Modeling of Stress in Drills with Curved Cutting Edges

BAROIU Nicuşor1,a, BOAZU Doina2,b, VASILACHE Cosmin-Alexandru2,c and TEODOR Virgil1,d

1”Dunărea de Jos” University of Galaţi, Department of Manufacturing Engineering,

47 Domnească st., 800008, Galaţi, România

2”Dunărea de Jos” University of Galaţi, Department of Applied Mechanics,

47 Domnească st., 800008, Galaţi, România

anicusor.baroiu@ugal.ro,

bdoina.boazu@ugal.ro,

ccosmin.vasilache@ugal.ro,

dvirgil.teodor@ugal.ro

Keywords: helical drill with curved cutting edges, FEM analysis, strains, deformations.

Abstract. In this paper, it is presented an analysis of the strains and deformation state for a new

constructive type of cutting tool — the helical drill with three curved cutting edges. The analysis

was developed in the application Ansys Workbench, after a definition of the drill’s geometry in the

CATIA environment. It was modeled a specifically load, according to the geometry of the variable

working angle of the new drill type. They are presented numerical examples, in comparison with a

standard drill, for the diameter of 20 mm.

Introduction

The analysis of the strains which appear in the drilling process or the analysis regarding the loss

of stability, it is frequently using the finite element method.

The specific applications for the finite element analysis, with modules for 2D and 3D, were

developed from the need to simulate in a virtual environment the cutting machining process of the

metals [1,2,3,4,5,6]. The cutting process simulation is made in a controlled environment and

assumes the splitting of the product in a number of finite elements which may be analysed in

connection. Generally, the application which use the finite element analysis method are based on a

mathematical calculus model, used to approximate solutions of the complexes problems which may

not be solved with fundamentals theory [7,8,9].

In this paper, the issue is approach using the Ansys Workbench, the main working stages being:

- entering of input data for used materials — the Engineering Data module;

- defining of the cutting tool’s geometry or the import of a specific geometry from other CAD

applications: AutoCAD (.dwg, .dxf), CATIA (.CATPart), Inventor (.itp), SolidWorks (.sldprt),

Unigraphics NX (.prt) etc. — the Geometry module;

- generation of the mathematical modules for the geometry discretization, the links between

elements, the contact zones between these etc. — the Model module;

- establishing of the limit conditions by specifying the sliding planes of the elements, the forces

and torque direction of action — the Setup module;

- simulations and comparison of results for various machining conditions in order to establish the

optimum results — the Solution and Results modules [10].

Stages of the Finite Element Analysis in Ansys Workbench

The main objective is to verify the helical drill at the main stress, by simulating the real working

conditions, establishing in this way the angular, radial and axial deviations. They were considered

two geometry types of the drill, labeled with BTR — drill with straight line cutting edge and BTC

— curved cutting edge [11,12,13], for drills with diameter of φ20 mm. The axial forces and the

torque, measured by experimental tests are used for determining of the loading conditions and for

verification of the strains of the helical drills.

Applied Mechanics and Materials Vol. 371 (2013) pp 509-513Online available since 2013/Aug/30 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.371.509

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The Model Generations. The complex geometry of the helical drill is modelled by specification

of the Cartesian coordinates of some characteristic points. For this, the two helical drill’s types, with

two straight line cutting edges and with three curved cutting edges were modelled with the CATIA

software.

The main geometrical parameters and theirs values for drills BTR φ20 mm and BTC φ20 mm, are

presented in the Fig. 1 and in the Table 1.

Fig. 1. Geometrical and constructive parameters for BTR (a) and BTC (b) — φ20 mm

Table. 1. Geometrical and constructive parameters for helical drills STAS 575-80

Parameter Symbol BTR BTC

Drill’s diameter D [mm] 20 20

Drill’s core diameter d0 [mm] 3 2,5

Facet width f [mm] 1,9 1,9

Length of the helical flute l1 [mm] 140 140

Drill’s length L [mm] 238 238

Angle of the helical flute ω [o] 30 20

Angle of the chisel edge ψ [o] 55 -

Top working angle κ [o], κv [

o] 60 60

Periphery working angle κp [o] 60 5

The Discretization of Geometry, Establishing of Strains and the Limit Conditions. The

usual algorithm for the resistance calculus regard the helical drill as a bar embedded in the mounting

zone, see Fig. 2.

In the calculus with finite elements (in ANSYS, or in any similarly software), in order to capture

the construction of the cutting tool, it is preferred the modeling with solid elements (brick).

