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Mechanics of boring processesPart I

ARTICLE in INTERNATIONAL JOURNAL OF MACHINE TOOLS AND MANUFACTURE APRIL 2003

Impact Factor: 3.04 DOI: 10.1016/S0890-6955(02)00276-6

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I. Lazoglu

Koc University

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Yusuf Altintas

University of British Columbia - Vancouver

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Retrieved on: 02 February 2016
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International Journal of Machine Tools & Manufacture 43 (2003) 463476

Mechanics of boring processesPart I

F. Atabey a, I. Lazoglu b, Y. Altintas a,

a University of British Columbia, Department of Mechanical Engineering, Manufacturing Automation Laboratory, V6T 1Z4, Vancouver, Canadab Koc University, Department of Mechanical Engineering, 80910 Sariyer, Istanbul, Turkey

Received 1 February 2002; received in revised form 28 October 2002; accepted 13 November 2002

Abstract

Mechanics of boring operations are presented in the paper. The distribution of chip thickness along the cutting edge is modeledas a function of tool inclination angle, nose radius, depth of cut and feed rate. The cutting mechanics of the process is modeledusing both mechanistic and orthogonal to oblique cutting transformation approaches. The forces are separated into tangential andfriction directions. The friction force is further projected into the radial and feed directions. The cutting forces are correlated tochip area using mechanistic cutting force coefficients which are expressed as a function of chip-tool edge contact length, chip areaand cutting speed. For tools which have uniform rake face, the cutting coefficients are predicted using shear stress, shear angle andfriction coefficient of the material. Both approaches are experimentally verified and the cutting forces in three Cartesian directionsare predicted satisfactorily. The mechanics model presented in this paper is used in predicting the cutting forces generated byinserted boring heads with runouts and presented in Part II of the article [1]. 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Force modeling; Chip load; Single point boring; Orthogonal to oblique transformation

1. Introduction

The enlargement of holes is achieved via boring oper-ations. The hole diameter is either enlarged with a singleinsert attached to a long boring bar, or with a boringhead which has a diameter equal to the diameter of thehole to be enlarged. Long boring bars statically anddynamically deform under the cutting forces during bor-ing operations. Excessive static deflections may violatethe dimensional tolerance of the hole, and vibrationsmay lead to poor surface, short tool life and chipping ofthe tool. Predictions of the force, torque and power arerequired in order to identify suitable machine tool andfixture set up for a boring operation. A comprehensiveengineering model, which allows prediction of cuttingforces, torque, power, dimensional surface finish andvibration free cutting conditions, is required in order toplan boring operations in the production floor.

Although the other machining processes such as mill-

Corresponding author. Tel.: +1-604-822-5622; fax. 1-604-822-2403.

E-mail address:[email protected] (Y. Altintas).

0890-6955/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0890-6955(02)00276-6

ing, turning and drilling have been studied relativelybroader and deeper ([2], [3]), there were only a fewattempts to model the cutting forces and stability in bor-ing([410]). However, the mechanics and dynamics ofthe boring process have not been sufficiently modeledfor an effective prediction of boring process perform-ance. There are fundamental issues which make the bor-ing process somewhat difficult to model for a reliableprediction of process performance.

The boring inserts have nose radius, and may haveeither uniform or irregular rake face. The distributionsof chip thickness, therefore the cutting pressure ampli-tude and direction, vary as a function of tool nose radius,radial depth of cut and inclination angle. Since the bor-ing bar is long and flexible, it is not possible to removemuch larger depths of cuts than the nose radius of thetool, unlike the case of turning and face milling oper-ations. This leads to a non-linear, complex relationshipbetween the cutting force distribution, tool geometry,feedrate and depth of cut. Furthermore, the presence ofstatic and dynamic deflections may influence the engage-ment conditions, leading to variations in chip load distri-bution and the cutting pressure.

