Modelling cutting force in high speed milling Henri Paris - Christian Delhez Laboratoire Sols, Solides, Structures BP 53, 38041 Grenoble Cedex 9, France E-mail: [email protected]

RESUME. Aujourd’hui l’usinage grande vitesse s’applique à l’usinage de l’aluminium et à l’industrie du moule. Il est peu utilisé pour l’usinage de pièces en acier ou en fonte malgré l’amélioration des performances des outils de coupe. Au sein du laboratoire 3S, nous avons lancé une étude appuyée par une campagne d’essais ayant pour objectifs de déterminer plus finement les performances des outils de coupe pour identifier les couples outil-matière, de comprendre l’évolution des efforts de coupe en fonction des paramètres de coupe et plus particulièrement la vitesse de coupe et de s’assurer que les modèles d’effort de coupe sont toujours pertinents en usinage grande vitesse. Les résultats obtenus en évitant les problèmes liés aux phénomènes dynamiques sont encourageants. Ils annoncent une forte évolution de l’usinage dans les années à venir. ABSTRACT. Nowadays high speed milling mainly concerns alu alloy material or mold production. It is still lightly used for steel or cast iron parts. Cutting tools have great performances but their use area in high speed machining is not mastered yet. An experimental study of machining of traited steel, cast iron, titane alloy parts by coated carbide tools with high speed cutting has been led in 3S lab. The objectives were : (i) to test tool performances and define new tool-material couple, (ii) to understand cutting force evolutions depending on cutting parameters, particularly cutting speed, (iii) to test consistency of the main models used to determine cutting forces while milling. The dynamical effects of the dynamometer, part, tool and machine system were studied to have correct results. Encouraging results announce a great evolution of high speed machining in the next years. MOTS-CLES : Usinage grande vitesse ; Fraisage ; Modélisation. KEYWORDS : High speed machining ; Milling ; Modelling.

1. Introduction The present period made of international concurrency and research of the greatest rentability imposes more and more efficient machining techniques: parts must be machined faster and faster in the targeted quality [Sch 97]. The seventies brought high speed machining (HSM) in aeronautics domain. This new technique essentially machined parts with big rough-cuts in aluminium alloy material. The limits were due to the performances of machine-tools and cutters. It was impossible to extend the application field to ferrous materials as steels and irons. The present progress on the machine-tool stiffness, the power of the directors of numerical control, the power of high frequency spindle allow to envisage new applications. Furthermore, manufacturers now propose cutters able to machine steels and irons with high cutting speeds. Nowadays, industrials use high speed machining techniques to finish free forms of steel or iron molds. But this tendency to high-speed machine mechanical parts in steel or iron is still slight. It is the reason why we led a study on HSM for traditional milling operations as surfacing and grooved surfaces at the 3S lab. The main topic of the study was on the one hand to collect cutter-workpiece material couples for HSM techniques, and on the other hand to verify that models currently used to estimate cutting forces were still correct in HSM. A set of experiments was led to characterise mechanical forces of the cutter on the workpiece depending on the cutting speed. In the second section, the main models of cutting forces will be quickly presented and the issues of the dynamical stability of the machining operation and the impact of the dynamometer vibrations on the measure of forces will be discussed. Then in the third section, the approach and the protocol of the set of experiments will be developed. The fourth section will deal with the results of experiments: the current models can be applied on HSM to evaluate cutting forces. 2. Assessment of cutting forces in milling operations A sequence of the active parts of a tool removes material from the workpiece while milling. The number of working cutter teeth and the chip section on every tooth do not stay constant; they progress when the tool rotates. Two steps are necessary to evaluate the milling forces. The first step consists in characterising and modelling the instantaneous cutting force of a cutter tooth on the workpiece (figure 1). This resulting force directly depends on workpiece material properties, cutter geometry and variable cutting parameters. Therefore the resulting force moves when the cutter rotates. It is measured in X and Y by a dynamometer. Then it is changed in a system of

reference based on the cutter tooth to obtain a tangential force FT and a radial force FR .

