Download Determination of Actual Friction Factors in Metal Forming

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Article
Determination of Actual Friction Factors in Metal
Forming under Heavy Loaded Regimes Combining
Experimental and Numerical Analysis
Ana María Camacho 1, *, Mariano Veganzones 1 , Juan Claver 1 , Francisco Martín 2 ,
Lorenzo Sevilla 2 and Miguel Ángel Sebastián 1
1
2
*
Department of Manufacturing Engineering, Universidad Nacional de Educación a Distancia (UNED),
Madrid 28040, Spain; [email protected] (M.V.); [email protected] (J.C.);
[email protected] (M.Á.S.)
Department of Civil, Material and Manufacturing Engineering, University of Malaga, Malaga 29071, Spain;
[email protected] (F.M.); [email protected] (L.S.)
Correspondence: [email protected]; Tel.: +34-913-988-660
Academic Editor: Magd Abdel Wahab
Received: 8 August 2016; Accepted: 29 August 2016; Published: 1 September 2016
Abstract: Tribological conditions can change drastically during heavy loaded regimes as experienced
in metal forming; this is especially critical when lubrication can only be applied at the early stage of
the process because the homogeneous lubricant layer can break along the die-workpiece interface.
In these cases, adopting a constant friction factor for the lubricant-surface pair may not be a valid
assumption. This paper presents a procedure based on the use of dual friction factor maps to
determine friction factors employed in heavy loaded regimes. A finite element (FE) simulation is
used to obtain the friction factor map for the alloy UNS A96082. Experiments were conducted using
four lubricants (aluminum anti-size, MoS2 grease, silicone oil, and copper paste) to determine the
actual friction curves. The experimental procedure is based on the application of lubricant only at the
beginning of the first stage of ring compression, and not at intermediate stages as is usual in typical
ring compression tests (RCTs). The results show that for small reductions (rh < 20%), the conventional
RCT can be applied because the tribological conditions remain similar. For large reductions
(rh > 20%), it is recommended to obtain an average value of the friction factor for every
lubricant-surface pair in the range of deformation considered.
Keywords: friction; lubricant; FE; tribology; metal alloys; forming; large deformations; experiments
1. Introduction
Friction reduction has typically been investigated due to its importance in mechanical processes
performance, systems performance, and wear prevention. An effective technique for improving
tribological performance is surface texturing, as demonstrated by Lu et al. in [1] where friction
reduction is achieved by generating square dimples of different sizes and geometries at the contact
surface. New coatings to prevent wear under severe conditions are also being investigated, as observed
in the work from Vandoni et al. [2], where the use of fiber laser sources for surface texturing of very thin
TiN coatings is presented as a good option for heavy loaded sliding regimes. Reduction of friction and
wear has been proposed in the recent work of Yazawa et al. [3] through a hybrid tribofilm consisting of
both coating and lubricant. In metal forming, friction is a very complex phenomenon due to the variety
of technological factors involved and their own interrelation. Not only friction reduction, but also
friction characterization has grown recently because tribological conditions between workpieces and
tools heavily influence material flow and tool life [4], as well as required loads, energy consumption,
surface quality, and the internal microstructure of the products obtained by plastic deformation.
Materials 2016, 9, 751; doi:10.3390/ma9090751
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Recent studies published by Hua et al. [5] and Zhang and Ou [6] show the enthusiastic interest of
the scientific community to develop new methods for friction characterization and to discover new
relationships between classical friction models, respectively. The most widely accepted methodology
to characterize friction between two surfaces is to define a friction factor at the work piece-die interface.
To evaluate the behavior of lubricants in metal forming processes, it is common to quantify the friction
factor using different indirect techniques, such as the open-die backward extrusion test [7], double cup
extrusion test [8], or ring compression test, among others. The ring compression test (RCT) has been
widely used and successfully applied since its initial development by Kunogi [9]; this method was
improved by the well-known work of Male and Cockcroft [10]. After its publication, many researchers
have subsequently justified its validity; one example is the work of Hawkyard and Johnson [11]
that analyzed the problem assuming homogeneous deformation, neglecting strain hardening, and
assuming a constant Tresca friction factor at the interface. Male performed a study to determine the
variations of the friction factor of metals during the compression processes at room temperature [12],
and later on, the same author investigated the applicability of the RCT to conventional metal forming
processes [13]. Carter and Lee [14] simulated the RCT using a finite element model, generating the
friction factor curves for a particular material, and they observed some differences compared to the
curves obtained by Male and Cockcroft in their 1965 work. These differences were related to the
assumption of homogeneous strain and a constant value of the friction factor at the workpiece-die
interface. Some years later Wang and Lenard [15] concluded that the temperature and strain rate were
the two most influential parameters on the Tresca friction factor form results of hot RCTs. Other works
have attempted to determine the dependence of friction on the material properties, strain rate, and
non-homogeneous deformation, using both metallic [16] and non-metallic materials [17]. From these
works it can be concluded that the RCT is an effective method for the determination of the friction
factor in the metal forming processes. However, it is inadvisable to use generic friction maps and tables
independent of the type of material and operating conditions, as demonstrated by several authors
in the scientific literature [7,18]. Particularly, during any transient metal forming operation, such us
forging, tribological conditions change during the process; this is especially critical when lubrication
can only be supplied at the early stage of the process and heavily loaded conditions are applied due
to the extreme changes during the forming process that occur to the lubricant layer at the interface.
In these cases, the consideration of the initial friction factor for the lubricant-surface pairs applied
to the entire operation can lead to an underestimation of the required forces and, consequently, of
the required energy to finish the operation. To determine the actual friction factors found during
these operating conditions, numerical simulation is required as a complementary analysis tool to
experiments. The Finite Element Method (FEM) is widely used in metal forming simulation because its
analysis capability has been probed under large deformations. The combination of experimental tests
with analytical and numerical techniques has become the most powerful methodology for researchers
in metal forming. As an example, Shahriari et al. [19] have studied the hot RCT of the superalloy
Nimonic 115 by combining simulation techniques and experimental tests while using a profile projector
as a method of measurement of ring dimensions. Zhu et al. [20] also determined the friction factor
of Ti-6Al-4V titanium alloy in hot forging by combining RCT results and finite element simulations.
Other analytical techniques such as the Upper Bound Theorem (UBT) also have considerable potential,
as demonstrated by Bermudo et al. in their recent work [21]. This paper presents an alternative use
of the RCT (by means of dual friction factor maps) to determine friction factors more adapted to
heavy loaded regimes that occur during metal forming by combining experiments with numerical
simulations by FEM.
2. Materials and Methods
2.1. Approach
In this work, a combination of experiments with numerical simulations by the FEM has been
selected to perform the analysis and the procedure followed is outlined in Figure 1.
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Figure 1. Outline of the methodology. RCT refers to ring compression test.
Figure 1. Outline of the methodology. RCT refers to ring compression test.
This
methodology
will
bebe
explained
inin
detail
hereafter,
and
it comprises
thethe
following:
This
methodology
will
explained
detail
hereafter,
and
it comprises
following:
Experimentaldetermination
determinationofofthe
the plastic
plastic flow curve for
in in
the
•  Experimental
for the
thematerial
materialUNS
UNSA96082
A96082used
used
RCTs.
the
RCTs.
