Design and modelling of a fixturing system for an optimal balancing of a part family

Dimensional errors of the parts of a part family cause the initial misplacing 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 this initial position depending upon that external load and the stiffness of the fixture. In this thesis, a comprehensive analytical model, consist of a kinematic and a mechanical model, of a 3-2-1 fixturing system is proposed. The kinematic model relocates the initially misplaced workpiece in the machine reference by the axial advancements of the six locators considering all the fixturing elements to be rigid. This repositioned part again displaces from the corrected position under the 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 relocate the workpiece, is also considered elastic at the contacts with the locators. The non-linear behavior of the contact deformation is linearized by the converging the deformation of locators till the required precision is attained. Using small displacement hypothesis with zero friction at contacts, Lagrangian formulation enables us to calculate the rigid body displacement of the workpiece, deformation of each locator following minimum energy, and stiffness matrix and mechanical behavior of the fixturing system. This displacement of the workpiece is again compensated by the advancement of the six axial locators calculated through the kinematic model.