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doi:10.1016/j.ijm

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International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017

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Spiral point drill temperature and stress in high-throughputdrilling of titanium

Rui Li, Albert J. Shih�

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Received 16 January 2007; accepted 25 January 2007

Available online 20 February 2007

Abstract

The spatial and temporal distributions of the temperature and stress of a 9.92mm diameter spiral point drill are studied in high-

throughput drilling of Ti–6Al–4V with 384mm3/s material removal rate (MRR). A finite element thermal model using the inverse heat

transfer method is applied to find the heat partition on the tool–chip contact area and convection heat transfer coefficient of cutting fluid.

The thermal model is validated by comparing experimentally measured and numerically predicted drill temperature with good

agreement. Thermo-mechanical finite element analysis is applied to solve the drill stress distribution. Modeling results confirm that the

supply of cutting fluid is important to reduce the temperature across the drill cutting and chisel edges. At 183m/min peripheral cutting

speed, 0.05mm/rev feed and 10.2mm depth of drilling, the drill peak temperature is reduced from 1210 1C in dry drilling to 651 1C with

cutting fluid supplied through the drill body. Under the same MRR, 61m/min peripheral cutting speed and 0.15mm/rev feed, the

analysis shows that the drill peak temperature is reduced to 472 1C. The temperature induced thermal stress combined with the

mechanical stress caused by cutting forces is analyzed to predict the location of drill failure. Applying the modified Mohr failure

criterion, the drill cutting and chisel edges are found to be prone to failure in dry and wet drilling conditions, respectively. This study

demonstrates the effectiveness of drill thermal and stress modeling for drilling process parameter selection and drill design improvement.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Finite element modeling; Temperature; Stress; Drilling; High-throughput; Titanium

1. Introduction

A major technical challenge in machining titanium (Ti)and Ti alloys is the high tool temperature. The inherentmaterial properties, particularly the low thermal conduc-tivity, of Ti and its alloys are the primary cause [1,2]. Hightool temperature softens the tool material and is detri-mental to the tool life. For drilling, since the tool isconstrained in a hole, the high temperature is significant inthe drill tip. This results in the limited material removalrate (MRR) and, subsequently, low productivity and highcost in machining Ti.

The research in high-throughput Ti drilling experimentshas demonstrated that advanced tool geometry design andproper process parameter selection can achieve high MRRwith satisfactory tool life [3]. It is known that the supply of

e front matter r 2007 Elsevier Ltd. All rights reserved.

achtools.2007.01.014

ing author. Tel.: +1734 647 1766.

ess: shiha@umich.edu (A.J. Shih).

cutting fluid and the selection of feed and cutting speed indrilling greatly affect drill temperature, stress, and life in Tidrilling [3]. The goal of this study is to quantify the spatialand temporal drill temperature and stress distributions inhigh-throughput drilling of Ti–6Al–4V, a commonly usedTi alloy.Several methods have been developed to experimentally

measure the drill temperature [4]. A common method is toembed insulated wires in the workpiece to form the hotjunction of a tool-work thermocouple [5–7]. The thermo-couple electromotive force (emf) generated when the toolcuts is recorded through the wire and is used to detect thedrill temperature. This method has good repeatability andtime response, but can only measure temperatures atdiscrete points in low-speed drilling due to the shortcontact period. Using an embedded foil tool-work thermo-couple overcomes these problems by replacing theembedded wires with a metallic foil. It can measure thetool temperature across the cutting edge [8]. Disadvantages

ARTICLE IN PRESSR. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172006

of the tool-work thermocouple method are the requirementof extensive calibration and limited measuring region andperiod. Commercial thermocouples can also be embeddedin the drill to measure the temperature [7,9–11]. It requirescareful specimen preparation to avoid damaging thethermocouple during drilling. Thermocouples can onlymeasure temperature at discrete points away from thecutting edge. Since the tool and work-materials are subjectto high temperature and undergo hardness change,metallurgical transformation, or even chemical composi-tion change, the micro-hardness measurement [12], scan-ning electron microscopy [13], and energy dispersive X-raymeasurement [14] have been developed to measure the drilltemperature. Similarly, drills coated with thermo-sensitivepaints can be utilized for temperature measurement [5,15].A common disadvantage of these methods is that they onlymeasure the peak temperature. Also, these methods requireextensive post-test sample preparation and analysis. Theinfrared thermal camera is not suitable for drill tempera-ture measurement because the drill-cutting region isembedded inside the workpiece.

