Panagiotis Kyratsis*. JOURNALS/12.27.pdfthe tool’s negative rake angle. The drilling tool is characterised by a geometry in which the normal rake and the velocity of the cutting

18 Int. J. Machining and Machinability of Materials, Vol. 10, Nos. 1/2, 2011

Copyright © 2011 Inderscience Enterprises Ltd.

Thrust force prediction of twist drill tools using a 3D CAD system application programming interface

Panagiotis Kyratsis* Department of Industrial Design Engineering, Technological Educational Institution of West Macedonia, Kila Kozani GR50100, Greece E-mail: [email protected] *Corresponding author

Nikolaos Tapoglou, Nikolaos Bilalis and Aristomenis Antoniadis Department of Production Engineering and Management, Technical University of Crete, Kounoupidiana, Chania GR73100, Greece E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

Abstract: Twist drills are geometrical complex tools and various researchers have adopted different mathematical and experimental approaches for their simulation. The present paper acknowledges the increasing use of modern CAD systems and subsequently, using the application programming interface (API) of a typical CAD system, drilling simulations are carried out. The developed DRILL3D software routine, creates, via specifying parameters, tool geometries, so that using different cutting conditions, realistic solid models are produced incorporating all the relevant data involved. The 3D solid models of the undeformed chips coming from both cutting areas are segmented into smaller pieces, in order to calculate every primitive thrust force component involved with high accuracy. The resultant thrust force produced, is verified by adequate amount of experiments using a number of different tools, speeds and feed rates. The final data derived consist of a platform for further direct simulations regarding the determination of tool wear, drilling optimisations etc.

Keywords: drilling thrust force; CAD based simulation; 3D modelling.

Reference to this paper should be made as follows: Kyratsis, P., Tapoglou, N., Bilalis, N. and Antoniadis, A. (2011) ‘Thrust force prediction of twist drill tools using a 3D CAD system application programming interface’, Int. J. Machining and Machinability of Materials, Vol. 10, Nos. 1/2, pp.18–33.

Biographical notes: Panagiotis Kyratsis obtained his Diploma in Mechanical Engineering from the Aristotle’s University of Thessaloniki – Greece, in 1992 and his MSc in Automotive Product Engineering and in CAD/CAM from Cranfield University – UK, in 1997 and 1999 respectively. He is currently a PhD candidate in the area of CAD-based manufacturing process simulations, Department of Production Engineering and Management, Technical University of Crete. His current position is a Lecturer in the Department of Industrial

Thrust force prediction of twist drill tools using a 3D CAD system API 19

Design Engineering, Technological Educational Institution of West Macedonia, Greece. His main research interests include manufacturing, CAD/CAM/CAE and product design.

Nikolaos Tapoglou obtained his Diploma from the Department of Production Engineering and Management, Technical University of Crete, Chania, Greece in 2006 and his Masters in Production Systems in 2008 from the Department of Production Engineering and Management, Technical University of Crete. He is currently a PhD candidate in the field of optimisation of manufacturing processes in the Department of Production Engineering and Management, Technical University of Crete. His main interests include CAD/CAM systems, simulation of cutting processes and cutting conditions optimisation.

Nikolaos Bilalis is a Professor of Computer Aided Manufacturing, Department of Production Engineering and Management, Technical University of Crete and the Director of CAD Laboratory. His research interests are technologies for product and process development and integration, CAD/CAM/CAE/CAPP, rapid prototyping and rapid tooling, virtual environments for product development, product innovation and manufacturing excellence. He serves as a Consultant to the industry and he has an extensive participation in numerous European and national research projects.

Aristomenis Antoniadis obtained his Diploma in Mechanical Engineering from the Aristotle’s University of Thessaloniki, Greece, in 1984 and his PhD from the same university in 1989. His current position is as Associate Professor in the Department of Production Engineering and Management, Technical University of Crete. His research interests are in manufacturing, CAD/CAM/CAE, reverse engineering and bioengineering. He authored seven books, 27 journal papers and 70 conference papers. He participated in a number of national and European projects.

1 Introduction

Drilling still remains one of the most financial beneficial and commonly used machining processes, whereby the operation involves making holes in a variety of materials. Although many other processes contribute to the production of holes, drilling is distinguished. The process involves feeding a rotating cutting tool, along its axis of rotation, into a stationary workpiece. The axial feed rate is usually very small when compared to the peripheral speed. The most commonly used tool is the twist drill, which is mainly available in diameters from 0.25 to 80 mm (Boothroyd and Knoght, 2006).

