A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

Tolerancing decisions can profoundly impact the quality and cost of the mechanism. To evaluate the impact of tolerance on mechanism quality, designers need to simulate the influences of tolerances with respect to the functional requirements. This paper proposes a mathematical formulation of tolerance analysis which integrates the notion of quantifier: “For allacceptable deviations (deviations which are inside tolerances),there existsa gap configurationsuch asthe assembly requirements and the behavior constraints are verified” & “For allacceptable deviations (deviations which are inside tolerances), andfor alladmissible gap configurations, the assembly and functional requirements and the behavior constraints are verified”. The quantifiers provide a univocal expression of the condition corresponding to a geometrical product requirement. This opens a wide area for research in tolerance analysis. To solve the mechanical problem, an approach based on optimization is proposed. Monte Carlo simulation is implemented for the statistical analysis. The proposed approach is tested on an over-constrained mechanism.

► Formulation uncertainty is ubiquitous in tolerance analysis problems.
► To create a logical foundation of tolerance analysis, the formal logic formulation is tested.
► Its development is based on the quantified constraint satisfaction formulation.
► Monte Carlo simulation has been used in conjunction with the optimization to calculate the probability of the functional operation of an assembly.