为建立高精度的数控机床综合误差补偿模型，提出一种针对机床定位误差的解耦分离建模方法。通过对数控机床温度场与定位误差进行测量，研究机床在不同工况下温度场与定位误差的变化规律，基于该规律定义机床定位误差敏感度的概念，采用灰色关联度算法建立定位误差敏感度矩阵并优化了测温点。根据机床定位误差变化规律，利用多元回归和GM(1,n)算法对机床几何基准误差和热误差进行解耦分离建模，并将上述模型进行线性叠加构建机床定位误差综合模型。在不同工况条件下对一台VXC-560型加工中心进行在线补偿，试验结果表明机床x轴在冷态条件下的定位误差从11.1 μm降低到4.5 μm，降幅为59.5%，在热态条件下的最大定位误差由34.9 μm降低到8.2 μm，降幅为76.5%，并验证了采用误差模型直接驱动机床硬件进行补偿的新思路，具有一定的工程应用前景。
In order to establish a high-precision comprehensive position errors compensation model for CNC machine tools, a positioning error decouple-separating method is put forward. Temperature data and positioning errors are measured for 3-axis CNC machine tools, the variation of temperature fields and positioning error has been studied. Based on this regularity, a new concept of error-sensitive degree is defined, and constructs error-sensitive degree matrix by grey correlation algorithm, and optimizes the measurement point. Though the research of the position error variation, the thermal error and geometric basic error is decoupled and modeled each other by multiple linear regression and GM(1,n) algorithm. Then position error comprehensive model is established by linear superposition method. Though the on-line compensation experiment on VXC-560 type machine tools under different working conditions, the result shows that positioning error of x axis in cold-state is reduced from 11.1 μm to 4.5 μm, decreasing range is 59.5%.The positioning error of x axis in thermal state is reduced from 34.9 μm to 8.2 μm, decreasing range is 76.5%, and verifies the new compensation idea of directly driving hardware by a error model of machine tools. It has certain engineering application prospect.
[1] JOSEF M，JERZY J，ECKART U，et al. Thermal issues in machine tools[J] CIRP Annals Manufacturing Technology，2012，61(2)：771-791.
[2] RAMESH R，MANNAN M A，POO A N. Thermal error measurement and modeling in machine tools：Error compensation in machine tools-a review：Part II：Thermal errors[J]. International Journal of Machine Tools and Manufacture，2000，40(9)：1257-1284.
[3] 王海同，李铁民，王立平，等. 机床热误差建模研究综述[J]. 机械工程学报，2015，51(3)：119-128. WANG Haitong，LI Tiemin，WANG Liping，et al. Model of review on thermal error modeling of machine tools[J]. Journal of Mechanical Engineering，2015，51(3)：119-128.
[4] 要小鹏，殷国富，方辉. 五轴机床误差建模与补偿解析新算法研究[J]. 四川大学学报，2013，21(5)：1084-1089. YAO Xiaopeng，YIN Guofu，FANG Hui. A new synthesis error modeling and compensating algorithm of the five-axis machine tools[J]. Journal of Sichuan University，2013，21(5)：1084-1089.
[5] 张成新，高峰，李艳，等. 基于分段拟合的机床大尺寸工作台热误差补偿模型[J]. 机械工程学报，2015，51(3)：146-152. ZHANG Chengxin，GAO Feng，LI Yan，et al. Model of thermal error compensation of large size worktable for machine tools based on piecewise fitting [J]. Journal of Mechanical Engineering，2015，51(9)：146-152.
[6] 王维，杨建国. 基于插值算法的数控机床复合误差补偿技术[J]. 上海交通大学学报，2014，48(1)：12-15. WANG Wei，YANG Jianguo. Compound error compensation technique for CNC machine tools based on interpolation method[J]. Journal of Shanghai Jiao Tong University，2014，48(1)：12-15.
[7] 阳红，方辉，刘立新，等. 基于热误差神经网络预测模型的机床重点热刚度辨识方法[J]. 机械工程学报，2011，47(11)：117-124. YANG Hong，FANG Hui，LIU Lixin，et al. Method of key thermal stiffness identification on a machine tool based on the thermal error neural network prediction model[J]. Journal of Mechanical Engineering，2011，47(11)：117-124.
[8] ABULSHAHED A M，LONGSTAFF A P，FLETCHE S. The application of ANFIS prediction models for thermal error compensation on CNC machine tools[J]. Applied Soft Computing，2015，27(2)：158-168.
[9] ENEKO G A，AITOR O，JAVIER O，et al. Methodology for the design of a thermal distortion compensation for large machine tools based in state-space representation with Kalman filter[J]. International Journal of Machine Tools & Manufacture，2013，75(11)：100-108.
[10] CUI G W，LU Y，GAO D，et al. A novel error compensation implementing strategy and realizing on Siemens 840D CNC systems[J]. International Journal of Advanced Manufacturing Technology，2012，61(5-8)：595-608.
[11] The International Organization for Standardization. ISO 230-3-2007 test code for machine tools-Part 3 ：Determination of thermal effects [S]. Geneva：International Standard Organization，2007.
[12] LI Y X，YANG J G，GELVIS T. Optimization of measuring point for machine tool thermal error based on grey system theory[J]. International Journal Advance Manufacture Technology，2008(35)：745-750.
[13] ZHU Shaowei，DING Guofu，QIN Shengfeng，et al. Integrated geometric error modeling，identification and compensation of CNC machine tools[J]. International Journal of Machine Tools and Manufacture，2012，52(1)：24-29.
[14] LI Zihan，YANG Jianguo，FAN Kaiguo，et al. Integrated geometric and thermal error modeling and compensation for vertical machining centers[J]. International Journal Advance Manufacture Technology，2015，76(5-8)：1139-1150.
[15] FENG Wenlong，LI Zihan，GU Qunying，et al. Thermally induced positioning error modelling and compensation based on thermal characteristic analysis[J]. International Journal of Machine Tools and Manufacture，2015，93(6)：26-36.
[16] ZHANG Jianfu，FENG Pingfa，CHUANG Chen，et al. A method for thermal performance modeling and simulation of machine tools[J]. The International Journal of Advanced Manufacturing Technology，2013，68(5-8)：1517-1527.
