End mill design and machining via cutting simulation

Computer-Aided Design 40 (2008) 324–333www.elsevier.com/locate/cad

End mill design and machining via cutting simulation

Jae Hyun Kim, Jung Whan Park∗, Tae Jo Ko

School of Mechanical Engineering, Yeungnam University, 214-1 Daedong, Gyoungsan, Kyoungbuk, 712-749, Republic of Korea

Received 20 June 2007; accepted 19 November 2007

Abstract

This paper describes a design process for an end mill. A solid model of the designed cutter is constructed together with the computation of thecutter’s geometry, wheel geometry, and wheel positioning data for fabricating end mills with the required cutter geometry. The main idea of theprocess is to use the cutting simulation method to obtain the machined shape of an end mill by using Boolean operations between a given grindingwheel and a cylindrical workpiece (raw stock). The major design parameters of a cutter, such as rake angle and inner radius, can be verified byinterrogating the section profile of its solid model. This study investigates the relationship between various dimensional parameters and proposesan iterative approach to obtain the required geometry of a grinding wheel and cutter location (CL) data for machining an end mill that satisfies thedesign parameters. This research was implemented using a commercial computer aided design (CAD) system with API function programmingand is currently used by a commercial tool maker in Korea. It can eliminate the need to produce a physical prototype during the design stage andcan be used in virtual cutting tests and analyses.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Design; End mill; Cutting simulation; Solid modeling

1. Introduction

High-speed machining (HSM) technology using ball-endedmilling tools has been widely adopted due to its variousadvantages, such as productivity, machining accuracy, surfacequality, and production cost. The cutting tool used in a CNC(Computer Numerical Control) machine plays a vital role inaccomplishing a successful HSM process; it directly affectsthe quality of a machined surface. In addition, it is practical todevelop cutting tools with high performance and long productlife at a low price [1].

The material, coating, and shape of an end mill are keyfactors in improving cutter performance, where the shapemainly affects the machining accuracy and dynamic stability.The shape elements of an end mill include relief angle, rakeangle, and helix angle; these are the main determinants ofmachinability and they are interrelated [3].

It is difficult to model the exact three-dimensional shapeof an end mill because a certain part of the shape (e.g., thehelical groove) is not determined until the actual machiningstage. If we have no three-dimensional solid model of the

∗ Corresponding author. Tel.: +82 53 810 3524; fax: +82 53 810 4627.E-mail address: [email protected] (J.W. Park).

0010-4485/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2007.11.005

designed end mill, we need to make a physical prototype andcarry out cutting tests in order to improve the cutter shape [2].Therefore, it would reduce the cost and time for designing anend mill if we could use its three-dimensional solid model. Inaddition, it is also beneficial for the required grinding wheelgeometry and CL data to be computed using the solid model.One of the methods to predict a proper three-dimensional shapeis cutting simulation: a helical groove shape and sectionalprofiles can be obtained by grinding simulation for the givenwheel geometry and CL data (i.e., wheel paths), where a seriesof Boolean operations between the wheel and the cylindricalblank (i.e., raw stock) is performed. Major design parameters– rake angle, inner radius and cutter width – can then beevaluated from the sectional profile curve, which facilitatesdigital interrogation of cutter geometry and prediction ofthe required wheel geometry and CL data computation formachining as well.

It is also required that the machining condition (i.e., wheelgeometry and positioning data) to fabricate the end mill thatsatisfies given dimensional parameters (e.g., rake angle) bedetermined, which is called the ‘inverse problem’ [2]. It isnecessary to predict the helical groove shape as accurately aspossible because it determines the rake angle, etc. However,it is the combination of the grinding wheel geometry and its

http://www.elsevier.com/locate/cad

mailto:[email protected]

http://dx.doi.org/10.1016/j.cad.2007.11.005

J.H. Kim et al. / Computer-Aided Design 40 (2008) 324–333 325

positioning data that generates the helical groove shape, whichmakes it difficult for a designer to predict the shape analytically.So it is usual for a designer to determine the required machiningconditions using a trial and error method that requires manyvery tedious hours of manual work. More efficient way ofpredicting machining conditions should be presented.

There are a few previous studies on predicting the profilecurve for the helical groove of an end mill, which canbe categorized into two methodologies: direct method andanalytical analysis. The ‘direct method’ approximates thegrinding wheel as a set of a finite number of thin disks wherebythe intersections of primitive wheels and the workpiece arecalculated to obtain a profile curve [2,3,8,9,11], and leads tographical visualization [4]. Alternatively, the latter method triesto find the profile curve based on mathematical constraintssuch that the common normal vector at the contact point of awheel and the workpiece should meet the rotational axis of thewheel [5,6,10,12].

