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International Journal of Machine Tools & Manufacture 46 (2006) 1388–1394

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A model for cutting forces generated during machiningwith self-propelled rotary tools

L. Li, H.A. Kishawy�

Department of Mechanical Engineering, University of New Brunswick, Post Office Box 4400, Frederiction, NB, Canada E3B 5A3

Received 17 September 2005; accepted 4 October 2005

Available online 8 November 2005

Abstract

In this paper, a force model for self-propelled rotary tool is presented. Conventional oblique cutting force predictions were reviewed

and extended to predict the cutting forces generated during machining with the self-propelled rotary tools. The model presented is based

on Oxley’s analysis and was verified by cutting tests using a typical self-propelled tool. Good agreement was obtained between the

predicted and the experimentally measured forces under a wide range of cutting conditions. The effect of different cutting conditions on

the friction coefficient along the chip/tool interface and tool rake face normal force were also presented and discussed.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Cutting force; Self-propelled rotary tool; Chip flow angle; Friction coefficient

1. Introduction

Machining with rotary tools has received a considerableattention from researchers during the past decades [1–7].More recently, the superior wear resistance has encouragedseveral researchers to utilize these tools to machine difficultto cut materials [8–11]. In cutting with a rotary tool, acircular insert is used and allowed to freely rotate about itsaxis. As a result of the insert rotation the wear isdistributed over the entire circumference of the circularinsert, thus providing a longer tool life. In addition, theinsert rotation provides a self-cooling feature that reducesthermally induced wear. For example, during hard turningwith self-propelled tool no crater wear was reported whileunder the same cutting condition, crater and flank wearwere observed when conventional cutting tools were used[11]. Based on studying the heat transfer during cuttingwith rotary tools it was shown that a minimum tooltemperature can be achieved at an optimum rotationalspeed of the insert [12].

e front matter r 2005 Elsevier Ltd. All rights reserved.

achtools.2005.10.003

ing author. Tel.: +1506 458 7767; fax: +1 506 453 5025.

ess: kishawy@unb.ca (H.A. Kishawy).

The rotation of the circular insert makes the kinematicsof the process much more complicated as compared toconventional cutting. It has passed a long way since thediscovery of the advantage of cutting using rotary toolsand most of the research is related to the applications ofrotary tool and how it will benefit the machining process.Several researchers have explored the theoretical analysisof rotary cutting [1–2,4–6,12]. Shaw et al. [1] gave theprimary study on rotary tool machining and presented ananalysis to quantify the velocity relations in rotary cutting.Armarego and Karri [2,4–6] presented a more comprehen-sive analysis for cutting with rotary tools and predicted theforces generated during machining with rotary tools.However, their analysis did not consider the radius of thecutting insert. In addition, their experimental validationwas achieved by using a tool with straight cutting edge thatwas given an additional motion along the edge direction tosimulate rotary tools.According to the open literature all the available analysis

for cutting with rotary tool are based on using straightcutting edge that is allowed to slide parallel to the edgedirection to simulate the rotary motion except the recentlypresented model for prediction of chip flow angle [13].Modeling of the process based on a typical rotary tool

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Nomenclature

Bw absolute undeformed chip widthBwr relative undeformed chip widthBx insert effective cutting edge widthf feedfy equivalent feed on the tool rake faceFC cutting forceFR force component normal to FC and FT in

oblique cuttingFT feed forcei inclination angleir rotary tool insert effective inclination angleiw the angle between workpiece absolute velocity

direction and the intersection direction ofcutting edge normal plane Pn and cutting edgeplane Ps

iwr the angle between workpiece relative velocitydirection and the intersection direction ofcutting edge normal plane Pn and cutting edgeplane Ps

M transformation matrixNr insert revolutionr insert radiusR resultant force at shear zone or tool–chip

interfaceRm the resultant force in machine coordinate systemRX, RY, RZ coordinate system transformation matricest1 undeformed chip thicknessVw workpiece absolute velocityVwr workpiece relative velocityw orthogonal cutting chip width, tube shape

workpiece wall thicknessa tool rake anglean normal rake angle, rotary tool insert effective

rake angleZc chip flow angle, relative chip flow angle in rotary

cutting processw the difference of iw and iwrO resultant chip flow direction

w

αn

ηc

FR

FT

Fc

t1V

i

O

Q

B

Cuttingvelocity

X Y

Z

Fig. 1. Conventional oblique cutting forces [14].

