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Research Papers

Form Tolerance Evaluation of Toroidal Surfaces Using Particle Swarm Optimization

[+] Author and Article Information
Yong Wang

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.wangyong@umich.edu

Lin Li1

Department of Mechanical Engineering, University of Michigan-Ann Arbor, 1023 H. H. Dow, 2350 Hayward Street, Ann Arbor, MI 48109-2136lilz@umich.edu

Jun Ni

Department of Mechanical Engineering, University of Michigan-Ann Arbor, 1023 H. H. Dow, 2350 Hayward Street, Ann Arbor, MI 48109-2136junni@umich.edu

Shuhong Huang

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.shhuang1@hust.edu.cn

1

Corresponding author.

J. Manuf. Sci. Eng 131(5), 051015 (Sep 24, 2009) (9 pages) doi:10.1115/1.4000103 History: Received October 09, 2008; Revised August 02, 2009; Published September 24, 2009

Toroidal surfaces are used in many machinery parts such as ball bearing races, bull nose and indexable endmills, continuously-variable transmissions, and enveloping worm gears. Torisity, the form tolerance of toroidal surfaces, plays an important role in mechanical design and quality control such as component functionality, assemblability, and interchangeability. Compared with simple forms, such as planes, spheres, cylinders, and cones, toroidal surfaces are more complex and the evaluation of torisity has not been thoroughly performed. This paper proposes a nonlinear approach to evaluate torisity information using particle swarm optimization (PSO). Three sets of PSO parameters are compared based on the least-squares objective function and minimum-zone objective function using toroidal geometry characteristics. The effectiveness and robustness of the PSO approaches are validated by experiments on simulated entire, outer, inner, thrust, and endmill toroidal surfaces, which appear in various machinery components. Compared with previous studies in torisity evaluation, the proposed approach is more efficient in the ability to provide the form tolerance and the surface profile information simultaneously. The proposed approach is also more consistent with the tolerance zone definition of ASME standard Y14.5M on dimensioning and tolerancing.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A torisity model which is consistent with ASME Y14.5M

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Figure 2

A standard entire toroidal surface (a) and an arbitrary entire toroidal surface (b)

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Figure 7

Sample points on the outer toroidal surface

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Figure 8

Sample points on the inner toroidal surface

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Figure 9

Sample points on the thrust toroidal surface

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Figure 10

Sample points on the endmill toroidal surface

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Figure 4

Sampled points on the entire toroidal surface

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Figure 5

Convergence curves for the entire toroidal surface

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Figure 6

Form tolerance results of the entire toroidal surface

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