Clearly, the cutting simulation approach in this paper isbasically same as the direct method in a respect that it triesto obtain a machined result. However, the main difference isthat our approach creates a complete three-dimensional solidmodel, and thereby facilitates accurate geometric analysis butalso further engineering analysis such as with the finite elementmethod (FEM).

Considering the inverse problem, we can find relevantworks for finding wheel setting conditions and wheel geometrydata [2,3,7] by use of a numerical search method. Someprevious work successfully demonstrated the practical useof developed software by adopting the direct method [2,3].In our approach, the geometric interrelationship among thedesign parameters of an end mill, a grinding wheel and wheelpositioning data was investigated; thereby a straightforwardsearch becomes possible. In addition, the cutting simulationapproach was adopted in calculating the geometric parametersof the end mill during the search flow. So it possibly performsa more efficient and accurate prediction of the required wheelgeometry and positioning data. Section 2 describes the basicdimensional parameters and their relationships in a typical endmill and grinding wheel, followed by three-dimensional solidmodeling of the cutter using the cutting simulation mentionedin Section 3. The prediction of wheel geometry, positioningdata, and grinding tool-path generation are presented with someillustrative examples in the following sections.

2. Dimensional parameters

Fig. 1 and Table 1 show the geometric dimensions that definethe shape of end mills. It should be noted that the helical grooveand neck groove shape will not be determined by the designparameters but by other factors, such as grinding wheel shapeand grinding positions. Therefore, it is not straightforward toanalytically verify the dimension of the helical flute and neckgroove shape (see Fig. 2).

3. Cutter shape modeling

The three-dimensional shape of an end mill is constructedby sweeping the sectional profile curve of the helical groove

(a) Section dimensions.

(b) External shape dimensions.

Fig. 1. Basic geometry of end mills.

Fig. 2. Helical groove and neck part of the cutter.

Table 1Parameters to define end-milling cutter dimensions

Ø1 First relief angle Ø2 Second relief angleγ Rake angle Ri Radius of inner circleRc Chamfer length Ds Shank diameterβ Helix angle Dc Cutter diameterLc Cutter length Ls Shank lengthL Overall length N f Number of flutes

along the predefined helix (see Fig. 2). We adopted the cuttingsimulation approach where the end mill shape is divided intoshank, neck, and flute. First, the shank model is based on thedimensional parameters of the wheel and the relative positionof the grinding wheel and workpiece (see Fig. 3). The neckis then modeled by a cutting simulation of the blank andgrinding wheel in which the sectional profile curve of thecutter is retrieved. The helical flute shape is then modeled bysweeping the section curve along the predefined guide curve.Additional dimensions include the number of flutes (N f ), leadvalue (pitch), and neck length.

3.1. Shank and neck modeling

The shank model is constructed as a cylindrical solidbased on the diameter (Ds) and length (Ls) as shown inFig. 1(b). To prepare neck modeling via cutting simulation,the grinding wheel and workpiece (blank) need to be modeled,

326 J.H. Kim et al. / Computer-Aided Design 40 (2008) 324–333

(a) Wheel dimensions.

(b) Relative positions of wheel and blank.

Fig. 3. Wheel geometry and positioning.

and dimensional information, as shown in Fig. 3(a), is used.In addition, the positions of the grinding wheel and workpieceare configured based on the relative positioning data shown inFig. 3(b). The models are positioned as shown in Fig. 4(a), andthe workpiece is moved along a helical curve for the cuttingsimulation (see Fig. 4(b)).

It is notable that the applied end mill maker utilizesstandardized wheels whose geometry (i.e., cross-sectionalprofile, wheel diameter) is already specified. Also it is worthdescribing the offset value and wheel height (xw and yw inFig. 3(b)). Both xw and yw have an effect on the inner radiusof the machined end mill, which means that changing yw alsoresults in a different inner radius (see Fig. 3(b)). However, wehad better fix one of them to simplify the problem for practicalapplication. So the applied tool maker adjusts xw in order tocontrol the inner radius (Ri ), while yw is set to an empiricallyspecified value.

