Influence of the tool overhanging and of machining strategy on defects in high speed ball end milling S. B. DONYO, F. MESLIN, J.C. HAMANN, F. LE MAITRE, Ecole Centrale de Nantes – LMM 1, rue de la Noë - BP 92101 44321 Nantes Cedex 3 France [email protected] [email protected] [email protected]

ABSTRACT : The effect of tool overhanging is studied with the help of experiment designs using a specific workpiece geometry in 3 axes milling. Two types of operating procedures are tested, i.e., machining with XY parallel planes (constant Z machining) or with YZ parallel planes (copying). The effect of cutting conditions, tool length, surface orientation as well as machining strategy on the geometrical quality of the worpiece and on the machined surface integrity are studied. It is shown that a great part of these effects can be analyzed using simple considerations on the cutting force distribution at the tool-workmaterial contact area. Modeling of this distribution allows for amachining strategy optimization in order to get the best compromise between surface quality and material removal rate. KEY WORDS : milling, surface quality, tool geometry

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1. INTRODUCTION The overall objective is to analyze the effect of the tool overhanging on the workpiece quality with respect to the machining strategy and the surface orientation, for finishing operations. For a fine control of the processing parameters, a set of tests has been performed using a simplified workpiece design as shown in figure 1. This test workpiece is made of surfaces that correspond to various difficulty levels.

Figure 1. Test workpiece with location of measured

2. DEFINITION OF THE EXPERIMENTAL PROCESS The workpiece is made of a 42 CrMoMn 8 steel. The tool is à two teeth hemispherical milling cutter of 16mm in diameter for the active part and the shank. Teeth are made with two indexable P25 uncoated carbide inserts. The cutting conditions are chosen in order to produce a theoretical scallop height of 0.025 mm : • rotational speed : 10000 rev.min-1 • programed feed rate : 8m.min-1 • feed per tooth : 0.4 mm • sweeping pitch : 1.2 mm • finishing oversize (depth of cut) : 0.7 mm Two machining « stratetegies » are considered, i.e. copying, where the tool path is located in the ZX plane and the sweeping pitch is over the Y axis, and constant Z machining where the tool path is parallel to the XY plane and the sweeping pitch parallel to the machined surface. • Surfaces A and C make an angle of 40° with the XY plane. The tool path is going down from A et B. These conditions are the best ones concerning the tool-workpiece contact and the tool path, whatever the strategy (copying or constant Z).

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• Surfaces B and D make an angle of 82° with the XY plane. The tool path is climbing up these surfaces and these conditions are very difficullt in copying but less severe in constant Z. • Surfaces E and F are parallel to the XY plane. The tool axis is perpendicular to the surfaces which are machined with the center of the cutter (i.e. with a very low cutting speed) for both strategies. The results concerning these surfaces will not be presented here. The connecting « surface » are of two types. Surfaces A and B and B and C are connected with a fillet of 20 mm in diameter while the other connections are sharp corners. Parameter Tool overhanging Tool wear Machining Strategy

Level (-1) Short (3 × ¯) New insert Constant Z

Level (1) Long (6 × ¯) 50 % of insert life copying

Table 1. Cotrolled parameters

The controlled parameters are studied over two levels as shown in table 1. Noise parameters are introduced such as insert re-indexing or the change of the insert. The tool gauge is measured once for each tool overhanging and is not adjusted after the change or the re-indexing of the inserts. The experimental set is defined in table 2. Since the test workpiece is made of two stamps, the experiences are organized by pairs in order to assess the influence of controlled parameters while minimizing the effect of positioning errors during the machining or during the measurement. 2.1. Measured parameters Surface finish The surface roughness parameters Ra and RT are measured by conventional means (stylus sensing), using a stylus displacement perpendicular to the main direction of machining marks, i.e. the sensing direction changes according to the machining strategy. RT can be compared with thescallop height, however these parameters do not give a reliable indication on the ease of surface polishing, an operation that is usually made manually after machining. For a better consideration of this operation two additional parameters do not give a reliable indication on the ease of surface polishing, an operation that is usually made manueally after machining. For a better consideration of this operation two additional parameters are measured on soft replicas of he surfaces using a non contacting laser beam profilometer : • the average polishing depth • the theoretical volume to be removed by polishing

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These quantities are measured over a sample surface of 31.25 mm2, and correspond to the amount of material located between two planes representing 0.1 and 90 % of supporting area.

