A statistical approach for three-dimensional tolerance redesign of mechanical assemblies

Abstract

The unified Jacobian–Torsor model has been developed for performing three-dimensional tolerance analysis in both deterministic and statistical situations. The aim of this paper is to develop a statistical approach for three-dimensional tolerance redesign of mechanical assemblies by integrating the unified Jacobian–Torsor model and Monte Carlo simulation to guide the designer to choose tolerances more economically. To implement the proposed approach, a unified Jacobian–Torsor model is created based on the assembly functional requirement and assigned initial tolerance values. The Monte Carlo simulation is employed to iteratively evaluate the model using sets of random numbers as inputs so as to make this deterministic model become a stochastic one. The simulation is stopped as the number of iterations increases to the pre-specified number of iterations, the statistical results of functional requirement are obtained as well as corresponding contribution percentage of each functional element to the total functional requirement is calculated. The results are verified by comparing the statistical results of functional requirement with the specified design specification, while the contribution percentage chart can help the designer determine which tolerance should tighten or loosen. After several iterations, once the statistical result of functional requirement is sufficiently close to the design specification, the final result of tolerance values can be obtained and three-dimensional tolerance redesign of mechanical assembly is achieved. A numerical example is given to demonstrate the application of the proposed method, and the comparison with the deterministic tolerance redesign method exhibits that the proposed method has better economic effect.