The boundary condition is defined for the case when the

drill is considered embedded in the zone of the Morse cone. In

this case on the drill action the global axial force Fa and the

external torque Mext in the direction of the drill’s longitudinal

axis, the same with the feed direction, in the same time,

perpendicularly to the surface of the machined piece, see Fig.

3.

In Table 2, they are presented the data needs for the calculus

of the chip thickness, for a drill with curved cutting edges, with

diameter of φ20 mm, for a feed s=0.16 mm/rot., considering the

curved cutting edge divided in ten units with equal length.

In the Setup module of the Ansys application, the

establishing of the boundary conditions was done by selecting the pressure direction on the cutting

edge of the two drill’s types. In these conditions, using the FBlend option was created a surface

unity needed to apply the pressure, with offset of 1 mm from the cutting edges of the two drill’s

types.

Fig. 2. Simplifing ipothesis for

helical drill

510 Innovative Manufacturing Engineering

In the case of the drill with straight lined

cutting edge, was considered a single value

of the pressure both for the two main cutting

edges and for the chisel edge, Fig. 4. For the

drill with curved cutting edge, due of the

variable thickness of the chip, the main

cutting edge were divided in 10 equal length

units. On each of these unit it is applied the

calculated pressure, according to the Table 2

and Fig. 4. In both cases, the pressure is

considered normal to the cutting edge.

Table 2. Values needed for the

chip thickness (a) calculus

– BTC φ20, for sd= 0.053 mm,

κv= 60o

Results Evaluation

The simulations for the imposed machining conditions aim the establishing of the total deformation,

the equivalents strain, the reaction of force and torque and the linear buckling by defining the scale

factor of the force up to the critical force. The final results are presented as charts for the two

different geometries of the

drills.

The drill’s deformation was

analyzed from the point of view

of geometry modification and

the working parameters, in Fig.

5, being presented the

deformation values for the two

geometry types.

The evaluation of the strain

state at the load composed from

the axial force and the

torque was made using the

von Mises criteria, see Fig.

6.

The equivalent von

Mises strain is calculated

with relation [14]:

p

[daN/mm2]

a

[mm]

380 0.043

385 0.041

395 0.039

410 0.036

420 0.033

440 0.030

470 0.025

525 0.020

700 0.012

a. b.

Fig. 5. Total deformation: BTR Ø20 mm (a) BTC Ø20 mm (b)

a. b.

Fig. 6. Equivalent von Mises strain: BTR Ø20 mm (a) BTC Ø20 mm (b)

Fig. 3. Bounding condition for the helical drill

a). b).

Fig. 4. Pressure repartisation at drills with straight line cutting

edges (a) and curved cutting edges (b)

Applied Mechanics and Materials Vol. 371 511

( ) ( ) ( ) ( )2 2 2 2 2 2 2ech x y x y x y xy yz zx

13 N mm

2σ σ σ σ σ σ σ τ τ τ = − + − + − + + +

(1)

or, using the main strains, [14]

( ) ( ) ( )2 22 2ech 1 2 2 3 3 1

1N mm

2σ σ σ σ σ σ σ = − + − + −

. (2)

From the condition ech aσ σ≤ , which must be accomplished at the composed load, it is

determined the total force and the admissible torque, Fig 7.

The verification for the establishing of the elastic equilibrium for the two helical drill’s geometry

was made by linear analysis, in order to determine the scale of force for the stability loose. After the

linear analysis of the buckling, the tow drill’s deformed shape results, Fig. 7a. and 7b.

a).

b).

Fig. 7. The elastic equilibrium stability: BTR Ø20 mm (a) BTC Ø20 mm (b)

Conclusions

The main objective of the linear static analysis is to obtain information regarding the way in

which some of the parameters which are involved in the drilling process have a certain influence on

the process in case of the two different geometry comparison.

From the data analysis, with the Ansys Workbench, for the establishing of the drill with straight

lined cutting edge and the drill with curved cutting edge, it is possible to extract the following

conclusions:

- the total deformation is bigger at the drill with curved cutting edge, an explanation for this fact

may be the core diameter decreasing due of the increasing of the flute number;

- the equivalent strains are lower for the drill with curved cutting edges;

- the total torque is higher for the drill with curved cutting edges regarding the drill with straight

line cutting edges due to the longer main cutting edge in this first case;

- the buckling coefficient λ is 1.5 in the case of the drill with standard cutting edges and 0.5 for

the drill with curved cutting edges. This fact shows a better behaviour for the drill with standard

cutting edges (for drills with the same length and load corresponding to the same feed). As for

stability the length has a great importance we consider that the drill with curved cutting edges may

be successfully used for holes with small length.

512 Innovative Manufacturing Engineering

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Applied Mechanics and Materials Vol. 371 513

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