To solve the spatial and temporal distributions of thedrill temperature, an inverse heat transfer method has beendeveloped [16]. Thermocouples embedded in the drillprovide the temperature input data for the drill finiteelement thermal model. This model estimates the cuttingedge heat generation rate by minimizing the discrepancybetween the measured and predicted temperature at thethermocouple locations. This method has been demon-strated in dry drilling of commercially pure Ti at lowcutting speed (up to 73.2m/min) using the setup with astationary drill and thermocouple wires routed throughholes in the drill body [16]. This setup is adequate for drydrilling but not suitable for the high-throughput drilling ofTi because of the need to use cutting fluid and theinterference of cutting fluid with thermocouple wires inthrough-the-drill holes. In this study, shallow grooves wereground on the side (margin surface) of the drill body toguide the thermocouple wires from the drill tip to outsideof a stationary drill.

Most of the drill thermal analyses by previous research-ers were conducted under the dry condition. In drillingwith a supply of cutting fluid, so called wet drilling, theresearch on drill temperature is limited. Arai and Ogawa[17] measured drill temperature using the embedded wiretool-work thermocouple method in drilling Ti–6Al–4Vwith an external cutting fluid supply. Kalidas [18] modeledthe workpiece temperature in drilling cast aluminum (Al)356 with an external cutting fluid supply. Due to the hightemperature in Ti drilling, supplying the cutting fluid viathrough-the-drill holes is necessary to enhance the drill life[3]. To the best of our knowledge, no research publicationis available on the analysis of spatial and temporal drilltemperature distributions with an internal cutting fluidsupply. This research is aimed to fill this gap. In this paper,the spatial and temporal drill temperature distribution inhigh-throughput (384mm3/s MRR) drilling of Ti–6Al–4V

with an internal cutting fluid supply is studied using theinverse heat transfer method.The drill temperature and cutting forces can be used as

inputs to analyze the spatial and temporal distributions ofthe drill stress. For high-throughput Ti drilling, the drilltemperatures and forces are both very high. Severedeformation and highly localized stresses are expected inthe drill and will eventually lead to the drill failure. Thedrill deformation has been studied by Bono and Ni [10]using a finite element model for drilling Al 319. The stressdistribution in the drill has also been investigated bothexperimentally [19] and numerically [20]. This studyconducts more in-depth drill stress analysis using thethermo-mechanical finite element model and predicts theinitial failure location in a spiral point drill. The von Misesstress of the drill used in high-throughput drilling ofTi–6Al–4V has been presented in Ref. [21]. For the WC–Cotool material, the brittle fracture is different from thefailure of ductile metals predicted using the von Misesfailure criterion [22–24]. More advanced analysis ofWC–Co at microstructure level has been conducted[25,26]. In this paper, three most frequently used brittlefailure criteria, Rankine, Mohr–Coulomb [27], and mod-ified Mohr criteria [28], are compared to select the mostsuitable failure criterion for drilling. The location in thedrill likely to initiate the failure is identified in the analysis.In this paper, the experimental setup of Ti drilling tests

and drill temperature measurements are first introduced.The inverse heat transfer and finite element modeling of thedrill are then discussed. The drill temperature measurementand validation are presented. Finally, the drill stress,deformation, and failure analyses are performed.

2. Experimental setup and design

The drilling experiment was conducted in a Mori SeikiTV 30 computer numerical control (CNC) verticalmachining center. Fig. 1(a) shows the experimental setupwith a rotating 25mm diameter Ti–6Al–4V bar and astationary 9.92mm diameter spiral point drill (KennametalK285A03906). Two fluid jets, under 0.2MPa pressure, canbe identified shooting from the drill body. Under the drillholder was a Kistler 9272 dynamometer to measure thethrust force and torque. As shown in Fig. 1(b), the tips of0.127mm diameter thermocouples (OMEGA 5TC-TT-E-36-72), denoted as TC1 and TC2, are embedded ingrooves hand ground on the drill flank face and locatedclose to the cutting edge. An X–Y coordinate is defined atthe center of the S-shaped chisel edge in the spiral pointdrill. The Y-axis is parallel to the tangent at the apex of thecurved cutting edge. Coordinates of the tips of twothermocouples are identified in Fig. 1(b). Thermocouplesare covered with cement (Omega OB-400) to secure theposition and prevent the contact with the rotating work-piece. Unlike the setup in dry drilling with thermocouplewires going through holes inside the drill body [16],thermocouple wires in this study were routed up the drill

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Fig. 1. Experimental setup: (a) workpiece, drill, fluid hose and dynamometer; and (b) top view and coordinates of thermocouple tips on drill flank face.

