A novel modelling method of geometric errors for precision assembly

Geometric errors are inevitably observable on machining parts and have huge influences on the assembly quality and precision of mechanical system. The modelling of geometric errors is the key issue for the prediction of their effects on the assembly quality. Although various approaches for the representation and analysis of geometric errors have been proposed, most of them only consider orientation and position deviations but do not consider form errors. However, in mechanical system, since the non-uniform distribution of the altitudes of form errors on parts surface inevitably leads to non-uniform contact states, further causing the local surface deformations and non-uniform stresses on contact surfaces, even very small form errors propagate and accumulate through assembly parts and lead to malfunction as well as decreased assembly accuracy stability. The paper proposes a method for the representation of geometric errors based on Non-Uniform Rational B-Splines (NURBS) surface, which can consider form errors and characterize the altitude distribution of geometric errors on the machined surface. Machining Characteristic Model (MCM), representing the distribution characteristics of geometric errors on the surfaces machined under the same machining process, is established by averaging a number of surface models of geometric errors. The developed mathematical models of geometric errors can be implemented in COMPUTER-AIDED DESIGN (CAD) system so that a method to integrate geometric errors in CAD model is presented. The resulting solid model (i.e. REALISTIC GEOMETRIC SOLID MODEL) is the representation of parts geometry considering geometric errors. Realistic assembly model is established through the relative positioning of REALISTIC GEOMETRIC SOLID MODELS, which realizes the consideration of parts geometric errors in the virtual modelling of mechanical assembly. The efficiency and feasibility of the proposed methods are verified in the experimental study.