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Modeling of turning process cutting forces for grooved tools Girishbabu Parakkal 1, Rixin Zhu 2, Shiv G. Kapoor, Richard E. DeVor

*

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 140 Mechanical Engineering Building, 1206 West Green Street, Urbana, IL 61801, USA Received 26 February 2001; accepted 2 August 2001

Abstract A mechanistic modeling approach to predicting cutting forces for grooved tools in turning has been developed. The model assumes the existence of an equivalent orthogonal cutting operation for any oblique operation. The effects of tool nose radius and chip flow have been incorporated by defining a set of equivalent groove parameters. Two calibration methods have been presented for the model. A variety of commercial grooved inserts were chosen to validate the model. The workpiece material used was AISI 1018 steel. The force predictions from the model were found in good agreement with the measured forces. The effects of cutting conditions and groove parameters on the cutting forces and their implication in designing grooved tools were also determined. 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction In moving from art to science in machining, cutting tools have gradually evolved from tools with a flat rake face to tools with complex rake face features including obstructions and grooves. Grooved tools have been applied in turning operations for better chip breakability, reduced cutting forces, improved surface finish and reduced tool wear [1]. Recently, several researchers have addressed the modeling of cutting forces for grooved tools. These include slip-line solutions by Shi and Ramalingam [2], the finite element method by Strenkowski and Athavale [3], and the mechanistic approach by Zhu et al. [4]. However, all of this work is focused on orthogonal cutting and the model extensibility to oblique cutting and turning has not been discussed. In turning operations, the cross-sectional geometry of a grooved tool is not constant along the cutting edge. Also, the chip flow and chip curl in turning become three-dimensional due to the effect of tool nose radius and groove geometry [5]. All these features should be accounted for in the develop-

* Corresponding author. Tel.: +1-217-333-3543; fax: +1-217-2449956. E-mail address: [email protected] (R.E. DeVor). 1 Current address: i2 Technologies, Dallas, TX, USA. 2 Current address: Oracle Corporation, Redwood Shores, CA, USA.

ment of cutting force models for grooved tools in turning. In this work, mechanistic force models for grooved tools in oblique cutting and turning are developed. The oblique cutting model is developed first, assuming the existence of an equivalent orthogonal cutting operation for any oblique operation. The turning model is then presented by defining the equivalent oblique cutting edge and a set of equivalent groove parameters. Two calibration methods are described for the turning force model. Finally, experimental results with commercial grooved inserts are shown to validate the proposed turning force model. The effects of cutting conditions and groove parameters on the cutting forces and their implication in designing grooved tools are also studied.

2. Model development A typical grooved tool (shown in Fig. 1) can be characterized by the rake angle (a), primary land length (Lc), groove width (wg), groove backwall height (hg), groove depth (dg) and groove profile (Pg). The geometry of the groove profile determines the groove entry angle (x). For a conventional grooved tool, the groove profile is curvilinear. When a grooved tool is used in machining, the primary land length will be less than the natural contact length for a flat tool and the chip will flow into the

0890-6955/02/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 1 ) 0 0 1 2 1 - 3

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Nomenclature a ab aen an as x xe f fn fg fng h hc geL gL ai Ac bi ci d dg f F Fa Fc Fcg Fcng Fg Flon Fng Fog Fr Frad Fsg Fsng Ft Ftg Ftan hg hge i ie Kn Kf Lc Lce Lcm Lcn mc ⬘ mr⬘ n rn N

Rake angle Back rake angle in turning Equivalent normal rake angle in turning Normal rake angle Side rake angle in turning Groove entry angle Equivalent groove entry angle in turning Shear angle with flat rake faced tool in orthogonal cutting Shear angle with flat rake faced tool in oblique cutting Shear angle with grooved tool in orthogonal cutting Shear angle with grooved tool in oblique cutting Chip back flow angle Chip flow angle in oblique cutting Equivalent lead angle in turning Nominal lead angle in turning Cutting constants for specific normal cutting energy Chip load Cutting constants for specific friction energy Cutting constants for shear angle Depth of cut in turning Groove depth Feed per revolution in turning Friction force on the rake face with flat rake faced tool Lateral force in oblique cutting Cutting force in oblique cutting Main cutting force with grooved tool Cutting force in normal cutting plane with grooved tool Friction force due to the chip–groove contact Longitudinal force in turning Normal force on the shear plane with grooved tool Friction force on the rake face with grooved tool in oblique cutting Friction force on the primary rake face Radial force in turning Shear force on the shear plane with grooved tool Shear force in normal cutting plane with grooved tool Thrust force in oblique cutting Thrust force with grooved tool Tangential force in turning Groove backwall height Equivalent groove backwall height in turning Inclination angle Equivalent inclination angle in turning Specific normal cutting energy in mechanistic model Specific friction energy in mechanistic model Primary land length Equivalent land length in turning Primary land length on the main cutting edge Primary land length on the nose cutting edge Moment arm on the shear plane with grooved tool Moment arm on the primary rake face with grooved tool Material constant for natural contact length in turning Turning tool nose radius Normal force on the rake face with flat rake faced tool