Table 1

Experiment process parameters for high-throughput drilling of Ti–6Al–4V

with 4.97mm/s feed rate and 384mm3/s material removal rate

Experiment

D183 W183 W91 W61

Cutting fluid supply Dry Wet Wet Wet

Peripheral cutting speed (m/min) 183 183 91 61

Feed (mm/rev) 0.051 0.051 0.102 0.152

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017 2007

body in hand ground grooves around the drill body surfaceto avoid the interference with the supply of cutting fluid.

Four drilling experiments, designated as D183, W183,W91, and W61, are listed in Table 1. Symbols D and Wrepresent the dry and wet (internal cutting fluid supply)drilling conditions, respectively. The number represents theperipheral cutting speed in m/min. The first experiment,D183, was a dry drilling at 183m/min peripheral cuttingspeed and 0.051mm/rev feed. Using the cutting fluid andmaintaining the same MRR (384mm3/s) and feed rate(4.97mm/s) as in Exp. D183, three drilling tests, Exps.W183, W91, and W61, were conducted at 183, 91, and61m/min peripheral cutting speed and 0.051, 0.102, and0.152mm/rev feed, respectively. The depth of drilling was10.2mm and the drilling time was 2.0 s in all fourexperiments.

3. Drill thermo-mechanical modeling procedure

Thermo-mechanical finite element modeling was con-ducted in two steps. The first step is a thermal modelingincorporating the inverse heat transfer solution to calculatethe heat partition on the tool–chip contact area and theconvection heat transfer coefficient of cutting fluid and

drill temperature distribution. Based on the analyzeddrill temperature results, the mechanical modeling isconducted to calculate the drill deformation and stressdistributions.

3.1. Finite element model

SolidWorksTM and AbaqusTM were applied for the drillsolid model construction and finite element analysis,respectively. Detailed geometrical data of the spiral pointdrill are available in Ref. [16]. Fig. 2 shows the drill solidmodel and finite element mesh, which is composed of88,104 four-node tetrahedral elements. As shown in thesolid model of the drill tip in Fig. 2(a), half of the chiseledge is represented by two elementary cutting tools (ECTs)and the cutting edge is represented by five ECTs. For eachECT, oblique cutting analysis [16] was conducted tocalculate the heat generation rate, qtool, at the cuttingedge. The heat partition factor K is utilized to convert theheat generation rate by friction on the tool–chip interfaceqf to qtool

qtool ¼ qfK , (1)

where qf is the product of the friction force Ff and the chipvelocity Vc. Ff and Vc are derived from the measured thrustforce, torque, and chip thickness of each ECT [16]. Theheat partition factor K determines the ratio of heattransferred to the tool and can be calculated as [29]:

K ¼ 1� 1þ 0:45kt

kw

ffiffiffiffiffiffiffiffiffipdw

V cl

s !�1, (2)

where kt and kw are the thermal conductivities of WC–Codrill and Ti–6Al–4V workpiece material, respectively. dw isthe diffusivity of Ti and l is the tool–chip contact length.All thermal properties are temperature-dependent.

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Fig. 2. The 3D spiral point drill model: (a) top view of solid model with

seven marked ECTs on drill chisel and cutting edges; and (b) side view of

finite element mesh for themo-mechanical analysis (number of elements:

88.104).

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172008

In this study, the tool–chip contact length is

l ¼ sac, (3)

where s is the ratio of the tool–chip contact length to thechip thickness ac. The value of s is assumed to be constantacross the chisel and cutting edges and is determined by theinverse heat transfer solution.

The initial condition of finite element analysis is auniform temperature of 20 1C in the drill. The boundarytemperature on the bottom surface at the end of the drill,opposite from the drill tip, is assumed 20 1C.

The boundary condition of free convection with air isapplied to the whole drill surface for dry drilling becausethe drill does not rotate in the experiment. The heat flux ofa vertical wall due to free convection in air is applied on thedrill surface [16,30].

For wet drilling, the drill surface exposed to air has thesame free convection as the drill in dry drilling. For thedrill surface immersed in the hole and through-the-drillholes with cutting fluid flowing, the boundary condition isforced convection. The heat flux q00fluid is

q00fluid ¼ hðT � T fluidÞ, (4)

where h is the convection coefficient of cutting fluid andTfluid is the fluid temperature, which is assumed to be 20 1C.The inverse heat transfer analysis is applied to solve h.

