An iterative method of statistical tolerancing based on the unified Jacobian-Torsor model and Monte Carlo simulation

This paper focuses on exploring an iterative method of statistical tolerance design to guide designers to select tolerances more economically and effectively. After having identified the assembly functional requirement (FR) and the functional elements (FEs) of corresponding tolerance chain, the expression of a unified Jacobian-Torsor model can be derived. Monte Carlo simulation is employed to generate random variables simulating the variations of small displacement torsor associated with the FE pairs with all the generated random values being within the intervals constrained by the corresponding tolerance zones. Then, the real multiplication operations are repeatedly executed to this model, a large number of real torsor component values of FR will be obtained and we can perform statistical analysis for these simulated data to get the statistical limits of the assembly FR in the desired direction. The tolerances of critical FEs may need to be adjusted to satisfy the assembly FR imposed by the designer, and the percentage contribution of each FE to the assembly FR can help determine these critical tolerances that need to be tightened or loosened. Once the calculated FR is in close agreement with the imposed FR, the iterative process can be stopped, and the statistical tolerance redesign is achieved. The effectiveness of the proposed method is illustrated with a case study. Compared with the deterministic tolerancing method, the results show that the proposed method is more economical and that can relax significantly the precision required, manufacturing and inspection costs can then be reduced considerably.