滚珠丝杠进给系统仿真建模

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In order to obtain a relatively accurate second-order mathematical model of a ball screw feed drive system in design stage, a simulation modeling method was proposed to establish a model reference adaptive system based on Lyapunov stability theory with a second-order system as a reference model and the theoretical model as a controlled object. A mechanical model for the ball-screw feed drive system was established with consideration of viscous friction and transmission stiffness, a simulation model of the model reference adaptive system was constructed using MATLAB/ Simulink, and a second-order methematical model of the feed drive system was deduced from the simulation results of case study. The results indicated that the output of the second-order model can perfectly track that of the theoretical model, and the relative error between the results of the two models is within 0. 314% when 1 ms pulse signal imposes at the same time.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。