Abstract The feed system of machine tool has complex nonlinear dynamic behaviors in the process of machining, which will affect the machining accuracy of parts. The two-degrees-of-freedom dynamical model of the feed system with clearance and friction is established, where the torsion and load disturbance are considered. By using the averaging method, the approximate analytical solution of the feed system of the machine tool is solved. The approximate analytical solutions are verified by the numerical solutions, when the worktable moves at a constant speed or the worktable is at the working point. And the approximate analytical solutions are in good agreement with the numerical solutions. According to the Lyapunov stability analysis, the stability of the steady-state solutions of system is judged by the maximum real part of the eigenvalues. The analysis results show that, the amplitude of the amplitude-frequency response of system decreases when the friction force increases. As the clearance increases, the resonance frequency decreases gradually. When the lead of the ball screw increases, the resonance frequency increases gradually. The numerical simulation analysis of the system shows that when the worktable is at the working point, the angle displacement of the lead screw chatters while it reaches the maximum or minimum value of the vibration angle displacement.

中文翻译：

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带间隙和摩擦的二自由度机床进给系统的强迫振动

摘要 机床进给系统在加工过程中具有复杂的非线性动态行为，会影响零件的加工精度。建立了带间隙和摩擦的进给系统的二自由度动力学模型，其中考虑了扭转和载荷扰动。采用平均法求解机床进给系统的近似解析解。当工作台匀速运动或工作台处于工作点时，近似解析解通过数值解进行验证。并且近似解析解与数值解非常吻合。根据李雅普诺夫稳定性分析，系统稳态解的稳定性由特征值的最大实部来判断。分析结果表明，随着摩擦力的增加，系统幅频响应的幅值减小。随着间隙的增加，共振频率逐渐降低。当滚珠丝杠的导程增加时，共振频率逐渐增加。系统的数值模拟分析表明，当工作台处于工作点时，丝杠角位移在达到振动角位移的最大值或最小值时发生颤振。