Influence of the radius of the generatrix of flank surface on the geometric parameters of the cutting wedge of the twist drill

. Drills with various flank surface shapes are widely used to machine holes. Drill teeth have flank surfaces of various shapes, flat, conical and helical. In this work, we have investigated the influence of radius of the generatriх in the form of a circular arc on the geometric parameters of the cutting wedge. It has been found that the range of changes in the clearance and rake angles along the cutting edge decreases with the decreasing radius of generatrix forming rake. It was found that a tool with a minimum permissible radius of curvature has the best distribution of rake and clearance angles of the blade along the cutting edge . The improvement reaches up to 40% compared conical flank surface. It was also found that in the case, when the generatrix radius decreases, the cutting edge increases by 18% compared to conical flank surface, which reduces the stress along the entire cutting wedge.


Introduction
Flank shape is critical to the performance and tool life of a twist drill.There are different types of shape of twist drills: involute-helical surface [1], flat [2] and conical [3] -the most popular choice when designing a drill.
When designing, the geometric parameters of the cutting part of the drill take into account the rigidity and strength of the drill, the rake angle, as well as wear and abrasion of its flank surface [4].In particular, the parameters are the drill point angle , the chisel angle ψ, the rake angle  and the clearance angle .
For rationale for choosing of research objects, solid drills with two and three cutting teeth various flank surfaces, gash, flute profile shapes, and tip designs were used.The focus of this research was on solid drill designs with a unique flank surface shape and flute profile that provided a cutting wedge's geometry with a point that smoothly passed away from the main cutting edge to the drill's center.The rake angle values take on negative values near center when the flank surface is flat.This leads to increased cutting forces and decreased productivity, low stability of drilling and hole breaking [5].A limitation is placed on the production of three-flute drills when the back surface is conical.A limitation is placed on the production of three-flute drills when the back surface is conical.When shaping the flank surface, the smaller angle between the teeth causes overcutting of the neighboring tooth, especially in sharpened drill designs with a large clearance angle.The helical flank is the best choice for two-flute designs in terms of clearance angle distribution along the main cutting edge and rake angle along the cutting edge.
The distribution of the clearance angle on the main cutting edge, the cutting wedge on the chisel cutting edge, and the shape and location of the point are all related in some way, but there aren't enough studies that fully explore this relationship to date [6].Additionally, there is a chance that the grinding wheel will cut into the neighboring tooth while shaping a tooth when the clearance angle is high.The flank surface's shape can be created with a formgenerating curved generatrix and guide to address these limitations.This flank shape will provide controlled clearance angle distribution along the main cutting edge.The sharpening of the main cutting edge is necessary to ensure the rake angle at the specified values in the cutting edge, where the radius is less than 1/3 R [3].The research and development of tool materials and their configuration, as well as the application of nanocomposites based on aluminum oxide, are crucial to tool manufacturing.These modifications increased the potential for nanomodification of the cutting surfaces by making it possible to observe the intricate processes taking place during processing [7,8].The gash can have a variety of shapes, including straight [9][10][11], an arc projected on the cutting edge in a radial section [2], and curvilinear [12] in the form of a spline projected onto the cutting edge.Each of these gashs can be applied to a three-flute drill design.However, as in the situation with the flank surface, there are a number of limitations.A direct gash changes the profile of the cutting part in the axial section [13], which leads to a sharp change in geometric parameters and the emergence of stress concentration zones [14].
Radial gash is by far the most common solution for three-flute drills.Actual-to-date research do not consider the relationship between radius of gash and main cutting edge shape.Therefore, stress concentration zones arise due to changes in geometric parameters along the cutting edge [15][16][17][18].The gash should provide the smooth connection from the main cutting edge to the chisel edge of the drill [19].In addition, there are designs of drills with a flat gash of the rake surface [4,6,20,21].Disadvantages in modern twist drill designs include: small rake angle values along the cutting edge, even negative when approaching the center; rake angles at the periphery are too large.As a result, there is an hight change in the value of the rake angle, which leads to a variety of cutting conditions along the drill's cutting wedge.
The research object is a drill design that ensures the consistency of the angle of cutting wedge  along the main cutting edge up to the gash section.
To do this, this design will comprehensively take into account the shape of the rake surface formed by the curvilinear generatrix and generator lines, the shape of the gash specified by the spline in the radial section, the profile of the flute and the point angle that determine the shape of the main cutting edge.Due to the high low wear resistance of cutting materials, a promising direction is the use of arc-PVD and multilayer composite coatings to protect the cutting tool blade [22][23][24].Thus, Ti-TiN-(TiCrAl)N coating (FCVAD technology) provides increased performance and wear resistance for ceramic tools [25].Multilayer coatings are used for carbide cutting tools also to prevent brittle fracture of the cutting part, in particular the Cr,Mo-(Cr,Mo)N-(Cr,Mo,Zr,Nb,Al)N coating, which contains two cubic phases (Cr,Mo,Al)N and (Zr,Nb,Al)N [26].
The formation of new approaches to the calculation and modeling of drills, as well as the development of new technologies for processing modified flank surfaces, is carried out on the basis of analytical calculation methods using the fundamental principles of the theory of design of cutting tools with shaped screws surfaces.The formation of new approaches to the calculation and modeling of drills, as well as the development of new technologies for processing modified flank surfaces, is carried out on the basis of analytical calculation methods using the fundamental principles of the theory of design of cutting tools with shaped screw surfaces.
The obtained relationships will be adapted to control equipment in real time on multi-axis CNC machines for the manufacture of cutting tools and their regrinding using advanced approaches to recreating the restored object in the digital CAM-system [27][28][29][30][31].To reduce the rake angle  at the periphery, a drill design with two conical sections of the cutting surface with different point angles  is used.At the periphery, the cone has a smaller point angle , for example, for an angle 2 118°, the second cone has an point angle  70°.As a result, with this drill design, the rake angle at the periphery can be reduced by 7-8°, which will relieve the load on the areas most susceptible to wear [32].
These problems can be eliminated by using special flank surface of the twist drill.For this purpose, the generatrix line that forms the flank surface will be made in the form of a circular arc, and not in a straight line like traditional twist drill designs.The generatrix line is implemented technologically as a result of the movement of the grinding wheel coordinate system along generator line.

