OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 5 4 3 of the flank surface: conical and toroidal with different radii of the generatrix of the toroidal surface Rt (Rt min, 1.25 R, 2.5 R) was carried out. The radius of the toroidal flank surface varied from 2.5 R (the drill design is comparable in geometry to a drill with a conical sharpening) to the minimum possible radius of the generatrix of the toroidal flank surface Rt min. The minimum radius of the flank surface generatrix Rt min was determined by the following equation: min ctan( / 1) . sin( ) t R R ϕ = ϕ (3) The investigation of geometric parameters along the cutting edge was carried out by determining the angle between the tangent to the rake (flank) surface at the control point and the perpendicular (tangent) to the flank surface at the control point (fig. 5). Analysis of the drill-to-workpiece contact zones was a major aspect for determining the rake height directly affected by the resulting mechanical loads in the SolidWorks Simulation CAE system (fig. 6). Mechanical forces were applied to this region in FEM simulations. Therefore, the load in this analysis was applied at an angle that is set tangent to the trajectory of the cutting wedge in the zone of feed per revolution f (0.2 mm/rev). The zone of cutting forces application was reshaped depending on the width of the cut layer at different radii of curvature of the cutting edge at a constant feed. The tool was fixed along a cylindrical surface. The minimum mesh element size should be at least three times smaller than the chip thickness to simulate chip formation that corresponds to a very fine local mesh. Since the shape of the axial section of the drill varies in the work, the shape of the uncut chip also changes. Therefore, to set the loading zone, it is important to analyze the cut layer with one constant feed (S = 0.2 mm/rev) for different profile shapes of the producing surfaces (table 2). In the obtained diagrams, a significant decrease in the uncut chip at the periphery is observed with a decrease in the radius of curvature of the generatrix of the flank surface, which indicates a decrease in the forces acting on the cutting edge and the formation of more favorable conditions for the cutting process. In this work, to carry out FEM, the model mesh was three-dimensional polyhedral – tetrahedrons. While such mesh elements are capable of providing a high degree of adaptation to the complex geometry of the cutting part of a drill with a toroidal flank surface, its use is associated with high computational complexity of the calculation. Also, to obtain reliable results, it is necessary that the size of the mesh elements more than three times smaller than the thickness of the chips being removed. Due to these limitations, the mesh size was chosen to be 0.02 mm in order to obtain reliable results of stresses on the cutting part of various drill designs (fig. 7). Fig. 5. Defining the rake angle on a drill with the toroidal flank surface a b Fig. 6. Model of a drill with the toroidal flank surface in the SolidWorks Simulation CAE system: a – isometric view of the model with a mesh; b – side view of applied loads
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