The cutting forces are usually predicted as a function
https://www.researchgate.net/publication/238184738_Machining_Process_Modeling_A_Review?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/245521594_Dynamic_Stability_of_a_Cantilever_Boring_Bar_with_Machined_Flats_under_Regenerative_Cutting_Conditions?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/245521594_Dynamic_Stability_of_a_Cantilever_Boring_Bar_with_Machined_Flats_under_Regenerative_Cutting_Conditions?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/229395749_Cutting_Dynamics_and_Stability_of_Boring_Bars?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/35104218_Dynamic_modeling_and_dynamic_analysis_of_the_boring_machining_system?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/222734310_A_study_of_cutting_process_stability_of_a_boring_bar_with_active_dynamic_absorber?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/238184738_Machining_Process_Modeling_A_Review?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==


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464 F. Atabey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 463476

of uncut chip area that changes in a complex manner in

boring due to nose radius and geometry of the tool, and

cutting conditions. If the tool rake face has an irregular

geometry due to chip breaking grooves and chip-tool

contact restriction features, the cutting coefficients areidentified using mechanistic models. A series of cutting

tests are conducted with the specific tool at differentspeeds, radial depth of cuts and feedrates. The coef-

ficients are evaluated by curve fitting the forceexpressions to the measured cutting forces and chipgeometry. If the rake face of the tool is smooth and uni-

form, it is possible to model the cutting edge as an

assembly of oblique cutting edges [11]. The cutting

pressure at each discrete oblique cutting edge element is

modeled by applying the orthogonal to oblique trans-

formation method proposed by Armarego [12,13]. Bothapproaches have been considered in this article.

The paper is organized as follows; first the complexgeometry of the chip is modeled analytically for various

cutting conditions and tool geometry. The cutting forces

are modeled as friction and tangential cutting forces. The

friction force is resolved in the radial and feed directions,

and the direction of the friction force, i.e. the effective

lead angle, is experimentally evaluated from the ratio of

the two. The effective lead angle is predicted from thegeometry of the chip and tool, and the prediction is

improved by a mechanistic model based on regression

analysis applied to the model and measurements. The

cutting coefficients are modeled as empirical functionsof cutting speed, cutting edge contact length and uncut

chip area. The forces are modeled using orthogonal to

oblique cutting transformation when the rake face of thetool is smooth. This method requires only the toolgeometry, shear stress, shear angle and average friction

coefficient of the orthogonal cutting process for a spe-cific work material. The paper contains experimentalverification of proposed models which are used to pre-dict the cutting forces in all three directions.

2. Chip geometry cut by single insert

The fundamental geometry of a boring insert is

characterized by a corner radius (R), side cutting edge

angle (g) and end cutting edge angle (gc) (Fig. 1). The

rake face of the tool may have either flat face or irregularchip breaking and chip contact reduction grooves which

affect the cutting mechanics. The cutting edge does notusually have chamfer or curvature unless the workpiece

material is not hardened steel. The chip area, and there-

fore the cutting force distribution, vary as a function of

the depth of cut (a), feedrate (c), side cutting edge angle

(g) and end cutting edge angle (gc).Fig. 2 also illustrates the relative positions of the insert

at successive revolutions of the workpiece in four differ-

ent configurations. Nine various tool-workpiece inter-

Fig. 1. Friction force distribution along the cutting edge contact

lengthLc.

ferences can be also defined with respect to the cornerradius (R), depth of cut (a), feedrate (c), side cuttingedge angle (g

) and end cutting edge angle (gc) Notice

that the material left behind (uncut material) depends on

the feedrate (c) and corner radius (R), and is expected

to be large when the feedrate is considerably greater. The

uncut material also determines the surfacefinish quality.While large corner radius and small feedrate create good

surface, small corner radius and large feedrate leaves

more material (i.e., feed marks) behind causing a

rougher surface finish. The most common case encoun-tered in boring applications is when the feedrate is less

than the nose radius of the insert. Therefore, only fivecommon interferences have been considered (Figs. 3 and

4). The uncut chip area is evaluated by discretizing the

chip into small differential elements in three separate

regions as shown in Fig. 3. In the following, the calcu-

lation of the uncut chip area (A) and cutting edge contact

length (Lc) are explained for only the first configuration.

(The uncut chip areas and cutting edge contact lengthsare calculated with the same manner for the other con-

figurations shown in Fig. 4).For Region 1 in Fig. 3, the uncut chip area of each

differential element is approximated by subtracting the

area of the triangle AoBB from the area of the circular

ring sector AODD;

AOBB,i 1

2|OB|i|OB|isin(qi),

AODD,i 1

2qiR

2, A1,iAODD,iAOBB,i

(1)
https://www.researchgate.net/publication/245371947_Manufacturing_Automation_Metal_Cutting_Mechanics_Machine_Tool_Vibrations_and_CNC_Design?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/245371947_Manufacturing_Automation_Metal_Cutting_Mechanics_Machine_Tool_Vibrations_and_CNC_Design?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==


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465F. Atabey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 463476

Fig. 2. Illustration of four different uncut chip area configurations defined with depth of cut (a), feedrate (c), and corner radius of the tool (R).

