Transcript
Page 1: Investigations Into the Clearance Geometry of End Mills

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 signifCc.int 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.

2 .

a

a

A

A,B B

Be F

f

f l

f2

G

HB

HSS 1

j

Ll .L2 M2

MFL

P

PMC

PKC ,, 'P' 'P,'

'P2'

r

r'

;* 1

INTRODUCTION

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.

END KILL TOOL GEOMETRY

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.

mill.

NOMENCLATUKE

Axial depth o f cut

Radial depth of cut

Area

Symbols for different radii

Body

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

Point

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

mm

mm

mmlrev.

mmlrev.

mm

mm

m

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

S

S

S

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

0'1.0'2

'a

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

Page 2: Investigations Into the Clearance Geometry of End Mills

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'

3. ANALYSIS ApiD DEFINLTIONS

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:

where:

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

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4 .

4 . 1

4.2

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:

pirposes)

(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<@<20D,the variation in o for the P curve is only about 0,25' while for t and c Zurves both'yield a variation of about 20'. The variation in angle of the P curve is 2.5% which in practical terms can be regarded' as a constant clearance profile. For curves t and c the variation for the Same interval is about 200%. From Fig. i(d) it can he observed that both 4 and up have a value of 10" as shown in equation (10).

TEST PROCEDURE

To grind the PMC clearance geometry on high speed steel tool blanks a universal dividing head geared to the table of a universal milling machine was used. The grinding wheel was fitted into the main spindle of the machine. (Fig. 8(a)).

A tool holder was manufactured which held a single tool blank. This tool holder was used f o r both the tool grinding operation and for milling. The tool blanks were made of standard 6 m square turning tool blanks of M2 high speed steel. (fig. 8(b)).

Nine different pre-calculated grinding feeds (f ) were used to produce a variety of clearance angles (Table 8(c)) (Fig. 8 ( d ) ) . For comparative performance tests a set of tool blanks with the same clearance angles hut with flat flanks were also ground. All the finished ground tools were checked and measured fo r clearance angles and straightness of flanks before the machining tests were undertaken. Fig. 8(e) shows the traced profiles of the cutters (the profile tracer transforms circular traced profiles into linear profile lines). Fig. 8(f) shows the concave profiles of the flat tools.

Machining tests

Machining test were carried out using EN19 workpiece material with a hardness of 300 HBN. The material was 5 m thick. The machine tool was a "Ramhaudi" vertical spindle milling machine with a I 5 kw main drive and an infinitely variable feed drive. (See Fig. 9) The machining conditions used during the test series were as follows:

2

Orthogonal peripheral climb milljng: Depth of cut a 5mm Width of cut a' 5mm Surface cutting speed V Feed rates f2 0.05, 0.08 and 0 , I mmftooth

40 mlmin.

Coolant dry

Wear measurement

Flank wear was selected as the tool life criterion and measurements were made using a tool room microscope. The unused length of tool cutting edge was used as a datum. Since a variety of clearance angles were tested the wear volume per unit depth of cut was used as the basis for comparative test results.

Calculation of the wear area "A" for PMC tools

The area of wear is shown in Fig. 10. The boundaries of the area were defined by three lines:

(i) The PMC of the high feed; curve ( 2 ) (ii) The PMC of the low feed; curve (1) (iii) The tool rake face.

4 . 4

5 .

5.1

5 . 2

5 .3

6 .

7.

'The intersection "P" between curves ( I ) and ( 2 ) occurred at the distance V B , which is equal to the flank wear measured from the rake face. This condition was met by shifting factor Ax in the i direction in equation ( 3 ) of curve ( 2 ) . The value of the area A (actual wear) is the difference between the numerical integration of a?ea A2 between angle 0 , angle y , and curve ( 2 ) . and area A 1 between the same a%gles and 5urve ( I ) .

Calculation of wear area f o r flat tools

For flat tools the following mathematical equation for calculating the wear area was derived, assuming the worn flank to be a flate surface:

A = 'r VB2 (tan (of + yf) - tan y,) ............... (11) where of and yf are the tool side clearance and rake angles.

VB is the flank wear measured from the rake face.

TEST RESULTS

PMC ground inserts and flat flank inserts were tested using various combinations of feed rates and clearance angles. Wear values were calculated for each minute of cutting time.

PMC tools

Fig. 11 shows wear area in mm2 for PMC tools versus cutting time fo r a feed rate of 0.08 mm per tooth. Since the wear values for different clearance angles show large variations, a logarithmic scale was selected for plotting the results. The selected wear criterion for tool evaluation was 1.0 x

For a feed rate of 0.05 mm per tooth the wear levels were minimal and a wear criterion of 0,6 x m2 was selected. The various cumes for feed rates of 0.05 and 0.1 mmltooth are not given in the paper. Normalised tool life plots fo r all tests are shown in Fig. 12. It will be observed that a definite optimum clearance exists in the region of a = 12'. However. there is only a slight dependancy betwefen optimal clearance angle and feed rate.

