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Research Papers

Robust Machine Tool Thermal Error Modeling Through Thermal Mode Concept

[+] Author and Article Information
Jie Zhu, Jun Ni, Albert J. Shih

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109

J. Manuf. Sci. Eng 130(6), 061006 (Oct 10, 2008) (9 pages) doi:10.1115/1.2976148 History: Received February 20, 2008; Revised May 25, 2008; Published October 10, 2008

Thermal errors are among the most significant contributors to machine tool errors. Successful reduction in thermal errors has been realized through thermal error compensation techniques in the past few decades. The effectiveness of thermal error models directly determines the compensation results. Most of the current thermal error modeling methods are empirical and highly rely on the collected data under specific working conditions, neglecting the insight into the underlying mechanisms that result in thermal deformations. In this paper, an innovative temperature sensor placement scheme and thermal error modeling strategy are proposed based on the thermal mode concept. The modeling procedures for both position independent and position dependent thermal errors are illustrated through numerical simulation and experiments. Satisfactory results have been achieved in terms of model accuracy and robustness.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simplified spindle model

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Figure 2

First four thermal modes with temperature fields and time constants: (a) mode I, (b) mode II, (c) mode III, and (d) mode IV

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Figure 3

Weight distribution of thermal modes

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Figure 4

Heat input for spindle expansion simulation

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Figure 5

Simulation and modeling results of the spindle model

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Figure 6

Linear extrapolation examination of the thermal error model

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Figure 7

Frequency sensitivity examination of the thermal error model: (a) T=20min, (b) T=40min, and (c) T=10min

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Figure 8

Experimental setup for spindle thermal expansion

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Figure 9

Experimental results of test 1: (a) spindle speed, (b) spindle expansion, and (c) temperature variations

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Figure 10

Measured and modeled results of the spindle experiment

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Figure 11

Spindle speed, measured and predicted thermal errors for robustness verification: (a) test 2 and (b) test 3

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Figure 12

Temperature variations after each test: (a) test 1, (b) test 2, and (c) test 3

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Figure 13

Weight distributions of the first three thermal modes: (a) sensor 1, (b) sensor 2, and (c) sensor 3

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Figure 14

Z-axis structure of an EDM machine (Courtesy of Sodick Inc., Schaumburg, IL)

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Figure 15

Weight distribution of thermal modes for the Z-axis unit

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Figure 16

Temperature field distributions of the dominant thermal modes (front view of the column): (a) mode 1, (b) mode 3, and (c) mode 4

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Figure 17

Temperature sensor placement on the front surface of the Z-axis unit

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Figure 18

Comparison of thermal error model training and verification without considering the position effects: (a) model training at Z=320mm, (b) modeling training at Z=160mm, (c) model verification at Z=320mm and (d) model verification at Z=160mm

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Figure 19

Linear positioning errors along Z-axis model training and verification with residual errors: (a) model training and (b) model verification

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