The international journal of advanced manufacturing technology, tập 59, số 1 4, 2012

Int J Adv Manuf Technol (2012) 59:1–7
DOI 10.1007/s00170-011-3472-6

ORIGINAL ARTICLE

Dynamics of the guideway system founded
on casting compound
Bartosz Powałka & Tomasz Okulik

Received: 31 December 2010 / Accepted: 13 June 2011 / Published online: 30 June 2011
# The Author(s) 2011. This article is published with open access at Springerlink.com

Abstract The work presents a new technology for the
assembly of ball guideway systems which involves the use
of a thin layer of a casting compound. The experimentally
verified simulation research presented in the work indicates
that the use of the casting compound between the guide rail
and the bed of the machine tool positively influences the
dynamics of the system. The paper is concerned with the
comparison between the new solution with the guide rail
assembly technology presently in use on the basis of a
guideway system consisting of a body and a milling table.
The dynamics was compared with the use of a frequency
response function which had been determined in an impulse
test. The proposed solution is characterised by a higher
dynamic stiffness, which may directly influence the
precision of the machined surfaces.
Keywords Casting compound . Ball rail system .
Guideways . Dynamics

1 Introduction
Linear ball guideways, which are now being used more
often in modern machine tools, have replaced the previously used slide guideways. A considerable disadvantage of
the slide guideway system was the stick–slip phenomenon
B. Powałka (*) : T. Okulik
Institute of Manufacturing Engineering,
Faculty of Mechanical Engineering and Mechatronics,
West Pomeranian University of Technology, Szczecin,
Piastów 19,
70-310 Szczecin, Poland
e-mail:
T. Okulik
e-mail:

which occurred while machining at a low feed rate [1, 2].
This would contribute to the deterioration in the accuracy of
the machine tool positioning. Fortunately, the use of ball
guideways eliminated this phenomenon. The introduction
of ball guideway systems improved the operating properties
of the machine tool frame system by reducing the resistance
to motion and increasing the permissible feed speed. It also
assisted in simplifying the assembling technology compared to the slide guideway system. However, the main
disadvantage of the ball guideway system is its low
damping. Low damping might lead to vibrations, which
may, in turn, lead to the appearance of chatter marks on the
machined surface.
Machine tool constructors have tried to improve the
dissipation parameters of the machine tool body system in
various ways. One of the applied solutions is the use of
composite materials which have high damping qualities

coupled with the high specific stiffness for the construction of the machine tool body system. Such properties of
the composite are achieved by using a material with high
Young module and a material with high damping. Choi
and Lee [3] proposed a spindle construction of carbon
fibre–epoxy, which resulted in an increased natural
frequency and damping than that of the steel spindle.
Suh et al. [4] proposed the use of a carbon fibre composite
laminate for the construction of the spindle cover. Other
examples of the use of composite materials for the
improvement of dynamic stiffness regarded headstock [5]
and machine tool columns [6].
Kim et al. [7] designed a three-axis ultra-precision CNC
grinding machine whose bed was made of resin concrete
which contributed to the increase in the damping capacity.
The effectiveness of the use of resin concrete for the
construction of the bed was verified in the impulse test as
well as while machining hard and brittle materials.


2

The article by Kim et al. [8] presents a research on
sandwich structures composed of fibre-reinforced composite materials, polymer foams and resin concrete in regard to
their use for the construction of a micro-EDM machine
structure. The constructed prototype was characterised by
good stiffness and dissipation properties.
Another interesting way of increasing the damping in
machine tools is the use of viscoelastic materials to
dissipate energy [9, 10]. The concept of viscoelastic
materials is based on the use of constrained layer damping

CLD [11, 12]. The vibration damping mechanism in the
structures consisting of a viscoelastic layer bounded by
steel sheets on both sides was examined by Chen et al. [13],
who used the theory devised by Ungar [14].
Wakasawa et al. [15] examined structures packed with
balls. The use of such structures allowed for a considerable
increase in the damping capacity. The research took into
consideration the influence of the ball size, ball arrangement as well as the degree in which they were packed
together and the direction of excitation on the increase and
stability of the damping capacity.
An increase in the damping capacity might also be
achieved thanks to the use of cementitious materials [16].
Rahman et al. [17] investigated the influence of machining
on two lathes, a ferrocement bed lathe and cast iron bed
lathe, on the tool life. The improvement in tool life for the
ferrocement bed lathe was attributed to its higher damping
capacity.

Fig. 1 a The view of the samples used in the investigation. b The
characteristics of the load used in the investigation

Int J Adv Manuf Technol (2012) 59:1–7

Fig. 2 The schema of the test stand for determining the deformations
of the contact layer

An increase in the dissipation properties might also be
achieved using polymer inserts in the construction of the
guide carriage [18]. The use of a polymer impregnated
concrete damping carriage was compared with a steel

damping carriage. The polymer impregnated concrete
damping carriage appeared to be a better solution than the
steel damping carriage due to the increase in the damping
capacity within the frequency range of up to 650 Hz.
The application of the casting compound, presented in
this paper, was motivated by the need to eliminate machine
tool bed grinding required before guide rail assembly. The
grinding operation is expensive, especially in the case of
large-size machine tools. If the machine tool bed is finished
by milling instead of grinding, it will increase productivity
and cut production costs considerably. Milled surfaces are
expected to have a lower contact stiffness than ground
surfaces which is due to the lower real contact area. In this
paper, a layer of EPY (tradename) casting compound [19] is
applied between a guide rail and the machine tool bed as
the damping material to compensate for the decrease in

Fig. 3 The graph of the deformations registered for sample C by the
sensor located inside the sample for the examined thicknesses of the
EPY resin layer in comparison with the reference sample A


Int J Adv Manuf Technol (2012) 59:1–7

3

Fig. 6 Schema of the physical model of the milling table
Fig. 4 Comparison of the contact stiffness for various thicknesses of
the EPY resin layer

contact stiffness. EPY material is used in the seating of
main engines, gears, power generators, compressors,
bearings, stern tubes, tanks and many other naval
machinery. First, we examined the effect of the thickness
of the EPY layer and machining method on the contact
stiffness and damping capacity. The obtained results were
used to build a simulation model of a machine tool
guideway system presented in chapter three. Model
research presented in the work indicated that the use of
a thin layer of EPY improves the dynamic characteristic
of the machine tool. The positive influence of the use of
the EPY layer obtained as a result of numerical
simulations was confirmed experimentally.

2 Static tests of the samples
In order to verify the new method of assembling the ball
guide rails with the use of a layer of EPY, it was checked
how its usage influences contact stiffness and damping of
the joint of the guide rail and the bed sample. Therefore, the
experimental research was conducted by means of the use
of three bed samples of various surface quality and
roughness of the assembling surface. The surface of sample
B (Ra =4.095 μm, Rz =21.80 μm) was precisely milled. The

Fig. 5 Comparison of the damping capacity for various thicknesses of
the EPY resin layer

surface of sample C (Ra =8.152 μm, Rz =39.50 μm) was
milled with a worn cutter, while the surface quality of
sample D (Ra =7.898 μm, Rz =39.28 μm) was like the

surface of a billet. Figure 1a presents the samples used
during the research. Additionally, sample A (Ra =0.126 μm,
Rz =1.27 μm), whose surface was ground in accordance
with the current assembling technology, was used in the
research as a reference point for comparison.
The guide rail was fixed to the bed sample using an
intermediate layer of EPY resin with the thickness of 0 to
5 mm. The thickness of 0 mm was assumed to be a state in
which a surplus of the thin EPY layer on the sample was
squeezed out by the rail. The intermediate layer filled
only the irregularities of the surface resulting from the
machining.
The samples were subject to quasi static compression
on the INSTRON testing machine and their force–
displacement responses were measured. Figure 2 presents
a schema of the research stand for determining the
deformations in the contact layer on the joint of the rail,
the EPY layer and the bed sample. Figure 1b presents the
characteristics of the quasi static load used during the
research. The loading force increased sinusoidally to the
value of Fmax =80 kN, in time t2=80 s. Time t1 and t3
were equal to 2 s.
Figure 3 presents the displacements registered for sample
C by the sensor situated inside the sample for all the
examined thicknesses of the EPY resin layer in comparison
to the reference sample (A), which corresponded to the
guide rail current assembling technology. It might be
noticed on the graph that the use of the thin (0 mm) layer
of EPY resin slightly increases the deformations of the