Flat tools

Similar curves were plotted using the flat tool test results. Fig. 1 3 shows the wear area propagation for a feed rate of 0,08 mmltooth and the normalised tool life f o r the flat tools is presented in Ffg. 14. In this case the optimum appears to be independent of feed rate and the optimal clearance angle is af = 10'.

Comparison between flat and PMC t oo l flanks

The comparison was made for a feed rate of 0,08 mmltooth at which the same tool wear criterion was used. Fig. 15 shows a more pronounced optimum clearange angle and an increased tool life in case of the flat flank tools. The difference in tool life is about 40%.

In the case of PMC tools the optimum is not so well defined which allows for a higher degree of error in production.

DISCUSSION

In previous studies [7.11] it was predicted (on the basis of a theoretical analysis), and verified experimentally in drilling that there should be an optimal clearance angle for cutting tools. The results described in this paper again confirm the existance of an optimal clearance angle; in this case for end-milling.

However. differences in the actual values of the optimal angles for drilling and milling were noted; which may he due to differences In the modes of operation of these tools. Further investigations are being undertaken to establish possible reasons for these differences.

CONCLUSIONS

nun2.

It is possible to grind a curved tool flank that very closely fulfils a constant clearance angle requirement in the case of orthogonal rotary cutting t o o l s .

An optimal clearance angle for straight flute end mills does definitely exist. For PMC tools the optimum is in the region of 12" and for flat tools, 100.

When the clearance angle reduces to 7' or increases to about 1 7 O , tool life drops by 50%.

The results show that flat flank cutters yield a higher tool life than PMC cutters. This is in contradiction to claims made by some commercial organisations. It should, however, be noted that since the tests were carried out using single point straight cutting edge tools and not with comercially available end mills, no definite

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conclusions can be drawn at this stage.

1.

2 .

3.

4 .

5 .

6 .

7.

a .

9 .

10.

11.

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

$1

Fig.5: Comparison between Linear and Rotary Clltters.

Fig.6:

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

Geometry:

I ---/ Effective Body - Be

Fig.2: Total corner wear, VBc Note : The flank wear VB is,

i n this case, very small.

\

Fig.3: Various angles and lands in the case of the flat flank End Mill.

Note : Vc is tangential to the material flow line (MFL)

(C) (d)

Fig.7: Peripheral milling curve concave "C" and straight "t" flank shapes with reference to the actual milling curve "PI" .

Lhe clearance angle size. f(b) and (d) are enlargements).

Note : ( a ) and (b) show the curve shape, and ( c ) and (d) show

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Page 5: Investigations Into the Clearance Geometry of End Mills

Fig.S(a): PMC Grinding System F i g . S ( b ) : Tool Holder

"f

2.4 5.3 7.50 10.79 13.92 19.32 23.40 27.6 35 .8

4.55

f * GEARS

2.65 24.24.28/72.86.100 5.83 24.24.78/56.86.100 8 . 2 3 28.32.56/72.86.100 11.76 32.40.56/72.86.100 15.12 32.40/86.100 20.79 44.40/86.100 24.95 44.48/86.100 29.11 56.44/86.100 36.75 56.40/72.86

I2 11x1

:ting values.

Fig.B(d) :

__ . -. . . . 0 -. , . ..

\

~ . -. . . .

. , , . ..+. . . .. , - -- -. .- . . . . -.. .. . ~ _ . . .. . .

- . . .. . . <. I . ____ .

-. . . . . . . . :

. . . _ .

I .

One flat flank and three FUC tools. ~ R O = ~ R O

2,4

5.3

7.5

10,s

13.9

19,3

23.4

27,6

35.8

Fig.S(e): Traced profiles of I'YC Tools

aK -

2 9 5

5

7

10

14

18

22

26

30

F i g . B ( f ) : Traced profiles of rlat tools

;Re -

-2

0,5

3

5,5

10

14

17

20.5

25

Fig.9: Milling Set Up.

2

FLAW

- x

Fig.lO: Definition of the wear area in YMC Tools.

culoc, Rt DI

Fig.11: Wear area propagation versus cutting time, for PXC Geometry.

Fig. 12: Tool I ife versus clearance angles, for I'MC Geometry.

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Fig.13: Wear area propagation versus cutting time, (Flat Flank Geometry.) 7- ~~

Fig.14: Tool life versus clearance angles (Flat Plank Geometry.)

., 011

Fig. 15: Comparison of tool life versus clearance angles (Flat Flank and PMC types).

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