Simulation-based solid carbide end mill design and geometry optimization

ORIGINAL ARTICLE

Simulation-based solid carbide end mill designand geometry optimization

Anhai Li & Jun Zhao & Zhiqiang Pei & Ningbo Zhu

Received: 26 September 2013 /Accepted: 13 January 2014 /Published online: 28 January 2014# Springer-Verlag London 2014

Abstract Designing a high-performance solid carbide endmill is difficult due to the complex relationship between endmill geometry and numerous or conflicting design goals.Earlier approaches of computer-aided solid end mill designare limited to only a few design aspects. This article presents athree-dimensional finite element method of milling processfor solid carbide end mill design and optimization. The soft-ware was secondarily developed based on UG platform, inte-grating the parametric design with the development of thetwo-dimension drawing of solid carbide end mill. The three-dimension finite element simulation for milling Ti-6Al-4Valloy was performed and the geometrical parameters wereoptimized based on the objective of low cutting force andcutting temperature. As a result, a simulation-based designand optimization of geometrical parameters of tool structureand cutting edge is possible. The optimized results, for thegeometrical parameters of tool structure and cutting edgewhen milling titanium alloy using a 20-mm diameter solidcarbide end mill, is a 12-mm diameter of inner circle, fourflutes, a 45 ° helix angle, and a 9 ° rake angle of the sidecutting edge.

Keywords Solidcarbideendmill .Toolstructuredesign .Toolgeometry . FEM .Optimization

1 Introduction

Solid end mills are widely used as the cutting tools in ma-chining the integral structures. However, even today, the de-sign of an efficient and powerful solid carbide endmill is still avery difficult task. The complex geometry compared to othertypes of cutting tools incorporates numerous conflicts of de-sign objectives such as low cutting forces and cutting temper-ature, high wear resistance and torsional and bending strength,high milling stability and machined surface integrity, enoughtool rigidity and chip evacuation capability, and more [12, 16].Handling those interdependencies requires a high level ofexperience from the tool designer.

In order to achieve high efficiency machining with a solidend mill, increasing the number of flutes and improving toolrigidity will be beneficial for cutting with high feed and largedepth of cut. It is essential to increase the moment of inertia ofthe cross-sectional area of tool. In addition, favorable flutegeometry can achieve excellent chip control, thus realizing thehigh-performance end mill [7]. However, some tradeoffsshould be considered. For example, large flute promotessmooth chip control at the expense of reducing the tool rigid-ity, even leading to vibration, and thus makes it difficult toincrease the number of flutes.

The geometric modeling of the cutting tools is an importantaspect for the design and manufacturing engineers from theviewpoint of shape realization. Tandon et al. [15] establishedthe model of the end mill by mathematically expressing thegeometry of the cutting tools in terms of various biparametricsurface patches. Kim et al. [6] developed an end mill designmethodology using cutting simulation, in which a solid modelof the cutter was obtained. The cutter model can be used as aninput model for FEM analysis. Kim and Ko [5] developed thedesign and manufacturing technology of end mill with highcutting performance in machining hardened steel based on thesimulation program of the helical flute grinding. Ku and Chia

A. Li : J. Zhao (*) :N. ZhuKey Laboratory of High Efficiency and Clean MechanicalManufacture ofMOE, School ofMechanical Engineering, ShandongUniversity, 17923 Jingshi Road, Jinan 250061, People’s Republic ofChinae-mail: [email protected]

A. Lie-mail: [email protected]

Z. PeiSeco Tools (Shanghai) Co. Ltd., Shanghai 200233, People’sRepublic of China

Int J Adv Manuf Technol (2014) 71:1889–1900DOI 10.1007/s00170-014-5638-5

[8] reported the design and development of a multi-purposecarbide end mill to suit all kinds of cutting processes whichwill uncover the background information on different kinds ofend mill structures, tool materials, and various surface treat-ments on the cutter. Xu and Zhao [18] proposed an accurateparametric end mill geometric model based on the end millgeometric parameters and the positioning of the grindingwheel.