X

t (θ) FR (θ) FY (θ)

θθ

R (θ)

FX (θ)

Y FT (θ) ft

Figure 1: Model of the force of the cutter on the workpiece in milling operation The second step consists in determining the tangential force resulting from the force of every cutter-tooth while milling. This force has an interest because the power used by the spindle to machine can be calculated from it. The instantaneous cutting forces can be summed to obtain the resulting force of the cutter on the workpiece.

2.1

Cutting force model

The resulting force can be determined without any problem. The main difficulty consists in modelling the instantaneous force of the cutter on the workpiece. Most of the literature authors [Rot 97] [Mon 91] [Alt 89] lean on models where the cutting force is proportional to the chip section. Those models can be expressed by equations [1] and [2] FT(θ) = KT . t(θ). d

[1]

FR(θ) = KR. t(θ). d

[2]

where FT and FR are the tangential and radial instantaneous cutting forces, KT and KR are cutting force coefficients, t(θ) the instantaneous thickness of the chip, d the depth of cut, ft the feed by tooth.

Martellotti’s model [Mar 41] has been used to evaluate the thickness of the chip. This model considers a circular trajectory of the cutter tooth. It is expressed by equation [3]. Spiewak [Spie 95] proposed a more rigorous model but Martelotti’s model error is small and can be accepted to exploit the experiments. t(θ) = ft . sin(θ)

[3]

In those models, KT and KR coefficients mainly depend on the properties of the materials of the workpiece and the cutter. They can be experimentally determined by orthogonal turning. Of course the orthogonal cutting cannot be applied on milling operations. KT and KR coefficients can also be determined in milling in considering the impact of the variation of the chip thickness. Some authors [Spe 94] [Fu 84] propose a finer model based on the impact of the chip thickness. Those models put in evidence that the cutting force coefficients decrease with the chip thickness and can be expressed by equations [4] and [5] where h is the instantaneous thickness of the chip.

2.2

KT = Kt . hm

[4]

KR = Kr . hm

[5]

The dynamical phenomena

Chatters can be appearing while milling. They are mainly due to the auto excitation created by the cutter teeth on the material. Every tooth removes a part of material with a variable thickness indeed. The chip thickness depends on the trace of the previous tooth and the position of the current tooth in the material. Furthermore the system (composed of the cutter, the machine-tool and the workpiece) can have a frequential answer that can lead to an instability towards chatter. This situation must be avoided because the machined surface will be rough and the increase of the cutting force variations can break down the cutter. Smith in [Smi 90] points out the zones of instability in HSM. The main factors are the frequency of the rotation of the spindle and the depth of cut [Dav 98, Jen 99a] (figure 2). Altintas [Alt 95] proposes an analytical method able to determine those zones of stability. The method has been made finer by Jensen [Jen 99a] in considering the edge radius of the tool and the cutter spiral. Experiments validate the method [Jen 99b]. Those characteristics appear during our experiments. In order to interpret the results of the experiments, we must detect the zones of instability by getting a frequential analysis of the signal coming from the dynamometer. Left figure 3 points out a result of analysis in a stable situation. The peak of frequency is linked to the crossing of cutter teeth in the material. Right figure 3 points out an unstable

situation. Peaks of frequency are due to chatter and the specific frequency of the dynamometer.

Figure 2. Lobes of stability in high speed machining [Jen 99a].

