Jianfeng Gou, Guangpeng Zhang, Li Meng, and  Yan Jiang. Research on three-dimensional modeling and cutting force prediction mathematical model of integral end mill based on differential geometry principle. Dynamic Systems and Applications 29 (2020) No. 4, 1241 – 1254

https://doi.org/10.46719/dsa202029417

ABSTRACT.
The integral end mill has many kinds of cutters, and its geometric rhythm is complex. The validity of the mathematical model will directly affect the cutter structure and milling performance. Based on this, this paper uses the differential geometry principle to establish the three-dimensional model of end milling cutter, and constructs the cutting force prediction model. At first, this paper briefly introduces the design method, method and parameters of the end mill model at home and abroad. In view of the difficulty in modeling the end milling cutter, the differential equation is established according to the geometric principle, the integral end milling cutter is discretized into micro elements by mathematical method, and the milling force is divided into three components. The coordinate system is used to predict the milling force, and the influence of the size of the helix angle, the cutting amount, the cutting depth, the change of the feed per tooth and the milling method on the cutting force is discussed. Through the simulation analysis, the validity of the end mill model is verified, and the best milling performance is obtained by changing the feed rate of each tooth and the reverse milling method.

Key words: integral end mill; mathematical modeling; chip force