Due to the numerous parameters of the structural andgeometric characteristics for helical end mills, many of thedetailed parameters, especially rake or flank width of sidecutting edge and end cutting edge, are usually determinedaccording to the technical manuals with regard to specificworkpiece material. However, with the emergence of ad-vanced materials and new hard-to-machine materials, the pa-rameters, which can not be determined from the experience ortechnical manuals, need to be selected and optimized by usingnew algorithms or methods. Therefore, generic methods toselect and optimize tool geometrical parameters are necessaryto be provided for end mill design and geometrydetermination.

It is a critical step to model and simulate the machiningprocesses in the realization of high quality machined parts.Accurate models of solid end mills used in the machiningprocesses are required to precisely simulate the machiningoperations. However, most approaches of simulation-basedend mill design focus on a limited number of geometricalaspects such as optimization of cross-section geometry oroptimization of structure and cutting edge parameters.

In this paper, the parameter optimization method of helixangle, cross-section of helical groove, and number of flutes forsolid end mills was proposed based on three-dimensionalfinite element simulation technology, providing parameterdesign guidance for the design and manufacture of end mills.

2 Parametric modeling of solid carbide end mill

To make a simplification in the tool design process and toshorten the tool manufacturing period, the designers need todevelop a three-dimension model and to draw the engineeringdrawing of the tool at the initial stage of tool design, offering aguide for the practical manufacturing process.

The CAD software UG NX provides the developing toolsUG/Open for the users or the third-party developers. The UG/Open contains the following modules [3], such as API,MenuScript, UIstyler, GRIP, GRIP NC, and C++. To ensurethe achievement of the rapid design system for the solid endmill, it is necessary to develop the language in order to createthe link or interface of UG program functions and the devel-oped language. UG/Open API module was chosen as theinterface of the developing language to the system, and this

module is compatible with the C/C++. Furthermore,Microsoft Visual C++6.0 was used for the system developing.

The developed rapid design system for the solid end millincludes menu, user interface, parameter-driven program, andmodel output. The system block diagram of the rapid designsystem is shown in Fig. 1. Menu design is the programentrance of the design system, including the main menu andthe secondary menu. The start button can be added by meansof altering the menu section of the UG NX software, and thenthe system can be opened after the start of the main program ofUG NX. User interface is composed of welcome interface,parameter input interface, and graphics auxiliary, providingusers with a simple and user-friendly operating environment.Parameter-driven program includes interface program, param-eter reader program, parameter debugger program, and pa-rameter modeling program. Interface program, as the interfaceto the design system and the UG NX platform, is responsiblefor the callback of the user interface and initializing themodeling environment. Parameter reader program is in chargeof reading the designed parameters input in the interactiveinterface for end mill, and the designed parameters are tem-porarily stored in the temporary data storage unit. Parameterdebugger program is utilized to check whether the designedparameters can be used for creating the solid end mill throughthe mathematical algorithms set in advance, returning to mod-ify, if not, succeed. Parameter modeling program is the core ofthe design system, achieving the parametric modeling of thesolid end mill through the secondary development of the UGNX platform. The three-dimension model and the engineeringdrawing of the solid end mill can be created and output by thegraphics rendering capabilities of the UG NX platform. Thedesign process of the solid carbide end mill is simplified.

UG/Open API, MenuScript, UIstyler, and C/C++ modulesare applied in the developed rapid design system. The flowchart of the rapid design system for solid carbide end mill isillustrated in Fig. 2. Firstly, the menu file section was designedusing the MenuScript module, and the compiled MEN filewas embedded into the UG system. Secondly, the user inter-face file was designed using DLG file generated by UIstylermodule, and the interactive user interface was customized.Thirdly, the parameter checking of the user input data wasimplemented using mathematical algorithms in the C/C++module. Lastly, one can go in the welcome interface by meansof menu response and the main interface by means of functioncallback. The three dimensions of the end mill was created bycalling the API function, then the developing process of thesolid carbide end mill was complied using Microsoft VisualC++6.0. The created model was eventually stored in the DLLfile.

The helical line model, the sectional groove model, and theundercut groove model were established. The side cuttingedge was created by the scanning method, while the endcutting edge was specifically designed. After the checking

1890 Int J Adv Manuf Technol (2014) 71:1889–1900

and optimizing of the created end mill compared with the realone, the software interface of the design system compiledthrough Visual C++ and UG Open secondary developingtechnology for the solid carbide end mill is shown in Fig. 3.The main structural and geometric parameters involved in thedesign system for the solid carbide end mill are shown inFig. 4. And the included parameters to define end millingcutter dimensions are detailed in Table 1. The developeddesign system is capable of achieving the checking of inputparameters, calculating of the geometrical parameters of thetool structure and the cutting edge, and generating of the three-dimension modeling and two-dimension drawings.