Fig. 7 Difference in the investigated models


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Int J Adv Manuf Technol (2012) 59:1–7

Fig. 10 The view of the stand for the milling table examination

Fig. 8 Frequency response function for direction Y for the analysed
models

contact layer, i.e. there is a slight decrease in the static
stiffness. It was found that an increased thickness, over
2 mm of the EPY resin layer significantly reduces the
contact stiffness of the joint.
The contact stiffness and the damping capacity were
determined as a result of the conducted quasi static compression tests on the bed samples. Figures 4 and 5 present the
experimentally obtained coefficient values. The first bar in
each graph corresponds to reference sample A machined in
accordance with the technology used so far. The second bar
corresponds to the samples which were not ground (B, C, D)
and where the intermediate contact layer was not used. The
subsequent bars correspond to the samples with an increasing thickness of the intermediate layer. It might be noticed on
graph 4 that the contact stiffness of the samples without the
EPY layer (13,085 N/μm—sample B) is close to the stiffness
with the ‘0’ layer (11,789 N/μm—sample B). In the case
of sample B, for which the value of the contact stiffness
for the ‘0’ thickness is the highest, a 25% decrease in
stiffness was observed in comparison to sample A. Based

on the comparison between Fig. 5 it might be concluded
that the highest damping capacity of 0.412 appears for the

Fig. 9 Frequency response function for direction Z for the analysed
models

‘0’ thickness of EPY layer. The damping capacity for the
‘0’ thickness of the resin layer is the highest for sample B
and it is ten times higher than for sample A (0.038). Thus,
the use of the thin layer of EPY on the milled surface
might have a positive influence on the dynamic stiffness
of the system: a slight decrease in static stiffness will be
compensated by a significant increase in damping capacity.
Since the most promising results were obtained for the
assembly of guide rails on the milled surface (sample B)
with the use of the ‘0’ thickness layer of EPY (0 mm), only
this solution is compared to the traditional solution in
regard to its dynamic stiffness in the simulation research.

3 Dynamic response of the milling table model
The contact stiffness and damping capacity obtained from
the static experimental research were used to build a
simulation model of the milling table mounted to the bed
using guide rails. The goal of the analysis was to
investigate the influence of a decrease in contact stiffness
with the simultaneous increase in damping capacity on the
dynamic stiffness observed for the guide rail mounted to the
bed via intermediate layer of EPY resin. Figure 6 presents a
schema of the physical model of the milling table together
with the assumed location of the machining force. The

simulation research was conducted for two variants of the
guideway system assembly.
In the first simulation model, the stiffness and damping
parameters corresponded to the current technology for
assembling the guide rails (steel–steel contact, parameters

Fig. 11 Schema of the test stand used for the dynamics tests


Int J Adv Manuf Technol (2012) 59:1–7

5

Fig. 14 The location of the points used in the comparative analysis

Fig. 12 The location of the measurement points in the dynamics tests

of sample A). The stiffness and damping parameters
implemented in the second model tested in the simulation
were those for assembling the guide rails on a thin layer of
EPY (steel–EPY layer–steel contact, parameters for sample
B for 0 mm EPY). Figure 7 schematically presents the
models used in the numerical simulation.
It follows that since the machining force has a dynamic
character, its dynamic characteristics play a very important
role in the evaluation of machine tool performance. The
dynamics of the machine tool are frequently represented in
terms of frequency response functions (FRFs). The amplitude of FRFs and, in turn, the level of vibrations depends
on the stiffness and damping parameters of the machine
tool. Thus, the frequency response function can be used to

evaluate the impact of a simultaneous decrease of the
contact stiffness and an increase of damping capacity on the
dynamic performance of the guide rail mounted via the
intermediate layer of the EPY.
Figures 8 and 9 present the frequency response functions
obtained for the simulation model of the milling table, for
direction Y (Fig. 8) and direction Z (Fig. 9), respectively.

Fig. 13 A fragment of the guideway connection with a thin layer of
EPY resin—the second stage of the investigation

Direction X was disregarded due to the fact that for the
prepared model the stiffness in this direction depended
mainly on the stiffness of the lead screw and, thus, the
differences in FRF for the two considered models were
negligibly small. It might be noticed on the graphs that the
use of the thin layer of EPY reduces the amplitude of the
system’s response to the dynamic excitation. For direction Y,
there was a decrease in the amplitude of about 58%
compared to the technology for assembling guide rails
used so far as well as a slight decrease in the natural
frequency from the value of 553 Hz to the level of 547 Hz.
For direction Z, a decrease of about 54% in the amplitude
was observed, while maintaining the same resonance
frequency of the simulated system. Numerical simulation
on a simple model indicated that the use of the thin layer of
EPY positively influenced the dynamic stiffness of the
examined guideway system.

4 Experimental dynamic tests

As numerical simulations presented in section 3 show there
is an improvement of dynamic properties of the milling
table model with its guideway when a thin layer of EPY is
used. The authors were encouraged to perform an experimental verification of the obtained results. The test stand

Fig. 15 FRF at point 12 due to excitation at point 23 in direction +Y


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Int J Adv Manuf Technol (2012) 59:1–7

Fig. 17 Vibration mode at 455.4 Hz

Fig. 16 FRF at point 12 with excitation at point 22 in direction −Z

used for this purpose, presented in Fig. 10, is geometrically
similar to the simulation model.
The stand consisted of a body element with a table
supported by the linear ball bearings. The body was
made of grey cast iron. The mass of the body element
was ca. 314 kg. The guideway connection was made
with the use of ball guideway elements of Bosch-Rexroth
which consisted of two guide rails of 25 and 1,410 mm
in length, on which four guide carriages of 25 in length
and catalogue number 1605-213-10 were moving (two
carriages per each rail). The carriages of the guideway
system had the preload equal to 2% of their dynamic
load capacity. The dynamic load capacity of each
carriage was 22,800 N. A table, also made of grey cast

iron, with a mass of 69.4 kg was mounted on top of the
carriages. The guideway elements were founded with the
use of side fixing slits in accordance to the recommendations of the guideway system producer. The screw
connections of the guideway system were tightened up
with a torque recommended by the producer. In addition,
a turned lead screw with an external diameter of 24 mm
and the lead of 6 mm was used to position the table.
Front-end Scadas III was used during the investigation
of dynamics for the data acquisition. The excitation was
performed by means of a Kistler modal hammer. Kistler and
PCB accelerometers were used for measuring system
response. The measurement data were processed with the
use of LMS Test Lab software. Figure 11 presents the
experimental set-up used for investigation of dynamics.

Thirty-three measurement points were located on the
tested object including: eight points on the guide rails, eight
points on each body element, four points on guide carriages
(one on each carriage) and 13 measurement points on the
table. Triaxial accelerometers were used to measure the
vibration signal in each measurement point. The location of
the measurement points is presented in Fig. 12.
During the investigation, the tested system was
excited successively at two points. One of the excitation points was located in the central point of the table
and the direction of excitation for this point corresponded to −Z. The second excitation point was located
on the side surface of the table near the guide carriage. In
this case the direction of excitation corresponded to +Y.
The frequency response functions were determined for
each of the tested directions based on 30 realizations of
the excitation signal.

Investigations were conducted for the guideway with and
without a thin layer of EPY (Fig. 7). First, the test stand
was assembled in accordance with the assembling technology recommended by the producer of the guideway
systems. Between the guide rail and the body element there
was a steel–steel contact. Then the guideway system was
disassembled and a thin layer of EPY was inserted between
the guide rail and the body element. During the assembly,
the surplus of the intermediate layer was squeezed out only
to fill the irregularities on the contact surfaces of the
guideway system. Figure 13 presents a fragment of the
guideway connection with a thin layer of EPY used during
the second stage of the investigation. Excitations and
measurements points are shown in (Fig. 14).
Figure 15 shows FRF at point p12 due to excitation at
point p23 (Figs. 12 and 14) within the frequency range
from 30 to 1,000 Hz. Application of the EPY results in a
decrease of amplitudes in the vicinity of dominant
resonances. The observed amplitude reduction varies from
18% for the dominating mode around 309 Hz to 40%, for

Table 1 Modal parameters of the investigated object
Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Mode 7

Mode 8

fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%] fn [Hz] ζ [%]
With EPY
Without EPY

62.0
62.8

3.41
3.23

77.6
80.3

1.93
1.71

86.9
88.1

1.49
1.71

305.9

308.43

0.64
0.57

329.1
332.2

0.66
0.55

452.0
455.4

0.94
0.47

488.2
495.5

0.60
0.31

606.3
621.6

0.54
0.47

Int J Adv Manuf Technol (2012) 59:1–7

the 605 Hz resonance. Figure 16 presents the FRF
measured at point p13 due to excitation at point p22.
Similarly, an improvement of the dynamic performance of
the system is observed. A significant drop of FRF
amplitude has been observed in the vicinity of 500 Hz
(about 48%). The amplitude reduction and also a
decrease of resonance frequencies can be attributed to
the increased damping introduced by the application of
the EPY layer. Table 1 summarizes the modal parameters
of the compared configurations.
An improvement of damping ratios (ζ) is more significant for modes that exhibit relative table–machine tool bed
motion. For instance, the damping ratio of Mode 6 has
improved by 100%. This mode is visualized in Fig. 17.

