Mechanics of micro-milling with round edge tools

CIRP Annals - Manufacturing Technology 60 (2011) 77–80

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Mechanics of micro-milling with round edge tools Y. Altintas (1)*, X. Jin Manufacturing Automation Laboratory, Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada1

A R T I C L E I N F O

A B S T R A C T

Keywords: Cutting Force Micro tool

This paper presents analytical prediction of micro-milling forces from constitutive model of the material and friction coefficient. The chip formation process is predicted with a slip-line field model which considers the strain hardening, strain-rate and temperature effects on the flow stress of the material. The cutting force coefficients are identified from series of slip-line field simulations at a range of cutting edge radii and chip loads. The predicted cutting force coefficients are used to simulate micro-milling forces. The proposed chain of predictive micro-milling model is experimentally proven by conducting brass cutting tests with a 200 mm diameter helical end mill. ß 2011 CIRP.

1. Introduction Micro-milling operations are used in producing miniature parts found in biomedical, electronics, sensors, die and mold industry. Compared to the chemical manufacturing processes, micro-cutting has the advantage of fabricating small components with complex three-dimensional features [1]. The diameter of the micro mills ranges from 25 mm to 1.0 mm, with flute heights of 2–10 mm and cutting edge roundness of 5–20 mm depending on the application. Chip loads per flute range from 1 mm to 20 mm in micro-milling; hence chip formation occurs around the round cutting edge zone. In comparison to micro-milling, the dimensions are typically an order of magnitude higher in macro-milling operations; hence the academic and industrial challenges are therefore different in each field. Tool geometry, cutting speed, chip load and depth of cut must be properly selected to avoid premature wear and breakage of the micro-mill flute, as well as producing smooth surface finish with desired accuracy on the miniature parts. The mechanics and dynamics of micro-cutting must be modelled in order to predict the process behaviour ahead of costly physical trials. The prediction of cutting forces, temperature distributions and vibrations by relying on the work material properties, tool geometry and cutting conditions has been increasingly studied in recent years. The chip is partially sheared and plastically ploughed around the round cutting edge. Park and Malekian [2] proposed a mechanistic force model which considered both the shearing and ploughing dominant cutting regimes, and considered the effect of tool edge radius indirectly. Bissacco et al. [3] incorporated the ratio between the uncut chip thickness and cutting edge radius on oblique cutting force model. Fang [4,5] proposed a generalized slip-

* Corresponding author. 1 http://www.mal.mech.ubc.ca. 0007-8506/$ – see front matter ß 2011 CIRP. doi:10.1016/j.cirp.2011.03.084

line field model with a round edge tool to predict the shearing and ploughing forces. Fang’s model is general, and applicable to both micro and macro cutting operations. Wang and Jawahir [6] extended Fang’s model to include grooved tools by assuming constant flow stress along the slip-lines obtained from the average values of strain, strain-rate and temperature in the shear zones. Childs [7] investigated the size effects and modelled the cutting force as a function of shear angle, tool edge radius and uncut chip thickness. Afazov et al. [8] modelled the milling forces from finite element simulation of orthogonal cutting by including the effect of uncut chip thickness, tool edge radius and cutting velocity. This paper presents a predictive model in simulating micromilling forces from material’s constitutive model and friction coefficient between the tool and chip materials. There has been no mechanistic calibration used throughout the proposed process model chain. A slip-line field model, which includes the temperature, stress, strain-rate and strain hardening effects on the material properties, is developed by extending the model proposed by Fang [5]. The cutting forces acting on the single cutting edge are predicted through slip-line field model as detailed by the authors in [9]. The predicted cutting forces are used to express cutting force coefficients as nonlinear functions of tool edge radius and chip thickness, mimicking mechanistic models. The milling forces are then predicted by adjusting the cutting force coefficients as the chip varies. The predicted cutting forces are experimentally validated. Tool geometry, run-out and the effects of dynamometer dynamics are considered. 2. Cutting force coefficient estimation from slip-line field model The slip-line field model of orthogonal micro-cutting process proposed by Jin and Altintas [9] is extended to predict the cutting forces in micro-milling. The effect of the tool edge radius is included in the slip-line field model as shown in Fig. 1. The Johnson–Cook constitutive model [10] is applied to include the

[()TD$FIG]

