Research Papers

Geometric Error Compensation With a Six Degree-of–Freedom Rotary Magnetic Actuator

[+] Author and Article Information
Alexander Yuen

Manufacturing Automation Laboratory,
Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: alexjyuen@alumni.ubc.ca

Yusuf Altintas

Fellow of ASME
Manufacturing Automation Laboratory,
Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: altintas@mech.ubc.ca

Manuscript received April 18, 2018; final manuscript received July 12, 2018; published online August 31, 2018. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 140(11), 111016 (Aug 31, 2018) (10 pages) Paper No: MANU-18-1256; doi: 10.1115/1.4040938 History: Received April 18, 2018; Revised July 12, 2018

This paper presents a methodology to compensate the tooltip position errors caused by the geometric errors of a three-axis gantry type micromill integrated with a six degree-of-freedom (6DOF) rotary magnetic table. A geometric error-free ideal forward kinematic model of the nine-axis machine has been developed using homogenous transformation matrices (HTMs). The geometric errors of each linear axis, which include one positioning, two straightness, pitch, roll, and yaw errors, are measured with a laser interferometer and fit to quintic polynomial functions in the working volume of the machine. The forward kinematic model is modified to include the geometric errors which, when subtracted from the ideal kinematic model, gives the deviation between the desired tooltip position with and without geometric errors. The position commands of the six degree-of-freedom rotary magnetic table are modified in real time to compensate for the tooltip deviation using a gradient descent algorithm. The algorithm is simulated and verified experimentally on the nine-axis micromill controlled by an in-house developed virtual/real-time open computer numerical controlled (CNC) system.

