GA-SVR Model for Predicting Geometric Errors of CNC Machine Tools
-
摘要: 为了统一数控机床在机测量系统不同几何误差建模方法,并建立更精确的几何误差模型。仅考虑速度和空间位置对机床误差的影响,提出一种遗传算法优化支持向量回归机(GA-SVR)建模方法。以X轴为例,利用BP、GA-BP、SVR和GA-SVR算法建立误差模型,进行了建模精度比较。试验结果表明,基于GA-SVR算法的3种几何误差建模精度更高,定位误差、直线度误差和角度误差预测值与实测真值的最大残差分别为0.179 6 μm、0.067 57 μm和0.019 2",更适合于机床3种几何误差精确建模和误差补偿。Abstract: In order to unify the number of geometric error modeling methods for the machine measurement system, a more accurate geometric error model is established. Only the effect of the speed and spatial position on the machine error, a genetic algorithm to optimize the supporting vector return machine (GA-SVR) modeling methodis proposed. Taking the X-axis as an example, the error model is established by BP, GA-BP, SVR and GA-SVR algorithm, and modeling accuracy is compared. The experimental results show that the three geometric error based on the GA-SVR algorithm are higher, the maximum residuals of positioning errors, linearity errors, and angular error predictive values and measured truth are 0.179 6 μm, 0.067 57 μm and 0.019 2", respectively. More suitable for three geometric errors of machine tools and precise modeling and error compensation.
-
Key words:
- CNC machine tools /
- geometric error /
- GA-SVR /
- influencing factors /
- error modeling
-
表 1 加工中心21项几何误差
误差分类 X轴 Y轴 Z轴 垂直度误差 位置误差 沿X $ {\delta _x}(x) $ $ {\delta _x}(y) $ $ {\delta _x}({\textit{z}}) $ ${\varepsilon _{XY} }$ 沿Y $ {\delta _y}(x) $ $ {\delta _y}(y) $ $ {\delta _y}({\textit{z}}) $ 沿Z $ {\delta _{\textit{z}}}(x) $ $ {\delta _{\textit{z}}}(y) $ $ {\delta _{\textit{z}}}({\textit{z}}) $ $ {\varepsilon _{XZ}} $ 角度误差 绕X $ {\varepsilon _x}(x) $ $ {\varepsilon _x}(y) $ $ {\varepsilon _x}({\textit{z}}) $ 绕Y $ {\varepsilon _y}(x) $ $ {\varepsilon _y}(y) $ $ {\varepsilon _y}({\textit{z}}) $ $ {\varepsilon _{YZ}} $ 绕Z $ {\varepsilon _{\textit{z}}}(x) $ $ {\varepsilon _{\textit{z}}}(y) $ $ {\varepsilon _{\textit{z}}}({\textit{z}}) $ 表 2 不同位置下4种算法建模比较
算法建模 BP神经网络 GA-BP算法 SVR GA-SVR X定位
误差均方误差/μm2 1.960 0 0.528 0 0.006 737 0.000 084 72 最大残差/μm 2.099 7 2.066 0 0.279 5 0.179 6 Y向直线度
误差均方误差/μm2 2.567 6 1.289 8 0.011 94 0.000 095 34 最大残差/μm 2.846 2 2.812 2 0.874 8 0.024 9 Z向直线度
误差均方误差/μm2 6.855 4 5.875 2 0.007 065 0.000 096 53 最大残差/μm −4.2913 −4.012 0 −1.123 3 0.032 9 X俯仰角
误差均方误差/("2) 0.334 0 0.016 6 0.000 653 0 0.000 084 07 最大残差/(") −0.324 7 −0.292 0 0.148 8 0.019 2 X偏摆角
误差均方误差/("2) 0.019 06 0.014 2 0.002 414 0.000 090 44 最大残差/(") −0.283 5 0.217 4 −0.231 4 0.017 1 表 3 不同速度下4种算法建模比较
算法建模 BP神经网络 GA-BP算法 SVR GA-SVR X定位误差 均方误差/μm2 1.233 5 0.707 9 0.010 62 0.000 099 80 最大残差/μm −2.760 1 −1.389 0 −0.567 2 0.022 1 Y向直线度误差 均方误差/μm2 0.711 8 0.405 6 0.001 362 0.000 098 37 最大残差/μm −1.314 0 −1.259 1 −0.280 2 0.025 4 Z向直线度误差 均方误差/μm2 0.839 3 0.186 4 0.000 346 3 0.000 098 94 最大残差/μm −1.872 9 −0.610 7 0.328 6 0.067 57 X俯仰角误差 均方误差/("2) 0.016 8 0.008 7 0.004 823 0.000 088 94 最大残差/(") 0.224 2 0.197 5 −0.099 3 0.005 7 X偏摆角误差 均方误差/("2) 0.021 8 0.016 8 0.003 9 0.000 098 29 最大残差/(") 0.293 8 −0.115 1 −0.106 4 0.005 6 -
[1] 董泽圆, 李杰, 刘辛军, 等. 数控机床两种几何误差建模方法有效性试验研究[J]. 机械工程学报, 2019, 55(5): 137-147 doi: 10.3901/JME.2019.05.137DONG Z Y, LI J, LIU X J, et al. Experimental study on the effectiveness of two different geometric error modeling methods for machine tools[J]. Journal of Mechanical Engineering, 2019, 55(5): 137-147 (in Chinese) doi: 10.3901/JME.2019.05.137 [2] 李金和. 基于体对角线误差检测的数控机床几何误差辨识方法研究[J]. 组合机床与自动化加工技术, 2019(1): 79-85LI J H. An identification strategy research of CNC machine tool geometric errors based on body diagonal errors measurement[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2019(1): 79-85 (in Chinese) [3] 杜正春, 杨建国, 冯其波. 数控机床几何误差测量研究现状及趋势[J]. 航空制造技术, 2017(6): 34-44DU Z C, YANG J G, FENG Q B. Research status and trend of geometrical error measurement of CNC machine tools[J]. Aeronautical Manufacturing Technology, 2017(6): 34-44 (in Chinese) [4] 郭世杰, 姜歌东, 梅雪松, 等. 