NUMERICAL MODELING OF THE POWER CYLINDER SYSTEM FOR INTERNAL COMBUSTION
ENGINE WITH AN EMPHASIS ON RING PACK DESIGN
By
Chao Cheng

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering – Doctor of Philosophy
2014

ABSTRACT
NUMERICAL MODELING OF THE POWER CYLINDER SYSTEM FOR INTERNAL COMBUSTION
ENGINE WITH AN EMPHASIS ON RING PACK DESIGN
By
Chao Cheng
Modeling the piston ring behavior is crucial for the engine power cylinder system. The dynamic
and thermal characteristics directly affect engine performance, e.g. frintion loss, wear, blowby
loss, etc. This dissertation describes a numerical model of the power cylinder system focusing
on the ring pack design.
A three-dimensional piston ring model is developed using finite element method. The model
predicts the piston ring conformability with the cylinder wall as well as the separation gap
between the interfaces. In addition, the ring model also predicts the interaction between the
ring and piston groove sides. This means, the ring axial lift, twist, contact with the groove sides along
the circumferential direction are all calculated simultaneously with the radial conformability prediction.

The numerical model is then verified through experiment measurement. This validation
includes a ring tension force measurement as well as a light-tightness measurement. Good
agreement has been found between the measured and calculated result.
Thermal load is believed having significant influence on the ring pack performance, especially
for the top compression ring, which is under the most severe operating condition. The thermal
load influences are included in the model. In addition, a new lubrication model is implemented
to the existing model with the consideration of flow factor for the ring pack lubrication and
tribology analysis.

A simulation study of the second ring dynamics for a modern diesel engine is presented. Two
phenomena are focused for this study, one is the second ring fluttering and the other is ring
collapse. Both these phenomena are closely related to gas dynamics and could result in engine
blowby increase. The mechanism and the conditions at which these phenomena occur are
given. The second ring dynamic behavior over an engine cycle is then studied considering 3D
effect. The contact forces, in both radial and axial directions, and the twist angles can be found
at each engine crank angle.
The piston ring model provides the geometry for three-dimensional gas dynamics analysis. In
addition to the gas flow paths that the current two-dimensional models predict, including
through the ring end gap, through the ring-groove sides as ring flutters, through the ring front
face when ring radially collapses, gas can flow through an additional path across the ring. This
gas flow path is formed due to the variance of ring axial displacements along the circumference.
The variant lift occurs for rings with asymmetric cross-sections. Even for rings with symmetric
cross-section, the ring can also undergo different circumferential lift due to influences like
piston secondary motion. When this different circumferential lift occurs, gas can flow from the
piston land above the ring, through the crevice between the ring-groove sides, to the volume
behind the ring for the ring segment that stays bottom seated. The gas can travel
circumferentially through the volume behind the ring, until a point that the ring segments lift
and stay top seated against the groove top side. Then the gas can flow from the volume behind
the ring, through the crevice between the ring-groove bottom sides, to the piston land below
the ring.

Copyright by
CHAO CHENG
2014

To my parents, Shulin and Liqin.
To my wife, Mengyang.

v

ACKNOWLEDGEMENTS

First, I would like to thank my advisor, Dr. Harold Schock. It is my great honor to work with Dr.
Schock at the Energy and Automotive Research Lab at Michigan State University. Dr. Schock has
always been supportive and patient with me, providing invaluable motivations through my
research. His faith and encouragement have helped me overcome the difficulties during my
graduate study.
I would also like to thank Dr. Guoming Zhu, Dr. Elisa Toulson and Dr. Dennis Miller for serving as
my committee members of my thesis defence. I would like to express my special thanks to Dr.
Zhu for his encouragement and discussions on my research as well as my graduate life. Dr.
Toulson and Dr. Miller also deserve special recognitions for their insightful suggestions to
improve my research.
I was very fortunate to have the opportunity to work with Mr. Mulyanto Poort from Rescale
and Dr. Dan Richardson from Cummins. Mulyanto Poort has helped me get familiar with power
cylinder modeling and provided numerous invaluable suggestions for my research. Dr. Dan
Richardson has provided numerous supports and invaluable advises on my research that will
benefit for my entire career.
It is not possible to complete my research without the support from my friends and colleagues:
Dr. Andrew Huijsen, Ali Kharazmi, Ravi Vedula, CJ Maines, Ati Sedigheh Tolou, Nariman
Mansouri, James Holly JR., Jenny Higel, Jeff Higel, Tom Stuecken, Brian Rowley, Trevor Ruckle.
They have made the lab a fun place to work, especially Ali, whose discussion on the model and

vi

the post-processing of the result is highly appreciated. I would like to express my special thanks
to Tom, Brian and Trevor for helping me set up the experiment.
I would also thank my friend, Dr. Xiankai Song, for the discussions and so many invaluable
suggestions on my numerical modeling.
Finally, I would like to thank and express my gratitude to my wife Mengyang and to my parents,
Shulin and Liqin. Although we have been spending considerable amount of time on the two
sides of the earth, they are always there, loving, supporting, and being patient with me.

vii

TABLE OF CONTENTS
LIST OF TABLES............................................................................................................................................ x
LIST OF FIGURES ....................................................................................................................................... xii
Chapter 1 NUMERICAL MODELING OF ENGINE POWER CYLINDER SYSTEM ..................................... 1
1.1
Motivation ................................................................................................................................... 1
1.2
Objective ...................................................................................................................................... 2
1.3
Previous efforts........................................................................................................................... 4
1.3.1 Piston .............................................................................................................................. 4
1.3.2 Ring pack ......................................................................................................................... 5
1.4
Dissertation structure ................................................................................................................ 7
Chapter 2 ENGINE POWER CYLINDER SYSTEM ....................................................................................... 9
2.1
Introduction ................................................................................................................................ 9
2.2
Piston ......................................................................................................................................... 13
2.3
Ring pack.................................................................................................................................... 15
2.3.1
Top compression ring.............................................................................................. 16
2.3.2
Second compression ring ........................................................................................ 17
2.3.3
Oil control ring ........................................................................................................ 20
2.3.4
Key ring nomenclature ............................................................................................ 21
2.4
Cylinder ...................................................................................................................................... 23
2.5
Connecting rod ......................................................................................................................... 26
2.6
Wrist pin .................................................................................................................................... 27
Chapter 3 THREE-DIMENSIONAL RING-CYLINDER WALL AND RING-PISTON GROOVE CONTACT
MODELING................................................................................................................................................. 28
3.1
Introduction .............................................................................................................................. 28
3.2
Finite element analysis formulation ...................................................................................... 28
3.2.1 Governing Equations .................................................................................................... 29
3.2.2 Finite Element Analysis ................................................................................................. 33
3.2.3 Ring-Cylinder Wall Contact Modeling .......................................................................... 39
3.2.4 Ring-Groove Side Contact Modeling ............................................................................ 51
3.2.5 Result of Ring-Cylinder Bore Contact ........................................................................... 53
3.2.6 Application on EcoMotors 2-Stroke Engine.................................................................. 56
3.2.6 Result of Ring-Cylinder Bore-Groove Side Contact ...................................................... 63
Chapter 4 RING THERMAL LOAD INFLUENCE ....................................................................................... 68
4.1
Introduction .............................................................................................................................. 68
4.2
Model Description .................................................................................................................... 70
viii

4.3
Ring Heat Transfer Result ........................................................................................................ 74
4.3.1
Ring Temperature Distribution ............................................................................... 74
4.3.2 Result of Ring-Cylinder Bore and Ring-Groove Contact ............................................... 80
4.3.3 Application on EcoMotors 2-Stroke Engine ................................................................. 83
Chapter 5 RING-CYLINDER LINER LUBRICATION AND WEAR ............................................................. 87
5.1
Introduction .............................................................................................................................. 87
5.2
Asperity Contact Model ........................................................................................................... 89
5.3
Hydrodynamic Contact Model ................................................................................................ 93
5.4
Wear ........................................................................................................................................... 97
5.5
Simulation Result ...................................................................................................................... 99
Chapter 6 VALIDATION OF NUMERICAL MODEL................................................................................ 107
6.1
Introduction ............................................................................................................................ 107
6.2
Piston Ring Pressure/Force Distribution Measurement ................................................... 107
6.3
Piston Ring/Cylinder Bore Conformability Test .................................................................. 113
Chapter 7 SIMULATION ANALYSIS OF RING DYNAMICS AND TRIBOLOGICAL BEHAVIOR ............ 116
7.1
Introduction ............................................................................................................................ 116
7.2
Second Ring Flutter and Collapse Simulation with CASE .................................................. 116
7.3
3D Ring Dynamic Simulation Analysis.................................................................................. 138
Chapter 8 CONCLUSION AND RECOMMENDATION .......................................................................... 164
8.1
Conclusion ............................................................................................................................... 164
8.2
Limitations and Recommendations ..................................................................................... 166
BIBLIOGRAPHY ........................................................................................................................................ 168

ix

LIST OF TABLES
Table 2-1 Definitions of key piston geometries ............................................................................ 14
Table 3-1 Constraint forces and separation gaps ......................................................................... 56
Table 3-2 Main parameters for the ring ....................................................................................... 64
Table 3-3 Constraint forces between ring and groove side.......................................................... 65
Table 4-1 Piston heat flow proportional distribution ................................................................... 69
Table 4-2 Ring material properties and convection coefficients .................................................. 72
Table 4-3 Constraint forces and separation gap size with temperature influence ...................... 82
Table 5-1 Tabulated values for
Table 5-2 Constants for

.............................................................................................. 91

approximation ................................................................................ 92

Table 6-1 Normalized standard deviation of ring measurement rig .......................................... 111
Table 7-1 Ring pack configuration for Case 1 ............................................................................. 121
Table 7-2 Ring pack configuration for Case 2 ............................................................................. 123
Table 7-3 Ring end gap size for sensitivity study ........................................................................ 131
Table 7-4 Percentage engine blowby and the indication of second ring lift or cross-over point
..................................................................................................................................................... 133
Table 7-5 Contact forces in axial direction at 90 CAD ................................................................ 142
Table 7-6 Contact forces in axial direction at 180 CAD .............................................................. 143
Table 7-7 Contact forces in axial direction at 270 CAD .............................................................. 145
Table 7-8 Contact forces in axial direction at 360 CAD .............................................................. 146
Table 7-9 Contact forces in axial direction at 450 CAD .............................................................. 148

x

Table 7-10 Contact forces in axial direction at 540 CAD ............................................................ 149
Table 7-11 Contact forces in axial direction at 630 CAD ............................................................ 151
Table 7-12 Contact forces in axial direction at 720 CAD ............................................................ 152

xi

LIST OF FIGURES
Figure 2-1 Engine power cylinder system ..................................................................................... 10
Figure 2-2 Engine strokes for 4-stroke engine .............................................................................. 11
Figure 2-3 Power distribution for diesel engine ........................................................................... 12
Figure 2-4 Mechanical friction power distribution ....................................................................... 12
Figure 2-5 Power cylinder system friction distribution ................................................................ 13
Figure 2-6 Key piston geometries ................................................................................................. 14
Figure 2-7 Piston skirt profile ........................................................................................................ 15
Figure 2-8 IC engine ring pack: (a) gasoline engine and (b) diesel engine ................................... 16
Figure 2-9 Top compression ring .................................................................................................. 17
Figure 2-10 Second compression ring........................................................................................... 18
Figure 2-11 Ring fluttering scenario ............................................................................................. 19
Figure 2-12 Ring collapse scenario ............................................................................................... 20
Figure 2-13 Oil control ring: two piece oil control ring (left), three piece oil control ring (right) 21
Figure 2-14 Ring ovality ................................................................................................................ 22
Figure 2-15 Cylinder bore distortion............................................................................................. 25
Figure 2-16 Floating liner setup .................................................................................................... 26
Figure 3-1 Finite element of an arbitrary domain ........................................................................ 29
Figure 3-2 Hexahedron element (a) and parent element (b) ....................................................... 34
Figure 3-3 Parent element coordinate system ............................................................................. 35
Figure 3-4 Ring Cross-Section ....................................................................................................... 40
Figure 3-5 Normalized ring curvature ........................................................................................... 41
xii

Figure 3-6 Free shape ring mesh with hexahedron elements ...................................................... 42
Figure 3-7 Flow chart solving ring-cylinder bore contact ............................................................. 45
Figure 3-8 Constrained Nodes on One Cross-Section ................................................................... 46
Figure 3-9 Initial forces at ring tips ............................................................................................... 48
Figure 3-10 High stiffness springs at contact locations ................................................................ 49
Figure 3-11 Gap vector between free shape and deformed ring ................................................. 50
Figure 3-12 Flow chart of force release method .......................................................................... 51
Figure 3-13 Constraints at ring face and ring sides ...................................................................... 53
Figure 3-14 Free shape and deformed ring meshes ..................................................................... 54
Figure 3-15 Constraint force and separation gap ......................................................................... 55
Figure 3-16 EcoMotors OPOC engine geometry showing intake and exhaust ports ................... 57
Figure 3-17 Boundary condition for ring-bridge contact .............................................................. 58
Figure 3-18 Constraint force conditions ....................................................................................... 58
Figure 3-19 Bridge contact pressure distribution calculation ...................................................... 60
Figure 3-20 Pressure distribution for ring gap at middle of bridge case ...................................... 60
Figure 3-21 Pressure distribution for ring gap at middle of port case ......................................... 61
Figure 3-22 Pressure distribution for one tip at bridge and one tip in port case ......................... 62
Figure 3-23 Constraints on ring cross-section .............................................................................. 63
Figure 3-24 Deformed ring shape after installed into the cylinder liner and piston groove ........ 65
Figure 3-25 Twist angle along ring circumference ........................................................................ 66
Figure 4-1 Heat flow through the piston ...................................................................................... 69
Figure 4-2 Ring cross-section heat transfer boundary conditions................................................ 71
xiii

Figure 4-3 Ring temperature distribution ..................................................................................... 74
Figure 4-4 Ring cross-section temperature distribution............................................................... 75
Figure 4-5 Ring cross-section temperature distribution from COMSOL ...................................... 76
Figure 4-6 Ring free shape with and without temperature influence .......................................... 78
Figure 4-7 Normalized ring radius with and without temperature influence .............................. 79
Figure 4-8 Losing conformability due to thermal influence ......................................................... 80
Figure 4-9 Contact force and separation gap with temperature influence .................................. 81
Figure 4-10 Contact force with and without temperature influence ........................................... 83
Figure 4-11 Pressure distribution for ring gap at middle of bridge case with temperature
influence ....................................................................................................................................... 84
Figure 4-12 Pressure distribution for ring gap at middle of port case with temperature influence
....................................................................................................................................................... 85
Figure 4-13 Pressure distribution for one tip at bridge and one tip in port case with temperature
influence ....................................................................................................................................... 86
Figure 5-1 Stribeck diagram .......................................................................................................... 88
Figure 5-2 Asperity distribution for rough surfaces...................................................................... 90
Figure 5-3 Asperity contact pressure ............................................................................................ 93
Figure 5-4 Schematic diagram of lubrication between surfaces .................................................. 94
Figure 5-5 Viscous part of shear stress for different oil film thickness ........................................ 96
Figure 5-6 Viscous part of shear stress at different surface roughness ....................................... 97
Figure 5-7 In-cylinder gas pressure ............................................................................................... 99
Figure 5-8 Oil film thickness for top ring .................................................................................... 100
Figure 5-9 Oil pressure force for top ring ................................................................................... 101
Figure 5-10 Asperity contact pressure for top ring .................................................................... 102
xiv

