基于向量投影响应面的数控机床几何误差分配方法

doi:10.13229/j.cnki.jdxbgxb20211089

吉林大学学报(工学版) ›› 2022, Vol. 52 ›› Issue (2): 384-391.doi: 10.13229/j.cnki.jdxbgxb20211089

• 车辆工程·机械工程 • 上一篇

基于向量投影响应面的数控机床几何误差分配方法

章子玲¹(),胡雄¹,亓寅²,王微¹,陶志强³,刘志峰^4,⁵()

^1.上海海事大学物流工程学院，上海 201306
^2.鹰潭市技工学校，鹰潭 335001
^3.北京联合大学机器人学院，北京 100027
^4.吉林大学数控装备可靠性教育部重点实验室，长春 130022
^5.吉林大学机械与航空航天工程学院，长春 130022

收稿日期:2021-10-22 出版日期:2022-02-01 发布日期:2022-02-17
通讯作者: 刘志峰 E-mail:zhangziling1119@126.com;lzfjlu@jlu.edu.cn
作者简介:章子玲（1987-），女，讲师，博士.研究方向：结构机构可靠性设计及精度设计，起重机械信号处理及状态评估，智能算法.E-mail：zhangziling1119@126.com
基金资助:
国家自然科学基金项目(51905334);国家科技重大专项项目(2019ZX04001001);上海市青年科技英才扬帆计划项目(19YF1418600)

An approach for error allocation of machine tool based on vector projection response surface method

Zi-ling ZHANG¹(),Xiong HU¹,Yin QI²,Wei WANG¹,Zhi-qiang TAO³,Zhi-feng LIU^4,⁵()

^1.Logistics Engineering College，Shanghai Maritime University，Shanghai 201306，China
^2.Yingtan Vocational and Technical College，Yingtan，335001，China
^3.College of Robotics，Beijing Union University，Beijing 100027，China
^4.Key Laboratory of CNC Equipment Reliability，Ministry of Education，Jilin University，Changchun 130022，China
^5.School of Mechanical and Aerospace Engineering，Jilin University，Changchun 130012，China

Received:2021-10-22 Online:2022-02-01 Published:2022-02-17
Contact: Zhi-feng LIU E-mail:zhangziling1119@126.com;lzfjlu@jlu.edu.cn

摘要/Abstract

摘要：

以几何误差为研究对象，基于多体系统理论，建立了数控机床综合误差模型；运用向量投影响应面法，建立了加工精度可靠度模型和可靠性敏感度模型，以评估加工精度可靠度并获取几何误差分布参数对可靠度的影响排序，实现几何误差参数的合理优化和可靠度的整体提升。最后，通过案例分析验证了该方法的正确性。

关键词: 数控机床, 加工精度可靠度, 敏感度, 向量投影响应面法

Abstract:

Taking the geometric errors as the research object， this paper presents an approach for the error allocation of CNC machine tool based on the vector projection response surface. Based on the multi-body system theory， a comprehensive error model of machine tool was established to reveal the quantitative relationship between the machining accuracy and geometric errors of the machine tool； by applying the vector projection response surface method， a machining accuracy reliability model was developed to predict and evaluate the machining ability of machine tools， then a machining accuracy reliability sensitivity model was proposed to sequence the influence of distribution parameters of geometric errors on the machining accuracy reliability， and therefore it conducted the identification and optimization of the geometric errors which have larger affect to the machining accuracy reliability. Hence， a general approach for the error allocation of machine tools was formed to realize the reasonable optimization of the geometric error parameters and overall improvement of machining ability of machine tool. The proposed approach was implemented to a four-axis CNC machining center， and the results verified the effectiveness and competitiveness of the approach.

Key words: CNC machine tool, machining accuracy reliability, sensitivity, vector projection response surface method

中图分类号:

TH161

章子玲,胡雄,亓寅,王微,陶志强,刘志峰. 基于向量投影响应面的数控机床几何误差分配方法[J]. 吉林大学学报(工学版), 2022, 52(2): 384-391.