Figure 3. Spectral analysis of stable and unstable situations Sensors must be located between the cutter and the spindle or the workpiece and the machine-tool to measure the cutting forces. They make it possible to collect the force of the cutter to the workpiece at every moment. The sensors must disturb as little as possible the behaviour of the workpiece, machine-tool, cutter system. The most employed technology is a quartz dynamometer with a great stiffness but with a specific frequency relatively low by frequencies generated by the cutting operation. The signal coming from the dynamometer can be disturbed by the vibrations of the dynamometer [Ben 96]. The results given by the dynamometer

become very disturbed by inertia as soon as the rotate speed tends a to value depending on the specific frequencies of the system [Chu 94]. A first solution to remedy to this problem consists in filtering the signal. It is quite easy to perform but the main drawback is that it highly modifies the shape of the signal. Lapujoulade [Lap 98] has proposed to carry out an accelerometrical balance. That solution is difficult to be performed because it is necessary to know the mechanical characteristics of the workpiece-dynamometer system and the treatment chain of forces and accelerations. Chung [Chu 94] has proposed a method of balance based on the knowledge of transfer function of the dynamometer. To reduce the vibration disturbances on measures, the specific frequencies of the system composed of the workpiece and the dynamometer put on the machinetool have been characterised. Figure 4 points out the spectral analysis of the answer of that system under a step function. Rotate frequencies of the cutter have been chosen from this information to avoid the resonance.

Figure 4. Spectral analysis of the answer to an echelon of the dynamometer-workpiece system to a step function.

3. The set of experiments A set of experiments has been performed on a 5-axis machining center Hermle equipped with a 15000 rot/mn spindle. This rotation limit due to the machine-tool lets hard materials (treated steel) be machined. The measure of the cutting forces can be made by a Kistler dynamometer with 3 components. The signals answering

from quartz component are then amplified and transmitted to a PC computer. They are treated through Labview application.

3.1

The protocol for experiments

The cutting forces in current machining and high speed machining must be compared. The progress of the cutter depending on the cutting speed must also be studied. For that, the approach was the following: first of all, an experiment was performed with the cutting conditions preconised by the cutter manufacturer, then those cutting conditions were progressively increased. They were stopped when either the maximal performances of the spindle were achieved or the cutter was broken down. The experiment was configured to monitor the evolution of the cutting force on a tooth. Only one cutter tooth was removing the material. It is the case for a slot milling by a cutter with two teeth, a surface cut by a cutter with four teeth and a radial engagement equal to the cutter radius. The specific frequency of the workpiece-dynamometer system was identified before every experiment in order to choose cutting speeds avoiding resonance. The signals coming from the dynamometer were systematically studied by a spectral analysis to detect if the running point was or was not in a zone of instability. The monitoring of the wear of the cutter is done by the analysis of the tangential FT and radial FR forces. The radial force highly increases when the cutting speed increases during the experiment. This characteristic can be interpreted by the fact that the radial force highly increases while the cutter achieves its lifetime (figure 5). 600 500 400 N e w 300 t o 200 n s 100

Ft max Fn max Ft moyen Fn moyen

0 0

50

100

150

200

vitesse m/mn

Cutting speed m/mn Figure 5. cutting force evolution depending on the cutting speed.

Most of the experiments were repeated twice to validate the results. Some experiments were repeated five times for specific cutting parameters. No deviation was noticed among the various experiments made in the same conditions.

3.2

Analysis of results from an experiment.

The result obtained on our experiment made in correct stability conditions is considered now. Figure 6 point out the evolution of the FX and FY forces of the cutter on the workpiece. The milled material is a stainless steel (Z3 CND 17 11 02) whose hardness is 300HB milled by a 2T cutter, monobloc carbide, X.Treme coat, Suntell enterprise, diameter 15, two teeth. The machining consisted in milling a slot of 15 mm width. The cutting parameters were the following: cutting speed 500m/mn, feed 0.1mm/tooth and depth 1mm. The shape of the obtained curves makes it possible to identify the entrance and the exit of the cutter tooth. The obtained forces are stable and well balanced on every tooth. 6 4

Volt

2 Fx

0 0,03 -2

0,035

0,04

0,045

Fy

-4 -6 tem ps (seconde) Time (seconds)

Figure 6. Forces of the cutter on the workpiece measured in the system of reference of the dynamometer while cutting (1 volt = 70 N.) The cutting forces in projection on the direction of the cutting speed and on the direction normal to the cutting speed are necessary to evaluate the cutting force coefficients. The system of reference is therefore linked to the tooth. The mapping from the dynamometer reference (o,x,y,z) to the reference linked to the cutter (more specifically the tooth of the cutter) can be expressed by equation [6] and [7]. FT = Fy. Cos(θ) – Fx. sin(θ)