3.2. Inverse heat transfer solution

Inverse heat transfer utilizes the temperature measuredat thermocouple TC1 as an input to predict the heatgeneration rate at the drill chisel and cutting edges. Thedrill temperature at TC2 is predicted using the finiteelement model and compared with experimental measure-ments to validate the accuracy of the inverse heat transfersolution.The flowchart for inverse heat transfer solution of heat

partition on the tool–chip interface is shown in Fig. 3.Using measured thrust force and torque at the start ofdrilling, cutting forces in each ECT can be calculated [16].The chip thickness and shear angle associated with eachECT are measured from the machined chip to estimate thechip speed Vc. Based on this information, the frictionalforce and heat generation rate qf can be determined. Theheat partition factor K is required to find the amount ofheat transferred to the drill qtool for thermal finite elementanalysis.By assuming an initial value for s, the values of l, K, and

qtool can be calculated and applied to nodes on the chiseland cutting edges of ECT. The spatial and temporaltemperature distribution of the drill can then be solved.The inverse heat transfer method is applied to solve s byminimizing an objective function, Obj, determined by theexperimentally measured and finite element modeledtemperature at specific thermocouple locations, as shownin Fig. 1(b) as TC1, on the drill flank face.The discrepancy between the experimentally measured

temperature at thermocouple j at time ti, Tti

j

���exp

, and finite

element estimated temperature at the same thermocouple

location and time, Tti

j

���est, determines the value of the

objective function

Obj ¼Xni

i¼1

Xnj

j¼1

ðTti

j jexp � Tti

j jestÞ2, (5)

where ni is the number of time intervals during drilling andnj is the number of thermocouples selected to estimate theobjective function.With the cutting fluid supply, the first step is to find an

appropriate estimation of the convection coefficient ofcutting fluid, h. This is also solved using the inverse heattransfer method, as illustrated by the flow chart in Fig. 4.Exp. W183 uses the same cutting speed and feed as Exp.D183, therefore is assumed to have the same tool–chipcontact length, s. This s is used in conjunction with theexperimentally measured thrust force, torque, and chipthickness to calculate the heat generation rate, qtool, anddrill temperature distribution. The convection coefficient h

is then determined by iteration to minimize the objectivefunction, Obj.Once the convection coefficient of cutting fluid h is

determined, it will be used in the forced convectionboundary conditions in Exps. W91 and W61. At different

ARTICLE IN PRESS

Measure the

thrust force and

torque in drilling

Calculate the

friction force Ff in

each ECT

Measure

the chip

thickness

in each

ECT

Calculate

the chip

velocity Vc

in each

ECTCalculate the

heat generation

by friction qf in

each ECT

Iteration of s and

the heat partition

factor K

Calculate the

heat generation

on ECT qtool

Calculate the

drill temperature

distribution

Determination of

s and K

Objective

function Obj

< cutoff value?

Golden

section

optimization

method

Initial

value of s

Yes

No

Convection

from air or

cutting fluid

Fig. 3. Flow chart of the inverse heat transfer solution of heat partition on tool–chip interface.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017 2009

cutting speeds and feeds in Exps. W91 and W61, the valuesof s and heat partition factor K are calculated following thesame procedure shown in Fig. 3.

3.3. Finite element drill stress analysis

The drill stress is solved using thermo-mechanical finiteelement modeling. The combination of thermal stress dueto high temperature in the drill and mechanical stresscaused by the cutting force applied on ECTs determines thespatial and temporal distributions of the drill stress. Thesame 3D finite element mesh (Fig. 2(b)) used for thermal

modeling is applied for stress analysis. The bottom (awayfrom the tip) of the drill is assumed to be fixed. Cuttingforces in each ECT are assumed to be uniformly distributedacross the edge of the ECT. These distributed forces areconverted into forces on nodes comprising the cutting andchisel edges.

4. Drill temperature analysis results

The temporal and spatial drill temperature distributionsin four experiments, Exps. D183, W183, W91, and W61,are presented.

ARTICLE IN PRESS

s from Exp. D183

Iteration of h

Calculate the drill temperature

distribution

Determination of h

Objective function Obj

< cutoff value?

Golden section

optimization method

Initial value of h

Calculate the heat generation

on ECT qtool

Measure the thrust force, torque and chipthickness in each ECT

Yes

No

Fig. 4. Flow chart of the inverse heat transfer solution of cutting fluid convection coefficient.