Figure 5-11 Hydrodynamic contact pressure for top ring .......................................................... 103
Figure 5-12 Asperity Friction Pressure ........................................................................................ 104
Figure 5-13 Hydrodynamic Friction Pressure ............................................................................. 105
Figure 5-14 Instantaneous ring face wear for top ring ............................................................... 106
Figure 6-1 Ring pressure/force measurement rig ...................................................................... 108
Figure 6-2 Ring test rig alignment ............................................................................................... 109
Figure 6-3 Measured contact force at different circumferential locations ................................ 110
Figure 6-4 Measured and calculated contact forces .................................................................. 112
Figure 6-5 Normalized measured and calculated contact force................................................. 113
Figure 6-6 Ring “light-tightness” measurement ......................................................................... 114
Figure 6-7 Ring “light-tightness” measurement result ............................................................... 115
Figure 7-1 Second ring inertial force, gas pressure force and zoom-in net force ...................... 117
Figure 7-2 Second ring fluttering scenario.................................................................................. 119
Figure 7-3 Second ring radial collapse scenario ......................................................................... 121
Figure 7-4 Inter-ring, second land gas pressure and ring in-groove locations ........................... 122
Figure 7-5 Inter-ring, second land pressures and ring in-groove locations ................................ 124
Figure 7-6 Second land pressure comparison............................................................................. 125
Figure 7-7 Instantaneous gas flow across second ring ............................................................... 127
Figure 7-8 Ring bottom seating stability ..................................................................................... 129
Figure 7-9 Ring top seating stability ........................................................................................... 130
Figure 7-10 In-cylinder pressure and second land pressure with cross-over point ................... 132
Figure 7-11 Inter-ring pressure and ring locations for second ring lift case .............................. 135
xv

Figure 7-12 Instantaneous flow through second ring end gap and ring face ............................. 135
Figure 7-13 Inter-ring pressures and ring locations for second ring non-lift case ..................... 136
Figure 7-14 Instantaneous flow through top ring end gap for second ring non-lift case .......... 137
Figure 7-15 Inter-ring gas pressure ............................................................................................. 139
Figure 7-16 Ring acceleration ..................................................................................................... 140
Figure 7-17 Ring twist angle at 90 CAD ....................................................................................... 141
Figure 7-18 Deformed ring at 90 CAD ......................................................................................... 141
Figure 7-19 Ring twist angle at 180 CAD..................................................................................... 142
Figure 7-20 Deformed ring at 180 CAD ....................................................................................... 143
Figure 7-21 Ring twist angle at 270 CAD..................................................................................... 144
Figure7-22 Deformed ring at 270 CAD ....................................................................................... 144
Figure 7-23 Ring twist angle at 360 CAD..................................................................................... 145
Figure 7-24 Deformed ring at 360 CAD ....................................................................................... 146
Figure 7-25 Ring twist angle at 450 CAD..................................................................................... 147
Figure7-26 Deformed ring at 450 CAD ....................................................................................... 147
Figure 7-27 Ring twist angle at 540 CAD..................................................................................... 148
Figure 7-28 Deformed ring at 540 CAD....................................................................................... 149
Figure 7-29 Ring twist angle at 630 CAD..................................................................................... 150
Figure 7-30 Deformed ring at 630 CAD ....................................................................................... 150
Figure 7-31 Ring twist angle at 720 CAD..................................................................................... 151
Figure 7-32 Deformed ring at 720 CAD ....................................................................................... 152
Figure 7-33 Radial Constraint Force at 0 DEG over a Cycle ........................................................ 153
xvi

Figure 7-34 Axial Constraint Force at 0 DEG over a Cycle .......................................................... 154
Figure 7-35 Radial Constraint Force at 45 DEG over a Cycle ...................................................... 155
Figure 7-36 Axial Constraint Force at 45 DEG over a Cycle ........................................................ 156
Figure 7-37 Radial Constraint Force at 90 DEG over a Cycle ...................................................... 157
Figure 7-38 Axial Constraint Force at 90 DEG over a Cycle ........................................................ 158
Figure 7-39 Radial Constraint Force at 135 DEG over a Cycle .................................................... 159
Figure 7-40 Axial Constraint Force at 135 DEG over a Cycle ...................................................... 160
Figure 7-41 Radial Constraint Force at 180 DEG over a Cycle .................................................... 161
Figure 7-42 Axial Constraint Force at 180 DEG over a Cycle ...................................................... 162
Figure 7-43 Ring Twist Angle over a Cycle .................................................................................. 163

xvii

Chapter 1 NUMERICAL MODELING OF ENGINE POWER CYLINDER SYSTEM
1.1

Motivation

As the reserved crude oil becomes less and less and more tighten emission regulations have
been issued by the government over the years, producing an internal combustion engine with
great fuel efficiency and low emission without losing its durability and comfortability becomes
vital for any automakers to survive nowadays. Computer modeling has proven a powerful way
in engine design that considers all the above factors for the automakers because it is rapid and
cheap compared with prototypes. Besides, the computer model can also provide valuable data
that is not possible to be measured.
The internal combustion engine has been existing for more than a hundred years. However, its
physics has not been yet fully understood as the cyclic behavior represents very complex
processes as combustion, thermodynamics, heat transfer, dynamics, solid mechanics, fluid
mechanics, tribology, et al are all involved simultaneously over engine cycle in a very short time
period.
The reciprocating engine power cylinder system consists of piston, ring pack, cylinder bore and
cylinder head. The primary function of the piston is to transfer the thermal energy from the
combusted gas into mechanical energy that drives the vehicle. The combustion of the gas/air
mixture occurs in the combustion chamber which is comprised of the piston head, cylinder bore
and the cylinder head. The main purpose of the ring pack is to seal the combustion chamber
that prevents gas leaking into the crankcase. In addition, the ring pack also controls the

1

lubrication oil distribution between the rings and the cylinder wall. On one hand, it is desired to
have lubrication oil evenly distributed along the circumferential direction between the paths
that the piston travels; on the other hand, it is also critical to prevent the oil traveling into the
combustion chamber, which may result in severe oil consumption and emission problems.
It is believed that the piston and ring pack together account for as high as 35% of the entire
engine mechanical loss. Excessive mechanical loss means not only lower engine efficiency; but
also shorter engine lift. In addition, engine emission is also closely related to the piston ring
sealing ability. Thus, the piston and piston ring pack are important factors regarding to engine
performance.
This focus of the dissertation is the engine power cylinder system modeling with an emphasis
on the piston ring pack. A three-dimensional piston ring model is built with finite element
method, evaluating the ring deformation and constraint loads in both static and dynamic
conditions.

1.2

Objective

As discussed in the previous section, the two major factors driving the modern engine
development are the fuel efficiency and engine pollutant emission, which are directly affected
by friction, blowby loss and lubrication oil consumption. These factors are directly associated
with the performance of the engine ring pack. Thus a thorough understanding of the ring pack
behavior is crucial for designing an engine that meets all the requirements.

2

The existing two dimensional (2D) numerical models of the ring pack are proven to be useful
qualitatively. However, the 2D model is limited in providing detailed result as the complex
processes are believed to be three-dimensional (3D) phenomena.
Friction occurs between the ring front face and the cylinder liner as the two sliding surfaces
have relative movement. Although lubricant oil is provided for the ring pack to reduce the
friction, it cannot be eliminated. The friction varies ring to ring, crank angle to crank angle, and
also along the circumferential direction due to the non-evenly distributed ring-cylinder bore
contact pressure. The cylinder bore distortion due to mechanical bolting and thermal load is
another source that makes the ring-cylinder bore interaction a more complex 3D problem.
Wear is generated between the ring front face and the cylinder bore due to the contact and
sliding motion. Because of this wear, the piston rings change their geometries as the engine is
running, especially during the engine break-in. The change in ring geometries can affect the
friction, as well as the sealing capacity of the ring. Thus this needs to be considered for the
computational model.
Blowby refers to the gas flowing from the combustion chamber past the ring pack into the
crankcase. One of the major gas paths is the ring end gap. However, if the ring front face loses
contact with the cylinder bore, a direct path is formed thus a sharp increment in blowby can be
found. Besides, as the piston rings moves up and down in the piston grooves, the gas also
travels behind the rings. The gas dynamics is highly coupled with the ring dynamics, which is
influenced by the piston secondary motion.
All these phenomena mentioned above demand a 3D ring pack model that can provide better
understanding of the processes and practical suggestions in design.
3

1.3

Previous efforts

Numerical models have been widely used to understand the complex phenomena of the
internal combustion engine and improve it during its over 100 years’ history. The numerical
models include variant disciplines: combustion, fluid dynamics, heat transfer, solid mechanics,
dynamics, tribology, etc. All these models need to be solved simultaneously in order to obtain
high fidelity results.
1.3.1 Piston

In order to model the ring pack behaviors, the piston motion and dynamics are necessity as the
compression rings and oil control ring are nested in the piston groove. Over the years, several
piston dynamics models were built.
Panayi developed a finite element analysis code that simulates piston dynamics, with the
consideration of piston deformation under gas pressure, thermal load, body load and
elastohydrodynamic load [1, 2]. Piston secondary motions, including the motion along the wrist
pin and piston tilt, are predicted by the code. The model also simulates the lubrication and
friction between the piston skirt and the cylinder wall along the piston periphery. Piston skirt
wear can also be obtained over one engine cycle.
PISDYN is a similar package for piston dynamics analysis developed by Ricardo [3]. Wong, V.,
Tian, T., et al., presented a model that calculates piston behavior and the impact force on the
cylinder liner which is believed as the source of piston slap excitation [4]. Keribar described a
comprehensive piston skirt lubrication model, which is used in parallel with a piston secondary
dynamic analyzer to characterize the lubrication oil film’s influence on piston motions [5].
4

Piston skirt lubrication behavior is also investigated by Kim, et al[6], and Malagi, et al[7].
Kageyama, et al, developed an experimental method to measure the piston skirt contact with
the cylinder liner and the skirt deformation [8]. First, the relationship between the skirt contact
pressure, skirt deformation and the skirt inner strain was determined statically. Then the skirt
dynamic contact pressure and the skirt deformation were obtained known the skirt inner strain.
Patel, et al, developed a piston secondary dynamics model with an emphasis on the piston to
cylinder bore contact [9]. The influences of engine speed, in-cylinder peak pressure timing,
nominal piston to cylinder bore cold clearance and the piston pin offset were studied for the
piston to bore contact. Taylor, et al[10], measured piston secondary motion and piston
temperature from experiment.
1.3.2 Ring pack

Along with the piston dynamics model developments, the modeling of ring pack is also vastly
investigated. Coupled with the gas dynamics, constrained by the piston groove and the cylinder
wall, the ring pack dynamics become a very complex problem. Several numerical models have
been proven predicting the ring dynamics and gas dynamics well [11-15].
CASE-RING [16] is a code for ring pack evaluation and analysis developed by Mid-Michigan
Research LLC. The CASE-RING is used for ring pack dynamics, including the ring axial motion,
radial motion as well as twist. The code also predicts tribological phenomena between the rings
and their interacting counterparts. Both hydrodynamic friction and asperity friction can be
obtained. Ring face/cylinder wall wear and the ring/groove sides wear are then found using the
wear model. Starved lubrication for the top ring is considered when the lubrication oil is not

5

supplied enough due to oil evaporation. In addition, progressive wear between the
ring/cylinder wall and the ring/groove sides are obtained in a progressive and adaptive manner,
which is the material removed is considered and the ring is resurfaced gradually during engine
operation.
Ejakov simulated the ring pack kinematics and gas dynamics for a deactivated cylinder [17]. The
GESIM software was used to model the in-cylinder pressure trace for every cycle considering
heat transfer losses and the RING program was used for ring pack kinematics and gas dynamics
analysis. The influences of the inter-ring gas pressures and the ring dynamics on engine blowby
were then studied since engine blowby is an important factor determining engine efficiency.
Furthermore, Ejakov also modeled the three-dimensional ring twist in the piston grooves using
space beam elements [18]. The gas flow areas above and below the rings were then obtained
for gas dynamics analysis. Associated with ring dynamics, engine blowby is recognized as the
gas leaking from the combustion chamber into the crankcase. The engine blowby has been
modeled and studied by several researchers [12-14, 19-21].
Liu, et al, developed a three-dimensional (3D) finite beam element ring model for static analysis
[22]. The ring/cylinder wall and ring/groove conformabilities were calculated; cylinder bore
distortion was considered as well as the ring lapping process. The model assumes half of the
piston ring assuming the ring is symmetric about the ring back (opposite to the ring end gap). In
addition, Liu also modeled the ring pack dynamics and the gas flow based on the same 3D ring
model [23, 24]. A heavy-duty diesel engine was then simulated using the model and variance
along the ring circumference was regarding the ring motion and gas flow. Tomanik, et al, [25]
built a ring contact force measurement rig and showed similar contact force distribution with
6

the simulation result from Liu [22]. In addition, other ring pack performances were also
investigated by Tomanik, including ring conformability to distorted bore, piston ring and ring
groove wear as well as a new criterion for ring conformability [26-30].
Ma, et al, computed the piston ring contact force distribution with three different numerical
constraint models: gap element, cable element and thermal liner element models [31]. Sun
modeled the piston ring and cylinder bore contact based on thermal elastic theory, with the
assumption that the ring deflection only takes place at the ring plane and the non-uniform
temperature distribution on the ring is neglected [32]. Tejada, et al, showed different ring pack
configurations’ impacts on oil consumption and engine blowby [33]. The ring dynamics model
was adopted for ring/groove wear and ring/cylinder wall wear for a diesel engine by Tian, et al,
[13]. The results showed that the worn top ring face profile could scrape up oil on the cylinder
wall into the combustion chamber due to the ring dynamic twist and the piston tilt. Chui
modeled the elastohydrodynamic lubrication for the ring pack to evaluate its tribological
performance [34, 35]. In his model, oil consumption is considered due to evaporation, which is
also considered by De Petris [11, 36]. Thus, the top ring is not always in the fully flooded
lubrication condition. As a result, starved lubrication could occur for the top ring depending on
the operation condition. Other ring pack models also consider oil consumption [15, 37-40].

1.4

Dissertation structure

This dissertation is organized as follows. An overview of the engine power cylinder system is
given in Chapter 2. This includes the main components of the power cylinder system and their
functions. A 3D finite element model of the piston rings is then presented in Chapter 3. The

7

ring-cylinder wall contact and ring-groove contact analysis is summarized. Thermal load
influence on piston rings is discussed in Chapter 4. . In Chapter 5, the lubrication, friction and
wear models are shown between the contacting components with examples given. Chapter 6
presents an experimental test to measure the ring-cylinder wall contact pressure/force and the
test results are used to validate the numerical model. Simulation analysis of the ring dynamics
and the tribological results are discussed in Chapter 7. This includes a second ring dynamic
analysis using conventional 2D model as well as a novel 3D simulation study of a scraper ring
under dynamic load condition. The dissertation is then concluded in Chapter 8 where the
limitations and recommendations for future work are pointed out.

8

Chapter 2 ENGINE POWER CYLINDER SYSTEM
2.1

Introduction

The internal combustion engine converts thermal energy of the combustible fuel into
mechanical energy that moves the piston and eventually the crankshaft. This energy conversion
process occurs within the engine power cylinder system. The power cylinder system comprises
the following components: piston, piston rings, cylinder liner, wrist pin and connecting rod. The
piston is the main component that delivers the mechanical energy through reciprocating
motion. And this reciprocating motion is transmitted into rotational motion of the crankshaft to
output power through the connecting rod. The connecting rod small end is connected to the
piston through the wrist pin, and the rod big end is connected to the crankshaft. Combustion
occurs above the piston in the combustion chamber, which is sealed by the ring pack, especially
the top compression of the ring pack. Figure 2-1 shows these major components of the power
cylinder system.

