Fixture Layout and Clamping Force Optimization for Large-Scale Workpiece Using Augmented Lagrangian Method

The Fixture layout and clamping force are well known as important factors that influences the localization accuracy of the workpiece. Considering the unique characteristics of the Large-Scale workpiece in practice, we, in this paper, propose a unified method of optimizing an existing fixture configuration under heavy-duty condition based on Algmented Lagriangian Method (ALM). We fir- stly derived the models of localization error and static force equilibrium which describe the kinematic condition and quasi-static process of the fixture-workpiece system. Then, we introduce Hertz contact theory to better describe the nonlinear relationship of the local deformation and the contact force. Further, we define the minimum norm of the position error of critical points as the objective function and formulate a multi-constrained problem of solving the optimized fixture configuration. By using the ALM, the nonlinear constrained programming is transformed into an unconstrained one through which we obtain the optimal solution. Finally, a numerical example is presented and compared with the results of FEA simulation.