Y. Altintas, X. Jin / CIRP Annals - Manufacturing Technology 60 (2011) 77–80

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face contact and the ploughing force caused by the round edge. The comparison between the predicted and experimentally measured micro-turning forces with 20 mm tool’s cutting edge radius is shown in Fig. 2 [9]. The forces are normalized by the width of cut (w). Since the cut brass was about 17% softer than the one used in the Johnson–Cook material model [10], initial yield strength A and strain-hardening coefficient B are reduced by 20%. The simulated tangential and feed forces agree with the measurements. The details of the slip-line field model can be found in [9]. A series of brass cutting simulations are preformed at different uncut chip thicknesses (h 2 [1, 50] mm) and tool edge radii (r 2 [0.001, 8] mm). The predicted cutting forces by slip-line field model are shown in Fig. 3. The simulations exhibit the sensitivity of the forces when the uncut chip thickness is less than edge radius of the tool. The cutting forces are then modelled as: F t ¼ K t ðh; rÞhw;

Fig. 1. Slip-line field model of orthogonal micro-cutting process [9].

     e˙ T  Tr m s ¼ ðA þ Be Þ 1 þ C ln 1 e˙ 0 Tm  Tr

d

[()TD$FIG]

Fig. 2. Simulated cutting forces from slip-line field model. Material: Brass 260 with parameters A = 90 MPa, B = 404 MPa, C = 0.009, n = 0.42, m = 1.68 (see Eq. (1). Tool edge radius = 20 mm, primary rake angle = 58. Cutting speed = 200 m/min. See [9] for details.

p

K t ðh; rÞ ¼ K t1 ðhÞ þ K t2 ðh; rÞ ¼ at h t þ bt h t r qt d p K f ðh; rÞ ¼ K f 1 ðhÞ þ K f 2 ðh; rÞ ¼ a f h f þ b f h f r q f

(1)

where e˙ and e˙ 0 are the equivalent and reference plastic strain rates, T, Tm and Tr are the material’s cutting zone, melting and room temperature, respectively, n is the strain hardening index, and m is the thermal softening index. Parameters A, B and C represent the yield strength, strain and strain-rate sensitivities of the material. Based on the experimentally identified tool-workpiece friction parameters from micro-turning, the total cutting forces are evaluated by integrating the forces along the entire chip-rake

(2)

where the cutting force coefficients are curve fitted to the simulated forces as follows:

strain hardening, strain-rate, and thermal softening effects on the flow stress of the material in the primary shear zone, which is expressed as: n

F r ¼ K f ðh; rÞhw

) (3)

The empirical constants (a, b, d, p and q) relate the sensitivity of the forces to the edge radius and chip thickness. The first term athdt is independent of tool edge radius, and it could be considered as the force coefficient when the tool is perfectly sharp. The nonlinearity increases when the size of the tool edge radius is comparable with the uncut chip thickness. The identified constants in Eq. (3) are listed in Table 1.

[()TD$FIG]

Fig. 3. Simulated cutting forces from slip-line field model. Material: Brass 260. See Eq. (1) and Fig. 2 for material properties. Cutting speed = 25 m/min and tool’s primary rake angle = 58.

[()TD$FIG]

Y. Altintas, X. Jin / CIRP Annals - Manufacturing Technology 60 (2011) 77–80

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Table 1 Constants for the cutting force coefficients of material Brass 260 at cutting speed 25 [m/min]. Units of chip thickness and edge radius are in [mm].

Kt [N/mm2] Kf [N/mm2]

a

d

b

p

q

914.4 629.4

0.0004 0.0002

62.21 78.24

0.8144 0.7868

0.2302 0.2469

3. Prediction of micro-milling forces The cutting force coefficients identified from the slip-line field model are used to predict micro-milling forces. Tangential (dFt) and radial (dFr) forces acting on a cutting edge with a differential depth of cut dz are expressed as (Fig. 4): dF t ðfÞ ¼ K t hðfÞdz;

dF r ðfÞ ¼ K f hðfÞdz

f 2 ðfst ; fex Þ

(4)

where f is the instantaneous immersion angle of the tool, and fst and fex are the entrance and exit angles of the cutter, respectively. The forces are zero when the edge is out of cut. The instantaneous chip thickness h(f) is evaluated by considering the exact kinematics of the milling [11], general tool geometry and the effect of radial run-out of flutes [12]. The elemental forces are resolved into feed and normal directions:  dF x ðfÞ ¼ dF t cosðfÞ  dF r sinðfÞ (5) dF y ðfÞ ¼ dF t sinðfÞ  dF r cosðfÞ   9 > 2p > df > dF x f þ ði  1Þ > = N 0 i¼1   Z N a X > 2p > > df > F y ðfÞ ¼ dF y f þ ði  1Þ ; N 0 i¼1 F x ðfÞ ¼

N Z X

a

(6)

