Integrated tolerance optimisation with simulated annealing

Abstract

Tolerance is one of the most important parameters in design and manufacturing. The allocation of design and machining tolerances has a significant impact on manufacturing cost and product quality. This article presents an analytical model for simultaneously allocating design and machining tolerances based on the least-manufacturing-cost criterion. In this study, tolerance allocation is formulated as a non-linear optimisation model based on the cost-tolerance relationship. A new global optimisation algorithm, simulated annealing, is employed to solve the non-linear programming problem. An example for illustrating the optimisation model and the solution procedure is provided.

Cost–Tolerance Function. A New Approach for Cost Optimum Machining Accuracy

“…For reasons of comparison the case study that is quoted in [11] is dealt with here using the new cost-tolerance function (28): The piston and cylinder bore of an engine assembly has three nominal dimensions 50.8 mm (piston diameter) -50.856 mm (cylinder bore diameter) -0.056 mm (clearance between the piston and cylinder bore). The tolerance zone of the latter is Ϯ 25m.…”

“…The tolerance zone of the latter is Ϯ 25m. The cost-tolerance functions that are given in Table 1 were produced via curve fitting of the relevant cost-tolerance curves of [11]. The cylinder bore length has been taken as double that of the piston.…”

“…In order to attain a minimum machining cost for a specified accuracy Ϯ t, it is necessary, as is clear from the above, to solve the problem of the optimum determination, not only of the number of the required intermediate operations, but also of their respective machining accuracies. Most applications in industrial practice deal with this problem on the basis of an empirical and/or trial-and-error mode, whereas contributions to solve it in a systematic way using optimisation methods (algorithms) have only recently appeared [2][3][4][5][6][7][8][9][10][11][12]. Tolerance bar-charts, relative cost factors, cost of scrap and cost-tolerance functions are employed in these methods.…”

Integrated total cost and Tolerance Optimization with Genetic Algorithm

“…Zhang and Wang [18], proposed mathematical models with the consideration of manufacturing process for continuous cost function and solved it first time by using non-traditional optimization technique called simulated annealing. Zhang [19] approached the problem in a totally different manner by introducing a new concept of interim tolerances, which help to determine appropriate manufacturing process and solved the problem using a non-linear programming technique (mixed penalty function approach).…”

“…Zhang [19] approached the problem in a totally different manner by introducing a new concept of interim tolerances, which help to determine appropriate manufacturing process and solved the problem using a non-linear programming technique (mixed penalty function approach). AlAnsary and Deiab [1] adopted a model similar to that proposed by Zhang and Wang [18] and solved the model by considering worst-case stack-up criteria using a genetic algorithm. Singh et al [13] solved the same model for four different stack-up conditions using a genetic algorithm.…”