In real machining, it is the workpiece that is transformed,although computation time can be reduced if the wheel istransformed rather than the workpiece. The transformation(i.e., rotation and translation) of the grinding wheel in a cuttingsimulation is obtained from the lead value of the end mill aswell as the number of flutes. Fig. 5 illustrates the approximated

Fig. 4. Positioning and transformation of the grinding wheel and blank.

Fig. 5. Approximate swept volume by the wheel transformation.

Fig. 6. Computation of lead value.

swept volume generated by the wheel transformation in the caseof a four-flute end mill.

The wheel transformation matrix M is expressed as shownin Eq. (1), where θC and ZC represent the cumulative rotationangle and translation distance, respectively. Then the wheel willbe transformed from θ = 0 (z = 0) to θ = θC (z = ZC ). Inneck modeling, ZC corresponds to the neck length (i.e., Lneck).Additionally, the lead value (i.e., pitch) Lv is expressed asEq. (2), as shown in Fig. 6, where θC = Lneck/Lv or θC =

ZC/Lv . It should be noted that θC and ZC are slightly extendedjust for obtaining stable plane intersection (i.e., sectioningor neck splitting in Section 3.2). In addition, the overalltransformation is applied as a finite number of discrete steps(e.g., angular step = δθ ).

M = Rot(z, θC ) • Trans(z, ZC )

=

cos θC sin θC 0 0

− sin θC cos θC 0 00 0 1 ZC0 0 0 1

(1)


Fig. 7. Neck modeling.

Fig. 8. Extraction of sectional profile curve.

Fig. 9. Profile discrepancy due to the discrete wheel transformation.

Lv =π • Dc

tan βwhere β = helix angle, Dc = cutter diameter.

(2)

Now it is possible to subtract the wheel swept volumefrom the workpiece using Boolean operations between thetransformed wheel shape and the workpiece (Fig. 7(a)). Thecomplete neck can be modeled by repeating this modelingoperation N f − 1 times around the cutter axis, as shown inFig. 7(b).

3.2. Helical flute modeling

The sectional profile curve of the end mill can be obtainedfrom the neck model, where the neck is split by a planethat is perpendicular to the cutter axis, as shown in Fig. 8.Although the ideal profile follows a smooth curve, the extractedprofile curve contains a certain unwanted discrepancy due to thediscrete wheel transformation operation (see Fig. 9). Therefore,the angular step, δθ , should be configured as a small enoughvalue such that the maximum deviation εmax is less than thegiven tolerance.

We found the relations of angular step vs. maximum devia-tion and computing time for the example case where the max-imum deviation is linearly proportional to the angular step inan approximate fashion (see Fig. 10). In the case that the givenaccuracy is 0.01 mm, for example, the angular step can be setto be 1◦ since εmax is 0.007 mm, which is the case of our work.

The helical flute shape is modeled by sweeping the profilecurve, where the initial profile curve at the end of the neckpart is rotated and translated up to the cutter length (Lc inFig. 1). Fig. 11 shows the positioning and sweeping of theprofile curves, and the flute shape.

3.3. Computation of cutter geometry

The rake angle, inner radius, and cutter width parametersare computed based on the sectional profile curve, which iscomposed of lines and arcs. The ideal rake angle is defined asthe angle between the tangent vector and the line to the cutteraxis as shown in Fig. 12(a). In practice, on the shop floor, anapproximate rake angle, as shown in Fig. 12(b), is more usual.We obtained the approximate rake angle by finding the end millouter curve, the cutter end point on the curve, and the point-on-predefined-length on the profile curve, as shown in Fig. 13.

The inner radius of the end mill can be obtained by findingthe minimum distance between the profile curve and the cutteraxis, as shown in Fig. 14. Finally, the cutter width is definedas the distance between two consecutive section curves on thesection plane.

4. Prediction of wheel geometry and positioning data

It was shown in Section 3 that we can construct a solid modelof end mills by simulating the machining operation where themachining conditions – the grinding wheel geometry and theCL or wheel positioning data (i.e., wheel setting angle, centerpoint and offset value shown in Fig. 3(b)) – are provided.Conversely, it is also a requirement that we should determinethe machining conditions to fabricate an end mill that satisfiesgiven dimensional parameters, such as rake angle, etc. It is wellknown that the performance of an end mill is related to itsgeometric parameters in which the rake angle, inner radius, andcutter width are specifically critical. The rake angle is knownas a major factor that affects the cutting force and surfacefinish [3]. Because the helical groove shape determines the rakeangle, we should predict its shape as accurately as possible.However, it is a combination of the grinding wheel geometryand its positioning data that generates the helical groove shape,which makes it difficult for a designer to analytically predict theshape.

