Study of the specific cutting power in milling: application to no approximate cutting forces models. Manuel San Juan; Felipe Montoya; Gonzalo Velasco E.T.S. Ingenieros Industriales •Universidad de Valladolid Paseo del Cauce s/n •47011 - Valladolid (Spain) Tf. 34.983.423000 Ext. 24429 •Fax. 34.983.423310 e-mail: [email protected]

ABSTRACT. In the application of model cutting forces in the industry, an important simplification is necessary because the experimental work to calibrate these models has very important costs both in money and in time. With this objective, a team work in the Israel Institute of Technology proposed a modelization technique based in the instantaneous study of chip thickness, for a particular pair of machine tool and insert milling. In this paper, a particular study of this methodology has been made. Some results have been presented to instantaneous specific cutting power, with different cutting conditions, and finally some particularities of this experimental technique have been analysed in the evaluation of forces in other different conditions.

KEY WORDS: Cutting forces, milling process, no aproximate models

Introduction. The cutting forces of the end milling process have been studied in many works, they have development different models fundamentally to analyse the specific cutting power or, in general, the specific cutting coefficients. The simplest models studied main forces whereas the more complex ones made estimations of coefficients and forces on time evolution on the effects of milling tool position, tool deflection, tool and workpiece vibration an other parameters. All these models need to make an important experimental work to calibrate the coefficients, and the introduction of little variations in conditions of process have to need a new calibration model process. Other problems about the limited application of these models are related whit particular new tools geometry. An other important problem in the calibration process is to reduce the instabilities and vibration in milling, which reduce the rapid study of forces. This effect is related

with the dynamics of machine tool and dynamometer systems. The force signals are dirty and complex to analyse. A [San-Juan.98b]the study on cutting forces and the unformed chip thickness has been made, where unlinearity between both parameters can be appreciated and related with the dynamics of process. The cutting speed increased notably. Different works have been carried out to analyse this problem. The solutions that have been proposed have collateral problems that reduce the precision in the calibration process, like the filtered signal techniques and are made to introduce approximations. But [Rotberg.97]proposed a different no approximate model that have to respond at traditional models. The main goal to this fast method is the reduction in the number of experimental measurements that are needed evaluated the forces in new conditions, and the possibility to use the model with different tool geometries. The procedure principles are fundamentally to carry out one experiment for each combination of workpiece material, cutter tooth geometry and axial depth. In this experiment a single tooth cutter is used in a slot-milling process, selecting the maximun feed per tooth allowed for the specific tool. The cutting forces measured should be used for prediction of forces for any cutter diameter, teeth number, entrance-exit angles and any feed per tooth equal to or less than the one tested. To predict the cutting forces the chip-thickness values are the reference and the forces values are considered the same in two different processes if the instantaneous chip-thickness is the same.

1.

Specific cutting power

The study of specific cutting power has been development in time domain normally in average term. But the analysis systems have been improved and the instantaneous study has been possible employing sort constant time. In no approximate models, the instantaneous study of cutting forces in a milling operation has been considered to estimate the cutting forces in other milling conditions. The instantaneous specific cutting power has been analyse, and finally the chip thickness has been considered to be the most important factor in a study where tool, workpiece material and machine are the same. Therefore, the study of chip geometry in new milling conditions has been enough to estimate the time evolution of cutting forces.

Slot-milling process. This process has been selected in the study, because the evolution of chip thickness, and also the forces, is favourable to reduce the dynamic excitation of tool. At the beginning the thickness has a progressive increase and it is reduced at the end. A series of tests have been glared towards the study of the simplest milling process using a tool with only one insert ISO P20-P30 (ISCAR APKT-PDR 1003HM (IC 50M)). With this configuration the process has been repeated working with different conditions on an F-111 steel.

d

Pz

Pr

Vc

n

af

(mm)

(mm)

(mm)

(m/min)

(rpm)

(mm/plq)

14

1.5

14

61.6

1400

0.33

Table Erreur! Argument de commutateur inconnu.

A rotating cutting force dynamometer has been used (Kistler 9124A) for measuring of projected force on X, Y and Z axes. Afterwards tangential and radial forces have been calculated. Showing Fig. 1 we can make some particular comments: Ft, Fr The cutting conditions are not very stable, because some oscillations can be observed. When the thickness chip is increased the oscillations are more important. Fz The force is noticeable inferior to the other projected forces and its evolution is not symmetric like the thickness chip. The maxim force is advanced with respect to maxim chip. Mz The measurement of torque has fewer problems with the dynamic excitation, and the oscillations that are seen are not important. Nevertheless the asymmetric evolution is noticeable, too.

Fig. Erreur! Argument de commutateur inconnu.. Cutting forces in 1-insert slot-milling: Ft, Fr, Fz y Mz.

Therefore, the cutting process selected doesn’t guarantee the stability to study the specific cutting power, the oscillations related with the natural frequencies of rotatory dynamometer and the milling machine are shown. Like [Rotberg.97] introduced a digital low pass filter to arrange the signals, we applied a FIR (Finite Impulse Response) filter. A Hamming low pass filters with a frequency of 100 Hz and order 50 was used to smooth the signal. In Fig 2 we can observe the temporary evolution of tangential and radial cutting forces in the new conditions. The maximum values were reduced, even though the reduction of oscillations were the most important effects in signals.