3 Optimization of the geometrical parameters of toolstructure and cutting edge

3.1 Finite element modeling for cutting process

3.1.1 Constitutive model

The constitutive model of dynamic response to workpiecematerial deformation process in the milling process can beexpressed as a function of stress, strain, strain rate, and tem-perature. The thermo-mechanical behavior of titanium alloy ismodeled using the Johnson-Cook constitutive equation [4].

σ ¼ Aþ Bεn� �

1þ Clnε ˙

ε ˙0

Þ #

1−T−T room

Tmelt−T room

� �m� �"ð1Þ

The variables σ , ε , and ε0 represent the equivalent flowstress (megapascal), the equivalent plastic strain rate, and thereference plastic strain rate, respectively. T, Troom, and Tmelt arethe absolute temperature, the room temperature, and the meltingtemperature of the workpiece material, respectively. A, B, C, m,and n are the yield strength (megapascal), the hardening modu-lus (megapascal), the strain rate sensitivity, the thermal softeningcoefficient, and the strain hardening exponent, respectively.

The Johnson-Cook constitutivemodel is composed of threecomponents, which are the strain hardening effect of thematerial, the relationship between flow stress and strain rate,and the relationship between flow stress and temperature. TheJohnson-Cook constitutive parameters for Ti-6Al-4V alloy inthe simulation is shown in Table 2.

3.1.2 Chip fracture criterion

Cockroft-Latham fracture criterion was adopted as the chipseparation criterion, given by Eq. (2).

Z ε f

0

σ1dε f ¼ Da ð2Þ

SecondaryMenuMain Menu

MenuDesign

ParameterInput Interface

UserInterface

Parameter-drinvenProgram

ModelOutput

WelcomeInterface

GraphicsAuxiliary

ParameterReader

InterfaceProgram

ParameterDebugger

ParameterModeling

Three-dimensionalModel Output

DrawingOutput

Fig. 1 System block diagram ofthe rapid design system for solidcarbide end mill

Menu file UI FileParameter-

drivenprogram

User inputdata storage

Parameterchecking

NO

Menu ScriptModule

XX.menFile

YES

UI StylerModule

XX.dlgFile

VisualC++

XX.dllFile

UI StylerModule

XX.c&XX.h File

VisualC++

XX.dllFile

UG/OpenAPI Module

Fig. 2 Flow chart of the rapiddesign system for solid carbideend mill

Int J Adv Manuf Technol (2014) 71:1889–1900 1891

where εf is the equivalent plastic strain, σ1 is the maximumprimary stress, andDa is a material constant. Once the integralvalue of the maximum tensile stress along the plastic strainreaches Da, the chip separates from the workpiece.

3.1.3 Tool-chip contact model

Sticking-sliding friction model was defined as the tool-chipcontact model to describe the frictional behavior of the tool-

Fig. 3 Software interface of the design system for the solid carbide end mill


chip interface, and the frictional shear stress in the tool-chipcontact area can be expressed as Eq. (3).

τ f < τ critical the sticking areað Þτ f ≥τcritical the sliding areað Þ

�ð3Þ

To perform the shift from sticking to sliding condition, asliding criterion τcritical is considered [10]

τ critical ¼ min μσn; τ sð Þ ð4Þ

where τf is the frictional shear stress (megapascal), μ is thefriction coefficient, σn is the normal stress applied to the chipcontact surface (megapascal), and τs is the shear strength(megapascal).

