考虑摩擦影响的重型车床横向进给伺服系统建模与分析

Modeling and Analysis of Cross Feed Servo System of Heavy Duty Lathe Subjected to Friction

进给伺服系统的性能对数控(Computer numerical control,CNC)机床的跟踪及定位精度、零件加工表面质量等有着重要的影响。摩擦的非线性还会导致系统产生爬行行为。结合Karnopp摩擦模型的建模思想,对导轨接触面建立一种改进的Stribeck摩擦模型,针对闭环控制的某重型车床的横向进给系统,建立综合考虑轴的扭转刚度、齿轮的啮合刚度、丝杠螺母副接触刚度、丝杠轴和轴承轴向刚度、导轨接触面摩擦的进给伺服系统的多自由度力学模型和数学模型,研究低速进给下各个刚度变化对工作台输出的影响,找出机械传动系统中的刚度薄弱环节。现场试验测试工作台不同进给位置下的临界爬行速度,得出临界爬行速度与丝杠的轴向刚度的关系,理论分析与试验结果相吻合。所得结论可为该重型车床横向进给伺服系统的优化设计和性能预测提供理论支持。

The performance of feed servo system has an important effect on the path tracking and positioning accuracy of computer numerical control（CNC）machine tool and the machined surface of the workpiece.The nonlinearity of friction can lead to stick-slip behavior of the feed servo system.A modified Stribeck friction model is established based on the ideas of the Karnopp friction model.The cross feed servo system of a heavy duty lathe with closed loop control is studied.The multiple degree of freedom mechanical and mathematical models of the cross feed servo system subjected to torsional stiffness of shaft,meshing stiffness of gears,screw pair contacting stiffness,axial stiffness of the bearing and the ballscrew,kinematical friction force between up and down guide way are established.Effects of stiffness on worktable are studied at low velocity.Also,the weak element of the mechanical transmission system is found out.In the field test,the critical stick slip feed velocity at different feed position is measured.And the relationship between the critical stick slip velocity and the axial stiffness of the ballscrew is obtained.The theoretical analysis and the experiment results match well.The research conclusions can provide theoretical support for the optimal design and performance prediction of feed servo systems of heavy duty lathe.