Copyright © 2018 by ASME
Topics: Errors , Kinematics
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Zhang, G. , Veale, R. , Charlton, T. , Borchardt, B. , and Hocken, R. , 1985, “ Error Compensation of Coordinate Measuring Machines,” CIRP Ann., 34(1), pp. 445–448. [CrossRef]
Okafor, A. C. , and Ertekin, Y. M. , 2000, “ Derivation of Machine Tool Error Models and Error Compensation Procedure for Three Axes Vertical Machining Center Using Rigid Body Kinematics,” Int. J. Mach. Tools Manuf., 40(8), pp. 1199–1213. [CrossRef]
Shen, H. , Fu, J. , He, Y. , and Yao, X. , 2012, “ On-Line Asynchronous Compensation Methods for Static/Quasi-Static Error Implemented on CNC Machine Tools,” Int. J. Mach. Tools Manuf., 60, pp. 14–26. [CrossRef]
Uddin, M. S. , Ibaraki, S. , Matsubara, A. , and Matsushita, T. , 2009, “ Prediction and Compensation of Machining Geometric Errors of Five-Axis Machining Centers With Kinematic Errors,” Precis. Eng., 33(2), pp. 194–201. [CrossRef]
Ma, L. , Bazzoli, P. , Sammons, P. M. , Landers, R. G. , and Bristow, D. A. , 2016, “ Modeling and Compensation of Joint-Dependent Kinematic Errors in Robotic Manipulators,” International Symposium on Flexible Automation (ISFA), Cleveland, OH, Aug. 1–3, pp. 458–464.
Xiang, S. , and Altintas, Y. , 2016, “ Modeling and Compensation of Volumetric Errors for Five-Axis Machine Tools,” Int. J. Mach. Tools Manuf., 101, pp. 65–78. [CrossRef]
Aggarwal, S. K. , Horsley, D. A. , Horowitz, R. , and Pisano, A. P. , 1997, “ Micro-Actuators for High Density Disk Drives,” American Control Conference, Albuquerque, NM, June 6, pp. 3979–3984.
Kobayashi, M. , and Horowitz, R. , 2001, “ Track Seek Control for Hard Disk Dual-Stage Servo Systems,” IEEE Trans. Magn., 37(2), pp. 949–954. [CrossRef]
Herrmann, G. , Turner, M. C. , Postlethwaite, I. , and Guo, G. , 2004, “ Practical Implementation of a Novel Anti-Windup Scheme in a HDD-Dual-Stage Servo-System,” IEEE/ASME Trans. Mechatronics, 9(3), pp. 580–592. [CrossRef]
Zheng, J. , and Fu, M. , 2008, “ Nonlinear Feedback Control of a Dual-Stage Actuator System for Reduced Settling Time,” IEEE Trans. Control Syst. Technol., 16(4), pp. 717–725. [CrossRef]
Elfizy, A. T. , Bone, G. M. , and Elbestawi, M. A. , 2005, “ Design and Control of a Dual-Stage Feed Drive,” Int. J. Mach. Tools Manuf., 45(2), pp. 153–165. [CrossRef]
Choi, Y. M. , and Gweon, D. G. , 2011, “ A High-Precision Dual-Servo Stage Using Halbach Linear Active Magnetic Bearings,” IEEE/ASME Trans. Mechatronics, 16(5), pp. 925–931. [CrossRef]
Yuen, A. , and Altintas, Y. , 2017, “ Constrained Trajectory Generation and Control for a 9-Axis Micromachining Center With Four Redundant Axes,” IEEE/ASME Trans. Mechatronics, 23(1), pp. 402–412. [CrossRef]
Kim, O.-S. , Lee, S.-H. , and Han, D.-C. , 2003, “ Positioning Performance and Straightness Error Compensation of the Magnetic Levitation Stage Supported by the Linear Magnetic Bearing,” IEEE Trans. Ind. Electron., 50(2), pp. 374–378. [CrossRef]
Deng, Y. , Jin, X. , and Zhang, Z. , 2015, “ A Macro-Micro Compensation Method for Straightness Motion Error and Positioning Error of an Improved Linear Stage,” Int. J. Adv. Manuf. Technol., 80(9–12), pp. 1799–1806. [CrossRef]
Kono, D. , Matsubara, A. , Yamaji, I. , and Fujita, T. , 2008, “ High-Precision Machining by Measurement and Compensation of Motion Error,” Int. J. Mach. Tools Manuf., 48(10), pp. 1103–1110. [CrossRef]
Yu, D. P. , Hong, G. S. , and Wong, Y. S. , 2012, “ Profile Error Compensation in Fast Tool Servo Diamond Turning of Micro-Structured Surfaces,” Int. J. Mach. Tools Manuf., 52(1), pp. 13–23. [CrossRef]
Dyck, M. , Lu, X. , and Altintas, Y. , 2017, “ Magnetically Levitated Rotary Table With Six Degrees of Freedom,” IEEE/ASME Trans. Mechatronics, 22(1), pp. 530–540. [CrossRef]
Yuen, A. , and Altintas, Y. , 2016, “ Trajectory Generation and Control of a 9 Axis CNC Micromachining Center,” CIRP Ann., 65(1), pp. 349–352. [CrossRef]


Grahic Jump Location
Fig. 4

Z-axis positioning errors and the resultant quintic polynomial fit

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Fig. 3

Side view of nine-axis machine tool with linear offsets

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Fig. 2

Geometric errors for a single degree-of-freedom feed drive

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Fig. 1

Nine-axis micromachining center and corresponding axes of the machine tool

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Fig. 8

Geometric errors for Z-axis positions −4 mm to 76 mm

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Fig. 5

Simulated tooltip errors with and without compensation for a circle on the xy plane of radius 1 mm

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Fig. 6

Geometric errors for X-axis positions −40 mm to 40 mm

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Fig. 7

Geometric errors for Y-axis positions −40 mm to 40 mm

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Fig. 9

Compensating position commands when moving only Z-axis where xf, yf, and zf are the compensating commands of the translational axes of the rotary table and af, bf, and cf are the compensating commands of the rotational axes of the rotary table

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Fig. 10

Three-axis spiral toolpath

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Fig. 11

Tooltip errors with and without compensation



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