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Ng Nog Nr Pg t tc tce wc wce wg wge wgm wgn V

181

Normal force due to the chip–groove contact Normal force on the rake face with grooved tool in oblique cutting Normal force on the primary rake face Groove profile Deformed chip thickness Uncut chip thickness Equivalent uncut chip thickness in turning Cutting width Equivalent cutting width in turning Groove width Equivalent groove width in turning Groove width on the main cutting edge Groove width on the nose cutting edge Cutting velocity

In a previous work [4], a mechanistic force model has been developed for grooved tools in orthogonal cutting. In the mechanistic modeling approach, the forces on the rake face (normal force N and friction force F) are assumed proportional to the chip load, Ac as follows:

Fig. 1.

Grooved tool geometry.

groove. A typical type of chip–groove contact is such that the chip contacts only the groove entry and exit edges (as shown in Fig. 2). Under this situation, reduced cutting forces and desirable chip shapes have been found [2,4] and the effect of groove profile shape has been shown to be insignificant [6,7].

N⫽KnAc

(1)

F⫽KfAc,

(2)

where, Kn and Kf are defined as the specific normal cutting energy and friction energy, respectively. The orthogonal cutting model uses the measured cutting forces and deformed chip thickness with flat tools to calibrate Kn, Kf and the shear angle f by the following forms: ln(Kn)⫽a0⫹a1·ln(tc)⫹a2·ln(V)⫹a3·a

(3)

⫹a4·ln(tc)·ln(V) ln(Kf)⫽b0⫹b1·ln(tc)⫹b2ln(V)⫹b3·a

(4)

⫹b4·ln(tc)·ln(V) ln(f)⫽c0⫹c1·ln(tc)⫹c2·ln(V)⫹c3·a⫹c4·ln(tc)·ln(V),

(5)

where, tc is the uncut chip thickness, V is the cutting velocity, a is the rake angle, and ai, bi, ci (i=0,%,4) are empirical constants. After the calibration is done with flat tools, the prediction of cutting forces with grooved tools is based solely on the grooved tool geometry by taking force and moment equilibrium equations around a chip body (as shown in Fig. 2): Fng· sin(fg)⫹Fsg· cos(fg) ⫽[Nr⫹Ng· cos(h⬘)⫺Fg· sin(h⬘)]· cos(a)

(6)

⫹[Fr⫹Fg· cos(h⬘)⫹Ng· sin(h⬘)]· sin(a), Fng· cos(fg)⫺Fsg· sin(fg) Fig. 2.

Orthogonal grooved tool model.

⫽[Ft⫹Fg· cos(h⬘)⫹Ng· sin(h⬘)]· cos(a)

(7)

