Design of optimal measurement strategies for geometric tolerances control on coordinate measuring machines

This study is concerned with a vast industrial problem: the inspection of physical components and subsystems for checking their conformance to dimensional and geometric tolerance specifications. Although a number of non contact optical devices are being currently developed for such a task, Coordinate Measuring Machines (CMM) are still universally adopted thanks to their superiority in terms of accuracy in the measurement of point coordinates. However, their unsurpassed metrological quality for this basic operation is counterbalanced by a fundamental problem that is plaguing practitioners in the sector of industrial metrology. The problem is usually referred to as methods divergence and can be stated as follows. On one hand, the machines probe the part surface point-wise and economic constraints force the point sample to be small. On the other end, geometric errors, as defined by tolerance standards, depend heavily on extreme values of the form deviations over the related surface so that a full-field inspection is virtually required. For example, straightness error is the minimum distance between two parallel lines enclosing the actual feature. Thus extreme points are more important than the others in determining the straightness error. This problem, translated in statistical terms, means using a small sample of form deviations to make inference on a quantity dependent on extreme values of the population, thereby unlikely to be in the sample. Thus sample-based evaluation of geometric errors is naturally prone to be substantially biased and uncertain, especially when the surfaces exhibit systematic form deviations. In spite of this, common practice in industry is to probe very few points according to very simple sampling strategy (uniform, random, stratified). The software packages sold with the machines contain algorithms of computational geometry which are selected by purely economic criteria (easy to implement, fast to compute) regardless of their implications on measurement quality. Moreover, user awareness of the importance of evaluating measurement uncertainty in the inspection of geometric tolerances is exceedingly limited. This is no wonder if we consider that the ISO committees have been working for several years on different four methods for uncertainty evaluation in CMM measurement tasks (ISO 15530 family) and still now only one standard has been officially delivered (ISO 15530-3, march 2004). Uncertainty calculation using calibrated objects).