慢刀伺服车削刀具补偿算法优化
2022-04-25郭航言康敏周玮
郭航言，康敏,2，周玮
慢刀伺服车削刀具补偿算法优化
郭航言1，康敏1,2，周玮1
（1.南京农业大学 工学院，南京 210031；2.江苏省智能化农业装备重点实验室，南京 210031）
慢刀伺服；刀具路径；坐标变换；几何补偿；表面粗糙度；面型精度
与普通光学曲面相比，复杂光学曲面具有独特的光学性能，如简化光学系统、优化成像质量等，故其应用领域广泛[1-5]。例如，环曲面是一种典型的非球状类复杂光学曲面，具有较好的光学特性，可以在2个相互垂直的方向上形成不同的屈光度[6]。基于这一特性，环曲面镜片广泛应用于矫正散光[6-7]。但是，传统的车削加工工艺难以满足复杂光学曲面（如环曲面）的质量要求。慢刀伺服车削技术作为新兴的超精密加工方法，具有较高的加工效率和较好的加工质量，近年来已经应用于复杂光学曲面的车削加工[8-12]。
1 刀具路径规划
以环曲面为例，对慢刀伺服车削刀具路径规划流程进行说明，如图1所示。首先，根据环曲面的数学表达式建立相应的三维模型和数学模型，用于面型分析和刀具路径仿真分析；然后，利用刀触点生成算法将环曲面离散为一系列刀触点，得到相应的刀触点轨迹；最后，利用刀具补偿算法求解计算一系列刀位点坐标，得到相应的刀位点轨迹，从而获得可以用于数控加工的代码[17,22]。
1.1 刀触点生成
目前，常用的刀触点生成方法是等参数生成方法，包括等角度法和等弧长法2种[16-17,21]。等角度法的优点是算法简单、编程容易实现；但缺点是对于直径较大的工件，工件外圈的刀触点存在较大的离散误差，而内圈离散误差较小，导致工件外圈的加工质量相对较差。等弧长法的优点是离散误差受工件直径的影响较小，基本保持稳定；但缺点是算法比较复杂，且无论工件直径较大或较小，工件内圈都会存在较大的离散误差[16-17,21]。基于这2种方法的优缺点，对于直径不是很大的工件，多采用等角度法。因此本文提出的算法和开展的试验，均在等角度法的基础上进行。采用等角度法生成的刀触点轨迹方程可用式(1)表示。
图1 慢刀伺服车削刀具路径规划流程
1.2 刀具补偿
由于车削所用刀具的刀尖带有圆弧半径，在车削加工中，刀尖与工件的接触点（称为刀触点）并非固定点，而是刀尖圆弧上一系列变化的点，因此需要寻找一固定点来确定刀具的位置（该固定点称为刀位点），所以需要进行刀具形状补偿[23-24]。
1.2.1 坐标变换
图2 直角坐标系下求解存在的问题
图3 坐标系变换图
1.2.2 几何补偿
图4 基于坐标变换的几何补偿算法原理图
2 仿真分析
为了检验本文提出的补偿算法的合理性，选择环曲面利用Matlab软件编写相应程序进行仿真分析，环曲面方程可用式(7)表达[26]。仿真时，取h=140 mm，=100 mm，离散角Δ=8°，进给速度f=1 mm/r，工件半径w=20 mm，刀尖圆弧半径t=140 mm，刀具前角=0°，后角=10°。
图5 不同算法下的结果对比
图6 刀具路径仿真结果
3 试验验证
根据上述刀具补偿算法的理论研究和仿真分析，对仿真结果进行试验验证。首先，针对上述不同算法，利用Matlab软件编写了适用于慢刀伺服车削并能自动生成加工代码的程序。然后，在本实验室自行研制的实验装置上完成了环曲面的加工，用于验证本文提出的刀具补偿算法的可行性。图7为本实验室自行研制的高精度慢刀伺服车削平台。加工的工件材料为聚甲基丙烯酸甲酯（PMMA），进给速度f=0.01 mm/r，切削深度p=0.04 mm，其余参数参照上述仿真程序。
图7 高精度慢刀伺服车削平台
图8 在不同刀具补偿算法下加工得到的环曲面工件
图9 表面粗糙度的测量方法
为评价加工的环曲面工件的面型精度，使用MQ686三坐标测量机对工件表面的面型进行测量。经过数据处理后，得到面型误差分布情况，如图11所示。得到环曲面的面型误差后，计算面型误差最大值和最小值的差值，就可以得到环曲面的面型精度，面型精度用（Peak-to-Valley）表示[17]。
图10 不同刀具补偿算法下得到的表面粗糙度测量结果
图11 不同刀具补偿算法下得到的面型误差分布情况
4 结论
[1] YAMAMOTO T, MATSUDA R, SHINDOU M, et al. Monitoring of Vibrations in Free-Form Surface Processing Using Ball Nose End Mill Tools with Wireless Tool Holder Systems[J]. International Journal of Automation Technology, 2021, 15(3): 335-342.