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⫺[Nr⫹Ng cos(h⬘)⫺Fg· sin(h⬘)]· sin(a), Fng·m⬘c⫽Nr·m⬘r⫹[Ng· cos(h⬘)⫺Fg· sin(h⬘)]·(wg⫹Lc) (8) ⫹[Ng· sin(h⬘)⫹Fg· cos(h⬘)]·hg, where, Nr and Fr are the normal and friction forces at the tool primary land contact, Ng and Fg are the normal and tangential friction forces at the groove backwall contact. Other force components shown in Fig. 2 are the shear force and force normal to shear plane (Fsg and Fng), and cutting and thrust forces (Fcg and Fng). The resultant forces on the shear plane are assumed to act at a moment arm mc⬘ measured from the tip of the tool (Point O). Similarly, the resultant normal and friction forces on the primary land are assumed to act at a moment arm mr⬘ measured from the tip of the tool. The chip flow back flow angle h is estimated from the empirical power law relationship proposed by Nedess [8]. The forces due to tool primary land contact (Nr and Fr) are obtained from a restricted contact tool model [4]. The mechanistic force model for grooved tools in orthogonal cutting is further extended here to oblique cutting and turning. The following sections describe the details. 2.1. Oblique cutting model For any oblique cutting operation performed with a tool of given geometry at an inclination angle i, a layer of material of width wc and thickness tc and a cutting speed V, Rubenstein [9] proposed an equivalent orthogonal operation performed with the same tool removing a layer of the same width at the same speed but with the uncut chip thickness reduced to tccos(i). The shear force Fsn and cutting force Fcn in the normal cutting plane shown in Fig. 3(a) are assumed to be equal to the shear force Fs and cutting force Fc in the equivalent orthogonal cutting shown in Fig. 3(b). The normal cut-

ting plane is perpendicular to the cutting edge. The relationship between the normal shear plane angle fn in oblique cutting and the shear angle f in the equivalent orthogonal cutting is as follows: cot(fn)⫽cot(f) cos(i)⫺ tan(an)·[1⫺ cos(i)].

(9)

Based on the equivalence between oblique cutting and orthogonal cutting, a mechanistic force model for grooved tools in oblique cutting is developed. The model is based on the grooved tool geometry and the specific normal cutting energy and friction energy for flat tools. For any oblique cutting condition (tc, wc, V, i, an), an equivalent orthogonal cutting operation is first formed with reduced uncut chip thickness tccos(i). The specific normal cutting energy Kn, the specific friction energy Kf and the shear angle f for a flat tool in equivalent orthogonal cutting can then be calculated from Eqs. (3)–(5) by substituting the reduced uncut chip thickness tccos(i) in the equations. After the cutting parameters (Kn, Kf, f) are determined for a flat tool in equivalent orthogonal cutting, given a set of groove parameters (Lc, wg, hg, x), the orthogonal grooved tool model can be used to determine the shear force Fsg, cutting fore Fcg and shear angle fg for a grooved tool. The corresponding normal shear plane angle fng for a grooved tool in oblique cutting can be determined by substituting fg in Eq. (9). Based on Rubenstein’s assumption, we have Fsng equal to Fsg and Fcng equal to Fcg, where Fsng and Fcng are defined as the shear force and cutting force in the normal cutting plane of a grooved tool in oblique cutting, respectively. The normal force Nog and friction force Fog on the rake face of a grooved tool in oblique cutting can be determined by Fsng⫽Nog· cos(fng⫺an)⫺Fog· cos(hc) sin(fng⫺an)

(10)

Fcng⫽Nog· cos(an)⫹Fog· cos(hc) sin(an),

(11)

where, the friction force Fog is assumed to be in the direction of chip flow defined by the angle hc shown in Fig. 3(a). It should be noted that Nog and Fog are the total forces on the grooved tool rake face due to the primary land contact and groove backwall contact. The chip flow angle hc is assumed equal to the inclination angle i [10]. The normal force Nog and friction force Fog for a grooved tool in oblique cutting can be resolved into three external force components by [11]: Fc⫽Nog· cos(i) cos(an)⫹Fog·[sin(hc) sin(i)

(12)

⫹cos(hc) cos(i) sin(an)] Ft⫽⫺Nog· sin(an)⫹Fog· cos(hc) cos(an)

(13)

Fa⫽Nog· sin(i) cos(an)⫹Fog·[sin(hc) cos(i)

(14)

⫺cos(hc) sin(i) sin(an)], Fig. 3.

Equivalence between oblique cutting and orthogonal cutting.

where, Fc is the cutting force parallel with the cutting

G. Parakkal et al. / International Journal of Machine Tools & Manufacture 42 (2002) 179–191

velocity, Ft is the thrust force perpendicular to the finished work surface, and Fa is the lateral force perpendicular to Fc and Ft, as shown in Fig. 3(a).

