynamic equations of HUS flexible parallel platform. The elastic dynamic equations are discretely solved by Newmark method. The elastic dynamic response of platform and the maximum dynamic stress of support link are analyzed. And the dynamic test experiment is conducted. The results show that the maximum displacement of support point by elastic deformation is 2. 45 mm,and the error of axis x is significantly greater than those of axes y and z. Experimental results are consistent with the simulated results,thereby validating the effectiveness of the numerical model. The influence of elastic deformation onload pointing accuracy is analyzed,and the maximum position error due to elastic angular displacement is1. 35 m.