基于微分变化构造法的数控机床几何误差补偿方法

为了使得机床误差建模与补偿过程紧密联系,同时避免雅可比矩阵繁琐的计算,提出一种基于微分变化构造法的机床几何误差补偿方法。根据坐标系微分变化矩阵建立机床几何误差模型。基于机床正向运动链顺序建立各个运动轴微分变化矩阵,结合各个运动轴几何误差对应的微分运动矢量计算得到运动轴几何误差对刀具精度影响,相加得到刀具坐标下的综合微分变化矩阵,通过机床正向运动学模型将刀具综合误差转换到工作台坐标系下得到机床刀具位置误差。采用微分变化构造法提取各个运动轴微分变化矩阵相应子矩阵构造得到机床雅可比矩阵,计算刀具坐标系综合误差对应运动轴补偿量得到机床补偿加工代码,微分变化构造法无需额外计算,且重新使用建模过程建立的矩阵。在北京精雕Carver800T加工中心进行实验,补偿后工件总误差降低了30%左右,验证了基于微分变化构造法的几何误差补偿方法的有效性。

Differential Change Construction Based Geometric Error Compensation for Machine Tools

In order to make error compensation of machine tools relate to error modeling closely, and to avoid the tedious calculation of Jacobian matrix, a geometric error compensation method of machine tools based on differential change construction was proposed. At first, geometric error modeling of machine tools was developed using differential change matrices of coordinate frames. According to the forward kinematic chain of the machine tool, differential change matrix of each axis was established. The differential motion vector of each axis was obtained according to the properties of geometric errors. On the basis, the impacts of geometric errors of each axis on the precision of the tool were calculated. The integrated differential motion vector in the coordinate frame of tool was obtained by adding these impacts together. Then, based on homogeneous motion matrix of forward kinematics chain of the machine tool, the integrated geometric error model of the machine tool was established by transforming the integrated differential motion vector to coordinate frame of the working table. Next, the differential change construction was used to extract the corresponding column vector of differential change matrix of each axis to establish Jacobian matrix of the machine tool. The Jacobian matrix can compensate the integrated differential motion vector in the coordinated frame of tool. The differential change construction does not need extra calculation, and reuses the differential change matrices established in modeling. At last, the workpiece cutting experiments were carried out on Carver800T three axis machine tool. The results show that the geometric error compensation based on differential change construction is effective.