3.1.4 Tool-work geometrical model and meshing

A rectangular block of Ti-6Al-4V alloy with a dimension of5×5×25 mm was selected in the simulation. Three-dimensional model of the workpiece material was createdusing advanced computer-aided design packages (UG NX).The model was transformed to STL format file and importedinto the DEFORM software. Remeshing and adaptive meshtechnology was used to prevent distortion of the mesh density.The workpiece was meshed into 50,000 tetrahedral meshgrids, and the minimum mesh size is 0.2125 mm. In order toreduce the simulation time and improve the simulation accu-racy, the meshing window technology in Deform-3D wasadopted to make the part of the workpiece to be machinedlocally refined, and the mesh density ratio inside to outside thewindow is 10,000:1. The meshed workpiece is shown inFig. 5a.

rε

βDm Dc

LL1 L2

(a) External shape dimensions

αc1

αc2

dc

bc1bc2

γ0

r1γdbd1

bd2αd1

αd2

(b) Section dimensions of helical groove

Fig. 4 Basic geometry anddimensional parameters ofstraight shank end mill. [6] aExternal shape dimensions. bSection dimensions of helicalgroove

Table 1 Parameters to define end milling cutter dimensions

Parameters Definition

Dc Cutter diameter

Z Number of flutes

L Overall length

L2 Cutter length

dc Diameter of inner circle

γ0 Rake angle of side cutting edge

αc1 First relief angle of side cutting edge

αc2 Second relief angle of side cutting edge

r1 Chip groove radius

αd1 First relief angle of end cutting edge

αd2 Second relief angle of end cutting edge

β Helix angle

Dm Shank diameter

L1 Overhang length

L3 Effective cutter length

rε Nose radius

bc Rake width of side cutting edge

bc1 First flank width of side cutting edge

bc2 Second flank width of side cutting edge

γd Rake angle of end cutting edge

bd1 First flank width of end cutting edge

bd2 Second flank width of end cutting edge

Table 2 Johnson-Cook parameters for Ti-6Al-4Valloy [2]

A (MPa) B (MPa) C m nε0 (s−1)

Troom(K) Tmelt(K)

418.4 394.4 0.035 1.0 0.47 10−5 293 1950


The three-dimensional model of the solid end mill wascreated using the developed end mill rapid design system.The structural and geometric parameters were the same asthose used in the experiments to be mentioned below. A 4-flute end mill possesses a cutter diameter of 20 mm, a helixangle of 45 °, a cutter length of 40mm, a rake angle of 9 °, anda nose radius of 0.8 mm. WC-Co cemented carbide wasselected as the tool substrate material, and TiN as the coatingwith a thickness of 3 μm.

The developed end mill model was imported into theDEFORM software. To reduce the computational workloadand computing time, only the effective cutting part of the endmill was meshed. It was meshed into 80,000 tetrahedral ele-ments, and the minimum mesh size is 0.3581 mm. Themeshing window technology was also adopted to make thepart of the end mill to be machined locally refined, and themesh density ratio inside to outside the window is 10,000:1.The meshed end mill is shown in Fig. 5b.

3.1.5 Boundary conditions and process parameter settings

The boundary conditions were used to constrain the move-ment of the workpiece in the three directions. The end millwas defined only to move in the feed direction and to rotationaround its central axis. The movement velocity in the feeddirection was corresponding to the feed per tooth and spindlespeed. By adjusting the position of the tool and the workpiece,the cutting depths can be set to certain values. The cuttingsimulation time can be refined by changing the simulationsteps and the length of each step. The environment tempera-ture in the simulation is 20 °C.

3.2 Verification of finite element model

To verify the simulated results of finite element model, millingexperiments were carried out to measure and to compare thecutting forces under different cutting parameters withsimulation.

3.2.1 Experimental setup and procedure

Ti-6Al-4V alloy with a nominal composition of Ti togetherwith 5.6 % Al, 3.86 % V, 0.18 % Fe, <0.01 % Si, 0.02 % C,0.023 % N, <0.01 % H, and 0.17 % O was used in theexperiments. Workpiece with block sizes of 100×100×20 mm was prepared using electrical discharge machining.The cutting tool used in the experiment was a 20-mm diameterof solid end mill (catalog number: JHP750200R080.0-TRIBON) made by SECO Inc.

The machine used for the milling tests was a 3-axis CNCvertical machining center (Daewoo Ace-V500), equippedwith variable spindle speed from 80 to 10,000 rpm, and a15-kW motor drive. A Kistler-type 9257B dynamometer wasmounted on machine table to measure the cutting forces andthe instantaneous cutting force components in x-, y-, and z-directions, Fx, Fy, and Fz were recorded down through a type2825A-02 DynoWare signal analyzer software after amplifiedusing a type 5070A multi-channel charge amplifier. The feeddirection is in y direction. The average of the ten peak valueswas used in the cutting force analysis. The machining testswere carried out in the type of down-milling operation, anddry cutting. The parameters throughout these trials are detailedin Table 3. Experiments are repeated till consistencies of theexperimental values are obtained.