0

10

20

30

0 1

Heat

gen

era

tio

n r

ate

per

un

it

len

gth

, q'tool (

W/m

m)

D183 W183 W91 W61Exps.

Chisel Cutting edge

0.2 0.4 0.6 0.8

Relative distance from drill center (r/R)

edge

Fig. 5. The heat generation rate per unit length q0tool at seven ECTs after

1.9mm depth of drilling.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172010

4.1. Exp. D183

The s and heat generation rate in Exp. D183 is solvedfirst. By minimizing Obj using the measured temperature atTC1, the value of s is solved as 7.0. This is comparable tothe values of s obtained in a previous study of drilling CPTi using the same drill geometry [16]. Applying the s andtemperature-dependent material properties, K and qtoolvary both spatially and temporally. To compare the heattransferred to each ECT, qtool is divided by the length ofthe ECT cutting edge to calculate the heat generation rateper unit length of contact, denoted as q0tool. Results of q0toolafter 1.9mm depth of drilling, i.e., the drill cutting edgefully engaged in the workpiece, are shown in Fig. 5.Consistently, ECTs at the cutting edge have a much higherq0tool than those at the chisel edge.

The finite element thermal model is validated bycomparing with the experimentally measured temperatureat thermocouple TC2, which is not used as the input forinverse heat transfer analysis and is therefore an indepen-dent measurement. As shown in Fig. 6, the modeltemperature matches well with experimentally measuredtemperature at TC2 as well as TC1, the input of the inverseheat transfer analysis.

To quantify the discrepancy between the experimentaland modeling results, the root mean square (RMS) error,eRMS [16,31] between the measured and predicted tempera-tures, and the percentage error, p, defined as the ratio ofeRMS to the highest measured temperatures, are comparedin all four experiments. The results of eRMS and p at TC1and TC2 are listed in Table 2. For Exp. D183, the eRMS atTC2 is very close to that of TC1. The p of both

thermocouples is 1.4%. In summary, the low eRMS and p

at two thermocouples throughout the drilling processvalidates the proposed method to predict the spatial andtemporal drill temperature distributions.The temporal change of the ECT temperature at drill

chisel and cutting edges in four drilling tests vs. the drillingdepth is shown in Fig. 7. When an ECT is engaged incutting, the temperature of the ECT increases immediately.For dry drilling (Exp. D183), the ECT temperaturescontinue to increase after the initial rapid jump, whichoccurs upon engagement. This is detrimental to the drilllife.The chisel edge temperature is higher than that of the

cutting edge only at the very beginning, when the cutting

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Table 2

Root mean square and percentage errors of the predicted and measured

temperatures

Experiments TC1 TC2

D183 eRMS (1C) 9.9 9.7

p (%) 1.4 1.4

W183 eRMS (1C) 31.3 28.7

p (%) 4.6 4.34

W91 eRMS (1C) 33.0 22.2

p (%) 4.8 3.34

W61 eRMS (1C) 7.1 10.4

p (%) 1.0 1.54

Fig. 6. Comparison of the measured and calculated temperatures at TC1

(input of inverse heat transfer analysis) and TC2 (for validation).

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017 2011

edge has not engaged the workpiece. After drilling to adepth of 1.9mm (the point length), ECT 7 becomes thehottest ECT and remains so until the end of drilling.

The spatial drill temperature distribution of Exp. D183at 10.2mm depth of drilling is shown in Fig. 8(a). Hightemperatures are concentrated along the cutting edge at thedrill tip. The peak temperature is located on the cuttingedge near the drill margin. The peak temperature is high,1210 1C, which is close to the limit of WC–Co toolmaterial.

4.2. Exp. W183

Assuming s does not change with the supply of cuttingfluid at the same cutting speed and feed, the convectioncoefficient h for the cutting fluid is solved using the inverseheat transfer solution, and is found to be 15000W/m2K.This value is in the range reported in published experi-mental data [18]. As shown in Fig. 5, at the same cuttingspeed and feed, the supply of cutting fluid results in higherq0tool because of the lower tool and workpiece temperaturesand higher cutting forces. Fig. 6 shows that the discrepancybetween the experimental and modeling results is small atthermocouples TC1 and TC2. The eRMS and p, as shown inTable 2, are larger in Exp. W183 than those in Exp. D183.This is primarily due to the thermocouple measurementnoise induced by cutting fluid, as shown in Fig. 6. Theprediction is still accurate. For both thermocouples, p isless than 5.0%.As shown in Fig. 7, the temporal distributions of the

