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.
Highlights
Fixtures are used to support, locate and hold a workpiece at a desired orientation in machine space during manufacturing [1,2,3]
The article is composed as follows; Section 2 presents the kinematic model of the reconfigurable fixturing system, by considering large displacement transformation for the repositioning of the workpiece
A fixturing system, having six locators and two clamps, considered as three dimensional springs, is shown in Figure 9. {F } is taken as machining force at any point on the workpiece, {T} is the moment of cutting tool, [KE]1 and [KE]2 are the stiffness matrices of clamps, {XE}1 and {XE}2 are the external displacements of clamps and [K]1, [K]2, . . . [K]6 are the stiffness matrices of the locators
Summary
Fixtures are used to support, locate and hold a workpiece at a desired orientation in machine space during manufacturing [1,2,3]. Baseplate repositioning will eliminate the position uncertainty due to local geometric errors and avoid the use of high DOF machines at each machine center; instead, a single fixture can perform the workpiece repositioning at each machine center. To determine the relative positioning error (due to geometrical defects or due to deformation under load) between the workpiece and the tool before and during machining or between the two parts during assembling; 2. The proposed system aims to perform automatic on-line or off-line workpiece repositioning operation It ensures the pre-positioning of complex parts for precise machining operations. The article is composed as follows; Section 2 presents the kinematic model of the reconfigurable fixturing system, by considering large displacement transformation for the repositioning of the workpiece. This case study identifies the vibrational attributes of the fixturing system, while taking into consideration the stiffness of each locator and clamp, as well as the mass of the baseplate-workpiece assembly
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