(a) Workpiece (b) Coated carbide tool

Fig. 5 Meshing of workpieceand tool. aWorkpiece. bCoatedcarbide tool


3.2.2 Experimental results and the verification

The morphology of the simulated chips and the chips obtainedfrom experiments is shown in Fig. 6. Comparing the morphol-ogy of the simulated and the experimental observed chips, agood similarity can be distinguished, illustrating the effective-ness of the finite element model.

Figure 7 shows the comparison of the simulated cuttingforces with the measured cutting forces under different cuttingparameters. As can be seen in the figures, the overall trend ofthe variation to cutting forces versus cutting parameters isconsistent with that of measured cutting forces. So, the simu-lation results agree well with the experiments, and the reliabil-ity of the developed finite element model is confirmed. Hence,this finite element simulation model can be used to predict thecutting force and chip morphology accurately during high-speed milling of titanium alloy. This provides basis for theoptimizing of structural and geometric parameters of solidcarbide end mill.

3.3 Optimization of the geometrical parameters

The cutting force and cutting temperature were simulatedusing the verified finite element model, and the tool structuraland geometrical parameters were optimized based on lowcutting force and cutting temperature. Firstly, the three-dimensional models of the solid end mills with various struc-tural and geometrical parameters were produced utilizing thepreviously developed end mill rapid design system, accordingto some fixed parameters detailed in Table 4. The end millswith different helix angles (30, 35, 40, 45, 50, and 60 °) aregiven in Fig. 8a, and the end mills with different number of

flutes are shown in Fig. 8b. The end mill models wereimported into the DEFORM software, and were used insimulation of machining Ti-6Al-4V alloy. The average valueof at least ten peak values of the cutting forces was adopted asthe cutting force and the maximum temperature on the toolsurface was adopted as the cutting temperature.

3.3.1 Helix angle

Helix angle of the end mill has a decisive role in the toolstrength and its cutting performance and a direct impact on thechip break effect. Helix angle is equivalent to the cutting edgeinclination angle of a general tool. The angle magnitude androtation direction are the main parameters to describe theattribute of helix angle [9]. The increasing of helix angle will

Table 3 Design matrix of cuttingparameters used in the millingtests

Experiment No. Cutting speed vc(m/min)

Feed per tooth fz(mm/z)

Axial depth ofcut ap (mm)

Radial depth ofcut ae (mm)

1 40 0.1 20 1

2 60 0.1 20 1

3 80 0.1 20 1

4 100 0.1 20 1

5 120 0.1 20 1

6 80 0.1 5 1

7 80 0.1 10 1

8 80 0.1 15 1

9 80 0.1 20 0.4

10 80 0.1 20 0.6

11 80 0.1 20 0.8

12 80 0.02 20 1

13 80 0.04 20 1

14 80 0.06 20 1

15 80 0.08 20 1

16 80 0.12 20 1

Fig. 6 Comparison of simulated chips with the experimental results (vc=80 m/min, ap=20 mm, ae=1 mm, fz=0.1 mm/z)


cause the value of actual rake angle to increase, and toolcutting edge becomes shaper. Meanwhile, the cutting lengthevolved in cutting is increased, and the bearing load subjectedto a unit cutting length is reduced, thereby increasing the toollife time. The rotation direction of the helical edge was

classified as left hand and right hand. For the right handrotation direction, which is the most widely used, the chipsslide up the top of the helical edge.