The main characteristic is the combination of both cutting and extrusion of metal, at the chisel edge, in the centre of the cutting tool. The high thrust caused by the feeding motion, first extrudes the metal under the chisel edge. Then it shears under the action of the tool’s negative rake angle. The drilling tool is characterised by a geometry in which the normal rake and the velocity of the cutting edge are functions of their distance from its centre (Nelson and Schneider, 2001). The cutting action on the chisel edge has been found to be closer to that of orthogonal cutting at relatively high negative rake angles and very low cutting speeds resulting in discontinuous chip formation. By contrast, the cutting action on the main cutting edges (cutting lips) has been reported to be similar to that of the classical oblique cutting process but with variable cutting speeds, inclination

20 P. Kyratsis et al.

angles and normal rake angles along the lip from the chisel edge corner to the outer corner (Audy, 2007).

The thrust force acting on the drilling tool is an important aspect of the process. Its magnitude combined with the dimension of the chip produced makes the evaluation of a number of different issues i.e., stresses developed, tool wear, process economy, optimisation possible (Childs et al., 2000; Shaw, 1989). The present paper is dealing with a novel approach in which the drilling thrust force is calculated using 3D solid modelling via the programming of a general purpose CAD system. Tools, workpieces and undeformed chips can be derived and used in order to calculate the thrust force with a limited amount of time necessary for the prediction.

2 Modelling approaches

An important issue in the design and operation of machine tools in any metal cutting process is the inquiry of a functional relationship between cutting parameters (i.e., speed, feed, depth of cut) and the cutting forces. The geometry and cutting mechanics of a twist drill have been studied over the years using a number of different approaches such as mathematical (geometrical), empirical and numerical (Grzesik, 2008; Trent and Wright, 2000; Ehmann et al., 1997).

In the mathematical approach, the tool was described analytically by extremely complicated equations. A number of researchers based their results on a thorough analysis of the drill point sharpening method. This approach, resulted in the creation of a number of models with complicated equations in 3D space, which were mathematically solved, in order to create the geometry of the drilling tool involved (Galloway, 1957; Tsai and Wu, 1979; Fujii et al., 1970a, 1970b; Paul et al., 2005). In addition, different mathematical approaches were followed in order to design and simulate the drilling tools directly from the manufacturing process of grinding using again a geometrical approach (Armarego, 2000; Kang and Armarego, 2003a, 2003b). The impact of the flute geometry and the drill point variations were further examined with the same approach in order to simulate their performance (Hsieh, 2005; Hsieh and Lin, 2005; Wang and Zhang, 2008a, 2008b).

The experimental approach, is based on a large amount of experiments that are carried out in order to save in a database different parameters for further use in experimentally derived equations (Armarego et al., 2000; Agapiou, 1993a, 1993b; Koehler, 2008; Claudin et al., 2008; Abrao et al., 2008; Hamade et al., 2006). Other researchers use modern statistical and artificial intelligence tools in order to minimise the amount of experiments needed and derived equations based on these methods without performing extensive experiment plans (Laporte et al., 2009; Tsao, 2008; Tsao and Hocheng, 2008; Basavarajappa et al., 2008; Hayajneh et al., 2009). In addition to the fact that a considerable amount of time is required for the drilling simulation, another disadvantage is that the whole procedure is based on a variety of restrictions and limitations. This is true mainly because they were based on 2D strategies and the geometry of the tools was defined using the principles of projective geometry.

In the numerical approach, a number of problems are tackled using the finite element method in order to establish models for issues such as: burr formation, cutting forces


prediction, tool deformations and temperature distribution. Typical approaches for the numerical modelling of metal cutting are the Lagrangian and Eulerian methods (Guo and Dornefield, 2000; Kadirgama et al., 2008; Bagci and Ozcelik, 2006; Chen, 1997; Singh et al., 2008; Zitoune and Collombet, 2007).

