Moving Heat Source Method
Here is the idealized diagram of shear plane moving heat source:
The temperature distribution along the shear plane was assumed as the same as that along a uniform band source of heat moving obliquely through an infinite solid. Similarly, the temperature distribution or average temperature at the chip/tool interface also can be approximatedly obtained.
Image Source Method
To avoid giving rise to two different temperature on either side of a same plane due to partition principle, Chao and Trigger approximated the uniform plane heat source at the interface by a grid of point sources. Assuming that the angle between the rake and flank faces was right and that the tool surfaces were insulated, the grid of real and fictious image point sources is shown as follows:
Then they used an iterative procedure to obtain the final interfacial temperature distribution and later extended their work to include the frictional heat source at the tool/work interface.
Dimensional Analysis
Kronenberg postulated that the temperature at the tool/chip interface was dependent on the following important variables: chip area, cutting speed, a specific cutting force, a thermal conductivity, and the product of density and specific heat. Applying the principle of dimensional analysis, two dimensionless groups of variables were derived. Then the experimental results were fitted in the following: