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Erschienen in: The International Journal of Advanced Manufacturing Technology 3-4/2020

08.07.2020 | ORIGINAL ARTICLE

Simultaneous servo error pre-compensation and feedrate optimization with tolerance constraints using linear programming

verfasst von: Heejin Kim, Chinedum E. Okwudire

Erschienen in: The International Journal of Advanced Manufacturing Technology | Ausgabe 3-4/2020

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Abstract

Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs between productivity and quality in manufacturing. This paper proposes a novel linear programming approach for combined servo error pre-compensation and feedrate optimization, subject to contour error (tolerance) and kinematic constraints. The incorporation of servo error pre-compensation into feedrate optimization allows for faster motions without violating tolerance constraints. Experiments carried out on a 3D printer and precision motion stage are respectively used to demonstrate up to 43% and 47% reduction in cycle time without compromising part quality using the proposed approach compared with the independent approach.

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Literatur
1.
Zurück zum Zitat Altintas Y, Verl A, Brecher C, Uriarte L, Pritschow G (2011) Machine tool feed drives. CIRP Ann 60(2):779–796CrossRef Altintas Y, Verl A, Brecher C, Uriarte L, Pritschow G (2011) Machine tool feed drives. CIRP Ann 60(2):779–796CrossRef
2.
Zurück zum Zitat Tomizuka M (1987) Zero error tracking algorithm for digital control. ASME J Dyn Sys Meas Control 109(1):65–68CrossRef Tomizuka M (1987) Zero error tracking algorithm for digital control. ASME J Dyn Sys Meas Control 109(1):65–68CrossRef
3.
Zurück zum Zitat Zhang D, Chen Y, Chen Y (2016) Iterative pre-compensation scheme of tracking error for contouring error reduction. Int J Adv Manuf Technol 87(9-12):3279–3288CrossRef Zhang D, Chen Y, Chen Y (2016) Iterative pre-compensation scheme of tracking error for contouring error reduction. Int J Adv Manuf Technol 87(9-12):3279–3288CrossRef
4.
Zurück zum Zitat Ernesto CA, Farouki RT (2010) Solution of inverse dynamics problems for contour error minimization in CNC machines. Int J Adv Manuf Technol 49(5):589–604CrossRef Ernesto CA, Farouki RT (2010) Solution of inverse dynamics problems for contour error minimization in CNC machines. Int J Adv Manuf Technol 49(5):589–604CrossRef
5.
Zurück zum Zitat Altintas Y, Khoshdarregi MR (2012) Contour error control of CNC machine tools with vibration avoidance. CIRP Ann 61(1):335–338CrossRef Altintas Y, Khoshdarregi MR (2012) Contour error control of CNC machine tools with vibration avoidance. CIRP Ann 61(1):335–338CrossRef
6.
Zurück zum Zitat Zhang K, Yuen A, Altintas Y (2013) Pre-compensation of contour errors in five-axis CNC machine tools. Int J Mach Tool Manuf 74:1–11CrossRef Zhang K, Yuen A, Altintas Y (2013) Pre-compensation of contour errors in five-axis CNC machine tools. Int J Mach Tool Manuf 74:1–11CrossRef
7.
Zurück zum Zitat Yang S, Ghasemi AH, Lu X, Okwudire CE (2015) Pre-compensation of servo contour errors using a model predictive control framework. Int J Mach Tool Manuf 98:50–60CrossRef Yang S, Ghasemi AH, Lu X, Okwudire CE (2015) Pre-compensation of servo contour errors using a model predictive control framework. Int J Mach Tool Manuf 98:50–60CrossRef
8.
Zurück zum Zitat Gordon DJ, Erkorkmaz K (2013) Accurate control of ball screw drives using pole-placement vibration damping and a novel trajectory prefilter. Precis Eng 37(2):308–322CrossRef Gordon DJ, Erkorkmaz K (2013) Accurate control of ball screw drives using pole-placement vibration damping and a novel trajectory prefilter. Precis Eng 37(2):308–322CrossRef
9.
Zurück zum Zitat Chin JH, Lin TC (1997) Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools. Int J Mach Tool Manuf 37(7):947–967CrossRef Chin JH, Lin TC (1997) Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools. Int J Mach Tool Manuf 37(7):947–967CrossRef
10.
Zurück zum Zitat Song D, Ma J, Jia Z, Gao Y (2017) Estimation and compensation for continuous-path running trajectory error in high-feed-speed machining. Int J Adv Manuf Technol 89(5-8):1495–1508CrossRef Song D, Ma J, Jia Z, Gao Y (2017) Estimation and compensation for continuous-path running trajectory error in high-feed-speed machining. Int J Adv Manuf Technol 89(5-8):1495–1508CrossRef
