考虑非线性弹性力的滚珠丝杠系统分岔与混沌特性分析

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应用弹性力学位移法及Galerkin法建立了数控机床进给系统滚珠丝杠的数学模型,指出非线性弹性力作用下的滚珠丝杠系统可以用有阻尼的Duffing方程来描述,并用林滋-庞加莱奇异摄动法求得系统的自由振动二次近似解析解.通过参数辨识仿真及试验研究对模型进行验证,发现在进给系统运动过程中,受轴向力、径向力、扭矩等多种载荷作用的影响,滚珠丝杠系统会发生非线性振动,出现分岔及混沌现象,系统刚度随工作台位置的不同而变化,呈现出非线性规律,使运行中的系统固有频率不稳定.根据工作台振动加速度时间序列和频谱图存在的混沌特征,断定进给系统是一个非线性动力学系统,可为数控机床的动态系统辨识提供依据. Adopting the displacement method of elasticity and Galerkin theory,the mathematical model of ball screw is established for feed system of CNC machine tool.It indicates that the ball screw system under nonlinear elastic force can be described by damping Duffing equation,and the approximated quadratic solution is obtained by L-P singular perturbation.Via the simulation of parameter identification and the experimental investigation,it is concluded that the work table carry the axial force,the radial force,the torque and other kinds of load functions in the motor process of feed system,then nonlinear vibration appears,the rigidity changes along with the change of work table position by a nonlinear rule,and the system natural frequency gets unstable.According to the chaos characteristic existing in the vibratory acceleration time series and the frequency spectrogram of the work table,it can be determined that the feed system is a nonlinear dynamic system.