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Research Papers

Optimal Design of Measurement Point Layout for Workpiece Localization

[+] Author and Article Information
LiMin Zhu1

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. Chinazhulm@sjtu.edu.cn

HongGen Luo

 GE Global Research Center, Shanghai 201203, P.R. China

Han Ding

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

1

Corresponding author.

J. Manuf. Sci. Eng 131(1), 011006 (Dec 29, 2008) (13 pages) doi:10.1115/1.3039515 History: Received May 13, 2006; Revised October 19, 2008; Published December 29, 2008

This paper presents a methodology for the optimal design of the measurement point layout for 3D workpiece localization in the presence of part surface errors and measurement errors. A number of frame-invariant norms of the infinitesimal rigid body displacement, two of which give Riemann metrics on the Euclidean group, are defined to quantify the localization accuracy required by manufacturing processes. Then, two types of indices, both frame invariant and scale invariant, are derived to characterize the sensitivities of the accuracy measures to the sampling errors at the measurement points. With a dense set of discrete points on the workpiece datum surfaces predefined as candidates for measurement, planning of probing points to accurately recover part location is modeled as a combinatorial problem focusing on minimizing the accuracy sensitivity index. It is shown that if the number of measurement points is large enough, there is no need to optimize their positions, and that if the systematic error component of the sampled geometric errors is not negligible as compared with the random error component, addition of measurement points offers no guarantee of a smaller upper bound of the localization error. A heuristic floating forward search algorithm is employed to efficiently find a near-optimal solution. Two relevant problems of sensor placement optimization for geometric imperfection diagnosis and fixture fault diagnosis are also briefly revisited in the same framework. Examples are given to illustrate the effectiveness of the proposed design criteria and algorithm.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Fitting a nominal geometry to the inspected data

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Figure 5

Sensitivity index value versus sample size

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Figure 6

Values of the design criteria calculated from the optimal point set and the randomly generated point sets

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Figure 7

Computational time versus sample size

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Figure 8

The simulation model for measurement point planning

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Figure 9

Values of the design criterion calculated from the optimal point set and the randomly generated point sets

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Figure 10

Values of the accuracy measure computed from the optimally selected and the randomly selected data

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Figure 2

Positional and directional deviations of a critical point caused by the localization error

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Figure 3

Flowchart of the measurement point planning algorithm

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Figure 4

Feasible measurement points on the trimmed algebraic surface

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