THE EFFECT OF SAMPLING IN CIRCULAR SUBSTITUTE GEOMETRIES EVALUATION

Coordinate Measuring Machines (CMMs) are widely used in dimensional me trology applications of the manufacturing industry. CMMs perform the d imensional control of machined parts by measuring a set of points of t he manufactured part and by,fitting a substitute geometry, which is a geometric element with known analytical representation (line,plane, ci rcle, etc.). The substitute geometry is then used to determine positio n, dimension and form of the element and the accordance of the manufac tured part with the design tolerances. Therefore, the precision of the substitute geometry estimate is the basis for a reliable and accurate dimensional measurement. Two important factors that affect the precis ion of the estimate are the number and the position of measured (or sa mpled) points. The present work is addressed to the definition of the relationship between the number and position of sampled points and the errors of the estimate of radius and position of the centre of circul ar profiles (holes or shafts) with the Least Squares Method. A new app roach to the problem is proposed and the analytical solution of the pr oblem is presented. Using the identified equations it is possible to e valuate the distributions of the estimate errors and therefore to dete rmine their confidence limits. As will be discussed, as the number of sampled points increases the confidence limits of the errors may incre ase or decrease, depending on the spectra of the machined profiles. Th e problem of the definition of the optimal number and angular position of the sampled points is analysed and a solution is proposed. Finally , the last part of the present work is an application of these equatio ns to a real case of turning operation of steel. (C) 1998 Elsevier Sci ence Ltd. All rights reserved.