L. Li, H.A. Kishawy / International Journal of Machine Tools & Manufacture 46 (2006) 1388–1394 1389

geometry to predict the forces generated will enable a morerealistic analysis that will provide information about theeffect of circular edge radius and facilitate an effectiveselection of process parameters.

In this paper an attempt has been made to utilize Oxley’sanalysis for oblique machining and extend it to predict theequivalent oblique cutting forces generated when using self-propelled rotary tools. A previously presented model bythe authors [13] for predicting the chip flow angle in rotarytools is also utilized here to predict the cutting forces.

2. Method for force prediction in conventional oblique

cutting

In oblique machining, the chip flow direction is nolonger normal to the cutting edge. This complex conditionimpedes the analysis in oblique cutting. However, attemptshave been made to approximate the analysis and predictthe cutting forces [14]. According to the machine coordi-nate system, conventional oblique cutting forces are shownin Fig. 1. Armarego and Brown [15] pointed out theirexperimental observation for the oblique cutting in termsof cutting forces and chip flow angle. For a given normalrake angle an and other cutting conditions, the cuttingforce FC and feed force FT are nearly independent ofinclination angle i. The chip flow angle was also elaboratedby following the Stabler’s chip flow rule [16]. Lin et al. [17]extended this method and detailed that the oblique cuttingforce FC and feed force FT could be obtained from theorthogonal cutting with zero inclination angle and usingthe normal rake angle (an) as the rake angle (a). The thirdforce component FR (i.e., normal to FC and FT) wascalculated by considering the inclination angle i. The

resultant force vector R can be expressed as

½R ¼ �FR;FT;�FC�T. (1)

The resultant force R was considered to be acting in theplane normal to the tool rake face and having the resultantfriction force direction. Since the normal plane to the rakeface contains the resultant force R and the resultant frictionforce F (F acts along the chip flow direction), there shouldbe no force component normal to this plane. This is carriedout by rotating the machine coordinate system around theY-axis to make X-axis in the direction of the cutting edge,

ARTICLE IN PRESSL. Li, H.A. Kishawy / International Journal of Machine Tools & Manufacture 46 (2006) 1388–13941390

and around the X-axis to place the rake face in the X–Y

plane. Finally, rotate the system around Z-axis to align theY-axis along the chip flow direction. The coordinatetransformation system from the machine coordinate tothe final one can be expressed as

M ¼ RZð�ZcÞRX ð�anÞRY ðiÞ (2)

where RX, RY, and RZ are the coordinate systemtransformation functions for the given rotation anglearound X-, Y-, and Z-axes, respectively. The resultantforce R in the finally created coordinate system is Rfinal,given by

Rfinal ¼ RZð�ZcÞRX ð�anÞRY ðiÞR. (3)

The expression for FR can be obtained by setting the X

direction component to zero in Rfinal as

FR ¼FCðsin i � cos i sin an tan ZcÞ � FTcos an tan Zc

sin i sin antan Zc þ cos i. (4)

The cutting force FC and feed force FT can be obtainedusing Oxley’s theory [14,18,19].