Figure 9 shows the simulated cutting force and cuttingtemperature versus various helix angles when milling Ti-

0100200300400500600700800

40 60 80 100 120Cutting speed, v c(m/min)

Fx(

N)

Fx_exp Fx_sim

0100200300400500600700800


Fy(

N)

Fy_exp Fy_sim

0100200300400500600700800


Fz(N

)

Fz_exp Fz_sim

(a) Cutting forces vs. cutting speed (ap=20mm, ae=0.4mm, fz=0.1mm/z)

0100200300400500600700800

5 10 15 20Axial DOC, a p(mm)

Fx(

N)

Fx_exp Fx_sim

0100200300400500600700800


Fy(

N)

Fy_exp Fy_sim

0100200300400500600700800


Fz(

N)

Fz_exp Fz_sim

(b) Cutting forces vs. axial depth of cut (vc=80m/min, ae=1mm, fz=0.1mm/z)

0100200300400500600700800

0.4 0.6 0.8 1Radial DOC, a e(mm)

Fx(

N)

Fx_exp Fx_sim

0100200300400500600700800


Fy(

N)

Fy_exp Fy_sim

0100200300400500600700800


Fz(N

)

Fz_exp Fz_sim

(c) Cutting forces vs. radial depth of cut (vc=80m/min, ap=20mm, fz=0.1mm/z)

0100200300400500600700800

0.02 0.04 0.06 0.08 0.1 0.12Feed per tooth, f z(mm/z)

Fx(

N)

Fx_exp Fx_sim

0100200300400500600700800

0.02 0.04 0.06 0.08 0.1 0.12Feed per tooth, f z(mm/z)

Fy(

N)

Fy_exp Fy_sim

0100200300400500600700800

0.02 0.04 0.06 0.08 0.1 0.12

Feed per tooth, f z(mm/z)

Fz(N

)

Fz_exp Fz_sim

(d) Cutting forces vs. feed per tooth (vc=80m/min, ap=20mm, ae=1mm)

Fig. 7 Comparison of simulated cutting forces with the experimentalresults. a Cutting forces vs. cutting speed (ap=20 mm, ae=0.4 mm, fz=0.1 mm/z). b Cutting forces vs. axial depth of cut (vc=80 m/min,

ae=1 mm, fz=0.1 mm/z). c Cutting forces vs. radial depth of cut (vc=80 m/min, ap=20 mm, fz=0.1 mm/z). dCutting forces vs. feed per tooth(vc=80 m/min, ap=20 mm, ae=1 mm)


6Al-4Valloy. It can be seen from Fig. 9a that with the increasein helix angle, the peak values of cutting force in the x-direction Fx decrease, while the peak values of cutting forcein the y- direction Fy increase. However, the resultant cuttingforces firstly decrease and then increase, that is, there exits afavorable helix angle to a minimum peak value of the resultantforce. Moreover, the end mill cutter with smaller helix anglecan obtain larger cutting force Fx, while on the contrary, theend mill cutter with larger helix angle can receive smallercutting force Fx due to its sharper cutting edge. But end millwith too large helix angle possesses the lower strength of thecutting edge.

The simulated cutting temperature increases with the in-crease in helix angle (Fig. 9b). This can be explained thatlarger helix angle increase the friction of tool-chip interface,leading to the difficulty of chip flowing and the slowness ofspreading out of cutting heat, resulting in the increasing ofcutting temperature. Therefore, the end mill cutter with a 45 °helix angle should be selected for milling titanium alloy,considering the cutting edge strength, loading condition, andthermal condition of the cutter.

3.3.2 Tool sectional groove

The tool sectional groove of the solid end mill was arranged inhigh back section type, whose basic parameters are shown inFig. 5b. The parameters include the rake angle of side cuttingedge γ0, the rake width of side cutting edge bc, the chip grooveradius r1, the first relief angle of side cutting edge αc1, the firstflank width of side cutting edge bc1, the second relief angle ofside cutting edge αc2, the second flank width of side cuttingedge bc2, and the nose radius rε, etc.

The rake angle of side cutting edge of solid end milldetermines the sharpness and strength of the cutting edge.Cutting force, cutting temperature, and even tool life, can becomparatively affected by the rake angle in the machiningprocess. Figure 10 illustrates the simulated cutting force andcutting temperature versus various rake angles when millingTi-6Al-4V alloy. As shown in the figures, the increased rakeangle consequently reduces the cutting force and cutting tem-perature. This can be attributed to the sharp cutting edge usingthe end mill with large rake angle, reducing the cutting force,cutting power, and cutting temperature, consequently raising

