Variation Analysis of Non-Rigid Assembly Using FEM and Fractals

Abstract

Many studies on the assembly of non-rigid parts suggest that the part variation affects the assembly dimensional quality. However, little is known about how the detailed microstructure of part variation influences the assembly dimensional quality. In this paper, a new method based on the finite element method (FEM) and fractal geometry is proposed to explore the influence of the part variation microstructure on the assembly dimensional variation. In the new method, a special fractal function, the Weierstrass-Mandelbrot (W-M) function, is used to extract and represent the characteristics of the part variation microstructure. FEM is applied to analyze the deformation of non-rigid parts by integrating the part variation microstructure. The contribution of the detailed part variation to the final assembly deformation is obtained by the influence coefficients method. The proposed method is implemented by using commercial software tools, ANSYS and Matlab. The proposed method is illustrated through a case study on an assembly of two flat sheet metal parts. This new approach should benefit high precision assemblies.