IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
OCTOBER 5-8, 2014, HONOLULU, U.S.A. / 1
Modeling of Specific Cutting Energy in MicroCutting using SPH Simulation
Dattatraya Parle, Ramesh K. Singh, and Suhas S. Joshi#
Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai-400076, India
# Corresponding Author / E-mail: [email protected] TEL: +91-22-25767527, FAX: +91-22-2572 6675
KEYWORDS : Micro-cutting, Specific cutting energy, SPH formulation
This work employs SPH method to simulate orthogonal micro-cutting process using LS-DYNA
software. SPH is a meshless method suited for large deformation problems typically that occur in
micro-cutting and overcomes limitations of other FE formulations. Process of micro-cutting
modeling using SPH simulations have been benchmarked with experiments for cutting of AISI 1045.
The purpose of this study is to investigate stress, strain, cutting forces and specific cutting energy in
micro-cutting using SPH simulations under various parametric conditions. These results of microcutting process are in agreement with the fundamental machining behavior of ductile materials.
Thus, this work demonstrates capability of SPH formulation in modeling of orthogonal micro-cutting
with fairly accurate results overcoming limitations of other formulations, especially when the scale of
the process is reduced to micro-cutting.
1. Introduction
NOMENCLATURE

mi
i
i
h
d
W

f
b
V
u
A, B, C, m, n


T
Fc
SPH
FEM
ALE
Metal cutting is a complex process, in which several
mechanisms are at work simultaneously, and they interact with
each other. Further, the complexities in the simulation of
machining process increase multi-fold due to a reduction of
scale during micro-cutting. In spite of extensive research on
micro-cutting, many facets of the material deformation during
machining have not been completely understood or simulated.
Search for effective analytical, experimental and numerical
techniques still continues. Finite element method has been
used as an alternative to the analytical and experimental
approaches in metal cutting process since early 1970's. Until
the late 1990s, the majority of researchers used their own FEM
codes. However, use of commercially available software
packages has dramatically increased over the last ten years due
to limitations on using customized FEM codes. Several
researchers have successfully performed simulations using
either general purpose commercial FEA softwares such as
ANSYS, Abaqus, LS-DYNA, MSC.Marc or specialized
numerical codes such as DEFORM, AdvantEdge, etc. [1].
Mackerle [2, 3] presented a bibliography of efforts related to
numerical simulation of metal-cutting operations.
The FE simulation of micro-cutting requires explicit
dynamic non-linear numerical formulation. Most of the past
efforts in modeling of micro-cutting involve use of Lagrangian,
Eulerian, Arbitrary Lagrangian–Eulerian (ALE) formulations.
Domain
Mass of particle
Density of particle
ith particle
Smoothening length
Distance between particle
Kernel function
Rake angle
Feed
Width of cut
Cutting speed
Specific cutting energy
Johnson-Cook parameters
Strain
Flow stress
Temperature
Cutting force
Smoothed Particle
Hydrodynamics
Finite Element Method
Arbitrary Lagrangian–Eulerian
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IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
Recently, researchers began investigating suitability of SPH
formulations in metal cutting simulations. Use of SPH is a
new topic for many researchers to investigate its applicability
and very few studies are available in literature [4-10]. This
work therefore, this work employs SPH method to simulate
orthogonal micro-cutting process in the frame-work of LSDYNA. The process of micro-cutting is modeled using SPH
simulations and has been benchmarked with experiments for
cutting on AISI 1045 steel. The purpose of this work is to
understand micro-cutting process by studying stress, strain,
cutting forces and specific cutting energy under various
parametric conditions.
This work therefore presents SPH-based simulations to
investigate the parametric effects in micro-cutting process. The
simulations are validated using micro-cutting experiments.
2.2 Micro-cutting model set-up using SPH
In this work, orthogonal cutting and a corresponding 2D
geometrical model are considered. The geometry of workpiece
is 1 x 0.5 mm rectangle with 0.2 mm cutting width. SPH
particles are created in the workpiece. The workpiece contains
total 3,09,630 SPH particles. Tool is meshed with solid
elements. The workpiece particles are constrained in all
directions at the bottom edge. A cutting speed is applied in xdirection to the tool. Node to surface contact is defined
between the workpiece and the tool. However, sticking
phenomenon along chip-tool interface is not considered in the
friction model. Fig. 1 shows a scheme of simulation for
orthogonal micro-cutting.
Mass, distance and smoothening length of particles are
defined for workpiece SPH particles. The total mass of all
particles should be equal to the mass of the workpiece
calculated analytically. Smoothing length is another important
parameter in numerical modeling using SPH particles. The
typical parameters required in SPH formulations are shown in
Fig. 2. To keep enough particles neighboring a particle,
variable smoothing length is the best option i.e. smoothing
lengths vary during the calculation process.
2. Micro-cutting simulations using SPH
2.1 Basics of SPH
SPH is a Lagrangian technique that was initially
developed in the 1970’s as a means to simulate astrophysical
phenomena [11, 12]. In SPH, a kernel approximation is used
to calculate spatial derivatives within randomly distributed
interpolation points. A function f(r) can be thus estimated by
the relation:
f r  
 f  r 'W  r  r ' , h d 
r'
(1)