5 Discussion and conclusions
The impulse tests conducted on the described test stand
validate the statement that the use of a thin layer of EPY
improves the dynamic performance of the object. An
increase in the dynamic stiffness of the system was
obtained for two tested perpendicular directions Z and Y.
An increase in the dynamic stiffness resulting from the
increased damping capacity in the EPY layer occurred in the
areas of dominant resonances. These resonances are responsible for the dynamics of the tested system. This means that
the decrease in stiffness resulting from the use of the thin layer
of EPY is compensated with a significant increase in damping
capacity. The increase might be caused by the convection of
the mechanical energy of vibrations into the thermal energy on
the resin–steel contact [12, 13] or by an increase of the

effective contact surface as the resin fills all the irregularities
of the connected surfaces [19]. The explanation for the
complex mechanism of the damping of vibrations in the thin
layer of EPY resin is beyond the range of this work.
The presented proposal for the assembly of guideway
systems that make use of a layer of EPY resin might be
very attractive from the practical point of view. The
attractiveness results from the reduction in the costs of
preparing the assembled surfaces for the guide rails by
eliminating the expensive grinding operation. An undeniable advantage of the method is also its simplicity as it
does not require the construction of any special equipment. The solution presented in the work is the subject
of patent application no P388153 in the Patent Office of
the Republic of Poland.
Acknowledgement The work was financed from the resources for
science in the years 2009–2010 as a research project no. N503
174637.

7
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.

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Szczecin


Int J Adv Manuf Technol (2012) 59:9–19
DOI 10.1007/s00170-011-3469-1

ORIGINAL ARTICLE

Drilling performance of green austempered ductile iron
(ADI) grade produced by novel manufacturing technology
Anil Meena & M. El Mansori

Received: 17 January 2011 / Accepted: 13 June 2011 / Published online: 7 July 2011
# Springer-Verlag London Limited 2011

Abstract Machinability study on drilling of green austempered ductile iron (ADI) grade was conducted using a
TiAlN-coated tungsten carbide drill. The green ADI grade
was produced by a novel manufacturing technology known
as continuous casting-heat treatment technology to save
energy and time in foundry. However, in spite of good
combination of strength, toughness and enhanced wear
resistance, the microstructural properties of ADI sometimes
lead to machinability issues. The effect of cutting parameters on cutting force coefficients, chip morphology, and
surface integrity of the drilled surface were discussed.
Results showed that the strength properties of novel ADI
are comparable to that of ASTM grade 1 ADI, whereas
percent elongation is comparable to that of ASTM grade 2
ADI. Results obtained also showed that the combined effect
of cutting speed at its higher values and feed rate at its
lower values can result in increasing cutting force coefficients and specific cutting energy. At higher cutting speed,
hardness values increases at the subsurface layer of the
drilled surface due to plastic deformation.
Keywords Austempered ductile iron . Novel manufacturing
technology . Drilling . Cutting force coefficients . Surface
integrity

1 Introduction
Austempered ductile iron (ADI) is an alloyed heat-treated
ductile cast iron [1]. In recent years, ADI has emerged as a
A. Meena (*) : M. El Mansori
Arts et Métiers ParisTech,
LMPF-EA 4106, Rue Saint Dominique, BP 508,
51006 Châlons-en-Champagne, Cedex, France
e-mail:

major engineering material due to its high strength and
hardness, coupled with substantial ductility and toughness
[2]. The attractive properties offered by ADI are attributed
to a unique “ausferrite” microstructure that is induced by
austempering heat treatment process [3]. Ausferrite consists
of graphite nodules embedded in a matrix of acicular ferrite
and carbon enriched austenite [4]. However, this unique
microstructure significantly affects mechanical and thermal
machining properties due to its high strength, hardness, and
the inclination of its retained austenite to strain hardening,
which leads to short contact length and higher mechanical
loads on the cutting tool’s edge [5]. From the machinability
point of view, the characteristics of ADI derived from the
austenite are a low thermal conductivity and high workhardening coefficient [6]. The austenite lattice has a higher
tendency to deform due to the greater number of sliding
planes, while the increase in strength and hardness during the
deformation also results as a transformation of retained
austenite to martensite. During machining, the chips are
formed on the basis of catastrophic failure in narrow shear
surface due to low thermal conductivity of austenite. In such a
way, unfavorable, segmental chips are formed [7]. This limits
the use of the material in the various industrial sectors and
causes: the formation of built up edges (BUEs) when carbide
tools are used, low tool life, increased cutting forces, and the
appearance of unfavorable tough chips during machining.
From the open literature [8–12], it was found that very
few studies have dealt with the drilling of ADI specifying
the effects of cutting parameters on chip morphology and
the resultant chip formation process. Drilling is, however, a

major machining process for many applications. Indeed
ADI material, thanks to its high strength to weight ratio and
enhanced mechanical properties, predestine this material to
act as a substitute for forged steel and cast iron components.
As such, ADI with current applications in connecting rod
and crankshaft is of increasing interest in automobile


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Int J Adv Manuf Technol (2012) 59:9–19

industries for which drilling is one of the most critical
machining processes. An insightful understanding of the
machinability of ADI material can lead to a better process
economics, increased process stability, improved tool life, and
reduced tooling cost. Due to its high strength and hardness
properties, the cutting tools for machining ADI should
fundamentally yield at the same time; have high temperature
hardness and strength, show excellent hot chemical inertness
as well as high toughness at the higher temperatures [13]. To
meet all these requirements, TiAlN-coated tungsten carbide
tools have been used for all experiments. Titanium-based
coatings, especially TiAlN (titanium aluminum nitride), are
used in a broad range of machining operations. TiAlN
coatings are well known for their excellent wear and
oxidation resistances, which enable improved machining
process at high material removal rates. During high
temperature applications of this coating, a very dense and
strongly adhesive layer of aluminum oxide (Al2O3) is formed

by aluminum atoms diffusing to the surface preventing
further oxidation. Because of its super saturated metastable
phase, the TiAlN-coatings also show age hardening effect,
which increases its hardness at the higher temperatures [14].
This paper thus focuses on the feasibility of novel
manufacturing technology to produce ADI and its impacts
on the material properties of ADI. It also focuses on the
Fig. 1 Schematic representation
of conventional and novel heat
treatment process for ADI

experimental studies of cutting force coefficients, chip
morphology, and surface integrity of drilled surface while
drilling green grade of ADI with TiAlN-coated tungsten
carbide tools under flooded conditions for different speed–
feed rate combinations.

