主轴热误差的改进累积法建模研究

Modeling Research on Machine Tool Spindle Thermal Error Based on Improved Cumulative Method

为提高机床的加工精度,针对主轴热误差建模,结合最小二乘原理和F分布检验提出了一种改进的累积新算法。对一台立式加工中心,采用激光位移传感器和分布的温度传感器同步测量主轴热变形及温度变化;对获取的建模数据,结合方差分析和F分布检验确定累积阶次K的最小值,在提高热误差建模精度的同时降低算法的复杂度;并进行累积算子求和,构建K(>N+1)阶累积方程组,再运用最小二乘原理得出K阶累积广义均值的正规方程组,最后通过矩阵求解实现回归建模及参数估计。最后,对机床变工况条件下主轴热误差进行了实验与建模预测。结果表明:改进累积法的建模精度高于普通累积法,同时保证了建模效率。

To improve the accuracy and efficiency of machine tool thermal error modeling,a newimproved cumulative method was proposed by using the least squares method and F distribution test.For a vertical machining center,the temperature and thermal deformation of spindle were measured simultaneously by using distributional temperature sensors and laser displacement sensor.The minimum value of cumulative order K was determined by using variance analysis and F distribution test,which can not only improve thermal error modeling accuracy,but also reduce the complexity of algorithm.Cumulative operator sum and K（〉 N ＋ 1）order cumulative equations were built,and then the normal equations of K order cumulative general average were obtained based on the principle of least squares.Regression modeling and parameter estimation were realized by using the matrix calculation.Finally,the thermal error on machine tool spindle under the changing working condition was calculated and the results showthat the modeling accuracy of improved cumulative method is higher than the ordinary cumulative method,while cumulative method model construction time is not far longer than other.