Mechanics of boring processes—Part II—multi-insert boring heads

International Journal of Machine Tools & Manufacture 43 (2003) 477–484

Mechanics of boring processes—Part II—multi-insert boring heads

F. Atabeya, I. Lazoglub, 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

Holes with large diameters are usually bored with boring heads having multiple inserts. This article presents a mathematicalmodel for the cutting force system as a function of tool goemetry, chip load, cutting edge contact length and process parameters(such as feedrate, cutting speed, radial depth of cut) based on the physics, kinematics and mechanics of the boring process. Themodel also includes the possible process faults such as axial and radial runouts on each insert and deviation between the longitudinalhole and boring head axes. The cutting forces for each insert are modeled as presented in Part I of the article (Atabey, Lazogluand Altintas, Int J Mach Tools and Manuf (submitted 2001)). The cutting forces contributed by all inserts having radial and axialrunouts are modeled, and compared favorably with experimental measurements. When the runouts are absent in the system, thenormal cutting forces are zero due to force cancellations. However, when there are runouts on the inserts, while feed force isconstant, the cutting forces normal to the hole axis become periodic at the tooth passing frequency.

The model developed here can be used in the process planning of boring operations with inserted boring heads so that the surfacefinish and dimensional quality of the holes are maintained by avoiding excessive forced vibrations. 2003 Elsevier Science Ltd. All rights reserved.

1. Introduction

Holes, such as engine cylinder bores, are bored usinginserted boring heads. The boring heads are used asalternatives to single point boring bars. The diameter ofthe boring head is equal to the finish diameter of thehole, and inserts are symmetrically distributed aroundthe circumference of the boring head in order to provideforce cancellations in the plane perpendicular to holeaxis. The entire hole can be bored using larger feedratesdue to the presence of multiple inserts on the boringhead. The feasibility and quality of the boring operationvery much depend on the required torque, power fromthe spindle, the structural stiffnesses of machine tool andworkpiece, and feed marks left on the bore surface. Theprocess performance also strongly depends on the toler-ability of process faults such as radial and axial runoutsof the inserts on the boring head as well as the amount

∗ 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)00277-8

of the misalignment between the longitudinal hole andboring head axes.

Although significant research has been performed inturning and milling [2,3], boring received less attentionin the literature except by a few researchers [4–6]. Theystudied the mechanics of single point specific and simpli-fied boring bars, and they were not general enough forthe industrial applications. One of the main difficultiesin modeling the boring process is due to the fact thatsince most of the inserts have nose radius and non-zeroinclination angles, the chip load distribution along thecutting edge–workpiece contact is quite dependent onfeedrate and radial depth of cut. This makes the mode-ling of boring process quite challenging. For single pointboring operations, comprehensive models of chip loadand cutting force predictions, based on both mechanisticand classical cutting mechanics, are presented in Part Iof this article [1].

Part II of the article here extends the mechanics ofboring process to cover the boring heads with multipleinserts. The chip load and cutting force contributed byeach insert is predicted using the model developed forsingle insert boring bars [1]. When the inserts areassembled on the boring head, there may be misalign-

478 F. Atabey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 477–484

ment causing radial and axial runouts which lead toirregular distribution of chip load for each insert. Inaddition, when the boring head axis is not aligned withthe hole axis, each insert will remove rotational angledependent chip load. The irregular distribution of chiploads leads to unbalanced cutting forces in thrust andradial forces which affect the hole quality as well ascausing forced vibrations. The mechanics of hole expan-sion using inserted boring heads with process faults aremodeled and experimentally validated in the followingsections.

2. Mechanics of boring processes with multipleinserts

A sample boring head with two inserts is shown inFig. 1. The inserts are arranged with symmetrical angularpositions on the boring head in order to cancel the forceson the inserts in X and Y directions, hence the total forcein the XY plane is aimed to be zero. The force cancel-lation leads to better tolerances with multi-insert boringbars with a large operational length-to-diameter ratio(L/D), provided that the inserts are symmetricallyaligned and located on the boring head without offsetsor process faults.