Methods
The mechanism for studying the geometric and operational characteristics of drills is based on a computer-aided design system for create drill designs with a flank surface formed along a generatrix line in the form of a circular arc.
The initial construction feature and geometric parameters for drills are presented in Figure 1, where a is the  -clearance angle, f -the width of the land of a drill, D -the diameter of the drill, ds -the core diameter, Rk1, Rk2 -are the radiuses of the circular arcs forming the profile of the helical groove KK,  -the inclination angle of the helical groove.The projection of the cutting edge can be specified by analytical relationship.Depending on the shape of the cutting edge, the design methodology includes two groups of cutting edge designs [33].The determination of the helical projection into the radial section of the cutting edge groove is described by the following equation: where P -the coordinates of the helical groove profile in the radial section, RKΞ -are the coordinates of the cutting edge in projection into the radial section.
This solid 3D-model was studied for the magnitude of internal stresses under load in the CAE-system SolidWorks Simulation.Simulation data is presented in Table 1.Control results of internal stresses for 4 designs of twist drills -one with conical flank surface and three designs with flank surface shaping by generatrix line in the form of a circular arc with a change in radius R (R, 1.25 R, 2.5 R ).
Table 1.Results of CAE analysis of drill with direction and flank radius shapes of generatrix line.As a result of the modeling, a correlation was established between the change in the inclination angle of the cutting edge projection on the radial section plane and radii of generatrix line R (Fig. 2).As a result, it was found that reducing the guide radius leads to an increase in the length of the cutting edge and a significant reduction in cutting forces.

Result and discussion
A study was conducted of changes in the rake and back angles in twist drills obtained as a result of the operation of a computer-aided design system.The analysis of the angles on the solid model of the drill was carried out in the axial section obtained as a result of the plane touching the cylinder, the generatrix of which coincides with the feed rate vector (Fig. 3).Using the proposed method in the last paragraph, we obtain control results for 4 designs of twist drills -one with conical flank surface and three designs with flank surface shaping by generatrix line in the form of a circular arc with a change in radius R (R, 1.25 R, 2.5 R ).The initial value of the rake angle  is 30°, the clearence angle  is 22°.Based on the results of the analysis of the graphs, it was found that drills with flank surface shaping along a generatrix by arc have a more uniform smooth decrease in the rake angle from the periphery to the center.The trend of changes in the rake and clearance angles of the new drill design is generally identical to the trend of changes in the geometric parameters of drills with conical flank surface (Fig. 4).The rake angle  takes the greatest values, and the clearance angle  is the smallest at the periphery of the drill.As the radius of the generatrix of the flank surface decreases, a increase in the rake angle and an decrease in the clearance angle.A graph of the dependence of the sharpening angle of the cutting wedge  on the ratio of the radius at the controlled point on the drill bit to the radius of the drill is presented in Figure 5.This tendency makes the change in the angle of the cutting wedge from the periphery to the center more uniformly and proportionally.In total, integrally along the full length cutting edge, the value of the cutting wedge is distributed more evenly and has improved by 40%.Which also correlates with an improvement in the stress state along the entire cutting wedge compared to design drill with conical flank surface.

Conclusion
In this study, the results of the correlation between the radius of curvature of the drill flank surface and the rake and clearence angles were obtained for the first time.It was found that the use of shape from the flank surface of a circle obtained using an arc as a generatrix is effective and preferable compared to existing drill designs.

Fig. 1 .
Fig. 1.Scheme of construction feature and geometric parameters of the drill.

Fig. 2 .
Fig. 2.Graph of the relationship between the change in the inclination angle of the projection of the cutting edge on the radial section plane: blue -with conical sharpening of the flank surface; yellowwith flank surface shapinf along a generatrix with a radius 2.5 R; red -with flank surface shapinf along a generatrix with a radius 1.25 R; green -with flank surface shaping along a generatrix with a radius R.

Fig. 4 .Fig. 5 .
Fig. 4. Graphs of the dependence of the rake and clearance angles of various drill designs on the ratio of the radius at the controlled point on the cutting edge to the radius of the drill: a) -with conical sharpening of the flank surface; b) -with flank surface shaping along a generatrix with a radius 2.5 R; c) -with flank surface shaping along a generatrix with a radius 1.25 R; d) -with flank surface shaping along a generatrix with a radius R.