Investigations Into the Clearance Geometry of End Mills

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  • Investigations Into the Clearance Geometry of End Mills

    S . Kaldor, P. H. H. Trendler, T. Hodgson, Technical Services Department, Council for Scientific and Industrial Research/South Africa - Submitted by Prof. G. F. Micheletti (1 )

    The clearanre geometry o f end mills has a influence on cutter performance. variations i n clearance geometry affect cutter performance has not heen fully investigated. In this paper a modified definition of the clearance profile of cutting tools is applied w i t h the objective o f mnintainins ii constant clearance angle in the direction of material flow. Single poinL orthogonal milling tests were carried out with HSS blanks, each ground o n a specially adapted machine t o o l , t o a particular clearance angle in accordance with the proposed rlearance profile. on similar cutters, albeit with flat flanks. The wear propagation was measured and the effect of clearance angle on tool life determined. optimum clearance angle for each of the two types of cutter.

    However, the degree to which

    Comparative tests were carried out

    The results show a definite

    I .


    2 .




    A,B B

    Be F


    f l




    HSS 1


    Ll .L2 M2




    PKC ,, 'P' 'P,'




    ;* 1


    The performance of end mills has important economic implications in view of the wide usage of this type of cutter in the metal-working industry. Of particular significance is the tool life. Previous studies have shown that the scatter in tool life and variations in the surface integrity obtained during milling can have significant effects on productivity and product quality. [1-7.9,10]

    Of importance too is the effect of clearance geometry on performance. However the degree to which variations in clearance geometry affect cutter performance has not been fully investigated.

    This paper refers to investigations that were undertaken to determine the effect of the peripheral clearance geometry on tool life.


    The end mill can be defined as a rotary multi-tooth cutter, having an axially advancing helical flute configuration. (Fig. 1). From the functional point of view, end mill geometry can he divided into three parts: (a) The shank; for supporting the end mill in the tool

    (b) The body; which contains the fluted part of the end holder.



    Axial depth o f cut

    Radial depth of cut


    Symbols for different radii


    Effective body

    Symbol f o r f ,/2nRo

    Feed rate

    Actual cutting feed

    Clearance profile generating feed rate

    Symbol for f2/2nRo

    Hardness Brine11

    High speed steel

    Direction f o r x vectors

    Direction for y vectors

    Clearance lands

    Type of HSS Material Flow Line


    Peripheral clearance curve

    A peripheral clearance curve when f = 0

    PHC line

    A PMC line when f = F1 ; (PMC1)

    A PKC line when f = F2 ; (PMC2)

    Co-ordinate in the moving system

    Co-ordinate in the fixed system

    Position vector in the fixed system








    Position vector in the fixed system when f = fl mm

    (c) The front edge of the cutter; commonly referred to as the point.

    The shank design affects, inter alia. cutter stability and workpiece surface finish.

    The body of the end mill (Fig. 1) is largely responsible for chip removal. The cutting process along the body tends to be nearly constant at any given cross section, apart from minor variations related to factors such as the coolant and chip flow rate. It 1s assumed that these variations are negligible.

    The point of the end mill is subject to the most severe wear. The cutting operation in this domain is a com- bination of face milling and slab milling. Both operations affect the corner of the tool, which is the weakest part of the cutter. (Fig. 2).

    2.1 The end mill body

    Fig. 3 depicts a t pica1 end mill tooth geometry, in the tool working plane. [8.9]

    it will be noted that the almost circular oriented cutting line o r the Material Flow Line (MFL) yields Significant variations in the actual clearance angles, measured between the flank and the tangential direction of the MPL along the relief flanks which may be flat o r concave in shape; both

    Position vector in the fixed system when f = f2 mm

    Ro Cutter outer radius mm




    T.W 't'

    U *

    $1 . t 2 VB

    VBC V

    X,Y x' .y'

    x' 1 rY'2

    x ' 2 .Y' 2 7.

    Cutting edge

    Shank of tool

    Symbol for sin 4 Tool wear

    Straight clearance line

    Peripheral speed vector for f = 0

    Peripheral speed vectors for fl and f2

    Flank wear width m

    Corner flank wear mm

    Cutting speed mlmin.

    Co-ordinate axis in the moving system mm

    Co-ordinate axis in the fixed system mm

    mlmin . mlmin.

    Co-ordinate axis in the fixed system when f = fl mm

    Co-ordinate axis in the fixed system when f - f2 mm Co-ordinate axis and axis of rotation of the tool mm

    a General clearance angle

    fe Working side clearance i a

    Tool side clearance angle for f = fl and f2 aE afI,afi a Clearance measured on the PMC flank P

    Q Clearance measured on the straight flank

    y f Tool side rake angle

    4 Angle of rotation and co-ordinate in the moving system 0' Angle of rotation and co-ordinate in the fixed system



    Angle values of 0 ' for f = fl and f2

    Angle used f o r the wear area calculations

    Annals of the CIRP Vol. 33/1/1984 33

  • o f which are in common use.