9

Figure 2-1 Engine power cylinder system
A complete engine cycle consists of 4 different strokes for a 4-stroke engine along with the
piston reciprocating motion. These 4 strokes are intake stroke, compression stroke, expansion
stroke and exhaust stroke as shown in Figure 2-2.

10

Figure 2-2 Engine strokes for 4-stroke engine
As for a modern diesel engine, which is known for its better efficiency over its gasoline
counterpart, only about 40% of the energy produced by the engine is converted to the engine
output power. About 4 – 15% of that energy is wasted as mechanical friction loss. And the rest
of the energy, which is almost over half of the chemical energy is dissipated as other forms, e.g.
heat transfer, blowby loss, etc as shown in Figure 2-3 from the study by Richardson [41].

11

Figure 2-3 Power distribution for diesel engine
And about half of the mechanical friction loss is attributed to the friction in the power cylinder
system, including the piston, ring pack and the connecting rod as shown in Figure 2-4 [41]. The
other part is due to the friction of other components, e.g. the valve train system, the crankshaft
bearings, etc.

Figure 2-4 Mechanical friction power distribution

12

The friction loss distribution among piston, piston ring pack and the connecting rod for the
power cylinder system can be found in Figure 2-5 [41]. As can be found, the piston and ring
pack account for higher friction loss than the connecting rod.

Figure 2-5 Power cylinder system friction distribution

2.2

Piston

The piston of an internal combustion engine is the main component to transmit the thermal
energy into mechanical energy. High pressure gas from the combustion of the fuel-air mixture
pushes the piston downward to deliver mechanical energy. Thus the working condition for the
piston is severe. Pistons in small engines are made of aluminum while for large lower speed
applications, the pistons are made of cast iron [42]. Figure 2-6 shows a typical piston for diesel
engine with the definitions of the key geometries shown in Table 2-1.

13

Figure 2-6 Key piston geometries

Table 2-1 Definitions of key piston geometries
No.

Definitions

1

Piston Crown

2

Piston Skirt

3

Top Land

4

Second and Third Land

5

Top Groove

6

Second and Third Groove

The piston skirt generally has a barrel/parabolic profile that promotes hydrodynamic lubrication
due to the edge effect (Figure 2-7). This skirt profile needs to be optimized in order to minimize

14

piston friction. Piston skirt also grows outward in the radial direction at high temperature
during engine operation.

Figure 2-7 Piston skirt profile

2.3

Ring pack

The ring pack is typically comprised with three rings: two compression rings and one oil control
ring. The main functions of the ring pack are listed as following:


To seal the combustion chamber in conjunction with the piston lands and the cylinder
wall, in order to prevent the high pressure gas from leaking into the crankcase that is
wasted in producing power.



To control the lubrication oil from getting into the combustion chamber from below the
piston as well as to distribute the lubrication oil evenly on the cylinder wall.

15



To transfer heat from the piston to the cylinder wall, and eventually to the cooling
system. Since the piston crown in exposed to the combustion chamber, it is critical to
reduce the piston temperature in order to guarantee the piston’s working condition.

Figure 2-8 shows typical ring packs for modern gasoline and diesel engines.

Figure 2-8 IC engine ring pack: (a) gasoline engine and (b) diesel engine

2.3.1

Top compression ring

The top compression ring is the first ring and the main component sealing the combustion
chamber for engine blowby control. The top ring is also under the most severe working
condition since it is directly exposed to the combustion gas and usually under high pressure and
high temperature.

16

The top compression rings for gasoline engine usually have a rectangular cross-section.
However, for diesel engine operation, the top compression rings usually are keystone rings
(Figure 2-9) which promotes the break-up of the deposits between the ring and piston groove,
thus reduce the possibility of micro-welding between the piston ring and the piston groove. The
top compression ring usually has parabolic or barrel profile at its front face in order to enhance
the hydrodynamic lubrication between the ring face and the cylinder wall interface (Figure 2-9).

Figure 2-9 Top compression ring

The sealing capability of the top compression ring has significant influence of engine blowby
because of the high gas pressure gradient across the top ring. Engine blowby is recognized as
the high pressure gas leaking into the crankcase through the ring pack. Thus, the top
compression ring is desired to conform to the cylinder wall evenly along the ring circumference.
Also due to the high gas pressure gradient across the top ring, the top ring stays against the
bottom side of the piston groove most time during the engine cycle.
2.3.2

Second compression ring

17

The second ring is a scraper ring which is recognized as 80% for scraping the lubrication oil
down and 20% for sealing the combustion chamber. Because of the wedge effect, the scraper
ring promotes hydrodynamic lubrication during the up-strokes (compression and exhaust
strokes) and scrapes oil down during the down-strokes (intake and expansion strokes). Figure
2-10 shows two types of second rings: one is scraper ring and the other is Napier ring. For the
second ring, static twist is usually introduced by cutting off the ring material at one of the back
corners. If the lower inside corner is cut-off, the ring is a negative static twisted ring; while if the
upper inside corner is cut-off, the ring has a positive static twist configuration.

Figure 2-10 Second compression ring

Although the gas pressure gradient across the second compression ring is much lower than that
of the top ring, the second ring also has noticeable effect on gas dynamics. Due to this lower
pressure gradient across the second ring, the ring inertial force becomes competitive to gas
pressure force. The inertial force may lift the second ring up at late compression stroke such
that the second ring stays against the top flank of the groove. This process may repeat
depending on the pressure build-up above the second ring when it is top seated. This unstable
axial in-groove motion is recognized as ring fluttering. The scenario of ring fluttering is shown in

18

Figure 2-11. When the ring fluttering occurs, another gas flow path between the ring and
groove sides is open. As a result, blowby gas may increase.

Figure 2-11 Ring fluttering scenario

It is also possible for the second ring to move inward in the radial direction. This radial
movement is known as ring radial collapse. The scenario of ring collapse can be found in Figure
2-12. When the ring radial collapse occurs, the gas above the ring can flow past the ring directly
between the ring face and the cylinder wall to the lower land. Severe engine blowby can occur
at this ring collapse condition. It depends on the ring and piston design which of the two
conditions occur, ring fluttering or ring collapse. It is also possible that the two conditions occur
simultaneously.

19

Figure 2-12 Ring collapse scenario

It was found that the static twist has significant influence on the second ring fluttering and
radial collapse. Second ring with negative static twist is more likely to flutter than a positive
static twist second ring. However, if the second ring is lifted against the top flank of the groove,
the positive static twist configuration will be more like to collapse than the negative twist
configuration.
2.3.3

Oil control ring

The oil control ring is used to meter and distribute lubrication oil onto the cylinder wall. There
are generally two types of oil control rings: 1. two-piece oil control ring and 2. three-piece oil
control ring (Figure 2-13). The two-piece oil control ring consists a ring body with two rails and a
helical spring on the back providing the ring tension force. The three-piece oil control ring
consists of two segments and an expander in between the two segments. The expander
provides the radial force to conform the ring to the cylinder wall and also the axial force to push

20

the ring against the top and bottom sides of the groove. The oil control ring is a two-direction
scraper ring that scrapes oil in both upward strokes and downward strokes. During the
downward strokes, the bottom rail/segment scrapes oil directly back into the crankcase. The
top rail/segment scrapes oil back into the groove through the oil control ring expander.
Generally, holes at the back of the oil control ring groove can be found along the circumference
in order to allow the oil draining to the crankcase. In some piston design, instead of using these
holes at the back of the groove, cast slots are introduced at the bottom edge of the groove for
oil drain as an easier solution. During the upward strokes, the bottom rail/segment scrapes oil
into the groove through the expander. The recovery of oil scraped by the top rail/segment
during these upward strokes depends on the external force on the top rail/segment. At times
the external axial force on the oil control ring overcomes the expander force. As a result, an oil
flow crevice is formed between the oil control ring and the groove sides allowing the oil drain
into the groove and eventually back to the crankcase.

Figure 2-13 Oil control ring: two piece oil control ring (left), three piece oil control ring (right)

2.3.4

Key ring nomenclature

For all three piston rings, the ring tension force is important since The diametral load of the ring
is defined as the load acting at the load acting at the locations ±90° from the ring end gap that
21

also closes the ring gap. The tangential load is defined in this way: the piston ring is surrounded
by a flexible band, the force at the end of the flexible band that closes the ring end gap when
pulling. An empirical relationship between the diametral load and the tangential load is:
(2-1)
The ring radial pressure distribution is commonly known as defined by the ring ovality. The
piston ring ovality is another important property of the ring determining the ring performance.
From ISO 6621-2, in the ring ovality measurement test, the ring is enclosed in a flexible steel
tension band. The two ends of the flexible band are pulled until the ring end gap is closed. Then
the ring ovality is defined as the difference in diameter that through the ring end gap and ring
back (0° to 180°) and the diameter perpendicular to this (90° to 270°) as shown in Figure 2-14.
Negative ovality rings are widely used to reduce the pressure concentration at the ring tips,
especially when the piston rings are under high temperature condition during engine operation.

Figure 2-14 Ring ovality
22

Thus, based on the configuration shown in Figure 2-14, the ring ovality is defined as

2.4

.

Cylinder

The cylinder of a reciprocating engine is the part through which the piston travels. The cylinder
may be sleeved or sleeveless depending on the metal used for the engine block. For example, a
cast iron engine block generally does not require cylinder sleeve because the iron is hard
enough to resist wear between the piston ring and the cylinder wall. However, for aluminum
alloy engine blocks that can be found in almost all daily drive cars, cylinder sleeves are required
since the aluminum alloy is not hard to enough to resist wear between the piston ring and
cylinder wall interface.
Cylinder liners, or cylinder sleeves, are manufactured nowadays using the centrifugal casting
process. The centrifugal casting process refers to the technique for casting, which is a
permanent mold is spinning continuously along its center line at a constant speed. At the same
time, molten metal is poured to the mold and thrown toward to the inside wall of the mold.
Then the molten metal is solidified after cooling. The spinning orientation of the casting
machine can be either horizontal or vertical, depending on the parts it is producing. Horizontal
spin is preferred for long and thin cylinder; while vertical spin is preferred for short and wide
cylinders. Aluminum engines without sleeves can also be found. The aluminum cylinders are
treated with nickel silicone alloy coating or other plasma coating that help reduce cylinder
wear. Other techniques have also been explored by the researchers in order to reduce engine
friction. One method is to introduce dimples at the mid-stroke to the cylinder walls [43]. This
helps reduce friction because at the mid-stroke, the piston rings are generally under

23

hydrodynamic friction since the piston speed is high. By introducing the dimples to the cylinder
wall, the effective area of contact between the ring faces and the cylinder wall has been
reduced. This leads to reduction of viscous friction as claimed.
Typical surface roughness for cylinder liner is 0.4~0.5

. This roughness has been reduced

significantly, which could help reduce engine oil consumption. Rougher cylinder walls can help
retain lubrication oil on the liner surface between micro-valleys, which is similar to the dimpleliner [43]. As a result, friction between the ring/cylinder wall and piston skirt/cylinder wall
interfaces can be reduced due to the lubrication oil in the micro-valleys. However, this microvalley retained oil is not scraped from the liner during engine down strokes and can stay
exposed to high temperature gases. As a result, more oil is evaporated and the oil consumption
increases.
Cylinder liners are no longer circular when the engine is in operation. The deformation results
from mechanical distortion from bolting the cylinder block to the cylinder head; thermal
distortion when the thermal load on the liner is not uniform; mechanical load when piston and
ring pack are slapping into the liner; etc. Cylinder bore distortion is measured from experiment
by researchers [44]. For modeling concern, the cylinder bore distortion is usually defined by a
Fourier series [30, 44]:
(2-2)

where

is the deviation from roundness,

and

of the series.
The orders of the distortion are recognized as:

24

are Fourier coefficients and is the order

0 order

Change in bore diameter

1st order

Bore eccentricity

2nd order

Oval deformation

3rd order

3 lobe deformation

4th order

4 lobe deformation

Figure Figure 2-15 shows a piston bore deformation. The blue curve shows the ideal round bore
without distortion. The green, red and yellow curves are bore shape under different distortion
conditions.

Figure 2-15 Cylinder bore distortion

25

Figure 2-16 Floating liner setup

Floating cylinder liners Figure 2-16 are used for piston and ring pack friction force
measurement. A floating liner refers to the liner supported by load transducers, instead of
bolted to the cylinder block directly. Thus, by measuring the force on the load transducers, the
piston and ring pack friction force can be estimated [45-50].

2.5

Connecting rod

The connecting rod connects the reciprocating moving part, the piston through the small end to
the rotating moving part, the crankshaft through the big end. Thus, the connecting rod has both
the reciprocating motion property as well as the rotating motion property. It is often
recognized that

of the connecting rod mass is for reciprocation and

26

for rotation.

2.6

Wrist pin

The wrist pin connects the piston to the small end of the connecting rod. Thus, forces from the
combustion are transmitted to the connecting rod through the wrist pin.
The wrist pin has two different configurations: semi-floating and fully-floating configurations.
For the semi-floating configuration, the wrist pin is either fixed relative to the piston or fixed
relative to the connecting rod small ending. For the semi-floating configuration with wrist pin
fixed relative to the piston, the pin has interference fit with the journal in the piston. The other
configuration, with the wrist pin relatively fixed to the connecting rod small end, is
implemented with interference fit at the connecting rod instead of piston. However, in this
design, the piston lubrication can be affected since all the oscillations from the connecting rod
are transferred to the pin-boss. On technique for solving this problem is to drill oil traveling
paths from the oil ring groove to the pin-boss to enhance lubrication at this level.
For the fully-floating configuration, bearing surfaces can be found between the small end of the
connecting rod and the wrist pin, as well as between the piston and the pin. No interference fit
is used so the wrist pin is free to rotate. This floating design improves the scuff resistance and
reduces the wear rate.

27

Chapter 3 THREE-DIMENSIONAL RING-CYLINDER WALL AND RINGPISTON GROOVE CONTACT MODELING
3.1

Introduction

Piston ring pack has significant influence on engine power cylinder system performance as
discussed in the previous chapters. The areas piston ring pack affects include lubrication,
friction, wear, fuel consumption, emission, heat transfer, etc. Thus, thorough understanding of
the ring pack behavior is necessary for engine power cylinder system design improvement.
Significant amount of effort has been committed into the ring pack dynamic, tribological
behaviors. All these behaviors are closely related to the interaction between the ring/cylinder
wall interface and the ring/piston groove interface. However, these interactions nowadays are
still less understanding areas. This chapter presents a three-dimensional ring-cylinder wall and
ring-piston groove contact model solving the above problem.

3.2

Finite element analysis formulation

Finite element method (FEM hereafter) is a numerical technique finding approximate solutions
for differential equations. Instead of solving the very complex geometry that the existing
mathematical tools are not capable of, FEM solves the boundary or initial value problem by
dividing the complex geometry into simple small elements. Thus, approximated solutions for
problems with complicated geometries under certain boundary condition can be obtained by
solving a system of equations.

28

The formulation of the piston ring/cylinder ball and piston ring/groove contact finite element
model is discussed in the following paragraphs.
3.2.1 Governing Equations

The basic of this finite element model is the theory from material of elasticity, focusing on the
displacement at certain loading condition. And the governing equations for the problem are
shown in the following :
i.

Balance equation

ii.

Strain-stress relation

iii.

