A practical evaluation approach to form deviation for surface of revolution based on optimal interpolation of generating line

Abstract

This paper proposes a practical approach to evaluating form deviation of surface of revolution based on the coordinate measurement data of discrete points. In this approach, the generating line of a surface of revolution to be inspected is represented approximately by the combination of straight line and circular arc segments under the condition of satisfying the pre-specified approximation accuracy. The form deviation of a measured point is calculated relative to its corresponding straight line or circular arc segment along the approximate generating line, and thus no specific calculation to compensate the influence of probe radius to the measured data is necessary. The localization errors of the inspected contour surface are evaluated using the minimum zone criterion or the least squares criterion to achieve the correct form deviation of the whole contour. Because it is guaranteed that the difference between the deviation definitions for a measured point, one relative to the original contour and the other to the approximate contour, is not larger than the value of the approximate accuracy pre-specified in the restructure operation of the generating line, the evaluation precision of the form deviation for the contour surface is sufficiently reliable. The effectiveness and the efficiency of the approach are verified with a practical evaluation example to a surface of revolution. Moreover, a weighting calculation taking into consideration of the distribution density of measured points is introduced for the least squares criterion in order to obtain a rational evaluation result for the measured points with non-uniform distribution on the inspected surface.