where,
W r  r ' , h d  r ' = kernel function which can be Gaussian,
polynomial, spline, etc.
h = smoothening length which defines a domain containing
particles in interaction with particle i.
The value of a function at particle i is approximated using
the values of the functions at all the particles that interact with
particle i. The continuous volume integrals are written as sums
over discrete particles using Eq. 2:
f  ri  
N

j 1
mj

f  r i W  r  r ' , h 
OCTOBER 5-8, 2014, HONOLULU, U.S.A. / 2
(2)
j
where,
mj and j are the mass and density of the each particle,
respectively.
SPH is a meshless method, which does not require a
computational grid to perform simulations. Rather, SPH
operates by representing the material as a group of Lagrangian
particles. These particles interact with one another based on a
smoothing length and a statistical kernel function. Essentially,
the smoothing length provides an individual particle search
radius to find neighboring particles, while the kernel function
is used to provide how strongly or weakly the particles interact.
Using SPH, a user no longer needs to be wary of mesh (size,
smoothing and tangling), adaptive re-meshing or a chip
separation criterion, which is essential in other formulations
during micro-cutting.
In present work, uncut chip thickness used is in the range
of 5-25 m and at a lower uncut chip thickness, these issues
become very critical, hence, SPH has been used in this work.
122
Fig. 1 Scheme of simulation for micro-cutting a. Tool-workpiece
geometry b. Enlarged workpiece showing SPH particles
Fig. 2 Important input parameters for SPH particles
In this work, a total 27 SPH based micro-cutting
simulations were performed on medium carbon steel (AISI
1045) using a full-factorial design. Table 1 shows the levels
and factors which were used in the micro-cutting simulations.
Three levels of rake angle, feed and cutting speed were
selected.
IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
*CONTROL_SPH, *SECTION_SPH and *ELEMENT_SPH
are SPH specific commands that are required to perform SPH
simulations of micro-cutting in LS-DYNA, whereas all other
inputs are similar to Langrangian based simulations.
 *CONTROL_SPH: Used to define controls for
computing SPH particles. This also defines space
dimensions for SPH particles.
 *SECTION_SPH: Used to define section properties for
SPH particles i. e., smoothening length and distance
between SPH particles.
 *ELEMENT_SPH: Used to define elements and mass
for SPH particles.
Table 1 Factors and their levels during micro-cutting simulations
Level
Rake Angle
(Deg)
Feed (m)
Cutting Speed
(m/min)
0
1
2
0
5
10
5
15
25
3
30
300
The cutting tool is modeled as a rigid-body whereas
workpiece is modeled as an elasto-plastic body. Table 2 shows
overall tool and work material properties used in the
simulation of orthogonal micro-cutting. Elasto-plastic
behavior of workpiece is modeled using Johnson-Cook (J-C)
[13] constitutive material model and is given by Eq. 3.