Test n°

Strategy

Free length

Tool wear

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Copying Copying Copying Copying Copying Copying Copying Copying Constant Z Constant Z Constant Z Constant Z Constant Z Constant Z Constant Z Constant Z

Short Long Short Long Short Long Short Long Short Long Short Long Short Long Short Long

New

Tool change

Indexing

Yes

No

No

Yes

Yes

No

No

Yes

Yes

No

No

Yes

Yes

No

No

Yes

New Worn Worn New New Worn Worn

Table 2. Experiment design

2.2. Geometrical characteristics Flat surfaces are controlled with a 3D measurement machine. The measured parameters are defined in table 3. The fillets between surfaces A and B or C and D are controlled with an opaque profile projector (episcope) using a rot as template. The output value corresponds to the maximum distance between the rod and the fillet. This distance is corrected in order to eliminate the influence of AB angle and CD angle, θ angle measured previously (table 3). In these conditions, the error measured in the fillet gives an information on the machine response to « high acceleration » conditions, on the tool positioning quality and on the influence of the rigidity of the system to variable machining depth. The raduis of the tool path is 2 mm in the fillet area. Running this path in copying with a constant feed rate of 8 m.min-1 requires a acceleration of 8.9 m.s-2, i.e. approx. 0.9 g. In the case of a constant Z machining the quality of the fillet is given by the positioning of the tool, with no influence of the acceleration capability of the machine.

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Type of measurement Flatness

A 5

θ angle ref. A

B

C

5

5

D 5

5

θ angle ref. B

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Table 3. Measurements on flat surfaces 3. Results The experiment design is analyzed using standard statistical techniques such as analysis of variance, in order to highlight the most significant factors. We call u, v and w the explanatory variables associated with the machining strategy, the free length of the tool and the surface orientation, respectively. These variables are coded over two levels, (-1) and (+1), as reported in table 4. The contrast associated with the levels of each most significant factors is than calculated in order to define the best combinations. Table 5. summarizes the results and give the most significant factors or factors interactions with the best combination. The associated contrasts give a idea about the magnitude of the effect of these factors. Levels -1 1

Strategy u copying Constant Z

Free length v Short long

Orientation W 40° 82°

Table 4. Coding of the associated variables 3.1. Flat surfaces From an overall point of view the best results are obtained in constant Z machining providing that the tool overhanging is short enough . As expected, the best results are obtained on surfaces A and C where the cutting conditions are more favourable. For a long overhang and /or for surfaces B and D, copying provides the best results. Analysis of connecting surfaces The best results are obtained in copying with a short overhanging. Actually the machine tool used for performing the test cannot accelerates up to the required values in order to follow the theoretical path in the radius area. The feed rate slows down during the machining of the fillet, thus decreasing the required acceleration level. For the machining of the corners between surfaces E and A or D and F, the problem comes from the CAM system in constant Z machining. As a matter of fact coming from the horizontal surface to the sloping one the point of tangency between the tool and the machine surface changes. On the edge, both tangents are valid. Furthermore in the case of constant Z machining, the sweeping pitch is defined parallel to the machined surface. This situation is very « confusing » for the CAM

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system and the response will depend on the actual software that is used. In our case, the actual sweeping pitch is greatly reduced in the corner area. As a consequence, the connecting surfaces are responsible of a productivity drop, which magnitude depends on the machine tool performance in the case of copying and on the CAM system capability for the constant Z machining strategy. Parameter

Factor

Contrast

St. Dev.

unit

Best comb.