3. Cutting force prediction in self-propelled rotary tool

cutting processes

The rotation of the circular insert adds anothercomplication to the relations among the chip, tool and

Zc ¼ atan

R y2y1

sinO1rt1ðyÞdyþR p=2y2

sinO2rt2ðyÞdyþR y3p=2 sinO3rt3ðyÞdyþ

R y4y3

sinO4rt4ðyÞdyR y2y1

cosO1rt1ðyÞdyþR p=2y2

cosO2rt2ðyÞdyþR y3p=2 cosO3rt3ðyÞdyþ

R y4y3

cosO4rt4ðyÞdy

0@

1A. (5)

workpiece. The presented model accounts for the insertrotation as well as insert radius through its effect on thechip flow direction. However, it should be mentioned herethat, the presented force model is limited for the case oftube-end cutting using self-propelled rotary tools. Tosimplify the analysis, the following assumptions are made:

(1)

Insert radius is much larger than the tube thickness. (2) Continuous chip is formed with uniform velocity at all

the points on the chip.

(3) The resultant force at the tool–chip interface balances

resultant force at the primary deformation zone.

(4) Collinearity exists between the friction force direction

and the direction of relative chip flow on the tool rakeface.

(5)

There is no workpiece material side flow during thechip formation process.

The predictions of cutting forces have been explored fororthogonal cutting [14,18,19], conventional oblique cutting[15–17], and nose radius tip cutting [20,21]. The currentrotary tool force model applies Armarego et al. [4–6]transformation from rotary cutting to conventional ob-lique. In the early stage of this investigation [13], the

velocity relations and relative chip flow direction have beenobtained during the cutting process with self-propelledrotary tools. Considering that the insert radius is muchlarger than the tube thickness, the equivalent cutting edgeis considered as a straight line. In this analysis, thepreviously presented force model for orthogonal machining[14,18,19] is extended to conventional oblique cutting, andthen used in the equivalent conventional oblique cutting ofthe rotary cutting. The analysis accounts for the noseradius and the effect of chip flow angle to predict the forcesgenerated during cutting with self-propelled rotary tools.In this equivalent conventional oblique cutting, thecutting velocity is the relative undeformed chip velocity,Vwr, the undeformed chip thickness is the relativeundeformed chip thickness, Bwr, the rake angle is the sameas the insert working rake angle, an, and cutting edgeinclination angle is iwr. Fig. 2 illustrates the relationbetween different coordinate systems to analyze thekinematics of cutting with rotary tools. The cutting forceFC and feed force FT are calculated using Oxley’sorthogonal cutting force prediction method with theworkpiece relative velocity, Vwr, undeformed chip width,Bwr, and feed f. Eq. (4) is employed to calculate FR usingthe relative inclination angle iwr, effective normal rakeangle an, and the relative chip flow angle Zc. The chip flowangle Zc is calculated by considering the nose radius of theinsert such that:

The equivalent oblique cutting force prediction is underthe original coordinate system in Fig. 2(b). A resultantforce R is used to express the three predicted componentsin relative velocity coordinate system as Eq. (1). In order tocompare the predicted and the experimental results, theresultant force R is resolved in the machine coordinatesystem. The resultant force in machine coordinate systemRm is expressed as

Rm ¼ Ryð�wÞR, (6)

where w is

w ¼ iw � iwr. (7)

So the three elements in Rm are the values correspondingto the output measured using the dynamometer duringcutting test. The flow chart in Fig. 3 summarizes the self-propelled rotary tool cutting force prediction method.

4. Experimental work

A self-propelled rotary tool was employed in the currentinvestigation to carry out the machining tests. A typicalrotary tool consists of a tool holder and a circular insertfixed to the tool holder’s cartridge. Uncoated carbide

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X

Y

ZMachinespindle directionCross slide

direction

X

Y

Z

PS

iW

iwr

iwr

iW

cutting edge

intersection lineof Ps and Pn

X

Y

Z

PS

iW

iwr

iwr

iW

cutting edge

intersection lineof Ps and Pn

(a) (b) (c)

Fig. 2. The coordinate system transformations in the cutting force prediction process. (a) Machine coordinate system; (b) original coordinate system; and

(c) machine coordinate system for cutting forces.