chisel and cutting edge temperatures of Exp. W183, ascompared to those of Exp. D183, illustrate the effects ofcutting fluid to reduce and maintain the drill temperatureat a much lower level. Drill temperatures in Exp. W183reaches a steady state level shortly after the correspondingECT is fully engaged with the workpiece. The chisel edge(ECTs 1 and 2) also has a low temperature. In Exp. W183,ECT 6 has a slightly higher temperature than that of ECT7, which is a different trend than that of Exp. D183. Thespatial temperature distribution of Exp. W183 after10.2mm of drilling is shown in Fig. 8(b). The peaktemperature has moved inside to ECT 6 as compared toExp. D183 in Fig. 8(a). The radial distance from the peakdrill temperature on cutting edge to the drill margin is 0.36and 1.09mm for Exps. D183 and W183, respectively. Thisis beneficial because, away from the drill margin, ECT 6has a smaller rake angle and stronger cutting edgegeometry than ECT 7 to withstand the high temperaturerelated tool strength softening. Under the same cuttingspeed, the internal cutting fluid supply has a significanteffect on the peak drill temperature, reducing it by almosthalf to 651 1C after 10.2mm of drilling.

4.3. Exps. W91 and W61

Assuming the same convection coefficient h as in W183,the s in Exps. W91 and W61 remains at 7.0, the same as thevalue in Exp. W183. The decrease of cutting speed (andcorresponding increase of feed to maintain the same MRR)does not change the value of s, but as shown in Fig. 5, itleads to a lower heat generation rate q0tool and drilltemperature.The inverse thermal modeling is accurate for Exps. W91

and W61. Fig. 6 shows the close correlation between themeasured and predicted temperatures at TC2. The eRMS

and p of TC2, as listed in Table 2, are comparable to thoseof Exp. W183. Fig. 7 shows the temporal development ofECT temperature remains nearly constant for each of the

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Fig. 7. Temperature distributions along drill chisel and cutting edges as a function of drilling depth.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172012

three tests in which cutting fluid was used. The decrease ofcutting speed and increase of feed have reduced thetemperature at ECT 6, which has the highest temperatureamong all ECTs. The peak temperature, as shown in Figs.8(c) and (d), has reduced from 651 1C in Exp. W183 to602 1C and 472 1C in Exps. W91 and W61, respectively.However, the drill stress will increase as a result of theincrease in feed and decrease in temperature. This will bequantified in Section 6.

5. Drill deformation

Under high temperatures and stresses in drilling, the drilldeforms both axially and radially. The increase in drilltemperature expands the drill length and diameter due tothermal expansion. The force at the cutting edge decreasesthe drill length but increases the drill diameter. Thecombinational effect of temperature and stress changesthe drill geometry and affects the shape of the hole.

The shape of the deformed drill for Exp. D183 after10.2mm of drilling is shown in Fig. 9 with 20 timesamplification of deformation. The drill deformation isquantified by two parameters: the change in the drill lengthand the diameter. The change in length is defined by thechange of total length from the drill tip to the base afterimposing the temperature and cutting force on the drill.The change of diameter is the difference between thediameter of the originally round drill and the largestenclosing diameter of the drill after 10.2mm of drilling.

Table 3 lists the change in drill length and diameter infour drilling experiments. In all experiments, the thermalexpansion effect outweighs the mechanical force effect inincreasing the total length and diameter of the drill. Thedrill expands the most, 18.4 mm in length and 12.0 mm in

diameter, in dry drilling, Exp. D183. In wet drilling, thedrill deformations are not as significant, about 7 mmincrease in length and 3 mm increase in diameter.The mechanical force effect (without considering the

thermal expansion effect) on the change in length anddiameter is also listed in Table 3. The drill shortens in axialdirection and expands in radial direction, but thedeformation is one order of magnitude lower than thatunder thermo-mechanical conditions. This concludes thatthe effect of thermal expansion outweighs the mechanicalforces in drill deformation.