Fig. 3. Uncut chip area calculations for Configuration #1 (gL 0,a R(1+ singL)) and definitions of the regions.

The total chip area in Region 1 is evaluated by dis-crete summation of all differential elements in the curved

region bounded by JEG.

A1n

i 1

A1,i (2)

Region 2 is considered to be a rectangle, although oneside of it (i.e., side KE) has a slight curvature caused by

the corner radius of the previous tool position. Area of

Region 2 can be approximated as,

A2|MG||KM| (3)

Region 3 is a simple triangle and its area is calcu-lated as,

A3 1

2|KM||LM|sin(gL) (4)

Finally, total uncut chip area is found by adding the

areas for each region,

A A1 A2 A3 (5)

The total cutting edge contact with the work

material is,

Lc Lc1 Lc2 (6)

where Lc1, Lc2 are the contact lengths in Regions 1 and2, respectively. If the number of discrete elements in

Region 1 is given as n, the contact length in Region 1

will be equal to summation of the discrete contact

lengths (i.e., Lc1 =n

i = 1

|DD| = Rn

i = 1

i). Similarly, Lc2


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Fig. 4. Uncut chip area configurations (#2#5) considered in the model process.

is the contact length of Region 2 and equal to the length

ofMG. Hence the chip area can be identified geometri-cally as a function of radial depth of cut (a), feedrate (c)

and insert geometry (R, g, gc).

3. Modeling of cutting forces in boring

The cutting forces are represented by the tangential

force (Ft) and friction force (Ffr). Later, friction force is

resolved into the feed (Ff) and radial directions (Fr)

(Figs. 1, and 5). Since the chip thickness distribution at

each point along the cutting edge contact point is differ-

ent and dependent on the insert geometry (R, g, gc)

feedrate (c) and radial depth of cut (a), the distribution

of the force along the cutting edge-chip contact zone also

varies. At any contact point, the differential cutting

forces are modeled as a function of local chip area (dA)and chip-cutting edge contact length (dLc),

dFt dFtc dFte Ktc.dA Kte.dLc

dFfr dFfrc dFfre Kfrc.dA Kfre.dLc(7)

where dFtc, dFfrc, are contributed by the removal of thechipand dFte, dFfrearedue to cutting edge-finish surfacerubbing. The edge contact constants (Kte,Kfre) are depen-

dent on the cutting edge condition and preparation. Thecutting coefficients (Ktc, Kfrc) are dependent on the localrake, inclination, chipflow angles, cutting conditions andwork-tool material properties. They can be determined

Fig. 5. Illustration of force directions in boring process.


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either mechanistically by conducting cutting tests with

each insert, and curve fitting the force measurementsagainst the chip geometry, or using classical laws of cut-

ting mechanics such as orthogonal to oblique cutting

transformation proposed by Armarego [13]. Bothapproaches are presented here for boring operations.

3.1. Mechanistic modeling of cutting forces

3.1.1. Identifications of the cutting force coefficients

The cutting force coefficients are determined for twosets of selected inserts (i.e., Kennametal CPMT-32.52

K720 and Valenite CCGT432-FH) used in boring A1

6061-T6 workpiece material. The procedure is generaland applicable to other insert geometries as well. The

tangential (Ft) and friction (Ffr) forces are modeled as

follows,

Ft Ftc Fte Ktc.A Kte.Lc

Ffr Ffrc1 Ffrc2 Ffre Kfrc1.A1 Kfrc2.A2 Kfre.Lc(8)

Unlike Ft, Ffr is considered as having two compo-

nents. The uncut chip area, A1 covers Region 1 and A2covers Regions 2 and 3 as illustrated in Fig. 3. The direc-

tion of total friction force is defined by effective leadangle (fL), which is the angle between the friction forceand feed directions (Fig. 1). For relatively large radial

depth of cuts, the effective lead angle (fL) tends toapproach the side cutting edge angle (gL) of the insert.In such a case, the magnitude ratio ofFr/Ffdecreases.

