Producibility models for position tolerancing problems

At the design stage, the tolerancing scheme attached to the print of a mechanical part is engineered to guarantee the functional aptitude of a part and its proper interaction with other parts in the assembly. At the manufacturing stage, it is often necessary to evaluate the producibility or yield of a product, which is crucial to the successful commercialization of the product. The mapping between various tolerance constraints and basic manufacturing process characteristics, and producibility, however, is somewhat hampered by the lack of quantitative methods. The objective of this study is to develop solution methods for the producibility of fours sets of position tolerancing problems. The first problem deals with the deterministic tolerance transfer of a subset of position tolerance problems and the solution methodology is based on a mathematical optimization. The second problem addresses the probabilistic producibility of composite position tolerance, and numerical approximations to the computation of relevant probabilities are developed. The third and fourth problems study the influence of inaccuracies of a functional gauge and a CMM (Coordinate Measuring Machine), respectively, on the producibility of a single or dual-hole pattern controlled by a position tolerancing scheme.