The most used approach to solve tolerance analysis problems for flexible products is the method of influence coefficients that combines the finite element analysis with statistical analysis in order to establish a relationship between the product deviation and part deviation and to foresee the statistical distribution of stresses. The key of this relationship is the sensitivity matrix for the deviations and stresses that can be evaluated by different methods of influence coefficients. Therefore, the aim of this work is to make a review of these methods applying them to evaluate on some single parts the statistical distribution of deviations and stresses due to operating conditions, i.e. due to the displacements applied to the part during its working.

This work shows a free-body model for tolerance analysis, that uses the force free-body diagrams and the functional equations’ sensitivities, by simulating the geometrical tolerances together with the dimensional ones. The geometrical tolerances were related to the deviations due to the manufacturing process (i.e. the manufacturing signature). Moreover, weight and friction forces were simulated too. A sensitivity analysis on the developed free body model aimed to evaluate the number of points to discretize the circular bodies and how to calculate the point clouds barycentre in order to reduce the simulation time. A case study was used to exemplify the application of the proposed free-body method with and without considering the manufacturing signature. The results show that the free body model is able to solve assembly problems and the manufacturing signature significantly influences the values of the functional requirement on the product and, therefore, it is impossible to neglect it.