Presenting a mathematical approach for tool life modeling based on Weibull distribution and dependent on machining conditions

Document Type : Original Article

Authors

1 Associate Professor, Department of Industrial Management , South Tehran Branch, Islamic Azad University, Tehran, Iran.

2 Assistant Professor, Department of Business Management, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.

10.48308/jimp.16.1.35

Abstract

Introduction: Currently, machining processes constitute a vital part of global manufacturing processes. The importance of these processes can be observed through the financial flow resulting from their use. One of the fundamental issues in utilizing machining processes for product manufacturing is tool wear. To date, various studies with diverse assumptions have been conducted to analyze wear characteristics under different conditions to satisfy various objectives. Traditional models for analyzing tool life and wear, which are often based on deterministic equations, do not consider the variations that occur in cutting processes, and for this reason, the actual tool life rarely matches the values predicted by these methods. In recent years, there has been increased attention to the use of statistical distributions for predicting tool life. Among them, the use of the Weibull distribution is of particular importance. The main challenge of these approaches is the accurate estimation of the tool life distribution function based on real data. Moreover, with changes in machining conditions, the tool life distribution function may change, estimating the distribution parameters for tool life more challenging. Additionally, due to the suitable fit of cutting tool life with the Weibull distribution, estimating the parameters of this distribution is complex due to its specific characteristics.
Method: In this research, a hybrid method is presented that uses the design of an experiment based on the Box-Behnken model and applies a mathematical transformation to experiments on real tool life data to determine the parameters of the tool life distribution. This method is such that the relationship between the tool life distribution parameters and the machining conditions, including spindle speed, feed rate, and depth of cut, can be described by a polynomial equation. In this method, the golden section search technique will be used to fit the obtained data to the appropriate tool life distribution. Finally, the proposed methodology is implemented on a case study, and the results are reported.
Result and discussion: After obtaining the values of the shape and scale parameters of the Weibull distribution at each level of experiments designed by the Box-Behnken methodology, the relationship of these parameters with machining conditions can be modeled using a full quadratic function. In this paper, the shape and scale parameters of the Weibull distribution are reported at each level of experiments, followed by the value of the SSE function obtained in the optimization process using the GSS algorithm. The results indicate desirable error values in the application of the proposed methodology. Furthermore, with the implementation of the proposed methodology in this paper, the R2 value for the shape parameter is 92.52%, and for the scale parameter, 96.80%. The appropriate correlation between the full quadratic model for each of the Weibull distribution parameters with the data obtained from the life of cutting tools indicates the adequacy of the proposed methodology in practical applications.
Conclusions: In this paper, a hybrid methodology was developed to achieve two practical objectives, using the design of the experiment, mathematical transformations on the obtained data from tool life, and the implementation of the golden section search algorithm. The first goal is to estimate the parameters of the Weibull distribution under specific machining conditions. This will determine the distribution of cutting tool life under specific machining conditions based on the Weibull distribution. The second goal is to identify changes in the tool life distribution based on changes in machining conditions. For this purpose, in the presented methodology, the relationship between the Weibull distribution parameters and machining conditions is determined as a complete square model. Finally, the proposed method in this paper is implemented on a milling process with specific information, and the results obtained from it are reported.

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References

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