The generalized mathematical model of the failure of the cutting tool

Abstract

Abstract. We offer a mathematical model which takes into account the following factors: the spread of the cutting properties of the tool, parameters spread of gear blanks and consideration of the factor of a possible fracture of the cutting wedge tool. The reliability function, taking into account the above-mentioned factors, has five parameters for which assessment we propose a method according to our experience. A numerical illustration of the method is shown in the article. We suggest using the model in the optimization mode of the cutting tool preventive measures. IntroductionEfficiency of tooling on metal cutting machines is largely dependent on the reliability (stability) of cutting tools. This efficiency can be increased at the cost of the rational use of the cutting tools life. In addition, by predicting the durability of cutting tools, the cost of tool maintenance of machine-building enterprises can be reduced. These enterprises are characterized by a very wide range of consumable cutting tools [1]. The task of forecasting of cutting tools durability and efficiency improvement of the tool life are complicated by the fact that the cutting tools life (Mean-Time-Between-Failures (MTBF) according to the terminology of the reliability theory) is a random variable that depends on many factors: cutting parameters, cutting properties of tools, the type of cutting, hardness of work pieces, the value of allowances for processing, pre-stress and strain state, vibration, geometric errors of the machine and other factors [2][3][4][5][6][7].Cutting tools properties even in one batch are subject to variety. Hardness of work pieces and machining allowances are subject to variety too. All these factors, and the stochastic nature of the process of wear and tear of the cutting tool active part results in the gain of the tool life, and, however, the tool life of even one batch of the cutting tools varies fairly considerably (15-35%) [8].For the purpose of the efficiency increase of the resource use of the cutting tool, it is necessary to organize the monitoring and replacement system of the cutting tool with account of the specified dispersion factors. This requires the development of a mathematical model of the resource use of the cutting tool, adequately considering the mentioned factors.