Finite
Element
modelling
simulate
RCTs,
considering
flow
curve
previously
obtained.
•  Finite
Element
modelling
toto
simulate
RCTs,
considering
thethe
flow
curve
previously
obtained.
Experimental
performance
of RCTs
according
the alternative
procedure
presented
in this
•  Experimental
performance
of RCTs
according
to thetoalternative
procedure
presented
in this paper.
paper.
This procedure
on the application
of lubricant
onlybeginning
at the beginning
of the
first
This
procedure
is based is
onbased
the application
of lubricant
only at the
of the first
stage
stage
during
the
compression
of
the
rings
and
not
at
intermediate
stages
as
usual
in
typical
during the compression of the rings and not at intermediate stages as usual in typical RCTs.
RCTs. representation of the dual friction factor map, which includes both the friction curves
•
Graphical
 obtained
Graphical
the dual friction
factor map,simulations.
which includes both the friction curves
by representation
experiments inof
laboratory
and by numerical
obtained
by
experiments
in
laboratory
and
by
numerical
•
Selection of the friction factor according to the deformationsimulations.
stage.

Selection of the friction factor according to the deformation stage.
2.2. Determination of the Plastic Flow Curve
2.2. Determination of the Plastic Flow Curve
Before starting the numerical simulation, the flow curve of the material UNS A96082 (Sanmetal
Before starting
the numerical
simulation,
thehad
flow
of the material
UNSCorrection
A96082 (Sanmetal
SA, Zaragoza,
Spain) used
in the experimental
tests
to curve
be determined.
The Bulge
Factor
SA, Zaragoza,
Spain)
experimental
had toofbe
The UNS
BulgeA96082
Correction
Method
(BCFM) [22]
wasused
usedintothe
obtain
the plastic tests
flow curve
thedetermined.
aluminum alloy
by
Factor
(BCFM)
wascontrolled
used to obtain
the plastic
flow curveDuring
of theuniaxial
aluminum
alloy UNS
means
ofMethod
compression
tests[22]
under
conditions
in the laboratory.
compression
A96082
by meansundergoes
of compression
tests under once
controlled
conditions
in the laboratory.
During
tests,
the specimen
plastic deformation
the yield
stress is achieved,
after the elastic
uniaxial
thethere
specimen
undergoes
plastic at
deformation
once the friction
yield stress
regime
[23].compression
In the plastictests,
regime,
is a uniform
deformation
first; afterwards,
at the is
workpiece-compression
dies’
interfaces
a non-uniform
deformation,
so a correction
factor
is
achieved, after the elastic
regime
[23]. causes
In the plastic
regime, there
is a uniform
deformation
at first;
required
to calculate
the flow
correctly [24].
afterwards,
the friction
atstress
the in
workpiece-compression
dies’ interfaces causes a non-uniform
To accomplish
goal, controlled
formingto
under
quasi-non-friction
was
performed
deformation,
so a this
correction
factor is required
calculate
the flow stressconditions
in correctly
[24].
in the laboratory.
During
compression
each specimen,
appropriate measurements
gathered
To accomplish
thisthe
goal,
controlled of
forming
under quasi-non-friction
conditionswere
was performed
toin
obtain
the flow curve
according
to the BCFM. of
In Figure
2, both curves
(before and
after application
the laboratory.
During
the compression
each specimen,
appropriate
measurements
were
ofgathered
BCFM) are
represented.
to obtain
the flow curve according to the BCFM. In Figure 2, both curves (before and after
application of BCFM) are represented.
Materials 2016, 9, 751
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Figure 2. Plastic flow curve of the Aluminum alloy UNS A96082.
To
characterizethe
thematerial
material
and
to implement
its plastic
properties
into
the element
finite element
To characterize
and
to implement
its plastic
properties
into the
finite
model,
model,
the
flow
curve
according
to
Hollomon’s
expression
is
presented
(Equation
(1)):
the flow curve according to Hollomon’s expression is presented (Equation (1)):
 (MPa) = 500·0.1 0.1
(1)
σ (MPa) = 500·ε
(1)
where K = 500 MPa is the strength coefficient and n = 0.1 is the strain hardening exponent. They have
where
K = 500 MPa
strength
coefficient
andofn the
= 0.1
is the
strain hardening
exponent.
been determined
as isa the
result
of potential
fitting
data
obtained
in the plastic
zone ofThey
the
have been determined
as a result
of potential
fitting
of the data
obtained in the plastic zone of the
stress-strain
curve by uniaxial
compression
tests
of cylindrical
specimens.
stress-strain curve by uniaxial compression tests of cylindrical specimens.
2.3. Lubricants
2.3. Lubricants
Lately, there is a growing interest in the use of green lubricants due to environmental concerns
Lately,
there is
growing interest
the form
use of
of liquid
green or
lubricants
due
to environmental
[25,26].
Lubricants
areacommonly
applied in
in the
solid films
at the
die-workpiece
concerns
[25,26].
Lubricants
are
commonly
applied
in
the
form
of
liquid
or
films
at The
the
interface to minimize adhesion, the interaction between surfaces and, therefore,solid
friction
[27].
die-workpiece
interface
to
minimize
adhesion,
the
interaction
between
surfaces
and,
therefore,
most common lubricants in use are oils and greases. Oils are basically composed of a base oil and
friction [27].
The most
common
lubricants
in use
and
Oils the
are basically
of a
specific
additives.
These
additives
are added
toare
theoils
base
oilgreases.
to provide
lubricantcomposed
its properties
base
oil
and
specific
additives.
These
additives
are
added
to
the
base
oil
to
provide
the
lubricant
and performance characteristics. On the other hand, grease comprises a base oil, additives, andits
a
properties
and thickener
performance
Onthat,
the in
other
hand, grease
a base
additives,
thickener. The
maycharacteristics.
be any material
combination
withcomprises
the base oil,
willoil,
produce
the
and a thickener.
The thickener
any material
that,used
in combination
the base
oil, will
produce
solid
to semi-fluid
structure.may
Thebemain
thickeners
in greases with
include
lithium,
aluminum,
the
solid
to
semi-fluid
structure.
The
main
thickeners
used
in
greases
include
lithium,
aluminum,
calcium soaps, and clay, either alone or in combination. Lithium soap is the most common thickener
calcium
soaps, and
clay, either
alone
or in combination.
soapas
is the
mostcase
common
thickener in
in
use today.
However,
many
applications
use solidLithium
lubricants
in the
of molybdenum
use today. However,
manynitride,
applications
use solid lubricants(PTFE)
as in the
of molybdenum
disulphide
(MoS2), boron
polytetrafluoroethylene
or case
Teflon,
and graphite.disulphide
These are
(MoS2 ), boron nitride, polytetrafluoroethylene (PTFE) or Teflon, and graphite. These are mainly used
mainly used in warm and hot forming where liquid lubricants are not recommended. These
in warm and hot forming where liquid lubricants are not recommended. These lubricants are widely
lubricants are widely used in the metal-mechanical industry [28].
used in the metal-mechanical industry [28].