    It has been assumed that variations in clearance angles located behind a i.e. along the flank in the direction uf the MFL have a cfonsiderable influence on tool performance. This has influenced some tool designers to produce convex clearance profiles under such names as eccentric or rliptic clearance shapes, with a view to minimising variations in clearance angles. (Fig. 4 ) .

    The method being used by some manufacturers to create the "eccentric" profile on the peripheral lands of the tool, is to tilt the grinding wheel forward towards the point of the end mill in plane Pr. The magnitude of this inclination determines the size of the peripheral clearance a f'


    End mill users have differing opinions with regard to the performance of cutters produced with convex clearance geometries. In order to determine if convex ground geometry is justified, investigations were carried out with the view to obtaining answers to the following questions:

    (i) Is it possible to grind a curvature that would fulfil a constant angle requirement?

    (ii) To what excent does the eccentric profile fulfil the constant clearance requirement?

    (iii) Does an optimal clearance angle in respect of tool life exist, for both convex and flat clearance profiles?

    (iv) Is there any significant difference in tool life between convex and flat profiles?

    The effects of various clearance profiles on tool performance were investigated by means of an orthogonal grinding and milling system. The orthogonal cutting concept was selected in order to minimise the number of geometric errors that could be expected in commercially produced end mills.

    The development of a convex clearance profile that results in an almost constant clearance angle is discusssed in some detail.

    3. I Assmptions

    For the purpose o f the analysis it was assumed that:

    (a) A linear slope of the clearance profile in the Cartesian co-ordinates r , Q, would be the optimal of the end mill point shape in respect of tool life, and

    (b) An optimal clearance angle related to tool life does exist.

    Both the above assumptions were previously made in connection with drills c5.6.71. In this case it was assumed that drills have a linear MFL in plane P , due to their axial feed direction. However, in peripherafi milling the feed is in the radial direction of the tool, which yields a curved MFL in plane P of the end mill. Since the geometry of end mills is basfically different to that of drills, the matter had to be investigated separately.

    The assumption that the linear slope clearance profile is the optimal shape in respect of tool wear of drills [7], allows maximum tool material to be included in the cutting wedge for given cutting and clearance angles. In this case the tool wedge is strongest and permits maximum heat conduction from the cutting edge into the cutter body, thereby reducing the edge temperature. The same theory can be considered for the end mill by modifying the geometry from a straight to a curved configuration.

    Since the clearance profile is related to the curved MFL the attainment of a constant clearance angle would necessitate the optimal clearance profile being curved as well. (Figs 5(a) and 5(b)).

    In order to define clearance shapes for both rotary and linear cutting tools, the following may be stated: the correct shape of the curved clearance profile would have to be a certain convex shape that will create a similar wedge angle, albeit curved, (between the tool flank and the surface generated during machining), to that of a linear cutting tool.

    The following generalised definition for the linear slope clearance shape is proposed: the clearance gap which is formed by superimposing both curved shapes generated by high and low feed rates on the tool flank and workpiece, respectively, will result in the desired equivalent to a linear clearance being obtained.

    The machined profile created by a given rotary tool under given cutting conditions was analysed and the shape of the curve thus generated was called the Peripheral Milling Curve (PMC).

    3.2 Peripheral Milling Curve (PMC)

    The milling curve created by any given point P on the periphery of a rotary cutter (F ig . 15) consists oi two basic movements; rntation and linear translation in the feed direct i on.

    These mnvements are defined as follows:

    (i) Rotary movement

    x = no cos 0 = no sin .............................. ( 1 )

    x' = 9- f .................................. ( 2 ) (ii) translatory movement in the "x" direction:

    2n y' = 0

    The superimposing of equations ( I ) and (2) yields the following position vector:

    ;*(o) = (RO cos 0 + f) i + (RO sin $1 J ... ( 3 ) The angle $ is the independent variable, located in the moving co-ordinate system (x, y) while :' is defined in the fixed co-ordinate system (x', y').

    The corresponding angle 6' in the fixed co-ordinate system can be calculated thus:

    ( 4 )

    In order to define both curves needed for the definition of the clearance angle, two feeds were selected:

    (i) The maximal expected actual cutting feed, for a particular type of cutter, fi and

    (ii) the theoretical feed used to define the flank profile of the cutter tooth, f 2 . In this case f2 will also be the flank grinding feed.

