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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

Professor
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.

FIGURES IN THIS ARTICLE
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Copyright © 2018 by ASME
Topics: Errors , Kinematics
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Figures

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Fig. 1

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

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Fig. 2

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

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Fig. 3

Side view of nine-axis machine tool with linear offsets

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Fig. 4

Z-axis positioning errors and the resultant quintic polynomial fit

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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. 8

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

Tables

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