混合链式液压调平机构的动力学特性

Dynamic characteristic of hydraulic leveling mechanism with a hybrid kinematic chain

为了研究混合链式液压调平机构的举升能力和调平能力等动力学性能,对举升过程中作平动的工作平台的欧拉角微分表达式和变分表达式进行改写,基于拉格朗日法建立调平机构的动力学数学模型,其过程包括采用复数矢量法建立各刚体质心速度方程、推导调平机构的动能方程、基于虚功原理推导调平机构的广义力方程、推导各液压油缸驱动力的动力学解析解。利用MATLAB软件对所建数学模型进行工程实例仿真,分析不同负载下3个液压油缸的驱动力,并对仿真结果进行试验验证。研究结果表明:自动液压油缸驱动力和从动液压油缸驱动力与变幅液压油缸驱动力相比对负载变化更敏感;自动液压油缸驱动力和从动液压油缸驱动力的相对大小由两者的缸筒内径和活塞杆直径决定,所建立的各液压油缸驱动力的解析解既可用于工程设计计算和分析,也可用于机构优化设计。

To research the dynamic performance of the hydraulic leveling mechanism with a hybrid kinematic chain,such as lifting capacity and leveling ability,a dynamic mathematical model was established based on the Lagrange approach after rewriting the differential expression and the variational expression for the Euler angle of the working platform in the lifting process.The process were as follows:the complex vector method was used to establish the mass center velocity equations of the rigid bodies;the kinetic energy equation of the leveling mechanism was derived;the generalized force equations of the leveling mechanism were derived based on the principle of virtual work,and the dynamic analytical solutions of the driving forces of each hydraulic cylinder were deduced.The MATLAB software was used to simulate the mathematical model,and the driving forces of three hydraulic cylinders under different loads were analyzed.The simulation results were tested and verified by experiments.The results show that both loads of automatic hydraulic cylinder and driven hydraulic cylinder are more sensitive than the load of luffing hydraulic cylinder when different loads are applied in the working platform.The relative size of the load of automatic hydraulic cylinder and that of the driven hydraulic cylinder is determined by the diameters of the non-rod chamber and the piston rod.The analytic solutions of the loads of hydraulic cylinders can be used both in engineering design calculation and mechanism optimization design.