Fig. Erreur! Argument de commutateur inconnu. Tangential and radial cutting forces: measured (at the top) and digital filtered (on the bottom).

Instantaneous specific cutting power. The evaluation of instantaneous tangential specific cutting power has been made to consider the tangential cutting forces signal filtered and the instantaneous chip geometry:

Ks =

Fti b ⋅ti

[ Erreur! Argume nt de commut ateur inconnu. ]

The thickness chip has been considered in first approximations that had a sinusoidal evolution. This approximation may be possible to consider the cutting conditions employed and the maximum value of 0,33 mm. This can be seen in Fig. 3 versus the angular position in cutting process. A unique angular reference system has been employed to analyse the cutting forces and the chip geometry. In the same figure we can also see that the angular evolution of forces cover more than 180º degrees, like other authors have considered and proposed that at the beginning and at the end of process cutting process doesn’t exist but do in deformation work in workpiece.

Fig. Erreur! Argument de commutateur inconnu. Angular evolution of chip geometry, tangential and radial forces.

In the same procedure, the instantaneous radial specific cutting power has been estimated to consider the radial cutting forces. In some cases the specific radial coefficient has been defined like a ratio between tangential and radial forces.

Fri = Kr ⋅Fti

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Fig. Erreur! Argument de commutateur inconnu.. Instantaneous specific cutting power. Angular evolution.

We can observe their time evolution in a slot-milling process after the use of digital filters in the evaluation of forces, Fig. 4.

Fig. Erreur! Argument de commutateur inconnu.. Instantaneous radial specific cutting powers. Angular evolution.

As we know, the cutting forces increased with the decrease of chip thickness, the amplitude of the specific cutting coefficients increased in the same way. We noted that in the beginning and in the end of the insert’s work the values increased rapidly and in the middle zone the values were more stable (2000 N/mm2). Nevertheless, as we showed in the time evolution of cutting forces, the specific coefficients weren’t symmetric. Similar distribution could be observed in the Fig. 5. around the specific radial coefficient. This effect is a problem to apply the no approximated model because the chipthickness has been considerate the reference, even though now we need to take into consideration if the process is an up milling or a down milling.

Fig. Erreur! Argument de commutateur inconnu.. Specific cutting power vs. thickness chip.

Later, the influence of cutting feed in the specific coefficients were analysed, taking into consideration three different steeps (90, 260 and 460 mm/min). As can be observed in Fig. 7 the increment of feed modified the chip thickness in similar ways and consequently the power in cutting process.

Fig. Erreur! Argument de commutateur inconnu.. Specific cutting power vs. time. Different feed speeds.

Finally, the cutting speed was considered like a variable. The specific coefficients were estimated, but now the feed per revolution, that fundamentally defined the geometry of the chip, was considered like a constant value and the cutting forces in this condition presented similar values in the three different situations (Fig. 8).

Fig. Erreur! Argument de commutateur inconnu.. Specific cutting power vs. angular position. Different cutting speeds.

In a final work, four different inserts were used to estimate the specific cutting power. The workpiece and cutting conditions were carried out on four tests with a similar helical insert geometry. The cutting forces as well as other parameters like the rugosity were measured. The evolution of specific cutting power can be seen in Fig. 9. The difficulty in cutting process for a particular uncovered insert could be analysed like the rugosity that increased rapidly.

Fig. Erreur! Argument de commutateur inconnu.. Specific cutting power vs. angular position. Different inserts qualities.

2.

No approximated model: fast evaluation of cutting forces.

As we know, the results of cutting tests that were analysed in the last pages can be used like a base of data in the estimation of cutting forces in other new conditions. Up-milling and down-milling. In Fig. 8 and Fig 9 we can see the time evolution of forces in two end milling process. The oscillations associated with dynamic problems typical of a non-stable process were present in real conditions, the signal needs to be cleaned to analyse the validity of forces estimated. The digital filter inserted an important reduction of increase at the beginning of up-milling process or at the end in a down-milling process. Nevertheless, the maximum value had significant magnitude.

Fig. Erreur! Argument de commutateur inconnu.. Down milling: Ft, Fr measured (left) and filtered (right).

Fig. Erreur! Argument de commutateur inconnu.. Up milling: Ft, Fr measured (left) and filtered (right).

In the estimation the force functions were simply given a value of zero in not work angular positions, as maybe there would be that to make in the filtered sign previously commented to obtain a most realistic profile.

Fig. Erreur! Argument de commutateur inconnu.. Application of no approximate method: estimate Ft and Fr in up milling (left) and down milling (right).

