An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools

Abstract

The machining industry raises an ever-growing concern for the significant cost of cutting tools in the production process of mechanical parts, with a focus on the replacement policy of these inserts. While an early maintenance induces lower tool return on investment, scraps and inherent costs stem from late replacement. The framework of this paper is the attempt to predict the tool inserts Mean Up Time, based solely on the value of a cutting parameter (the cutting speed in this particular turning application). More specifically, the use of the Cox Proportional Hazards (PH) Model for this prediction is demonstrated. The main contribution of this paper is the analytic approach that was conducted about the relevance on data transformation prior to using the Cox PH Model. It is shown that the logarithm of the cutting speed is analytically much more relevant in the prediction of the Mean Up Time through the Cox PH model than the raw cutting speed value. The paper also covers a numerical validation designed to show and discuss the benefits of this data transformation and the overall interest of the Cox PH model for the lifetime prognosis. This methodology, however, necessitates the knowledge of an analytical law linking the covariate to the Mean Up Time. It also shows how the necessary data for the numerical experiment was obtained through a gamma process simulating the degradation of cutting inserts. The results of this paper are expected to help manufacturers in the assessment of tool lifespan.

Machine Tool Component Health Identification with Unsupervised Learning

“…These influences are cumbersome to reproduce in purely physical models approaches, wherefore many recently published PHM approaches in manufacturing incorporate statistical models. Prominent examples for the application of data driven models in monitoring are described by e.g., [10][11][12][13][14][15], relevant studies on data-based approaches for prognosis are described by [9,[16][17][18]. Both the PHM approach, as well as the applied learning algorithm strongly impact the capabilities and performance of the application.…”

A Study of Proportional Hazards Models: Its Applications in Prognostics

“…Ding various cutting speeds and feed rates. In the work of Equeter et al [73], the authors converted the cutting speed of the tool to logarithmic form and used it as a covariate of PHM to predict the average available time of the tool. The logarithmic conversion of cutting speed data can provide more accurate prediction results, as demonstrated by a numerical case.…”

A Systematic Literature Review of Cutting Tool Wear Monitoring in Turning by Using Artificial Intelligence Techniques

“…This type of wear is favoured by the tool manufacturers, as it is considered as the steadiest and most predictable [17,18]. Prominence of other kinds of wear generally comes from poor cutting parameters choice [8]. In turning, the main cutting parameters are: cutting speed, feed rate, and depth of cut.…”

“…The industrial practice occasionally contributes to this trend, by using lower cutting parameter values in order to slow the wear process and replace the tool in time [5]. Therefore, the tool life estimate is a recurring research in machining, and several approaches have been attempted, from early empiric laws [6] to stochastic modeling [7], to more advanced statistical models such as the Proportional Hazards model [8], and in recent years, Artificial Intelligence (AI) methods.…”