Force constraint-based approach to compute the position and orientation of parts assembled by multiple non-ideal planes

Abstract

The occurrence of position and orientation deviations (PODs) during the assembly of rigid components, which is caused by non-ideal morphologies on the manufactured surface, directly affects the performance of the mechanical product. Moreover, the generated PODs are influenced by the deformation of the contact points because of the assembly force. Therefore, to control the product performance in the design stage, the PODs should be computed considering both the non-ideal morphologies of the mating surfaces as well as the forces acting on the assembly. However, most existing approaches to POD computation ignore the effects of the assembly force. Moreover, they often focus on assemblies with a single mating plane. To address this problem, a force constraint-based approach is proposed in this study, which considers both the non-ideal morphologies of multiple mating planes and the assembly forces. The principle of force balance is employed to determine whether the assembly is completed. Different tentative positions and orientations are determined according to the strategies of progressively approaching position and orientation, and recursion of degrees of freedom (DOFs). An unbalance indicator was established in this study to determine whether the force balance in the direction of each DOF is satisfied. As long as the force balance of all DOFs to be constrained is achieved, the assembly of parts is considered to be finalised, and the final PODs are acquired. Finally, the PODs of a typical assembly with multi-mating planes and the guiding accuracy of a sliding workbench are computed according to the non-ideal morphologies modelled from the perspective of manufacturing errors, thereby validating the proposed approach.