第4期 2017年4月
组合机床与自动化加工技术
Modular Machine Tool & Automatic Manufacturing Technique
文章编号：10012265(2017)04005604
DOI: 10. 13462/j. cenki. mmtamt. 2017. 04. 014
主轴热误差的改进累积法建模研究
衰江，周成一，庄丽阳，邱自学，高传耀
No.4 Apr.2017
（1.南通大学机械工程学院，江苏南通226019：2.南通第五机床有限公司，江苏南通226661）摘要：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，再运用最小二秉原理得出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。关键词：主轴；热误差；累积法：建模
中图分类号：TH161;TG506
文献标识码：A
Modeling Research on Machine Tool Spindle Thermal Error Based on Improved Cumulative Method
YUAN Jiang', ZHOU Cheng-yi', ZHUANG Li-yang', QIU Zi-xue', GAO Chuan-yao
(1. School of Mechanical Engineering, Nantong University, Nantong Jiangsu 226019, China ; 2. Nantong No. 5 Machine Tool Company Lid, Nantong Jiangsu 226661, China)
Abstract : To improve the accuracy and efficiency of machine tool thermal error modeling, a new improved cumulative method was proposed by using the least squares method and F distribution test. For a vertical ma-chining 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 chan-ging working condition was calculated and the results show that the modeling accuracy of improved cumula-tive method is higher than the ordinary cumulative method, while cumulative method model construction
time is not far longer than other.
Key words; spindle; thermal error; cumulative method; modeling
0引言
近年来，随着机床制造水平的快速发展，机床主轴发热导致的变形问题成为影响加工精度的主要原因1)。为有效控制热误差以提高机床加工精度，国内外学者进行了大量的研究，在热误差建模方法上提出了灰色理论、神经网络、最小二乘支持向量机34]等多种算法，这些算法有的精度较高但建模时间长，有的建模精度不够理想、鲁棒性差，因此还需要寻求高效率、高精度的建模算法以适应现场热误差补偿的需要
收稿日期：20160720；修回日期：20160815
累积法具有简单、直观，不直接处理模型的误差项等特点[56]，其建立的模型可以保证平均误差为零，绝对误差最小。袁江"等人成功将其运用到主轴热误差建模上，且建模精度、建模效率相比较传统的最小二乘法已经有所改善。但该方法在应用中也存在以下两个主要问题：①普通累积法采用K=N+1的累积阶次，其建模精度比最小二乘法没有显著改善；②随着累积阶次K的增加，建模精度虽有提高，但计算量增加、建模效率下降[8]
为提高机床主轴热误差建模的精度和效率，本文
*基金项目：江苏省前瞻性联合研究项目（BY201605304）；制通市重大科技创新专项费助（XA2014011）
作者简介：袁江（1968—），男，江苏南通人，南通大学副教投，碳士，研究方向为机电系统测控技术，（E-mail)yuanjiang68@126.com 万方数据