To simulate different friction conditions during experimental tests, four lubricants (namely
To simulate different friction conditions during experimental tests, four lubricants (namely
aluminum anti-size, MoS2, silicone oil, and copper paste) were used and characterized by means of
aluminum anti-size, MoS2 , silicone oil, and copper paste) were used and characterized by means of
the RCT. Aluminum anti-size has excellent lubricating, anticorrosive, and anti-seize properties due
the RCT. Aluminum anti-size has excellent lubricating, anticorrosive, and anti-seize properties due to
to the aluminum structure that provides excellent behavior in high temperature conditions (until 600 °C).
the aluminum structure that provides excellent behavior in high temperature conditions (until 600 ◦ C).
It is recommended to prevent early wear of surfaces. MoS2 grease contains a mineral oil as a base, an
It is recommended to prevent early wear of surfaces. MoS2 grease contains a mineral oil as a base, an
organic thickener, and additives for use in high pressure conditions;
it is widely used in cases where
organic thickener, and additives for use in high pressure conditions; it is widely used in cases where
oscillations, vibrations, and impact loads are encountered under moderate temperatures. Silicone oil
oscillations, vibrations, and impact loads are encountered under moderate temperatures. Silicone oil
can be used for metallic and non-metallic components; it is characterized by a low viscosity level and
can be used for metallic and non-metallic components; it is characterized by a low viscosity level and a
a high resistance against decomposition by heat. The last lubricant is the copper paste; it is typically
high resistance against decomposition by heat. The last lubricant is the copper paste; it is typically
used to prevent wear by corrosion in high temperature and high load applications.
used to prevent wear by corrosion in high temperature and high load applications.
Materials 2016, 9, 751
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2.4. Finite Element Model
2.4. Finite
Element
Model
A finite
element
model has been developed in DEFORM F2™ (Scientific Forming Technologies
Corporation,
Columbus,
OH,has
USA)
accomplish
goal ofF2™
creating
a friction
factorTechnologies
map for the
A finite element
model
beentodeveloped
in the
DEFORM
(Scientific
Forming
specific
material
UNS
A96082.
This
FE
code
is
a
computer
aided
engineering
software
specifically
Corporation, Columbus, OH, USA) to accomplish the goal of creating a friction factor map
for the
designed
for
metal
forming
analysis.
The
DEFORM
(Scientific
Forming
Technologies
Corporation,
specific material UNS A96082. This FE code is a computer aided engineering software specifically
Columbus,for
OH,
USA)
preprocessor
uses
graphical user
interface
to assemble
the dataCorporation,
required to
designed
metal
forming
analysis.
Thea DEFORM
(Scientific
Forming
Technologies
Columbus,
OH, USA)
preprocessor
uses a graphical user interface to assemble the data required to run
run the simulation.
Input
data includes:
the simulation. Input data includes:

Object description: all data associated with an object, including geometry, mesh, temperature,
•
Object
description:
all data associated with an object, including geometry, mesh, temperature,
material,
etc.
material,
etc.

Material data: data describing the behavior of the material under the conditions which it will
•
Material
data:
data describing
the behavior of the material under the conditions which it will
reasonably
experience
during deformation.
reasonably
experience
during
deformation.

Inter object conditions: describes how the objects interact with each other, including contact and
•
Inter
object
conditions:
friction
between
objects.describes how the objects interact with each other, including contact and
friction between objects.

Simulation controls: definition of parameters such as discrete time steps to model the process.
•
Simulation controls: definition of parameters such as discrete time steps to model the process.
The main concepts of the preprocessing stage are explained in detail hereafter.
The main concepts of the preprocessing stage are explained in detail hereafter.
The geometrical relationships of the dimensions of the rings and the operating parameters
The geometrical relationships of the dimensions of the rings and the operating parameters
involved in the process were based on those used by Sofuoglu and Rasty in their tests [17]. The most
involved in the process were based on those used by Sofuoglu and Rasty in their tests [17]. The
common
dimensional
ratio used
thisintype
problem
is the relation
between
outer diameter:
inner
most
common
dimensional
ratio in
used
thisof
type
of problem
is the relation
between
outer diameter:
diameter:
height,
6:3:2,6:3:2,
respectively,
commonly
named
thethe“canonical
Specific
inner
diameter:
height,
respectively,
commonly
named
“canonicalaspect
aspect ratio”.
ratio”. Specific
dimensions
used
in
the
rings
tested
are
shown
in
Figure
3.
dimensions used in the rings tested are shown in Figure 3.
Figure
Figure 3.
3. Geometry
Geometry of
of the
the rings
rings tested
tested by
by RCT.
RCT.
Symmetry conditions are typically applied in the literature about RCTs due to the axisymmetric
Symmetry conditions are typically applied in the literature about RCTs due to the axisymmetric
nature of this problem. This can be observed in the finite element modelling of RCT in works of
nature of this problem. This can be observed in the finite element modelling of RCT in works of
reference such
such as
as the
the ones
ones realized
realized by
by Sofuoglu
Sofuoglu et
et al.,
al., where
where bi-dimensional
bi-dimensional models
models using
using finite
finite
reference
element codes
codesANSYS
ANSYS
[7] Abaqus
and Abaqus
have
been developed.
this, an
element
[7] and
[16,17] [16,17]
have been
developed.
ConsideringConsidering
this, an axisymmetric
axisymmetric
modelwith
wasthe
created
the finite
element
software
DEFORM
F2™
(Scientific
Forming
model
was created
finitewith
element
software
DEFORM
F2™
(Scientific
Forming
Technologies
Technologies Columbus,
Corporation,
Columbus,
OH, USA);
symmetry
conditions
were
imposed,
only
half
Corporation,
OH,
USA); symmetry
conditions
were
imposed,
so only
half ofsothe
model
was
analyzed.
of the
model was analyzed.
and
thethe
workpiece
is modelled
as aasdeformable
body.
The
Flat platens
platens are
aremodelled
modelledasasrigid
rigidparts
parts
and
workpiece
is modelled
a deformable
body.
workpiece
has been
meshed
with with
first order
continuum
elements
of quadrilateral
shapeshape
and the
mesh
The workpiece
has been
meshed
first order
continuum
elements
of quadrilateral
and
the
contains
approximately
2200
elements.
mesh contains approximately 2200 elements.
Regarding the
modelled with
with aluminum
aluminum alloy
alloy UNS
UNS A96082,
A96082, whose
whose
Regarding
the material,
material, each
each ring
ring has
has been
been modelled
plastic flow curve was determined previously from the compression test, as explained above. The flow
plastic flow curve was determined previously from the compression test, as explained above. The
stress data are introduced as tabular data because this is the most highly recommended method to
flow stress data are introduced as tabular data because this is the most highly recommended method
follow the true behavior of the material:
to follow the true behavior of the material:
. (2)
(2)
 σ= σ, ε,,ε,TT

where
where

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σ: effective
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ε: effective plastic strain,
.

: effective
flowrate,
stress,
ε:
effective
strain
T:
temperature
 work
: effective plastic strain,
In this paper
 : effective
straincold
rate,forming conditions are considered, so the flow stress does not depend on the
strain
ratetemperature
as the temperature is considered constant and equal to 20 ◦ C.