  A  B 
p

n

    

 
1

C
ln

    1 
0

  


p
 T  T ro o m

T
 melt  T ro o m




m
OCTOBER 5-8, 2014, HONOLULU, U.S.A. / 3
3. Results and Discussion



(3)
This section presents various results obtained using SPH
simulations of micro-cutting and experimental validation of
cutting forces.
3.1 SPH Simulation results
In the post-processing of FE simulation, fundamental
machining results such as stress and strain have been studied.
Fig. 3 shows a typical von-Mises (VM) stress contour plot
obtained by the SPH simulation. The maximum von-Mises
stress in the shear zone is 1324 MPa for a typical case shown
in Fig. 3. Similarly, a typical strain plot obtained using SPH
simulation is shown in Fig. 4. For given cutting conditions,
machining strain is found to be 2.145.
In SPH formulation, kinematics of material separation is
inherently captured. Hence, a separate chip formation criterion
is not required as in Lagrangian and Eulerian formulations.
The material damage is incorporated at SPH nodes through a
loss of cohesion as neighboring SPH particles are separated
from each other. When the distance between the particles is
more than a critical distance, the material is assumed to have
failed.
Table 2 Work and tool material properties
Material
Density
Young’s
modulus
Poisson's
ratio
Model
AISI 1045
[14]
AISI 1045
7800 kg/m3
200000 MPa
Tungsten carbide
15800 kg/m3
680000 MPa
0.3
0.24
Johnson-Cook
A (MPa)
B (MPa)
553.10
600.80
Rigid Isotropic
C
m
0.234 0.013
n
1.0
Fig. 3 von-Mises stress plots
(Process parameters: V=3 m/min, =5, f=25m)
2.3 Summary of LS-DYNA inputs used for SPH based
simulations of micro-cutting
This section presents summary of LS-DYNA commands
used during micro-cutting simulations. Input file commands
are divided into following two blocks and input file must
begin with *KEYWORD and end with *END:
 Control block: This block is used to define solution
control and output parameters
 Model block: This block is used to define elements,
nodes, contact, boundary conditions, material
parameters, etc.
Fig. 4 Plastic strain distribution
(Process parameters: V=3 m/min, =5, f=25m)
Micro-cutting simulations use consistent set of units.
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IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
3.2 Benchmarking of micro-cutting simulations using
experiments
OCTOBER 5-8, 2014, HONOLULU, U.S.A. / 4
Fig. 7 shows a typical plot of cutting force vs. time
obtained from SPH simulations and the experiments. Average
cutting force obtained by the experiment in the steady state
region is 15.94 N. Similarly, the average cutting force in the
steady-state region during SPH simulations is 13.98 N. Error
in SPH simulation and experimental average cutting force is
9.22% for given cutting condition. Both plots show an initial
unsteady region followed by a steady-state region.
The validation of SPH simulation involves a comparison
of cutting force obtained from simulation with those obtained
from the experimental results. The micro-cutting experiments
were performed on a three-axis multipurpose miniature
machine tool developed by Mikrotools (see Fig. 5). The
inserts is made of Tungsten Carbide with three cutting edges
and mounted in an insert holder. Workpiece (see Fig. 6) was
prepared using wire-EDM and mounted on a force measuring
dynamometer (Kistler Minidyne 9256C2) using a workpiece
holder. Orthogonal micro-cutting experiments were monitored
using CCD-based OMM camera which travels with the tool.
Limited experiments were performed to benchmark FEA
simulations. Table 3 shows various cutting parameters used
during experiments.
Cutting Force (N)
25
20
15
10
Experiments
SPH Simulation
5
0
0
0.1
0.2
Time (s)
0.3
Fig. 7 Cutting Force vs. Time
(Process parameters: V=3 m/min, =5, f=25 micrometer)
3.3 Chip morphology
Continuous chips are observed during micro-cutting
experiments as well as corresponding SPH simulations under
various cutting conditions. Table 4 shows comparative chips
obtained under three different cutting conditions. Chips are
observed using CCD camera during micro-cutting experiments.
Fig. 5 Experimental set-up
Table 4 Chip obtained using experimental and SPH simulation
Case
Exp. 1
 = 0
f = 25 m
V= 3 m/min
Exp. 2
 = 5
f = 25 m
V= 3 m/min
Fig. 6 Typical workpiece used during micro-cutting
experiments
Table 3 Cutting conditions for micro-cutting experiments
