The virtual constraint model and its application to tolerance analysis

The geometrical element chain method (GECM) is a tolerance analysis approach based on parametrical driving theory, with the principle of functional dimension driving being its key theoretical basis. Currently, the functional dimension driving theory cannot cover the implicit constraints and the geometrical constraints in the 3D models, thus the application of GECM has been limited. To solve this problem, this paper presented the concept of virtual constraint model (VCM) of the products' 3D models, and constructed the algorithm of tolerance analysis oriented to VCMs to extend the application scope of GECM. Firstly, the mapping matrix between functional dimension set and the modeling parameter set was constructed, and a necessary and sufficient condition of the existence of the mapping relation was given. Secondly, the concept of VCM was put forward, and the tolerance analysis algorithm of the VCM was constructed. Finally, an example was given to illustrate the validity and effectiveness of the approach in this paper.