For a turning operation with tool nose radius rn, feed per revolution f and depth of cut d, Colwell’s [12] method is used to define an equivalent oblique cutting edge by linking two extreme points of the undeformed chip section (shown as dashed line in Fig. 4). The equivalent lead angle associated with this oblique cutting edge geL is determined by

冉 冊

x1−x2 , y1−y2

(15)

where, y1⫽冑r −f /4, x1⫽f/2

(16)

y2⫽rn⫺d, x2⫽

(17)

2 n

2

冦

−冑r2n−(rn−d)2,

d⬍rn(1−sin(gL)) , −rn cos(gL)−[d−rn(1−sin(gL))] tan(gL), dⱖrn(1−sin(gL))

and gL is the nominal lead angle with the main cutting edge. The equivalent inclination angle i, and normal rake angle aen associated with the equivalent oblique cutting edge are given by ie⫽tan−1[tan(ab) cos(geL)⫺tan(as) sin(geL)]

aen⫽tan−1{[tan(ab) sin(geL)

(19)

⫹tan(as) cos(geL)]· cos(ie)}, where, ab is the back rake angle and as is the side rake angle. The chip load is computed according to

2.2. Turning model

geL⫽tan−1

183

(18)

Ac⫽f·d⫺2·

再冢

冪r − 4

f · 2·rn⫺ 4

2 n

冣

f2

冉 冊冎

r2n f ⫺ · sin−1 , 2 2rn

(20)

and the equivalent uncut chip width wce and uncut chip thickness tce (shown in Fig. 4) are equal to wce⫽冑(x2−x1)2+(y2−y1)2

(21)

tce⫽Ac/wce.

(22)

In order to incorporate the effects of chip flow and tool nose radius, the equivalent groove parameters are defined along the section perpendicular to the equivalent oblique cutting edge (see Fig. 4). For a conventional grooved turning insert, two profiles can be used to characterize the grooved tool geometry. One profile is defined on the main cutting edge with Lcm as the primary land length and wgm as the groove width. The other profile is defined on the center of nose cutting edge with Len as the primary land length and wgn as the groove width. The equivalent land length Lce associated with the equivalent oblique cutting edge is calculated by extending the work of Rahman et al. [13] as Lce⫽AL/wce

(23)

Lcn b⬘+b⬙ ·Lcn· AL⫽2p· rn⫺ , d⬍rn(1⫺ sin(gL)) 2 360

(24)

Lcn b⬘+90−gL ·Lcn· AL⫽2p· rn⫺ 2 360

(25)

冉 冊 冉 冊

[d−rn(1− sin(gL))]·Lcm , dⱖrn(1⫺ sin(gL)), ⫹ cos(gL) where, b⬘⫽sin−1

冉 冊

冉 冊

f rn−d , b⬙⫽cos−1 . 2rn rn

(26)

The equivalent groove width wge is determined by wge⫽(rn⫺Lcn)⫹

Fig. 4.

Equivalent cutting edge and groove parameters in turning.

(wgn+Lcn−rn) , d⬍rn(1⫺ sin(gL)) cos(geL−gL)

wgm dⱖrn(1⫺ sin(gL)) wge⫽ cos(geL−gL)

(27) (28)

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The equivalent groove backwall height hge is equal to the nominal backwall height hg. The equivalent groove entry angle xe can be obtained from the vector method as described by Rahman et al. [13]. After the equivalent oblique cutting edge and its associated equivalent groove parameters are determined, the prediction of cutting forces for grooved tools in tuning can take place. First, the equivalent oblique cutting conditions (tce, wce, V, ie, aen) and equivalent groove parameters (Lce, wge, hge, xe) are taken as input to the oblique cutting model to obtain the force components Fc, Ft, and Fa. These force components can then be transformed to the external coordinate system in turning by Ftan⫽Fc

(29)

Flon⫽Ft· cos(geL)⫺Fa sin(geL)

(30)

Frad⫽Ft· sin(geL)⫹Fa· cos(geL),

(31)

where, Ftan is the tangential force, Flon is the longitudinal force, and Frad is the radial force as shown in Fig. 4. 2.3. Model calibration for turning Two calibration methods are proposed for the turning force model with grooved tools. The first method uses only flat tools in calibration. For each calibration test, the turning parameters (geL, Ac, ie, aen, tce, wce) are determined first. The measured turning forces (Ftan, Flon, Frad) with flat tools are transformed to the normal force N and friction force F on the rake face of the equivalent oblique cutting operation through Eqs. (29)–(31) and Eqs. (12)–(14). The specific normal cutting energy Kn and specific friction energy Kf are then determined by Eqs. (1) and (2). The shear angle on the normal cutting plane of the equivalent oblique cutting operation is determined by fn⫽tan−1

