Drilling of carbon composites using a one shot drill bit.

Part II: empirical modeling of maximum thrust force

Marta Fernandesa,*, Chris Cookb

aSchool of Electrical, Computer and Telecommunications Engineering,

University of Wollongong, Northfields Avenue, 2522 New South Wales, AustraliabFaculty of Engineering, University of Wollongong, Australia

Received 23 September 2004; accepted 22 March 2005

Available online 6 June 2005

Abstract

In order to extend tool life and improve quality of hole drilling in carbon composite materials, a better understanding of ‘one shot’ hole

drilling is required. This paper describes the development of an empirical model of the maximum thrust force and torque produced during

drilling of carbon fiber with a ‘one shot’ drill bit. Shaw’s simplified equations are adapted in order to accommodate for tool wear and used to

predict maximum thrust force and torque in the drilling of carbon composite with a ‘one shot’ drill bit. The mathematical model is dependent

on the number of holes drilled previously, the geometry of the drill bit, the feed used and the thickness of the workpiece. The model presented

here is verified by extensive experimental data.

q 2005 Published by Elsevier Ltd.

Keywords: Drilling; Mathematical model; Carbon composite; Tool wear

1. Introduction

The increasing popularity of carbon composites in

industry and the constant need to maximize productivity

has lead researches to look at methods of optimizing the

drilling process. For example, as part of the production

process for modern aircraft where thousands of holes must

be drilled into composite materials as part of the

manufacturing process for a single set of ailerons. There

are several problems associated with drilling carbon

composites, as already discussed in part I of this paper. In

Part I of this study, the maximum thrust force produced

during drilling was shown to be related to the wear of the

drill bit, and many researchers drilling carbon composite

with various drills relate the force before break through to

delamination and consequently the quality of the hole [2–6].

Being able to accurately predict the thrust force could

therefore be used to optimize the drilling parameters during

drilling, avoiding defects and optimising the drilling

process.

0890-6955/$ - see front matter q 2005 Published by Elsevier Ltd.

doi:10.1016/j.ijmachtools.2005.03.016

* Corresponding author.

Neural Networks have been used to predict thrust force

and torque in drilling operations [7–10], as has fuzzy logic

[11]. These methods allow the development of a model

without the understanding of the mechanical process.

However, without this understanding system optimization

can become a very difficult task.

Shaw’s simplified equations have been successfully used

by several authors to predict thrust force and torque on

drilling carbon composites with new twist drills [12,13].

There are two short-comings for these models: the twist drill

bits are not the best choice for drilling carbon composites

(as explained in Part I of this paper) and Shaw’s equations

only hold for new (or re-sharpened) drill bits. This would

not be realistic for a practical application where drilling with

a new or re-sharpened drill bit only happens about once

every 500 holes drilled. A mathematical model that

accounts for other drill bit shapes and also for tool wear is

therefore, necessary.

The data resulting from the experiments described in Part I

of this paper will be used. The experiments consisted of

drilling different thicknesses of carbon fiber at various speeds

using a 5 mm diameter ‘one shot’ drill bit. The typical thrust

force Fz and torque Tz produced while drilling carbon

composite with a one shot drill bit for each thickness can be

seen in Fig. 1.

International Journal of Machine Tools & Manufacture 46 (2006) 76–79

www.elsevier.com/locate/ijmactool

Fig. 1. Typical thrust force and torque at 0.06 mm/rev.

Typical Thrust from current experiments

Typical thrust curve used by Shaw [1]

Steady state

ThrustForce [N]

Distance [mm]

Max Thrust force (Fmax)

Fig. 2. Analogy from maximum thrust force and Shaw’s thrust force.