4.1. Relationships between parameters

Usually the wheel geometry and its positioning data formachining end mills with given cutter geometry are determinedusing a trial and error method. Therefore, a more effectivemanner of predicting these parameters is required. This leadsto a study of the relationship between such parameters,which make it possible to predict the required conditions.The dimensional parameters of the designed cutter, grindingwheel, and relative positioning data are defined as illustrated inFigs. 1 and 3. We investigated the relationship between theseparameters using the cutting simulation method described inSection 4, which includes cutter rake angle, inner radius, cutter


Fig. 10. Relationships between angular step, accuracy, and computing time.

Fig. 11. Helical flute modeling.

(a) Ideal.

(b) Approximate.

Fig. 12. Definition of rake angle.

width, and the grinding wheel geometry along with the wheelpositioning data. A few relationships between parameters areshown in Fig. 15.

Fig. 15(a) represents the relationship between the innerradius and offset values (Ow in Fig. 3(b)). The change inrake angles corresponding to the given wheel setting angle (in

Fig. 13. Point data to calculate rake angle.

Fig. 14. Inner radius and cutter width.

Fig. 3(b)) is shown in Fig. 15(b), and is an inverse relationship.Fig. 15(c) shows the relationship between cutter widths andthe first wheel thickness (t1 in Fig. 3(a)), which results in anincrease in t1, and that causes a huge machining area on thehelical groove. Finally, Fig. 15(d) shows the effect of the firstwheel angle (θ1 in Fig. 3(a)) on the cutter width. It shows thatθ1 is also related to the cutter width, Cw, but the rate of change(i.e., slope) of θ1 is less than that of t1. As a result, we foundthat there were no cross-coupling relationship between theseparameters, such as setting angle and offset value. Thus, userscan adjust the rake angle solely by changing the setting angleparameter.

Table 2 summarizes the behavior of the cutter geometrybased on the results of this study where some parameter valueshave very little effect on the cutter geometry (i.e., t2, θ1, θ2).In addition, based on cutting simulation tests, it can be shownthat the shape of a sectional profile curve is locally influenced


Fig. 15. Relationships between parameters.

Fig. 16. Local influence of the wheel geometry on the shape of the sectionalprofile curve.

Table 2Estimated relationships between parameters

Wheel parameter Cutter geometry Behavior

Pw (xw , yw) Inner radius (Ri ) (xw, yw) ∝ Riα (setting angle) Rake angle (γ ) α ∝ 1/γ

t1 Cutter width (Cw) t1 ∝ 1/Cw

t2, θ1, θ2 Cutter width (Cw) Fixed

by every parameter in the wheel geometry (t1, t2, θ1, θ2 inFig. 3(a)), as shown in Fig. 16.

4.2. Computation of wheel geometry and positioning data

As described above, it is necessary to compute the wheelgeometry and its positioning data for machining an end mill thatsatisfies a given geometry. This procedure can be implementedusing a simple iterative process as shown in Fig. 17. Once thedesign parameters – rake angle, inner radius, and cutter width– are provided, the offset value (xw in Fig. 3(b)) is determinedby calculating the inner radius, which is directly proportionalto the offset value, as shown in Table 2. Next, the setting angle(α in Fig. 3(b)) for the given rake angle is determined. They areinversely proportional to each other. Finally, the first thicknessof the wheel geometry (t1 in Fig. 3(a)) is determined by thecutter width condition.

The basic way of calculating the cutter design parameters inFig. 17 is facilitated by splitting the constructed solid model

Fig. 17. Prediction of the wheel geometry and position.

to obtain a section profile curve. However, we need a moreefficient way since the described cutting simulation approachrequires a certain repetition in Boolean operations at everywheel transformation step from θ = 0 (z = 0) to θ = θC (z =


Fig. 18. Cutter profile curve extraction using an intersecting body.

ZC ), as shown in Section 3.1. Moreover, this whole processshould be repeated for given machining conditions.

The idea is summarized as follows. The Boolean operationbetween the wheel and the blank workpiece is performedat θ = 0 (z = 0). Also, the intersecting solid body inFig. 18 is similarly transformed to θ = θC (z = ZC ) toobtain a set of solid bodies (i.e., each solid body is copiedand transformed). Then, the section profile curve is computedby splitting the resultant solid bodies to calculate designparameters. It was observed that the computing time reducedto about 20% compared with that of Section 3. Also, thecomputation accuracy demonstrated no differences because theresultant solid bodies were a dual in overall Boolean operations.