[6]

FR = Fx . cos(θ) + Fy. sin(θ)

[7]

Figure 7 represents the evolution of the cutting forces in the system of reference linked to the cutter tooth. FT and FR vary from 0 at the entrance in the workpiece (θ = 0), increase to a maximum at θ = π/2 when the chip thickness is maximum and fails to 0 at the exit of the tooth (θ = π). 300 250 200 Newton

150

FN

100

FT

50 0 -50 0

0,5

1

1,5

2

2,5

3

3,5

-100 radian

Figure 7. Forces of the cutter on the workpiece calculated in the system of reference linked to the tooth. We now have an interest for the evolution of the cutting force coefficient. The evolution of the chip thickness must be modelled from 0 to π. The chip section can be modelled by the following equation [8] where ft is the feed by tooth and d the cut depth. S(θ) = ft .d .sin(θ)

[8]

The evolution of the coefficients characterising the cutting force coefficient is then determined by the equations [9] and [10]. [9]

KR = FR / S(θ)

[10]

MPa

KT = FT / S(θ)

8000 7000 6000 5000 4000 3000 2000 1000 0 0

1

2 radian

Figure 8. Evolution of the cutting force coefficients

3

4

Figure 8 point out the evolution of those coefficients. The values of KT and KR at θ = 0 and θ = π are not revealing because the measured forces and the chip section are very close to 0. It is noticed that KT and KR increase when the chip thickness decreases what is true to the equations [3] and [4]. 4 The results The results obtained from the various experiments made it possible to determine, on one hand the evolution of the cutting force coefficients depending on the cut thickness and the forces depending on the cutting speed and on the other hand the evolution of the cutting forces depending on the chip thickness. The cutting force coefficient KT progresses depending on the chip thickness of course. Figure 9 points out the results of an experiment and compares them to a smoothing leaning on the model (equation 4). The correlation is very good for a cut thickness higher than 0.03 mm. The cutting forces are very weak for the small cut thickness and numerical errors are significant in this case. Therefore it is very difficult to interpret results in this range. The curve ’KS constr’ corresponds to the cutting force coefficient evolution when the experiment was made with the cutter manufacturer’s cutting conditions. The cutting force coefficient obtained while experimenting is lower than the one given by the cutter manufacturer. 14000 12000

Experiment

10000

Model

MPa

"KS constr" 8000 6000 4000 2000 0 0

0,02 0,04 0,06 0,08 0,1 Instantaneous chip thickness (m m ² )

0,12

Figure 9. Evolution of the cutting force coefficient depending on the cut depth.

4.1

Evolution of the cutting forces depending on the cutting speed.

The cutting speed and the milled materials were changed while experimenting. Cutting speed incompatibles with the cutter were not achieved because of the limits

of the machine-tool. The table on figure 10 summaries the maximal speeds for the various materials of the workpiece used for the experiments and the initial speeds preconised by the cutter manufacturers.