With v=1 Pol. Depth W = -1 W=1

RT

Ra

u v u.v u.v

-36.95 17.6 45.6 56.2

4.0 4.0 7.98 7.82

u u u.v w wv uv W=-1

4.1 4.2 11.63 1.7 -1.8 3.1

1.9 1.9 3.9 0.5 1.0 0.82

µm µm µm

w u uw uv W=-1

u(1), v(-1) u(-1), w(-1 u(-1), w(1) u(-1), w(1) 0.042 -0.023 0.02 0.016

0.0045 0.0036 0.009 0.0073

mm u(1), v(-1) u(-1), w(-1) u(-1), v(-1) u(-1), w(1)

W=1 θ angle

Fillet rad.

u v uv u v uv

u(1), v(-1) u(-1)

µm

W=1

Flatness

u(1), v(-1) u(1) u(1), v(-1) u(-1)

0.21 0.08 0.17 0.38 0.32 0.32

0.026 0.026 0.05 0.05 0.05 0.1

Deg.

u(1), v(-1) u(-1)

mm

u(1), v(-1) u(-1)

Table 5. Summary of the effect of the most significant factors on the various parameters

4. Discussion A deeper analysis shows that the difference of results is not really related to the machining strategy itself but to the force distribution on the tool resulting from this

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strategy. In ball end milling the force distribution develops according to the three directions of the space but also changes periodically with time, as shown hereafter. 4.1. Calculation of the bending force The contact geometry has been described in detail by [HOC 1995]. As shown in figure 2, the contact in each plane can be described with the help of a contact angle βi varying between βimin et βimax. The static part of the force is given by the chip cross section in the XZ plane while the time dependant part is defined by the cross section evolution in the XY plane. In both planes, the uncut chip thickness is given according to the angle βi by equation 1.

ei ( β )= δi ⋅sin β i

(1)

Figure 2. Evolution of the uncut chip thickness in the different planes δ1 is the feed per tooth and δ2 the sweeping pitch in the case of constant Z machining and conversely for the case of copying. Only the force component that is perpendicular to the tool axis produces bending, and the X component generates the most important effect according to the surface geometry. Usually the sweeping pitch is higher than the feed per tooth. As a consequence, if we assume that the force value is proportional to the chip cross section, the « static part » of the X component is higher in the case of constant Z machining, while the force oscillation amplitude is higher in the case of copying. The value of δ2min is given by the tilt angle of the tool, i.e. by the angle between the tool rotation axis and the normal of the machined surface. The worst case corresponds to a 90° tilt angle, as shown in figure 3.

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Figure 3. Evolution of the X component of the force over one revolution

Let KT and KR be the tangential and radial specific cutting coefficients, the X component of the force is given by equation 2, with β1 being time dependant.

Fx Rδ2 = [cos 2β 2 ]ββ22 minmax + Rδ1 ⋅sin β1 [sin β 2 ]ββ22 max min 2 K T ⋅K R 4

(2)

4.2. Influence of the tilt angle From surface A or C to surface B or D the bending direction but also the bending amplitude change. Generalizing the result of equation 2 to a surface making an angle

π  − β 2min with the XY plane gives equation 3 for the static part of the tool 2 

of 

bending.

(

(3)

Fx Rδ2 β β = cos β 2min [ cos 2 β 2 ]β 22 min − sin β 2min [ 2 β 2 + sin 2 β 2 ]β 22 max max min K T ⋅K R 4

)

The term within brackets is the static coefficient. When machining surface A or C the X component of the force which tends to « push » the tool away from the machined surface is 2.27 times lower than the one observed during the machining of surfaces B or D. Figure 4 shows the evolution of the static coefficient, according to the tilt angle of the tool. When the angle is negative the surface is machined in reverse cutting [HOC 1995]. We can see on this figure that for the current cutting

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conditions + 15° is an optimal angle according to the static bending of the tool, because the the static coefficient is zero.