T : work
A constant
friction
model orconditions
shear friction
model was assumed
for stress
a range
of friction
factors,
In
this paper
cold forming
are considered,
so the flow
does
not depend
on“m”,
the
from
0
to
0.6.
This
friction
model
considers
a
friction
factor,
m,
to
quantify
the
interface
friction
and
its
strain rate as the temperature is considered constant and equal to 20 C.
analytical
expression
is (Equation
A constant
friction
model or (3)):
shear friction model was assumed for a range of friction factors,
τ =a m
·k
(3)
“m”, from 0 to 0.6. This friction model considers
friction
factor, m, to quantify the interface friction
and its
analytical
expression
(Equation
(3)):is constant and it only depends on the shear flow stress,
This
model assumes
thatisfriction
stress
(3)
m k stress is null, whereas for sticking conditions
k. For example, for perfect lubrication (m =0) friction
(m = This
1), friction
equals
shear
flowisstress.
This
model
has
been demonstrated
to bestress,
more
model stress
assumes
that the
friction
stress
constant
and
it only
depends
on the shear flow
realistic
than Coulomb’s
friction
model(m
in =metal
forming
analysis
because
normal
pressures
are often
k.
For example,
for perfect
lubrication
0) friction
stress
is null,
whereas
for sticking
conditions
higher
flowstress
stresses
so the
Coulomb’s
friction
provides
stresses highertothan
shear
(m
= 1),than
friction
equals
the
shear flow
stress.model
This model
hasfriction
been demonstrated
be more
flow
stresses.
realistic than Coulomb’s friction model in metal forming analysis because normal pressures are
simulation
controls,
F2™
is a numerical
code offriction
implicit
methodology
that
oftenRegarding
higher than
flow stresses
so theDEFORM
Coulomb’s
friction
model provides
stresses
higher than
uses the
Newton-Raphson
method for solving the equations. The model includes 200 steps and the
shear
flow
stresses.
step Regarding
increment is
defined ascontrols,
10. The DEFORM
number ofF2™
stepsisisa given
by Equation
simulation
numerical
code of (4):
implicit methodology that
uses the Newton-Raphson method for solving the equations.
The model includes 200 steps and the
x
n
=
(4)
step increment is defined as 10. The number of steps
V · is
∆tgiven by Equation (4):
where
n
x
V  t
(4)
where
n: number of steps,
n:
of steps,of the primary die,
x: number
total movement
x:
total
movement
of the primary die,
V: primary die velocity,
V:
die increment
velocity, per step
∆t:primary
is the time
t: is the time increment per step
The
The completed
completed model
model after
after preprocessing
preprocessing is
is presented
presented in
in Figure
Figure 4,
4, where contact
contact nodes
nodes at the
beginning of the compression process are shown at the die-workpiece interfaces.
interfaces.
Figure
Figure 4.
4. Finite
Finite Element
Element model
model by
by DEFORM
DEFORM F2™
F2™ after
after preprocessing.
preprocessing.
The
deformed rings
rings after
aftercompression
compressionand
andextreme
extremefriction
friction
conditions
shown
in Figure
5b
The deformed
conditions
areare
shown
in Figure
5b for
for
comparison.
explained
in [18],
when
a ring
preform
is compressed
in the
plastic
between
comparison.
As As
explained
in [18],
when
a ring
preform
is compressed
in the
plastic
fieldfield
between
flat
flat platens, a high friction factor results in an inward flow of material (m = 0.6); however, a low
friction factor results in an outward flow of material (m = 0.04).
Materials 2016, 9, 751
7 of 16
platens, a high friction factor results in an inward flow of material (m = 0.6); however, a low friction
7 of 16
7 of 16
outward flow of material (m = 0.04).
Materials 2016, 9, 751
Materials
2016, 9, 751
factor results
in an
(a)(a)
(b)(b)
Figure
Finite
Element
Method
(FEM)
simulation
RCT
for
different
friction
conditions.
(a)
Initial
Figure
Finite
Element
Method
(FEM)
simulation
RCT
for
different
friction
conditions.
(a)
Initial
Figure
5.5.5.
Finite
Element
Method
(FEM)
simulation
ofofof
RCT
for
different
friction
conditions.
(a)
Initial
mesh
(axisymmetrical
model);
(b)
Deformed
samples
for
different
friction
conditions
(top:
m
=0.6;
0.6;
mesh(axisymmetrical
(axisymmetricalmodel);
model);(b)
(b)Deformed
Deformedsamples
samplesfor
fordifferent
differentfriction
frictionconditions
conditions(top:
(top:mm==0.6;
mesh
bottom:
m
=
0.04).
bottom:mm==0.04).
0.04).
bottom:
2.5. Experimental
Procedure
2.5.
2.5.Experimental
ExperimentalProcedure
Procedure
Experimentaltests
tests
were
conducted
determine
thedual
dual
friction
factor
mapofofthe
the
Experimental
tests
were
conducted
totodetermine
friction
factor
map
Experimental
were
conducted
to determine
the dualthe
friction
factor
map of
the aforementioned
aforementioned
lubricants
material
UNS
A96082
under
specific
forming
conditions.
Accordingly,
aforementioned
lubricants
forfor
material
UNS
A96082
under
specific
forming
conditions.
Accordingly,
lubricants
for material
UNS
A96082
under
specific
forming
conditions.
Accordingly,
experimental
experimental
compression
tests
were
realized
using
rings
treated
with
the
lubricants
presented;
compression compression
tests were realized
using
rings treated
with treated
the lubricants
presented;
this purpose,
experimental
tests were
realized
using rings
with the
lubricantsfor
presented;
forfor
thisuniversal
purpose,test
the
universal
testmachine
machine
HOYTOM
HM-100kN
(HOYTOM
S.L.,Leioa,
Leioa,
Spain)
the
machine
HOYTOM
HM-100kN
(HOYTOM
S.L., Leioa,
Spain)S.L.,
(Figure
6a) and
flat
this
purpose,
the
universal
test
HOYTOM
HM-100kN
(HOYTOM
Spain)
(Figure
6a)
and
flat
platens
as
forming
tools
(Figure
6b)
were
used.
platens6a)
as forming
tools (Figure
6b) were
used.
(Figure
and flat platens
as forming
tools
(Figure 6b) were used.
(a)(a)
(b)(b)
Figure
Equipment
and forming
tools. (a)
Universal test
machine HOYTOM
HM-100kN; (b)
Detailed
Figure
6.6.6.
Equipment
and
Figure
Equipment
andforming
formingtools.
tools.(a)
(a)Universal
Universaltest
testmachine
machineHOYTOM
HOYTOMHM-100kN;
HM-100kN;(b)
(b)Detailed
Detailed
view
of
flat
platens.
view
viewof
offlat
flatplatens.
platens.
conductthe
theRCTs,
RCTs,each
eachring
ringwas
wasplaced
placedononthe
thebottom
bottomplate
plateofofthe
thetest
testmachine
machine
ToToconduct
To
conduct
the
RCTs,
each
ring
was
placed
on
the
bottom
plate
of
the
test
machine
(compression
(compressionarea)
area)after
afterlubrication
lubricationofofthe
thecontact
contactsurfaces;
surfaces;then,
then,the
thetop
topplate
platewas
waspositioned
positioned
(compression
area)
aftercontact
lubrication
of
the
contact
surfaces;
then,
the
topcontact
plate was
positioned
making
contact
with
making
with
the
upper
surface
of
the
ring.
