Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations

Selection of an appropriate sampling strategy and of the correct fitting algorithm are two of the key issues in the practice of modern coordinate metrology. A recent report described the development of new techniques for modeling the form errors of machined part features and illustrated their use in identifying and understanding the relation of form errors to machining process variables. In this report, these mathematical tools are further developed and applied for the determination of optimum, reasonably-sized probing patterns for measurement under time and economic constraints. The focus of the work reported here is on full internal cylindrical surfaces. The technique is, however, of general utility and can be employed with any nominal feature geometry. Its application does, in many cases, produce significant improvements in the uncertainty of derived geometric dimensioning and tolerancing parameters with modest or no increase in measurement time. In contrast to most work on these problems, extensive use is made of process-dependent information in selection of sampling protocol and data analysis method. Since the method begins with an understanding of the form errors introduced into the part by the particular manufacturing regime, at least partial benefit can be seen even when the sample pattern optimization is employed in conjunction with commercial, off-the-shelf CMM control and data analysis software.