In order to determine the edge cutting force coef-

ficients (Kte, Kfre, Kre and Kfe), twenty four experimentshave been conducted with Valenite CCGT 432-FH insert

at 0.8 mm corner radius, constant 1.5 mm depth of cut

and 150 m/min cutting speed but varying feedrate (c)

from 0.0250.19 mm/rev. The cutting forces are meas-ured in three orthogonal directions, (Ft, Fr, Ff). Per-

forming linear regression leads to the following tangen-tial force equation,

Ft 4721.4 2438.5Lc[N] Lc1.9556 [mm] (9)

whereLcis the cutting edge contact length that is depen-dent on depth of cut and feedrate. The above equation

is valid only ifLc

greater than 1.9556 mm which corre-

sponds to zero feedrate for 1.5 mm depth of cut. Zero

feedrate refers to the rubbing process that is the source

of the edge cutting forces. Therefore, substitution of

value of 1.9556 mm in the equation above gives tangen-tial edge cutting force (Fte) for given depth of cut (a=1.5 mm) and zero feedrate (i.e., Fte = Ft|Lc = 1.9556 =47.33[N]). The tangential edge cutting force coefficient,Kte, is determined as Kte = Fte/Lc = 24.24 N/mm. Kte,represents the tangential rubbing force per unit cuttingedge contact length. Following the same procedure, the

radial, feed and friction edge cutting forces (Fre, Ffe andFfre, whereFfre= F2re + F2fe) and corresponding edge cut-

Table 1

Edge cutting force coefficients for the Valenite CCGT432-FH insert

Force model Measured edge Edge cutting force

cutting forces Fte, coefficients Kte, Kre, Kfe,

Fre, Ffe, Ffre N Kfre N/mm (Lc 1.9556

mm)

Ft= 2438.5Lc 47.41 24.244721.4

Fr= 417.74Lc 16.53 8.45800.40

Ff= 933.47Lc 45.59 23.311779.9

Ffr= F2r+ F2f 48.49 24.79

ting force coefficients (Kre, Kfe, and Kfre) are found asseen in Table 1.

Another set of tests was conducted with Valenite

CCGT432-FH insert at different combinations of the cut-

ting parameters within the ranges of 0.0250.19 mm/revfeed rate, 75275 m/min cutting speed and 0.253.25mm depth of cut. After removing edge forces (Fe Ffre)from the measured cutting forces, regression analysis is

applied to the cutting forces (Fc, Ffc) which led to the

following relationships for the cutting force coefficients,

Ktc eb0Ab1Vb2,Kfrc1 e

m0Lm1c1 Vm2,Kfrc2 (10)

en0Ln1c2Vn2

where Lc1, Lc2, V are cutting edge contact lengths (in

mm) in Region 1 and 2, and cutting speed (in m/min),

respectively. bo, b1, b2, m0, m1, m2, no, n1, and n2 areempirical constants obtained using the least-squaresmethod on the experimental data. Their values are; b

=7.9477, b1 = 0.0853, b2= 0.2750, mo= 8.1965, m1= 0.6737, m2= 0.4210,no= 9.6152, n1 = 0.0241and n2 = 0.7597.Ktc, Kfrc1, Kfrc2 are given in N/mm

2.

Once the friction cutting force coefficients, Kfrc1, andthe uncut chip area (A), and the cutting edge contact

length (Lc,) are determined, the radial (Fr) and feed

forces (Ff) are predicted as components of the friction

force (Ffr,). However, this requires that the friction forcedirection, which is defined by the effective lead angle(f

L) to be known. The prediction of the effective lead

angle consists of two steps; As mentioned above, the

uncut chip area (A) is divided into two regions and the

friction cutting force (Ffrc) has been expressed separately

(Ffrc1 and Ffrc2) in each region for accurate predictions.In the above equations, the cutting force coefficients

change inversely as functions of the uncut chip area (A),the cutting edge contact length (Lc), and the cutting

speed (V). The variation of the cutting force coefficientswith uncut chip area and cutting edge contact length rep-resents the effects of the tool geometry on the cutting

forces. The relationships between the cutting force coef-

ficients and the uncut chip area (A), and cutting edge


7/15


contact length (Lc) are non-linear due to the corner radius

of the tool and the chip breaking groove along the cut-

ting edge. On the other hand, decrease of the cutting

force coefficients with cutting speed is attributed to thereduction in the maximum shear stress of the materialand average friction coefficient at high speeds. As noted,

the effect of each parameter in the equations of eachcutting force coefficient is different. For the depth of cutswhich are larger than the corner radius (R), the effect of

the cutting edge contact length on the friction cuttingforce coefficient (Kfrc2) is not as significant as comparedto the case in which the depth of cut is less than R. This

may be due to the fact that the straight side of the tool

dominates the cutting process for the larger depth of

cuts. Thus, the friction cutting force coefficient (Kfrc2)does not change much with the depth of cut due to theuniform distribution of friction force on the straight side

of the tool.

