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An analytical model for repositioning of 6 D.O.F fixturing system

Published online by Cambridge University Press:  16 November 2012

Sajid Ullah Butt ,
Jean-François Antoine  and
Patrick Martin
Sajid Ullah Butt*
Affiliation:
LCFC, Arts et Métiers, 4 rue Augustin Fresnel, 57078 Metz, France
Jean-François Antoine
Affiliation:
LCFC, Arts et Métiers, 4 rue Augustin Fresnel, 57078 Metz, France IUT Nancy-Brabois, département GMP, Le Montet, Rue du Doyen Urion, 54601 Villers-lès-Nancy, France
Patrick Martin
Affiliation:
LCFC, Arts et Métiers, 4 rue Augustin Fresnel, 57078 Metz, France
*
a Corresponding author: sajid-ullah.butt@ensam.eu
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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 relocate 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.

Keywords

Fixturing systemfixture designmechanical modellingoptimal balancingpositioning errorLagrangian formulation
Type
Research Article
Information
Mechanics & Industry , Volume 13 , Issue 3 , 2012 , pp. 205 - 217
Copyright
© AFM, EDP Sciences 2012

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