冋

册

tce cos(aen)/t , 1−tce sin(aen)/t

(32)

where, t is the deformed chip thickness. After Kn, Kf, and fn are calculated for each calibration test, the calibration Eqs. (3)–(5) can be determined through regression analysis by substituting tce and aen in the equations. As described in the above analysis, the calibration method only using the flat tools requires the measurement of deformed chip thickness, which is a tedious and impractical process. Furthermore, it is difficult to measure the chip thickness for a discontinuous chip formation process. These drawbacks limit the applicability of this method in an industrial environment. As an alternative, a calibration method using only one flat insert and one grooved insert is proposed here. It has been shown from a design of experiment analysis [7] that the primary land length and groove width are the two grooved tool para-

meters that affect the cutting forces significantly. Their effects have also been found dependent on the feed rate. Thus, as a first step in the modeling approach, equivalent land length and equivalent groove width (normalized by the uncut chip thickness) are included in the calibration equation. The calibration equations are as follows: ln(Kn)⫽a0⫹a1 ln(tce)⫹a2 ln(V)⫹a3aen ⫹a4 ln(V)ln(tce)⫹a5

Lce wge ⫹a tce 6 tce

ln(Kf)⫽b0⫹b1 ln(tce⫹b2 ln(V)⫹b3aen ⫹b4 ln(V)ln(tce)⫹b5

(33)

(34)

Lce wge ⫹b6 . tce tce

By using Eqs. (33) and (34), the normal force Nog and friction force Fog for grooved tools in oblique cutting and turning can be calculated directly from grooved parameters without resorting to the equivalent orthogonal cutting model. In the calibration process, the groove width for a flat tool is treated as zero and the primary land length for a flat tool is assumed equal to the natural contact length. In turning, the feed rate is the most significant factor influencing the natural contact area. Hence, for the simplicity of analysis, the natural contact length is assumed proportional to the feed rate, namely, Lcflat⬇n·f,

(35)

where the value of constant n depends on the work/tool materials combination. As a summary, a procedure to obtain the cutting forces in turning for grooved tools is shown in Figs. 5 and 6.

3. Experimental work A number of cutting experiments were conducted on a Frontier-L1 Mori Seiki CNC lathe. A digital data acquisition system was used to record the cutting forces. The tool holder was mounted on a Kistler 9257A 3component dynamometer. Signals from the dynamometer were passed through a Kistler charge amplifier (Model 5004) and into an A/D converter in a Micron PC using the LABVIEW software. The workpiece material was AISI 1018 steel. A variety of commercial grooved inserts from different manufacturers were chosen to validate the model. These grooved inserts include: Kennametal TNMG432, Carboloy TNMG432-MR4, Sandvik TNMG432, and Mitsubishi TNMG432. The profiles of the grooved inserts were measured using a high accuracy (resolution of 0.0001 mm) contour measuring machine—Mitutoyo Contracer CBH-400. For each grooved insert, two profiles were measured with one on the main cutting edge and the other one on the center of nose cutting edge.

G. Parakkal et al. / International Journal of Machine Tools & Manufacture 42 (2002) 179–191

185

In order to validate the turning force model for grooved tools and the two proposed calibration methods, two sets of experiments were performed. The first set of experiments used the Carboloy TNMA432 flat insert for calibration and the model is validated for Sandvik grooved insert. The second set of experiments used the Kennametal TNMA432 flat insert and TNMG432 grooved insert for calibration and the model is validated for other three grooved inserts. Based on the experimental observation of the natural contact area with flat inserts, the constant n in Eq. (35) was found to be around 8.0 for the 1018 steel used in this work.

4. Results and discussion

Fig. 5. Flow chart of grooved force model—calibration method 1.

Fig. 6. Flow chart of grooved force model—calibration method 2.

The measured profiles are shown in Fig. 7 and their associated groove parameters are listed in Table 1. The parameters listed in Table 1 suggest that there are some variations in the values of primary land length and groove width along the main cutting edge and nose cutting edge.

