On the mechanics of the grinding process, Part III—thermal analysis of the abrasive cut-off operation

Abstract

This is Part III of a 3 part series on the Mechanics of the Grinding Process. Part I deals with the stochastic nature of the grinding process, Part II deals with the thermal analysis of the fine grinding process and this paper (Part III) deals with the thermal analysis of the cut-off operation. Heat generated in the abrasive cut-off operation can affect the life of resin bonded grinding wheels and cause thermal damage to the workpiece. Thermal analysis of the abrasive cut-off operation can, therefore, provide guidelines for proper selection of the grinding conditions and optimization of the process parameters for improved wheel life and minimal thermal damage to the workpiece. In this investigation, a new thermal model of the abrasive cut-off operation is presented based on statistical distribution of the abrasive grains on the surface of the wheel. Both cutting and ploughing/rubbing that take place between the abrasive grains and the work material are considered, depending on the depth of indentation of the abrasives into the work material. In contrast to the previous models, where the apparent contact area between the wheel and the workpiece was taken as the heat source, this model considers the real area of contact, namely, the cumulative area of actual contacting grains present at the interface as the heat source. It may be noted that this is only a small fraction of the total contact area as only a small percentage of the abrasive grains present on the surface of the cut-off wheel are in actual contact with the workpiece at any given time and even a smaller fraction of them are actual cutting grains taking part in the cut-off operation. Since, the Peclet number, N Pe in the case of cut-off grinding is rather high (a few hundred), the heat flow between the work and the contacting abrasive grains can be considered to be nearly one-dimensional. In this paper, we consider the interaction between an abrasive grain and the workpiece at the contact interface. Consequently, the heat source relative to the grain is stationary and relative to the workpiece is fast moving. The interface heat source on the grain side as well as on the workpiece side is equivalent to an infinitely large plane heat source with the same heat liberation intensity as the circular disc heat source. However, it will be shown in the paper that the contacting times are different. For example, the abrasive grain contacts the heat source, as it moves over the wheel-work interface, for a longer period of time (∼ milliseconds) whereas the workpiece contacts the heat source for shorter period of time (∼ a few microseconds). The temperature in the grinding zone is taken as the sum of the background temperature due to the distributed action of the previous active grains operating in the grinding zone (global thermal analysis) and the localized temperature spikes experienced at the current abrasive grain tip-workpiece interfaces (local thermal analysis), similar to the work reported in the literature [Proc Roy Soc (London) A 453 (1997) 1083]. The equivalent thermal model developed in the present investigation is simple and represents the process more realistically, especially the heat partition. The model developed provides a better appreciation of the cut-off operation; a realistic estimation of the heat partition between the wheel, the workpiece, and the chip; thermal gradients in the workpiece due to abrasive cut-off operation, and an insight into the wear of the cut-off wheels.