The quantification of sampling error in coordinate measurement
This work was canied out between October 1986 and February 1989 at the School of Engineering, University of Warwick. The thesis begins with a review of the configurations of coordinate measuring machines in common use and an investigation into the types and magnitudes of the errors incurred due to various phenomena associated with the design, deformation or misalignment of the machine components. Some of the more significant of these errors are then measured and tabulated with a view to using them as a comparison to further work. Methods by which these errors can be rectified are then briefly reviewed. Chapter 2 is concerned with the inadequacies associated with current coordinate measuring machine software algorithm design. Measurement practices are reviewed and sources of inconsistency or potential misinterpretation are identified. Sampling error is singled out as being of particular significance. Chapter 3 reviews geometric element fitting procedures and the errors that can result from ill advised measuring practice. Systematic and random error analyses of the errors incurred in the estimates of geometric parameters are reviewed and an original investigation is performed into the errors incurred in parameters due to not considering all possible data (sampling error.) Chapter 4 presents an assessment of the nature of the problem of sampling error and outlines the way in which a robust algorithm for the formal quantification of these errors should be formulated. Chapter 5 then identifies the criteria that would maximise the implementability of an algorithm of this type. An algorithm satisfying these particular requirements is duly developed. Finally, chapter 6 consists of an investigation into the effect of probe geometry on the phenomenon of sampling errors. A method is then developed whereby the probe geometry that will minimise sampling error can be readily selected.