Strain-displacement relation

Figure 3-1 Finite element of an arbitrary domain

For any part of an arbitrary body Ω, which can be considered as a small element, under load at
its boundaries Γi, the element must be in equilibrium due to the internal stress developed
(Figure 3-1). This leads to the balance equations of this small element:

29

(3-1)
(3-2)
(3-3)
where
,

,
,

and
,

,

are the normal stresses on the planes perpendicular to the x, y and z axis;
and

are shear stresses, the first index denotes the axis the plane is

perpendicular to and the second index indicates the direction of the shear stress, for example,
is defined as the shear stress on the plane perpendicular to the y axis and along the x
direction;

,

and

are body forces along three different orientations respectively.

For an isotropic material, the following relations hold:

(3-4)
(3-5)
(3-6)
Thus, for a 3D problem with isotropic material, there are six unknowns for one element, which
are

,

,

and

,

,

.

From Hooke’s law for isotropic material, the relation between stress and strain in 3D can be
expressed as:
(3-7)
(3-8)
30

(3-9)
(3-10)
(3-11)
(3-12)

in the above equations are engineering shear strains, which have the relation with shear
strain as:
(3-13)
(3-14)
(3-15)

The same relationships can be expressed in the form of stresses as the functions of strains, as
shown in the following:
(3-16)
(3-17)
(3-18)
(3-19)
(3-20)
(3-21)

31

In the above relationship, is the normal strain,

is the Young’s modulus of the material and

is the Poisson’s ratio.
It can also be expressed using shear modulus, which is defined as:
(3-22)
Thus,
(3-23)
(3-24)
(3-25)
In a matrix form, the above relations can be expressed as:

(3-26)

And C is the constitutive matrix:

(3-27)

The constitutive matrix defines the stress-strain relationship.

Another important relation is the Strain Displacement Relation. The strain is a normalized
measure of displacement and it is related to the displacements as:
32

(3-28)
(3-29)
(3-30)
(3-31)
(3-32)
(3-33)
where ,

and

are displacements in the x, y and z directions respectively.

The above relationship can also be expressed in a matrix form:

(3-34)

where

3.2.2 Finite Element Analysis

Eight-node hexahedron element is used to model the 3D ring. A basic hexahedron element is
shown in the Figure 3-2 (a) below. An arbitrary shaped hexahedron element needs to be

33

mapped to its parent element – a cubic element with all its sides equal to unit (Figure 3-2 b)
thus only the parent element’s shape function needs to be calculated.

Figure 3-2 Hexahedron element (a) and parent element (b)

In FEM, interpolation method is widely used to represent the quantities (displacements,
temperature, etc) at element nodes. This interpolation function is called shape function. For the
parent element with the prescribed coordinate system (Figure 3-3), the shape functions for the
parent element are defined as:

(3-35)
(3-36)
(3-37)

34

(3-38)
(3-39)
(3-40)
(3-41)
(3-42)

Figure 3-3 Parent element coordinate system

The way the shape function is defined ensures that the value of the shape function
to 1 at node , and 0 at node when

is equal

and the summation of all the shape function for one

element is equal to one. The displacement of any point within the element can then be
expressed using interpolation as the summation of the product of the shape function and the
displacements at its 8 nodes.
The displacement can be found using the following relation:

35

(3-43)

where

(3-44)

where

denotes the displacement in the

displacements in

and directions for the

direction for the

node, and

and

are

node respectively.

And as will be discussed later, a hexahedron element with arbitrary dimensions would be
mapped to the parent element using Jacobian matrix such that it is not necessarily to construct
shape functions for each element.

The approximate solution of the balance equation may lead to a non-zero value (residual) in the
right side of the equations as:
(3-45)
(3-46)

36

(3-47)

in the above equation is the residual.
Galerkin’s method is trying to reduce the residual over the entire domain by making the
integration of the weighted residual equal to zero. In order to generate as many equations as
unknowns and not lose the generality, Galerkin’s method uses the shape function itself as the
weight function.
(3-48)

(3-49)

where
Now, the governing equations can be written in the matrix form for one element:
(3-50)

where

is the element stiffness matrix and

is the load vector.

Integration is involved in the evaluation of element stiffness matrix and load vector. Gaussian
quadrature is introduced here to calculate these integrations numerically.

37

Gaussian quadrature converts integration into summation of a series of polynomials evaluated
at certain points. In a 3D domain with

,

and

the

integration is calculated as:

(3-51)

Two node Gaussian quadrature yields the exact value of the integration of up to third order
polynomial. Gaussian quadrature requires the function to be integrated from -1 to +1 in all
directions. For integrations with other upper and lower limits, the integration domain should be
mapped to the parent domain first using Jacobian matrix.
As mentioned above earlier, in engineering applications, quite often the domain one’s working
on is non-rectangular. Or sometimes the regular rectangular element cannot define the domain
properly. And to write the shape function individually for each element becomes tedious and
impossible as the number of element increases. In this case, one could map the actual element
to a parent element using Jacobian matrix, which is unique.
In this case, the integration for the stiffness matrix becomes:

(3-52)

where ζi , ηj and

are Gaussian quadratures;

element.
The Jacobian is defined as:
38

is the determinant of Jacobian of one

(3-53)

With the Jacobian, the first derivatives of a shape function with respect to x, y and z can be
transformed to the derivatives with respect to ,

and . And the following relations hold:

and

(3-54)

Known the Jacobian matrix, both the inverse of Jacobian matrix and the determinant of
Jacobian can be expressed explicitly.
3.2.3 Ring-Cylinder Wall Contact Modeling

The 3D ring finite element analysis program is presented in this section solving the interaction
between the piston ring front face and the cylinder wall [51].
This study describes a 3D analytical ring model to addresses the pressure/force distribution and
the ring conformability between the ring-cylinder bore interface. The main contribution of this
work is that it solves the problem from the minimum strain energy point of view without any
unrealistic boundary condition assumptions. The penalty method is used to find the contact
pairs between the ring and the cylinder liner. The finite element model is described in the
following sections along with experimental measurement validation.
The piston ring cross-section geometries (Figure 3-4) need to be input to the model. This
including the ring thickness and radial width

, as well as the ring’s keystone angle
39

and

if

any. In addition, the bevel angle and length at any corner also need to be specified since they
introduce ring static twist after installing the ring into the piston groove.

Figure 3-4 Ring Cross-Section

Another important input to the model is the ring outer diameter (OD) profile at its free state.
The free state profile can be either measured using a coordinate measurement machine (CMM)
or from a computer aided design (CAD) model. Figure 3-5 shows an example of the ring free
state profile, normalized by the ring radius opposite to the ring end gap. As the center of the
free state ring is really arbitrary, the point that yields the OD at the ring back (opposite to the
ring end gap) equal to the cylinder bore inside diameter (ID) is picked as reference center. The
selection of the ring center will not result in any difference on the result. The ring free state
profile shown in Figure 3-5 is the normalized radius that the ring radius at any circumference
location is normalized by the one at the ring back.
40

Figure 3-5 Normalized ring curvature

Figure 3-5 only shows one half of the ring assuming the ring is symmetric about the crosssection at the ring back.
The free state ring is then meshed using 8-node hexahedron element and is shown in Figure
3-6.

41

Figure 3-6 Free shape ring mesh with hexahedron elements

The penalty method is a widely used for solving contact problems [52, 53]. Compared to the
other popular method, the Lagrange multiplier method, the order of the system is not
increased using the penalty approach. Thus penalty method was chosen to solve the present
ring-cylinder bore contact problem.
The base constrained optimization problem can be formulated using the principle of minimum
total potential energy. This principle is a fundamental concept used in structure analysis
analyzing structure deformation. It states that a structure should deform to a stationary state
that minimizes its total potential energy, including the elastic strain energy and potential

42

energy from the applied force. This principle is used to formulate the ring-cylinder bore contact
problem. The formulation can then be expressed as:
To find nodal displacement:
that minimizes the ring potential energy defined as:
(3-55)
and subject to the constraint:
(3-56)
where

is the radius of the

cross-section at the ring face and

is the radius of the

cylinder wall.
The minimization of the potential energy requires the derivative of

with respect to

vanishing, which is:
(3-57)
At the same time, the constraint implies that if the node on the ring front face is in contact with
the cylinder bore, the constraint force should be non-zero and along the radial direction
pointing inward to the center of the cylinder bore; on the other hand, if the node on the ring
front face is not in contact against the cylinder bore, the constraint force should be zero. It is
obvious that high nonlinearity is involved in the present contact problem. The penalty method
is used to solve

by instead solving a sequence of specially constructed unconstrained

optimization problem. That is, with the penalty method, an additional term that accounts the
constraints is introduced into the system potential energy found in (3-55) as:
(3-58)

43

where is the penalty number and represents the node geometric constraint and can be
expressed in the matrix form as:
(3-59)
Here, is the gap between the node’s initial free state position and the final deformed state
and matrix

projects the nodal DOF to the gap. Now, the minimization of the modified

potential energy accounting for the penalties requires the derivatives of

with respect to

to

vanish, which yields the following relation:
(3-60)
From equation (3-60), the penalty method converts the geometric nonlinearity into material
nonlinearity by modifying the potential energy term. The penalty method introduces a penalty
term into the system potential energy formula as expressed in (3-58). If the penalty number is
equal to zero, then equation (3-58) becomes identical to equation (3-55). The penalty number
is typically a very large number such that a large cost is added to the objective function when
the solution points lie outside of the original feasible region. Thus by minimizing the modified
potential energy accounting for the penalty term, the ring displacement is found and the
constraint is satisfied. The recommended range for the penalty number found in literature [52]
is:
(3-61)
A flowchart for solving the ring-cylinder bore contact problem using penalty method can be
found in Figure 3-7.

44

Figure 3-7 Flow chart solving ring-cylinder bore contact

In this approach, geometric relations and constraint force directions are used to check the
constraint violation during the penalty method iteration. The steps are outlined as:
I.

Build/update the global stiffness matrix and force vector.

II.

Calculate the nodal displacement under the current force condition.

III.

Calculate the constraint force for the nodes that are in contact with the cylinder bore.

45

IV.

Check the constraint violation: for the nodes not under constraint force, they should
not move beyond the cylinder bore surface; for the nodes under constraint force, the
constraint force direction should be inward, pointing to the center of cylinder bore.

V.

If no constraint mentioned in step 4 is violated, the stationary state of the ring is found;
otherwise, return to step 1 until all the constraints are satisfied.

The nodes used for the constraint violation check are the upper and lower ones at the specified
cross-sections on the ring front face as shown in Figure 3-8. If the upper and lower nodes satisfy
the constraint criterion, it is assumed the corresponding cross-section is also satisfied.

Figure 3-8 Constrained Nodes on One Cross-Section

For a ring with a symmetric cross-section under uniformly distributed temperature, the upper
and lower constraint forces should be equal in magnitude and in the same direction. Different

46

constraint forces develop when a twisting moment on the ring occurs, due to cross-section,
asymmetry, temperature gradient, non-uniform gas pressure, etc.
One challenge with the penalty method is to identify the correct contact pair on the two
surfaces: the constrained nodes on the ring front face and the corresponding infinitesimal
constraint surface on the cylinder wall. For the constrained nodes on the ring, the locations at
the ring deformed state are not known. For the constraint surface, either for a circular bore or a
distorted bore with a known distortion pattern, the geometry and the normal direction of any
infinitesimal surface can be found. The unknown is which infinitesimal constraint surface will be
in contact with the constrained nodes after the ring deformation.
In order to overcome the difficulties in identifying the contact pairs, a force release approach is
adopted by initially applying a pulling force at the ring tips as shown in Figure 3-9. The approach
can be considered as the reverse process of removing the ring from the piston with a ring
clamp. The direction of the initial force is along the line that connects the ring tips and its
magnitude should be chosen with care. The reason is that the ring under this force is desirable
to be as close to the constrained bore surface as possible. One simple criterion in choosing the
initial force is that under the initial pulling force, all nodes at the ring front face should not
move beyond the constraint bore surface and at the same time, the ring end gap should be
greater or equal to zero, so that no overlap occurs at the ring tips. The finite element model can
be used to find the appropriate initial force.

47

Figure 3-9 Initial forces at ring tips

The purpose of the initial force is only to assist in finding the infinitesimal constraint surface on
the cylinder liner that restrains the corresponding ring node. This force must vanish eventually
due to its fictional nature, and it needs to be released gradually to guarantee the convergence
of the constraint infinitesimal surface. In this work, the force is halved at each step until the
force difference between the two consecutive steps is less than 0.1 N. And in each step, the
penalty method approach is employed to obtain the constraint pair in current step.
The matrix

described previously denotes the points that constrain the ring along the

circumference. The constraint point can be considered that there is a very stiff spring which can
only be compressed and not tension is allowed. The direction of the spring placement is always
along the cylinder bore radial direction.

48

Figure 3-10 High stiffness springs at contact locations

The penalty applied to the ring can be considered as defining the stiffness of the spring that
pushes the ring back into bore shape (Figure 3-10).
The gap vector defines the displacement a ring node should undergo from its free state to
deformed condition (Figure 3-11). The gap does not necessarily along the cylinder bore radial
direction. This is because when the ring is pushed into the bore shape, the nodes not only have
radial displacement, but also a tangential displacement.

49

Figure 3-11 Gap vector between free shape and deformed ring

The flowchart using the force release method is shown in Figure 3-12. The “Contact Analysis”
part here refers to the procedures described in Figure 3-7.

50

Figure 3-12 Flow chart of force release method

As the nature of the constraint force, it cannot be calculated directly. Instead, it can be
obtained knowing other applied force conditions and the ring condition. Thus, known the
displacement , the constraint forces are found in the following way:
(3-62)
This constraint force satisfies the equation:
(3-63)
which is the state with minimum potential energy of the ring under the prescribed constraints.
3.2.4 Ring-Groove Side Contact Modeling

The interaction between the ring-groove side interface is becoming a more time limiting factor
for piston ring application, thus needs to be considered in modeling. Similar to constructing the
51

ring-cylinder bore contact formulation, the ring-groove side contact can also be considered. In
addition to the constraints in the radial direction only shown in

(3-56),

the

constraints in the axial direction between the ring and groove sides should also be included.
This yields:

(3-64)
In this case,

is still the outer radius at the ring

radius of curvature. And
respectively; while

and

and

cross-section and

is the cylinder liner

are the z-coordinates of the ring top and bottom sides

are the coordinates of the groove top and bottom sides

respectively.
The constraints require that the ring outer radius should stay in contact (for the “=” case) or
within (for the “<”) case the cylinder wall surface. In addition, the ring top side should stay in
contact with the groove top side (for
side (for

case) if it is in contact or below the groove top

case) if it is not in contact. Similarly, the ring bottom side should stay in

contact with the groove bottom side (for
bottom side (for

case) if it is in contact or above the groove

case) if it is not in contact.

