Algorithms for the Optimal Distribution of Resources in the Task of Manufacturing of the Broaching Tools for Production of the Aircraft Engines

Abstract

An approach is proposed to solving of the task of planning of reproduction of the broaching tools with the use of the residual life of its present composition. A criterion was formed for selection of the optimal solution - the minimal number of the tools (broaches), needed for a guaranteed performance of the task. The authors considered a procedure for estimation of the probability of implementation of the work assignment by a kit of manufactured broaching tools, based on the law of distribution of the number of the working tool cycles. An algorithm was developed for calculation of the minimal number of the necessary broaches, which ensured performance of the task with a set guaranteed probability. The algorithm for evaluation of the possibility of using the broaches with a residual resource envisages construction of a conditional law of distribution of the number of the cycles remaining before their disposal, depending on the number of the used cycles. Knowing the law of distribution of the number of the operating cycles of the new broach and the conditional law of distribution of the remaining cycles of the broaches with the remaining resource, it is necessary to calculate the probability, that a set of a predetermined number of the new broaches and the broaches with the remaining resource of the known values of the used cycles ensure implementation of the work assignment. A formula was derived for calculation of the probability of performance of the task by a mixed kit of broaches. The authors presented an example of calculation of the sought probability for a cassette with a mixed kit of four broaches. The algorithm for selection of the optimal mixed sets is based on formation of all possible versions of the use of the broaches with remaining resource and estimation of the probability of performance of the work assignment for each of them. In order to form a complete set of options of different numbers of new broaches and broaches with different residual resources the authors proposed an algorithm for generation of permutations with repetitions based on the lexical order. For selection of the optimal use of the broaches with the remaining resources a calculation was done of the probability of performance of the work assignment for each of the possible configuration options. The optimal option is chosen from the condition of performance of the work assignment with a probability, which is not less than the required guaranteed probability at the lowest costs for the purchase of new broaches. The results were presented of formation of options of the use of the existing broaches with the known residual resources, the reliability of each option was calculated, and recommendations were formed for selection of the best option, proving applicability of the proposed approach.