转台-摆头式五轴机床几何误差测量及辨识[J]. 光学 精密工程, 2018, 26(11): 2684-2694 doi: 10.3788/OPE.20182611.2684GUO S J, JIANG G D, MEI X S, et al. Measurement and identification of geometric errors for turntable-tilting head type five-axis machine tools[J]. Optics and Precision Engineering, 2018, 26(11): 2684-2694 (in Chinese) doi: 10.3788/OPE.20182611.2684 [5] ZHANG Y, YANG J G, XIANG S T, et al. Volumetric error modeling and compensation considering thermal effect on five-axis machine tools[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2013, 227(5): 1102-1115 doi: 10.1177/0954406212456475 [6] 王建平, 戴一帆, 洪晓丽. 精密机床神经网络法精度建模[J]. 国防科技大学学报, 2002, 24(1): 89-93 doi: 10.3969/j.issn.1001-2486.2002.01.021WANG J P, DAI Y F, HONG X L. Neural network method of accuracy model building for precision machine tools[J]. Journal of National University of Defense Technology, 2002, 24(1): 89-93 (in Chinese) doi: 10.3969/j.issn.1001-2486.2002.01.021 [7] FAN K G, YANG J G, YANG L Y. Orthogonal polynomials-based thermally induced spindle and geometric error modeling and compensation[J]. The International Journal of Advanced Manufacturing Technology, 2013, 65(9-12): 1791-1800 doi: 10.1007/s00170-012-4301-2 [8] FAN K G, YANG J G, YANG L Y. Unified error model based spatial error compensation for four types of CNC machining center: Part II—unified model based spatial error compensation[J]. Mechanical Systems and Signal Processing, 2014, 49(1-2): 63-76 doi: 10.1016/j.ymssp.2013.12.007 [9] 冯文龙, 沈牧文, 姚晓栋, 等. 大型龙门机床的直线度误差建模及误差补偿[J]. 哈尔滨工业大学学报, 2015, 47(7): 31-36 doi: 10.11918/j.issn.0367-6234.2015.07.004FENG W L, SHEN M W, YAO X D, et al. Modeling for straightness error of large CNC gantry type machine tools and error compensation[J]. Journal of Harbin Institute of Technology, 2015, 47(7): 31-36 (in Chinese) doi: 10.11918/j.issn.0367-6234.2015.07.004 [10] 肖慧孝, 姚晓栋, 冯文龙, 等. 大型数控机床导轨直线度误差测量与实时补偿[J]. 机械科学与技术, 2015, 34(1): 90-93XIAO H X, YAO X D, FENG W L, et al. The Straightness error measurement and real-time compensation of large CNC machine tool guideways[J]. Mechanical Science and Technology for Aerospace Engineering, 2015, 34(1): 90-93 (in Chinese) [11] 杨洪涛, 耿金华, 丁小瑞, 等. 数控机床力-几何误差的PSO-SVM建模[J]. 应用科学学报, 2014, 32(3): 325-330 doi: 10.3969/j.issn.0255-8297.2014.03.015YANG H T, GENG J H, DIN X R, et al. Force-geometric error modeling of CNC machine tools using PSO-SVM[J]. Journal of Applied Sciences, 2014, 32(3): 325-330 (in Chinese) doi: 10.3969/j.issn.0255-8297.2014.03.015 [12] 周恒飞, 叶文华, 郭云霞, 等. 基于支持向量回归机的数控机床几何误差元素建模研究[J]. 航空制造技术, 2019, 62(17): 50-57ZHOU H F, YE W H, GUO Y X, et al. Research on geometric error modeling of CNC machine tools based on support vector regression[J]. Aeronautical Manufacturing Technology, 2019, 62(17): 50-57 (in Chinese) [13] 苗恩铭, 龚亚运, 成天驹, 等. 支持向量回归机在数控加工中心热误差建模中的应用[J]. 光学 精密工程, 2013, 21(4): 980-986 doi: 10.3788/OPE.20132104.0980MIAO E M, GONG Y Y, CHENG T J, et al. Application of support vector regression machine to thermal error modelling of machine tools[J]. Optics and Precision Engineering, 2013, 21(4): 980-986 (in Chinese) doi: 10.3788/OPE.20132104.0980 [14] 余文利, 姚鑫骅, 傅建中, 等. 贝叶斯证据框架下的LS-SVM多工况数控机床热误差建模[J]. 中国机械工程, 2014, 25(17): 2361-2368 doi: 10.3969/j.issn.1004-132X.2014.17.017YU W L, YAO X H, FU J Z, et al. Modeling of CNC machine tool thermal errors based on LS-SVM within Bayesian evidence framework[J]. China Mechanical Engineering, 2014, 25(17): 2361-2368 (in Chinese) doi: 10.3969/j.issn.1004-132X.2014.17.017 [15] 谭峰, 萧红, 张毅, 等. 基于统一框架的数控机床热误差建模方法[J]. 仪器仪表学报, 2019, 40(10): 95-103TAN F, XIAO H, ZHANG Y, et al. Thermal error modeling method of CNC machine tool based on unified framework[J]. Chinese Journal of Scientific Instrument, 2019, 40(10): 95-103 (in Chinese)