2 Experimental procedure and sample preparation
2.1 Workpiece material
Specimens were produced by a novel manufacturing
technology known as continuous casting-heat treatment
technology developed by the integration of the casting
(metallic mold) and heat treatment process in the foundry
[15]. In this process, spheroidization and inoculation were
performed when the molten material temperature reached
1,450°C. Spheroidization was done in tundish ladle and
subsequently inoculation was done in a pouring ladle. For
spheroidization and inoculation FeSi–Mg (ferrosilicon
magnesium) and FeSi (ferrosilicon) were used, respectively.
The molten material was then poured in a metallic mold to

make the specimens of size 180 mm ×30 mm×15 mm
rectangular blocks. In the temperature range of 1,000–
1,100°C, the casting was shaken free of the metallic mold

Pouring
Casting shake-out

Austenitization

Temperature (°C)

Novel
process

Quenching
Austenite

Pearlite
Austempering
Ausferrite

Bainite

Conventional
process
Ms

Austenitizing

Austempering

Time


Int J Adv Manuf Technol (2012) 59:9–19

11

Fig. 2 Experimental setup

Coolant supply
Drill tool

Dynamometer
Workpiece material

and put in a muffle furnace for austenitization. The
austenitization treatment was then carried out at 900°C
for 90 min. After austenitization, the specimens were
quenched down to 500°C in a fluidized bed furnace (at
room temperature) and then austempered in another
fluidized bed for 90 min at 370°C and then air cooled. A
schematic representation of the conventional heat treatment process using a sand mold and novel heat treatment
process using a metallic mold are shown in Fig. 1. The
chemical composition of the obtained specimens is as
follows: 3.54% carbon (C), 2.54% silicon (Si), 0.29%
manganese (Mn), 0.18% molybdenum (Mo), 1.19%
copper (Cu), 0.63% nickel (Ni), 0.0095% sulfur (S), and
0.043% phosphorus (P).
Alloying elements such as nickel, molybdenum, and

copper are usually added in ADI to alter the transformation
behavior of ADI [16]. The alloying elements added in ADI
also increase the hardenability of the matrix sufficiently to
ensure that the formation of pearlite is avoided during the
quenching process [17]. Carbon in the range of 3–4%
increases the tensile strength but has a negligible effect on
elongation and hardness [17], Si within the range of 2.4–
2.8% increases the impact strength of ADI and lowers the
ductile brittle transition temperature [17], Mn level in ADI
should be restricted to less than 0.3%, it strongly increases
hardenability [18], Mo is added as a hardenability agent in
ADI, it should be restricted below 0.2% [17], the higher Cu
content increases the austenite fraction in the final matrix
[18] and up to 2% Ni increases the hardenability of ADI,
and it also decreases the reaction rate of austempering [19].
Spheroidization and inoculation practices are important
for the production of spheroidal graphite and to control the
graphite nodule counts and its size in the matrix [17].

Spheroidizing, or magnesium treatment, of cast iron is a
means of modifying the solidification structure. It promotes
the graphite phase precipitates to grow as spherical particles
instead of flakes, thus resulting in a cast iron with
significantly improved mechanical properties [20]. It
prevents unwanted slag to store as a mass, and it promotes
the dispersion of microparticles, which act as potential sites
for graphite nucleation during solidification. Hence, an
effective spheroidizing process also gives a good basis for
inoculation [21]. Inoculation is the process of increasing the
numbers of nucleating sites from which eutectic graphite

grows during solidification. Most inoculants are based on
ferrosilicon that contains 70–75% silicon or ferrosilicon–
graphite mixtures [22].
Tensile testing of samples was performed according to
ASTM E-8 standard. The test was carried out at a constant

2 mm
Fig. 3 Tool tip (TiAlN-coated tungsten carbide drill tool)


12

Int J Adv Manuf Technol (2012) 59:9–19

Table 1 The drilling test matrix used in this work utilizing the four
feeds marked A–D (0.06–0.12 mm/rev) and five speeds marked 1–5
(10–90 m/min)
RPM (m/min)

398
(10)
1

1,194
(30)
2

1,989
(50)
3

2,785
(70)
4

3,581
(90)
5

Feed (mm/rev)
0.06

A

24

72

119

167

215

0.08
0.10

B
C

32
40

95
119

159
199

223
278

286
358

0.12

D

48

143

239

334

430

The value shown corresponds to the tool feed in millimeters per

minute

engineering strain rate of 10 mm/min on an MTS (material
testing system) servo-hydraulic machine (MTS810) at room
temperature in an ambient atmosphere. Hardness test was
performed using a Buehler MacroVickers 5112 tester with
an applied load of 20 kgf. The hardness value is the average
of five different values taken in the different zones for each
sample.
2.2 Drilling test and experimental design
The drilling experiments were carried out using the Deckel
Maho five axis machining center of model DMU 80 P
(Fig. 2). The machining tests were conducted using the
TiAlN-coated tungsten carbide tools of diameter 8 mm. The
tool was produced by Sandvik Coromant with tool
reference R840-0800-30-A0A 1220 (helix angle 30°, point
angle 140°). The tool tip of the drilling tool is shown in
Fig. 3. Ecocool cat+ has been used as a coolant with a
Fig. 4 Microstructure of green
ADI grade produced by novel
manufacturing technology

20 µm

viscosity of 35 mm2/s at 40°C. A 5× 4 matrix was
developed (see Table 1) that covered four tool feed rates
0.06, 0.08, 0.10, and 0.12 mm/rev and five cutting speeds
10, 30, 50, 70, and 90 m/min (corresponding to the spindle
speeds of 398, 1,194, 1,989, 2,785, and 3,581 rpm,
respectively). The resulting feed rates in millimeters per

minute are shown in Table 1. For example, case A5
corresponds to cutting speed of 90 m/min (3,581 rpm)
and feed of 0.06 mm/rev (215 mm/min), respectively. Each
experiment has four repetitions. Chips were collected after
each experiment. Thrust and torque components acting on
the tool post were measured with a two-component
dynamometer of type 9271A made by Kistler. Surface
roughness measurements Ra (arithmetic surface roughness)
were performed inside the holes using a stylus-based
instrument (Hommel wave) having an accuracy of 0.5 μm
with a cut-off length of 0.8 mm.
2.3 Sample preparation
ADI samples for metallography were polished, etched, and
examined using standard metallographic techniques. The
number of graphite nodules per square millimeter was
determined on the unetched sample surface by taking the
average of 10 different regions using an optical microscope.
The morphology, microstructure, hardness, and average
thickness of chips were investigated after mounting in cold
resin and metallographic preparation. Chip morphology and
microstructure were investigated with an optical and scanning electron microscopes. Microhardness measurements
were conducted using a 1600-5101 MicroMet analog microindentation hardness tester. A load of 50 gf and a dwell time
of 10 s was used for microhardness measurements.


Int J Adv Manuf Technol (2012) 59:9–19

13

Table 2 Comparisons of the graphite morphology and mechanical properties of novel ADI and conventionally produced ADI

ADI

Graphite (%)

Novel ADI

9.0

ASTM grade 1
ASTM grade 2
Conventional ADI [36]

8.9

Tensile strength
(MPa)

Yield strength
(MPa)

885

645

850

550

1,050
1,082

700
782

3 Results
3.1 Workpiece characterization
The obtained microstructure (Fig. 4) consists of a matrix of
acicular ferrite and carbon enriched austenite with graphite
nodules embedded in it. The gray needles and the white region
between the needles in the micrograph is known as ausferrite
matrix and the white bulky region is untransformed austenite
volume (residual austenite) [23]. Image analysis of optical
micrographs of unetched samples gave a volume fraction of
graphite of 9%, with a mean nodular graphite density of
1,200 nodules/mm² and a mean graphite nodule size of 8 μm.
Such a microstructure provides higher strength and
elongation properties as compared to the as-cast ductile
iron. The graphite morphology and mechanical properties
of novel ADI and conventionally produced sand mold ADI
is shown in Table 2. As shown in Table 2, the graphite
nodule counts of novel ADI is higher than that of
conventional ADI. This can be explained by the increase
in heat transfer and solidification rates in a metallic mold as
compared to the sand mold which gives rise to higher
nodule counts. It can be seen (Table 2) that the strength
properties of novel ADI are comparable to that of ASTM
grade 1 ADI while elongation percentage is comparable to
that of ASTM grade 2 ADI.
Fig. 5 Measured thrust and
torque for the case A5 (cutting

speed=90 m/min and feed=
0.06 mm/rev)

Nodule count
(nodule/mm2)
1,200

Elongation (%)

7.5

Hardness (HV)

300–310

10
169

7
10.3

303

The novel manufacturing technology using the die casting
leads to the production of ADI with fine-grained microstructure
and low porosity by improving the feed of molten metal into
the casting. It acts as an attractive alternative for lightweight
alloys where the strength to weight ratio becomes a key design
variable. It increases the graphite nodule counts and decreases
the grain size as compared to the conventional sand-cast ADI.

