The heat transfer aspects of abrasive cutoff operation are investigated analytically. The analytical results lead to integral expressions for a dimensionless temperature of cutting interface as a function of dimensionless time and two dimensionless parameters. A rather simple expression is given which approximates the integral equations in a wide range of parameters. These results are dependent upon an important cutting parameter, namely, the “energy per unit volume” or the work necessary for removing a unit volume of chips. It is concluded that, if energy per unit volume decreases with downfeed faster than the latter to about −0.3 power, there exists a critical downfeed at which the temperatures will be maximum. For slower rates of decrease, lower temperatures are obtained at lower downfeeds. The partition functions for energy per unit volume, thermal penetration of the wheel, and experimental temperature measurements will be given in subsequent papers.

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