Modeling of Abrasive Wear in a Piston Ring and Engine Cylinder ...

Tribology Transactions, 47: 17-22, 2004
Copyright C○ Society of Tribologists and Lubrication Engineers
ISSN: 0569-8197 print
DOI: 10.1080/05698190490279074
Modeling of Abrasive Wear in a Piston Ring
and Engine Cylinder Bore System C✐
Engine-related improvements such as more efficient engine
components, improved engine oils, and high-performance coating
materials, need to be verified in terms of their effects on the
tribological performance of the piston ring/cylinder bore system.
The main purpose of this research is to develop an abrasive
wear model for the piston ring/cylinder bore system during
steady-state operation by considering the effects of temperature,
load, oil degradation, surface roughness, and material properties.
The model can be used either in theoretical modeling or
integrated with finite element analysis. Based on a laboratory
simulator, a three-body abrasive wear model has been developed
to model the wear progression of the piston ring/cylinder
bore system during steady state operation. The proposed novel
abrasive wear model addresses the effects of temperature, load,
oil degradation, surface roughness, and material properties. The
feasibility of the proposed model is illustrated by a numerical
example.
KEY WORDS
Abrasive Wear; Engine Oils; Piston-Rings
INTRODUCTION
To meet tough automotive competition and stringent government
regulations, more efficient engine components, improved
engine oils, and high performance coating materials have been
developed within the automotive industry. As part of the overall
performance evaluation of these developments, the tribological
performance of the ring/bore system must be determined. In an
internal combustion engine, the tribological performance of the
piston ring/engine cylinder bore system has long been recognized
as important in achieving desired engine efficiency and durabil-
SIMON C. TUNG (Member, STLE)
General Motors Research and Development Center
Chemical and Environmental Sciences Lab
Warren, Michigan
and
YONG HUANG
Georgia Institute of Technology
School of Mechanical Engineering
Atlanta, Georgia
Presented at the STLE/ASME Tribology Conference
in Ponte Vedra Beach, Florida
October 27-29, 2003
Final manuscript approved August 19, 2003
Review led by Gary Barber
17
ity in terms of power loss, fuel consumption, oil consumption,
blowby, and even harmful exhaust emissions. The wear rate of
the piston ring/cylinder bore system is high initially, decreases afterward,
then reaches a steady state. Ring/bore wear ultimately
results in poor performance and decreased oil economy, eventually
requiring an engine overhaul. Use of real engine tests
for the evaluation of tribological performance is very costly and
time consuming. One way to speed up the process, while maintaining
accuracy of the prediction, is to develop mathematical models
for each wear mechanism.
Like any other complicated physical system, several wear
mechanisms contribute to the wear progression for the piston
ring/cylinder bore system. As reviewed by Becker, et al. (1), the
three important wear mechanisms mentioned over the years are:
corrosion, abrasion, and adhesion. Corrosion is the dominant
mechanism when the engine runs either very cold or very hot.
Abrasion results from the cutting and plowing action of hard particles.
Adhesion is usually described as occurring when the oil film
between the ring and the bore is so thin that metal-to-metal contact
occurs. Other wear mechanisms, such as oxidation and splat
delamination (Becker and Ludema (2)), have been reported also.
Generally, corrosion has been successfully reduced by the use
of thermostats and by the addition of corrosion inhibitors to engine
oils (1); abrasion and adhesion are common during the running-in
period because of the surface roughness of both the ring and the
bore; abrasion, oxidation, and delamination wear are the main
mechanisms during the steady-state period. Whatever the main
wear mechanisms are for a specific piston ring/cylinder bore system,
the total wear volume loss for both the ring and the bore
is the sum of the contribution from each mechanism that is observed.
The real wear progression of the piston ring/cylinder bore
system is quite complex and is a function of several factors, such as
metallurgy of the contacting materials, surface finish and integrity,
operating conditions of the components, and lubricant properties.
