数控插齿机的误差建模与误差补偿解耦

Error Modeling and Error Compensation Decoupling of CNC Gear Shaper

为提高数控插齿加工精度,需对其误差进行补偿。通过分析插齿机床的运动特点,建立了插齿机运动模型;基于机床误差运动学原理,推导出用齐次变换矩阵描述的刀具相对于工件的误差模型;基于小误差补偿运动假设和微分变换原理,对各轴运动副的误差补偿量与刀具相对于工件的位置及方向误差模型间存在的耦合关系进行了解耦,获得了影响插齿加工精度的各运动副位置或方向误差补偿量。

In order to improve the machining accuracy of a CNC gear shaper,the errors should be compensated. The motion characteristics of the CNC gear shaper were analyzed and a motion model was created. The error model of tool related to the part was established with the homogeneous trans- formation matrix. Couples effects exited between the joint variables and position/orientation of the cutting points. Adjusting one joint usually resulted in changes in multiple components in the tool-- part relation. A volumetric error compensation model was created by coupling the error compensation motions based on the rigid body kinematics with small error assumption and coordinate transformation method. Finally, the position and orientation compensation values of the joint variables can be ob- tained with the model, which gives the theoretical basis of the error compensation for the machine.