A Practical Method for Redesigning Statistical Tolerances Using Monte Carlo Simulation

Abstract

This paper presents a practical method for redesigning statistical tolerances by combining the unified Jacobian-Torsor model and Monte Carlo simulation. After having identified the assembly functional requirement (FR) and determined the functional elements (FEs) encountered in tolerance chain, the specific expression of Jacobian-Torsor model can be obtained. Monte Carlo simulation is employed to repeatedly evaluate the model using sets of random values as inputs to make this deterministic model become a statistical model. Once the real multiplication operations have been performed on this model, we can get large amount of simulated data, from which we can obtain the statistical limits of the assembly FR in the desired direction. The percentage contribution of each FE to the total FR can help the designer redesign the tolerances of the critical FEs to respect the specified FR. This redesign process may need to be repeated several times until the calculated FR is consistent with the specified FR, so the tolerance values that need to be determined are obtained, and the redesign of statistical tolerances is achieved. The effectiveness of the proposed method is illustrated by taking the crank-connecting rod mechanism of piston aeroengine assembly as an example.