Although the piston ring/cylinder bore wear progression has
received intensive attention in the literature, only a few researchers
have attempted to model the wear of the piston ring
and/or cylinder bore (Gangopadhyay (3)), considering the large

18 S. TUNG AND Y. HUANG
NOMENCLATURE
A = amplitude of the stroke
Acontact = contact area between the piston ring and the cylinder bore
a = constant
d = wear depth
d0 = wear depth during the running-in phase
dt = time interval
Fparticle = force supported by the abrasive particle
f = sliding frequency
K, K0 = constants
Kabrasion = process related abrasive wear coefficient
ˆKabrasion = process related abrasive wear coefficient considering the
effects of surface roughness and oil degradation
Kdegradation = wear coefficient modification due to oil degradation
Kroughness = wear coefficient modification due to the surface roughness
L = piston ring width
N = normal load
Nparticle = number of total generated wear particles within a time
interval
literary body of experimental investigations on this issue. To the
authors’ knowledge, most of the proposed models simply used Archard’s
abrasive wear equation or a modified form of this equation
(Gangopadhyay (3); Tingand Mayer (4); Visscher, et al. (5); Priest
et al. (6)). These documented models are insufficient to address
the wear progression of the piston ring and/or cylinder bore. A successful
wear model should include variables from hydrodynamics,
contact mechanics, materials engineering, and chemistry (Ludema
(7)).
Abrasion is generally considered to be a dominant wear mechanism
for the piston ring/cylinder bore system. In this work, modeling
of abrasive wear for the steady-state period will be addressed
in detail. The proposed novel abrasive wear model addresses the
effects of temperature, load, oil degradation, surface roughness,
and material properties. The feasibility of the proposed model will
be illustrated by a numerical example. The model can be further
applied in theoretical modeling or integrated with finite element
analysis. To fully model the wear progression, adhesive wear, oxidation,
and delamination should also be included and modeled in
addition to abrasive wear, depending on observed wear patterns
for a specific coated or uncoated piston ring/cylinder bore system
and the specified operating conditions (running-in or steady state).
These issues will be addressed in a future investigation.
In researching the wear progression of the piston ring/cylinder
bore system, the use of a laboratory simulator, such as a reciprocating
machine, has been verified as an effective approach (Becker
and Ludema (1); Barber, et al. (8)). In this study, abrasive wear of
the piston ring/cylinder bore system is modeled based on such a
simulation and this approach is illustrated by a numerical example.
MODELING OF ABRASIVE WEAR FOR PISTON
RING/CYLINDER BORE SYSTEM
Two-Body and Three-Body Abrasive Wear Mechanisms
Abrasive wear is damage to a component surface that arises
because of the motion relative to that surface of either harder
nparticle = number of particles in the unit apparent contact area
n = constant
P = uniform pressure between the ring and the bore
Pa
= hardness of the abrasive particle
Pt
= hardness of the piston ring or the cylinder bore
Pw
= hardness of the workpiece
pabrasion% = the percentage of total normal force support by abrasive
particles
T ( ◦C) = temperature
t = elapsed time
t0
= the moment when steady-state wear starts
V(t) = sliding velocity of the piston ring
Vwear-abrasion = volume loss due to abrasion within a time interval
ˆVwear-abrasion = volume loss due to abrasion within a time interval
during the steady-state period considering the effects of
surface roughness and oil degradation or of a particle
w = piston ring thickness
x = sliding distance
λ = dimensionless film thickness
θ = average roughness angle of the abrasive particle
asperities or perhaps hard particles trapped at the interface. Assuming
abrasive wear is a process in which a hard sharp indenter
scratches along the surface of a softer counter workpiece, the
workpiece volume loss Vwear-abrasion due to abrasive wear can be
expressed as:
xNtan θ
Vwear-abrasion = [1]
3Pw
Equation [1] is similar to Archard’s wear equation, which
asserts that wear volume loss is directly proportional to the load,
but inversely proportional to the surface hardness of the wearing
material.
If wear depends on the presence of free wear-particles, the main
mechanism is called three-body abrasion. If the wear-producing
agent is the hard counterface itself, or the abrasive particle is constrained
within the counterface, it is called two-body abrasion.
For a three-body condition, by using a lapping machine with the
abrasives between two sliding surfaces, Rabinowicz, et al. (9) developed
empirical wear volume loss equations as a function of the
sliding distance (x), the normal load (N), the average roughness
angle of the abrasive particle (θ), hardness of both base wearing
material (tool or workpiece), and the abrasive particle as Eq. [2].
