A more general form of the equation is where At high temperature zones crater wear occurs.
This somewhat offsets the tool wear from increased cutting speeds.
Malakooti and Deviprasad (1989) introduced the multi-criteria metal cutting problem where the criteria could be cost per part, production time per part, and quality of surface.
Also, Malakooti et al. (1990) proposed a method to rank the materials in terms of machinability.
Malakooti (2013) presents a comprehensive discussion about tool life and its multi-criteria problem.