Zi-ling ZHANG,Xiong HU,Yin QI,Wei WANG,Zhi-qiang TAO,Zhi-feng LIU. An approach for error allocation of machine tool based on vector projection response surface method[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 384-391.

图/表 6

图1

表1

数控机床的理想特征矩阵和误差特征矩阵"

相邻体	体间理想静止、理想运动特征矩阵	体间实际静止、运动误差特征矩阵
0-1 X轴	$C 01 p = I 4 × 4$	$Δ C 01 p = I 4 × 4$
0-1 X轴	$C 01 s = 100 x 010000100001$	$Δ C 01 s = 1 - Δ γ x Δ β x Δ x x Δ γ x 1 - Δ α x Δ y x - Δ β x Δ α x 1 Δ z x 0001$
1-2 Y轴	$C 12 p = I 4 × 4$	$Δ C 12 p = 1 - Δ γ x y 00 Δ γ x y 100 00100001$
1-2 Y轴	$C 12 s = 1000 010 y 00100001$	$Δ C 12 s = 1 - Δ γ y Δ β y Δ x y Δ γ y 1 - Δ α y Δ y y - Δ β y Δ α y 1 Δ z y 0001$
0-4 Z轴	$C 04 p = I 4 × 4$	$Δ C 04 p = 10 Δ β x z 0 01 - Δ α y z 0 - Δ β x z Δ α y z 10 0001$
0-4 Z轴	$C 04 s = 10000100 001 z 0001$	$Δ C 04 s = 1 - Δ γ z Δ β z Δ x z Δ γ z 1 - Δ α z Δ y z - Δ β z Δ α z 1 Δ z z 0001$
4-5 B轴	$C 45 p = I 4 × 4$	$Δ C 45 p = 1 - Δ γ y b 00 Δ γ y b 1 - Δ α y b 0 0 Δ α y b 1 Δ z y b 0001$
4-5 B轴	$C 45 s = c o s B 0 - s i n B 0 0100 s i n B 0 c o s B 0 0001$	$Δ C 45 s = 1 - Δ γ B Δ β B Δ x B Δ γ B 1 - Δ α B Δ y B - Δ β B Δ α B 1 Δ z B 0001$

