An Analytical Model for Repositioning of 6 D.O.F Fixturing System

Abstract

Dimensional errors of the parts from a part family cause the initial misplacement of the workpiece on the fixture affecting the final product quality. Even if the part is positioned correctly, the external machining forces and clamping load cause the part to deviate from its position. This deviation depends on the external load and the fixture stiffness. In this article, a comprehensive analytical model of a 3-2-1 fixturing system is proposed, consisting of a kinematic and a mechanical part. The kinematic model relocates the initially misplaced workpiece in the machine reference through the axial advancements of six locators taking all the fixturing elements to be rigid. The repositioned part then shifts again from the corrected position due to the deformation of fixturing elements under clamping and machining forces. The mechanical model calculates this displacement of the part considering the locators and clamps to be elastic. The rigid cuboid baseplate, used to precisely re-locate the workpiece, is also considered elastic at the interface with the locators. Using small displacement hypothesis with zero friction at the contact points, Lagrangian formulation enables us to calculate the rigid body displacement of the workpiece, deformation of each locator, as well as the stiffness matrix and mechanical behavior of the fixturing system. This displacement of the workpiece is then finally compensated by the advancement of the six axial locators calculated through the kinematic model.