Geometrical Simulation of Multiscale Toleranced Surface With Consideration of the Tolerancing Principle

Surface quality and accuracy are the most important factors that affect the performance and life cycle of products. Surface deviations are confirmed to be nonstationary random signals. They show characteristics of randomness, irregularity and multiscale. For precise components, those deviations, i.e., the location/orientation deviations, form deviations, waviness and roughness are constrained by different scales of tolerances. In addition, tolerancing principles are specified to deal with the relationship between geometrical and dimensional deviations of the workpiece. Conventional modeling methods are unable to express surfaces with those features. This paper proposed a new method for geometrical modeling of multiscale toleranced workpiece with consideration of tolerancing principles. The workpiece deviations are decomposed into different scale of deviations. Each scale of deviations is expressed as the products of the normalized deviations and deviation factors. To balance the conflict between computing time and accuracy, a multilevel displaying method is developed. Those deviations are presented at different levels. In the simulation, each scale of tolerances and the tolerancing principles are integrated into the geometrical model of the workpiece. At the end of this paper, a case study was carried out to validate the proposed method.