Figure 3-13 shows the constraints at the ring front face, top and bottom sides at one crosssection. In this case shown in the figure, the two nodes at the ring front face top and bottom
edge are constrained in the radial direction by the cylinder wall surface. And the four corner
nodes, as numbered 1, 2, 3 and 4, are constrained in the axial direction by the groove sides. It is
not necessary the nodes constrained in the radial direction coincide with the nodes constrained
in the axial direction. For example, in most cases, the groove side has a short radial length such
that it would not constrain the ring at its outside bottom corner (node 2 in this case).
52

Figure 3-13 Constraints at ring face and ring sides

3.2.5 Result of Ring-Cylinder Bore Contact

When the free state ring is installed into the cylinder liner, the ring is constrained at its front
face by the cylinder wall. Every point on the ring front face needs to be tracked whether it is in
contact with the cylinder wall or not. However, due to the computation time and resource, it is
not possible with the existing computation tool. And the most important thing is how the
contact force/pressure distributes along the ring circumference. Thus, in this study, the ring is
specified constrained at thirteen different cross-section locations along the circumference. The
middle constraint locates at the ring back front face. Other constraints are symmetric about the
ring back and distribute with an increment of about 30°.
The free shape ring mesh and the deformed ring mesh without temperature compensation are
shown in Figure 3-14.
53

Figure 3-14 Free shape and deformed ring meshes

The green mesh in Figure 3-14 represents the free shape ring while the red mesh represents
the deformed ring shape under the cylinder bore constraints without temperature
compensation. It is obvious that the ring is pushed inward from its free state. The constraint
forces that push the ring to its deformed position are shown in Figure 3-15. The blue and red
bars represent the constraint forces at a certain circumference location at the upper and lower
corners at ring face. And the green and purple dots show the separation gaps between the ring
face and the cylinder bore.

54

12

35

10

28

Force (N)

8

21

6
14

4

Gap (um)

Contact Force and Separation Gap

7

2
0

0
-180 -150 -120

-90

-60

-30

0

30

60

90

120

150

180

Circumference Location (DEG)
Force (up)

Force (low)

Gap (up)

Gap (low)

Figure 3-15 Constraint force and separation gap

From Figure 3-15, it is found that the two contact forces at the same cross-section are identical
since the ring has a symmetric cross-section and there is no twisting moment on the ring. The
plot also shows that the constraint force at the ring back is the highest. At the cross-sections
approximately 30 degrees away from the ring back, the lowest constraint forces are found for
the sections that are in contact against the cylinder wall. The constraint forces at the ring tips
vanish such that the ring separates from the cylinder wall in its front face at its two tips. The
separation gap is defined as the radial distance between the cylinder wall ID and the ring tip OD.
A 34

separation gap is found for this specific ring from the FEA model. Details of the contact

forces and the separation gaps are listed in Table 3-1.

55

Table 3-1 Constraint forces and separation gaps
Location

0°

30°

60°

90°

120°

150°

~180°

Force, Up (N)

10.3

0.8

3.4

7.5

4.7

6.2

0.0

Force, Low (N)

10.3

0.8

3.4

7.5

4.7

6.2

0.0

Gap, Up (μm)

0

0

0

0

0

0

34

Gap, Low (μm)

0

0

0

0

0

0

34

3.2.6 Application on EcoMotors 2-Stroke Engine

The 3D ring FEA model is applied to EcoMotors 2-Stroke opposite piston opposite cylinder
(OPOC) engine for friction analysis. The contact pressure distributions between the ring and
bridge surfaces were calculated. The ring was examined for three different boundary
conditions: ring gap at the middle of bridge; ring gap at the middle of port; and one ring tip at
bridge and the other in the port. In each of the boundary condition, two cases were analyzed:
the first case assumed the constraint forces are at the middle of the bridges and the second
case assumed the constraint forces are at the bridge edges.
The EcoMotors OPOC engine cylinder is shown in Figure 3-16.

56

Figure 3-16 EcoMotors OPOC engine geometry showing intake and exhaust ports

The bridge is defined as the cylinder wall between two adjacent ports. The ring-bridge contact
study only focuses on the contact at the exhaust ports side. However, the contact between the
ring and bridge at the intake ports side can be analyzed very similar to that of the exhaust side.
The three boundary conditions discussed in this study are:
1. Ring gap is at the middle of bridge (both ring tips are in the bridge area, BC1).
2. Ring gap is at the middle of port (both ring tips are in the port area, BC2).

57

3. One tip is at the bridge area and the other tip is in the port area (BC3).
These three boundary conditions are shown in Figure 3-17.

1. Ring gap at middle of bridge

2. Ring gap at middle of port

3. One tip at bridge and one at port

Figure 3-17 Boundary condition for ring-bridge contact

In each of the three above boundary conditions shown in Figure 3-17, the ring-bridge contact
was analyzed with two constraint cases. The two cases have different locations of the
constraint force applied on the bridge. One case is assuming the constraint force is applying at
the middle of the bridge (CBM); while the other case has two constraint forces at the two edges
of each bridge (CBE). These constraint conditions are illustrated in Figure 3-18.

Figure 3-18 Constraint force conditions

58

With the constraint forces solved from the finite element analysis simulation, the contact
pressure distribution on each bridge can be obtained using a force-pressure balance correlation
knowing the ring-bridge contact area. The average pressure on a bridge is calculated first as the
constraint force on the bridge divided by the ring-bridge contact area. It is assumed that the
pressure distributes linearly on the bridge from one edge to the other. Figure 3-19 shows how
the pressure distribution on the bridge is calculated for both constraint force at middle of
bridge and at bridge edges cases. The method leads to that the pressure at the middle of the
bridge is always equal to the average pressure. The pressures away from the middle of the
bridge follow the rule described below. For the constraint at the middle of bridge case, the
bridge local pressure is related to the position between the ring node and the bridge surface. A
ring node here is a node of a ring mesh element located on the ring front face. As forces which
represent constraints are applied to the free ring, if a node on the ring is located beyond a
curved bridge that represents the bridge surface, the pressure will be high since the ring face
needs to be pushed back to the ring-bridge interface; while if a node locates within the bridge
radius, the pressure at this location is low as there is no contact at that point. The distances
between the bridge and the ring points away from the bridge middle are very small. For the
constraints at bridge edges case, the linearly distributed pressure is calculated based on the
two constraint forces at the bridge edges. If the constraint force is high on one bridge edge, the
pressure should also be high near this bridge edge; and if the constraint force is low at one
bridge edge, the pressure would also be low.

59

Figure 3-19 Bridge contact pressure distribution calculation

The pressure distribution for the ring gap at the middle of bridge boundary condition case (BC1)
is shown in Figure 3-20.

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 3-20 Pressure distribution for ring gap at middle of bridge case

60

From Figure 3-20 (a) and (b), the contact pressure distributions for the two cases showed good
agreement not only in the pressure magnitude, but also the pressure distribution pattern on
each bridge. From the two plots, the bridge in contact with the ring back shows the highest
pressure. No pressure was found for the bridge at 150° and 210° locations, which means the
ring is not in contact with the bridge at these locations, or at least the contact pressures are
supposed to be very low due to the limitation of the ring coordinate measurement tolerance.
The ring tips are not in contact with the bridge as no pressure was observed at the bridge
constraining the ring tips.
Similarly, the pressure distributions for the ring gap at the middle of port (BC2) are shown in
Figure 3-21.

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 3-21 Pressure distribution for ring gap at middle of port case

From Figure 3-21 (a) and (b), the pressure distribution configurations of the two cases also
show good agreement too. The highest pressures at the bridge edge locating at 165° and 195°

61

(closest to the ring back) are 668 KPa for the CBM case and 600 KPa for the CBE case
respectively. In addition, the bridges at 135° and 225° did not show contact with the ring.
The one tip at the bridge and one tip in the port boundary condition case (BC3) results are
shown in Figure 3-22 (a) and (b) for the constraint at middle of bridge and bridge edges
respectively. In Figure 3-22, the right tip is in the port while the left tip is at the bridge.

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 3-22 Pressure distribution for one tip at bridge and one tip in port case

Slight difference in pressure magnitude can be found from Figure 3-22. For the bridge locating
at 323.4°, the constraint at middle of bridge (CBM) case shows the contact pressure drops to
zero at one edge, while from the constraints at bridge edges (CBE) case, it does not vanish on
the same bridge edge. A similar difference is also found for the bridge locating at 83.4°. Other
than that, good agreement is found between these two results. The highest pressures at the
ring back are 603 KPa for the CBM case and 634 KPa for the CBE case respectively.

62

3.2.6 Result of Ring-Cylinder Bore-Groove Side Contact

Another example is given in this section for ring-cylinder bore-groove side contact using a
scraper ring. The scraper ring has a taper face and cut-off at the ring inner upper corner, which
promotes positive twist when installing the ring into the piston groove. The cross-section of the
scraper ring is shown in Figure 3-23.

Figure 3-23 Constraints on ring cross-section

From Figure 3-23, four nodes of the cross-section at a given circumference location are
considered for the ring-piston groove side interaction and are numbered as node 1, node 2,
node 3 and node 4 as shown. These four nodes are constrained by the groove in the axial
direction. This means node 1 and 2 should stay in contact or above the groove bottom side;
while node 3 and 4 should stay in contact or below the groove top side. Two nodes on the ring
front face are constrained by the cylinder bore in the radial direction, at the front face top and

63

bottom edges respectively. The groove has zero uptilt angle at its top and bottom sides. The
nominal clearance between the groove and ring axial thicknesses is 0.1 mm.
The main parameters describing the ring are listed in Table 3-2.
Table 3-2 Main parameters for the ring
Ring Material

Steel

Modulus of Elasticity

200.0 GPa

Poisson’s Ratio

0.3

Cylinder Bore Diameter

108.0 mm

Coefficient of Thermal
Expansion

13.0E-6 /°C

Thermal Conductivity

45 W/mK

Ring/Gas Convective
Coefficient

25 W/m K

Ring/Oil Film Convective
Coefficient

100 W/m K

2

2

The scraper ring is a ring with negative ovality. The ring also has a positive static twist due to
the cut-off at the inner top corner.
The constraint locations along the ring circumference are equally spaced with about 30° from
one butt end to the other. The number of constraint locations is found to be able to represent
the ring/cylinder liner/groove side contact force/pressure distribution pattern and also save
calculation time. Increasing constraint locations will increase computation time exponentially;
while decreasing the constraint locations may result in the contact force/pressure pattern not
being able well represented.
64

The deformed ring shape is shown in Figure 3-24 after installed into the cylinder liner and
piston groove. The displacement in the z-direction (axial direction) is amplified by 100 times in
order to illustrate the ring deformation distinctly.

Figure 3-24 Deformed ring shape after installed into the cylinder liner and piston groove

In this case, the ring back and ring butt ends are in contact with the groove bottom side; while
the ring touches the groove top side at about 60° from the end gap (120° from the ring back).
The constraint forces between the ring and the piston groove sides are important since it
dictates the contact pattern which will affect the ring-groove side wear eventually. Table 3-3
lists the constraint forces between the ring and piston groove for the scraper ring at four
constrained node locations shown in Figure 3-23.
Table 3-3 Constraint forces between ring and groove side
Force
(N)

0°

30°

60°

90°

120°

150°

~180°

ND_1

0.49

0.0

0.0

0.0

0.0

0.0

1.51

ND_2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

ND_3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

ND_4

0.0

0.0

0.0

0.0

-2.0

0.0

0.0

65

Table 3-3 shows that for the cross-section that are in contact with the groove bottom (at ring
back and ring end), the contact occurs at the lower inner node (node 1 in Figure 3-23). And for
the cross-section that touches the groove top, the contact occurs at the upper outer node
(node 4 in Figure 3-23). This contact pattern is due to the fact that the ring twists positively,
which results in a two-point contact between the ring and the groove sides.
In addition to the axial displacement variance, the ring twist angle also varies along the
circumference shown in Figure 3-25 for one half of the ring. The other half is symmetric at the
ring back.

Figure 3-25 Twist angle along ring circumference

66

The twist angle plot shows that the scraper ring twists positively as expected from the cut-off at
the ring inner top corner. However, the magnitude of the twist decreases from the ring back to
the ring end gap. The maximum positive twist occurs near the ring back at less than 0.8°. And
the minimum positive twist is found at the ring ends with slightly higher than 0.2°.

67

Chapter 4 RING THERMAL LOAD INFLUENCE

4.1

Introduction

Piston rings are subject to different temperature conditions depending on engine operating
conditions: during engine start-up, the thermal load on the piston rings is relatively low; after
engine warm-up, piston rings are usually under high temperature condition, especially the top
compression ring, which is exposed directly to the combusted gases in the combustion
chamber. Thus, besides many other functions including gas and lubrication oil control, the
piston ring is also responsible to dissipate heat from the piston to the cylinder liner, which is
cooled by coolant fluid, in order to reduce the piston temperature.
The thermal load on the piston ring is believed to have an important impact on both functions
mentioned above. As a result, the piston ring’s conformability and the contact force/pressure
can alter significantly between the low and high temperature conditions. This thermal effect is
especially essential for the top compression ring, which is typically under the highest thermal
load. Thus, a temperature distribution analysis for the ring is necessary for the ring thermal
deformation as well as the ring-cylinder liner-groove contact analysis.
As claimed by Mierbach A., et al [54], 31% of heat flow from the piston is through the ring pack
for pistons with cooling channels. For pistons that do not have internal cooling channels, this
ring pack heat flow value becomes 44% (Figure 4-1).

68

Figure 4-1 Heat flow through the piston

The proportional distribution of the possible routs of piston heat flow for a high-duty diesel
engine is shown in Table 4-1.
Table 4-1 Piston heat flow proportional distribution
Path of heat flow

with piston cooling

without piston cooling

Piston rings

31%

44%

Piston – cylinder

24%

29%

Piston crown

21%

27%

Cooling channel

24%

NA

69

It is known that the piston rings play significant roles regarding dissipating piston heat. The
consideration of ring thermal load becomes necessary in piston ring design. Due to the high
temperature difference between the cold and hot conditions, the ring end gap size needs to be
optimized. Small end gap is desired regarding to blowby control. However, the size of ring end
gap should also compensate the thermal expansion. Otherwise, the ring ends could collide,
which is recognized as “ring end gap butting”. In addition to the ring temperature difference
between the cold and hot conditions, in order for the piston ring to conduct heat, a
temperature gradient between the ring I.D. and O.D. should exist. Therefore, the I.D. of piston
ring undergoes greater thermal expansion than the O.D., depending on the thermal gradient. As
a result, the ring radius of curvature alters from the cold condition, and the contact
force/pressure varies as well. The temperature distribution on piston ring and the thermal load
influence are discussed in this chapter.

4.2

Model Description

The 3D heat transfer problem of the piston ring can be described by the 3D heat equation
below:
(4-1)
where

denotes the temperature, which is a function of three spatial variables

and

the time variable .
However, for a piston ring application as described in this study, the ring is moving rapidly with
the piston’s motion at over 1000 RPM. Thus the rate of temperature variance at any point can
70

be considered to be zero since heat spread process takes time and it would not be able to
change much in such a short duration between engine cycles when the engine is wormed up. In
this case, the temperature variation does not depend on time. Based on this assumption, the
time variant problem can be simplified as a steady-state problem and the governing equation
becomes:
(4-2)
with a convective boundary condition:
(4-3)
The ring front face is flooded with the lubrication oil film while other boundaries are exposed to
gas combustion products. Convection occurs between the ring surface and its corresponding
fluid. For this study, the convective boundary condition used is shown in Figure 4-2.

Figure 4-2 Ring cross-section heat transfer boundary conditions
71

In Figure 4-2, the ring has a keystone cross-section. The boundaries are the interfaces between
the ring cross-section edges and the gases above, behind and below the ring as well as between
the ring front face and the oil film on the cylinder liner. The example used here is a top
compression ring, which is typically under much more severe thermal load condition than the
second compression ring and the oil control ring since it is exposed to the hot combustion gas
directly.
As piston rings moving along the axial direction with the movement of piston, the temperature
on the ring front face varies since the cylinder liner temperatures vary from top to bottom.
However, the boundary condition at the ring front face in this study assumes the average
cylinder liner temperature.
The ring material properties and the convection coefficient between the ring and the
surrounding fluids are listed in Table 4-2.