表1

图2

图3

图4

图5

参考文献 21

1	Zhang Zi-ling, Liu Zhi-feng, Cai Li-gang, et al. An accuracy design approach for a multi-axis NC machine tool based on reliability theory[J]. The International Journal of Advanced Manufacturing Technology, 2017, 91(5-8): 1547-1566.
2	Zhang Zi-ling, Qi Yin, Cheng Qiang, et al. Machining accuracy reliability during the peripheral milling process of thin-walled components[J]. Robotics and Computer Integrated Manufacturing, 2019, 59: 222-234.
3	刘志峰, 刘广博, 程强, 等. 基于多体系统理论的精密立式加工中心精度建模与预测[J]. 吉林大学学报: 工学版, 2012, 42(2): 388-391.
	Liu Zhi-feng, Liu Guang-bo, Cheng Qiang, et al. Precision modeling and prediction of precise vertical machining center based on theory of multi-body system[J]. Journal of Jilin University(Engineering and Technology Edition), 2012, 42(2): 388-391.
4	Cai Li-gang, Zhang Zi-ling, Cheng Qiang, et al. A geometric accuracy design method of multi-axis NC machine tool for improving machining accuracy reliability[J]. Eksploatacja I Niezawodnosc-Maintenance and Reliability, 2015, 17(1): 143-155.
5	Cai Li-gang, Zhang Zi-ling, Cheng Qiang, et al. An approach to optimize the machining accuracy retainability of multi-axis NC machine tool based on robust design[J]. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2016, 43: 370-386.
6	曲兴田, 赵永兵, 刘海忠, 等. 基串并混联机床几何误差建模与实验[J]. 吉林大学学报: 工学版, 2017, 47(1): 137-144.
	Qu Xing-tian, Zhao Yong-bing, Liu Hai-zhong, et al. Modeling and experiment of spatial geometric errors of hybrid serial parallel machine tool[J]. Journal of Jilin University(Engineering and Technology Edition), 2017, 47(1): 137-144.
7	李国龙, 陶小会, 徐凯, 等. 数控机床转台位置相关几何误差的快速测量与辨识[J]. 吉林大学学报: 工学版, 2021, 51(2): 458-467.
	Li Guo-long, Tao Xiao-hui, Xu Kai, et al. Rapid measurement and identification of position dependent geometric errors of CNC machine tool turntable[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 458-467.
8	李圣一, 戴一帆, 尹自强, 等. 精密和超精密机床精度建模技术[M]. 长沙: 国防科技大学出版社, 2007.
9	Helton J C, Johnson J D, Sallaberry C J, et al. Survey of sampling-based methods for uncertainty and sensitivity analysis[J]. Reliability Engineering & System Safety, 2006, 91(10/11): 1175-1209.
10	吕震宙, 宋述芳, 李洪双, 等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京: 科学出版社, 2009.
11	郑财, 黄贤振, 胡明伟, 等. 三轴数控机床加工精度可靠性分析[J]. 机床与液压, 2017, 45(15): 180-183, 160.
	Zheng Cai, Huang Xian-zhen, Hu Ming-wei, et al. Three axis NC machine tool machining accuracy reliability analysis[J]. Machine Tool & Hydraulics, 2017, 45(15): 180-183, 160.
12	Zhang Zi-ling, Cai Li-gang, Cheng Qiang, et al. A geometric error budget method to improve machining accuracy reliability of multi-axis machine tools[J]. Journal of Intelligent Manufacturing, 2019, 30(2): 495-519.
13	余治民, 刘子建, 艾彦迪, 等. 大型数控龙门导轨磨床几何误差建模与基于可靠性理论的精度分配[J]. 机械工程学报, 2013, 17: 142-151.
	Yu Zhi-min, Liu Zi-jian, Ai Yan-di, et al. Geometric error model and precision distribution based on reliability theory for large CNC gantry guideway grinder[J]. Journal of Mechanical Engineering, 2013, 17: 142-151.
14	孙志礼,张义民,何雪浤,等. 数控机床性能分析及可靠性设计技术[M]. 北京: 机械工业出版社, 2011.
15	Cheng Qiang, Zhao Hong-wei, Zhao Yong-sheng, et al. Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation[J]. Journal of Intelligent Manufacturing, 2018, 29(1): 191-209.
16	Zhang Zi-ling, Cheng Qiang, Qi Bao-bao, et al. A general approach for the machining quality evaluation of S-shaped specimen based on POS-SQP algorithm and monte carlo method[J]. Journal of Manufacturing Systems, 2021, 60: 553-568.
17	Zhang Zi-ling, Liu Zhi-feng, Cheng Qiang, et al. An approach of comprehensive error modeling and accuracy allocation for the improvement of reliability and optimization of cost of multi-axis NC machine tool[J]. The International Journal of Advanced Manufacturing Technology, 2016, 89(1): 561-579.
18	张明. 结构可靠度分析: 方法与程序[M]. 北京: 科学出版社, 2009.
19	Cheng Qiang, Wu Can, Gu Pei-hua, et al. An analysis methodology for stochastic characteristic of volumetric error in multiaxis CNC machine tool[J]. Mathematical Problems in Engineering, 2013(11): 863283.
20	Abdul W K. Calibration of 5-axis machine tools[D]. Beijing: School of Mechanical Engineering and Automation, Beihang University, 2010.
21	陈传海, 姚国祥, 金桐彤, 等. 基于响应面与遗传算法的主轴系统动力学建模及参数修正[J/OL]. [2021-08-10]. .

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基于向量投影响应面的数控机床几何误差分配方法

An approach for error allocation of machine tool based on vector projection response surface method

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