Three cutting force components, tangential, radial, andfeed forces (Ft, Fr and Ff) act on each boring head insertas presented in Part I of the article. The tangential (Ft)and radial (Fr) forces are combined to give resultantforce FR,i (i is the insert number) in the XY plane whichis perpendicular to hole axis (Fig. 1). The feed and radialforces are calculated from friction force (Ffr) and effec-tive lead angle (fL). The cutting forces are expressed asfunctions of chip load (A) and chip-cutting edge contactlength (Le) and cutting coefficients [1],

Ft � Ftc � Fte � Ktc.A � Kte.Lc

Ffr � Ffrc1 � Ffrc2 � Ffre � Kfrc1.A1 � Kfrc2.A2 � Kfre.Lc

Fr � FfrsinfL

Ff � FfrcosfL

(1)

where the tangential (Ktc, Kte,) and the friction force(Kfrc1, Kfrc2, Kfre) coefficients are found either usingmechanistic or orthogonal to oblique transformationmethods. The evaluation of cutting coefficients, effectivelead angle (fL), chip areas in the curved nose (A1) andrectangular (A2) regions and total chip contact length (Lc)are presented in detail in Part I of the article [1]. Thesame force convention and metal cutting mechanicsmodels are used here.

While the feed force (Ffi) has a constant directionaligned with the boring head axis, the tangential and rad-ial forces on each insert rotate with the boring head. The

Fig. 1. Illustration of a multi-insert boring head and cutting forcedirections.

tangential (Fti) and radial (Fri) forces for each insert (i)can be projected into the X and � orthogonal directionsand summed to evaluate total forces acting on the boringhead as in milling [7],

Fx(f) � �Ni � 1

(Ftisinfi�Fricosfi)

Fy(f) � �Ni � 1

( � Fticosfi � Frisinfi)

Fz(f) � �Ni � 1

Ffi(fi)

(2)

where fi is the angular position of the insert (i). By

479F. Atabey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 477–484

assigning a reference angular rotation angle to the firstinsert (i = 1), each insert position can be expressed as,

fi � f � (i�1)2pN

(3)

where N is the number of inserts on the boring head.The total torque (Tc) and power (Pc) drawn from thespindle drive are,

Tc(f) �D2�

N

i=1

Fti(fi)

Pc(f) � V�Ni=1

Fti(fi)

(4)

where D is the diameter of the boring head, V = πDnis the cutting speed and n (rev/s) is the spindle speed.

There are usually even numbers of inserts on boringheads in order to cancel cutting forces. If there are norunouts on the inserts, and the boring head and hole axesare perfectly aligned, the cutting forces in radial planewill cancel each other and only feed forces need to beconsidered. However, this ideal situation does hardlyexist in practice as explained in the following section.

Fig. 2. Illustration of radial and axial runouts, chip load variations between the inserts, and cutting force directions.

2.1. Insert runout in radial and axial directions

The geometry of the boring head with axial and radialrunouts is shown in Fig. 2. The intended radial depth ofcut is a that is equal to the nominal increase in the holeradius. The insert is fed in the axial direction as anamount of feed per tooth (c). The insert has a nose radiusof R with the center of O (Fig. 2). The center of theinsert’s radial nose is shifted from points O1 to O2 withthe presence of runout. The radial runout (�r) is definedas a displacement of insert nose center in the the radialdirection, and the axial runout (�f) is described by theoffset of the insert center in the feed direction. Since theoffset of one insert will influence the chip load left tothe following insert, the chip geometry removed by eachinsert is affected by the runouts on all inserts in the bor-ing head. A boring head with two inserts is used hereas an example and in the experimental validation tests.There are more than twelve possible uncut chip area con-figurations to be considered, depending on which of thetwo inserts has the offset in the radial, feed or in bothdirections. Only two configurations, which are definedin detail below, are considered for the presentation inthis paper.


