Generating variational geometry of a hole with composite tolerances

Tolerance is almost ubiquitous during the whole product life. However how to effectively embody and interpret the semantics of tolerance in three-dimensional computer-aided design systems is still an open issue. Variational geometry is recognized as one of the most promising solution for it. And the methods for systematically and efficiently generating the variational geometries of all kinds of geometric entities with tolerances are imperative. In this paper, a degree-of-freedom (DOF)-based approach is proposed for generating variational geometry of a hole with composite tolerances imposed on its centerline and surface at the same time. All possible combinations of tolerance requirements for a hole are discussed. And the mathematical models for variational geometries of the centerline and the surface of a hole are deduced. Furthermore two strategies for improving the efficiency of generating the variational geometry of a hole are presented. Finally, the algorithm is implemented and some test results are given. Note to Practitioners-This paper is motivated by the problem that the tolerance information in the current computer-aided-design CAD systems lacks the necessary engineering semantics, which causes tolerance information that cannot be correctly used and impedes the integration of CAD and computer-aided manufacturing (CAM). Existing approaches have partially solved the problem for the pattern of holes (POH) and plane feature based on variational geometry. But the computational efficiency with the variational geometry method is very insufferable due to a lot of Boolean intersection operation. In this paper, the hole feature is mainly considered because its tolerance specification is quite different from other features and is imposed on the centerline and the surface of a hole at the same time. First, the mathematical model is given for interpreting the engineering semantics of the tolerance of the centerline and the surface based on the variational geometry, respectively. Then, the tolerance principles are further considered for compensation between the above two types of tolerance. More important, a direct method, which can largely avoid the Boolean intersection operation, is proposed for generating the variational geometry. The computational efficiency is thus improved dramatically and the variational geometry is generated almost in real time. This enables virtual assembly and virtual inspection with the tolerance information to be possible.