A new approach to predict the flexibility and precision of manufacturing systems using geometric constraints and small displacement torsors

Abstract

Cost and quality of a product are prime drivers in manufacturing. It is important to optimize these variables for maximum benefit. It is to be noted that higher quality means a product which has fewer errors. The quality of product is associated with the precision of the manufacturing system but machines to produce such products are expensive. Therefore, a method of machine selection is devised based on tolerance range. In this study, mathematical formulation is developed for parallelism and perpendicularity constraints of a surface using the concept of torsors. Torsors represent any feature (plane, cylinder, point, etc.) only in terms of its degree of freedom. Torsors also have the advantage of being added during tolerance stack-up. Mathematical equations are developed for parallelism and perpendicularity as the function of surface parameters i.e. surface angles. Alternatively, the developed model can be used to control surface parameters to obtain the required tolerances. Maximum and minimum values of system parameters are calculated. Assuming that the parameters of the manufactured parts follow statistical distribution, random values of the surface parameters are generated and compared with the parallelism and perpendicularity constraints. It is concluded that the behavior of parallelism and perpendicularity tolerances is more precise if we control individual parameters. The results are in compliance with the proposed idea that a less precise machine can produce high quality product within a specific tolerance range as the machine need not control parallelism but only the dependent variables.