Since the friction force acts perpendicular to the cut-

ting edge contact length and is proportional to the uncut

chip area of each differential element along the cutting

edge, it can be predicted by assuming that each compo-

nent of the friction force passes through the gravity

center of each related region (Fig. 6). The friction force

component of each region is added up vectorially, andthe total friction force (Ffr) is obtained. It should be

noted that these vectorial friction force components are

Fig. 6. Illustration of chip geometry, gravity center and friction force

components.

Fig. 7. Determination of gravity center.

presented with the notation F

fr1, F

fr2 (Fig. 6) and are notidentical to the ones in the Eq. (8). Ffrc1, Ffrc2 and Ffre,

are the components contributing from each region to the

total friction force, and do not have vectorial meanings.

Determination of the gravity center of the uncut chip

area is shown in the following equation. The calculation

is executed with respect to the origin of the corner radiusC2 for a given tool position (Fig. 7).

XG ni=1AiXGi

AT, YG

ni=1AiYGiAT

(11)

where Ai, (XG, YG) and AT are the area of a differential

element, coordinate of the gravity center with respect toC2 and the total uncut chip area of Region 1, respect-

ively. Based on the definition of the friction force direc-tion, the regional lead angle (fL2) in Region 2 and 3 canbe assumed to be equal to the side cutting edge angle

(gL) of the tool along the straight line of the cutting edge.The total effective lead angle is determined from the sum

of two friction force vectors (Fig. 6).

The effective lead angle is evaluated from each cutting

test as follows,

fL arctanFr

Ff(12)


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Fig. 8. Effective lead angle variation withLc and V.

After processing the data, analysis has shown that

there were certain discrepancies betweenmeasuredandpredicted effective lead angles based on the aboveapproach (Fig. 8). These discrepancies are perhaps due

to the fact that the friction force (Ffr

) may not be exactly

acting perpendicular to the cutting edge. The difference

between the measured and predicted effective lead angle

(fL) has been investigated. This has revealed that theeffective lead angle shows linear variation with V andLc. Hence, it can be tuned in the calculation with a modi-

fication factor (Km) that is also a linear function of Lc,and V(Fig. 9).

fL Km(V,Lc)f

L (13)

where fL is the predicted effective lead angle based onthe regular procedure described above andfLis thefinalmodified-predicted effective lead angle (Fig. 10) where

Fig. 9. Variation of the effective lead angle modification factor Km

with V and Lc.

Fig. 10. Illustration of predicted and modified-predicted effective

lead angle.


9/15


Km1 1.07430.3567 103Lc 0.9763 104Vfor a R

Km2 0.0163 0.6299Lc 0.0013Vfor aR

(14)

where Lc, and V are given in mm and m/min.

The above identified modification factors show that

for a R, the effective lead angle (fL) has an almostconstant deviation along the cutting edge contact length

(i.e., the effects of Lc, and Vare negligible). However,

for a R, the deviation has a strong dependence on Lcand V. This may arise from the nature of the chip flow.For a R, the chip attempts to flow towards the centerof the corner radius with an almost constant deviation.However, along the straight edge, the chip is forced to

flow away towards the outside of the contact in the radialdirection and with a continuously diverging friction

force, causing the chip to curl. The enforcement of the

chip exhibits a continuous increase along the cutting

edge and reaches a maximum at the end of the contactlength. A schematic representation of the directional

variation of the friction force is shown in Fig. 11. It

should be noted that the cutting edge contact length inEq. (14) is the total contact length including Region 1.

The radial and feed force predictions are made basedon the predicted friction force (Ffr) and effective lead

angle (fL) as follows,

Fr Ffr.sin(fL)

Ff Ffr.cos(fL)(15)

Radial and feed cutting force components become,

Fig. 11. Deviation of the effective lead angle along the cutting edge contact length.

