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Research Papers

# Two-Sided Quadratic Model for Workpiece Fixturing Analysis

[+] Author and Article Information
Chen Luo

School of Mechanical Engineering,  Southeast University, Nanjin 211189, China e-mail: chenluo@seu.edu.cn

LiMin Zhu1

Han Ding

State Key Laboratory of Mechanical System and Vibration School of Mechanical Engineering,  Shanghai Jiaotong University, Shanghai 200240, Chinahding@sjtu.edu.cn

1

Corresponding author.

J. Manuf. Sci. Eng 133(3), 031004 (Jun 08, 2011) (11 pages) doi:10.1115/1.4003951 History: Received May 21, 2010; Revised March 24, 2011; Published June 08, 2011; Online June 08, 2011

## Abstract

This paper presents a novel model for workpiece positioning analysis. Existing fixturing models may underestimate the positioning error due to neglect of the curvature of one or both contacting bodies. By using surface-to-surface signed distance function, a two-sided quadratic model for fixture locating analysis is developed. A system of quadratic sensitivity equations, which relate locators’ source errors to the resulting workpiece localization error, are derived. The second-order geometric properties of both workpiece and locators are taken fully into account. The present model is more accurate than the existing linear model and one-sided quadratic model, which is verified through numerical examples. It has potential applications in fixture design, fault diagnosis, and tolerance analysis.

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## Figures

Figure 1

The workpiece located by three locators of the fixture: (a) and (b) Locators are cylinders with the same radius r; (c) and (d) locators are simplified as points

Figure 2

The workpiece located by three locators of the fixture: (a) and (b) Locators are cylinders with the same radius r; (c) and (d) locators are simplified as points

Figure 3

Point-to-surface signed distance function

Figure 4

Surface-to-surface signed distance function

Figure 5

Deviation of the workpiece due to locators’ errors

Figure 6

Locating Scheme 1

Figure 7

Distance of displacement at the inspection point q1 when locator p2 moved along Z-axis by 1 mm and p1 moved along y-axis from 0 to 10 mm

Figure 8

Locating Scheme2

Figure 9

Distance of displacement at the inspection point q1 when locator p3 moves long Z-axis from 0 to 10 mm

Figure 10

Distance of displacement at the inspection point q1 when locator p3 moves long Z-axis from 0 to 10 mm (the radius of the locators is 10 mm)

Figure 11

Distance of displacement at the inspection point q1 when locator p3 moved long Z-axis by 8 mm and the radius of the locators changes from 0.1 to 10 mm

Figure 12

Surface-to-surface signed distance function

## Errata

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