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Abstract
Taylor's equation for tool life has been examined at first from the view point of optimum and adaptive control of machine tools, and then general expressions of differential equations of tool wear have been derived from the mathematical view point. The tool wear ratet is a function of wear, cutting speed, feed rate and so on, which are functions of time. Applications of the method of variational calculus to problems of maximizing or minimizing functionals such as the volume of the metal removed for a certain time interval have been done by use of the differential equations mentioned above, and thus the optimum cutting speed, feed rate etc. can be determined. The meanings of some conventional criterion functions in control operations have been clarified from the standpoint of the differential equations.
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