Frc FrFre

Ffc FfFfe(16)

and corresponding cutting force coefficients areobtained as

Krc Frc

A, Kfc F

fc

A (17)

The mechanistic model presented in this paper can be

used for the dynamic cutting force model as the friction

force is related to the uncut chip area geometry. The

geometric factors are the cutting edge contact lengths

(Lc1and Lc2). And the assumption that the friction forces

pass through the gravity center of the regions.Applying the above procedure for the Kennametal

CPMT-32.52 K720 insert were resulted in the followingcutting force coefficients (Eq. 18) given in N/mm2,

Ktc e8.0428

A0.1696

V0.2512

Kfrc1 e7.7522L0.6093c1 V

0.2189

Kfrc2 e9.3082L0.0541c2 V

0.5470

(18)

and effective lead angle modification factors,

Km1 1.2963 0.0604Lc 0.0006Vfor a R

Km2 0.4138 0.7021Lc 0.0025VforaR

(19)

Edge cutting force coefficients were determined as,


10/15


Kte 13.777 [N/mm],

Kre 13.036 [N / mm],

Kfe 19.572 [N/mm],

Kfre 23.516 [N/ mm]

(20)

It should be noted that the trend of the variations ofthe cutting force coefficients and the effective lead anglemodification factor in the Kennametal insert are similarto the ones for the Valenite insert, but only the empirical

constants are different due to the differences between the

geometries of the two inserts. Some of these differencesare as the following; The Valenite tool has 5 side cut-ting edge angle (g

) while the Kennametal insert has 0,

the Valenite tool has 7relief angle while the Kenname-tal insert has 11, the grove geometries are different. Allthese geometrical differences are implicitly considered

in the empirical constants.

3.1.2. Experimental validation of the mechanisticmodel

Validation tests have been conducted with a work-

piece material of Aluminum 6061-T6. Two different

inserts have been used in the experiments:

1. Kennametal CPMT 32.52 K720 coated insert with

A12-SCFPR3 steel shank boring bar with 0side cut-ting edge angle,

2. Valenite CCGT432-FH Carbide PVD coated diamond

insert with A-SCLPR/L boring bar with 5side cut-ting edge angle g

In order to avoid chatter vibrations, the boring bar wasclamped to the tool holder with a short length to diam-

eter ratio (L/D= 2.5). Two sets of experiments for eachinsert were conducted with different combinations of the

cutting parameters within the ranges of 0.050.19mm/rev feedrate (c), 75275 m/min cutting speed (V),0.253.25 mm depth of cut (a). The first set of experi-ments was used to determine the empirical constants in

the equations for the estimation of the cutting force coef-

ficients. In order to validate the mechanistic model, asecond set of experiments was conducted under various

cutting conditions in the ranges of calibration. The

mechanistic model results in good force predictions hav-ing less than 10% of absolute average error both for Val-

enite and Kennametal inserts. Tangential forces Ft(both

fora Randa Rtogether) have 99.5% of correlation.

Friction forces for a R and a R have 93.5 and98.4% of correlations, respectively. The results of cut-

ting force prediction for the Valenite insert are presented

in Figs. 1218.

3.2. Orthogonal to oblique transformation

If the inserts rake face is uniformly flat without chipbreaking or contact reduction grooves, the boring inserts

Fig. 12. Friction force verification for a R .

Fig. 13. Friction force verification for a R.


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Fig. 14. Tangential force verification fora R and a R.

cutting edge can be considered as an assembly of oblique

cutting edge elements. Oblique cutting mechanics laws

lead to the prediction of cutting pressure at each discrete

cutting edge element, which depend on the discrete chiparea, edge geometry, and orthogonal cutting parameters

of the work material (i.e., shear stress, shear angle and

friction angle) which are mapped using classical mech-

anics laws proposed by Armarego [13]. The details of

the orthogonal to oblique cutting transformation can be

found in [11].

3.2.1. Orthogonal tests and identification of oblique

parameter

Orthogonal cutting parameters, shear stress (ts), fric-tion angle (ba), chip compression ratio (rc) have beenidentified by Ren [14] for carbide tools and P20 steelmaterial as functions of feedrate (c) and cutting speed

(V) as follows:

Fig. 15. Effective lead angle verification for a R and a R.

