Computer Aided Tolerance Analysis of Mechanical Parts Based on Variational Geometry Techniques

In spite of the impressive growth in functionality of modern CAD systems, the integration of tolerance information into solid models and the assessment of the effects of size and geometric tolerances on functional dimensions and parameters of parts and assemblies is still lacking in most systems. In the engineering design practice, tolerance analysis and synthesis computations, if any, are usually performed with very little support by computer tools and therefore hardly optimized, even though quality requirements and cost consideration might suggest a careful selection of the prescribed tolerances. The implementation of a tolerance analysis solver for 2D models based on variational geometry that was able to manage size and geometric tolerances, except for form tolerances, together with uncertainties on design parameters, was detailed in a previous work (Concheri, 1995). Aim of the present paper is to discuss the extension of such technique to the analysis of 3D mechanical parts built up of basic features (i.e. described in terms of prismatic, cylindrical, spherical and conical surfaces). Variational geometry techniques have been adopted in many commercial CAD systems in order to allow for dimensional variability of part geometry, but 3D parts are usually modelled following an hybrid approach; hence, contrary to 2D, in 3D a tolerance specific variational model must be extracted from the part definition. Such aspects and the other problems that derive from the extension of variational geometry to the 3D domain will be addressed. Finally, a 3D tolerance analysis based on the variational geometry paradigm will be presented.