11.
Zurück zum Zitat Liu W, Sun Y, Yuan X, Chen M (2016) A new approach to the pre-compensation of contour errors for three-axis machine tools using an adaptive cross-coupled controller. Int J Adv Manuf Technol 90 (9-12):3711–3725CrossRef Liu W, Sun Y, Yuan X, Chen M (2016) A new approach to the pre-compensation of contour errors for three-axis machine tools using an adaptive cross-coupled controller. Int J Adv Manuf Technol 90 (9-12):3711–3725CrossRef
12.
Zurück zum Zitat Liu W, Ren F, Sun Y, Jiang S (2018) Contour error pre-compensation for three-axis machine tools by using cross-coupled dynamic friction control. Int J Adv Manuf Technol 98(1):551–563CrossRef Liu W, Ren F, Sun Y, Jiang S (2018) Contour error pre-compensation for three-axis machine tools by using cross-coupled dynamic friction control. Int J Adv Manuf Technol 98(1):551–563CrossRef
13.
Zurück zum Zitat Pi S, Liu Q, Liu Q (2018) A novel dynamic contour error estimation and control in high-speed CNC. Int J Adv Manuf Technol 96(2):547–560CrossRef Pi S, Liu Q, Liu Q (2018) A novel dynamic contour error estimation and control in high-speed CNC. Int J Adv Manuf Technol 96(2):547–560CrossRef
14.
Zurück zum Zitat Duong TQ, Rodriguez-Ayerbe P, Lavernhe S, Tournier C, Dumur D (2019) Contour error pre-compensation for five-axis high speed machining: offline gain adjustment approach. Int J Adv Manuf Technol 100(1):3113–3125CrossRef Duong TQ, Rodriguez-Ayerbe P, Lavernhe S, Tournier C, Dumur D (2019) Contour error pre-compensation for five-axis high speed machining: offline gain adjustment approach. Int J Adv Manuf Technol 100(1):3113–3125CrossRef
15.
Zurück zum Zitat Okwudire C, Ramani K, Duan M (2016) A trajectory optimization method for improved tracking of motion commands using CNC machines that experience unwanted vibration. CIRP Ann 65(1):373–376CrossRef Okwudire C, Ramani K, Duan M (2016) A trajectory optimization method for improved tracking of motion commands using CNC machines that experience unwanted vibration. CIRP Ann 65(1):373–376CrossRef
16.
Zurück zum Zitat Duan M, Yoon D, Okwudire CE (2018) A limited-preview filtered B-spline approach to tracking control–with application to vibration-induced error compensation of a 3D printer. Mechatronics 56:287–296CrossRef Duan M, Yoon D, Okwudire CE (2018) A limited-preview filtered B-spline approach to tracking control–with application to vibration-induced error compensation of a 3D printer. Mechatronics 56:287–296CrossRef
17.
Zurück zum Zitat Fan W, Gao XS, Lee CH, Zhang K, Zhang Q (2013) Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol 69(5-8):1373–1388CrossRef Fan W, Gao XS, Lee CH, Zhang K, Zhang Q (2013) Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol 69(5-8):1373–1388CrossRef
18.
Zurück zum Zitat Erkorkmaz K, Chen QGC, Zhao MY, Beudaert X, Gao XS (2017) Linear programming and windowing based feedrate optimization for spline toolpaths. CIRP Ann 66(1):393–396CrossRef Erkorkmaz K, Chen QGC, Zhao MY, Beudaert X, Gao XS (2017) Linear programming and windowing based feedrate optimization for spline toolpaths. CIRP Ann 66(1):393–396CrossRef
19.
Zurück zum Zitat Bharathi A, Dong J (2016) Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints. Int J Adv Manuf Technol 82(5):1029–1040CrossRef Bharathi A, Dong J (2016) Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints. Int J Adv Manuf Technol 82(5):1029–1040CrossRef
20.
Zurück zum Zitat Zhang Q, Li SR (2013) Efficient computation of smooth minimum time trajectory for CNC machining. Int J Adv Manuf Technol 68:683–692CrossRef Zhang Q, Li SR (2013) Efficient computation of smooth minimum time trajectory for CNC machining. Int J Adv Manuf Technol 68:683–692CrossRef
21.
Zurück zum Zitat Guo J, Zhang Q, Gao XS, Li H (2015) Time optimal feedrate generation with confined tracking error based on linear programming. J Syst Sci Complex 28(1):90–95MathSciNetCrossRef Guo J, Zhang Q, Gao XS, Li H (2015) Time optimal feedrate generation with confined tracking error based on linear programming. J Syst Sci Complex 28(1):90–95MathSciNetCrossRef
22.