Table 4-2 Ring material properties and convection coefficients
Ring Material

Steel

Conduction Coeff.

45 W/mK

Convection Coeff. between ring
25 W/m2K
and surrounding gas
Convection Coeff. between ring
100 W/m2K
face and oil film

72

Finite element analysis is used again to calculate the temperature distribution for the piston
ring. With the additional thermal load, the constitutive relation for an isotropic linear elastic
material [55, 56] can be written as:
(4-4)
where

(4-5)

As can be found, an additional thermal load due to temperature change is imposed onto the
ring. This thermal load deforms the free state ring as can be found in the following sections.
For the simplified 2D piston ring heat transfer problem, the weighted residual form of the
governing heat equation under the boundary conditions discussed previously using Galerkin’s
method becomes:

(4-6)

The above expression can be rewritten as the matrix form:
(4-7)
(4-8)
(4-9)
(4-10)

73

4.3

Ring Heat Transfer Result

4.3.1

Ring Temperature Distribution

With the boundary condition defined in the previous section, the top compression ring crosssection temperature distribution was obtained using FEA approach and the result is shown in
Figure 4-3.

Figure 4-3 Ring temperature distribution

As the temperature distribution does not vary along the ring circumferential direction as
assumed, the temperature only depends on the radial and axial location. This temperature
distribution for one arbitrary cross-section can be found in Figure 4-4.

74

Figure 4-4 Ring cross-section temperature distribution

From Figure 4-4, the ring temperature decreases from its inner-top corner through the outerbottom corner. However, the temperature gradient cross the ring is very small as the maximum
temperature difference on the ring cross-section is within one Celsius.
The result was verified using the energy balance relationship such that the energy going into
the ring from its top and inner sides is equal to the outgoing energy from its bottom and outer
sides.
The 2D ring cross-section temperature distribution was verified with COMSOL, a commercial
finite element package that is widely in multi-physics engineering applications. The result is
shown in Figure 4-5.

75

Figure 4-5 Ring cross-section temperature distribution from COMSOL

From Figure 4-5,the highest and lowest temperatures across the ring cross-section are 214.14°C
(487.32 K) and 213.91 °C (487.06 K) respectively from the inner-upper corner through the
outer-lower corner. The temperature gradient from the FEM code is verified being very small.
The highest temperature from the FEM code showed good agreement with the COMSOL result.
Although the lowest one showed a bit more deviation, the margin was still very small.
The difference between the FEM code and COMSOL result likely resulted from the way how the
corner nodes who share two boundaries were treated. In the FEM code, the heat convection at

76

those nodes are the summation of the two boundaries, which can result in higher temperature
at the heat input side and lower temperature at heat output side.
From Figure 4-4 and Figure 4-5, the ring average temperature at the prescribed condition is
about 214 °C, which is much higher than room temperature (25 °C). The inner upper corner has
the highest temperature while the lowest temperature is found at the outer lower corner.
However, the temperature gradient across the ring is very small, due to the small dimensions in
both the radial and axial directions of the ring. These small dimensions do not provide high
thermal resistance with the material being used. Although the temperature gradient across the
ring is small, the temperature increase from the room temperature to the hot operation
condition is significant. This large temperature change does act as a thermal load that can cause
ring volumetric thermal expansion. Thus, the temperature influenced ring free shape must be
studied when analyzing the ring-cylinder wall contact.

77

Figure 4-6 Ring free shape with and without temperature influence

Figure 4-6 shows the ring at room temperature condition (blue mesh with shade) as well as the
ring after thermal expansion (red mesh). It clearly shows that the ring radius of curvature
increases. The ring radius growth along the circumferential direction is not as significant as in
the radial direction. However, the ring curvature length increases as well.
As for the room temperature condition (cold), the ring free shape normalized radius at high
temperature operation condition (hot) is also plotted, for comparison. The plot can be found in
Figure 4-7. The maximum radial growth for the ring is 0.33 mm. It is obvious the free shape has
changed significantly considering the temperature effect.

78

Figure 4-7 Normalized ring radius with and without temperature influence

With the influence of thermal load on the ring, the ring-cylinder bore conformability and the
contact force/pressure can vary. Particularly, if the radius of curvature at the ring end tips
increases greatly, the ring can lose its conformability near the ring end. Instead, point
contacting occurs at the ring tips as shown in Figure 4-8.

79

Figure 4-8 Losing conformability due to thermal influence

The loss of conformability results in separation gaps between the ring front face and the
cylinder wall, allowing gas to escape from the high pressure side to low pressure side. This
could be bad for engine blowby control. In addition, the loss of conformability also results in
high contact pressure at the ring tips. This is one of the reasons of the high wear typically found
at the ring end tips.
4.3.2 Result of Ring-Cylinder Bore and Ring-Groove Contact

The ring-cylinder liner contact was also analyzed for the temperature influenced free shape ring.
The constraint forces and separation gap sizes at the upper and lower edges along the ring

80

circumference with temperature influence can be found in Figure 4-9. The constraint force
pattern along the ring circumference shows that separation gaps also exist at the ring tips.
However, these gaps have been significantly reduced. And the constraint loads at the locations
about ±30° and ±120° away from the ring back are very small compared to other locations.
Slight difference in contact force can be found between the upper edge and the lower edge at
the same circumferential location. This results from the temperature difference across the ring
cross-section. The higher temperature at the ring inner upper corner and the lower
temperature at the outer lower corner introduce a twist torque that tends to twist the ring
negatively. The higher constraint force at the upper corner and lower force at the lower corner
form another moment that balances the temperature induced twist moment. The separation
gap at the ring tips also shows difference between the upper and lower edges with the upper
gaps slightly smaller than the lower ones.

12

2.4

10

2

8

1.6

6

1.2

4

0.8

2

0.4

0

0
-180

-150

-120

-90

-60

-30

0

30

60

90

120

150

180

Circumference Location (DEG)
Force (up)

Force (low)

Gap (up)

Gap (low)

Figure 4-9 Contact force and separation gap with temperature influence
81

Gap (um)

Force (N)

Contact Force and Separation Gap

The constraint forces and separation gaps around the ring circumference with temperature
influence are also listed in Table 4-3.
Table 4-3 Constraint forces and separation gap size with temperature influence
Location

0°

30°

60°

90°

120°

150°

~180°

Force, Up (N)

11.2

1.8

4.0

9.4

1.3

9.9

0.0

Force, Low (N)

11.1

1.6

3.9

9.4

1.3

9.6

0.0

Gap, Up (μm)

0

0

0

0

0

0

1.7

Gap, Low (μm)

0

0

0

0

0

0

1.8

It is also worthwhile to study how the constraint force pattern changes between the cold ring
and temperature influenced hot ring. Figure 4-10 shows the constraint forces at the upper and
lower edges along the ring circumference comparison between the conditions with and without
temperature influence. At the cold condition, the constraint forces at the upper and lower
edges are identical at the same circumferential location as explained in the previous section.
Only one bar plot is needed to represent the constraint forces at either edge at cold condition.
The constraint forces all increase with different magnitude except for the one at around 120°
away from the ring back with the consideration of the temperature compensation. The location
of the maximum constraint force shows agreement as at the ring back.

82

Contact Force
12
10

Force (N)

8
6
4
2
0
-180

-120

-60

0

60

120

180

Circumference Location (DEG)
Hot (up)
Hot (low)
Cold

Figure 4-10 Contact force with and without temperature influence

4.3.3 Application on EcoMotors 2-Stroke Engine

With the temperature compensation considered, the ring-bridge contact was analyzed in a
similar way as for the cold condition. Three boundary conditions were studied as well: the ring
gap at the middle of bridge; ring gap in the middle of port and one tip at the bridge one tip in
the port. In each of these conditions, two constraint patterns were used: one is the constraint
force at the bridge middle and the other is the constraint forces at the bridge edges. And the
contact pressure distributions were calculated in the same way as the previous cold condition.
The pressure distribution for the ring gap at the middle of bridge boundary condition case (BC1)
with temperature compensation is shown in Figure 4-11.

83

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 4-11 Pressure distribution for ring gap at middle of bridge case with temperature
influence

From Figure 4-11, the pressure distributions show agreement between the two constraint cases
regarding to pressure magnitudes at different bridges. The pressure distribution patterns
between these two cases also show good agreement except for at the bridges at 90° and 270°.
The result of the constraint at the middle of bridge case shows bigger pressure difference
across the bridge while the constraints at bridge edges case suggests a more homogeneous
distribution. Comparing the result to Figure 3-20 that did not consider temperature
compensation, it is found that the pressure distributions on the bridges locating at 30° and 330°
as well as 60° and 300° behave different with temperature compensation. This is due to that
face that the ring free shape is changed under the thermal load.

84

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 4-12 Pressure distribution for ring gap at middle of port case with temperature influence

Similarly, the pressure distributions at bridges for the ring gap at middle of port case (BC2) with
temperature compensation are shown in Figure 4-12. The two constraint cases showed good
agreement except the pressure distribution at the bridge locating at 75° and 285°. In addition,
the constraints at bridge edges case showed a little higher pressure at the bridges at 45° and
315°. Both results showed there is no pressure at the bridges locating at 135° and 225°. This
means the pressure is expected to be low at those locations as ring free shape measurement
error could be involved for the ring mesh.

85

a. Constraint at middle of bridge

b. Constraints at bridge edges

Figure 4-13 Pressure distribution for one tip at bridge and one tip in port case with temperature
influence

The bridge pressure distributions for the one tip at bridge and one tip in port case (BC3) are
shown in Figure 4-13. The ring right tip is in the port and the left tip is at the bridge area. The
two constraint cases showed great agreement regarding to the pressure magnitude as well as
the distribution pattern at different bridges. Comparing to the pressure distribution at the cold
condition, the results with temperature compensation showed the pressure pattern at the
bridge locating at 23.4° changed. This can be explained as the ring grew outward due to the
thermal load and thus the pressure is higher at the bridge edge that is closer to the ring tip.

86

Chapter 5 RING-CYLINDER LINER LUBRICATION AND WEAR
5.1

Introduction

Friction occurs between the contact surfaces when they have relative motions. The engine
power cylinder system has a major contribution to engine mechanical friction [57-63]. Engine
fuel economy also benefits from friction reduction [64, 65]. Stribeck diagram (Figure 5-1) is
typically used to define the friction coefficient between the contact pairs [42]. In the diagram,
the ordinate is the friction coefficient and the abscissa defines the operating condition, which is
the product of the lubrication oil viscosity
load

and the relative velocity , divided by the normal

on the surfaces.

The Stribeck curve can be divided into three zones: the boundary friction zone, mixed friction
zone and the hydrodynamic friction zone. The boundary friction zone is where asperity contact
occurs due to lack of lubrication supply. As a result, the friction coefficient is relatively high and
remains almost constant throughout the boundary friction zone. The hydrodynamic friction
zone is recognized as the hydrodynamic lubrication occurs. Thus, instead of asperity contact,
the two surfaces are separated by a thin lubrication oil film, in the order of less than one
micron. The hydrodynamic friction is caused by the share stress of the lubrication oil layer
between the two surfaces. Hydrodynamic friction increases as the oil viscosity or velocity
increases; but decreases as the normal load increases. Between the boundary friction zone and
the hydrodynamic friction zone is the mixed friction zone, where both boundary friction and

87

hydrodynamic friction can be found. Depending on the operating condition, the contact
pressure is carried differently by the asperity contact and hydrodynamic contact.

Figure 5-1 Stribeck diagram

Within the engine, the valvetrain system mainly experiences boundary friction, with a small
amount of mixed friction; the engine bearings experience mainly the hydrodynamic friction;
and the piston skirt mainly faces hydrodynamic friction. For the piston rings, both mixed friction
and hydrodynamic friction can be found. The top compression ring with a barrel face has mostly
hydrodynamic friction. However, lubrication oil may not be sufficient as the piston moves close
to TDC. As a result, asperity friction occurs for the top ring. For a scraper second compression
ring, hydrodynamic friction and asperity friction switches between the upward strokes and the
88

downward strokes. The oil control ring has asperity friction most of the time since the rails of
the oil control ring breaks the oil film thus hydrodynamic lubrication cannot form.
Boundary friction, also known as asperity friction, and the hydrodynamic friction are important
phenomena within the power cylinder system. The power cylinder system friction loss, wear
depend heavily on these phenomena. Thus, understanding the physics of these phenomena as
well as their contribution in carrying the contact load becomes important.

5.2

Asperity Contact Model

The Greenwood-Tripp model for the contact of two nominally flat rough surfaces is a widely
used model in asperity contact studies [66, 67]. The model describes the contact of two
surfaces depends on the topography of the surfaces and showed indistinguishable results from
the previous single rough surface models. They claimed that the asperity height of the rough
surface is very close to a Gaussian distribution, for non-worn surfaces.
For two rough surfaces separated by gap , the nominal gap is defined by:
(5-1)
where

is the composite standard deviation of the asperity heights distribution, which is

defined as:
(5-2)
In the above equation,

and

are the standard deviation of the asperity height distribution

of the two rough surfaces as shown in Figure 5-2.

89

Figure 5-2 Asperity distribution for rough surfaces

The contact load carried by the asperity

then can be expressed as:
(5-3)

where ,

and

are the functions of surface properties and the material property.

is a function of the asperity density

and the radius of curvature

of the surfaces and

can

be expressed as:
(5-4)
is the composite modulus of elasticity of the two contacting materials, and is defined as:
(5-5)
is the function that describes the integral of the Gaussian distribution of the asperity
heights.

is defined as:

90

(5-6)
It is clear that there is no close form solution for the evaluation shown in equation 5-6. Either
numerical solution or approximate solution are needed to evaluate this integration. Greenwood
and Tripp gave tabulated values for the integration as shown in Table 5-1. These values are
used to approximate the value of integration of

.

Table 5-1 Tabulated values for

0.0

0.61664

0.5

0.24040

1.0

0.08056

1.5

0.02286

2.0

0.00542

2.5

0.00106

3.0

0.00017

3.5

0.00002

4.0

0.00000

>4.0

0.00000

91

Some approximation models have been proposed to evaluate the integral

easily. A

power law approximation has been proposed by Hu et al [68]. The expression for the
approximation is:
(5-7)
The constants in the approximation are found to be:

and

.

Besides Hu’s approximation model, Arcoumanis et al [58] proposed a sixth order polynomial for
the approximation of

, which is approximated as:

C H 6  C5 H 5  C 4 H 4  C3 H 3  C 2 H 2  C1 H 1  C0 H   4.0
F5 ( H  )   6 
2
H   4.0
0


In this approximation,

are constants which can be found in Table 5-2 below.

Table 5-2 Constants for
Constant

approximation
Value
0.6167
-1.0822
8.0203 10-1
-3.1933 10-1
7.1624 10-2
-8.5375 10-3
4.2074 10-4

92

(5-8)

Figure 5-3 shows the relationship between the asperity contact pressure and the normalized
gap between the two flat surfaces with the

evaluated with Arcoumanis’ model.

Asperity contact pressure (Pa)

asperity contact pressure (Pa)

2.50E+09
2.00E+09
1.50E+09
1.00E+09
5.00E+08

3.99

3.79

3.59

3.39

3.19

2.99

2.79

2.59

2.39

2.20

2.00

1.80

1.60

1.40

1.20

1.00

0.80

0.60

0.40

0.20

0.00

0.00E+00

h/H_sigma
asperity contact pressure

Figure 5-3 Asperity contact pressure

From Figure 5-3, a nonlinear relation is found between the asperity contact pressure and the
normalized gap. And the asperity contact pressure decreases gradually as the gap increases
between the two contacting surfaces. The asperity contact pressure vanishes eventually when
the gap becomes greater or equal to 4 times of the normalized gap value.