M. Fernandes, C. Cook / International Journal of Machine Tools & Manufacture 46 (2006) 76–79 77

2. Shaw’s simplified equations

A full explanation of Shaw’s equations can be found in

[1]. Assuming that the specific cutting energy remains

constant,

�uf8T

Fd2(1)

And the thrust force and torque are equal to

F

d2HB

Z K1

f 1Ka

d1Ca

1 K cd

1 C cd

� �a CK2

c

d

� �1Ka

" #CK3

c

d2

� �

(2)

T

d3HB

Z K4

f 1Ka

d1Ca

1 K cd

1 C cd

� �a CK5

c

d

� �2Ka

" #(3)

Where,

F

Thrust force (N)

T

Torque (NmK1)

a, Ki (iZ1,5)

Constants to be determined

d

Drill diameter (mm)

f

Feed (mm/rev)

c

Length of chisel edge

HB

Hardness of the material

�u

Specific cutting energy

d1 d2 d3

Fig. 3. Drill bit diameter at ‘Break-Through’.

Assuming c/d constant the equations can be simplified:

F

d2HB

Z K6

f 1Ka

d1CaCK7

T

d3HB

Z K8

f 1Ka

d1Ca

5F Z K9ðfdÞ

1Ka CK10d2

T Z K11f 1Kad2Ka

(8>><>>:

(4)

The thrust force and torque estimated by Shaw’s

equations are average values during full engagement of

the drill bit, called the steady state region. In many

practical applications in the aerospace and other indus-

tries the drill bit breaks through before full engagement

and therefore the process does not reach the steady state

described in Shaw’s model. The thrust force is at a

maximum just before the drill bit breaks through, and

assuming this happens just after the drill bit fully

engages the workpiece (illustrated in Fig. 2), the

thrust/torque calculated by Shaw could be assumed to

be a fair approximation of the maximum thrust force

obtained in the experiments described here.

This scenario implies that the full diameter of the drill bit

is engaged. In other words, the values of thrust and torque

obtained by Shaw’s model can relate to the maximum thrust

force of the present process if the diameter used is the

diameter of the part of the drill bit which is fully engaged.

Hence, the diameter used for the calculations is not the

diameter of the drill bit, but the diameter of the drill bit at

the time of maximum thrust/torque. Hence, the diameter

will be related to the thickness of the workpiece as shown in

Fig. 3.

As previously explained, Shaw’s equations can be

greatly simplified if the relation c/d remains constant. In

the practical applications considered here, the diameter

varies for the same chisel edge, but the chisel edge of the

drill bit being used is only 0.2 mm and therefore the relation

c/d is much smaller than one. Hence, this variation will be

ignored and Shaw’s simplified equation will be used to

estimate thrust force. As explained and shown in Part I of

this paper, the torque remains fairly constant throughout the

cutting process; hence Shaw’s simplified equations will also

be used to estimate the torque.

y = –0.5847x – 0.1247

–0.1

0

0.1

0.2

0.3

0.4

0.5

–1.2 –1 –0.8 –0.6 –0.4 –0.2 0

log (fd)

log

(u)

0.6

Fig. 4. Plot of log(u) against log(fd).

M. Fernandes, C. Cook / International Journal of Machine Tools & Manufacture 46 (2006) 76–7978

3. Modelling using Shaw’s equations

The first step will be to calculate the value of ‘a’ using the

specific cutting energy based on the measured torque and

the diameter related to the thickness of the sample as

previously explained. The value of ‘a’ is dependent on the

combination drill bit and material of the workpiece and is

directly related to the torque produced during drilling. Since

it has been previously shown that the torque produced

during drilling is not significantly affected by tool wear it

will be assumed that for the range of settings used ‘a’ will be

constant. By plotting log(fd) against log(u) a value for a of

0.603 is obtained as shown in Fig. 4.

3.1. Estimating torque at Break-Through

Using ‘a’ above, Shaw’s simplified equation to estimate

torque (Eq. (4)) becomes,

T Z kf 0:39d1:39 (5)

Fitting experimental data to Eq. (5) and averaging the

resultant value of k,

T Z 0:13 � f 0:39d1:39 (6)

The results obtained by using Eq. (6) to estimate the

torque can be seen in Fig. 5. The estimated values agree

fairly well with the measured values. A few discrepancies

can be seen for some holes but taking into consideration that

01 15 29 43 57 71 85 99 113127141

0.1

0.2

0.3

0.4

0.5

0.6

Hole

Tor

que

[Nm

] Estimated Torq

Fig. 5. Measured and estimated tor

the torque is a very small signal (easily perturbed by noise)

the results are satisfactory.