In terms of practical application of the method, as could be observed in the Fig. 3, one of the first aspects that were expressed was that the cutting process evolved through an angle greater than 180º waited, therefore some authors indicated how in given circumstances even when the thickness of chip was negligible the forces were

meaningful (does not exist cut but exists a deformation work that it can be expressed by an increase of the superficial hardness). This compelled us to employ a given reference that would have associated a mistake due to light angle variations. On the other hand, the evolution of the forces did not present a symmetrical profile, such as was considered in the approximation accomplished with the thickness of chip varying in a sinusoidal way, something which supposes that that in the process of slot milling exist a jump between the estimate of the growing and diminishing thickness zone, while in the results shown in [Rotberg.97] the estimates adopt a form perfectly symmetrical.

Study of multi - insert processes. The evaluation of cutting forces for a multi-tooth turns out to be extremely simple when only there exists an insert working every instant, but in general conditions the cutting force components can be computed by the vectorial addition of forces on the different actives cutters.

Fig. 13. Application of not approximate method: estimate Ft and Fr (Z=3).

In Fig. 11 the accomplished estimation in the ideal situation in the one which all the elements had a similar workload is shown. In the calculation that was carried out on the forces in this operation only one of the edges as reference was considered, due to the need of applying a change in the coordinates for each of then. Due to this factor the module of the sum of tangential and radial forces as a meaningful parameter of the distribution charges, these have been collected in Fig. 12. As well, the evolution of torque in cutting process could be used. In this case with respect to the maximum values the estimation turns out to be acceptable compared to values measured, though the non-uniform distribution is seen despised.

Fig. 14. Module (Ft+Fr) and Mz (Z=3).

Tool eccentricity: effect in cutting forces. As we know the trajectories generated in a milling process can be modified by multiple features and phenomena characteristic of milling [Spiewak.94]: • tool eccentricity • spindle tilt • changes in the effective tool geometry due to machining parameters or type of operation • deflection of the machine, tool and workpiece • tool wear, etc. One of the more simplex phenomena to estimate is the tool eccentricity because this magnitude can be directly measured. The influence in the chip geometry can be quantified using a characteristic diameter of tool, different of nominal diameter and also different for each edge of tool. In ideal conditions, each elemental cutting edge on the insert root out equal thickness chips, and consequently the non-approximate model propose equal cutting forces in each cutter. In Fig. 14

Fig. 15 Eccentricity measurement.

the cutting forces for a 3-tooth insert tool shown are not equal and the time evolution are repeated in each rotation. Considering that the inserts used in test analysed didn’t present any wear, we could therefore consider that eccentricity of tool was the most important effect that modified the chip geometry. Now considering this new estimation of chip thickness, to apply the non approximated model, the values obtained shown in Fig. 16 are similar to measured forces.

Fig. 16. Cutting forces estimates in a 3-inserts tool. Tool eccentricity considered.

3. Conclusions. The instantaneous specific power has been studied and its use in a first approximation to estimate the cutting forces employing the no approximate model has been analysed. The practical application of this methodology has been analysed. The fundamental values are obtained in a slot-milling process when the cutting forces are presented even out of angular position of cutting process (0-180 degrees). This aspect has already been indicated by other authors that supposed cutting doesn’t exist a deformation work does exist which can be expressed by an increase of the superficial hardness. To reduce this effect we could employ an angular reference that could be a source of error in the estimation, related with little angle variations. On the other hand, the forces time evolution doesn’t present a symmetrical profile, such as is considered in the approximation accomplished with the thickness of chip varying in a sinusoidal way, something which supposes

that in the processes of slot-milling there exists a jump between the estimate of the up milling and down milling zones, while some authors present estimated forces with a perfectly symmetrical profile. Finally, a final adjustment to estimate adequately the instant geometry of the chip in the new conditions should be carried out, having observed how the incorporation of the corresponding values to the eccentricity of the tool notably improved the coherence of the model with the experimental results. The use of no approximated models could be interested in educational application, because the programming is simple. Bibliografía. [Cheng.97]. CHENG, P.J.; TSAY, J.T. y LIN, S.C.: "A study on instantaneous cutting force coefficients in face milling.” Int. Journal Machine Tools and Manufacturing. Vol. 37. Nº 10 (1997) pp 1393-1408. [Furet.98]. FURET, B. y GARNIER, S.: “Original study of the specific cutting coefficients for an automatic monitoring system in milling.” Int. Seminar on Improving Machine Tool Performance. CIRP. (1998) pp 787-796. [Rotberg.97]. ROTBERG, J.; SHOVAL, S. y BER, A.: “Fast evaluation of cutting forces in milling, applying no approximate models.” Int. Journal of Advanced Manufacturing Technology, Vol. 13 (1997) pp 17-26. [San-Juan.98]. SAN JUAN, M y MONTOYA, F.: “Study of cutting process in end milling by frequency analysis with multiple sensors.” Int. Seminar on Improving Machine Tool Performance. CIRP. (1998) pp 775-786. [San-Juan.98a]. SAN JUAN, M; FETECAU, C y MONTOYA, F.: “Incidencia del desgaste y la rotura de la herramienta en el espectro de las fuerzas de corte en fresado.” XII Congreso Máquinas-Herramienta y Tecnologías de Fabricación. (1998) pp 387-399. [Spiewak.94]. SPIEWAK, S. A.: "Analytical modeling of cutting point trajectories in milling.” Journal of Engineering for Industry. Vol. 116 (1994) pp 440-448.