[2] NAGAYAMA K, YAN Ji-wang. Deterministic Error Compensation for Slow Tool Servo-Driven Diamond Turning of Freeform Surface with Nanometric Form Accuracy[J]. Journal of Manufacturing Processes, 2021, 64: 45-57.
[3] ZHOU Xiang-dong, HUANG Xiao, BAI Jian, et al. Representation of Complex Optical Surfaces with Adaptive Radial Basis Functions[J]. Applied Optics, 2019, 58(14): 3938-3944.
[4] 吴志清, 唐清春. 刀具摆角对复杂曲面轮廓精度的影响研究[J]. 表面技术, 2018, 47(7): 139-145.
WU Zhi-qing, TANG Qing-chun. Influence of Tool Angle on Contour Precision of Complicated Surface[J]. Surface Technology, 2018, 47(7): 139-145.
[5] 耿军晓, 李立伟, 李友刚, 等. 五轴联动加工中进给速度的控制算法[J]. 表面技术, 2018, 47(7): 8-14.
GENG Jun-xiao, LI Li-wei, LI You-gang, et al. Control Algorithm of Feed Rate in Five-Axis Linkage Machining[J]. Surface Technology, 2018, 47(7): 8-14.
[6] 邱昕洋, 张彦钦, 王宏斌. 慢刀伺服加工环曲面的刀具路径规划方法[J]. 国防科技大学学报, 2020, 42(3): 121-127.
QIU Xin-yang, ZHANG Yan-qin, WANG Hong-bin. Tool Path Planning Method for Machining Toric Surface Based on Slow Tool Servo Technology[J]. Journal of National University of Defense Technology, 2020, 42(3): 121-127.
[7] 张豫. 环曲面设计角膜塑形镜对角膜表面大高度差异近视患者的临床疗效探讨[J]. 中外医疗, 2019, 38(21): 62-64.
ZHANG Yu. Clinical Effect of Orthokeratology on the Corneal Surface with Large Height Difference in Myopia Patients[J]. China & Foreign Medical Treatment, 2019, 38(21): 62-64.
[8] NING Pei-xing, ZHAO Ji, JI Shi-jun, et al. Ultra-Precision Machining of a Large Amplitude Umbrella Surface Based on Slow Tool Servo[J]. International Journal of Precision Engineering and Manufacturing, 2020, 21(11): 1999-2010.
[9] 林泽钦, 陈新度, 颜志涛, 等. 微透镜阵列的慢刀伺服加工表面粗糙度预测模型[J]. 哈尔滨理工大学学报, 2020, 25(3): 83-87.
LIN Ze-qin, CHEN Xin-du, YAN Zhi-tao, et al. The Surface Roughness Prediction Model of Microlens Array in Slow Tool Servo Cutting[J]. Journal of Harbin University of Science and Technology, 2020, 25(3): 83-87.
[10] 董青青. 慢刀伺服车削关键技术研究[D]. 长春: 长春工业大学, 2020.
DONG Qing-qing. Research on Key Technology of Slow Tool Servo[D]. Changchun: Changchun University of Technology, 2020.
[11] 赵亮, 程凯, 丁辉, 等. 超精密慢刀伺服金刚石车削加工的关键工艺问题研究[J]. 制造技术与机床, 2020(5): 85-88.
ZHAO Liang, CHENG Kai, DING Hui, et al. Investigation on Key Enabling Process Variables Ultraprecision Diamond Turning Using Slow Tool Servo[J]. Manufacturing Technology & Machine Tool, 2020(5): 85-88.
[12] 王东方. 大口径自由曲面超精密车削关键技术研究[D]. 北京: 中国科学院大学(中国科学院长春光学精密机械与物理研究所), 2020.
WANG Dong-fang. Research on Key Technologies of Ultra-Precision Turning for Large Aperture Optics[D]. Beijing: Institute of Physics, Chinese Academy of Sciences, 2020.
