滚珠丝杠进给系统的仿真建模

为在设计阶段获得滚珠丝杠进给系统相对精确的二阶数学模型,提出基于Lyapunov稳定性理论建立模型参考自适应系统,以二阶系统为参考模型,以理论模型为控制对象的仿真建模方法。结合实例,建立考虑粘性摩擦和传动刚度的滚珠丝杠进给系统理论模型,运用MATLAB/Simulink建立模型参考自适应系统仿真模型,并用仿真结果推导出进给系统二阶数学模型。结果表明:二阶模型的输出能很好地跟踪理论模型输出;对两模型输入1ms单位脉冲信号时,相对误差在0.314%以内。

Simulation modeling of ball screw feed drive systems

In order to obtain a relatively accurate second-order mathematical model of the feed drive in the design stage, a simulation modeling method was proposed to establish the model reference adaptive system based on Lyapunov stability theory, with the second-order model serving as reference model, and the theoretical model as controlled plant. A mechanical model for the ball-screw feed drive was established with due consideration of the viscous friction and transmission stiffness, a simulation model of the model reference adaptive system was constructed using MATLAB Software, and a second-order model of the feed drive system was derived from the simulation results of case study. The result indicates that the output of the second-order model can perfectly track that of the theoretical model, and the relative error between the two models is within 0.314% when 1 ms pulse signal imposed at the same time.