    Both feeds, f l snd f 2 , form the curves PMCl and PMCz (Fig . 6 ) and vectors V I and c'z which are tangential. to the PMC curves.

    The clearance anglej afe,+can then be calculated with reference tn vectors V l and V2. as follows:

    6, . t, 1311 . I t Z i

    ....................... (5 ) Cos a = fe

    substitution of the vector values in (5 ) yields:


    S - sin 0 F = fl/(2nRo)

    G = f /(2aRo) 2

    The maximal value of afe was calculated by derivation as follows:

    d d0

    which finally yielded:

    - (cos afe) = 0 ............................ (7)

    sin ,$ L F3 + G 3 ........................ (8) (C-F)2 (l+FG)

    For practical applications F can be assumed zero which increases the angle a fe to uf and equation (8) thus reduces to:

    sin 0 = G .................................. (9) Substituting equation (9) into (6) finally yields the solution:

    $ = af .................................... (10) Note that 0 is meaningful only in the region: - considering the feed direction. Consequently only this region is considered in the following study:

    The result described in equation (10) defines the position (4) on the curve at which the curve slope, with reference to the circle of rotation reaches its maximum. For example, if the same feed rate is chosen for both the cutting and the tool grinding processes and if the tool geometry is selected from the position of the curve where + = af, a varying

    2 2


  • 4 .

    4 . 1


    4 . 3

    clearance between the tool flank and the generated PMC will result, depending on the angle, #, at which cutting takes place. However. when the cutting tooth reaches the cutting position Q = D both curves will have the same slope values and the clearanfce angle will be reduced to zero.

    A plotting procedure was developed in order to illustrate the variation of the tool side clearance angle, a , as a function of the position angle, 6. The followifng were considered:

    (i) Feed direction towards 0 = 0 (see Fig. 6) (ii) Cutter rotation: anti-clockwise

    (iii) (L = 10" (This value was selected for practical

    (iv) Diameter of the grinding wheel: 100 rn (assumed).

    Figs 7(a) and (h) show the clearance profiles f o r three different tool flanks ground to the following shapes:


    (i) PHC , (ii) strfight, and

    (iii) concave (based on a grinding wheel, I00 mm dia.)

    The above curves are shown as P2. t, and c respectively and compared with the actual milling curve PI. Fig. 7(b) shows an enlargement of the active region of Fig. 7(a). The same examples are used to show the variation in the tool side clearance angle ( L ~ f o r the aforementioned shapes (Figs 7(c) and 7(d)).

    It will be noted that within the region 0

  • conclusions can be drawn at this stage.


    2 .


    4 .

    5 .

    6 .


    a .

    9 .



    a (iv) Further investigations using commercially

    available end mills are necessary. F i K . 6 : Convex "IJ" and

    BIBLIOGRAPHY straight "t" p r o f i I es .

    Yotc : On line A a t S Jp = It z 0

    .l # Lt = 0

    Kaldor. S , Trendler, P H H, "Tool Life Testing End Performance Evaluation in End Milling". 5th Seminar on "Efficient Metal Forming and Machining", CSIR, Pretoria, November, 1983 Von Turkovich, B F, "On the Tool Life of High Speed Steel Tools", Annals of CIRP. Vol. 27/1/1978 On "P", ,, = Const. OSG "Technical Guide End Milling" pp 36 to 40. Copyrights O S G Mfg Companv Tovokawa. Jaoan. 1982

    on line B

    - . ~ . . . Pekelharing, A J, "The Exit Failure in Interrupted Cutting", Annals of CIRP. Vol. 2,;/1/1978 Kaldor, S , Lenz, E, Investigation in Tool Life of Twist Drills", Annals of CIRP, Vol. 29/1/1980 Lenz, E. Mayer, J E. Lee. D G. "lnvestieation in Drillind. - 0 . ~ Annals of CIRP, Vol. 27/1/1978. Kaldor. S, Lenz, E, "Drill Point Geometry and ODtimisatlon". Trans. of ASME Eng. for Industry, Vol. 104. Feb: 1982 IS0 3002/1 "Geometry of the Active Part of Cutting Tools - Part I : General Terms, Reference Systems, Tool and Working nngles". 1977 (E)

    Kaldor, S, Moore, K, and Hodgson, T , "Drill Point Designing by Computer", Annals of CIRP, Vol. 32/1/83

    Vr i Y F L

    (b) Rotary Cutter


    Fig.5: Comparison between Linear and Rotary Clltters.


    PMCo Note :

    PMC, PMCl and PPIIco for high, low and zero feed rates. A l l curves are superimposed by shifting the curves in the K direction. to intersection point P.

    Fig. 1 : End Mill

    Point - P Hody - t l Shank - s Depth of cut - a


    I ---...


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