During the first set of experiments, a total of eight (23) calibration tests were conducted using Carboloy flat insert. The design of tests was based on the standard two-level factorial design [14]. The cutting conditions chosen for calibration were: speed from 150 to 300 m/min, feed rate from 0.1 to 0.22 mm/rev, normal rake angle from ⫺9.96° to ⫺4.98°. The depth of cut was 1.38 mm and the inclination angle and lead angle were ⫺5° and 0°, respectively. The calibrated equations for specific normal cutting energy Kn, specific friction energy Kf and normal shear angle fn are shown in Table 2 (significant terms determined from standard regression t test with significance level a=0.05 and marked as sig). After the calibration, eight validation tests were done using Sandvik grooved insert. The cutting conditions chosen for validation are shown in Table 3 and they are within the calibration ranges. The calibration equations along with the measured groove geometry are input to the turning model for force predictions. The measured cutting forces and predicted cutting forces are shown in Table 3. It can be seen in Table 3 that the predicted cutting forces are generally in good agreement with the measured cutting forces. The error in predictions is less than 8% and appears random. During the second set of experiments, a total of 16 ( 2×23) calibration tests were conducted using Kennametal flat insert and grooved insert. The cutting conditions chosen for calibration were: speed from 150 to 300 m/min, feed rate from 0.1 to 0.25 mm/rev, normal rake angle from ⫺5.97° to ⫺4.98°. The inclination angle ranged from ⫺6° to ⫺5°. The depth of cut was 1.38 mm and the lead angle was 0°. The calibrated equations for specific normal cutting energy Kn and specific friction energy Kf are shown in Table 4. After the calibration, eight validation tests were done for each of the Sandvik grooved insert, Carboloy grooved insert and Mitsubishi grooved insert. The cutting conditions chosen for validation are shown in Tables 5 and 6. The measured cutting forces and predicted cutting forces are shown in Tables 5 and 6. The results for

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Table 1 Measured groove parameters Lc (mm) Insert manufacturer Nose

Main

wg (mm) Nose

Main

hg (mm) Nose

Main

Carboloy Kennametal Mitsubishi Sandvik

0.42 0.27 0.1 0.3

2.89 2.63 3.42 3.38

1.54 2.01 1.87 1.68

0.12 0.1 0.05 0.09

0.12 0.11 0.05 0.1

0.51 0.4 0.11 0.32

Table 2 Calibration results using Carboloy insert tce low (mm) tce high (mm) 0.0732 ln(Kn)= sig. sig. sig. sig. R2=

0.156 8.1113 ⫺0.1167 ⫺0.0578 ⫺0.06 0.0183 0.9976

V low (m/min) 150 (N/mm2) *ln(tce) *ln(V) *aen *ln(tce)ln(V)

V high (m/min) 300

aen low (rad) ⫺0.194

⫺0.119

ln(Kf)= sig. sig. sig.

7.5914 ⫺0.2063 ⫺0.0973 ⫺0.0637 0.008 0.9834

(N/mm2) *ln(tce) *ln(V) *aen *ln(tce)ln(V)

R2=

Sandvik insert shown in Table 5 indicate that the force predictions are in very good agreement with measured forces. These are not surprising since the groove parameters of the Sandvik insert are close to those of the Kennametal insert. The results for Carboloy insert shown

Fig. 7.

aen high (rad)

fn= sig. sig. sig. sig. R2=

0.4179 0.0762 0.0111 ⫺0.0202 ⫺0.0319 0.981

(rad) *ln(tce) *ln(V) *aen *ln(tce)ln(V)

in Table 6 also suggest a good agreement between the measured cutting forces and predicted cutting forces. The error in predictions is less than 10% and appears random. For the results of Mitsubishi insert shown in Table 5, the tangential and longitudinal forces are

Measured profile of commercial inserts.

