Optimization of Gear Tolerances by Statistical Analysis and Genetic Algorithm

Abstract

The purpose of functional tolerancing process is to define the geometrical specifications(tolerances) of parts ensuring functional requirements. An important distinction in tolerance process is that engineers are more commonly faced with the problem of tolerance synthesis rather than tolerance analysis. In tolerance analysis the parts tolerances are all known and the resulting geometrical requirement respect is calculated. In tolerance synthesis, on the other hand, the geometrical requirement is known from design requirements, whereas the magnitudes of the parts tolerances to meet these requirements are unknown. In this paper, we focus on the gear tolerances, and we propose an approach based statistical analysis for tolerance analysis and genetic algorithm for tolerance synthesis. Usually, statistical tolerance analysis uses a relationship between parts deviations and functional characteristics. In the case of tolerance analysis of gears, thus relationship is not available in analytic form, the determination of a functional characteristic(e.g. kinematic error) involves a numerical simulation. Therefore the Monte Carlo simulation, as the simplest and effectual method, is introduced into the frame. Moreover, to optimize the tolerance cost, genetic algorithm is improved. Indeed, this optimization problem is so complex that for traditional optimization algorithms it may be difficult or impossible to solve it because the objective function is not available in analytic form. For the evaluation of the fitness of each individual based on Monte Carlo Simulation, the number of samples is the key of precision. By a large number of samples, the precision can be improved, but the computational cost will be increased. In order to reduce the computational cost of this optimization based on Monte Carlo Simulation and Genetic Algorithms, the strategy is to adopt different precision of fitness; different numbers of samples during the optimization procedure are introduced into our algorithms.