Fig. 3. Illustration of chip loads for the inserts; (a) In the case ofrunouts (ef1�c,er1 = 0) for Insert 1 and (ef2 = 0,er2 � 0) for Insert 2(b) In the case of no runouts.

1. Insert 1 has runout only in the feed direction and thatis greater or equal to feed per tooth (ef1�c, er1 � 0);Insert 2 has runout only in the radial direction ef2 �0, er2 � 0 where c [(mm//rev)/insert] is the feedrate pertooth. The resulting chip loads removed by insert 1 and2 are shown in Fig. 3.

2. Insert 1 has runout only in the feed direction and thatis less than feed per tooth (ef1 � c, er1 � 0); Insert 2has runout only in the radial direction (ef2 � 0, er2 �0). The corresponding chip loads removed by insert 1and 2 are shown in Fig. 4.

As it can be seen from the figures, the uncut chip areahas rather an irregular shape due to the runouts (�f and

Fig. 4. re 4. Illustration of chip loads for the inserts, in the case ofrunouts (ef1 � c,er1 = 0) for Insert 1 and (ef2 = 0,er2 � 0) for Insert 2.

�r). The cutting edge contact length (Lc) and uncut chipload (A) for each insert are calculated using methodspresented in Part I of the article [1]. When there are morethan two inserts on the boring head, the number andcomplexity of the uncut chip area configurations increasedepending on the distribution of the runout among theinserts. In such a case, each single uncut chip area con-figuration needs to be defined based on the inserts’ run-outs and their corresponding directions.

2.2. Deviation of the boring head from the hole center

The centers of the boring head and the hole are neededto be aligned for an accurate boring operation. When thecenter of the boring head has a deviation with respectto the hole center, the depth of cut varies with the angu-lar rotation of the boring head. The axes deviations areconsidered to be x and y in the axis coordinate sys-tem. The radial depth of cut becomes minimum whenthe angular position (f) of one of the two insertsbecomes (Fig. 5),

fmin � arctan�yx� (5)

The second insert, which is one pitch angle away fromthe first one, experiences the maximum radial depth ofcut at the following angular position,

fmax � fmin � p (6)

If we neglect the influence of radial and axial runouts,the variation of radial depth of cut only due to the mis-alignment of axes can be expressed as


Fig. 5. Illustration for the variation of radial depth of cut withrotation angle in the case of axis deviation.

For fmin � pffmin � 2p,

a(f) � ai�xycos(f�fmin � p)�R (7)

�1�cos�arcsin�xyR

sin(f�fmin � p)��For fminffmin � p,

a(f) � ai � xycos(f�fmin)�R (8)

�1�cos�arcsin�xyR

sin(f�fmin)��where xy = √x2 + y2.

The chip shape becomes dependent on radial and axialrunouts on each insert, as well as axes misalignment. Inorder to investigate the influence of axes misalignment,cutting forces are simulated for α range of axis misalign-ment ({x, y} = {0, 0}, {0.05, 0.05}, {0.1, 0.1} mm)with relative runouts of �f = 0.12 mm, �r = 0.10 mmwhile keeping the other insert as a reference with zerorunouts. The intended radial depth of cut (a) is 1.83 mmwith feedrate (c) of 0.07 mm. The simulated forces inthe X direction indicate that the influence of axis mis-match is negligibly small (Fig. 6) even with considerably

Table 1Cutting conditions. Cutting speed (V), hole diameter (D), feedrate per insert (c), the axial runout (�f), radial runout (�r = a2�a1).The maximumradial depth of cut delivered by inserts are indicated by a1 and a2

Test V [m/min] D [mm] c [mm/rev] �f [mm] �r [mm] a1 [mm] a2 [mm]

1 150 59.7 0.0600 0.09 0.20 1.485 1.2852 100 62.60 0.0700 0.12 0.10 1.830 1.7303 175 66.2 0.0550 0.14 0.18 1.100 0.920

Fig. 6. Variations of the Fx with various values of axes deviations.

large range of x and y. The influence of axes mis-match between the hole and boring head can, therefore,be neglected in practical analysis of boring forces exceptshifting of hole location which must be within the geo-metric tolerance of the part.