Once
was
made,
an
increment
of
the
load
making contact with the upper surface of the ring. Once contact was made, an increment of the
load
the
upper
surface
of the
ring. Onceincontact
was
made,
an increment
of
the
loadradius.
was applied
causing
a
was
applied
causing
a
reduction
height
and
the
deformation
of
the
inner
According
to
the
was applied causing a reduction in height and the deformation of the inner radius. According to the
alternativeapproach
approachpresented
presentedininthis
thispaper,
paper,the
thelubricant
lubricantwas
wasonly
onlyapplied
appliedat atthe
thefirst
firststage,
stage,asas
alternative
explained
previously.
explained previously.
Materials 2016, 9, 751
8 of 16
Materials 2016,
751
8 of 16
reduction
in9,height
and the deformation of the inner radius. According to the alternative approach
presented in this paper, the lubricant was only applied at the first stage, as explained previously.
The RCTs
RCTswere
wereconducted
conducted
three
different
for lubricant
each lubricant
intoorder
to generate
The
onon
three
different
ringsrings
for each
in order
generate
enough
enough
points
to
create
the
friction
map.
Compressions
were
applied
to
reach
loads
of
30,
50,kN.
andThe
70
points to create the friction map. Compressions were applied to reach loads of 30, 50, and 70
kN. velocity
The ramofvelocity
of the
of the test
machine
was
mm/s
in all The
of the
cases. The
ram
the upper
plateupper
of theplate
test machine
was
2.5 mm/s
in 2.5
all of
the cases.
conditions
of
conditions
of
the
process
are
specified
in
Table
1.
the process are specified in Table 1.
Table 1.
1. Ring compression
compression test
test conditions.
conditions.
Table
Temperature
Ram Velocity
Ram Velocity
Temperature
(◦ C)
(°C)
(mm/min)
(mm/min)
20
2.5
20
2.5
1st Stage Load
1st Stage Load
(kN)
(kN)
30
30
2nd Stage Load
2nd Stage Load
(kN)
(kN)
50
50
3rd Stage Load
3rd Stage Load
(kN)
(kN)
70
70
Rings at the end of every compression stage are presented in Figure 7.
Rings at the end of every compression stage are presented in Figure 7.
1st stage
2nd stage
3rd stage
Figure 7. Rings after each compression stage using four lubricants. From left to right: copper paste,
Figure 7. Rings after each compression stage using four lubricants. From left to right: copper paste,
silicone oil, MoS2 grease, aluminum anti-size.
silicone oil, MoS2 grease, aluminum anti-size.
In this
thethe
dimensional
changes
of the of
ringthe
for ring
each lubricant
the three
compression
thisfigure,
figure,
dimensional
changes
for each during
lubricant
during
the three
stages
can be observed.
changes will
be changes
explainedwill
in detail
in a subsequent
section.
compression
stages canThese
be observed.
These
be explained
in detail
in a subsequent
section.
2.6. Finite Element Model Validation
2.6. Finite
Model Validation
The Element
finite element
model has been validated with theoretical results obtained by
De Pierre
et
al.
[29]
by
an
analytical
forwith
the theoretical
canonical results
aspect obtained
ratio (6:3:2).
The finite element model has beenmethod
validated
by DeDue
Pierretoetthe
al.
dependency
of
the
method
with
the
material,
results
for
the
same
finite
element
model
and
different
[29] by an analytical method for the canonical aspect ratio (6:3:2). Due to the dependency of the
metallic
alloys
are
presented
in Figure
These
alloys
are (form
right): copper
UNS
method with
the
material,
results
for the8.same
finite
element
modelleft
andtodifferent
metallicalloy
alloys
are
C11000
and
aluminum
alloys
UNS
A92024
(both
flow
curves
are
imported
from
the
materials
library
presented in Figure 8. These alloys are (form left to right): copper alloy UNS C11000 and aluminum
of
DEFORM
F2™) and
UNS
A96082
in this work).
alloys
UNS A92024
(both
flow
curves(used
are imported
from the materials library of DEFORM F2™) and
The
biggest
differences
are
found
for
the friction factor m = 0.5. However, these differences
UNS A96082 (used in this work).
are minimum
the friction
coefficients
commonly
in cold these
forming
(m < 0.2).
The biggestfor
differences
are found
for themost
friction
factor m = used
0.5. However,
differences
are
Additionally,
a
comparison
of
the
dimensional
changes
in
diameter
obtained
by
experiments
anda
minimum for the friction coefficients most commonly used in cold forming (m < 0.2). Additionally,
finite
element
is shown
in Figure
9. In this
figure, it
be seen graphically
the
comparison
ofsimulation
the dimensional
changes
in diameter
obtained
bycan
experiments
and finite how
element
inner diameter decreases in both cases during the compression process (lubricants: silicone oil
simulation is shown in Figure 9. In this figure, it can be seen graphically how the inner diameter
and aluminum anti-size).
decreases in both cases during the compression process (lubricants: silicone oil and aluminum
anti-size).
Materials 2016, 9, 751
Materials
Materials 2016,
2016, 9,
9, 751
751
9 of 16
99 of
of 16
16
(a)
(a)
(b)
(b)
(c)
(c)
Figure
8.
Finite
element
model
Figure 8.
8. Finite
Finite element
element model
model validation
validation with
with theoretical
theoretical results
results obtained
obtained by
by De
De Pierre
Pierre et
et al.
al. [29].
[29].
Figure
validation
with
theoretical
results
obtained
by
De
Pierre
et
al.
[29].
(a)
Copper
alloy
UNS
C11000;
(b)
Aluminum
alloy
UNS
A92024;
(c)
Aluminum
alloy
UNS
A96082.
(a)Copper
Copperalloy
alloyUNS
UNSC11000;
C11000;(b)
(b)Aluminum
Aluminumalloy
alloyUNS
UNSA92024;
A92024;(c)
(c)Aluminum
Aluminumalloy
alloyUNS
UNSA96082.
A96082.
(a)
(a)
(a)
(b)
(b)
Figure
Figure 9.
9. Comparison
Comparison of
of experimental
experimental observations
observations and
and numerical
numerical results.
results. (a)
(a) Lubricant:
Lubricant: silicone
silicone oil;
oil;
Figure 9. Comparison of experimental observations and numerical results. (a) Lubricant: silicone oil;
(b)
(b) Lubricant:
Lubricant: aluminum
aluminum anti-size.
anti-size.
(b) Lubricant: aluminum anti-size.
Results
Results from
from the
the simulation
simulation are
are in
in good
good agreement
agreement with
with both
both analytical
analytical and
and experimental
experimental
Results
from
the
simulation
are
in
good
agreement
with
both
analytical
and
experimental
results,
results,
so
the
numerical
model
can
be
considered
validated.
results, so the numerical model can be considered validated.
so the numerical model can be considered validated.
