慢刀伺服車削刀具補償算法優化

郭航言，康敏,2，周瑋

慢刀伺服車削刀具補償算法優化

郭航言1，康敏1,2，周瑋1

（1.南京農業大學 工學院，南京 210031；2.江蘇省智能化農業裝備重點實驗室，南京 210031）

慢刀伺服；刀具路徑；坐標變換；幾何補償；表面粗糙度；面型精度

與普通光學曲面相比，復雜光學曲面具有獨特的光學性能，如簡化光學系統、優化成像質量等，故其應用領域廣泛[1-5]。例如，環曲面是一種典型的非球狀類復雜光學曲面，具有較好的光學特性，可以在2個相互垂直的方向上形成不同的屈光度[6]。基于這一特性，環曲面鏡片廣泛應用于矯正散光[6-7]。但是，傳統的車削加工工藝難以滿足復雜光學曲面（如環曲面）的質量要求。慢刀伺服車削技術作為新興的超精密加工方法，具有較高的加工效率和較好的加工質量，近年來已經應用于復雜光學曲面的車削加工[8-12]。

1 刀具路徑規劃

以環曲面為例，對慢刀伺服車削刀具路徑規劃流程進行說明，如圖1所示。首先，根據環曲面的數學表達式建立相應的三維模型和數學模型，用于面型分析和刀具路徑仿真分析；然后，利用刀觸點生成算法將環曲面離散為一系列刀觸點，得到相應的刀觸點軌跡；最后，利用刀具補償算法求解計算一系列刀位點坐標，得到相應的刀位點軌跡，從而獲得可以用于數控加工的代碼[17,22]。

1.1 刀觸點生成

目前，常用的刀觸點生成方法是等參數生成方法，包括等角度法和等弧長法2種[16-17,21]。等角度法的優點是算法簡單、編程容易實現；但缺點是對于直徑較大的工件，工件外圈的刀觸點存在較大的離散誤差，而內圈離散誤差較小，導致工件外圈的加工質量相對較差。等弧長法的優點是離散誤差受工件直徑的影響較小，基本保持穩定；但缺點是算法比較復雜，且無論工件直徑較大或較小，工件內圈都會存在較大的離散誤差[16-17,21]。基于這2種方法的優缺點，對于直徑不是很大的工件，多采用等角度法。因此本文提出的算法和開展的試驗，均在等角度法的基礎上進行。采用等角度法生成的刀觸點軌跡方程可用式(1)表示。

圖1 慢刀伺服車削刀具路徑規劃流程

1.2 刀具補償

由于車削所用刀具的刀尖帶有圓弧半徑，在車削加工中，刀尖與工件的接觸點（稱為刀觸點）并非固定點，而是刀尖圓弧上一系列變化的點，因此需要尋找一固定點來確定刀具的位置（該固定點稱為刀位點），所以需要進行刀具形狀補償[23-24]。

1.2.1 坐標變換

圖2 直角坐標系下求解存在的問題

圖3 坐標系變換圖

1.2.2 幾何補償

圖4 基于坐標變換的幾何補償算法原理圖

2 仿真分析

為了檢驗本文提出的補償算法的合理性，選擇環曲面利用Matlab軟件編寫相應程序進行仿真分析，環曲面方程可用式(7)表達[26]。仿真時，取h=140 mm，=100 mm，離散角Δ=8°，進給速度f=1 mm/r，工件半徑w=20 mm，刀尖圓弧半徑t=140 mm，刀具前角=0°，后角=10°。

圖5 不同算法下的結果對比

圖6 刀具路徑仿真結果

3 試驗驗證

根據上述刀具補償算法的理論研究和仿真分析，對仿真結果進行試驗驗證。首先，針對上述不同算法，利用Matlab軟件編寫了適用于慢刀伺服車削并能自動生成加工代碼的程序。然后，在本實驗室自行研制的實驗裝置上完成了環曲面的加工，用于驗證本文提出的刀具補償算法的可行性。圖7為本實驗室自行研制的高精度慢刀伺服車削平臺。加工的工件材料為聚甲基丙烯酸甲酯（PMMA），進給速度f=0.01 mm/r，切削深度p=0.04 mm，其余參數參照上述仿真程序。

圖7 高精度慢刀伺服車削平臺

圖8 在不同刀具補償算法下加工得到的環曲面工件

圖9 表面粗糙度的測量方法

為評價加工的環曲面工件的面型精度，使用MQ686三坐標測量機對工件表面的面型進行測量。經過數據處理后，得到面型誤差分布情況，如圖11所示。得到環曲面的面型誤差后，計算面型誤差最大值和最小值的差值，就可以得到環曲面的面型精度，面型精度用（Peak-to-Valley）表示[17]。

圖10 不同刀具補償算法下得到的表面粗糙度測量結果

圖11 不同刀具補償算法下得到的面型誤差分布情況

4 結論

[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 Com-pensation 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. Rep-re-sentation of Complex Optical Surfaces with Adaptive Radial Basis Functions[J]. Applied Optics, 2019, 58(14): 3938-3944.