6. Drill stress and failure prediction

WC–Co is a brittle material with highly different tensileand compressive strengths [22]. Three commonly usedfailure criteria for brittle materials are the Rankine,Mohr–Coulomb [27], and modified Mohr criteria [28]. Allfailure criteria used three principal stresses, denoted as s1,s2, and s3 with s14s24s3. The maximum and minimumprincipal stress, s1 and s3, along the drill chisel and cuttingedges in four experiments are shown in Fig. 10. Under allfour drilling conditions, the drill shows high tensile(positive) s1 and compressive (negative) s3 at the chiseledge. A peak of high compressive principal stress s3 isobserved at the location r/R (relative distance to drillcenter) ¼ 0.2. The whole cutting edge is under a state ofhigh compression with high compressive s1 and s3.The Rankine criterion is the simplest among the three

brittle material failure criteria. Rankine criterion, alsoknown as maximum normal stress criterion [27], states thatbrittle material fails when the principal stress either exceedsthe uniaxial tensile strength st or compressive strength sc.

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Fig. 8. Temperature distributions at the drill tip after 10.2mm depth of drilling in Exps: (a) D183, (b) W183, (c) W91, and (d) W61.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017 2013

The Rankine criterion can be expressed as s1 ¼ st ors3 ¼ sc.

Assuming that the maximum shear stress determines theonset of failure, the Mohr–Coulomb criterion or internal-friction theory, suggests that failure occurs when the Mohr’scircle of a point in the body exceeds the envelope created bytwo Mohr’s circles for uniaxial tensile strength st and

uniaxial compressive strength sc [27]. If the Mohr envelopeis simplified as a straight line, this criterion can be written as

s1st�

s3sc¼ 1. (6)

The modified Mohr criterion derives from the Rankinecriterion and considers the variation of material strength

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Table 3

Drill deformation under the thermo-mechanical and mechanical-only

conditions

Experiment

D183 W183 W91 W61

Length increase (mm) 18.4 7.66 6.84 6.79

Diameter increase (mm) 12.0 3.77 3.53 2.95

Length reduction by

mechanical load only (mm)

0.59 0.42 1.17 0.93

Diameter increase by

mechanical load only (mm)

0.28 0.29 0.38 0.41

-1000

0

1000

2000

3000

Max.

pri

ncip

al

str

ess, �

1 (M

Pa

)

D183 W183 W91 W61Exps.

Chisel edge

-4000

-3000

-2000

-1000

0

0 0.8 1

Min

. p

rin

cip

al

str

ess, � 3

(MP

a)

Relative distance from drill center (r/R)

0.2 0.4 0.6

Cutting edge

Fig. 10. Maximum principal stress, s1, and minimum stress, s3, along the

drill chisel and cutting edges after 10.2mm depth of drilling.Fig. 9. Drill deformation after 10.2mm drilling in Exp. D183 (scale factor

of deformation: 20).

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172014

with lateral compressive stress. It can be described by thefollowing equation

maxs1st;�

s3sc;s1st�

s1 þ s3sc

� �¼ 1. (7)

The tensile strength st and compressive strength sc aretemperature-dependent. During drilling, the drill tempera-ture and, subsequently, the strength vary temporally andspatially. Hence, the stress limits vary from point to point ina drill. To quantify how close the material is to failure,three dimensionless stresses sr ¼ maxððs1=stÞ;�ðs3=scÞÞ;sm�c ¼ s1=st � s3=sc; and sm�m ¼ maxððs1=stÞ;�ðs3=scÞ;

ðs1=stÞ � ðs1 þ s3=scÞÞ associated with the Rankine,Mohr–Coulomb, and modified Mohr criteria, respectively,are defined. The closer these dimensionless stresses are to 1.0indicates the higher likelihood of material failure.Fig. 11 compares these three dimensionless stresses in the

drill after 10.2mm drilling in Exp. D183. It is noticed thatvalues of sr and sm�m are about the same, but sm�c hasmuch lower value. The maximum values of sr and sm�mare 0.91 at the cutting edge. However, the maximum valueof sm�c is only 0.71, which is located at the chisel edge. Thisdifference lies in the fact that sm�c does not consider thelimit of normal stress. At the cutting edge, the stress state iscloser to the compressive strength than to the shear stresslimit as defined by the Mohr–Coulomb criterion. Based onthis observation, the modified Mohr criterion is selected toanalyze the drill stress because it includes the maximumnormal stress limit.The contour plots of sm�m of three wet drilling

experiments are shown in Fig. 12. Dry and wet drillingexperiments have a totally different pattern of sm�m. InExp. D183 (Fig. 11), the highest sm�m ( ¼ 0.91) is locatedat the cutting edge. This is primarily due to the highcompressive stress and the low tensile strength st andcompressive strength sc due to high temperature at thecutting edge. In Exps. W183, W91, and W61 (Fig. 12),sm�m at the cutting edge is much smaller compared withthat of Exp. D183, and the highest sm�m is located at thechisel edge. This is due to the increase of tensile strength st

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Fig. 11. Comparison of dimensionless stresses, sr, sm�c, and sm�m, after 10.2mm depth of drilling in Exp. D183.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–2017 2015

and compressive strength sc at low temperature, especiallyin the cutting edge. The supply of cutting fluid decreasesthe maximum sm�m from 0.91 in Exp. D183 to 0.75 in Exp.W183. Under the wet drilling condition, the maximumsm�m increases from 0.75 in Exp. W183 to 0.77 and 0.84 inExps. W91 and W61, respectively.

