Proportional hazard model for cutting tool recovery in machining

Abstract

The proportional hazard model is a statistical method capable of including information on environmental and operating conditions. In machining, in the reliability field of a cutting tool, the interest of using proportional hazard model is highlighted. On one hand, the environmental and operating conditions are described and taken into account as explanatory variables. Three covariates are considered, namely, the vibration signal, the hardness material, and the lubrication/cooling. On the other hand, a new baseline hazard function is designed according to phenomena of tiny tool breakage followed by a self-sharpening process. This latter phenomenon, which can be considered as a rare event, prompted us to study extreme value theory to propose an adequate baseline hazard function. The newly obtained baseline hazard function will be named generalized extreme value proportional hazard model. This function is obtained thanks to the Gumbel function and has the property to be non-monotonic, an increasing then decreasing function. An alternative option as a baseline hazard function, based on the flexible Weibull distributions, is also proposed. Results produced in this article show the impact of all these variables on the surface roughness of the machined parts. According to reliability studies, the premature replacement of the cutting tool implying financial losses can be delayed. This may be of particular significance and benefit, in terms of sustainable development, in the case of mass production, by limiting the frequency of tool replacement.