Abstract
Contour error compensation is an active research topic in five-axis CNC machining, especially in the manufacturing of sculptured surface parts. Nevertheless, current methods are mainly based on the mirror compensation principle, and fail to obtain a desired level of accuracy when processing parts with tight curvature feature. To address this issue, a global toolpath modulation-based contour error pre-compensation method is developed in this paper, which incorporates the error compensation issue into the stage of toolpath planning with a linear analytical solution. In this method, the nominal toolpaths used to machine the products is first expressed by dual B-spline curves, and then the instantaneous tracking error model of each individual drive is built with respect to control points of splined path. Afterward, the satisfaction condition of the spline control points for eliminating the contour error is yielded, which provides a possibility for compensating contour error in a global manner, and the neighbor-dependent coupling issue in error compensation between adjacent cutter location points is capable of being handled as well. On this basis, by applying the least-squares technique, the complicated contour error pre-compensation problem is further converted into a solution of simpler linear equation system. For enhancing its robustness when processing long toolpaths, an adaptive piecewise modulation strategy is also developed. Finally, both experiment and simulation are conducted to validate the proposed method, and the results demonstrate that the proposed method can significantly improve contour precision at low computational costs when compared with the existing pre-compensation method.
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References
Sun Y, Jia J, **ting XU, Chen M, Niu J (2022) Path, feedrate and trajectory planning for free-from surface machining: a state-of-the-art review[J]. Chin J Aeronaut 35(8):12–29. https://doi.org/10.1016/j.cja.2021.06.011
Tsao TC, Tomika M (1987) Zero phase error tracking algorithm for digital control[J]. ASME J Dynamic Systems, Measurement, and Control 10(4):349. https://doi.org/10.1115/1.3143822
Tsao TC, Tomizuka M (1987) Adaptive zero phase error tracking algorithm for digital control[J]. Journal of Dynamic Systems Measurement & Control. https://doi.org/10.1115/1.3143866
Torfs D, Schutter JD, Swevers J (1992) Extended bandwidth zero phase error tracking control of nonminimal phase systems[J]. J Dynamic Syst Measurement and Control 114(3):347–351. https://doi.org/10.1115/1.2897354
Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part III: high speed tracking and contouring control of feed drives[J]. Int J Machine Tools Manufacture 41(11):1637–1658. https://doi.org/10.1016/S0890-6955(01)00004-9
Altintas Y, Erkorkmaz K, Zhu WH (2000) Sliding mode controller design for high speed feed drives[J]. CIRP Annals - Manuf Technol 49(1):265–270. https://doi.org/10.1016/S0007-8506(07)62943-6
Kamalzadeh A, Erkorkmaz K (2007) Accurate tracking controller design for high-speed drives[J]. Int J Machine Tools Manuf 47(9):13931400. https://doi.org/10.1016/j.ijmachtools.2006.08.027
Yoram Koren (1980) Cross-coupled biaxial computer control for manufacturing systems[J]. J Dynamic Syst, Measurement, Control 102(4):265–272. https://doi.org/10.1115/1.3149612
Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring[J]. Annals of the Cirp 40(1):371–374. https://doi.org/10.1016/S0007-8506(07)62009-5
Srinivasan K, Kulkarni PK (1990) Cross-coupled control of biaxial feed drive servomechanisms[J]. J Dynamic Syst Measurement and Control 112(2):225–232. https://doi.org/10.1115/1.2896129
Barton KL, Alleyne AG (2007) Cross-coupled ILC for improved precision motion control: design and implementation[C]// American Control Conference. IEEE. https://doi.org/10.1109/ACCESS.2020.3007422
Xu W, Hou J, Li J, Yuan C, Simeone A (2020) Multi-axis motion control based on time-varying norm optimal cross-coupled iterative learning[J]. IEEE Access 8:124802–124811. https://doi.org/10.1109/ACCESS.2020.3007422
Yeh S, Hsu P (1999) Theory and applications of the robust cross-coupled control design[J]. J Dyn Syst Meas Control 121(3):524–530. https://doi.org/10.1115/1.2802506
Mumtazcan K, Melih C (2018) Development of a cross-coupled robust controller for a multi-axis micromachining system[J]. Journal of Dynamic Systems Measurement & Control 140(12):124501. https://doi.org/10.1115/1.4040443
Ouyang PR, Dam T, Pano V (2014) Cross-coupled PID control in position domain for contour tracking[J]. Robotica 33(6):1–24. https://doi.org/10.1017/S0263574714000769