[13] 张琦, 薛常喜. 自由曲面的慢刀伺服车削轨迹优化[J]. 激光与光电子学进展, 2020, 57(5): 052203.
ZHANG Qi, XUE Chang-xi. Optimization of Tool Path Generation for Freeform Surface by Slow Tool Servo Diamond Turning[J]. Laser & Optoelectronics Progress, 2020, 57(5): 052203.
[14] 蔡洪彬, 史国权. 主动控制加工误差慢刀伺服车削轨迹生成方法[J]. 吉林大学学报(工学版), 2019, 49(4): 1221-1227.
CAI Hong-bin, SHI Guo-quan. Tool Path Generation of Slow Tool Servo for Active Control Machining Error[J]. Journal of Jilin University (Engineering and Technology Edition), 2019, 49(4): 1221-1227.
[15] 牛恒泰, 康敏, 何成奎, 等. 离散曲面慢刀伺服车削刀具路径规划[J]. 机械科学与技术, 2018, 37(5): 721-728.
NIU Heng-tai, KANG Min, HE Cheng-kui, et al. Cutting Path Plan of Discrete Surface for Slow Tool Servo Turning[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(5): 721-728.
[16] 关朝亮. 复杂光学曲面慢刀伺服超精密车削技术研究[D]. 长沙: 国防科学技术大学, 2010.
GUAN Chao-liang. Study on the Technology of Slow Tool Servo Ultra-Precision Diamond Turning for Complex Optical Surface[D]. Changsha: National University of Defense Technology, 2010.
[17] 王兴盛. 复杂光学曲面慢刀伺服车削关键技术研究[D]. 南京: 南京农业大学, 2014.
WANG Xing-sheng. Research on the Key Technologies of Slow Tool Servo Turning for Complex Optical Surface[D]. Nanjing: Nanjing Agricultural University, 2014.
[18] 陈旭. 慢刀伺服车削机床PID参数优化及其刀具路径规划研究[D]. 南京: 南京农业大学, 2016.
CHEN Xu. Research on PID Parameter Optimization and Tool Path Generation of Slow Tool Servo Turning Machine [D]. Nanjing: Nanjing Agricultural University, 2016.
[19] 铁贵鹏. 自由曲面光学元件慢刀伺服加工关键技术研究[D]. 长沙: 国防科学技术大学, 2009.
TIE Gui-peng. Research on Key Technology in Turning of Freeform Optics Based on Slow Tool Servo[D]. Changsha: National University of Defense Technology, 2009.
[20] KHAGHANI A, CHENG Kai. Investigation on Multi- Body Dynamics Based Approach to the Toolpath Generation for Ultraprecision Machining of Freeform Surfaces[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2020, 234(3): 571-583.
[21] 牛恒泰. 复杂曲面慢刀伺服车削刀具路径规划及测量技术研究[D]. 南京: 南京农业大学, 2018.
NIU Heng-tai. Research on Slow Tool Servo Turning and Form Accuracy Measuring for Complex Surface[D]. Nanjing: Nanjing Agricultural University, 2018.
[22] 黄岳田. 单点金刚石车削复杂曲面技术研究[D]. 成都: 中国科学院大学(中国科学院光电技术研究所), 2019.
HUANG Yue-tian. Research on Single Point Diamond Turning Technology for Complex Surface[D]. Chengdu: Institute of Optics and Electronics, Chinese Academy of Sciences, 2019.
[23] 李佳伟, 杜文浩, 韩长庆. 慢刀伺服车削刀具半径定向补偿的分段逼近求解[J]. 中国机械工程, 2020, 31(17): 2017-2023.
LI Jia-wei, DU Wen-hao, HAN Chang-qing. Directional Tool Radius Compensation Solution of STS Turning Based on Segment Approximation[J]. China Mechanical Engineering, 2020, 31(17): 2017-2023.
[24] 马富荣, 靳伍银, 王安. 复杂曲面慢刀伺服加工刀具半径补偿方法[J]. 机械设计与制造, 2019(7): 189-192.
MA Fu-rong, JIN Wu-yin, WANG An. The Method of Tool Radius Compensation for Complex Surface by Using Slow Tool Servo Processing[J]. Machinery Design & Manufacture, 2019(7): 189-192.
[25] 何康, 黄春, 姜浩, 等. 基于MPI的高精度归约函数设计与实现[J]. 计算机工程与科学, 2021, 43(4): 594-602.
