Incorporation of form deviations into the matrix transformation method for tolerance analysis in assemblies

Abstract

Mathematical models for tolerance representation are used to assess how the geometrical variation of a specific component feature propagates along the assembly, so that tolerance analysis in assemblies can be carried out using a specific tolerance propagation method. Several methods for tolerance analysis have been proposed in the literature, being some of them implemented in CAD systems. All these methods require modelling the geometrical variations of the component surfaces: parametric models, variational models, DoF models, etc. One of the most commonly used models is the DoF model, which is employed in a number of tolerance analysis methods: Small Displacement Torsor (SDT), Technologically and Topologically Related Surfaces (TTRS), Matrix Transformation, Unified Jacobian–Torsor model. However, none of the DoF-based tolerance analysis methods incorporates the effect of form deviations. Among the non DoF-based methods, there are two that include form tolerances: the Vector Loop or Kinematic method and the Tolerance Map (T-Map) model, although the latter is still under development. In this work, a proposal to incorporate form deviations into the matrix transformation method for tolerance analysis in assemblies is developed using a geometrical variation model based on the DoF model. The proposal is evaluated applying it to a 2D case study with components that only have flat surfaces, but the proposal can be extrapolated to 3D cases.