Renton D, Elbestawi MA (2000) High speed servo control of multi-axis machine tools[J]. Int J Machine Tools and Manufacture 40(4):539–559. https://doi.org/10.1016/S0890-6955(99)00075-9
Tang L, Landers RG (2013) Multiaxis contour control—the state of the art[J]. IEEE Trans Control Syst Technol 21(6):1997–2010. https://doi.org/10.1109/TCST.2012.2235179
Yang S, Ghasemi AH, Lu X, Okwudire CE (2015) Pre-compensation of servo contour errors using a model predictive control framework[J]. Int J Machine Tools Manuf 98:50–60. https://doi.org/10.1016/j.ijmachtools.2015.08.002
Sun Y, Chen M, Jia J, Lee YS, Guo D (2019) Jerk-limited feedrate scheduling and optimization for five-axis machining using new piecewise linear programming approach[J]. Sci Chin (Technological Sciences) 62(07):5–19. https://doi.org/10.1007/s11431-018-9404-9
Yong T, Narayanaswami R (2003) A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining[J]. Computer-Aided Design 35(13):1249–1259. https://doi.org/10.1016/S0010-4485(03)00043-5
Xu Du, Huang Jie, Zhu Li-Min (2015) A complete S-shape feed rate scheduling approach for NURBS interpolator. J Comp Design Eng 2(4):206–217. https://doi.org/10.1016/j.jcde.2015.06.004
Wang Y, Yang D, Gai R, Wang S, Sun S (2015) Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation[J]. Int J Machine Tools Manuf 96:94105. https://doi.org/10.1016/j.ijmachtools.2015.06.009
Leng H, Yijie WU, Pan X (2008) Velocity planning algorithm for high speed machining of micro line blocks based on cubic polynomial model[J]. Comp Integrated Manuf Syst 14(2):336–299. https://doi.org/10.1016/j.commatsci.2008.03.016
Sencer B, Altintas Y, Croft E (2008) Feed optimization for five-axis CNC machine tools with drive constraints[J]. Int J Machine Tools Manuf 48(7–8):733–745. https://doi.org/10.1016/j.ijmachtools.2008.01.002
Beudaert X, Lavernhe S, Tournier C (2012) Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path[J]. Int J Mach Tools Manuf 57:73–82. https://doi.org/10.1016/j.ijmachtools.2012.02.005
Sun Y, Zhao Y, Bao Y, Guo D (2015) A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints[J]. Int J Machine Tools Manuf. https://doi.org/10.1016/j.ijmachtools.2015.07.002
Sun Y, Zhao Y, Bao Y, Guo D (2014) A novel adaptive-feedrate interpolation method for NURBS toolpath with drive constraints[J]. Int J Machine Tools & Manuf 77:74–81. https://doi.org/10.1016/j.ijmachtools.2013.11.002
Sun Y, Zhao Y, Xu J, Guo D (2014) The feedrate scheduling of parametric interpolator with geometry, process and drive constraints for multi-axis CNC machine tools[J]. Int J Machine Tools Manuf 85:49–57. https://doi.org/10.1016/j.ijmachtools.2014.05.001
Chen M, Sun Y (2019) Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools[J]. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-019-03586-5
Zhang Q, Gao XS (2016) Practical feedrate optimization for planar high precision contouring[C]//2016 IEEE International Conference on Information and Automation (ICIA). IEEE, pp 1872–1877. https://doi.org/10.1109/ICInfA.2016.7832124
Guo JX, Zhang K, Zhang Q, Gao XS (2013) Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system[J]. Computer-Aided Design 45(12):1538–1546. https://doi.org/10.1016/j.cad.2013.07.002
Zhang Q, Li S, Guo J (2014) Minimum time trajectory optimization of CNC machining with tracking error constraints[J]. Abstr Appl Anal 2014 (2014-7-17), 2014, 2014:1–15. https://doi.org/10.1155/2014/835098
Yang J, Aslan D, Altintas Y (2018) A feedrate scheduling algorithm to constrain tool tip position and tool orientation errors of five-axis CNC machining under cutting load disturbances[J]. CIRP J Manuf Sci Technol 23:78–90. https://doi.org/10.1016/j.cirpj.2018.08.005
Sun Y, Shi Z, Xu J (2022) Synchronous feedrate scheduling for the dual-robot machining of complex surface parts with varying wall thickness[J]. Int J Adv Manuf Technol 119(3):2653–2667. https://doi.org/10.1007/s00170-021-08512-2
Lo CC, Hsiao CY (1998) CNC machine tool interpolator with path compensation for repeated contour machining[J]. Computer-Aided Design 30(1):55–62. https://doi.org/10.1016/S0010-4485(97)00053-5
Yang X, Seethaler R, Zhan C, Lu, D, Zhao, W (2019) A model predictive contouring error precompensation method[J]. IEEE Trans Ind Electron 67(5):4036–4045. https://doi.org/10.1109/TIE.2019.2921294
Wang Z, Hu C, Zhu Y, Zhu L (2021) Prediction-model-based contouring error iterative precompensation scheme for precision multiaxis motion systems. IEEE/ASME Transactions on Mechatronics 26(5):2274–2284. https://doi.org/10.1109/TMECH.2020.3034675