Zurück zum Zitat Zhang Y, Ye P, Zhao M, Zhang H (2019) Dynamic feedrate optimization for parametric toolpath with data-based tracking error prediction. Mech Syst Signal Process 120:221–223CrossRef Zhang Y, Ye P, Zhao M, Zhang H (2019) Dynamic feedrate optimization for parametric toolpath with data-based tracking error prediction. Mech Syst Signal Process 120:221–223CrossRef
23.
Zurück zum Zitat Zhang K, Yuan CM, Gao XS (2013) Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Technol 66(9–12):1685–1697CrossRef Zhang K, Yuan CM, Gao XS (2013) Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Technol 66(9–12):1685–1697CrossRef
24.
Zurück zum Zitat 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. Int J Mach Tool Manuf 97:86–97CrossRef 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. Int J Mach Tool Manuf 97:86–97CrossRef
25.
Zurück zum Zitat Liang F, Zhao J, Ji S (2017) An iterative feed rate scheduling method with confined high order constraints in parametric interpolation. Int J Adv Manuf Technol Manuf 92(5):2001– 2015CrossRef Liang F, Zhao J, Ji S (2017) An iterative feed rate scheduling method with confined high order constraints in parametric interpolation. Int J Adv Manuf Technol Manuf 92(5):2001– 2015CrossRef
26.
Zurück zum Zitat Lu L, Zhang L, Ji S, Han Y, Zhao J (2016) An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems. Int J Adv Manuf Technol 83(9-12):2143–2157CrossRef Lu L, Zhang L, Ji S, Han Y, Zhao J (2016) An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems. Int J Adv Manuf Technol 83(9-12):2143–2157CrossRef
27.
Zurück zum Zitat Lai HY, Lin KY, Tseng SJ, Ueng WD (2008) On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk. Int J Adv Manuf Technol 37(1):104–121CrossRef Lai HY, Lin KY, Tseng SJ, Ueng WD (2008) On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk. Int J Adv Manuf Technol 37(1):104–121CrossRef
28.
Zurück zum Zitat 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. CIRP J Manuf Sci Technol 23:78–90CrossRef 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. CIRP J Manuf Sci Technol 23:78–90CrossRef
29.
Zurück zum Zitat Chen M, Sun Y (2019) Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools. Int J Adv Manuf Technol 103:567–584CrossRef Chen M, Sun Y (2019) Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools. Int J Adv Manuf Technol 103:567–584CrossRef
30.
Zurück zum Zitat Lam D, Manzie C, Good MC (2012) Model predictive contouring control for biaxial systems. IEEE Trans Control Syst Technol 21(2):552–559CrossRef Lam D, Manzie C, Good MC (2012) Model predictive contouring control for biaxial systems. IEEE Trans Control Syst Technol 21(2):552–559CrossRef
31.
Zurück zum Zitat Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring. CIRP Ann 40 (1):371–374CrossRef Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring. CIRP Ann 40 (1):371–374CrossRef
32.
Zurück zum Zitat Ramani KS, Duan M, Okwudire CE, Ulsoy AG (2017) Tracking control of linear time-invariant nonminimum phase systems using filtered basis functions. J Dyn Syst Meas Control 139(1):011001–1–011001-11CrossRef Ramani KS, Duan M, Okwudire CE, Ulsoy AG (2017) Tracking control of linear time-invariant nonminimum phase systems using filtered basis functions. J Dyn Syst Meas Control 139(1):011001–1–011001-11CrossRef
34.
Zurück zum Zitat Okwudire C, Huggi S, Supe S, Huang C, Zeng B (2018) Low-level control of 3D printers from the cloud: a step toward 3D printer control as a service. Inventions 3(3):56CrossRef Okwudire C, Huggi S, Supe S, Huang C, Zeng B (2018) Low-level control of 3D printers from the cloud: a step toward 3D printer control as a service. Inventions 3(3):56CrossRef
35.
Zurück zum Zitat Nocedal J, Wright SJ (2006) Numerical optimization. Berlin Nocedal J, Wright SJ (2006) Numerical optimization. Berlin
Metadaten
Titel
Simultaneous servo error pre-compensation and feedrate optimization with tolerance constraints using linear programming
verfasst von
Heejin Kim
Chinedum E. Okwudire
Publikationsdatum
08.07.2020
Verlag
Springer London
Erschienen in
The International Journal of Advanced Manufacturing Technology / Ausgabe 3-4/2020
Print ISSN: 0268-3768
Elektronische ISSN: 1433-3015
DOI
https://doi.org/10.1007/s00170-020-05651-w

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