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An orthogonal array based optimization algorithm for computer-aided measurement of worm surface

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Abstract

Being versatile and fast, a co-ordinate measuring machine is used for the measurement of worm. A best-fit surface is obtained from the measured points by a surface fitting method, which minimizes the root mean square of normal deviations. For this problem in discrete space, an iterative optimization algorithm based on an orthogonal array is developed. On minimizing the objective function, the deviations of worm parameters from the specified values are obtained. The algorithm is validated using input data points generated from a straight-sided in axial section worm (ZA worm) with known errors. The proposed algorithm requires fewer objective function evaluations and the result is highly repeatable as there are no random operations involved.

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Abbreviations

b :

half bottom width of worm groove

L :

lead

L m :

range reduction factor

M :

number of measured points

m :

module

nd :

normal deviation

n x , n y , n z :

unit normal vector along coordinate directions

N :

normal vector

N x , N y , N z :

normal vector along coordinate directions

Nc :

number of chromosomes

Ng :

number of genes per chromosomes

Nd :

number of binary digits per gene

p :

screw parameter (lead per radian)

p a :

axial pitch

Pcross :

cross over probability

Pmute :

mutation probability

r b :

root radius of worm

r p :

probe radius

S r :

range of search

x c ,y c , z c :

real surface coordinates (contact point)

x m , y m , z m :

measured coordinates (probe center point)

x w ,y w , z w :

worm surface coordinates (ideal)

z f :

form number of worm

ΔL :

error in lead

Δ α:

error in pressure angle

α:

axial pressure angle

γ:

lead angle at reference diameter

u,θ:

surface parameters

μ:

root mean square of normal deviations (objective function)

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Authors and Affiliations

  1. Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    L. V. Mohan & M. S. Shunmugam

Authors
  1. L. V. Mohan
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  2. M. S. Shunmugam
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Correspondence to M. S. Shunmugam.

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Mohan, L.V., Shunmugam, M.S. An orthogonal array based optimization algorithm for computer-aided measurement of worm surface. Int J Adv Manuf Technol 30, 434–443 (2006). https://doi.org/10.1007/s00170-005-0097-7

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  • DOI: https://doi.org/10.1007/s00170-005-0097-7

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