Fig. 16. Feed force verification for a R .
https://www.researchgate.net/publication/245371947_Manufacturing_Automation_Metal_Cutting_Mechanics_Machine_Tool_Vibrations_and_CNC_Design?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==https://www.researchgate.net/publication/245371947_Manufacturing_Automation_Metal_Cutting_Mechanics_Machine_Tool_Vibrations_and_CNC_Design?el=1_x_8&enrichId=rgreq-f3d3d8bf-4713-429b-88da-359bf0319f6b&enrichSource=Y292ZXJQYWdlOzIyMzA3MDIyMTtBUzoxMDI4MzE5MDIxNjcwNDhAMTQwMTUyODQ0NTI5NA==


12/15


Fig. 17. Feed force verification for a R.

ts[MPa] 507 1398.76c 0.327V

ba[deg] 33.6912.16c0.022V

rc 0.227 2.71c 0.00045V

(21)

wherec is the feedrate in mm/rev,Vis the cutting speedin m/min. The expressions are valid within 5 rakeangle range. Edge cutting coefficients K

te, K

re and K

fe(units are given in N/mm) have been also identified byRen [14] as the following,

Kte 0.1199 103V20.1487V 76.85

Kfe 0.1366 103V20.2007V 97.98

Kre Kte.sin(i)

(22)

Cutting forces as expressed in the general form of

Ft Ktc.bh Kte.b

Fr Krc.bh Kre.b

Ff Kfc.bh Kfe.b

(23)

Fig. 18. Radial force verification for a R and a R.

where b mm is the length of differential cutting edge

length, and the oblique cutting force coefficients aredefined as,

Ktc ts

sin(fn)

cos(bnan) tan(i)tan(h)sin(bn)

cos2(fn bnan) tan2(h)sin2(bn)

Kfc

ts

sin(fn)cos(i)

sin(bnan)


Krc ts

sin(fn)

cos(bnan)tan(h)sin(bn)


(24)

In general, Kte and Kfe are determined in the evalu-

ation of the orthogonal cutting test results. Because thereis no radial force component measured in orthogonal cut-

ting tests, Kre is not known. However, experimental

investigations have shown that radial cutting edge forceFre is very small and therefore negligible in the trans-

formation method. Oblique angle (i), normal rake (an),normal shear (fn) are evaluated as a function of differen-


13/15


Fig. 19. Evaluation of the oblique cutting parameters for three

regions of the uncut chip area.

tial cutting edge geometry [11] and evaluated for the

particular inserts used in this study.

3.2.2. Experimental validation of the orthogonal to

oblique transformation method

Valenite CTPGPL-16-3C insert with a nose radius,

sharp cutting edge and aflat rake face is selected to dem-onstrate the prediction of cutting forces using orthogonalto oblique transformation method. The uncut chip area

is divided into three regions (Region 1, 2 and 3, Fig. 19)

as presented before. Region 1 is discretized into equal

angular segmentsqi, where each element has a differentoblique geometry due to tool corner radius of the tool.However, in Region 2 and 3, the uncut chip areas are

uniform, and the oblique cutting parameters do not

change with location. The selected insert has zero back

rake (ar) and side cutting edge (g) angles, hence, thecutting in Region 2 and 3 can be considered to obey

orthogonal cutting mechanics laws.

Region 1: Uncut chip area, Ai, is calculated based on

Eq. (2). Approach angle yr= j, where j is the counterof the differential elements andqi is the uniform angular

increment of each differential element. The followingangles are determined as; Orthogonal rake angle aequals to arctan(tan(af).cos(yr)+ tan(ap).sin(yr)) whereaf, ar, yr, are the side rake, back rake, and side reliefangles, respectively. Oblique angle i is determined from

arctan(tan(ap).cos(yr) + tan(af).sin(yr)). Normal rakeangle an can be found as arctan(tan(a0). cos(i)) wherea0 is the orthogonal rake angle. Chip ratio, frictionangles and shear stress are given by Eq. (21). Normal

shear anglefnis equal to arctan rc.cos(an)1rcsin(an)

where anis the normal rake angle. Normal friction angle bn is

determined as arctan(tan(ba). cos(i)). By substituting theabove parameters into orthogonal to oblique transform-

ation given in Eq. (24), tangential, radial, and feed cut-

ting force coefficients for each differential element aredetermined.