It should be noted that other elements in the wheel geometry(t2, θ1, θ2 in Fig. 3(a)) are heuristically determined as t2 =

1.8t1, θ1 = 10◦, θ2 = 45◦, respectively. As a final note, allof the characteristics shown in Fig. 15 are linear and, by usingthis property, the number of iterations can be reduced to threeor four, for example, using a false position method.

5. Grinding tool path generation

In general, NC (numerical control) machining of a targetshape for the given cutter geometry requires a computationprocess of CL (cutter location) data that will be post-processed into NC codes for a specified NC machine. TheCL data at a given CC (cutter contact) point are defined bythe cutter position and orientation (i.e., cutter axis vector).Therefore, tool-paths for the variable-axis machining areobtained. Moreover, the machining of helical groove shapes indrilling or end mills requires somewhat complicated CC andCL data computation through certain mathematical analyses[7,13]. On the other hand, the cutting simulation methodologyin our work simplifies the CL data computation because it isunnecessary to generate CC data on the designed shape.

In helical groove machining using a grinding wheel, the CLdata represent the position and orientation of the wheel at aninstance while a grinding tool-path of the wheel is comprisedof consecutive CL data. Now that the wheel geometry andpositioning data can be obtained as shown in the previoussection (Section 4.2). Also, the tool-path can be generated by

Fig. 19. Example of a grinding tool-path.

Table 3Machine specification

Axis travel

X -axis 490 mm Y -axis 320 mmZ -axis 660 mm C-axis ±200◦

A-axis ∞

Resolution (mm) Diameter (mm)Linear 0.0001 Spindle 80Radial 0.0001 Wheel 200

simple wheel transformation: the translation and rotation usedin neck shape modeling (Section 3.1). Final NC commandsare generated via inverse kinematics of the five-axis machine(Walter helitronic power production) that is currently used in alocal tool production company.

Fig. 19 shows a typical grinding tool-path. Fig. 20 illustratesan NC machine with mechanical specifications as noted inTable 3. As a verification tool of the NC commands, adedicated simulation function has been implemented, whichdetects collision and axis stroke-over.

6. Illustrative example

We developed the described system on a basis ofUnigraphics R© Open API in an MS Windows R© environment.The main functions applied in this system include end


Fig. 20. Applied five-axis grinding machine.

Table 4Design and machining parameters

Dim. Value Dim. Value Dim. Value

β 30.03 Ri 1.89 R 0.5Ds 6.0 α 36.3 Dc 6.0Lc 35 Lneck 15 Ls 50Dw 150 t1 2.47 t2 4.5θ1 10 θ2 45 Ow −2.0Pw Xw = −2.0, Yw = 76.09, Zw = 0.0

mill shape modeling, prediction of wheel geometry andpositioning data, tool-path generation, and verification that canbe summarized as follows:

• Shape modeling by cutting simulationIt constructs a solid model in end mills by simulating real

machining operations where the geometry and positioningdata of the grinding wheel (i.e., machining conditions) areprovided. It can digitally compute the cutter geometry, suchas rake angle or inner radius, by interrogating the constructedsolid model.

• Prediction of wheel geometry and positioning dataIt finds out the machining conditions by which we

can fabricate an end mill that satisfies given dimensionalparameters (e.g., rake angle, etc), thereby eliminating sometedious manual work (i.e., trials and errors) when wemanufacture a new end mill.

6.1. Shape modeling

The solid model of a four-flute end mill with 6 mmdiameter (Ø6) is constructed that is currently fabricated by aKorean toolmaker. Table 4 shows related design and machiningparameters. It is noted that the required rake angle = 6◦ andthe inner radius = 1.89 mm (actually, the values are measuredthrough investigating ground cutters using a microscope).The constructed solid model and section profile curve ofthe designed cutter are shown in Fig. 21. The approximaterake angle was calculated as 5.91◦, and the inner radius was1.99 mm, which showed less than 5% of difference comparedto that of the above values. The overall model construction timewas about 1 min on a 2.8 GHz PC, where the angular step was1◦ (δθ in Section 3.2) for the given accuracy of 0.01 mm.

Fig. 21. Section profile curve and solid model of the designed cutter.