[4] 吳志清, 唐清春. 刀具擺角對復雜曲面輪廓精度的影響研究[J]. 表面技術, 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] 耿軍曉, 李立偉, 李友剛, 等. 五軸聯動加工中進給速度的控制算法[J]. 表面技術, 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, 張彥欽, 王宏斌. 慢刀伺服加工環曲面的刀具路徑規劃方法[J]. 國防科技大學學報, 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] 張豫. 環曲面設計角膜塑形鏡對角膜表面大高度差異近視患者的臨床療效探討[J]. 中外醫療, 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-Preci-sion 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] 林澤欽, 陳新度, 顏志濤, 等. 微透鏡陣列的慢刀伺服加工表面粗糙度預測模型[J]. 哈爾濱理工大學學報, 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. 慢刀伺服車削關鍵技術研究[D]. 長春: 長春工業大學, 2020.

DONG Qing-qing. Research on Key Technology of Slow Tool Servo[D]. Changchun: Changchun University of Technology, 2020.

[11] 趙亮, 程凱, 丁輝, 等. 超精密慢刀伺服金剛石車削加工的關鍵工藝問題研究[J]. 制造技術與機床, 2020(5): 85-88.

ZHAO Liang, CHENG Kai, DING Hui, et al. Investiga-tion on Key Enabling Process Variables Ultraprecision Diamond Turning Using Slow Tool Servo[J]. Manufacturing Technology & Machine Tool, 2020(5): 85-88.

[12] 王東方. 大口徑自由曲面超精密車削關鍵技術研究[D]. 北京: 中國科學院大學(中國科學院長春光學精密機械與物理研究所), 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] 張琦, 薛常喜. 自由曲面的慢刀伺服車削軌跡優化[J]. 激光與光電子學進展, 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, 史國權. 主動控制加工誤差慢刀伺服車削軌跡生成方法[J]. 吉林大學學報(工學版), 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. 離散曲面慢刀伺服車削刀具路徑規劃[J]. 機械科學與技術, 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 Tur-ning[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(5): 721-728.

[16] 關朝亮. 復雜光學曲面慢刀伺服超精密車削技術研究[D]. 長沙: 國防科學技術大學, 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] 王興盛. 復雜光學曲面慢刀伺服車削關鍵技術研究[D]. 南京: 南京農業大學, 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] 陳旭. 慢刀伺服車削機床PID參數優化及其刀具路徑規劃研究[D]. 南京: 南京農業大學, 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] 鐵貴鵬. 自由曲面光學元件慢刀伺服加工關鍵技術研究[D]. 長沙: 國防科學技術大學, 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 Gene-ration 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. 復雜曲面慢刀伺服車削刀具路徑規劃及測量技術研究[D]. 南京: 南京農業大學, 2018.

NIU Heng-tai. Research on Slow Tool Servo Turning and Form Accuracy Measuring for Complex Surface[D]. Nanjing: Nanjing Agricultural University, 2018.

[22] 黃岳田. 單點金剛石車削復雜曲面技術研究[D]. 成都: 中國科學院大學(中國科學院光電技術研究所), 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] 李佳偉, 杜文浩, 韓長慶. 慢刀伺服車削刀具半徑定向補償的分段逼近求解[J]. 中國機械工程, 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 Engine-e-ring, 2020, 31(17): 2017-2023.

[24] 馬富榮, 靳伍銀, 王安. 復雜曲面慢刀伺服加工刀具半徑補償方法[J]. 機械設計與制造, 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 & Man-ufacture, 2019(7): 189-192.

[25] 何康, 黃春, 姜浩, 等. 基于MPI的高精度歸約函數設計與實現[J]. 計算機工程與科學, 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] 楊軍, 康敏. 基于三彎矩法的環曲面金剛石切削刀具路徑規劃及其仿真分析[J]. 中國機械工程, 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] 馬富榮. 自由光學曲面的慢刀伺服車削及仿真[D]. 蘭州: 蘭州理工大學, 2018.

MA Fu-rong. Free-Form Optical Surface Processing in Slowing Tool Turning and Simulation[D]. Lanzhou: Lan-zhou 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江蘇省現代農機裝備與技術示范推廣項目（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，碩士研究生，主要研究方向為數控加工技術。

GUO Hang-yan (1998—), Male, Postgraduate, Research focus: numerical control processing technology.

康敏（1965—），男，博士，教授，主要研究方向為特種加工技術。

KANG Min (1965—), Male, Doctor, Professor, Research focus: special processing technology.

郭航言, 康敏, 周瑋. 慢刀伺服車削刀具補償算法優化[J]. 表面技術, 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.

責任編輯：萬長清