The high tool temperature promotes diffusion wear,while high stress induces brittle fracture. In dry drilling(Exp. D183), the temperature and dimensionless stress atthe cutting edge are both high, which results in the severedrill wear at the cutting edge and short drill life. In wetdrilling, the drill temperature is low, but the dimensionlessstress increases with the reduced cutting speed andincreased feed. Thus, the competing factors of temperatureand stress in the chisel edge indicate that an optimumcombination of the cutting speed and feed exists. A high-throughput drilling test using the same peripheral cuttingspeed but a smaller 3.97mm diameter drill shows that thedrill life is very short in dry drilling and the highest drill lifeoccurs at 91m/min cutting speed (0.102mm/rev feed) withan internal cutting fluid supply [3]. This drill life datamatches to the failure analysis results.

7. Concluding remarks

This study developed the computational models andexperimental procedures to predict the spatial and tempor-al distributions of drill temperature and stress for high-throughput drilling of Ti–6Al–4V with an internal cuttingfluid supply. The inverse heat transfer method with a finiteelement thermal model was applied to find the heatpartition on the tool–chip contact region and the convec-tion heat transfer coefficient of cutting fluid for the9.92mm diameter spiral point drill at 384mm3/s MRR.

This study showed that the highest temperature of the drilloccurred in the cutting edge under all four drillingconditions. The modified Mohr criterion predicted thatthe onset of drill failure would initiate in the cutting edgefor dry drilling and in the chisel edge for wet drilling.The supply of cutting fluid via through-drill holes was

found to be critical in reducing the drill temperature.Without cutting fluid, the temperature was high andcontinued to rise during drilling. The supply of cuttingfluid maintained the drill temperature at a constant levelduring drilling and was able to decrease the drill peaktemperature by half after 10.2mm drilling of Ti–6Al–4V.The supply of cutting fluid helped to prevent prematuretool failure due to high drill temperature. The maximumdimensionless stress of the modified Mohr criteriondecreased from 0.91 in dry drilling to 0.75 in wet drillingat 183m/min cutting speed. The results also suggested thatlower peripheral cutting speed and higher feed couldfurther reduce the drill temperature while maintaining thesame MRR, but the chisel edge would undergo increasinglyhigher stress.This study has identified several future improvements on

computational models. The sequential thermo-mechanicalanalysis in this paper assumed the stress solution wasdependent on a temperature field but there was no inversedependency. To simulate the drilling process more accu-rately, a coupled thermo-mechanical modeling will be usedto solve the stress and temperature simultaneously. Severalkey assumptions made in this study, including that theratio of the tool–chip contact length to the chip thickness isconstant across the chisel and cutting edges and indepen-dent of the cutting fluid supply and the same convectioncoefficient used for all wet drilling conditions should beconsidered for future improvements.

ARTICLE IN PRESS

Fig. 12. Distributions of dimensionless stress sm�m at the drill tip after 10.2mm depth of drilling in Exps.: (a) W183, (b) W91, and (c) W61.

R. Li, A.J. Shih / International Journal of Machine Tools & Manufacture 47 (2007) 2005–20172016

This study can be used to aid drill selection, drillgeometry design, and optimization of drilling processparameters. For spiral point drills, the chisel edge drillgeometry can be refined to reduce the peak compressiveprincipal stress at the relative distance to the drill center (r/R), 0.2. This improvement can potentially further enhancethe productivity of drilling Ti and other advancedengineering materials.

Acknowledgments

A portion of this research was sponsored by the HeavyVehicle Propulsion Systems Materials Program and Ad-vanced Materials for High BMEP Engines Program, Officeof Transportation Technologies, US Department of

Energy. Assistance from Parag Hegde and Paul Prichardof Kennametal and Dr. Ray Johnson of Oak RidgeNational Laboratory are greatly appreciated.

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