By incorporating material hardness data, the model can be applied
in the piston ring/cylinder bore system.
xNtan θ
Vwear-abrasion =
3Pt
xNtan θ
Vwear-abrasion =
5.3Pt
for Pt
< 0.8
Pa
� �−2.5 Pt
Pa
� �−6.0 Pt
for 1.25 > Pt
Pa
> 0.8 [2]
xNtan θ
Vwear-abrasion =
2.43Pt Pa
for Pt
Pa
> 1.25
The volume loss model for an abrasive particle can be simplified
as:
� n−1 �
P
Vwear-abrasion = K xNtan θ [3]
a
P n
t

where n and K are known functions of Pt
Pt
Pa
1.25 > Pt
Pa
Pt
Pa
Modeling of Abrasive Wear in a Piston Ring and Engine Cylinder Bore System 19
Pα
< 0.8, n = 1.0, K = 0.333
defined as follows (10):
> 0.8, n = 3.5, K = 0.189 [4]
> 1.25, n = 7.0, K = 0.416
Under some conditions, the hard abrasive particles are securely
constrained within one base material, which causes two-body abrasive
wear on the counter base material. The hardness of the abrasive
particle is commonly assumed to be infinite in modeling the
wear loss under a two-body condition, and the volume loss can be
expressed as (Rabinowicz (11)):
Vwear-abrasion = k xN
3Pw
where k is the dimensionless abrasive wear coefficient.
For the piston ring/cylinder bore system, the generated abrasive
particles are different for the different ring/bore pair. Cavdar,
et al. (12) believed that on the bore side there is a layer called
the oxide metal mixture (OMM) layer near the bore metal and
the organo-iron compound (OIC) layer near the oil film; on the
ring side there is the ring chemical layer. Becker, et al. (1) suggested
that detachment of oxide flakes is the primary material loss
mechanism for the bore. Based on a ferromagnetic method, iron
particles and Fe3O4 with flake geometry were observed from the
dynamometer test engines with a cast iron bore or sprayed steel
bore on aluminum, and iron oxide flake was also observed from
simulator tests of cast iron bores (1). Tung, et al. (2) observed similar
iron oxides and iron particles when using a cast iron bore or
sprayed steel bore. For cast iron bores, the graphite flakes in the
matrix also deform and detach with flake morphology (Cavdar and
Ludemal (12)). Fortunately the graphite flakes act as solid lubricants
to some degree. During the running-in period, there will be
adhesive wear due to metal-to-metal contact. Some abrasive particles
are generated as a result of the broken microwelds between
the asperities of the ring and the bore. Based on the above discussion,
iron and iron oxide with flake geometry are considered to be
the main abrasive particles produced in the piston ring/cylinder
bore system, and three-body abrasive wear is the main abrasive
wear mechanism.
Modeling Three-Body Wear Mechanism for the Piston
Ring/Cylinder Bore System
The laboratory simulator specified by Tung, et al. (2) is studied
here. Considering the condition between the interface of the
piston ring/cylinder bore system as shown in Fig. 1, a piston ring
with width L and thickness w slides along a cylinder bore longitudinally
with speed V(t). Assuming the interface to be a plane with
a uniformly distributed pressure P along the interface, the total
normal load N on the contact region can be calculated as:
[5]
N = PwL [6]
Fig. 1—Schematic of the piston ring/cylinder bore simulator system.
For the piston ring/cylinder bore system, part of the total normal
load is supported by microwelds under the adhesive wear
mechanism during the running-in period and part is supported
by the oil film through hydrodynamics. Assuming pabrasion %of
the total normal load is supported uniformly by every particle as
Fparticle, and nparticle is the number of particles in the unit apparent
contact area, the force balance can be expressed as:
Based on Eqs. [6] and [7],
Npabrasion% = FparticlenparticlewL [7]
Fparticle = pabrasion%P
nparticle
In predicting the volume loss due to abrasive wear, the rate
of oxide formation and removal are assumed equal to simplify
the problem. With this assumption, the total number of abrasive
particles formed during a time interval is:
[8]
Nparticle = nparticle Acontact = nparticlewL [9]
The total sliding length of the piston ring during a time interval
dt is approximated as:
� �
x = V(t)dt = Asin(2π f )dt [10]
Since the reciprocating cycle is very short (less than 1 second)
compared with the time required to change other parameters such
as hardness, the average sliding speed is used here. The sliding
length during time interval dt can be expressed as:
x = 2Af dt [11]
Assuming the probability of generating a free abrasive particle
is equal everywhere along the interface when the piston ring slides
along the cylinder bore, the average sliding distance for every
possible particle is approximated as x
= Af dt.