Start

Vwr , Bwr iwr

Input: f

Functions for Orthogonal cutting force prediction

Relative chip flow angle : ηc [13]

Input:Material properties & Initial conditions

Oblique cutting force in original coordinate system: R = [-FR , FT, -FC]T

Resultant force in machine coordinate system: Rm = Ry (-χ) R

Equivalent parameters on the tool rake face: Bx , fy

Resultant

End

Orthogonal cutting forces: FC , FT

Input: Vw , Bw , ir , αn , r, Nr

Fig. 3. The flow chart for cutting force prediction in rotary cutting.

Fig. 4. Cutting tool installation on the tool post.

L. Li, H.A. Kishawy / International Journal of Machine Tools & Manufacture 46 (2006) 1388–1394 1391

inserts with 27mm diameter, 01 rake angle and 01 flankangle are used. When the insert, cartridge, and tool holderare assembled, the cutting edge has 171 inclination angleand �51 rake angle. The tool is fed in the machine spindledirection, as shown in Fig. 4.The material used in this investigation was carbon

steel SAE1045 in form of tubes of 48mm diameter and2mm wall thickness. The material composition is shown inTable 1.The cutting forces were recorded using a 3-component

force dynamometer (Kistler 9251A) and three charge

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Table 1

Carbon (C) Manganese (Mn) Phosphorus (P) Sulfur (S)

0.43–0.50% 0.60—0.90% 0.04% 0.05%

Workpiece Rotary toolToolpost withdynamometer

Amplifier

Data acquisition board

Computer

Feed direction

Fig. 5. The schematic diagram of the dynamometer working system.

0.09 0.11 0.13 0.15 0.17 0.19 0.210

200

400

600

800

1000

feed (mm/rev)

forc

e (N

)

Radial force:predictionexperiment

Axial force:predictionexperiment

Cutting force:predictionexperiment

Radial force:predictionexperiment

Axial force:predictionexperiment

Cutting force:predictionexperiment

Radial force:predictionexperiment

Axial force:predictionexperiment

Cutting force:predictionexperiment

0.09 0.11 0.13 0.15 0.17 0.19 0.210

200

400

600

800

1000

feed (mm/rev)fo

rce

(N)

0.09 0.11 0.13 0.15 0.17 0.19 0.210

200

400

600

800

1000

feed (mm/rev)

forc

e (N

)

(a)

(b)

(c)

Fig. 6. The predicted and measured effect of feed on the cutting force at

different speeds: (a) cutting speed ¼ 120m/min, (b) cutting speed

¼ 170m/min, and (c) cutting speed ¼ 230m/min.

L. Li, H.A. Kishawy / International Journal of Machine Tools & Manufacture 46 (2006) 1388–13941392

amplifiers (PCB Charge Amplifier MOD 462A). To verifythe model prediction, three cutting speeds were employed:120, 170, and 230m/min. Four feeds were used including0.1, 0.125, 0.15, and 0.2mm/rev. The cutting was carriedout under dry conditions (Fig. 5).

5. Results and discussion

Fig. 6 shows a comparison between the predicted andmeasured cutting forces during machining with self-propelled rotary tool. The predicted forces are comparableto the measured ones. Also, the predicted effect of the feedand cutting speed is in agreement with the measured one.From the above comparison, the predictions have an errorpercentages about 15%. It should be mentioned here thatthe cutting tests have been repeated in all cases with anerror percentage less than 3%, where much lower predic-tion error percentages were recorded in the axial andcutting forces.