2.3. Simulation and experimental results

The proposed model is validated with α boring head(Valenite VPB PC%-4515) having two PVD diamondcoated inserts (Valenite CCGT432-FH). The nominaldiameter of the boring head can be set to the valuesbetween 55 mm and 70 mm. The workpiece material isA16061-T6, and the insert is the same as the onepresented in Part I of the article where the mechan-istically modeled cutting coefficients and identificationof chip loads are given. The intended depth of cut isassumed to be a2, and the radial runout is defined as�r = a2–a1. The cutting conditions are given in Table 1.

In the simulation, the boring head is rotated at discreteangular increments, and the corresponding chip load (A)and contact length (Lc) are evaluated by considering theradial and axial runouts as well as the tool geometry,feedrate (c) and intended radial depth of cut (a). Thecutting forces are predicted using the mechanistically


Fig. 7. Resulting and feed force variations with time, and chip load variations between the inserts for the cutting conditions of Test #1.




evaluated cutting coefficients as described in [1]. Thepredicted and measured forces are shown in Figs. 7–9.The feed force (Ff) is in the direction of longitudinal axisof boring head and it is constant. The plane forces (Fx,Fy) are periodic at tooth passing frequency (Nn/60) or atp angular periods due to the presence of radial and axialrunouts. Both have identical magnitudes but with a phaseshift, therefore, only total Fx forces are presented in thefigures. The error between the predicted and measuredcutting forces are less than 10% in both directions. Ifthere was no runout on the inserts, the inplane cuttingforces which bend the rotating boring head would havebeen zero due to force cancellations. However, as therunout magnitudes increase, the amplitude of the per-iodic forces in X and � directions increase, causing per-iodic bending or forced vibrations of the boring headwithin the hole. The periodic vibrations lead to poor sur-face quality as well as violation of hole dimensions whenthe vibration amplitudes are significant and the dynamicstiffness of the boring head attachment is low.

3. Conclusions

Mechanics of cutting with boring heads having mul-tiple inserts are presented. The chip geometry and con-tact length between the cutting edge and work materialare evaluated by considering the tool geometry, feedrate,radial depth of cut, the axial and radial runouts on eachinsert, as well as misalignment of hole and boring head

axes. The cutting forces acting on each insert is evalu-ated by the models presented in Part I of the article. Thetotal cutting forces acting on the boring head are mod-eled including runouts. If there is no radial and axialrunout, the bending forces on the boring head would bezero due to force cancellation provided by the even num-ber of inserts on the boring head. However, the axial andradial runouts lead to periodic cutting forces which areperpendicular to the longitudinal axis of boring head.The amplitude of the periodic forces increase with therunout, and they are dependent on the geometry of thetool, radial depth of cut and feedrate. The models areexperimentally proven and can be used in planning bor-ing operations to achieve acceptable hole surface anddimensional tolerances.

Acknowledgements

This research is sponsored by National Science andEngineering Research Council of Canada (NSERC),Milacron, Pratt & Whitney Canada, Caterpillar and Boe-ing Corporations.

References

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[3] K.F. Ehman, S.G. Kapoor, R.E. DeVor, I. Lazoglu, Machining pro-cess modeling: A review, J. of Manufacturing Science and Engin-eering, Trans. of ASME 119 (1997) 655–663.

[4] E.W. Parker, Dynamic stability of a cantilever boring bar withmachined flats under regenerative cutting conditions, JournalMechanical Engineering Science 12 (1970) 104–115.

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Mechanics of boring processes—Part II—multi-insert boring heads