Tolerance Design Based On Monte Carlo Simulation And Genetic Algorithms

The main objective of this paper is to present a frame of tolerances allocation. We consider the nonlinearly constrained tolerance allocation problems. Indeed, tolerances are allocated to achieve optimal ratio between the sum of the manufacturing costs (tolerances costs) and the risk (probability of the respect of geometrical requirements and assembly requirements).The techniques of Monte Carlo simulation and genetic algorithm are adopted to solve these problems.In the industrial cases, the optimization problem is so complex that for traditional optimization algorithms it may be difficult or impossible to solve it. Therefore, this optimization is realized by genetic algorithm. A genetic algorithm includes 3 steps: the initialization of the first population, the evaluation of the fitness of each individual of the population P and the definition of a new population by genetic operators. We propose Guo's Crossover operator which is improved in the design of fitness function according to the characters of the Monte Carlo Simulation for reducing computational expense.The probability estimation is realized by statistical tolerance analysis. Monte Carlo technique is easily the most popular tool used in tolerancing problems. Indeed, the appeal of Monte Carlo lies in its applicability under very general settings and the unlimited precision that can be achieved.An illustrative example (hyperstatic mechanism - two dimensional tolerances transfers) is given to demonstrate the efficiency of the proposed approach. Indeed, this example includes all problems: The tolerances transfers function is not linear because the gaps in the joints of mechanisms are considered and are not modelized by random variables. The cost function could be continue or discrete.