Altintas Y, Khoshdarregi MR (2012) Contour error control of CNC machine tools with vibration avoidance[J]. CIRP Annals - Manufacturing Technology 61(1):335–338. https://doi.org/10.1016/j.cirp.2012.03.132
Chin JH, Lin TC (1997) Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools[J]. Int J Machine Tools Manuf 37(7):947–967. https://doi.org/10.1016/S0890-6955(96)00088-0
Lam D, Manzie C, Good MC (2012) Model predictive contouring control for biaxial systems[J]. IEEE Trans Control Syst Technol 21(2):552–559. https://doi.org/10.1109/TCST.2012.2186229
Jia Z, Song D, Ma J, Gao Y (2017) Pre-compensation for continuous-path running trajectory error in high-speed machining of parts with varied curvature features[J]. Chi J Mech Eng 30(01):46–54. https://doi.org/10.3901/CJME.2016.0127.015
** XC, Poo AN, Hong GS (2009) Taylor series expansion error compensation for a bi-axial CNC machine[C]//2008 IEEE International Conference on Systems, Man and Cybernetics. IEEE, 2008, pp 1614–1619. https://doi.org/10.1109/ICSMC.2008.4811518
Feng HA, Xcx B, Anp A (2012) Generalized Taylor series expansion for free-form two-dimensional contour error compensation[J]. Int J Machine Tools Manuf 53(1):91–99. https://doi.org/10.1016/j.ijmachtools.2011.10.001
Khoshdarregi MR, Tappe S, Altintas Y (2014) Integrated five-axis trajectory sha** and contour error compensation for high-speed CNC machine tools[J]. IEEE/ASME Transactions on Mechatronics 19(6):1859–1871. https://doi.org/10.1109/TMECH.2014.2307473
A K Z, B A Y, B Y A, (2013) Pre-compensation of contour errors in five-axis CNC machine tools[J]. Int J Machine Tools Manuf 74(8):1–11. https://doi.org/10.1016/j.ijmachtools.2013.07.003
Ekm A, Uchiyama N (2013) Estimation of tool orientation contour errors for five-axis machining[J]. Robotics and Computer-Integrated Manufacturing 29(5):271–277. https://doi.org/10.1016/j.rcim.2013.01.002
Chen M, Sun Y, Xu J (2020) A new analytical path-resha** model and solution algorithm for contour error pre-compensation in multi-axis CNC machining[J]. J Manuf Sci Eng 142(6):1–14. https://doi.org/10.1115/1.4046749
Hu C, Yu J, Wang Z, Zhu Y (2022) An iterative contouring error compensation scheme for five-axis precision motion systems[J]. Mech Syst Signal Process 178:109226. https://doi.org/10.1016/j.ymssp.2022.109226
Langeron JM, Duc E, Lartigue C, Bourdet P (2004) A new format for 5-axis tool path computation, using Bspline curves[J]. Computer-Aided Design 36(12):1219–1229. https://doi.org/10.1016/j.cad.2003.12.002
Dong J, Wang T, Li B, Ding Y (2014) Smooth feedrate planning for continuous short line tool path with contour error constraint[J]. Int J Mach Tools Manuf 76:1–12. https://doi.org/10.1016/j.ijmachtools.2013.09.009
Song DN, Ma JW, Jia ZY, Gao YY (2017) Estimation and compensation for continuous-path running trajectory error in high-feed-speed machining[J]. Int J Adv Manuf Technol 89(5–8):1495–1508. https://doi.org/10.1007/s00170-016-9202-3
Cheng MY, Lee CC (2007) Motion controller design for contour-following tasks based on real-time contour error estimation[J]. IEEE Transactions on Industrial Electronics 54(3):1686–1695. https://doi.org/10.1109/TIE.2007.894691
Yeh SS, Hsu PL (2002) Estimation of the contouring error vector for the cross-coupled control design[J]. Mechatron IEEE/ASME Transac on 7(1):44–51. https://doi.org/10.1109/3516.990886
Jia Z, Song D, Ma J, Zhao X, Su W (2017) Adaptive estimation and nonlinear variable gain compensation of the contouring error for precise parametric curve following[J]. Sci Chin Technol Sci 60(10):1494–1505. https://doi.org/10.1007/s11431-017-9042-x
Zhu LM, Zhao H, Ding H (2013) Real-time contouring error estimation for multi-axis motion systems using the second-order approximation[J]. Int J Machine Tools Manuf 68:75–80. https://doi.org/10.1016/j.ijmachtools.2013.01.008
Liu Y, Wan M, **ao QB, Qin XB (2021) Combined predictive and feedback contour error control with dynamic contour error estimation for industrial five-axis machine tools[J]. IEEE Trans Ind Electron 69(7):6668–6677. https://doi.org/10.1109/TIE.2021.3097659
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Yang Liu: investigation, data curation, validation, writing—original draft; Mansen Chen: supervision, writing—review and editing; Yuwen Sun: methodology, resources, writing—review and editing.
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Liu, Y., Chen, M. & Sun, Y. Global toolpath modulation–based contour error pre-compensation for multi-axis CNC machining. Int J Adv Manuf Technol 125, 3171–3189 (2023). https://doi.org/10.1007/s00170-023-10857-9
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DOI: https://doi.org/10.1007/s00170-023-10857-9