数控机床几何误差混合径向基函数参数化建模  

Parametric modeling of mixed radial basis functions for geometric errors of CNC machine tools

作　　者：苏哲 郭世杰[1,2] 李帅 吕贺 SU Zhe;GUO Shijie;LI Shuai;LV He(School of Mechanical Engineering,Inner Mongolia University of Technology,Hohhot 010051,China;Inner Mongolia Key Laboratory of Robotics and Intelligent Equipment Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学机械工程学院,内蒙古呼和浩特010051 [2]内蒙古自治区机器人与智能装备技术重点实验室,内蒙古呼和浩特010051

出　　处：《机电工程》2025年第2期339-350,共12页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(52065053,52365058,52365064);内蒙古关键技术攻关项目(2021GG0255);内蒙古自治区高等学校创新团队发展计划支持项目(NMGIRT2213);内蒙古自治区直属高校基本科研业务费项目(ZTY2023005,JY20230043);内蒙古自治区高等学校青年科技英才支持计划项目(NJYT23043);内蒙古自然科学基金资助项目(2023LHMS05018,2023LHMS05017)。

摘　　要：针对数控机床几何误差参数化建模不够快速、准确的问题,提出了一种基于混合径向基函数插值(MRBFI)的几何误差参数化建模方法。首先,基于多体系统理论与齐次变换方法,建立了数控机床的综合误差模型;然后,根据测量辨识得到的机床几何误差项数据,构建了混合径向基函数插值方程,利用最小二乘法与水滴优化算法(WDO),对方程中的宽度系数以及权重系数进行了寻优,在WDO中加入了自适应步长调整,提高了迭代的速度与精度;最后,根据得到的最优解,建立了几何误差径向基函数的参数化模型,利用拟合优度量化了径向基函数插值拟合的精确性,将其应用于对数控机床的几何误差补偿,并比较了补偿前后的球杆仪圆轨迹,从而对结果进行了评估。研究结果表明:混合径向基函数插值拟合优于传统的正交多项式拟合,均方根误差与平均绝对误差较正交多项式拟合减少了52%和65%,误差补偿后圆轨迹圆度误差平均降低了45.2%。该方法可用于数控机床的几何误差补偿,其建模原理简单明了、模型精度高。To address the issue of fast and accurate geometric error parametric modeling of computer numerical control(CNC) machine tools,a geometric error parametric modeling method based on mixed radial basis function interpolation(MRBFI) was proposed.Firstly,the comprehensive error model of the CNC machine tool was established using the theory of the multi-body system and the homogeneous transformation method.Secondly,a hybrid radial basis function interpolation equation was constructed based on geometric error data obtained from measurement and identification processes.The equation incorporated a width coefficient and a weight coefficient,it was optimized by the least square method and the water drop optimization algorithm(WDO).To enhance the iteration speed and accuracy,an adaptive step size adjustment was introduced to the WDO algorithm.Finally,a parametric model of the radial basis function of geometric error was established utilizing the optimal solution derived from the optimization process.The accuracy of the radial basis function interpolation was quantified through the-goodness-of-fit.This compensation was applied to the CNC machine tool,and the results were evaluated by comparing the circular trajectory of the ball instrument before and after compensation.The research results indicate that the mixed radial basis function interpolation outperforms traditional orthogonal polynomial fitting,the root-mean-square error and average absolute error respectively reduce by 52% and 65%.Furthermore,the roundness error of the circular trajectory post-error compensation is reduced by an average of 45.2%,demonstrating significant improvements in error compensation capabilities.Thus,the MRBFI method proves to be an effective approach for geometric error modeling and compensation in CNC machine tools.The method can be used for geometric error compensation of CNC machine tools,and the modeling principle is simple and clear,and the model accuracy is high.

关 键 词：数控机床几何误差补偿 参数化模型 混合径向基函数插值 几何误差补偿 水滴优化算法 自适应步长调整 

分 类 号：TH161[机械工程—机械制造及自动化] TG659[金属学及工艺—金属切削加工及机床]