As the permanent metallic mold is used, direct heat treatment
can be made without cooling the casting. This reduces the
process time and energy requirement for heat treatment. In this
way, the novel manufacturing technology is a high-speed
production process which gives a good dimensional accuracy
and stability to the final product without any casting defect.
3.2 Cutting force coefficients and specific cutting energy
For a given chip section, any variation of cutting force with
cutting speed can be attributed to variation in cutting force
coefficient. The cutting force coefficient is influenced
largely by the cutting temperature [24]. The average torque
(N-m) and thrust force (N) generated during drilling for
each individual hole was calculated within the time period
corresponding to the drill’s first contact with the workpiece
surface and its complete retraction at the end of the drill
cycle, as shown in Fig. 5 (cutting speed 90 m/min and feed
rate 0.06 mm/rev). The average thrust force and torque


14

Int J Adv Manuf Technol (2012) 59:9–19

a

Kcc

Thrust cutting force coefficient (N/mm2)

7000

V = 10 m/min
V = 30 m/min
V = 50 m/min
V = 70 m/min
V = 90 m/min

6000

U
Ff
Mc
Pc
MRR
d
f

5000

4000

Cutting force coefficient associated to torque
(N/mm2)
Specific cutting energy (J/mm3)
Thrust force (N)
Torque (N-m)
Cutting power (W)
Material removal rate (mm3/s)
Drill diameter (mm)
Feed per revolution (mm/rev)

3000

2000

1000
0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

0,13

Feed rate (mm/rev)

b
Torque cutting force coefficient (N/mm2)

9000
V = 10 m/min

V = 30 m/min
V = 50 m/min
V = 70 m/min
V = 90 m/min

8000

7000

6000

5000

4000

3000
0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

0,13

The cutting force coefficients are normally the specific
cutting pressures developed during the machining process.
The variations of average thrust cutting force coefficients,
Kcf and Kcc, corresponding to different cutting speed and
feed rate are shown in Figs. 6a and 6b, respectively. It can
be seen from Fig. 6a, b that cutting force coefficients Kcf
and Kcc decreases with the feed rate. It can also be seen
(Fig. 6a, b) that the combined effect of cutting speed at its
higher values and feed rate at its lower values can result in
increasing cutting force coefficients. The variation of
specific cutting energy, the ratio of total cutting energy
input rate to the material removal rate, is shown in Fig. 7. It
can be seen (Fig. 7) that specific cutting energy (U)
decreases with increasing the feed rate and increases with
increasing the cutting speed. Results also showed that the
combined effect of cutting speed at its higher values and
feed rate at its lower values can result in increasing specific
cutting energy. From the obtained results, it can be
concluded that the strain hardening effect is more at the
higher cutting speed and lower feed rates, whereas thermal
softening effect is more dominated on increasing feed rate
at lower cutting speed.

Feed rate (mm/rev)
Fig. 6 Cutting force coefficients a thrust force and b torque
10

ð1Þ
À
Á
Kcc ðMc Þ ¼ ð8; 000 Â Mc Þ= d 2 Â f

ð2Þ

U ¼ Pc =MRR

ð3Þ

Where
Kcf

Cutting force coefficient associated to thrust force
(N/mm2)

V = 10 m/min
V = 30 m/min
V = 50 m/min
V = 70 m/min
V = 90 m/min

9

Specific energy (J/mm3)

components are then used to calculate the cutting force
coefficients (N/mm2) and specific cutting energy (J/mm3).

The cutting force coefficients corresponding to thrust force
(Kcf) [25] and torque (Kcc) [25,26] and specific cutting
energy (U) [25] are respectively defined by as follows:
À
Á
Kcf ¼ 2  Ff =ðd  f Þ½2 comes due to 2 cutting edgesŠ

8
7
6
5
4
3
0,05

0,06

0,07

0,08

0,09

0,1

Feed rate (mm/rev)
Fig. 7 Specific cutting energy

0,11

0,12

0,13


Int J Adv Manuf Technol (2012) 59:9–19

15

3.3 Chip analysis
Chips were collected after each experiment. The main
purpose of collecting chips is to investigate the effect of
cutting parameters on chip morphology, chip microhardness, and chip thickness. From the literature review [27–

29], it can be concluded that size and shape of the generated
chips during drilling operation have a great influence on the
surface roughness of the machined holes and cutting forces.
For drilling, small broken chips are desirable for their
ability to efficiently move along the flute and get out of the
hole. The chips rotate with the drill and impact the wall of

Chip morphology

10 m/min

Feed rate
(0.12 mm/rev)

3 mm

30 m/min

3 mm

3 mm

50 m/min

3 mm

3 mm

70 m/min

3 mm

3 mm

3 mm

90 m/min

0.12 mm/rev

0.10 mm/rev

0.08 mm/rev

0.06 mm/rev

Cutting speed
(50 m/min)

Chip micrograph
Feed rate
(0.12 mm/rev)

3 mm

Fig. 8 Variations of chip morphology and chip micrograph (SEM) with respect to different cutting speeds and feed rates


16

Percentage chane in chip microhardness (%)

a
80
f=0.06 mm/rev
f=0.08 mm/rev
f=0.10 mm/rev
f=0.12 mm/rev

70
60
50
40
30
20
10

0
10

30

50

70

90

Cutting speed (m/min)

b
180
Feed: 0.12 mm/rev

160

Average chip thickness (µm)

the drill or the interior of the flute. This impact produces
bending moment in the chips. Once the bending moment
causes chip’s maximum tensile strength to be exceeded, it
will fracture [30]. The morphological analysis of chips was
carried out with the purpose of studying the influence of
cutting parameters in the formation mechanism and to
identify cutting parameters, which promote better chip
evacuation as in drilling process. The average chip
thickness was measured to study the material deformation

involved in the chip formation process, and the chip
hardness was measured to assess the strain hardening and
thermal softening effect during machining.
The variations of chip morphology and chip micrograph with respect to different cutting speed and feed
rate are shown in Fig. 8. It is observed that on increasing
the cutting speed from 10 m/min to 90 m/min, the needleshaped chips transformed into the cone-shaped chips and
then finally into amorphous chips. The needle and small
cone-shaped chips are formed at low cutting speed as the
chips cannot curl sufficiently to follow the flute and
fracture prior to a complete revolution. At high cutting
speed and feed rate, the material removal rate is very high,
which is more likely to cause jamming of flute and causing
chips shape as amorphous, and it did not have consistent
chip curl radius. The chip is an arc-shaped type at the
lower feed rate (0.06 mm/rev) and high cutting speed
(50 m/min); it gets more helical with the cone diameter of
chip increases with feed rate and cutting speed. Feed rate
is considered as the most significant variable effecting
chip size. An increase in feed resulted in larger chips [31].
It is observed (Fig. 8) that as the cutting speed increases
the extent of discontinuities on the sliding sides of chips
decreases. Presence of streaks and micropores were more
evident as the cutting speed increases as a result of
softening and probably partial melting due to high rise of
temperature in the cutting zone.
The percentage change in chip microhardness with
respect to bulk material (Fig. 9a) presented here was
carried out in order to investigate the influence of cutting
parameters on the chip plastic deformation during drilling.
Astakhov et al. [32] stated that the microhardness of the

plastically deformed chips is uniquely related with the
preceding deformation and with the shear stress gained at
the last stage of deformation before the fracture. The
percentage change in chip microhardness is calculated
according to Eq. 4 [33]. It can be seen (Fig. 9a) that for
all feed rates, as the cutting speed increases, the percentage
change in chip microhardness first increases and then starts
to decrease. This can be explained by the fact that as cutting
speed increases, the material thermal softening during the
process of plastic deformation becomes greater [34].
Plot of average chip thickness for feed of 0.12 mm/rev
against cutting speed is shown in Fig. 9b. It can be seen that

Int J Adv Manuf Technol (2012) 59:9–19

140
120
100
80
60
40
20
10

30

50

70

90

110

Cutting speed (m/min)
Fig. 9 a Percentage change in chip microhardness and b average
chips thickness with respect to cutting speed (feed=0.12 mm/rev)

the average chip thickness decreases between cutting speed
of 10 and 50 m/min and then increases slightly between
cutting speed of 50 and 70 m/min and then further
decreases between cutting speed of 70 and 90 m/min. The
continuous and asymptotic decrease in the average chip
thickness (Fig. 9b) was due to the continuous and
asymptotic increase in the shear angle that occurs when
the cutting speed increases due to the strain hardening effect
[35].