2
Based on the three-body abrasive wear empirical model
of Rabinowicz, et al. (9), assuming a uniform temperature
distribution along the interface, the total tool volume loss

20 S. TUNG AND Y. HUANG
Vwear-abrasion for an ideal piston ring and cylinder bore system during
the time interval dt caused by Nparticle particles at an average
sliding distance Af dt under the normal load Fparticle is,
�
�
Vwear-abrasion =
�
=
�
=
NparticleK
� P n−1
a
P n
t
xFparticle tan θ
nparticlewLAfdt pabrasion%P
wLpabrasion%PK
nparticle
� P n−1
a
P n
t
� n−1 �
P
K tan θ
a
P n
t
�
tan θ Af dt [12]
The model can be further simplified as:
�
Vwear-abrasion =
� n−1 �
P
Af KabrasionK wLPdt [13]
a
P n
t
where Kabrasion = pabrasion% tan θ is the abrasive wear coefficient.
For a given piston ring/cylinder bore system, pabrasion% is
different for the running-in period and the steady-state period.
Thus, a different Kabrasion should be used for the running-in
and the steady-state periods. If there is more than one kind of
abrasive particle existing along the interface, the total tool volume
loss is made up of contributions from different kinds of
abrasive particles. In these cases, the value of Kabrasion associated
with each particle is different and needs to be determined
experimentally.
The hardness of the abrasive particles (metallic iron and/or iron
oxide) Pa and the ring/bore Pt can be expressed as an exponential
function of temperature (T is in ◦ C):
Pa = Pa0e −Kpa T −KPt T
, Pt = Pt0e
[14]
where Pa0 and Pt0 are the hardness of the abrasion particles and
the ring/bore measured at a reference temperature, respectively.
The flash temperature of the lubricated contacts is indispensable
information in determining the hot hardness of bore, ring,
and abrasive particle(s), if any. Considering the low coefficient of
friction of the piston ring and cylinder bore pair, the flash temperature
due to frictional heating is negligible compared with the
heating effect of the combustion chamber. To simplify the modeling
process, in the bench test, the temperature is stabilized at a set
point by a PID controller and considered as a constant under the
experimental operating conditions. In a real engine, this temperature
varies with the position of the crankshaft during every engine
stroke.
Modeling the Effects of Surface Roughness
and Oil Degradation
At the interface of the piston ring and the cylinder bore, it
is possible that a different lubrication regime exists as described
by the Stribeck curve, which is defined by a dimensionless film
thickness λ (the ratio between the oil film thickness and the composite
surface roughness). In the boundary lubrication regime,
some abrasive wear is expected to occur due to surface contact.
In the hydrodynamic lubrication regime, there should be no
abrasive wear because the surfaces are totally separated by an
oil film. In the mixed regime, the progress of wear depends on
the dimensionless film thickness. To take into account the effect
of surface finish, the wear coefficient Kabrasion should be mod-
Fig. 2—Transition model of wear coefficient modification due to surface
roughness.
ified by a factor which is a function of the dimensionless film
thickness.
As shown in Fig. 2, it is widely assumed that the wear constant
or wear coefficient modification decreases linearly as lubrication
conditions change from boundary to hydrodynamic
(Gangopadhyay (3); Visscher, et al. (5); Bell and Colgan (13)).
It can be represented mathematically as:
Kroughness(λ) =
�
K0 for λ ≤ ha
(hb − λ)
K0 for ha hb
[15]
where K0 is a dimensionless coefficient, which is determined by
the tribological property of the piston ring/cylinder bore sliding
pair.
