3D modelling of kinematic fields in the cutting area: application to milling

The work presented in this article deals with modelling the milling process. The exact position of the cutting edge within the modelling space is determined according to the different angles of orientation during milling, κ r , γ 0 , and λ s as reported by Albert et al. (Int J Adv Manuf Technol 55:843–854, 2011), the cutting edge angle, the rake angle by Merchant (J Appl Phys 16:267–275, 1945) and Oxley (International Journal of Machine Tool Design and Research 1:89–97, 1961), and the cutting edge inclination angle, respectively. For each insert position, the kinematic torsor is determined and any changes are analyzed. The instantaneous variation in kinematic and geometric cutting parameters is determined in the case of end milling with a milling tool with cutting inserts at several representative points on the cutting edge. These parameters represent the input data for an orthogonal cutting model at the point of the cutting edge being considered. The kinematic analysis shows variation of the vector velocity along the cutting edge and variation of the instantaneous feed for a tool rotation. If we consider an orthogonal configuration cutting model for each point of the cutting edge, these variations contribute to define different input data for the orthogonal configuration cutting model (cutting velocity and feed). The results of the cutting force and tangential forces are dependent of the kinematic description along the cutting edge. In a future work, we will discuss the generation of strain and strain rates gradients due to the variation of the velocities along the cutting edge. The variation in linear speed due to the rotation of the tool, the feed speed, and a combination of the two, influences the cutting angle, the clearance angle, and the instantaneous cutting speed V corth . Extra input into the orthogonal cutting model is instantaneous feed. This is determined analytically, based on a geometric representation of the area covered by the tool. The different calculation approaches will be described in this paper with a sensitivity study of the different cutting parameters.