An Uncertainty Approach for Fixture Layout Optimization Using Monte Carlo Method

The fixture layout is well known as an important factor that influences the localization accuracy of the workpiece in mass production. Meanwhile, due to the existence of the uncertain errors that originated from assembly and manufacture process, the positional variability which depends on the tolerance allocation has statistical features. In this work, we propose an uncertainty approach of optimizing the fixture layout to improve overall product quality. Firstly, we analyze the deterministic localization model and static equilibrium condition by introducing related uncertainty errors. Then, using the Monte Carlo Method (MCM), we randomly assign the fixture parameters from corresponding probability distributions. Further, we compute the norm of position error of critical point according to the principles of minimum potential energy and the Nonlinear Least Square Method (NLSM). After we sequentially search the minimal mean and variance of the position error in discrete point set domain, the optimal solution of the fixture layout is obtained. Finally, a numerical example is illustrated and compared with the result of FEA simulation.