ΔHv ð%Þ ¼

Hv ðchipÞ À Hv ðmaterialÞ
 100
Hv ðmaterialÞ

ð4Þ


Int J Adv Manuf Technol (2012) 59:9–19

17

500

3.4 Workpiece surface integrity

450

Microhardness (HV 0.05)

The term surface integrity is used to describe the quality
and condition of the final machined surface and, therefore,
encompasses both the surface analysis and subsurface
metallurgical alterations. For this purpose, the surface
roughness of the drilled holes, microhardness of the
subsurface layer of the machined surface, and hole diameter
deviations were examined.
Figure 10 shows the influence of cutting speed and feed
rate on the machined surface roughness (Ra) value. It was
found that surface roughness values at various cutting
conditions varied within the range of 0.32 to 1.73 μm. It
can be (Fig. 10) revealed that cutting speed has a significant
influence on the surface roughness produced. It is seen
(Fig. 10) that as the cutting speed increases from 10 to
50 m/min, the surface roughness value decreases for all
feed rates. Further increase in cutting speed from 50 to
90 m/min increases the surface roughness values. At higher
cutting speed, the low feed values give the better surface
finish. This can be explained by the higher temperature
generated in the cutting at higher cutting speed. Hence, the
shear strength of the material reduces and the material
behaves in a ductile fashion.

Results on the microhardness of the subsurface layer of
the machined surface are presented in Fig. 11. All values
were taken at a distance of 50 μm beneath the machined
surface. The mean hardness value of the subsurface layer
was higher than the mean hardness of the workpiece
material. It was due to the high cutting temperature
generated between tool–workpiece interfaces during the
drilling process. It can be observed (Fig. 11) that micro-

f = 0.06 mm/rev
f = 0.08 mm/rev
f = 0.10 mm/rev
f = 0.12 mm/rev

400

350

300

250

200
10

30

50

70

90

Cutting speed (m/min)
Fig. 11 Microhardness variations at a distance of 50 μm beneath the
machined surface for different cutting parameters

hardness values increases with cutting speed. These results
are expected due to high cutting temperature generated at
higher cutting speed.
Figure 12 shows the variation of hole diameter at
various cutting conditions. It can be observed (Fig. 12)
that at lower cutting speeds up to 50 m/min, there is no
significant variation in hole diameter. For cutting speed
higher than 50 m/min, variation of hole diameter
increases rapidly, which can be explained by the higher
temperature generated during machining at higher cutting
speed.

3

2,5

f = 0.06 mm/rev
f = 0.08 mm/rev
f = 0.10 mm/rev
f = 0.12 mm/rev

8,04
2

Hole diameter (mm)

Surface roughness Ra (µm)

8,05

f = 0.06 mm/rev
f = 0.08 mm/rev
f = 0.10 mm/rev
f = 0.12 mm/rev

1,5

1

0,5

8,03

8,02

8,01

0
0

20

40

60

80

100

Cutting speed (m/min)

8
10

30

50

70

90

Cutting speed (m/min)
Fig. 10 Workpiece surface roughness of drilled surface at various
cutting parameters

Fig. 12 Influence of the cutting parameters on hole dimensions


18

4 Conclusions

In this study, a novel manufacturing technology is developed to
produce green grade of ADI. The novel technology is
developed by the integration of casting (metallic mold) and
heat treatment in the foundry to save energy and time.
Conventionally, the ADI is produced by using sand mold and
heat treatment is performed after the cooling of casting at room
temperature. The metallic mold casting leads to the higher
production rate of near net shape ADI castings and the in situ
heat treatment for austempering. The green ADI grade has a
good combination of mechanical properties with strength
properties comparable to that of ASTM grade 1 ADI while
ductility is comparable to that of ASTM grade 2 ADI. Also, the
graphite nodule count of green ADI grade is higher as
compared to conventional ADI. This can be explained by the
increase in heat transfer and solidification rates in a metallic
mold as compared to the sand mold. Hence, drilling study of
green ADI grade was conducted using a TiAlN-coated
tungsten carbide drill. The effect of cutting parameters on
cutting force coefficients, chip morphology, and surface
integrity of the drilled surface were discussed. The following
conclusions can be drawn from drilling of green ADI grade:
1. The combined effect of cutting speed at its higher values
and feed rate at its lower values can result in increasing
cutting force coefficients and specific cutting energy.
2. The variation of cutting speed and feed rate has a
significant effect on chip morphology as the combination of higher cutting speed and feed values increases
the chip’s shape and size.
3. The percentage change in chip microhardness first
increases and then starts to decrease. This can be
explained by the fact that as cutting speed increases, the

material thermal softening during the process of plastic
deformation becomes greater.
4. Average chip thickness decreases with cutting speed.
5. Increase in cutting speed in the range of 50–90 m/min
deteriorates the surface finish and at higher cutting
speed the low feed value gives the better surface finish.
6. At higher cutting speed, hardness values increases at
the subsurface layer of the drilled surface due to plastic
deformation.

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Int J Adv Manuf Technol (2012) 59:21–35
DOI 10.1007/s00170-011-3478-0

ORIGINAL ARTICLE

Geometry of chip formation in circular end milling
Avisekh Banerjee & Hsi-Yung Feng &
Evgueni V. Bordatchev

Received: 20 April 2010 / Accepted: 14 June 2011 / Published online: 28 June 2011
# Springer-Verlag London Limited 2011

Abstract Machining along continuous circular tool-path
trajectories avoids tool stoppage and even feed rate
variation. This helps particularly in high-speed milling by
reducing the effect of the machine tool mechanical structure
and cutting process dynamics. With the increase in
popularity of this machining concept, the need for detailed
study of a valid chip formation in circular end milling is
becoming necessary for accurate kinematic and dynamic
modeling of the cutting process. In this paper, chip
formation during circular end milling is studied with a
major focus on feed per tooth and undeformed chip
thickness along with their analytical derivations and
numerical solutions. At first, the difference in the feed per

A. Banerjee
Department of Mechanical and Materials Engineering,

The University of Western Ontario,
London, ON, Canada N6A 5B
H.-Y. Feng
Department of Mechanical Engineering,
The University of British Columbia,
Vancouver, BC, Canada V6T 1Z4
e-mail:
E. V. Bordatchev
Centre for Automotive Materials and Manufacturing, Industrial
Materials Institute, National Research Council of Canada,
London, ON, Canada N6G 4X8
e-mail:
Present Address:
A. Banerjee (*)
Life Prediction Technologies Inc,
1010 Ploytek Street,
Ottawa, ON, Canada K1J 9J1
e-mail:

tooth formulation for end milling along linear and circular
tool-path trajectories is presented. In the next step, valid
formulation of the undeformed chip thickness in circular
end milling is derived by considering an epitrochoidal tooth
trajectory with a wide range of the tool-path radius. The
complex transcendental equations encountered in the
derivation are dealt with, by a case-based approach to
obtain closed-form analytical solutions. The analytical
solutions of undeformed chip thickness are validated with
results of numerical simulations of tool and tooth
trajectories for circular end milling and also compared

to the linear end milling. The close resemblance between
analytical and numerical calculations of the undeformed
chip thickness in circular end milling suggests validity of
the proposed analytical formulations. As a case study, the
cutting forces in circular end milling are calculated based
on the derived chip thickness formulations and an
existing mechanistic model. The calculation results
reiterate the need of taking into account adjusted feed
per tooth and valid chip thickness formulations in
circular end milling, especially for small tool-path radii,
for more realistic process modeling.
Keywords Circular end milling . Epitrochoidal tooth
trajectory . Feed per tooth . Undeformed chip thickness .
Closed-form formulation . Cutting force

1 Introduction
In the past decade, aerospace and die/mold industries have
identified the potential of tremendous time and cost saving
that can be achieved by high-speed machining (HSM)
technology. Hence, the popularity of HSM in end milling