Materials 2016, 9, 751
Materials 2016, 9, 751
10 of 16
10 of 16
3. Results and Discussion
3. Results and Discussion
3.1. Determination of Dimensional Variables
3.1. Determination
of Dimensional
Variables
Once RCTs have
been conducted
in the laboratory, it is possible to create the friction factor map;
to accomplish
thebeen
reductions
in height
(Equation (5))
innertoradius
(6))
that map;
each
Once RCTsthis,
have
conducted
in the laboratory,
it isand
possible
create(Equation
the friction
factor
ring
experienced
under
different
lubricants
have
to
be
obtained:
to accomplish this, the reductions in height (Equation (5)) and inner radius (Equation (6)) that each
h 
h1 obtained:
ring experienced under different lubricants have
0 to be
r (%) 
 100
h
h
h00 − h1
r h (%) =
· 100
(5)
(5)
 d  dh0 
 i ,0
i,1 
r (%)   (6)
  100
d
−
d
 ddii,0
i,1
,0


r d (%) =
· 100
(6)
di,0
where di,0 is the inner diameter of the ring at the beginning,
di,1 is the inner diameter of the ring at the
where
the inner
the ring
at the
beginning,
the height
inner diameter
the ring stage.
at the
end of dthe
stage,
h0 is diameter
the initialofheight
of the
ring,
and h1 is dthe
final
at every of
reduction
i,0 is
i,1 is
end
of the stage,
h0 is the initialchanges
height of
h1 is thedifferent
final height
at every
reduction
stage. To
To measure
the dimensional
ofthe
thering,
innerand
diameter,
methods
have
been proposed.
measure
theLenard
dimensional
changes of
inner diameter,
different
methods
have been
Wang
Wang and
[15] measured
thethe
diameter
with calipers
in two
directions
at theproposed.
middle and
on
and
Lenard
[15]
measuredHartley
the diameter
with
calipers in
two method
directions
the middle
and on the
end of
the end
of the
specimen.
et al. [30]
proposed
a new
byatusing
a ball-bearing
of known
the
specimen.
et al. [30]Shahriari
proposedeta new
method
by using
ball-bearing of known
diameter,
diameter,
andHartley
more recently,
al. [19]
combined
thea aforementioned
method
with a
and
more
recently,
Shahriari
et
al.
[19]
combined
the
aforementioned
method
with
a
profile
profile projector equipped with an X-Y micrometer table; however, this technique stillprojector
offered
equipped
with an X-Y
micrometer
table;the
however,
thisprofile
technique
still offered
problems
the
problems because
the method
assumes
deformed
possesses
a circular
shape because
which does
method
assumes
the
deformed
profile
possesses
a
circular
shape
which
does
not
match
perfectly
to
not match perfectly to reality. Goetz et al. [31] demonstrated that there are more types of profiles
reality.
Goetz
et
al.
[31]
demonstrated
that
there
are
more
types
of
profiles
besides
concave
and
convex,
besides concave and convex, which reduces the feasibility of the measurement process. For the sake
which
reducesand
the feasibility
measurement
process.
For the sake
of simplicity,
as there
is
of simplicity,
as there isofnothe
perfectly
established
procedure,
a profile
projector,and
TESA
VISIO
no
perfectly
established
procedure,
a
profile
projector,
TESA
VISIO
(TESA
SA,
Renens,
Switzerland)
(TESA SA, Renens, Switzerland) (Figure 10), has been used in this paper to take the measurements of
(Figure
10), plane.
has been used in this paper to take the measurements of the middle plane.
the middle
Figure
10. Details of the inner diameter measurement with profile projector TESA VISIO.
Figure 10. Details of the inner diameter measurement with profile projector TESA VISIO.
Table 2 shows the measurements obtained after performing the RCT with each ring in every
Table 2 shows the measurements obtained after performing the RCT with each ring in every stage
stage of the compression process. Each value of the diameter is the mean of three measurements, and
of the compression process. Each value of the diameter is the mean of three measurements, and each
each measurement is provided by the profile projector selecting eight points at 45 around the
measurement is provided by the profile projector selecting eight points at 45◦ around the diameter; the
diameter; the diameter of the circle is determined by fitting the data by the least-square method.
diameter of the circle is determined by fitting the data by the least-square method.
Materials 2016, 9, 751
11 of 16
Materials 2016, 9, 751
11 of 16
Table 2. Dimensional measurements after conducting the RCTs.
Table 2. Dimensional measurements after conducting the RCTs.
Lubricants
Lubricants
Aluminum
anti-size
Aluminum
anti-size
MoSMoS
2 grease
2 grease
Silicone
oil oil
Silicone
Copper paste
Copper paste
Forming Stage
Forming
Stage
11
22
33
11
22
3
3
11
22
3
3
11
2
2
3
3
Inner
Diameter
(mm) OuterOuter
Diameter
(mm)
Inner
Diameter
(mm)
Diameter
(mm)
5.1495.149
10.989
10.989
12.510
4.8034.803
12.510
13.680
4.2944.294
13.680
11.080
5.2595.259
11.080
4.878
12.754
4.878
12.754
4.476
13.735
4.476
13.735
10.842
5.0935.093
10.842
4.638
12.383
4.638
12.383
4.002
12.982
4.002
12.982
10.943
5.1025.102
10.943
4.800
12.538
4.800
12.538
4.377
13.598
4.377
13.598
AsAs
it can
bebe
seen
in all
allcases;
cases;while
whilethe
theinner
inner
diameter
it can
seenininTable
Table2,2,the
theouter
outerdiameter
diameter expands
expands in
diameter
increases
at at
thethe
first
stage
the compression
compressionprocess.
process.
increases
first
stageand
anddecreases
decreasesatatthe
thelast
last stages
stages during
during the
Images
(from
thathave
havebeen
beeninincontact
contact
with
Images
(fromthe
theprofile
profileprojector)
projector)of
of the
the rings’
rings’ surfaces
surfaces that
with
thethe
flatflat
platens
forfor
all all
lubricants
areare
shown
in in
Figure
11.11.
The
profile
projector
allows
platens
lubricants
shown
Figure
The
profile
projector
allowsfor
forthe
theopportunity
opportunitytotosee
thesee
contact
surfaces
of the workpiece
after each
stage. stage.
In all the
cases
an external
the contact
surfaces
of the workpiece
aftercompression
each compression
In all
the there
cases isthere
is an
ring
belonging
to
the
lateral
surface
of
the
ring
that
establishes
new
contact
once
the
compression
takes
external ring belonging to the lateral surface of the ring that establishes new contact once the
place;
this will lead
an inhomogeneous
contact
surface andcontact
it will surface
influence
friction
factorthe
so it
compression
takesto
place;
this will lead to an
inhomogeneous
andthe
it will
influence
canfriction
be onefactor
reason
to be
consider
this factor
m constant
the process.
sonot
it can
one reason
not to consider
thisthroughout
factor m constant
throughout the process.
Figure 11. Rings tested in the laboratory after each forming stage. Images obtained by TESA VISIO
Figure
11. Rings tested in the laboratory after each forming stage. Images obtained by TESA VISIO
profile projector.
profile projector.
