Polytope-based tolerance analysis with consideration of form defects and surface deformations

Tolerance analysis aims to evaluate the functional requirement of mechanical assemblies in the design stage. As one of the typical tolerance analysis methods, the polytope model has shown great potential in Computer-Aided Tolerancing (CAT) field based on a series of constraints. However, existing research outcomes on this topic rarely consider form defects and the combined effects of form defects and surface deformations. This limitation may cause inaccuracy of tolerance analysis results. Hence, this paper integrates form defects and surface deformations in polytope-based tolerance analysis. Specifically, form defects are considered based on the concept of Skin Model Shapes and surface deformations are calculated based on a Conjugate Gradient-Fast Fourier Transform (CG-FFT) method. Then, the modeling method of the new polytope model is elaborated based on surface types and different types of constraints. Moreover, a case study is conducted to explain the procedure of polytope-based tolerance analysis. Through operations of the polytopes, tolerance analysis results are obtained, and the comparison with conventional polytope analysis results shows the considerable effects of form defects and surface deformations. It is expected that the proposed method can have a more realistic and accurate analysis result because of its consideration of real surface contact status.