22

has been rapidly growing. A major concern in HSM is the
higher risk of instability in the end milling system resulting
from the higher acceleration and deceleration of the
machine tool during cutting motions with high spindle
speeds. This problem is aggravated especially when the tool
path has tangent or G1 discontinuities that lead to tool

stoppages. Also, fast ramping feed rate leads to higher
jerks. The discontinuous tool motions directly translate into
lower productivity and even damage through excessive
wear of the machine tool mechanical components. Thus,
innovative machine tool and motion drive designs, and
motion control algorithms have become popular research
topics. Moreover, researchers have also started looking into
tool-path optimization to obtain smooth and consistent
machining. This effort has lead to the use of higher order
tool-path trajectories, such as splines [1], quintic splines
[2], NURBS [3], etc. Such tool-path trajectories require
advanced interpolators, which are not commonly available
in commercial CNC controllers. A simplistic alternative to
higher order tool paths are biarc and arc-spline tool-path
segments, which provide G1 continuity along the entire tool
path. End milling along circular trajectories are preferred in
finishing operations for lower fluctuation of its curvature
along the tool path and the ability to maintain a limiting
feed rate calculated based on dynamic characteristics of
machine tool [4] over the entire trajectory. Moreover,
circular end milling also finds wide applications for
roughing operations like removing excess material, enlarge
holes and cavity openings [5]. They are preferred to the
alternate boring operations due to higher productivity
achieved through multiple cutting edges.
Physics-based and kinematic models of the cutting
process are commonly employed for modeling used in
process planning and optimization. Therefore, accurate
analysis and modeling of the chip formation is very
important for optimal planning of circular end milling

operations. The chip thickness formulation for circular end
milling has been addressed in some previous work with
numerical [6] and analytical [7] approaches. In the
numerical approach [6], parametric equations representing
tool-path trajectory and workpiece surface to be machined
are numerically solved to determine the undeformed chip
thickness. However, this approach does not provide any
insight into the geometry of chip formation and material
removal mechanism. The analytical modeling approach [7]
proposes a single closed-form formulation of the undeformed chip thickness without considering greatly varying
geometric cases of tool-path radius arising in practical
circular end milling operations. The assumption of the
defined delay angle being negligibly small is true for linear
end milling, but may not be applicable for all practical
circular end milling conditions. Moreover, the presented
results suggest that the chip thickness increases as tool-path

Int J Adv Manuf Technol (2012) 59:21–35

radius decreases without determining its value at very low
tool-path radius. Further, some work has also been done
towards cutting force modeling in circular end milling [5].
The undeformed chip thickness in circular end milling was
approximated by the same analytical formulation derived
for a linear end milling with a feed per tooth compensation
strategy. The paper also provides experimental measurement and analysis of the cutting force at low tool-path
radius, which is observed to be consistently smaller than the
predicted value. Although the results presented do not
address this observation from the chip formation point of
view, they clearly indicate the significant difference

between linear and circular end milling operations.
In this work, the mechanism of chip formation in
circular end milling is studied in detail. In Section 2, the
difference in feed per tooth for end milling along linear
and circular tool-path trajectories is studied. Based on this
difference, in Section 3, a case-based approach is adopted
to derive valid closed-form analytical formulations of
delay angle and undeformed chip thickness in circular end
milling, for different ranges of tool-path radius. In
Section 4, a numerical procedure is also implemented to
calculate the undeformed chip thickness and results are
compared to the proposed analytical formulations for
linear and circular end milling. Further, the proposed
case-based analytical formulation of undeformed chip
thickness in circular end milling is integrated with a
calibrated mechanistic cutting force model and cutting
force simulation results for different geometric test cases
are presented in Section 5. Finally, conclusions of the
derivation, numerical validation, comparison of chip
formation in circular and linear end milling, and the
application of the proposed analytical formulation for
improved cutting force calculation are presented in
Section 6.

2 Feed per tooth
Feed per tooth is defined as the distance advanced by the
cutting tool into the workpiece material per tooth revolution
[8]. In this section, feed per tooth for linear and circular end
milling operations are compared to study the material
removal characteristics. Figure 1a shows the comparison

of both linear and circular end milling operations with a
constant radial depth (say dr) while moving cutting tool
from position P1 to P2. During the linear end milling, areas
machined at different radial distances (da, db, dc) from tool
center O are equal (Aabb′a′a = Abcc′b′b). However, for circular
end milling with tool-path radius (R) and center C, it can be
observed that Aabb′a′a < Abcc′b′b. Different amounts of
material are removed at a, b, and c to accommodate the
difference between machined areas. Hence, in circular end


Int J Adv Manuf Technol (2012) 59:21–35

23

milling, the value of feed per tooth (f), programmed for tool
center, O shown in Fig. 1b does not remain constant along
the tool-path radial axis CO. A simple formulation for
adjusting feed per tooth (fadj) for circular end milling
measured along the tangent of the circular tool-path
trajectory is given as [5]:
fadj ¼ R Á Δb

ð1Þ

where Δβ is the angle the tool center rotates about the toolpath origin in one tooth period, as shown in Fig. 1b. The
above formula is applicable for cases where R is relatively
large and f is very small that allows the approximation of
the subtended arc length (OO′) by f as shown in Fig. 1b. To
obtain a more comprehensive and meaningful feed per

tooth adjustment formulation in circular end milling, the
unit machined area which is the area machined during one
tooth period and the tool-path radius (r), is also considered
into the adjusted feed per tooth formulation. The detailed
derivation of the formulation of adjusted feed per tooth
(fadj) is provided in Appendix A and given as:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2Þ
fadj ¼ f Á 1 þ ðr=RÞ2 þ 2 Á ðr=RÞ Á cosðqÞ
A detailed analysis of the above equation with respect to
the possible values of R results in a variety of fadj
represented by the gray-colored area in Fig. 1b. For
relatively large values of R (R >> r), the term (r/R)
approaches zero, and results in that Eq. 2 becomes fadj ≈ f.
In the range of 0≤R≤r, as R decreases, fadj increases rapidly.
Ultimately, for R→0, fadj → ∞, implying that the amount of
material removal in one tooth period increases infinitely.
Although this situation exists mathematically, it is difficult
to imagine it happening in actual machining. One explanation is that although fadj becomes ∞, engagement domain of
the tool also becomes zero as the tool simply rotates about
its own axis without tool movement and material removal.
Moreover, the assumption that R >> f is no longer valid,
and the mathematical formulation in Eq. 2 takes an
indeterminate form. This implies the need for further
rigorous study in to the chip formation in circular end
milling. For this purpose, the next section focuses on a
valid undeformed chip thickness analytical formulation to
understand the geometry of chip formation in circular end
milling operations.

3 Analytical formulation of undeformed chip thickness
The difference in the feed per tooth between linear and
circular end milling clearly suggests that process models for
linear end milling will provide only an approximation for
the circular end milling. The indeterminate form of the feed

per tooth in Eq. 2 for low tool-path radius (R) implies that
only variation in feed per tooth cannot provide a
comprehensive understanding of chip formation in circular end milling. In this section, the geometry of chip
formation is studied by considering the chip thickness
which is defined as the amount of material removed by
two consecutive tooth trajectories. For linear end milling,
a simplified formulation of the undeformed chip thickness (tc) in terms of tool rotation angle (θ) and feed per
tooth (f) is given as [9],
tc ¼ f Á sinðqÞ

ð3Þ

For circular end milling, the variation of f suggests that
the simplified formulation of undeformed chip thickness
cannot be used [6, 7]. Two consecutive (j−1)th and jth tooth
trajectories are shown in Fig. 2 in gray and black,
respectively. The figure represents up-milling operation of
a circular slot cut with entry angle of 0° and exit angle of
180°. The tool radius (r) and different values of tool-path
radius (R) with a center at point C are selected. Two
different coordinate systems are used and shown in Fig. 2a.
The first system is a global coordinate system represented
by X–Y axis with origin fixed at the tool-path center C. The
second system is a local coordinate system represented by

x–y axes about the instantaneous tool center O, which
rotates about center C. Figure 2a shows the case for R > r,
where for any point N on the current jth tooth trajectory
subtending a tool rotation angle of θN, there exists a point
M on the previous (j−1)th tooth trajectory subtending a tool
rotation angle of θM, such that the current jth tool center ON
is aligned to M and N. The amount of material removed
between the two consecutive passes are shown in gray area
with the feed per tooth distribution along the tool diameter
following (CO) shown by solid arrows. The undeformed
chip thickness (tc) for the jth tooth pass at tool rotation angle
θN can be represented by the distance MN. Figure 2b and c
show the tooth trajectories for R = r and R < r, respectively.
It can be observed through comparison of Fig. 2a, b, and c
that the nature of the feed per tooth variation along the toolpath axis CO is quite different. In Fig. 2a and b, the entire
engagement domain of the two fluted tool for a slot cut is
between 0° and 180°, but the starting tc (at θN =0°) is higher
for R = r and it becomes zero at the exit point. In Fig. 2c,
the tool engagement starts with even higher values of tc
than that in Fig. 2b and becomes negative before
approaching the exit point. As the tool-path center (C)
moves inside the tool circumference, a negative feed per
tooth in the reverse direction is also observed, as shown
with dotted arrows in Fig. 2c. This occurs due to the fact
that near the exit point of the current tooth pass, no material
is left to be machined. This can be called as backward
cutting, where the current tooth within the engagement