G. Parakkal et al. / International Journal of Machine Tools & Manufacture 42 (2002) 179–191

187

Table 3 Model validation for Sandvik insert—calibration method 1 Test #

1 2 3 4 5 6 7 8

Speed (m/min)

200 275 200 275 200 275 200 275

Feed (mm/rev)

0.15 0.15 0.2 0.2 0.15 0.15 0.2 0.2

DOC (mm)

1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38

Normal rake (°) Incl. angle (°) ⫺5.97 ⫺5.97 ⫺5.97 ⫺5.97 ⫺4.98 ⫺4.98 ⫺4.98 ⫺4.98

⫺6 ⫺6 ⫺6 ⫺6 ⫺5 ⫺5 ⫺5 ⫺5

Measured (predicted) Ftan (N)

Flon (N)

Frad (N)

560 541 695 662 555 525 672 641

299 285 334 308 296 274 315 292

201 198 242 229 204 201 240 232

(522) (489) (686) (638) (524) (490) (687) (638)

(303) (273) (363) (323) (287) (258) (342) (303)

(211) (191) (260) (232) (198) (182) (242) (216)

Table 4 Calibration results using Kennametal insert tce low (mm) 0.0732 Lce low 0.345

tce high (mm) 0.176 Lce high 2

V low (m/min) 150 wge low 0

V high (m/min) 300 wge high 2.37

aen low (rad) ⫺0.143

aen high (rad) ⫺0.119

ln(Kn)= sig. sig. sig.

8.0425 ⫺0.1188 ⫺0.0729 ⫺0.0149 ⫺0.0086 0.0617 ⫺0.0858 0.9789

(N/mm2) *ln(tce) *ln(V) *aen *ln(tce)ln(V) *Lce/tce *wge/tce

ln(Kf)= sig. sig.

7.3931 ⫺0.2481 ⫺0.1448 0.0034 0 0.1278 ⫺0.1786 0.98

(N/mm2) *ln(tce) *ln(V) *aen *ln(tce)ln(V) *Lce/tce *wge/tce

sig. sig. R2=

sig. sig. R2=

slightly over-predicted in this case. This is probably due to the fact that the Mitsubishi insert has a very narrow land length (0.1 mm, seen in Fig. 7) compared to other inserts. Under this situation, the value of land length is significantly below the calibration range shown in Table 4. Therefore, extrapolation error may occur in the prediction of cutting forces.

rate and lower cutting speed. It is evident in Fig. 9 that when the feed rate decreases, the cutting forces with the grooved tool are closer to the cutting forces with the flat tool. Under such conditions, the primary land length of the grooved tool will approach the natural contact length of the flat tool and the grooved tool will behave like a flat tool.

4.1. Effects of cutting conditions

4.2. Effects of groove parameters and implication

The combined nonlinear effects of feed rate and cutting speed on the resultant cutting force of grooved tools are shown in Fig. 8 for Kennametal grooved insert. The other conditions used in the simulations include depth of cut (1.38 mm), cutting speed (225 m/min), side rake (⫺6°), back rake (⫺6°), and lead angle (0°). It can be seen in Fig. 8 that with increasing feed rate and decreasing cutting speed, the resultant cutting force increases exponentially. Also, the rate of increase of cutting forces is slower when the feed rate is lower and/or the cutting speed is higher. Furthermore, it is found in Figs. 9 and 10 that the reduction in cutting forces from the flat tool to the grooved tool is more significant for higher feed

The combined effects of primary land length and groove width on the resultant cutting force of grooved tools are shown in Fig. 11. The other conditions used in the simulations include feed rate (0.2 mm/rev), depth of cut (1.38 mm), cutting speed (225 m/min), side rake (⫺6°), back rake (⫺6°), lead angle (0°), and groove backwall height (0.1 mm). For the range of investigation with primary land length from 0.1 to 0.5 mm and groove width from 1.5 to 4 mm, it is observed in Fig. 11 that the effects of primary land length and groove width are approximately linear. When the primary land length decreases and/or the grooved width increases, the resultant cutting force decreases. Usually the groove width is

201 198 242 229 204 201 240 232 (320) (283) (364) (322) (313) (277) (356) (315) 299 285 334 308 296 274 315 292 (575) (539) (711) (670) (568) (533) (703) (662) 560 541 695 662 555 525 672 641 (195) (179) (224) (206) (188) (173) (216) (198) 183 177 222 210 188 170 217 206 (288) (264) (323) (296) (282) (258) (316) (289) 242 224 283 257 245 217 271 256 (526) (503) (635) (608) (521) (497) (627) (601) 465 449 585 558 481 450 486 561 ⫺6 ⫺6 ⫺6 ⫺6 ⫺5 ⫺5 ⫺5 ⫺5 ⫺5.97 ⫺5.97 ⫺5.97 ⫺5.97 ⫺4.98 ⫺4.98 ⫺4.98 ⫺4.98 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 0.14 0.14 0.18 0.18 0.14 0.14 0.18 0.18 200 250 200 250 200 250 200 250

