A Mathematical Model of the Assembly Error for Flat Surfaces

Abstract

At the design, manufacturing and assembly stages of products, an analysis of the assembly accuracy is performed. When designing an assembly, you assign tolerances to the dimensions, shape, orientation, and location of parts. In the manufacture and assembly of products, you ensure quality by optimizing parameters. This article presents a new mathematical model based on a difference surface and an iterative algorithm for finding contact points. The difference surface was used to find the three starting points of contact. The initial plane equation was defined by these three points, that can support the part in a stable manner. It was assumed, that when mating, the moving part rotates relative to the stationary part by an angle, determined by the initial plane. The iterative algorithm repeats the search for contact points and the construction of a new plane. The orientation and location errors of the assembly of flat parts were studied using the developed mathematical model, taking into account the real geometry of the parts. The assembly of two planes after grinding was analyzed using numerical simulation. The analysis is statistically confirmed using the generated MATLAB simulation program. The results were showed that, in most cases, the assembly error is less than the form error of constituent planes.