S. No.
Rake Angle
(Deg)
Feed (m)
Cutting Speed
(m/min)
Exp. 1
Exp. 2
Exp. 3
0
5
10
25
25
25
3
3
3
Exp. 3
 = 10
f = 25 m
V= 3 m/min
124
Experiments
SPH
IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
OCTOBER 5-8, 2014, HONOLULU, U.S.A. / 5
3.4 Cutting forces
3.5 Specific cutting energy
A variation of cutting forces with the machining
parameters like cutting speed, rake angle and feed is illustrated
in Fig. 8. It is observed that cutting forces increase with an
increase in feed (see Fig. 8), whereas the forces decrease with
an increase in rake angle (see Fig. 9) and cutting speed (see
Fig. 10). Results of cutting forces are in agreement with the
fundamental machining behavior of ductile materials [15].
It is also observed that the effect of cutting speed is
minimum at lower feed and increases as feed increases. Fig. 9
also shows that experimental and simulated forces are in close
agreement.
Figs. 11 and 12 show that the specific cutting energy
increases with a decrease in feed. This increasing trend in the
specific cutting energy at lower feed is also termed as the size
effect [15]. Specific cutting energy is given by Eq. 4. In this
equation, cutting force obtained through SPH simulations is
used for calculating specific cutting energy during microcutting.
u 
Cutting Force (N)
12.5
10
V=3 m/min
V=10 m/min
V=30 m/min
5
5
10
15
20
Feed (micrometer)
25
Specific Cutting Energy
(N/mm2)
0
Fig. 8 Cutting force vs Feed
(Process parameters: =5, Tool: Sharp edge)
Feed = 5 micrometer
Feed = 15 micrometer
Feed = 25 micrometer
Experiments at 25 micrometer
20
15
7000
Cutting speed = 3 m/min
Cutting speed = 10 m/min
Cutting speed = 30 m/min
6000
5000
4000
3000
2000
0
10
5
10
20
Feed (Micrometer)
30
Fig. 11 Specific cutting energy vs Feed
(Process parameters: =5, Tool: Sharp edge)
0
0
5
Rake Angle (Degree)
10
7000
16
14
12
10
8
6
4
2
0
Specific cutting energy
(N/mm2)
Fig. 9 Cutting force vs Rake angle
(Process parameters: V=3 m/min, Tool: Sharp edge)
Cutting Force (N)
Cutting Force (N)
25
(4)
b f
In further analysis, the effect of cutting speed and rake
angle are investigated on the specific cutting energy. The
specific cutting energy is observed to decrease with an
increase in the cutting speed (see Fig. 11). This could be due to
a decrease in cutting forces at higher speeds. A decreasing
trend in specific cutting energy is observed with an increase in
rake angle (see Fig. 12). This could be explained by the
decrease in the cutting forces due to reduced ploughing at
higher rake angles.
15
7.5
Fc
V=3 m/min
V=10 m/min
V= 30 m/min
0
6
12
18
24
Cutting Speed (m/min)
0
5
10
6000
5000
4000
3000
2000
0
30
10
20
Feed (micrometer)
30
Fig. 12 Specific cutting energy vs Feed
(Process parameters: V=30 m/min, Tool: Sharp edge)
Fig. 10 Cutting force vs Cutting speed
(Process parameters: =5, Tool: Sharp edge)
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IWMF2014, 9th INTERNATIONAL WORKSHOP ON MICROFACTORIES
Chengli, S., Jianping, L. and Hu, H., “Influences
of Sequential Cuts on Micro-cutting Process
Studied by Smooth Particle Hydrodynamic (SPH)”,
Appl. Surf. Sci., Vol. 284, pp. 366-371, 2013.
4. Conclusions
Some of the main conclusions of this study are as follows:
 Orthogonal micro-cutting of medium carbon steel has
been modeled and simulated using SPH based
framework within LS-DYNA software.
 SPH simulation overcomes the challenges faced during
Lagrangian based simulations when feed decreases to 5
micrometer.
 Simulation results were benchmarked using specific
micro-cutting experiments.
 The predicted values of cutting forces match well with
the experimental data. The results also show trends that
are in agreement with the fundamental machining
behavior of ductile materials.
 It is observed that cutting forces increase with an
increase in feed, whereas the forces decrease with an
increase in rake angle and cutting speed.
 Specific cutting energy (also called as size effect)
increases nonlinearly as feed decreases. The specific
cutting energy is observed to decrease with an increase
in the cutting speed due to a decrease in cutting forces at
higher speeds.
 A decreasing trend in specific cutting energy is observed
with an increase in rake angle. This is due to the
decrease in the cutting forces due to reduced ploughing
at higher rake angles.
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