Material

Hardness

Vc recommanded Vc maxi when by the cutter experimented manufacturer

40 CMD 8 T

32 HRC

110

900

Z38 CDV5

48 HRC

70

550

45 NCD16

55 HRC

520

55 NCDV7

55 HRC

550

Z160 CDV12

58 HRC

400

FT25M

177 HV

150

650

Z3 CND18 09

200 HB

80

550

Z3 CND 17 11 02

300 HB

80

600

TA 6 V

32 HRC

50

225

Inconel 718

32 HRC

25

200

Figure 10: Maximal cutting speed of the various experiments

800

Effort Ft en N

700 Ft 25 M

600

55 NCDV 7

500

45 NCD 16

400

316 l

300

TA 6V

200

40 CMD 8 T

100 0 0

200

400

600

800

Cutting speed m/mn

Vitesse de coupe en M/min

Figure 11: Tangential force evolution depending on the cutting speed

Figure 11 points out the evolution of the tangential force FT depending on the cutting speed and various workpiece materials. It is noticed that the force is quite constant depending on the cutting speed. The force lightly increases when the running point comes close to the zones of instability. The obtained results clearly point out that the models currently used to estimate cutting forces can be applied to high speed milling. Furthermore, cutting speeds largely higher than those preconised have been tested successfully. It is a sign that a strong progress of high speed machining must be developed in the next years 5. Conclusion High speed machining in mechanical production still stays timid. The experiments point out that the cutters presently proposed by cutter manufacturers have strong performances and cutting speeds can be largely increased. The cutter manufacturers are very careful and propose cutting conditions lower than the cutter possibilities can do. No premature wear of the cutters was detected while experimenting. Therefore more experiments must be performed to confirm. Following the normal force, the radial force highly increases when the cutter lifetime was achieved. It would be very interesting in carrying on new experiments about this evolution in order to envisage cutter monitoring. References [Alt 89] Altintas Y., Yellowley I. — In-process detection of failure in milling using cutting force models, Journal of Engineering for Industry, vol. 111, pp 149-157(1989). [Alt 95] Altintas Y., Budak E. — Analytical prediction of stability lobes in Miiling , Annals of the CIRP, vol. 44, pp 357-362 (1995). [Ben 96] Benmohammed B., Lapujoulade F. — Evaluation des coefficients dynamiques de coupe, IDMME’96, Nantes, pp235-244, 1996. [Chu 94] Chung Y. L., Spiewak S. A. — A model of high performance dynamometer, Journal of Engineering for Industry, vol. 116, pp 279-288(1994). [Dav 98] Davies M.A., Dutterer B., Pratt J.R., schaut A.J. — On the Dynamics of HighSpeed Milling with Long, Slender endmills, Annals of the CIRP, vol. 47, pp 55-60 (1998). [Fu 84] Fu H. J., Devor R. E., Kapoor S. G. — A mechanistic model for the prediction of the force system in face milling operations, Journal of Engineering for Industry, vol. 106, pp 81-88(1984). [Jen 99a] Jensen S.A., Shin Y.C. — Stability analysis in face milling operations, Part 1 : Theory of stability lobe prediction, Journal of Manufacturing Science and Engineering, vol. 121, pp 600-605 (1999).

[Jen 99b] Jensen S.A., Shin Y.C. — Stability analysis in face milling operations, Part 2 : Experimental validation and influencing factors, Journal of Manufacturing Science and Engineering, vol. 121, pp 606-614 (1999). [Lap 98] Lapujoulade F., Coffignal G., Pimont J. — Cutting forces evaluation during high speed milling, IDMME’98, Compiegne, pp541-549 (1998). [Mar 41] Martellotti M.E. — An analysis of the milling process, Transaction of the ASME, vol 63 pp 677-700 (1941). [Mon 91] Montgomery D., Altintas Y. — Mechanism of cutting force and surface generation in dynamic milling, Journal of Engineering for Industry, vol. 113, pp 160168 (1991). [Rot 97] Rotberg J., Shoval S., Ber A. — Fast evaluation of cutting forces in milling, applying no approximate models, International Journal of Advanced Manufacturing Technology, vol 13, pp17-26 (1997). [Sch 97] Schulz H. — Fraisage grande vitesse des matériaux métalliques et non métalliques, SOFETEC, (1997) [Spe 94] Spence A. D., Altintas Y. — A solid modeller based milling process simulation and planning system, Journal of Engineering for Industry, vol. 116, pp 61-69(1994). [Spi 95] Spiewak S. — An improved model of the chip thickness in milling, Annals of the CIRP, vol 44, pp39-42 (1995) [Smi 90] Smith S., Tlusty J. — Update on High-Speed Milling Dynamics, Journal of Engineering for Industry, vol. 112, pp 142-149 (1990).