Materials 2016, 9, 751
12 of 16
Materials 2016, 9, 751
12 of 16
3.2.
Dual
Friction
3.2.
Dual
FrictionFactor
FactorMap
Map
The
friction
factor
map
waswas
obtained
by a by
finite
element
modelmodel
according
to the material
properties
The
friction
factor
map
obtained
a finite
element
according
to the material
of properties
the ring (aluminum
alloy
UNS
A96082).
By
overlapping
the
friction
curves
obtained
numerically
of the ring (aluminum alloy UNS A96082). By overlapping the friction curves obtained
and
through experimental
a quantitative
qualitativeand
assessment
of the
behaviorofofthe
each
numerically
and throughtesting,
experimental
testing, and
a quantitative
qualitative
assessment
lubricant
be realized,
considerations
about alternative
uses
of RCTsuses
are of
described.
behaviorcan
of each
lubricantand
can some
be realized,
and some considerations
about
alternative
RCTs
Figure
12 showsFigure
the dual
frictionthe
factor
obtained.
are described.
12 shows
dualmap
friction
factor map obtained.
Figure12.
12.Dual
Dualfriction
friction factor
factor map
results.
Figure
map for
for UNS
UNSA96082
A96082experimental
experimental
results.
The dual friction factors map plotted for alloy UNS A96082 (Figure 12) shows that the value of
dualfactor
friction
factors experimentally
map plotted for
A96082
shows that
the value
theThe
friction
obtained
foralloy
eachUNS
lubricant
can(Figure
only be12)
considered
constant
for of
thesmall
friction
factor
obtained
experimentally
for
each
lubricant
can
only
be
considered
constant
for
small
reductions in height (lower than 20% in most cases). Table 3 presents the friction factors
reductions
(lowerthe
than
20% in most
Tableresults.
3 presents
the friction
factors estimated
estimatedinbyheight
comparing
experimental
andcases).
simulated
However,
for reductions
higher
bythan
comparing
the
experimental
and
simulated
results.
However,
for
reductions
higher
than
this percentage, the assumption of a constant value for the friction coefficient throughout thethis
percentage,
assumption
of aTable
constant
valuethe
for ranges
the friction
coefficient
throughout
thefor
RCT
is no
RCT is nothe
longer
acceptable.
3 shows
of friction
factors
encountered
each
longer
acceptable.
3 shows
thecoefficient
ranges offor
friction
factors encountered for each lubricant, and the
lubricant,
and theTable
average
friction
each range.
average friction coefficient for each range.
Table 3. Friction factors determined by the RCT according to reduction in height.
Table 3. Friction factors determined by the RCT according to reduction in height.
Aluminum
Friction Factor (m)
MoS2 Grease
Copper Paste
Silicone Oil
Anti-Size
Aluminum
Friction
Copper Paste
Silicone Oil
SmallFactor
height(m)
reduction MoS2 Grease
Anti-Size
0.12
0.20
0.23
0.24
(rh < 20%)
Small height
0.12
reduction
(rh < 20%)
0.12 < m < 0.24,
Large height
reduction
Large height
0.12 < m < 0.24, mavg
> 20%)
mavg = 0.18
(rh >
reduction (r
20%) **
= 0.18
h
0.20
0.20 < m < 0.28,
0.20 < m < 0.28, mavg
m=avg0.24
= 0.24
0.23
0.23 < m < 0.27,
0.23 < m < 0.27, mavg
mavg==0.25
0.25
* Upper value: friction coefficients range; lower value: average friction coefficient.
0.24
0.24 < m < 0.39,
0.24 < m < 0.39, mavg
mavg = =0.32
0.32
* Upper value: friction coefficients range; lower value: average friction coefficient.
Materials 2016, 9, 751
Materials 2016, 9, 751
13 of 16
13 of 16
This
is reasonable
because
the tribological
conditionsconditions
are changing
the dies-workpiece
Thisbehavior
behavior
is reasonable
because
the tribological
areat changing
at the
interfaces
during
deformation
by heavily
regimes,
asregimes,
observed
in real transient
dies-workpiece
interfaces
duringcaused
deformation
causedloaded
by heavily
loaded
as observed
in real
metal
forming
such as open
dieopen
forging
or stamping.
On one
new contact
areas
transient
metaloperations,
forming operations,
such as
die forging
or stamping.
Onhand,
one hand,
new contact
corresponding
to the to
lateral
surfaces
of the of
ring
establishing
new contact,
and, on
the
hand,
areas corresponding
the lateral
surfaces
theare
ring
are establishing
new contact,
and,
onother
the other
hand,
the lubricant
layer large
during
largereductions
height reductions
is not to
expected
to be homogeneously
the
lubricant
layer during
height
is not expected
be homogeneously
distributed
at area
the contact
areato
according
to the inhomogeneous
contact pressures
profile
[32].
As an
atdistributed
the contact
according
the inhomogeneous
contact pressures
profile [32].
As an
example,
example,
shows the
contact
pressure
for a slim
it occurs
in theofearly
Figure
13a Figure
shows 13a
the contact
pressure
profile
for a profile
slim preform,
as itpreform,
occurs inasthe
early stages
open
stages
of open
die forgingcomponents,
of cylindrical
components,
Figure
presents
profile for a
die
forging
of cylindrical
and
Figure 13b and
presents
the13b
same
profilethe
forsame
a flattened-shape
flattened-shape
as in
the late
stages during
compression
of cylindrical parts.
preform,
as in thepreform,
late stages
during
compression
of cylindrical
parts.
(a)
(b)
Figure 13. Contact pressure profiles for different friction conditions. (a) Slim preform (d = 10 mm and
Figure 13. Contact pressure profiles for different friction conditions. (a) Slim preform (d = 10 mm and
h = 20 mm); (b) Flattened-shape preform (d = 10 mm and h = 3 mm).
h = 20 mm); (b) Flattened-shape preform (d = 10 mm and h = 3 mm).
As observed in the first case (Figure 13a), a minimum is detected at the center; this configuration
observed in
firstthe
caselubricant
(Figure 13a),
a minimum
is detected
at theresponse
center; this
configuration
can As
be favorable
to the
entrap
at this
area, resulting
in positive
against
friction.
can
be
favorable
to
entrap
the
lubricant
at
this
area,
resulting
in
positive
response
against
However, in the second case (Figure 13b) the maximum of the profile is presented around the friction.
center
However,
in the second
case (Figure
the maximum
the under
profilethis
is presented
around
thelubricant
center of
of the workpiece,
as expected
from13b)
classical
analysis of
[33];
configuration
the
the
workpiece,
as expected
fromand
classical
analysis the
[33];edge
under
configuration
layer
layer
at the center
could break
slip towards
of this
the workpiece.
In the
bothlubricant
cases, every
atcontact
the center
could
break
and
slip
towards
the
edge
of
the
workpiece.
