Dynamic mathematical model for the cutting force in chip segmentation

In cutting difficult-to-machine materials such as titanium alloy, stainless steel and superalloy, segmental chip appears. Despite much experimental work done on the observation of the process of chip segmentation and on the measurement of the periodical fluctuation of the cutting force, which affects the quality of finished surface and tool life, no mathematical description of the process of chip segmentation and no calculation formula for the periodically fluctuating force are available. Up to now, only formulas for static cutting force for flow type chip have been available. Based on a previous paper by the authors, the present paper describes mathematically the process of the chip segmentation; and with suitable mathematical treatment, a dynamic cutting force formula for chip segmentation is obtained. Using this formula, we may succeed in controlling the vibration in cutting and improve the quality of the finished surface.