Table 5Input parameters for the wheel geometry prediction


Ds 6.0 β 30.03 N f 4γ 6.0 Ri 1.89 Cw 0.9θ1 10.0 θ2 45.0 Tol. 0.01

Table 6Predicted wheel geometry and positioning data


Pw (yw) 76.79 Pw (xw) −2.093 α 37.641t1 2.135 t2 3.843 γ 6.01Ri 1.884 Cw 0.90

6.2. Prediction of wheel geometry and position

The input values for computation of the wheel geometry andpositioning data are listed in Table 5. The procedure shown inFig. 17 was used to obtain the results shown in Table 6 thattook 20 min on a 2.8 GHz PC. It should be noted that a trial anderror method requires at least half a day even with a dedicatedauxiliary software system.

6.3. Tool path generation and verification

A tool-path was generated to grind a helical groove in thedesigned cutter (Fig. 22) based on machining parameters asshown in Table 4. As previously described, four helical groovescan be machined by indexing (i.e., rotating) the workpiece. Inaddition, Fig. 23 shows the tool-path verification procedure inwhich solid models in a tooling system are constructed andsimulated, and interference detection is performed, such as thecollision between machine components or axis stroke-over.


Fig. 22. Tool path generation.

Fig. 23. Tool path verification.

7. Conclusions

We developed an end mill design methodology using cuttingsimulation, in which a solid model of the cutter was obtained.Also, the cutter geometry (e.g., rake angle) can be interrogated.The solid model facilitates graphical and numerical verificationof the cutter shape without constructing a physical prototype. Itcan also be used as an input model for FEM analysis, etc.

Secondly, we investigated the relationship between the cuttergeometry, wheel geometry, and positioning data. A simpleiterative process was developed to efficiently compute thewheel geometry and positioning data (i.e., CL data) that grindthe designed cutter geometry, which eliminates tedious trialsand errors. In addition, the tool-path generation and verificationfunction were developed.

A Korean tool maker (OSG Korea) who produces varioustypes of end mills is currently using the implemented systemfor the design and machining of commercial products on theshop floor. As future work, it is necessary to study the modeling

and grinding of complete end mill shapes, which includes CAEanalyses, etc.

Acknowledgements

This research was supported by the Program for the Trainingof Graduate Students in Regional Innovation (No. AROOKB-2201-220107) conducted by the Ministry of Commerce,Industry and Energy of the Korean Government.

References

[1] Reuteler A. Cutting tool technology in high-speed milling (HSM),FRAISA SA. 1997.

[2] Ko SL. Geometrical analysis of helical flute grinding and application toend mill. Transactions of NAMRI/SME 1994;22:165–72.

[3] Kim YH, Ko SL. Development of design and manufacturing technologyfor end mills in machining hardened steel. Journal of Materials ProcessingTechnology 2002;653–61.

[4] Ko SL, Pham TT, Kim YH. Visualization process for design andmanufacturing of end mills. LNAI, vol. 3613. Berlin Heidelberg:Springer-Verlag; 2005. p. 1133–6.


[5] Agullo-Batell J, Cardona-Foix S, Vinas-Sanz C. On the design of millingcutters or grinding wheels for twist drill manufacture a CAD approach.In: Proceedings of 25th machine tool design and research (MTDR)conference held in Manchester, England. 1985. p. 315–20.

[6] Ehmann KF. Grinding wheel profile definition for the manufacture of drillflutes. Annals of CIRP 1990;39/1:153–6.

[7] Ekambaram B, Malkin S. CAD software for helical flute grinding ofmilling cutter. Transactions of NAMRI/SME 1993;21:181–7.

[8] Tlusty J, Smith S, Zamudia C. Operation planning based on cuttingprocess model. Annals of the CIRP 1991;40/1:95–8.

[9] Kaldor S, Rafael AD, Messinger D. On the CAD of profile for cutters and

helical flutes geometrical aspects. CIRP 1988;37/1:53–6.[10] Sheth DS, Malkin S. CAD/CAM for geometry and process analysis of

helical groove machining. Annals of CIRP 1990;39/1:129–32.[11] Friedman M, Meister I. The profile of a helical slot machined by a form-

milling cutter. Annals of the CIRP 1973;37/1:53–6.[12] Kang SK, Ehmann KF, Lin C. A CAD approach to helical groove

machining mathematical model and model solution. International Journalof Machine Tools and Manufacture 1997;37/1:101–17.

[13] Hsieh J. Mathematical model and sensitivity analysis for helical groovemachining. International Journal of Machine Tools & Manufacture 2006;46:1087–96.

Documents

End mill design and machining via cutting simulation