Abstract
Parts with rapidly varied geometric features are often key components in high-end equipment and are difficult to process because of the special structures and the strict requirements. Due to the existence of rapidly varied geometric features and the moving characteristic of continuous-path running, the trajectory error will be formed during machining process, which seriously restricts the machining accuracy of such parts. Additionally, the formative trajectory error is more non-ignorable in high-feed-speed machining. Existing studies can hardly reduce this error for arbitrary free-form trajectories without sacrificing of the machining efficiency. Consequently, aiming at reducing this error thus improving the processing efficiency and precision, the estimation and compensation methods for the trajectory error in high-feed-speed continuous-path machining are proposed. The actual reachable feed speed is recognized based on geometry and drive constraints of the numerical control (NC) machine tool. The continuous-path running trajectory error is estimated by approximating the desired toolpath with spline curves. The error compensation approach by combining the mirror compensation and the Taylor’s expansion compensation is provided. The advantage of the proposed approach is that the continuous-path running trajectory error can be easily estimated and compensated only by analyzing and modifying the NC codes, which means an extensive feasibility for free-form toolpaths. Experimental results demonstrate the favorable performance of the proposed methods. This study provides an effective approach for reducing the multi-axis high-speed machining trajectory error and is significant for improving the machining precision and efficiency of the parts with rapidly varied geometric features in engineering.
Similar content being viewed by others
References
Zhao K, Jia ZY, Liu W, Ma JW, Ding LC (2016) Burr control for removal of metal coating from plastics substrate by micro-milling. Mater Manuf Process 31(5):641–647
Qiao Z, Wang T, Wang Y, Hu M, Liu Q (2012) Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining. Int J Mach Tools Manuf 53(1):107–117
Cho MH, Kim DW, Lee CG, Heo EY, Ha JW, Chen FF (2009) CBIMS: case-based impeller machining strategy support system. Robot Comput-Integr Manuf 25(6):980–988
Umehara T, Teramoto K, Ishida T, Takeuchi Y (2006) Tool posture determination for 5-axis control machining by area division method. JSME Int J Ser C 49(1):35–42
Lo CC (1999) Efficient cutter-path planning for five-axis surface machining with a flat-end cutter. Comput-Aided Des 31(9):557–566
Zhao H, Zhu LM, Ding H (2013) A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments. Int J Mach Tools Manuf 65:88–98
Sun SJ, Lin H, Zheng LM, Yu JG, Hu Y (2015) A real-time and look-ahead interpolation methodology with dynamic B-spline transition scheme for CNC machining of short line segments. Int J Adv Manuf Technol. doi:10.1007/s00170-015-7776-9
Wang J, Yau H (2009) Real-time NURBS interpolator: application to short linear segments. Int J Adv Manuf Technol 41(11–12):1169–1185
Baek DK, Ko TJ, Yang SH (2012) Fast and precision NURBS interpolator for CNC systems. Int J Precis Eng Manuf 13(6):955–961
Hu GQ, Zhang XY (2013) Application engineer manual for Siemens SINUMERIK840D sl/840Di sl numerical control system. National Defence Industry Press, Bei**g
Jia ZY, Song DN, Ma JW, Gao YY (2016) Pre-compensation for continuous-path running trajectory error in high-speed machining of parts with varied curvature features. Chin J Mech Eng. doi:10.3901/CJME.2016.0127.015
Suh SH, Kang SK, Chung DH, Stroud I (2008) Theory and design of CNC systems. Springer, London. doi:10.1007/978-1-84800-336-1
Slamani M, Mayer R, Balazinski M (2013) Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements. Int J Adv Manuf Technol 65(9–12):1669–1679
Tomizuka M (1987) Zero phase error tracking algorithm for digital-control. J Dyn Syst Meas Control-Trans ASME 109(1):65–68
Torfs D, Deschutter J, Swevers J (1992) Extended bandwidth error phase error tracking control of nonminimal phase systems. J Dyn Syst Meas Control-Trans ASME 114(3):347–351
Ramesh R, Mannan MA, Poo AN (2005) Tracking and contour error control in CNC servo systems. Int J Mach Tools Manuf 45(3):301–326
Lee J, Dixon WE, Ziegert JC (2012) Adaptive nonlinear contour coupling control for a machine tool system. Int J Adv Manuf Technol 61(9–12):1057–1065
Huo F, Poo AN (2012) Improving contouring accuracy by using generalized cross-coupled control. Int J Mach Tools Manuf 63:49–57
** XC, Zhan WS, Poo AN (2015) Improving CNC contouring accuracy by robust digital integral sliding mode control. Int J Mach Tools Manuf 88:51–61
Zhu LM, Zhao H, Ding H (2013) Real-time contouring error estimation for multi-axis motion systems using the second-order approximation. Int J Mach Tools Manuf 68:75–80
Kurt M, Bagci E (2011) Feedrate optimisation/scheduling on sculptured surface machining: a comprehensive review, applications and future directions. Int J Adv Manuf Technol 55(9):1037–1067
Dong J, Wang T, Li B, Ding Y (2014) Smooth feed rate planning for continuous short line tool path with contour error constraint. Int J Mach Tools Manuf 76:1–12
Jia ZY, Wang L, Ma JW, Zhao K, Liu W (2014) Feed speed scheduling method for parts with rapidly varied geometric feature based on drive constraint of NC machine tool. Int J Mach Tools Manuf 87:73–88
Zhang DL, Chen YH, Chen YP (2016) Iterative pre-compensation scheme of tracking error for contouring error reduction. Int J Adv Manuf Technol. doi:10.1007/s00170-016-8735-9
Eskandari S, Arezoo B, Abdullah A (2013) Positional, geometrical, and thermal errors compensation by tool path modification using three methods of regression, neural networks, and fuzzy logic. Int J Adv Manuf Technol 65(9):1635–1649
Li J, **e FG, Liu XJ, Li WD, Zhu SW (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol. doi: 10.1007/s00170-016-8580-x
Chen FJ, Yin SH, Ohmori H, Yu JW (2013) Form error compensation in single-point inclined axis nanogrinding for small aspheric insert. Int J Adv Manuf Technol 65(1):433–441
Deng YJ, ** X, Zhang ZJ (2015) A macro–micro compensation method for straightness motion error and positioning error of an improved linear stage. Int J Adv Manuf Technol 80(9):1799–1806
Mu YH, Ngoi KA (1999) Dynamic error compensation of coordinate measuring machines for high-speed measurement. Int J Adv Manuf Technol 15(11):810–814
Lo CC, Hsiao CY (1998) CNC machine tool interpolator with path compensation for repeated contour machining. Comput-Aided Des 30(1):55–62
** XC, Poo AN, Hong GS (2009) Improving contouring accuracy by tuning gains for a bi-axial CNC machine. Int J Mach Tools Manuf 49(5):395–406
Poo AN, Bollinger JG, Younkin GW (1972) Dynamic errors in type 1 contouring systems. IEEE Trans Ind Appl IA-8(4):477–484
Knott GD (2000) Interpolating cubic splines. Birkhäuser, Boston. doi:10.1007/978-1-4612-1320-8
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Song, Dn., Ma, Jw., Jia, Zy. et al. Estimation and compensation for continuous-path running trajectory error in high-feed-speed machining. Int J Adv Manuf Technol 89, 1495–1508 (2017). https://doi.org/10.1007/s00170-016-9202-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-016-9202-3