Employing fractals and FEM for detailed variation analysis of non-rigid assemblies

Many studies on non-rigid assemblies, or assemblies of non-rigid components, suggest that the component variation affects the assembly dimensional quality. However, little is known about how the variation of surface micro-geometry of assembly components influences the assembly dimensional quality. In this paper, a new method based on the fractal geometry and finite element method (FEM) is proposed to study such an influence. In the new method, a special fractal function, named the Weierstrass–Mandelbrot (W–M) function, is used to extract and represent the characteristics of surface micro-geometry of assembly components. FEM is applied to analyze the deformation of non-rigid assemblies by integrating the variation of component micro-geometry. The sensitivity matrix between the component variation and assembly variation is obtained by using the existing influence coefficients method. It is found that contributions of the surface micro-geometry of assembly components to the final variation of non-rigid assemblies could be substantial under certain conditions. The proposed method is illustrated through a case study on an assembly of two flat sheet metal components under different fixture-releasing conditions.