Table 4 Fixed parameters to es-tablish the three-dimensionalmodel of end mills

Parameters Dc (mm) L (mm) L1 (mm) L3 (mm) rε (mm) αc1 (°) αc2 (°)

Value 20 100 50 40 0.8 15 60

Parameters γd (°) αd1 (°) αd2 (°) bc (mm) bc1 (mm) bc2 (mm) bd1 (mm)

Value 0 15 30 3 3 3 3

(a) Different helix angle (Z=4, γ0=9°)

(b) Different number of flutes (β=40°, γ0=9°)

Fig. 8 The established three-dimensional model of end mills using the rapid design system. aDifferent helix angle (Z=4, γ0=9°). bDifferent number offlutes (β=40 °, γ0=9 °)


the tool durability. However, the cutting temperature increasesconversely after the rake angle exceeding 9 °. Too large rakeangle may reduce the cutting edge strength and raising thepossibility of cutting edge chipping in addition to the smallerheat dissipation area or heat accommodating volume, makingthe flowing of machined chips more difficult and eventuallybring the elevated cutting temperature [1]. Therefore, a 9 °rake angle is suggested to be used for the end mill whenmilling Ti-6Al-4Valloy as the result of low cutting force andcutting temperature.

As shown in Fig. 4b, for the end mill, the diameter of innercircle dc, which is tangent with the flute bottom, depends onthe rake width of side cutting edge bc and the chip grooveradius r1. The rigidity can be expressed as [11]

f ¼ F l3

3E I¼ 64 F l3

3Eπ d4cð5Þ

where F is the applied force (newton), E is the Young’smodulus of tool material (gigapascal), and l is the overhangof the end mill (meter). As can be seen from Eq. (5), the lagerthe diameter of inner circle is, the better the rigidity of the

cutting part for the end mill is. Furthermore, it is advisable, inthe premise of meeting the requirements of machining andtool design, to reduce the overhang for the purpose of ensuringenough rigidity of the solid end mill. The chip groove radiusought to be larger than the chip cross-sectional area in order toensure the methodically removal of chips. The chip grooveradius r1 can be calculated by the following equation.

r1≥ffiffiffiffiffiffiffiffiffiffiffiffiξ f zaeπ

rð6Þ

where ξ is the coefficient of chip deformation, and it can bedetermined in 1.5∼3.0.

The width of the tool rake face and the chip groove radiusare the critical parameters which affect the chip flowing spaceof the tool. When the width of the tool rake face and the chipgroove radius are both relatively small, chip jamming is proneto happen and the machined chips flow not smoothly, leadingto the increasing of cutting temperature and then reducing toollife. Hence, it is necessary to increase the width of the tool rakeface and the chip groove radius while maintaining adequatetool rigidity.

0100200300400500600700800900

1000

30 35 40 45 50 60Helix angle (°)

Cut

ting

for

ce, F

(N)

Fx_simFy_simFz_simResultant force

0

100

200

300

400

500

600

700

800

30 35 40 45 50 60Helix angle (°)

Cut

ting

tem

pera

ture

(°C

)

(a) Cutting force (b) Cutting temperature

Fig. 9 Simulated cutting forceand cutting temperature vs. helixangle (vc=80 m/min, fz=0.1 mm/z, ap=20 mm, ae=1 mm). aCutting force. bCuttingtemperature

0100200300400500600700800900

1000

3 5 7 9 11Rake angle (°)

Cut

ting

for

ce, F

(N)


0

100

200

300

400

500

600

700

800

3 5 7 9 11Rake angle (°)

Cut

ting

tem

pera

ture

(°C

)


Fig. 10 Simulated cutting forceand cutting temperature vs. rakeangle (vc=80 m/min, fz=0.1mm/z, ap=20 mm, ae=1 mm). aCutting force. bCuttingtemperature


Two sections of flank face are usually used for the end mill,that is, there exits the first flank face and second flank face forthe side cutting edge. The two-section flank face contributes toraising the strength of cutting edge, and is conducive toimproving the machined surface quality. The clearance angle,the same as the rake angle, determines the sharpness andstrength of the cutting edge. A larger clearance angle willbring about a sharper cutting edge; smaller cutting force,cutting temperature, and cutting power; as well as longer toollife. However, too large clearance angle will reduce thestrength of the cutting edge, and result in cutting edgechipping. In the meantime, the heat is difficult to spread out,making the flowing of machined chips more difficult andeventually causing the elevated cutting temperature. The rea-sonable limits to the clearance angle are between 10∼16° [9].Referring to [17], with the machining characteristics of titani-um alloy combined, a 15 ° clearance angle is chosen.