As can be noticed, the oblique cutting parameters

change around Region 1 due to the variation of the

approach angleyr. For each differential element, obliquetangential, radial, and feed forces are determined,

Ft,i Ktc,iA1,i Kte.Lc,i

Fr,i Krc,iA1,i Kre.Lc,i

Ff,i

Kfc

,i

A1,i

Kfe

.Lc,i

(25)

Then, by summing all the respective force compo-

nents, total cutting force values along the corresponding

directions can be determined in Region 1 as follows,

Fx1 N

i=1

Ft1,i

Fy1 N

i=1

(Ff1,isin(qi)Fr1,icos(qi))

Fz1 N

i=

1

(Ff1,icos(qi)Fr1,isin(qi))

(26)

For Region 2: The same equations are used in the

force prediction except that the uncut chip area isdetermined from Eq. (3) and approach angle yr= ,where g is the side cutting edge angle of the tool. Cut-ting force components in three orthogonal measurement

directions of dynamometer can be found similarly,

Fx,2 Ft2

Fy,2 Ff2sin(g)Fr2.cos(g)

Fz,2 Ff2cos(g)Fr2.sin(g)

(27)

For Region 3: The uncut chip area is given by Eq.


14/15


(4). The approach angle will be approximated as,

yrg2

. For this region, the edge cutting force compo-

nents are assumed to be zero due to the zero contact

length. Cutting force components are obtained by using

the equations presented above,

Ft,3 KtcA3

Fr,3 KrcA3

Ff,3 KfcA3

(28)

These oblique cutting forces contributed by Region 3

are obtained as,

Fx,3 Ft3

Fy,3 Ff3singl2Fr3cosgl

2

Fz,3 Ff3cosgl2F

r3singl2

(29)

The total forces in dynamometer directions, X, Y andZ are found as follows,

Fx Fx,1 Fx,2 Fx,3

Fy Fy,1 Fy,2 Fy,3

Fz Fz,1 Fz,2 Fz,3

(30)

Cutting tests were conducted with the material P20 mold

steel by using the Valenite TPC 322J uncoated VC2

grade CTPGL-16-3 C left-hand tool holder at different

cutting speeds and depth of cuts, but with constant 0.05

mm/rev feedrates. The tool had 5 side rake angle, 0back rake and side cutting angles, 11 side relief angleand 0.8 mm corner radius. The cutting speed was varied

from 100240 m/min , and depth of cut was changed inthe range of 0.6251.750 mm. Seven of the experimentalforce results and corresponding predictions are shown in

Fig. 20. Tangential force is predicted with less than 10%

average error; however, prediction error in radial and

feed forces rises to 25% in some cases. The variation is

attributed to geometric modeling errors, as well as the

use of classical mechanics laws in evaluating complex

chip formation process in boring with inserts.

4. Conclusions

A comprehensive model of single point boring oper-

ations has been presented. The chip geometry removed

by curved boring inserts is modeled as a function of tool

geometry, feedrate and radial depth of cut. Due to irregu-

lar distribution of chip load around the inserts cuttingedge, the amplitudes and directions of distributed cutting

forces change as a function of tool geometry and cutting

conditions. As a result, the cutting forces in boring have

Fig. 20. Comparison of measured and predicted tangential, radial and

feed forces using orthogonal to oblique transformation method.

a linear dependency with the chip area, but non-linear

dependency with the feedrate and radial depth of cut.

The cutting coefficients are evaluated mechanistically byconducting cutting tests at different feeds, speeds anddepth of cuts with inserts having irregular rake face

geometry. The cutting coefficients are estimated by cor-relating the chip geometry and forces using regression

analysis. The cutting coefficients for inserts having

smooth rake faces are modeled using orthogonal tooblique transformation method. The models are exper-

imentally proven for single point boring bars used in

industry. The models allow the process engineers to

investigate the influence of insert geometry, feed, speedand radial depth of cut, boring forces, torque and power.

The model is an essential foundation to study the forcedand chatter vibrations in boring operations with single

point boring bars and multi-insert boring heads.

Acknowledgements

This research is conducted at The University of BritishColumbia and sponsored by National Science and Engin-

eering Research Council of Canada (NSERC), Milacron,

Pratt & Whitney Canada, Caterpillar and Boeing Cor-

porations.

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