3 The 3D CAD-based approach

One of the main aims of the current research is to minimise the amount of the necessary testing, while increasing the quality of the derived simulation results. The current research is based on the concept that the increasing use of modern CAD systems provides an excellent platform for the development of CAD based tools for machining simulations and optimisations. In order to create the simulation, the application programming interface (API) of a general purpose CAD system was used, taking into account the powerful modelling capabilities and the versatility of up to date CAD software environments. The programming language used in the API was Visual Basic for Applications (VBA) and it was used for the development of the DRILL3D software routine. This routine can simulate the drilling operation using 3D solids for both the drilling tool and the workpiece. Moreover, this approach led to the generation of 3D solid models for the undeformed chip and the cut workpiece. The construction of a CAD based geometry of the undeformed chips, through the developed automatic recognition routine of their dimensional characteristics within DRILL3D, resulted in the calculation of the thrust force developed by the tool. Using a friendly interface, a user can easily introduce a number of different tool geometries and cutting conditions parameters. As a result, a number of different virtual drilling experiments can become readily available while calculating the tool thrust force.

The innovation of the proposed approach is the CAD-based principles used. A modern CAD system, with the assistance of its API, can be used to automate a number of steps towards manufacturing simulations. Different drill tools and workpieces can be created parametrically and an appropriate virtual motion can be programmed, in order to produce all the necessary solid models of the undeformed chip. Using these models, the thrust force of the tool can be calculated for every tool-workpiece material and geometry combination, with the assistance of a database containing the appropriate experimental coefficients.

The software creates automatically both the tool and workpiece 3D solid models and allows the user to select the motion fragment – step of the workpiece (in degrees), as well as the speed (in m/min) and the feed rate (in mm/rev). In addition, a number of parameters for setting up the initial conditions, before the work is initiated, is made available (drill kinematics parameters). Based on the data referred previously, DRILL3D produces two more 3D solid models, one describing the drilling action on the main cutting edges and another for the application of drilling in the area of the chisel edge. These models of the undeformed chip follow a procedure of being segmented into smaller pieces, in order to increase the accuracy of the thrust force calculation and after the automatic extraction of their main geometrical characteristics – the thrust force of the twist drill tool is calculated. The complete flow chart of the novel drilling simulation method is presented in Figure 1.


Figure 1 The flow chart for the drilling simulation (see online version for colours)

Figure 2 Conventional twist drill tool geometry (see online version for colours)


3.1 Tool description with 3D solid model

A common method of grinding the flank surfaces of the point of a twist drill is shown in Figure 2. The drill is rotated about axis AA, which is fixed in space and the flank is ground by the plane face of the grinding wheel G. Axis AA intersects in point O with the plane of the grinding wheel face. The motion of the wheel face in relation to the drill point may be deduced by considering the drill point as fixed and the wheel face rotating about the axis AA, the virtual motion of the wheel face being equal and opposite to the actual motion of the drill. A plane rotating about the fixed axis envelops a cone, so that the grinding wheel face envelops part of a conical surface in its motion relative to the drill point and the flank surface produced on the drill point is part of the surface of the cone. The vertex of the cone is the point O and the cone semi angle is the angle θ between the axis AA and the wheel face. The cone may be termed the grinding cone and this method of drill point grinding is referred to as conical grinding. A right hand coordinate system was used based on the following principles:

a the z-axis lies along the drilling tool axis (towards the drill shank)

b the y-axis lies along the common perpendicular which intersects with the extensions of the two cutting edges

c the x-axis is perpendicular to the y and z-axes (Galloway, 1957).

According to the model described above, a range of parameters have to be set in order to produce the desired variety of drilling tools. The aforementioned parameters are separated in two main categories. The first category determines the main shape of the tool:

R tool radius in mm

W tool web thickness in mm

p half point angle in deg (i.e., 2p = 118o)

h helix angle.

The second category (dealing with manufacturing parameters), determines the detail shape of the tool based on the conventional grinding method:

g distance of cone vertex along the x axis

s distance of cone vertex along the y axis

θ half cone angle.

