A quasi-Monte Carlo statistical three-dimensional tolerance analysis method of products based on edge sampling

The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems.

With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements.

The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously.

The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model.

The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection.

The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.