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The uncertainty of radius estimation in least-squares sphere-fitting, with an introduction to a new summation based method

The uncertainty of radius estimation in least-squares sphere-fitting, with an introduction to a new summation based method
The uncertainty of radius estimation in least-squares sphere-fitting, with an introduction to a new summation based method
This paper considers the sensitivity of three sphere-fitting algorithms to real-world measurement errors. It pays particular attention to nominally spherical surfaces, such as those typically measured by tactile and optical profilometers, addressing the limitations of sensor gauge range and angular tolerance. A recently proposed linear circle-fitting algorithm is extended to a sphere-fitting algorithm and its performance compared to two long standing sphere-fitting algorithms; namely linear and non-linear least-squares. Sources of measurement error in optical profilometers are discussed, and user defined scan parameters are optimised based on the results of a designed experiment. The performance of all three sphere-fitting algorithms are tested on a sphere superimposed with varying degrees of surface irregularities in a Monte Carlo simulation; this study shows that both linear routines display a negative skewness in their radius error distribution. Finally, a method of predicting radius uncertainty is offered that considers the surface residual that remains after sphere-fitting and relates this to the radius uncertainty of the chosen algorithm.
least-squares, sphere-fitting, design of experiment, monte carlo, uncertainty, surface metrology, profilometer
0141-6359
499 - 505
Cross, Kevin J.
70c14f28-9f45-4914-a3c7-cbeee038085d
McBride, John W.
d9429c29-9361-4747-9ba3-376297cb8770
Lifton, Joseph J.
e4b170b4-165c-4ae0-9e7d-9d53ab54247f
Cross, Kevin J.
70c14f28-9f45-4914-a3c7-cbeee038085d
McBride, John W.
d9429c29-9361-4747-9ba3-376297cb8770
Lifton, Joseph J.
e4b170b4-165c-4ae0-9e7d-9d53ab54247f

Cross, Kevin J., McBride, John W. and Lifton, Joseph J. (2014) The uncertainty of radius estimation in least-squares sphere-fitting, with an introduction to a new summation based method. Precision Engineering, 38 (3), 499 - 505. (doi:10.1016/j.precisioneng.2014.01.004).

Record type: Article

Abstract

This paper considers the sensitivity of three sphere-fitting algorithms to real-world measurement errors. It pays particular attention to nominally spherical surfaces, such as those typically measured by tactile and optical profilometers, addressing the limitations of sensor gauge range and angular tolerance. A recently proposed linear circle-fitting algorithm is extended to a sphere-fitting algorithm and its performance compared to two long standing sphere-fitting algorithms; namely linear and non-linear least-squares. Sources of measurement error in optical profilometers are discussed, and user defined scan parameters are optimised based on the results of a designed experiment. The performance of all three sphere-fitting algorithms are tested on a sphere superimposed with varying degrees of surface irregularities in a Monte Carlo simulation; this study shows that both linear routines display a negative skewness in their radius error distribution. Finally, a method of predicting radius uncertainty is offered that considers the surface residual that remains after sphere-fitting and relates this to the radius uncertainty of the chosen algorithm.

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More information

Accepted/In Press date: 20 January 2014
e-pub ahead of print date: 31 January 2014
Published date: July 2014
Keywords: least-squares, sphere-fitting, design of experiment, monte carlo, uncertainty, surface metrology, profilometer
Organisations: Mechatronics

Identifiers

Local EPrints ID: 382626
URI: http://eprints.soton.ac.uk/id/eprint/382626
ISSN: 0141-6359
PURE UUID: 2cca526a-f967-4359-9834-41f1e398736d
ORCID for John W. McBride: ORCID iD orcid.org/0000-0002-3024-0326

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Date deposited: 02 Nov 2015 14:46
Last modified: 15 Mar 2024 02:39

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Contributors

Author: Kevin J. Cross
Author: John W. McBride ORCID iD
Author: Joseph J. Lifton

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