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TECHNICAL PAPERS

# Fitting of Reference Surfaces for Engineering Surfaces by Nonlinear Least-Squares Technique

[+] Author and Article Information

Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai – 600036, India

M. S. Shunmugam

Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai – 600036, Indiashun@iitm.ac.in

J. Comput. Inf. Sci. Eng 6(4), 349-354 (May 30, 2006) (6 pages) doi:10.1115/1.2353851 History: Received August 09, 2005; Revised May 30, 2006

## Abstract

Engineering surfaces comprise form and waviness errors, which are separated from the measured surface by establishing a reference surface that represents these errors. An attempt is made for the first time to fit a reference surface for simultaneous separation of form and waviness errors. A second-degree polynomial and a set of sinusoidal functions are taken as basis functions to represent form and waviness, respectively, and fitting is done using a nonlinear least-squares method. Different examples of surfaces are considered and a comparison is also made with 3D Gaussian filter to bring out the nature of reference surfaces obtained by the present fitting approach.

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## Figures

Figure 1

Power spectral plot of a typical surface

Figure 2

Practical surfaces: (i) hard-turned surface, (ii) ground surface, (iii) stone-honed surface

Figure 3

Reference surfaces for practical surfaces (cutoff=0.1mm). (a) Gaussian filtering: (i) hard-turned, (ii) ground, (iii) stone-honed, (b) Least-squares fitting: (i) hard-turned, (ii) ground, (iii) stone-honed.

Figure 4

Hard turned surface (cutoff=0.25mm). (a) Hard turned surface superimposed on spherical form; (b) Gaussian filtering: (i) reference surface, (ii) roughness surface; (c) Least-squares fitting: (i) Reference surface; (ii) Roughness surface.

Figure 5

Cross-sectional profile of hard turned surface (cutoff=0.25mm). —— Surface profile, —— superimposed form profile, ………… Gaussian reference surface profile, LS reference surface profile.

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