The reason is due to the following three factors. The firstis that the prediction of the radial force uses the insertinclination angle as the cutting edge resultant inclinationangle, but the actual situation is that the cutting edge is anarc segment. There is a technical difficulty in measuring therelative chip flow angle, and no quantitative analysisapplies here. The second factor may be the tool adjustmentprocess. If the rotary tool insert cutting edge tip (firsttouching point) is not at the tube thickness center position,the actual chip flow and the actual relative chip flowdirection will be changed and finally affect the radial force.The third factor is that the magnitude of the radial force issmall, so the small change in the value will result in a highervalue of error percentage. Also the use of mean velocitywill affect the chip flow direction. No side flow wasassumed. In addition, tests showed burr formation undervarious conditions, and in some cases serrated-side chipswere formed. This will affect the absolute chip velocitycalculation and the prediction of the absolute chip flowangle. In this experiment, all the above-mentioned error

ARTICLE IN PRESSL. Li, H.A. Kishawy / International Journal of Machine Tools & Manufacture 46 (2006) 1388–1394 1393

sources were reduced as much as possible by repeating thecutting test several times. In all cases the measured forceswere almost the same with a difference of few Newtonswhen the magnitude was in the order of hundreds. Also,the tool position was adjusted to the tube-end position andthe machine dynamometer was recalibrated for theexperiment.

The predicted friction coefficients and normal forces areshown in Figs. 7 and 8. The friction coefficients decreasewith the increase of the feed. This trend was observed atdifferent velocities. It was also found that the frictioncoefficient decreases with the increase of cutting velocity.The variation trend of the friction coefficients in this modelis the same as that of the data obtained by Merchant(1945), and Lapsley et al. (1950) [22]. There is also atechnical challenge in measuring the rotary cuttingtool–chip interface friction coefficient. There is very slightchange in the normal force to the tool rake face withchanging cutting velocities. The tool rake face normal forcein Fig. 8 is not the result of force transformation of theoutput from the dynamometer to the tool rake face,because the relative motion of workpiece and insert, and

0.09 0.11 0.13 0.15 0.17 0.19 0.210

0.1

0.2

0.3

0.4

0.5

0.6

V=120 m/minV=170 m/minV=230 m/min

feed (mm/rev)

fric

tion

coef

fici

ent

Fig. 7. Comparison of friction coefficient vs. feed under various cutting

velocities.

0.09 0.11 0.13 0.15 0.17 0.19 0.210

200

400

600

800

1000

feed (mm/rev)

norm

al f

orce

(N

)

V=120 m/minV=170 m/minV=230 m/min

Fig. 8. Comparison of normal force vs. feed under various cutting

velocities.

the relative motion of chip and insert are different fromwhich discussed in the conventional cutting process.In the current model, material properties are used

directly according to Oxley’s theory with no need forcalibration, and relative chip flow angle was calculatedbased on the tool geometry and cutting conditions, whereprevious rotary tool force model [5] was based on findingthe relative chip flow angle by iteration and using databank of orthogonal cutting tests for different materials andvarious cutting conditions. In addition, an actual rotatingtool was used in the cutting tests. However, there arecertain limitations in the model’s ability to predict thecutting forces. The first is that the model has beendeveloped by assuming a flat tool rake face plane. Forthe rotary tool insert with a chip breaker, new mathema-tical methods and assumptions are needed in future study.The second limitation is that the force prediction in thismodel is based on Oxley’s theory which considers theplane-strain condition, and so the undeformed chipthickness should not be larger than 1/10 of the tubethickness.

6. Conclusion

A force model for the self-propelled rotary tool ispresented and validation of the model was carried out byconducting experiments under different cutting conditions.The predicted cutting forces were within the limits ofdivergence. The model was utilized to predict the frictioncoefficient at tool–chip interface for a typical self-propelledrotary tool. It was shown that increases in feed and cuttingvelocity results in lower friction coefficient. The normalforce on the tool rake face was found to be sensitive to thechanges in feed. There is only a slight difference in thevalue of the normal force for a given feed at differentcutting velocities.

Acknowledgment

The authors acknowledge the support of NaturalSciences and Engineering Research Council of Canada,NSERC.

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