The helix angle and radial run-out of the flutes are also considered in the model. The details of the general milling model have been presented before by Altintas et al. [11,12], and the algorithms have been integrated into an advanced milling process simulation system [13] and used in predicting micro-milling forces, vibrations, dynamic chip thickness and surface form errors. 4. Experimental validation The micro-milling tests have been performed on MIKROTOOL micro-machining center having a spindle speed range of 60,000 rev/min. The experimental setup is shown in Fig. 5. A two-flute carbide micro end mill (MITSUBISHI MS2MS) with 200 mm diameter and 308 helix angle is used in milling Brass 260 with 75 HRB hardness. Tool edge radius of the micro mill was measured to be 3.7 mm with an optical microscope shown as Fig. 4. The static run-out at the end mill tip was measured to be 0.6 mm with an optical microscope. The workpiece was fixed on a Kistler 9256 three component mini-dynamometer to measure the cutting forces. The vertical position of the tool tip with respect to the workpiece was aligned by moving the cutting tool down to the workpiece very slowly while a low voltage is applied on both tool and [()TD$FIG] workpiece. The reference position was recorded when the tool

Fig. 5. Set-up for micro-milling tests. Mikrotool CNC micro-machining center, Kistler 9256 mini-dynamometer, Brass 260 coupon.

came into contact with the workpiece and a short circuit signal was triggered. Several cutting tests at different spindle speeds and feed rates have been conducted to validate the predictive micro-milling model. The tool was inspected for wear and damage after each cut by a microscope integrated to the machine. The measured frequency response function (FRF) of the dynamometer indicates a bandwidth of 2000 Hz. Unless compensated, the harmonics of the milling forces may cause poor measurements with the dynamometer having the following transfer function (Fig. 6) and the modal parameters are listed in Table 2: qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 a þ bj a  bj 1 þ FðsÞ ¼ 0 2 þ þ 0 ; r ¼ zvn þ jvn 1  z2 (7)  sr sr ms k Sample experimental and simulation results are given in Fig. 7. Speeds between 45,000 and 60,000 rev/min have been deliberately avoided to prevent resonating the two modes (3403 Hz and 3067 Hz) of the dynamometer. The dynamometer’s modes are still slightly excited by the harmonics of high tooth passing frequencies (666 Hz and 1333 Hz), and appeared as distorted oscillations on the raw measurement data. When the measured forces are Kalman filtered [14] to compensate the distortion of cutting forces caused by the dynamometer dynamics, they agree well with the simulations. The correct measurement of micro-milling forces, [()TD$FIG]which are less than 1 N, would be difficult unless the dynamics of

Fig. 6. FRFs of dynamometer in X and Y directions.

Table 2 Modal parameters of dynamometer in X and Y directions.

Fig. 4. Micro-milling process. Two-fluted micro-mill with 200 mm diameter, 3.7 mm edge radius, 0.6 mm run-out and 308 helix angle.

X Y

vn (Hz)

z

a

b

m0

k0

3403 3067

0.0235 0.0276

1343 1065

14,870 14,570

5.493 1.823

2.87 8.650

[()TD$FIG]

80

Y. Altintas, X. Jin / CIRP Annals - Manufacturing Technology 60 (2011) 77–80

5. Conclusion The paper illustrates the analytical prediction of micro-milling forces directly from the material’s temperature and strain sensitive flow stress model. The cutting mechanics model is based on slipline field theory, which is used to predict the cutting force coefficients as a function of chip thickness and tool edge geometry. The cutting coefficients are then used in milling model which considers the helix angle, run-out and dynamics of the dynamometer. The authors have also used Finite Element method to predict the cutting force coefficients as an alternative method to slip-line field model. The research continues with the prediction of chatter vibrations and measurement of tool dynamics when the micro mill diameter is too small (<1.0 mm) to apply impact modal testing methods. Acknowledgement This research is supported by NCE AUTO 21 C303 and CFI grants of Canada. Cutting tools are provided by Sandvik Coromant and Mitsubishi Materials companies.

References

Fig. 7. Slot micro-milling with 50 mm axial depth of cut. Material: Brass 260. Tool: 200 mm diameter with two 308 helical flutes. Edge radius: 3.7 mm, run-out: 0.6 mm. (a) Spindle speed: 20,000 [rev/min], feed-rate c = 3 mm/rev/tooth. (b) Spindle speed: 40,000 [rev/min], feed-rate c = 5 mm/rev/tooth.

the dynamometer are considered. The simulations are carried out by using the cutting force coefficients predicted from slip-line field analysis (Table 1). The tool run-out, helical flute, edge geometry is considered, as well as the effect of the exact chip size as the tool rotates by the simulation system [13]. Considering that the micromilling forces are predicted directly from the constitutive model of the material, the simulation results fairly agree with the experimental measurements. Similar results are obtained at various feed rates and spindle speeds.

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