Figure 4. Evolution of the static coefficient according to the tilt angle

4.3. Influence of friction and flow stress The X component of the force results from the radial force applied to the tool during the chip formation. If we look at the chip formation in a cross section defined by a plane made by the Z and the β1 directions, as shown in figure 5, the tool material contact can be roughly split into three portions. The first part corresponds to rubbing effects on the flank side of the edge. This part is defined by a rubbing angle equal to the tool-chip friction angle µγ[MAI 1994]. The second part, along the edge bluntness radius, is a sticky contact with a 0 relative tool-workmaterial flow velocity. The tangential force over this second area, which gives the highest contribution to the radial force Fr is given by the shear flow stress of the machined material. The third part corresponds to the sliding contact of the chip on the tool face. The length of the sticky part can be estimated by the effective rake angle as shown in figure 5.

Figure 5. Force system and contact geometry associated with the chip formation

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The sticky contact lasts when γ eff = 1 [HAM 2000]. The effective rake is defined in the considered cross section according to the uncut chip thickness H1, by equation 4.

 H 1 ⋅sin γ− rβ (1 + sin γ− sin µγ)  γeff = arctan   ( ) H − r 1 − cos µγ 1 β  

(4)

With rβ being the edge bluntness radius. In the present case the maximum actual uncut chip thickness is 0.49 mm Figure 6 shows the evolution of the effective rake angle according to the actual uncut chip thickness, for a rake angle of 6°, an edge radius of 40 µm and a tool-chip friction of 15°.

Figure 6. Evolution of the effective rake angle according to the actual uncut chip thickness for rβ = 40µm and γ= 6° As a consequence, the contact conditions correspond to the first two portions defined above and the radial component of the force for a unit width of cut is given by equation 5.

Fr = τH 1 (1 + +

3 tan γ) + τrβ [(cos µγ− 1)

3 (sin α + cos γ+ (1 − cos µγ)cot α )

(5)

− (1 − cos α )cot α − (1 + sin γ)tan γ] With α being the clearance angle and assuming that the hydrostatic pressure on the edge is 3 ⋅τ . From this equation we can observe that the influence of friction (the µγangle) can be controlled by the value of the edge radius. Inserts exhibiting a low edge bluntness radius and a negative rake angle provide a more efficient compromise between insert toughness and sensitivity to the radial force, i.e. to bending. The « natural » tendency would have been the opposite, e.g. to use a high rake angle and a high edge radius in order to offset the effects of friction.

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5. Conclusion 5.1. Machining strategy Constant Z machining provides the best results providing that the tool overhanging and / or the bending force on the tool is moderate. This strategy generally results in a less uneven tool path, thus preventing the decrease of the feed rate in the critical areas. However connecting fillets or parts of the workpiece that require a long overhanging are better realized with a copying strategy. For this reason the milling of materials exhibiting a high friction will preferably use the copying technique. The tool axis should be tilted within a 10 to 20° range with respect to the normal of the machined surface. This conclusion is often found in literature and is confirmed here from a different point of view. 5.2. Machining conditions Comparing constant Z machining with copying for an equivalent removal rate leads to the conclusion that the sweeping pitch should be decreased an balanced by an increase in the feed rate for the constant Z solution. This results in a better surface finish and a higher accuracy of the workpiece. 5.3. Tool geometry Because of the low effective uncunt chip thickness, a tool geometry exhibiting a low edge radius and a negative rake angle is better suited for a compromise between tool toughness and low cutting forces. 6. References [HAM 2000] HAMANN, J.C., MESLIN, F., Identification of consitutive equation and friction in cutting by inverse method. In 3rd international CIRP Workshop on Modeling Machining Operations, January 2000. [HOC 1995] HOCK, St., SCHULZ, H., High speed milling of dies and moulds – cutting conditions and technology. Annals of the CIRP, 44/1 : 35-38, 1995. [MAI 1994] LE MAITRE, F., HAMANN, J.C. and GUILLOT, D., Selective transfer built up layer displacement in high speed machining. Annals of the CIRP, 43/1 : 69 – 72, 1994.

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