In
both
cases,
every
contact
pressure profile has a different friction condition associated with it and vice versa. This
pressure
profile
has any
a different
friction
associatedsuch
withas
it and
vicetribological
versa. This conditions
means that
means that
during
transient
metalcondition
forming operation,
forging,
during
transient
metal forming
operation,
such as
forging,
tribological
conditions change
during
changeany
during
the process
as a result
of different
stress
states,
so the establishment
of the initial
the
process
as
a
result
of
different
stress
states,
so
the
establishment
of
the
initial
friction
factor
for the
friction factor for the entire operation, as usual, should be reconsidered.
entireFurthermore,
operation, as in
usual,
should
be
reconsidered.
metal forming processes several types of lubrication can be distinguished [27].
Furthermore,
in metal
severalsotypes
of lubrication
be distinguished
In dry
forming there
is no forming
lubricantprocesses
at the interface
friction
is high. In can
boundary
lubrication[27].
thereIn
dry
is no lubricant
at organic,
the interface
friction isabsorbed
high. In boundary
lubrication
is a forming
thin filmthere
of lubricant,
generally
that issophysically
or chemically
adheredthere
to theis
amaterial
thin filmsurface.
of lubricant,
generally
organic,
thatremains
is physically
absorbed
or chemically
adhered
to the
As in the
former case,
friction
high. Full
film lubrication
occurs
when there
material
in the
former case,
friction
remains
high. Full
film lubrication
when
is a thicksurface.
layer ofAssolid
lubricant;
in this
case, the
conditions
affecting
friction are occurs
governed
bythere
the
isshear
a thick
layer of solid
lubricant;
in this
case,
theisconditions
affecting
friction
are governed
by the
strength
the lubricant
film.
When
there
a thick layer
of liquid
lubricant,
the lubrication
shear
strength
the lubricant in
film.
there isisa governed
thick layer
liquid
lubricant,
lubrication
conditions
are of
hydrodynamic;
thisWhen
case, friction
byofthe
viscosity
of the the
lubricant
and
conditions
hydrodynamic;
in this interface
case, friction
is governed
of the
lubricantlow.
and
the slidingare
velocity
at the contact
allowing
frictionbytothe
beviscosity
considered
relatively
the
sliding velocity
the contact
interface
allowing
friction
to be considered
relatively
low. However,
However,
the mostatcommon
situation
in metal
forming
operations
is mixed-layer
lubrication;
this is
the
most common
situation
in metal forming
operations
is mixed-layer
lubrication;
because
hydrodynamic
conditions
cannot be
maintained
at high pressures
andthis
lowis because
sliding
hydrodynamic
conditions
cannot
be maintained
at high
lowprocedure
sliding velocities.
Taking
velocities. Taking
this into
account,
it is necessary
topressures
establish and
a new
to determine
this
into account,
it is in
necessary
to establish
a new
procedure
determine
conditions of friction in
conditions
of friction
metal forming
processes
closer
to thoseto
actually
encountered.
metalAs
forming
processes
closer and
to those
actually[28],
encountered.
indicated
by Mandić
Stefanović
modelling results and their transfer onto real
As indicated
by Mandić
and
resultsconditions
and their in
transfer
ontoand
real
processes
highly depends
upon
theStefanović
similarity [28],
of themodelling
contact friction
modelling
processes
depends
upon thetosimilarity
of the contact
conditions
and
during thehighly
real process.
According
this, the friction
factor atfriction
the very
beginninginofmodelling
any forming
during
real friction
process.conditions
According
this,
the friction
factor at
very resulting
beginning
process,the
when
cantobe
significantly
different
to the ones
atof
theany
endforming
of the
process, can be far from reality. For small height reductions (lower than 20% in the case of the
Materials 2016, 9, 751
14 of 16
process, when friction conditions can be significantly different to the ones resulting at the end of the
process, can be far from reality. For small height reductions (lower than 20% in the case of the material
considered in this paper, UNS A96082) friction curves obtained experimentally for each lubricant are
clearly similar to some of the curves obtained by the finite element simulation. However, for high
height reductions (higher than 20% in the case of UNS A96082), this behavior is not observed, and
the experimental results fall into a friction factor range for each lubricant. In this case, the use of a
single average value of the friction factor assigned to every lubricant-component pair in the range of
deformation is recommended.
4. Conclusions
This paper shows that friction factors obtained for each lubricant-surface pair by the alternative
approach of the RCT technique seem to vary during the compression process, as observed in real
transient metal forming operations; thus, the points obtained do not entirely match a single curve of
the friction factor map plotted from the finite element simulation.
Based on these observations, the alternative approach of the RCT presented in this paper can be
successfully applied in the determination of friction conditions that are better adapted to real processes.
To obtain a friction factor closer to the actual one present in real forming processes, the new procedure
described in this paper is recommended:
•
•
For small deformation stages (rh < 20% in this work), the conventional RCT [10] can be applied, as
the tribological conditions will remain similar during the operation (Table 3). Particularly, in this
paper, friction factors obtained for small reductions were 0.12, 0.20, 0.23, and 0.24 for lubricants
MoS2 , aluminum anti-size, copper paste, and silicone oil, respectively.
For large deformations-reductions (rh > 20% in this work), it would be advisable to use the
alternative approach of the RCT presented in this paper (without any lubrication between steps),
and to obtain an average value of the friction factor assigned to every lubricant-component pair
in the range of deformation considered (Table 3). This average value was 0.18, 0.24, 0.25, and
0.32 for lubricants MoS2 , aluminum anti-size, copper paste, and silicone oil, respectively. Some
differences were also observed in the width of the range obtained for each lubricant, being small
for aluminum anti-size and copper paste (0.08 and 0.04, respectively) and bigger for MoS2 and
silicone oil (0.12 and 0.15, respectively). In these last two cases the determination of an average
value is more critical.
The methodology presented in this paper can be used in the real practice of forming processes as
follows. In incremental processes and those ones where lubrication can be applied between stages of
small deformations, the conventional RCT is advisable for taking into account that friction conditions
are more homogeneous with the application of incremental loads [34]. However, in those metal forming
operations where heavy loaded regimes occur and the lubricant cannot be applied in intermediate
stages, the lubricant layer is not constant during the forming process, and the tribological conditions
change throughout the operation. When a transient forming process, such as forging or stamping, is
being performed, the use of the alternative RCT approach is recommended. In this case, an average
value for the whole friction range should be estimated instead of applying the initial friction factor for
the entire operation, as usual. For more precise results, the friction factor should be selected according
to the deformation stage in each particular case. Thus, the friction factor values should be based on the
deformation level of each particular forming process, and this alternative approach of the RCT can
be valuable.
To help in this matter, dual friction factor maps, as presented in this work, can be an interesting
tool to determine friction coefficients at die-workpiece interfaces closer to those found in real
process conditions.
Acknowledgments: The authors would like to take this opportunity to thank the Research Group of the UNED
“Industrial Production and Manufacturing Engineering (IPME)” for the given support during the development of
Materials 2016, 9, 751
15 of 16
this work. This work has been financially supported by the funds provided through the Annual Grant Call of the
E.T.S.I.I. of UNED of reference 2016-ICF04.
Author Contributions: A.M.C. and M.A.S. conceived and designed the experiments; M.V. and J.C. performed the
experiments; A.M.C., F.M., and L.S. analyzed the data; and A.M.C. wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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article distributed under the terms and conditions of the Creative Commons Attribution
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