24

Int J Adv Manuf Technol (2012) 59:21–35

P2
dr

Abcc b b

P1
c
b
a

c
b
a
Aabb a a

f

Aabb a a

Abcc b b

P2
da

db

dc

O

P1

c

dr

b
a

c
b
a d
a db

f O

dc
Linear:
Aabb a a= Abcc b b

Circular:
Aabb a a< Abcc b b

R

β
C

(a)

Am

dr
current
tooth period

P

A
P

A
fadj

O′
x1

θ
f

r
O

R
B′
Δβ

B

previous
tooth period

C
(b)
Fig. 1 Feed per tooth: a comparison between linear and circular end milling, and b variation in circular end milling in one tooth period

domain does not machine material as it has been already
removed by the previous tooth trajectories.
3.1 Geometric representation of epitrochoidal tooth
trajectory
Figure 2 shows that undeformed chip thickness in circular
end milling is a function of several parameters related to
tool and tool path, such as tool-path radius (R), tool-path
angle (β), and tool rotational angle (θ). Hence, tooth

trajectory cannot simply be considered as a trochoid as in
the case of linear end milling [9]. However, the epitrochoidal tooth trajectory, defined as the trajectory of a point on
the circumference of a circular disk rolling over another
circular disk, will provide more accurate representation for
the circular case. The parametric equation of an epitrochoid
is given as:
(
X : R cosðbÞ þ r cosðb þ q Þ
P¼
ð4Þ
Y : R sinðbÞ þ r sinðb þ q Þ


Int J Adv Manuf Technol (2012) 59:21–35

25

Fig. 2 Adjustment of feed per
tooth and undeformed chip
thickness determination for
circular end milling based on
consecutive tooth trajectories:
a R > r; b R = r; and c R < r

r
N
M

jth pass

y

(j-1)th pass

N

ON

Y

x

M

f
C

X

OM

R

entry

exit

(a)

(j-1)th pass

jth pass
(j-1)th pass

N
M

N

th

N

j pass

M

exit

N

ON
C

ON

(b)

C
exit

(
M¼

YM : R sinðbM Þ þ r sinðbM þ DM Þ
(

N¼

XM : R cosðbM Þ þ r cosðbM þ DM Þ

XN : R cosðbN Þ þ r cosðbN þ DN Þ
YN : R sinðbN Þ þ r sinðbN þ DN Þ

OM
entry

ð5Þ

ð6Þ

where Θ is the tooth position angle along the epicycloidal
trajectory and can be represented by,
D ¼ q0 þ jΔ þ q

r

f

where P is the circumferential point on a disk with
radius r rolling over another disk with radius R. The
angles θ and β correspond to the subtended angle by the
point P to the tool and tool-path centers, respectively.
Using the parametric representation of an epitrochoid
given in Eq. 4, the point M for the (j− 1)th tooth trajectory
and the point N for the jth tooth trajectory (see Fig. 2) can
be represented as:

ð7Þ

where, θ0 is the initial tooth orientation angle; θ is the tool
rotational angle and Δ= 2π/N the lag angle between
adjacent cutting teeth, with N being the number of cutting
teeth. Moreover, the proportional relationship between θ

f OM
R

M

R=r

M

entry

(c)

and β for a selected feed per tooth (f) at the tool center can
be formulated as:
b ¼ kq ¼ k ðD À jΔÞ

ð8aÞ

where,
k ¼ fN =2pR ¼ M =R and M ¼ fN =2p

ð8bÞ

Hence, using Eqs. 7 and 8, the angles ΘM, βM and ΘN,
βN at points M and N, respectively, and considering θ0 =0,
in Eqs. 5 and 6, can be represented as:
DM ¼ ðj À 1ÞΔ þ q M
bM ¼ k ½DM À ðj À 1ÞĊ

DN ¼ jΔ þ qN
bN ¼ k ðDN À jΔÞ

'
ð9aÞ

'
ð9bÞ

Now, using the parametric equation of a circle, the
position of the jth tool center can be represented as:
&
XON : R cosðbN Þ
ON ¼
ð10Þ
YON : R sinðbN Þ


26

Int J Adv Manuf Technol (2012) 59:21–35

Based on fact that points ON, M, and N are collinear to
represent the undeformed chip thickness as MN, the
following condition is implied:
ðXM À XON Þ=ðYM À YON Þ ¼ ðXN À XON Þ=ðYN À YON Þ
) ðXM À XON Þ Á ðYN À YON Þ À ðXN À XON Þ Á ðYM À YON Þ ¼ 0

Substituting relations from Eqs. 5–10 into the equation

above, the following equation is obtained:
rfR sin½bM À ðbN þ DN ފ À R sin½bN À ðbN þ DN ފ
Àr sin½ðbM þ DM Þ À ðbN þ DN ފg ¼ 0

Substituting the above terms and assuming r≠0, the
equation based on the co-linearity of the points ON, M, and
N is given below,
R sin½k ðd þ ΔÞ À DN Š þ R sinðDN Þ À r sin½ðk þ 1Þd þ kĊ ¼ 0

ð12Þ
The above equation is transcendental in nature with δ
being the unknown. In order to obtain a valid closed-form
solution, Eq. 12 has to be solved for different geometric
cases with varied assumption for k and δ, selected based on
the realistic end milling conditions.

A delay angle (δ) defined as the difference between the
current (ΘM) and previous (ΘN) tooth positional angles is
introduced and given by,

3.2 Undeformed chip thickness

d ¼ DM À DN

The undeformed chip thickness (tc) can be represented by
the distance MN (see Fig. 2) and can be given as:

ð11Þ

Now, using Eqs. 9 and 11, some terms can be simplified

as follows,
bM À ðbN þ DN Þ ¼ k ðDM À DN Þ þ kΔ À DN ¼ k ðd þ ΔÞ À DN

ð b M þ DM Þ À ð b N þ D N Þ ¼ ð b M À b N Þ þ ð DM À DN Þ

tc ¼ MN ¼ ON N À ON M ¼ r À

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðXM À XON Þ2 þ ðYM À YON Þ2 ¼ r À r

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where r ¼ ðXM À XON Þ2 þ ðYM À YON Þ2
Now, using Eqs. 5–11, ρ can be derived as:

ð13Þ

¼ k ðd þ ΔÞ þ d ¼ ðk þ 1Þd þ Δ

r¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fR½cosðbM Þ À cosðbN ފ þ r cosðbN þ DM Þg2 þ fR½sinðbM Þ À sinðbN ފ þ r sinðbN þ DM Þg2

Implementing further simplification,

r¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r2 þ 4R2 sin2 ½kðd þ ΔÞ=2Š À 4rR sin½kðd þ ΔÞ=2Š sin½kðd þ ΔÞ=2 þ d þ DN Š

Substituting the above expression for ρ into Eq. 13, tc
can be expressed as:
&
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi'
tc ¼ r 1 À 1 þ 4ðR=rÞ2 sin2 ½kðd þ ΔÞ=2Š À 4ðR=rÞ sin½kðd þ ΔÞ=2Š sin½kðd þ ΔÞ=2 þ d þ DN Š

In the above equation, tc can be estimated only after δ
has been obtained by solving Eq. 12 for different
geometrical and physical conditions. Hence, tc will also
have different case-based formulations.
3.3 Case-based approach
The presence of tool-path radius in circular end milling
makes the formulation of undeformed chip thickness (tc)

ð14Þ

much more complex than that in linear end milling. This
necessitates the use of different geometrical and machining
conditions for deriving valid closed-form analytical formulations of tc. The input parameters involved in determining the delay angle (δ) in Eq. 12 and tc in Eq. 14 can be
categorized into three types. The parameters of the first type
are geometric: tool radius (r) and tool-path radius (R). The
second type includes the process parameters: feed per tooth
(f) and lag angle (Δ). The third type involves coefficients k