5.3

Hydrodynamic Contact Model

Hydrodynamic contact carries the contact pressure together with the asperity contact.
Reynolds’ equation is a widely used method modeling hydrodynamic pressure distribution. And
93

this model is also adopted to calculate the hydrodynamic lubrication pressure at the piston
skirt/cylinder wall interface as well as the piston ring face/cylinder wall interface. The onedimensional form of the Reynolds’ equation can be expressed as:
(5-9)
Here, the time derivatives,

and

denote the relative velocities between the two moving

surfaces along different direction. Thus, they can be considered constants and be replaced with
and . Then the one-dimensional Reynolds’ equation becomes:
(5-10)
A schematic diagram of this lubrication model is shown in Figure 5-4.

Figure 5-4 Schematic diagram of lubrication between surfaces

94

Known the pressure distribution, the shear stress resulted from the hydrodynamic friction can
be obtained. The shear stress is defined as a function consisting a viscosity and dynamic part,
and a pressure gradient part:
(5-11)
However, this shear stress model predicts that the viscosity term becomes unbounded as the
distance between the two surfaces approaches to zero. However, in practical, the breaking up
of the oil film by the asperities as the distance approaches to zero should cause the viscous
shear stress to approach to zero as well. Thus, this shear model is modified with flow factor
method proposed by Patir and Cheng [69]. The shear stress equation is then defined as:
(5-12)
where

,

and

are the flow factors.

In order to fulfill the condition that the shear stress stays bounded as the oil film thickness goes
to zero, it is essential that the flow factors approach to zero as fast as the decrement of oil film
thickness . The flow factors are defined by Patir and Cheng as:

n

, where

(5-13)
(5-14)
(5-15)

The viscous term of the shear stress equations can be written as:

(5-16)

95

Figure 5-5 shows both

and

into account for

, together with the viscous term with the flow factor taken

case. It is clear that without the flow factor,

approaches to zero. However,

goes to infinity as

does converge to a certain value when

goes to zero. In

this case, the viscous term of the shear stress is also bounded.

Viscous Term vs Oil Film Thickness for σ=0.4μ

Viscous Term (1/μm)

6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Oil Film Thickness h/σ
1/h

φ/h

viscous term

Figure 5-5 Viscous part of shear stress for different oil film thickness

Figure 5-6 illustrates to what value the viscous term of the shear stress converges to as the
distance approaches to zero for different surface roughness cases. It becomes clear that the
viscous term decreases as the surface roughness increases when the distance between the two
surfaces is zero.

96

Viscous Term at h/σ=0 vs Surface Roughness

Viscous Term at h/σ=0 (1/μm)

25
20
15
10
5
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Surface Roughness σ (μm)

Figure 5-6 Viscous part of shear stress at different surface roughness

5.4

Wear

Wear occurs at the interacting surfaces when two contacting surfaces have relative motion.
Wear can be categorized into different types: adhesive wear, abrasive wear, surface fatigue,
corrosive wear, etc.
Adhesive wear occurs between surfaces with friction/asperity contact as the surfaces are sliding
against each other.
Abrasive wear occurs between two surfaces when one of the surface is hard rough and the
other one is softer.
Surface fatigue occurs when cyclic loading is involved for a surface. As a result, the surface
material is weakened by the loading and materials are removed by the cyclic crack.
97

Corrosive wear refers to the process that chemical reaction occurs between the surfaces such
that surface material degradation occurs.
A huge amount of effort has been committed for engine wear modeling and analysis [28, 7076]. Considering the nature of wear and in order not to make the problem too complex, only
adhesive wear mechanism is considered for the power cylinder system. And Archard equation
[77] is adopted to model the wear. According to Archard, the surface volume removed between
the sliding surfaces is proportional to the sliding distance, the asperity contact load between
the two surfaces and inversely proportional to the hardness of the surface material.
(5-17)
where

is the removed volume;

asperity contact force;

is the wear coefficient determined empirically;

is the

is the sliding distance between the two surfaces and

is the

combined hardness of the two surface materials.
The local removed material volume can be obtained in the same manner:
(5-18)
where
contact,

denotes the local asperity contact pressure and

is the area of the local volume in

is the local sliding distance.

Sometimes it is more important to know the height of removed material, this can be found as:
(5-19)
Integrated over the entire engine cycle, the overall wear for one engine cycle can then be
obtained for one specific point.
A piston ring and groove side wear analysis for diesel engines has been conducted by Poort, M.
and Cheng, C., Richardson, Dan, et al [78].
98

5.5

Simulation Result

The asperity and hydraulic contact models are applied on a top compression ring for a heavy
duty diesel engine at full load operation condition. The approach can be summarized as: The
ring tension is an input to the model. And the ring pressure distribution profile (cam shape)
obtained from the 3D ring contact at static condition is also input. Besides, the gas pressure
behind the ring is superimposed on the ring during cycle analysis. The lubrication oil used for
this simulation is 10W40. And the in-cylinder gas pressure is plotted in Figure 5-7.

Figure 5-7 In-cylinder gas pressure

Under this condition, the oil film thickness for the top compression ring is shown in Figure 5-8.
99

Figure 5-8 Oil film thickness for top ring

The oil pressure force for the top ring is shown in Figure 5-9.

100

Figure 5-9 Oil pressure force for top ring

Figure 5-10 and Figure 5-11 show the asperity and hydrodynamic contact pressure for the top
ring over the cycle.

101

Figure 5-10 Asperity contact pressure for top ring

102

Figure 5-11 Hydrodynamic contact pressure for top ring

Figure 5-12 and Figure 5-13 show the asperity friction pressure and hydrodynamic friction
pressure respectively.

103

Figure 5-12 Asperity Friction Pressure

104

Figure 5-13 Hydrodynamic Friction Pressure

The instantaneous ring face wear for the top ring is shown in Figure 5-14.

105

Figure 5-14 Instantaneous ring face wear for top ring

106

Chapter 6 VALIDATION OF NUMERICAL MODEL
6.1

Introduction

The 3D piston ring/cylinder bore contact FEA model presented in the previous chapters is
compared with experimental measurement results.
Two experiment validations are used to verify the numerical model. One is by comparing the
piston ring/cylinder bore contact force distribution along the ring circumference. The other is
by comparing the separation gaps along the ring circumference as found by the numerical
method.

6.2

Piston Ring Pressure/Force Distribution Measurement

A test rig capable of measuring the piston ring/cylinder bore contact load at variable
circumferential locations is adopted to measure the contact force between the ring front face
and the cylinder wall. The test rig setup is shown in Figure 6-1. In this test, the contact forces
are only measured at five circumferential locations. Five locations may not be enough to
represent the continuous contact force distribution. However, the goal is to validate the
numerical model by comparing the numerical and measured results.

107

Figure 6-1 Ring pressure/force measurement rig

Miniature force transducers are used for measuring the force at the contact interfaces. The
load cells are mounted onto metallic shafts, which are supported by their own C-clamp
supporters. The C-clamps are not tightened such that the metallic shafts can slide with minimal
friction between the shaft and the C-clamp interface. The radial movements of the load cells
and the metallic shafts are constrained by the micrometers distributed circumferentially. These
micrometers are also supported by the C-clamps. However, these C-clamps are tightened and
the micrometers are not allowed to move in the radial direction. The ring supports are used to
support the piston ring by holding the bottom of the ring. Two circumferential slots can be
found which allow the load cells and the micrometers sliding along. Thus, the load cells can be

108

located at different circumferential locations to measure the ring/cylinder bore contact forces
at the desired locations. The output signals are recorded in the computer through a data
acquisition system.
The load cells can be located at different radial location by adjusting the micrometers at the
back of the load cells. This enables the test rig to account for variant cylinder bore diameters for
different engine sizes. This is achieved by adjusting the load cells to align with a reference
piston with known outer diameter (Figure 6-2). This load cell position is used as the reference
position. Then, by further fine tuning of the micrometers, the desired cylinder bore inside
diameter can be achieved.

Figure 6-2 Ring test rig alignment

109

A sensitivity study was carried out for the ring contact force test rig to evaluate the
performance of the rig. The ring/cylinder bore contact forces are measured five times. During
each measurement, the contact forces are recorded twenty times with a frequency of 1 Hz.
Since this is a static test, the measuring frequency is high enough to capture all variations
occurring during the test. These twenty measurements are averaged after each test run. And
the five averaged contact forces are used for sensitivity study. The averaged contact forces at
different circumferential locations are shown in Figure 6-3.

Average Contact Force
12.00
Contact force (N)

10.00
8.00
6.00
4.00
2.00
0.00
-167

-90

0

90

167

Circumferential location
Average Contact Force

Figure 6-3 Measured contact force at different circumferential locations

From Figure 6-3, it clearly shows that the contact forces are the highest at 90° away from the
ring back and lowest near the ring end gap (±167° away from the ring back). And the ring back
contact force is in between. The analysis method mentioned above refers to the first level
“Gage R&R” study used in some OEM’s. The “R&R” means repeatability and reproducibility. The

110

second level “Gage R&R” requires dissembling and reassembling the experiment test rig each
time taking the measurement data.
The contact forces at different load cell locations are then analyzed by calculating the
normalized standard deviations as shown in Table 6-1.

Table 6-1 Normalized standard deviation of ring measurement rig

Std Deviation

-167°

-90°

0°

90°

167°

0.48%

3.51%

7.09%

3.48%

1.44%

From the standard deviation values shown in Table 6-1, the experiment results show good
consistency. This means the ring/cylinder bore contact force test rig is robust. The load cell
location that shows the highest deviation is the one at 0° (at the ring back location). This is
likely due to the fact that the two load cells that locate 90° away from the ring back introduce
friction forces, which are almost in the direction of the normal force at the ring back. Thus, in
each measurement the friction force behaves differently. As a result, the contact force at 0°
shows higher variation, and also the highest standard deviation. This may be eliminated by
installing bearings at the load cell contact surface.
A comparison between the measured contact forces and the model predicted contact forces
are shown in Figure 6-4.

111

Ring-bore contact force
35
30

Force (N)

25
20
15
10
5
0
-167

-90

0

90

167

Circumference location
calculated

measured

Figure 6-4 Measured and calculated contact forces

It was found from Figure 6-4 that the model predicted contact forces are higher than the
measured forces at all five locations. However, they show the same contact force distribution.
That is at ±90° the highest constraint forces are observed, at ±167° the constraint forces are the
lowest.
The difference between the model predicted and measured absolute contact forces may be
attribute to the following factors: first, ring’s modulus of elasticity used in the model; second,
the measured ring free shape, as it is a discrete description of the ring defining the ring radius
at certain given locations; third, it was observed from the measurement that the ring may not
contact with the load cells at their centers, thus the contact locations may slightly change as
specified previously.

112

Another plot with the contact forces all normalized by the one at the ring back is shown in
Figure 6-5.

Figure 6-5 Normalized measured and calculated contact force

Great agreement is found between the measured and predicted normalized ring/cylinder bore
contact forces. As a result, the FEA model is proved to predict the constraint force at the
ring/cylinder wall interface. This provides details at the interface that can be adopted by other
software for gas dynamics, friction and wear analysis, etc.

6.3

Piston Ring/Cylinder Bore Conformability Test

Another experiment conducted to validate the numerical ring/cylinder bore contact model is
the ring/core conformability test. This is a straightforward method and the schematic diagram
of this experiment is shown in Figure 6-6.

113

Figure 6-6 Ring “light-tightness” measurement

The experiment is conducted by installing the piston ring into the cylinder liner. In this case, the
ring conforms to the cylinder bore. A light source is provided at one side of the ring and an
observer is placed at the other side to detect light. If the ring well conforms to the cylinder
bore, there should be no light; while if light is detected at any circumferential location, it means
the ring separates with the bore at that location. This observation result is shown in Figure 6-7
with the same ring modeled in the previous chapters.

114

Figure 6-7 Ring “light-tightness” measurement result

This measurement observation showed that light was detected at the ring end gap up to about
15° away from the end gap in both directions. This means the ring separated from the cylinder
wall near the ring tips. The light-tightness measurement (ISO6621 2) confirms the FEA result.

115

Chapter 7 SIMULATION ANALYSIS OF RING DYNAMICS AND
TRIBOLOGICAL BEHAVIOR
7.1

Introduction

In this chapter, a commercial software package CASE is used to simulate the ring pack behavior.
The focus is on the second ring dynamics due to different ring pack designs. In the second part
of this chapter, the 3D ring behavior under dynamic load during an engine cycle is given. The
ring deformation, dynamic twist angles, constraint loads are all calculated. At the end, the
friction and lubrication behavior is analyzed with the consideration of the variation along the
ring circumference.

7.2

Second Ring Flutter and Collapse Simulation with CASE

Analytical tools are widely used in design and troubleshooting process by the engine makers
nowadays since it evaluates the design with high fidelity and much more time and cost effective
than prototype. CASE is a code analyzing the cylinder-kit for four stroke IC engines. The cylinderkit tribological behavior and engine loss associated with the cylinder-kit system can be analyzed.
The example given in this section is a study on the second ring flutter and radial collapse for a
heavy-duty diesel engine using CASE [79].
Second ring fluttering is the consequence of external force unbalance, especially between gas
pressure force and inertial force. The other loads acting on the ring, including friction force, oil
film squeezing force, etc, are relatively small in comparison [17]. It is noted that while the
second ring friction is relatively low, the friction forces of the oil ring and the top ring during
116

high cylinder pressures can be large. However, this study is only evaluating the forces on the
second ring that cause it to flutter. Also, only the second ring flutter and collapse that occurs
around top dead center (TDC) firing conditions is described in this study. This region is also
considered the most important region for ring fluttering and collapse because of its significance
on blowby and oil consumption.
At the start of the compression stroke (180 DEG), the second ring sits against the bottom flank
of the piston groove. At this time the inertial force is holding the ring down as shown in Figure
7-1 for a general case. In Figure 7-1, negative direction denotes the downward direction.

Figure 7-1 Second ring inertial force, gas pressure force and zoom-in net force

117

As the piston starts moving upward compressing the gases in the cylinder, the pressure in the
cylinder will start building up. As a result, gases will leak past the top ring into the second land
region and will start pressurizing the second land. The pressure buildup in the second land will
be delayed from the pressure in the cylinder. The second land pressure will tend to hold the
second ring down (Figure 7-1 and Figure 7-2 Stage I).
In the middle of the compression stroke (280 DEG), the inertial force acting on the ring will
change directions. Prior to 280 DEG the inertial force holds the ring down. After this point the
inertial force will push the ring upward. If it becomes higher than the downward pressure force
acting on the ring, the ring will lift (Figure 7-2 Stage II).
Under these conditions, the ring moves upward to the top flank of the groove. As a result the
ring creates a seal with the top side of the groove (Figure 7-2 Stage III). Gas pressure in the land
above the second ring increases since gas is not allowed to flow around the side of the second
ring. This gas pressure force may then surpass the ring inertial force which is holding the ring up
and consequently push the ring back toward the groove bottom (Figure 7-2 Stage IV). Once the
ring is pushed downward off the top side of the groove, the pressure that has built up above
the ring will release around the ring sides. At this point, the pressure above and below the ring
will equalize and there will be no net pressure force acting on the ring (Figure 7-2 Stage II). The
major force that remains acting on the ring is the inertial force, which drives the ring back up to
the top side of the ring groove.
Once the ring is back on the top side of the ring groove, the cycle starts again. Pressure builds
up until it pushes the ring down. Pressures equalize which allows the inertia to push the ring
back up. This continues to repeat and is called ring fluttering (Figure 7-2).
118

The fluttering will continue until some point at which the pressure can push the ring to the
bottom side of the groove. This is often at about 450 CAD when the inertia force once again
changes direction and pushes the second ring down (Figure 7-1).

