球铰接杆式支撑臂展开过程中横向振动分析

Analysis of Transverse Vibration of an ADAM-Type Mast in Deployment Process

针对展开过程中球铰接杆式支撑臂时变构型的横向振动问题,推导了支撑臂等效连续体模型的各向等效刚度,基于Hamilton原理推导了支撑臂展开过程的控制方程,采用加权余量法将偏微分控制方程转化为常微分方程,利用Runge-Kutta法对方程进行了数值求解。计算结果表明:在收拢过程中,支撑臂末端的横向振幅越来越小,收拢过程是安全可靠的;而在展开过程中,末端的横向振幅随展开进程而增加,且振幅随末端负载质量增加而增加;若不考虑锁定冲击,展开速度对支撑臂横向振动的振幅影响可忽略,若考虑锁定带来的周期性冲击时,支撑臂的横向振幅将显著增大。为减小支撑臂的横向振动,必须对支撑臂展开速度加以限制。研究结果为航天器支撑臂在轨展开的控制提供了参考。

To solve the transverse vibration problem of the time-varying configuration of the ADAM-type mast in deploying process, the stiffness of ADAM-type mast is deduced on the basis of the equivalent continuum model, and then the governing equations of transverse vibration during deploying process are yielded based on Hamilton principle. Utilizing the weighted residual method, the partial differential government equations are transformed into ordinary differential equations, and the equations are solved numerically by using Runge-Kutta method. The calculational results show that transverse amplitude of the mast end decreases in retracting process. It means that retraction process is reliable and safe. While in deploying process, the transverse amplitude of the mast end increases with increase of deployment length and tip load of the mast. Effect of deploying velocity on the amplitude could be ignored if lock impact isn＇ t taken into account. If periodic lock impact is considered, the amplitude will increase obviously, and the deploying velocity should be limited to decrease the transverse vibration. The conclusions could be applied in the control of on-orbit deployment of the ADAM-type mast.