Based on the study of Visscher, et al. (5), ha is taken as 0.5 and
hb is taken as 4, so that Eq. [15] can be expressed as:
�
Kroughness(λ) =
K0
K0 for λ ≤ 0.5
(4 − λ)
3.5
for 0.5 4
Typically the film thickness varies throughout the engine cycle
(6), and this variation should be included in the above transition
model in modeling the wear progression of the piston ring and/or
cylinder bore in a real engine.
Under actual engine operating conditions, the lubricant will
go from a fresh to a degraded condition mainly due to exposure
to combustion products and heat conducted from the combustion
chamber. A significant difference in the wear factor has been
reported between fresh and degraded conditions of the same lubricant
by Priest, et al. (6). Here a linear relationship is used to
describe the change of wear coefficient with the degradation of
the lubricant as follows:
Kdegradation = 1 + at [17]
Since the temperature along the interface between the piston
ring and the cylinder bore is usually about 100 ◦ C under engine
operating conditions, the lubricant degradation rate is assumed
not to depend on temperature.

Modeling of Abrasive Wear in a Piston Ring and Engine Cylinder Bore System 21
Modeling of Volume Loss Due to Abrasive Wear
Combining the effects of surface roughness and oil degradation,
the wear volume loss due to abrasive wear ˆVwear-abrasion for
the piston ring and cylinder bore system during steady-state can
be expressed as:
�
ˆVwear-abrasion
�
=
Af KabrasionK
Af ˆKabrasionK
⎧
⎨
4 − λ
⎩ 3.5
�
0 for λ>4
� P n−1
� n−1 �
P
a
P n
t
Af KabrasionK
a
P n
t
wLPKroughness(λ)Kdegradationdt
�
wLP(1 + at)dt for λ ≤ 0.5 [18]
� P n−1
a
P n
t
�
wLP(1 + at)dt for 0.5

22 S. TUNG AND Y. HUANG
Fig. 5—Wear depth progression of the iron cylinder bore.
is considered constant here. Since the temperature is controlled
at 125 ◦ C in the tests, the hardness of both the bore and the abrasive
particles (iron oxide here) is considered unchanged as Eq.
[14]. Further, K is constant as well since it depends on the hardness
of the bore and the abrasive particle as defined in Eq. [4].
Kabrasion is a constant for the given piston ring/bore system during
the steady-state period, which can be determined experimentally
using a pin-on-disc test. So wPfKroughness(λ)KabrasionK( Pn−1 a
Pn )of
t
Eq. [20] is treated as a constant and determined as 0.0041 using
a curve-fitting technique based on the measurements (Tung and
Emley (2)).
Based on the observation (2), steady-state wear conditions
were reached after 5 hours of running. Based on the characteristics
of the simulator system (2), the wear depth of the iron bore
during the steady-state operation is approximated as (the runningin
wear depth is included as 0.7664 µm):
d = 0.7664 + 0.0041(t + 0.0479t 2 − 2.6042) [22]
Based on Eq. [22], the wear depth progression of the iron bore
is calculated and shown in Fig. 5. The increases in the wear rate at
longer times are attributed to the high oil degradation rate used
in this simulation.
SUMMARY
Modeling of the wear progression of the piston ring/cylinder
bore system is critical for advancing engine-related technologies.
Based on a laboratory simulator, a three-body abrasive wear
model has been developed to model the wear progression of the
piston ring/cylinder bore system during steady-state operation.
The proposed abrasive wear model addresses the effects of temperature,
load, oil degradation, surface roughness, and material
properties. The feasibility of the proposed model is illustrated by
a numerical example. The model can be further applied in theoretical
modeling or integrated with finite element analysis. To
fully model the wear progression, lubricant oxidation and surface
delamination should also be included and modeled in addition to
abrasive wear, depending on observed wear patterns for a specific
coated or uncoated piston ring/cylinder bore system and the specified
operating conditions (running-in or steady state). Combining
the effects of surface roughness and oil degradation, the wear volume
loss due to abrasive wear has been investigated. Based on
this model simulation, the wear rate of the engine cylinder bore
system is also calculated. The increases in the wear rate at longer
times are attributed to the high oil degradation rate used in this
simulation.
ACKNOWLEDGMENTS
The authors thank Drs. Michael L. McMillan and James A.
Spearot for their support. The authors also acknowledge the help
of Mr. Angelo G. Quintana.
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