4. Estimating maximum thrust force

The following equation (Shaw’s simplified equation) will

be used to estimate the maximum thrust force,

F Z K1ðfdÞð1KaÞ CK2 (7)

The maximum thrust force is strongly affected by tool

wear and therefore Shaw’s model has to be adapted in order

to accommodate for tool wear. In the experiments

conducted here, only data from the first holes drilled by a

drill bit was used in order to calculate K1Z76.56 and K2Z1.04 (using the least squares method), giving:

Fðf ;dÞ Z 76:56ðfdÞ0:39 C1:04d2 (8)

As seen in Fig. 6, the estimated values agree with the

measured values for the first holes drilled. It can also be seen

that the estimated values have the same trend as the

measured values for later holes, but the difference in

amplitude increases with the number of holes drilled.

5. Compensation for tool wear

This shows that although Shaw’s model can be used to

estimate thrust force on drilling of carbon composites using

a new ‘one-shot’ drill bit, the model needs to be adjusted for

tool wear, for example, consider:

Fðf ;d;wearÞ Z ToolwearCoefficient!ð76:56fd0:39 C1:047d2Þ

(9)

where the tool wear coefficient will be dependent on the

number of holes drilled by the drill bit. It is also expected that

tool wear will affect the thrust force differently for each of the

different thicknesses of workpiece being tested, so that:

ToolWearCo efficientðn; thicknessWorkpieceÞ Z k1n Ck2 (10)

where n is the number of holes drilled by a bit and k1 and k2

were calculated using experimental data for each thickness of

155 169 183 197 211 225 239 253 267 281 295

Number

Measured Torque

ue

que using Shaw’s equations.

01 17 33 49 65 81 97 113 129 145 161 177 193 209 225 241 257 273 289

50

100

150

200

250

300

Hole Number

For

ce [N

]

Estimated Force

Measured Force

Fig. 7. Measured and estimated maximum thrust force.

01 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290

50

100

150

200

250

300

hole number

For

ce [N

]

Estimated Force

Measured Force

Fig. 6. Measured and estimated maximum thrust force using Shaw’s

equations.

M. Fernandes, C. Cook / International Journal of Machine Tools & Manufacture 46 (2006) 76–79 79

workpiece. The estimated Thrust force calculated from Eq. (9)

was divided by the measured thrust force to give the tool wear

coefficient for each sample. Plotting the tool wear coefficient

against the respective hole number, and fitting a line of best fit,

the parameters k1 and k2 can be found and the maximum thrust

force Fmax (Fig. 2) will be,

F max2 mm sample Z ð0:003n C1:0467Þ!ð76:56ðfdÞ0:39

C1:047d2Þ ð11Þ

F max4 mm sample

Z ð0:0036n C1:2128Þ!ð76:56ðfdÞ0:39 C1:047d2Þ

F max5 mm sample

Z ð0:0035n C1:5159Þ!ð76:56ðfdÞ0:39 C1:047d2Þ

As seen in Fig. 7, the new model represents the drilling

process very well. Some discrepancies between the estimated

and measured values would be expected to result from noise on

the measured values, and also from the approximation in the

tool wear model. Although wear is dependent on spindle speed

and drilling time (number of holes), on this model it was

assumed that the rate of tool wear was constant for the range of

drilling parameters used.

6. Conclusions

It has been shown in this paper that Shaw’s simplified

equations can be used to provide good estimates of

maximum thrust force and torque for drilling of carbon

composites using a new ‘one shot’ drill bit. It has also

been shown that Shaw’s equation for thrust force does

not hold for older drill bits and has to be corrected for

the effect of tool wear. Furthermore, the tool wear

correction is dependent on the thickness of the work-

piece. A mathematical model has been developed which

successfully estimates maximum thrust force and torque

produced during drilling of carbon fibre using a one shot

drill bit. Applications for this model include: Finding the

feed which will keep the thrust force under a critical

value (and therefore, avoid delamination); Estimating tool

life for a certain application by relating the force

produced to the quality of the holes produced; and

enabling defects to be detected when actual forces

modelled exceed modelled limits.

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