Measured (predicted) Ftan (N) Flon (N) Measured (predicted) Ftan (N) Flon (N)

Frad (N)

Sandvik insert Mitsubishi insert Normal rake Incl. angle (°) (°) DOC (mm) Feed (mm/rev) Speed (m/min)

the major factor affecting the chip curl radius and the lower primary land length facilitates the ease of chip flow into the groove. However, as the primary land length decreases, the contact area of tool–chip interface also decreases. Consequently the normal and friction stresses acting on the tool rake face will increase and thus result in reduced tool strength and increased tool wear. Therefore, some balance is required to choose the primary land length in designing the groove parameters. Fig. 12 demonstrates the effects of primary land length and groove width on the average normal pressure acting on the grooved tool rake face. It is seen that the reduction of normal pressure with respect to increasing land length starts to converge between 0.3 and 0.4 mm. Within this range, a reasonable compromise among cutting forces, tool strength and chip curl can be achieved. 5. Conclusions 1. A mechanistic modeling approach to predicting cutting forces for grooved tools in oblique cutting and turning has been developed. The model assumes the existence of an equivalent orthogonal cutting operation for any oblique operation. The effects of tool nose radius and chip flow in turning have been incorporated by defining the equivalent oblique cutting edge and a set of equivalent groove parameters. 2. Two calibration methods have been presented for the turning model. The first method needs only flat tools in calibration but requires the measurement of shear angle. The second method needs both flat and grooved tools in calibration and is more applicable in an industrial environment. 3. The proposed force model has been validated using a variety of commercial grooved inserts. The predictions of the model and the experimental results have been shown to be in good agreement. 4. The proposed models have also been used to investigate the effects of cutting conditions and groove parameters on the cutting forces. The reduction in cutting forces from the flat tool to the grooved tool is more significant for higher feed rate and lower cutting speed. For the range of investigation, the primary land length and groove width have shown linear effects on the cutting forces. 5. The model provides a quantitative basis to aid in the selection of groove design parameters to strike a desired compromise among cutting force, tool strength, and chip curl.

1 2 3 4 5 6 7 8

Acknowledgements Test#

Table 5 Model validation for Mitsubishi and Sandvik inserts—calibration method 2

(217) (193) (254) (226) (210) (186) (246) (218)

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Frad (N)

188

The authors are grateful for the support of the NSFDARPA Machine Tool Agile Manufacturing Research

G. Parakkal et al. / International Journal of Machine Tools & Manufacture 42 (2002) 179–191

189

Table 6 Model validation for Carboloy insert—calibration method 2 Test #

1 2 3 4 5 6 7 8

Speed (m/min)

175 275 175 275 175 275 175 275

Feed (mm/rev)

0.13 0.13 0.19 0.19 0.13 0.13 0.19 0.19

1 1 1 1 1 1 1 1

Fig. 8.

Fig. 9.

DOC (mm)

Normal rake (°) Incl. angle (°) ⫺4.98 ⫺4.98 ⫺4.98 ⫺4.98 ⫺5.97 ⫺5.97 ⫺5.97 ⫺5.97

⫺5 ⫺5 ⫺5 ⫺5 ⫺6 ⫺6 ⫺6 ⫺6

Measured (predicted) Ftan (N)

Flon (N)

Frad (N)

387 373 493 464 371 364 480 456

231 203 235 207 222 206 237 211

190 173 223 209 193 180 225 202

(394) (358) (518) (474) (398) (362) (524) (456)

(218) (183) (255) (214) (223) (187) (261) (219)

(191) (160) (230) (193) (195) (164) (236) (199)

Effects of cutting conditions on grooved tool forces.

Comparison of flat and grooved tool forces with varying feed. Fig. 10. speed.

Comparison of flat and grooved tool forces with varying

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Fig. 11.

Fig. 12.

Effects of groove parameters on cutting forces.

Effects of groove parameters on rake face normal pressure.

Institute (MTAMRI) and the University of Illinois NSF Industry/University Cooperative Research Center for Machine-Tool Systems Research.

[4]

[5]

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