3.3.3 Number of flutes

Number of flutes is one of the most important structuralparameters for the solid end mill. Common end mills havetwo flutes or four flutes, and others have three flutes, six flutes,

or ten flutes. Figure 11 indicates the effect of number offlutes on chip room and rigidity of end mill. It can beseen from the figure, as for the end mill with certaindiameter, the more flutes for the end mill has, the largerthe diameter of the inner circle dc is, and the better thetool rigidity is. But at the same time, the chip room issmaller, leading to the flowing of machined chips moredifficult. So multi-flute end mills are generally used insemi-finishing and finishing machining.

Figure 12 shows the simulated cutting force and cuttingtemperature versus various flutes when milling Ti-6Al-4Valloy. As shown in the figures, the cutting force increasesslightly with the increase in number of flutes. This should beattributed to the increase of feed speed because of the increaseof number of flutes under the same cutting parameters.Simultaneously, the more flutes are engaged, the smallercutting load each flute is subjected to, leading to the slightincrease of cutting force and reduce of cutting temperature.However, too many flutes (exceeding four flutes) offer smallerchip room, and the chip flowing is retarded and cutting tem-perature is increased.

Combining the simulated results of cutting force and cut-ting temperature with the researches of engagement

Fig. 11 Effect of number of fluteson chip room and rigidity of endmill [8]

0100200300400500600700800900

1000

2 3 4 6Number of flutes

Cut

ting

for

ce, F

(N)


0

100

200

300

400

500

600

700

800

2 3 4 6Number of flutes

Cut

ting

tem

pera

ture

(°C

)


Fig. 12 Simulated cutting forceand cutting temperature vs.number of flutes (vc=80 m/min,fz=0.1 mm/z, ap=20 mm, ae=1 mm). aCutting force. bCuttingtemperature


uniformity by Song [13, 14], where it was convinced that themore flutes there is, the better the engagement uniformity is; itis advised that four flutes can be used when machining titani-um alloy.

To sum up, according to the finite element modelingand simulation results of three-dimensional machiningprocess in high-speed milling, the geometrical parame-ters of tool structure and cutting edge are optimized anddesigned. The optimization results are obtained as fol-lows: the end mill with four flutes, a 45 ° helix angle, a9 ° rake angle of the side cutting edge, and a 12-mmdiameter of inner circle is suggested to be used whenmilling Ti-6Al-4V titanium alloy. Furthermore, it is ad-visable, in the premise of meeting the requirements ofmachining and tool design, to reduce the overhang forthe purpose of ensuring enough rigidity of the solid endmill.

4 Conclusions

The software was secondarily developed based on UG plat-form, integrating the parametric design with the developmentthe two-dimension drawing of solid carbide end mill. Thecomputer-aided quick design of solid end mill was achievedand the tool design period was remarkably shortened. Thesolid carbide end mill was easily created, improving thequality and efficiency of tool design. The three-dimensionfinite element model for solid carbide end mill when millingtitanium alloy was generated. The geometrical parameters oftool structure and cutting edge, such as helix angle, rake angle,and number of flutes, etc., were optimized using finite elementsimulation, based on the target of low cutting force and cuttingtemperature. The optimized results, for the geometrical pa-rameters of tool structure and cutting edge when millingtitanium alloy using a 20-mm diameter solid carbide end mill,is a 12-mm diameter of inner circle, four flutes, a 45 ° helixangle, and a 9 ° rake angle of the side cutting edge.Furthermore, it is advisable, in the premise of meeting therequirements of machining and tool design, to reduce theoverhang for the purpose of ensuring enough rigidity of thesolid end mill. This provides the original reference data for thequick design of solid carbide end mill when milling titaniumalloy.

Acknowledgments This work is supported by the National BasicResearch Program of China (2009CB724402), the National NaturalScience Foundation of China (51175310), and the Fundamental ResearchFunds of Shandong University.

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Simulation-based solid carbide end mill design and geometry optimization