An important issue for the correct twist drill geometrical representation is the shape of the flute cross section. Α drill flute surface for straight cutting lips was considered. Galloway was the first to derive the condition which the flute surface must satisfy in order to have a straight cutting lip under conventional conical grinding conditions. That condition is described by the following equation:

2 2( ( /2) )/2 tan( )arcsin( )/2 tan( )

r WW hvr D p

−= + (1)


where (r, v) are the necessary polar coordinates for the flute cross section, with r varying from W/2 to D/2. The profile for the secondary (non-cutting lips) flute can be defined in a manner to perform easy chip removal, while at the same time ensures sufficient strength of the tool. It is worth mentioning that Galloway’s approach is purely geometrical, which means that it allows the analytical calculation of all the necessary characteristics of the tool (rake angle, nominal relief angle etc.) based on 2D analysis of a variety of geometrical planes.

The DRILL3D routine is used in order to produce the aforementioned geometrical description of the tool. The solid model of the twist drill fluted part is formed by sweeping helically the flute cross section described by equation (1). The twist drill point geometry is finalised by the Boolean subtraction of the grinding cones mentioned earlier.

3.2 The 3D penetration process

The virtual drilling process is separated in two parts. The first is based on the cutting action of the cutting lips and the second on the cutting action of the chisel edge. Both are treated in a similar way although they are treated individually. The final result is the creation of 3D solid models simulating the undeformed chip and the shape of the remaining workpiece geometries for each case. The tool is virtually moved transitionally towards the z-axis (feed) while at the same time, it is rotated around its z-axis of symmetry using a constant step. In every step, a Boolean subtraction of the tool model from the remaining workpiece model is carried out. The step value, for both cases, is selected comprising the motion accuracy, the calculation complexity and the CAD system capacity.

Figure 3 Steady state simulation of the cutting lips penetration into the remaining workpiece (see online version for colours)


Beginning with, a specially shaped workpiece is used, in order for the cutting lips to be directly engaged (steady state case), having a small hole in the middle (chisel edge area). A rotation step of one degree can be successfully incorporated into the model (Figure 3).

Following that, another workpiece of pure cylindrical shape with a diameter equal to each tool’s chisel edge is used. The step selected in that case, is in the range of 3–5° in order to achieve the appropriate motion accuracy without encountering software limitations due to extremely small size of the chip involved. Once more, the undeformed chip produced and the remaining workpiece involved, consist the outcome of the virtual cutting process in the area that comes in contact with the chisel edge (Figure 4). Both cases are very computing intensive and the simulations need to run for a significant amount of cycles in order to achieve constant chip geometry and simulate the steady state condition.

Figure 4 Steady state simulation of the chisel edge penetration into the remaining workpiece (see online version for colours)

Figure 5 illustrates the solid geometry of a number of chips produced in both the areas of cut (main edges and chisel edge). Every layer of the chip is cut by a different cutting edge and an angle of 210° is selected in order to emphasise their 3D motion. This approach, in contrast to former modelling efforts, is primitively realistic, since the produced remaining cut workpiece and the 3D geometry of the chip, are the results of the material removal, where the cutting tool enters the solid model of the workpiece. DRILL3D routine is able to output formats provided from the ‘host’ CAD system (.ipt, .sat, .iges, .stl, .dxf etc.) and offers realistic presentations of solid parts, chips and cut workpieces, which can be easily managed for further investigations individually, or as an input to other commercial CAD, CAM or FEA environments.


Figure 5 3D solid models of undeformed chip sets (main edges and chisel edge) (see online version for colours)

Figure 6 Cutting forces involved in drilling


3.3 Thrust force calculation from the 3D chip models

A well established model, such the Kienzle-Victor was used (Kienzle and Victor, 1957). The model introduces the specific cutting resistance in order to assess the main cutting force component:

(1 )mi iF K bh −= (2)

where: Ki is the specific cutting resistance, b is the width of cut and h the undeformed chip thickness. The main forces used in the current drilling simulation are depicted in the Figure 6.

The 3D models of the undeformed chip, produced earlier from both cases, were segmented into smaller pieces in order to achieve higher result accuracy. For each individual segmented solid model, a number of geometrical parameters were automatically recognised by the DRILL3D routine, and all this data was an input to the thrust calculation of the tool, based on the Kienzle-Victor method. In more detail, both the b and h equation parameters were directly recognised from each segmented piece of the undeformed chip solid model and the selection of the necessary coefficients Ki was made based on published data (Konig and Essel, 1973). Finally, the outcome was the separate calculation of the thrust force for both the tool areas (main cutting edges and chisel edge) by adding up all the primitive force components calculated (Figure 7). An example of a thrust force calculation is analytically presented in Figure 8.