HE Kang, HUANG Chun, JIANG Hao, et al. Design and Implementation of a High-Precision Reduction Function Based on MPI[J]. Computer Engineering & Science, 2021, 43(4): 594-602.
[26] 杨军, 康敏. 基于三弯矩法的环曲面金刚石切削刀具路径规划及其仿真分析[J]. 中国机械工程, 2018, 29(13): 1580-1587.
YANG Jun, KANG Min. Tool Path Generation and Simulation for Diamond Turning of Toric Surfaces Using Three Bending Moment Method[J]. China Mechanical Engineering, 2018, 29(13): 1580-1587.
[27] 马富荣. 自由光学曲面的慢刀伺服车削及仿真[D]. 兰州: 兰州理工大学, 2018.
MA Fu-rong. Free-Form Optical Surface Processing in Slowing Tool Turning and Simulation[D]. Lanzhou: Lanzhou University of Technology, 2018.
Optimization of Tool Compensation Algorithm for Slow Tool Servo Turning
1,1,2,1
(1. College of Engineering, Nanjing Agricultural University, Nanjing 210031, China;2. Key Laboratory of Intelligence Agricultural Equipment of Jiangsu Province, Nanjing 210031, China)
In order to improve the surface quality of complex surface in slow tool servo turning, the tool compensation algorithm was optimized.In view of the problems that normal compensation algorithm can easily lead to the decrease of the dynamic performance of-axis and large interpolation error in-direction compensation algorithm, a geometric compensation algorithm based on coordinate transformation was proposed in this paper.Coordinate transformation can improve the accuracy of the solution and simplify the algorithm.By using the geometric transformation relationship, the compensation component of-axis could be concentrated on the-axis, which not only ensured the dynamic performance of-axis, but also reduced the interpolation error.Taking the toric surface as an example, the tool compensation algorithm proposed in this paper was simulated and verified by experiments.The simulation results showed that the velocity of-axis fluctuates greatly under the normal compensation algorithm, while the-axis can keep uniform motion under the algorithm proposed in this paper.In the tool compensation link, compared with the algorithm proposed in this paper, the interpolation error under-direction compensation algorithm was larger, and the maximum interpolation error was more than 0.015 mm.The experimental results showed that the value of surface roughness of the toric surface was the largest under the normal compensation algorithm (=0.112 μm), which was much larger than that under the-direction compensation algorithm and the algorithm proposed in this paper.However,under the-direction compensation algorithm and the algorithm proposed in this paper,the value of surface roughness of the toric surface was similar (=0.066 μm and=0.062 μm respectively), which indicates that the tool compensation algorithm has little effect on the surface roughness on the premise of ensuring the dynamic performance of-axis.The values ofobtained under the normal compensation algorithm, the-direction compensation algorithm and the algorithm proposed in this paper was 16.9 μm, 13.8 μm and 8.8 μm respectively. Compared with normal compensation algorithm and-direction compensation algorithm, the accuracy of toric surface was improved by 92.0% and 56.8% respectively under the algorithm proposed in this paper, which shows that the tool compensation algorithm proposed in this paper can improve the surface machining quality.
slow tool servo; tool path; coordinate transformation; geometric compensation; surface roughness; form error
TG506
A
1001-3660(2022)04-0308-09
10.16490/j.cnki.issn.1001-3660.2022.04.032
2021-05-21；
2021-09-25
2021-05-21；
2021-09-25
2019江苏省现代农机装备与技术示范推广项目（6026A9）
Supported by the Demonstration and Extension Project of Modern Agricultural Machinery Equipment and Technology in Jiangsu Province in 2019 (6026A9)
郭航言（1998—），男，硕士研究生，主要研究方向为数控加工技术。
GUO Hang-yan (1998—), Male, Postgraduate, Research focus: numerical control processing technology.
康敏（1965—），男，博士，教授，主要研究方向为特种加工技术。
KANG Min (1965—), Male, Doctor, Professor, Research focus: special processing technology.
郭航言, 康敏, 周玮. 慢刀伺服车削刀具补偿算法优化[J]. 表面技术, 2022, 51(4): 308-316.
GUO Hang-yan, KANG Min, ZHOU Wei. Optimization of Tool Compensation Algorithm for Slow Tool Servo Turning[J]. Surface Technology, 2022, 51(4): 308-316.
责任编辑：万长清
