Tolerance analysis of flexible kinematic mechanism using DLM method

Due to the fact that there are unwanted variations in manufacturing processes, all parts produced in industry are not manufactured with nominal or exact dimensions. Therefore for each part dimension, a tolerance limit is prescribed. Also for all assemblies, a limit of variation is prescribed for a specified parameter of the assembly which is referred to as the assembly specification, and it could be the position of a point, a gap or geometry tolerance of a feature in the assembly. As a matter of fact, the performance of the assembly is measured by accuracy of the assembly specification which is a function of associated part tolerances. If the assembly specification has limits of variation in two or more directions, the correlation between these variations also impresses the limit of variation. To determine the bivariate distribution of the assembly specification, in terms of part tolerances, the direct linearization method (DLM) is used. In this paper, the coupler point (C.P.) position of a four-bar mechanism during one cycle of motion is considered as the assembly specification. The mechanism consists of flexible parts and is subjected to external loading. The extra variations of each part dimensions due to its flexibilities will impose new variations for the assembly specification. The influence of loading on variation of the assembly specification is modeled by the finite elements method (FEM) using CALFEM toolbox of MATLAB software. First, the valid domains of DLM are recognized by means of Monte Carlo simulation and then, the percent contribution of each manufacturing variable in assembly specification is determined by DLM method. The simulation results confirm that after loading the mechanism, mass production rejects are remarkably increased. The paper proposes that by decreasing the tolerance limits of those manufacturing variables that have the highest contribution in the assembly specification, the number of rejects could be decreased significantly.