Figure 7 Thrust force calculation based on 3D undeformed chip segmentation (see online version for colours)


Figure 8 Example of a thrust force calculation (see online version for colours)

4 Verification

The determination of the dimensions of the undeformed chip, together with the number of constant coefficients stored in material databases were the basis for the calculation of the applied thrust force during the drilling operation. A significant number of simulations were performed using the DRILL3D routine, utilising two different tools and four different values of feed rate for each one. All simulations were carried out for two different cutting speeds (Figure 9).

Figure 9 A table with the cutting parameters used in the experimental work

In order to assess the accuracy of the DRILL3D drilling simulation model in calculating the thrust force, the same experiments were conducted on a HAAS three-axis CNC machine centre with continuous speed and feed control within their boundaries and the specimen used was a CK60 plate. A Kistler type 9257BA three component dynamometer was positioned between the machine centre and the workpiece. The signal was processed by a type 5233A control unit and during the tests, the thrust force was displayed


graphically on the computer monitor and analysed to enable early error detection and ensure steady state condition (Figure 10). The control unit allowed the selection of the measurement range. During the experimental work, a range of 2KN and 5KN was selected for the measurement of the thrust force (Fz). The resulted sensitivity achieved was 2.50 mV/N and 1.00 mV/N respectively.

Figure 10 Experimental verification (see online version for colours)

Figure 11 Verifying the thrust force for each cutting edge (see online version for colours)


In order to be able to separate the thrust force created by the two areas (main cutting edges and chisel edge) two series of experiments were contacted. The first series, involved the direct drill of the workpiece, which means that the total thrust force was measured. During the second series, the workpiece was pre-shaped with a hole in the centre. The diameter of the hole was equal to the dimension of the chisel edge and as a result the thrust force of the main cutting edges was measured (Figure 11). All the pairs of experiments were conducted once.

Figures 12 and 13 depict the thrust force developed in the area of the main cutting lips and the total thrust force applied by the tool during the drilling process. On the same figures, the experimental results are presented. The accuracy of the CAD-based simulation performed, by the DRILL3D, was proven, by all the different cases performed.

As expected, approximately 60% of the total thrust force is mainly due to the cutting action of the chisel edge area. The material removal mechanism is extremely complex there. Near the bottom of the flutes, where the radii intersect with the chisel edge, the drill tool forms a cutting rake surface that is highly negative in nature. An indication of the inefficient material removal process is evident by the severe workpiece deformation taking place under the chisel point (such deformed products must be ejected by the drill to produce the hole). These products are extruded, and then wiped into the drill flute, where they blend with the main cutting edge chips.

Using the larger tool, the forces increase substantially as well as the undeformed chip geometry. In addition, in all cases, the total thrust force increased with the feed rate. This is expected, due to the larger dimensions of the undeformed chips produced when the feed rate rises. Using different cutting speeds – although a small increase in thrust force is depicted – in overall, its influence is very small compared to the rest of the parameters used.

Figure 12 Thrust force prediction for D = 10 mm twist drill tool (see online version for colours)


Figure 13 Thrust force prediction for D = 14 mm twist drill tool (see online version for colours)

5 Conclusions

Former research work was mainly based on 2D projective geometry principles or extremely complex 3D mathematical calculations, in order to achieve reliable results. The novelty of the current research is that the algorithm has been developed and embedded in a commercial CAD environment, by exploiting its modelling and graphics capabilities. DRILL3D software routine produces pure 3D solid models of both tools and workpieces. In addition, the full 3D geometry of the steady state undeformed chip produced, is derived from the tool and workpiece models. Using these pieces of information, prediction of the thrust force is achieved based on the segmentation of the undeformed chip 3D solid model and Kienzle-Victor method. The simulation results were verified by an appropriate number of experiments using the same manufacturing parameters, approving the capability and reliability of DRILL3D routine in thrust force prediction.

These 3D geometric definitions and their direct automatic recognition by the DRILL3D provide a solid environment for a number of downstream applications i.e., geometric assessment of tool stresses and wear, finite element analysis, applied torque prediction, optimisation of the drilling process.

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Documents

Panagiotis Kyratsis*. JOURNALS/12.27.pdfthe tool’s negative rake angle. The drilling tool is characterised by a geometry in which the normal rake and the velocity of the cutting