3D statistical tolerance analysis technique and the application in piston aeroengine assembly

The most important task for 3D assembly tolerance analysis is to check how the tolerances affect the quality or functionality of a product when the parts are assembled together. This paper presents the way 3D statistical tolerance analyses are implemented by integrating the unified Jacobian-Torsor model and Monte Carlo simulation techniques. To perform 3D statistical tolerance analysis, a unified Jacobian-Torsor model is established based on the effects that small displacements of a series of functional elements (FE) have on functional requirements (FR) of a product. The Monte Carlo simulation is then used to iteratively evaluate the model using sets of random numbers as inputs so as to make this deterministic model change into a stochastic model. Thus the statistical limits for the FR in the direction of analysis can be obtained after a large number of iterations and the goal of 3D statistical tolerance analysis is achieved. The effectiveness of the proposed approach has been validated by using a numerical example of piston aeroengine assembly. Although the example used is for a crank-connecting rod mechanism of piston engine, the approach presented is capable of handling complex statistical tolerance analysis problems in robots and intelligent equipments, automobile manufacturing and many other fields.