Figure 7-2 Second ring fluttering scenario

When the ring is on the top side of the ring groove, the pressure force not only pushes the ring
downward, but it also acts on the front face of the ring pushing it radially inward (Figure 7-3
Stage II). If the gas pressure acting on the ring face exceeds the tension of the ring plus the gas
pressure acting on the back of the ring, then the ring will collapse radially inward (Figure 7-3
Stage III). Once it collapses, the gases will escape past the ring face and equalize all around the
ring (Figure 7-3 Stage IV). Once again, there will be no net gas pressure on the ring and the
elastic tension of the ring will force the ring back out to the cylinder wall (Figure 7-3 Stage V).
This cycle will repeat, causing an unstable collapse. Figure 7-3 is a pictorial explanation of this
mechanism with a taper faced ring for illustration as most second rings for a diesel engine have
a taper face. High pressure gases can infiltrate between the ring face and the cylinder wall if the
ring face is not flooded with lubrication oil.
119

It will depend on the ring and piston design which of these two conditions occur: 1. Ring
fluttering or 2. Ring collapse. It may even be possible that both conditions occur at the same
time. In either case, the second ring is not sealing the gases and allows the gases to flow either
around the ring (in the fluttering case) or past the ring face (in the ring collapse case). Because
the second ring is not sealing gases in these two cases, high blowby could occur.
Fluttering or collapse of the second ring requires that the ring lifts to the top side of the ring
groove and seals the gases. If inertia is not strong enough to overcome the gas pressure that is
holding the ring down, the ring will remain seated on the bottom side of the ring groove. There
will be no ring flutter nor ring collapse.
The potential for ring fluttering and/or ring collapse is influenced by the operating conditions of
the engine. High intake manifold pressure may push more gas past the top ring. Thus the
second land gas pressure is higher and may tend to hold the second ring down, preventing it
from lifting. The ring inertial load increases quadratically with engine speed. High inertial force
could make the second ring more susceptible to lifting. Besides the operation conditions, design
parameters such as ring twist, and land clearance could also affect ring fluttering as they
determine the area on which the gas pressures act and ultimately the forces acting on the ring.
These influences will be discussed later in this study.

120

Figure 7-3 Second ring radial collapse scenario

The engine modeled in this study is a diesel engine. This work focuses on the full load rated
power condition at 1900 RPM.
Two different ring pack cases are studied in this work, including ring static twist, and end gap
size influences on second ring fluttering.
Two different ring pack cases are studied in this work, including ring static twist, and end gap
size influences on second ring fluttering.
Case 1 uses a negative static twisted second ring. The key geometries of the ring pack are
shown in Table 7-1.
Table 7-1 Ring pack configuration for Case 1
ring static twist

Negative

Top ring end gap

0.45 mm

second ring end gap

2.00 mm

121

With this configuration, the nominal engine blowby was found to be over 21 L/min/L-disp. The
in-cylinder pressure, second land gas pressure as well as top ring and second ring in-groove
motions are shown in Figure 7-4.

1600

0.75

1200

0.6

800

0.45

400

0.3

0

0.15
90

180

270

360

450

540

-400

Ring Location

Pressure (KPa)

Inter-ring pressure and ring locations

630
0

-800

-0.15

CAD
In-cyl

2nd_land

top ring

2nd ring

Figure 7-4 Inter-ring, second land gas pressure and ring in-groove locations

From Figure 7-4, it is obvious that the second ring lifts to the top side of the ring groove at
about 270 DEG because of the inertial force acting on the ring. The second ring then flutters off
the top side of the second ring groove. This fluttering continues until the inertial force of the
ring changes direction at about 450 DEG and pushes the ring down.
It should be noted that the pressure above the second ring (i.e. the second land pressure)
fluctuates with the ring fluttering. This shows how the pressure builds up, the ring is pushed
down off the top side of the ring groove, pressure equalizes, inertia pushes the ring up, and the
cycle repeats several times.

122

Also it can be seen that in general the second land pressure is very low. As a result, the pressure
above the top ring (cylinder pressure) is always greater than the pressure below the top ring
(second land pressure). This keeps the top ring seated on the bottom of the groove and there is
never any reverse flow of gases back into the combustion chamber (blowback).
In this case, the second ring was fluttering. However, under the right conditions, the ring could
have collapsed radially inward instead of flutter or could have collapsed and fluttered
simultaneously.
Unlike Case 1, a positive static twisted second ring was adopted for Case 2. In order to prevent
the second ring from lifting, the second ring end gap size is reduced by 50% in order to keep the
second land gas pressure relatively high. This configuration is expected to allow more pressure
to build up above the second ring such that the second ring does not lift nor flutter. These
geometries are shown in Table 7-2.
Table 7-2 Ring pack configuration for Case 2
second ring static
Positive
twist
Top ring end gap

0.45 mm

second ring end
1.00 mm
gap

The in-cylinder pressure, second land gas pressure, top ring and second ring in-groove motions
are plotted in Figure 7-5 for Case 2 and it is clear that second ring fluttering does not occur for
this case. This is because the pressures above the second ring are high enough to prevent

123

inertia from lifting the second ring. Since the ring remains bottom seated, as the second land
pressure build up, it holds the second ring down and the ring does not flutter.

1600

0.75

1200

0.6

800

0.45

400

0.3

0

0.15
90

180

270

360

450

-400

540

Ring location

Pressure (KPa)

Inter-ring pressures and ring locations

630
0

-800

-0.15

CAD
In-cyl

2nd_land

top ring

2nd ring

Figure 7-5 Inter-ring, second land pressures and ring in-groove locations

It was found that engine blowby for Case 2 is reduced by 15% compared to Case 1. This is
because in Case 1 the second ring is not sealing the gases very efficiently and allowing the gases
to flow around the ring as it flutters.
However, it should be noted that the second land pressure builds up higher than in Case 1. This
is because the second ring gap is smaller and because it is positive twist. Both features allow
pressure to build up quicker above the second ring holding it down and preventing inertial from
lifting the ring. If the second ring does not lift before top dead center it will not flutter.
If the second land pressure becomes too high, there can be a time when the cylinder pressure
falls below the second land pressure. This can lead to reverse flow of gases upward into the
124

combustion chamber and possible lift of the top ring. This condition may be bad for oil
consumption because the reverse gas flow may carry oil back into the combustion chamber
increasing oil consumption.
Figure 7-6 shows a comparison of the second land pressures for Case 1 and 2. It can be seen
that at 270 DEG the Case 2 second land pressure is higher than Case 1 pressure. It is high
enough to hold the ring down and prevents the fluttering of the second ring for Case 2. Since
Case 1 has second ring fluttering, the ring is not sealing the gases and the second land pressure
is very low. Also it is erratic because of the gases flowing past the fluttering second ring.

Second land pressures
1600

Pressure (KPa)

1200

800

400

0
90
In-cyl

180

270

360

CAD
2nd_land_case_1

450

540

630

2nd_land_case_2

Figure 7-6 Second land pressure comparison

Because of the difference in ring in-groove motions and second land gas pressures, the
instantaneous gas flow across the second ring is found significantly different for the two above
cases. The instantaneous gas flows through the second ring end gap and ring sides are shown in
125

Figure 7-7 (a) and (b) respectively. It was found that the major gas flow across the second ring
for Case 1 is the flow around the sides of the ring between the ring and groove (Figure 7-7 b).
And high-level gas flow fluctuation occurs with the fluttering second ring case due to the
opening and closing of this gas flow path around the ring sides.
The gas flow through the second ring end gap is relatively low for Case 1 compared to Case 2,
due to the lower pressure above the second ring and also because the gases are escaping past
the sides of the ring for Case 1. However, for Case 2, minimal gas travels around the sides of the
ring as the ring seals against the bottom flank of the groove during the entire cycle. The only
major gas flow path is through the ring end gap (Figure 7-a). And this gas flow through the ring
end gap is stable and much higher than that for Case 1.
In Figure 7-7, positive gas flow is defined as downward flow, from the second land to the third
land, or from the second groove into the third land. It has been found that the gas flow through
ring end gap is higher for Case 2 and gas flow around the ring sides is significantly higher for
Case 1. The resultant overall downward gas flow (blowby) for Case 2 is still lower than that for
Case 1 in this study.

126

Instantaneous flow across ring 2 gap
0.0025

Gas flow (Kg/s)

0.002
0.0015
0.001
0.0005
0
90

180

270

360

450

540

630

CAD
ring_2_case_1

ring_2_case_2

(a) Instantaneous gas flow across second ring end gap
Instantaneous flow across ring 2 sides
0.008
0.007

Gas flow (Kg/s)

0.006
0.005
0.004
0.003
0.002
0.001
0
-0.001

90

180

270

360

450

540

630

CAD
ring_2_case_1

ring_2_case_2

(b) Instantaneous gas flow across second ring sides
Figure 7-7 Instantaneous gas flow across second ring

As described above, the lift of the second ring and seating on the top side of the groove is a
necessary precursor for the second ring to flutter or collapse. This is illustrated in the two cases
127

cited in this study. In Case 1, the second ring lifts and then flutters off the top side of the ring
groove. In Case 2, the second ring remains bottom seated. This can be explained by the
different forces acting on the ring for these two cases.
As discussed in the previous section, Case 1, with a negative static twisted second ring, forms
an outer edge sealing between the ring and groove bottom sides. This configuration allows
gases to flow into the crevice between the ring and groove bottom sides. As a result, the net
downward gas pressure force becomes very low and the ring is much easier to be lifted by the
inertial force acting on the ring (Figure 7-8). On the contrary, Case 2 configuration with a
positive second ring static twist seals the groove bottom at the inner bottom corner. The inner
edge sealing prevents higher pressure gas moving beneath the ring. Thus, a higher gas pressure
gradient across the ring results in a larger downward pressure force. The ring is then harder to
be lifted by inertial force. Figure 7-8 is a simplistic illustration showing the gas pressure forces
acting on the sides of the rings.
The top and second ring end gaps can also significantly affect second ring fluttering or collapse.
The smaller second ring end gap in Case 2 blocks gases from flowing past the second ring. As a
result, the pressure can build up quicker above the second ring. This higher pressure above the
ring will help hold the ring down so that inertia cannot lift the second ring.
A larger top ring end gap can allow more gases to flow past the top ring also building up
pressure in the second land region.

128

Figure 7-8 Ring bottom seating stability

Similarly, the ring top seating stability (Figure 7-9) can be interpreted similarly as for the bottom
seating condition. However, it should be noted that since a negative twisted ring is easier to
move down, it will be less likely to collapse. Conversely, the positive twisted ring will be more
difficult to push down; therefore the ring will be more likely to collapse radially inward. In other
words, the pressure to push the positive twist ring has to be higher to push the ring down off
the top side of the groove. However, that high pressure is also acting on the ring front face
trying to push the ring backwards off the cylinder wall. Therefore it is more likely that the
129

pressure force pushing inward on the ring face can collapse the ring before the ring is pushed
downward.

Figure 7-9 Ring top seating stability

Overall, the configuration with positive static twist and a small second ring gap tends to
increase the pressure force holding the second ring down and promoting second ring in-groove
stability. A cross-over point is likely to occur for this configuration as seen from Figure 7-5:
130

second land pressure is very close to in-cylinder pressure, yet it does not surpass the in-cylinder
pressure. This positive twist ring is also more likely to collapse. Conversely, the configuration
with negative static twist, and a large second ring gap will tend to allow the second ring to lift
and subsequently flutter. However, ring radial collapse is less likely to occur.
A sensitivity study was conducted to learn the influence of top ring and second ring end gap
sizes on second ring lift. As a result, the study was done using a positive static twist second ring.
It may be easier for conditions to result in fluttering with negative twist rings, however, the
basic fundamental reasons for the second ring to lift and flutter would be the same as a positive
twist ring. The ring end gap sizes for the sensitivity study are shown in Table 7-3. It should be
noted that the 0.15 mm top ring end gap in a diesel engine would probably not be possible
because of end gap butting. However this was modeled to evaluate the theories of fluttering.
Table 7-3 Ring end gap size for sensitivity study
Top ring

second ring

(mm)

(mm)

Small

0.15

0.5

Nominal

0.45

1.0

Large

0.75

2.0

Two phenomena were monitored for this sensitivity study: 1. second ring lift and 2. gas pressure
cross-over point between the in-cylinder gas pressure and the second land pressure (Figure
7-10).

131

These two phenomena are important for the power cylinder system. Ring lift influences ring and
gas dynamics, as discussed in the previous sections. The cross-over point indicates the start of a
condition where the pressure between the top and second rings (second land) exceeds the incylinder pressure and can result in reverse blowby of gases into the combustion chamber. If the
blowback gases contain oil, then it may contribute to oil consumption.
In-cyl and second land pressures

Pressure (KPa)

1600
1200

cross-over point

800
400
0
0

90

180

270

360

450

540

630

720

CAD
in-cyl

2nd land

Figure 7-10 In-cylinder pressure and second land pressure with cross-over point

The engine blowby data for these cases are normalized by the Case 2 blowby discussed in the
previous section and are shown in Table 7-4. In addition, the second ring lift and fluttering
cases, and the cases where cross-over point occurs are indicated under the normalized blowby
values in Table 7-4.
It was found that the second ring lift occurs when the top ring end gap is small and the second
ring end gap is relatively large. This is because for this ring pack configuration, the second land

132

gas pressure is low. Thus the ring inertia force can easily overcome the pressure force to lift the
ring.
The cross-over point between the in-cylinder pressure and second land gas pressure is found for
large top ring end gap and small second ring end gap cases. This cross-over point results from
the fact that the second land gas pressure is higher and decreases with a lower rate than the incylinder pressure does. Reverse gas flow occurs during the cross-over region.
If the ring lifts or flutters, there is no cross-over point because the second land pressures are so
low.
Table 7-4 Percentage engine blowby and the indication of second ring lift or cross-over point
Top ring end gap

Normalized engine
blowby

Small

Nominal

Large

47.2%

67.6%

80.4%

Stable

Cross-over

Cross-over

59.5%

100.0%

127.4%

Lift

Stable

Cross-over

66.0%

116.1%

171.5%

Lift

Stable

Stable

Small
second
ring end

Nominal

gap
Large

The inter-ring gas pressures and the ring in-groove locations for the ring lift case can be found in
Figure 7-11 based on the small top ring end gap, large second ring end gap case. This clearly
shows that the second ring stays against the groove top around TDC. The top ring still stays
bottom seated near the firing TDC. This is very similar indication as the second ring is fluttering:

133

the second land pressure is very low and erratic. However, in this case, the second ring is
collapsing instead of fluttering near the firing TDC. The pressure behind the second ring is very
small because the ring is seated on the top side of the groove. Therefore the pressure is equal
to the third land pressure. The radial force on the ring front face from lubrication oil
hydrodynamic pressure generated when the ring is sliding along the liner and the infiltrated gas
pressure if the ring is not fully flooded then become higher than the ring tension and back
pressure force. This radial inward net force pushes the ring away from the cylinder bore (Figure
7-3). This hydrodynamic contact pressure is calculated by solving a Reynold’s equation with gas
pressures as boundary conditions. A direct gas flow path across the second ring is formed when
the ring collapses. Figure 7-12 shows the instantaneous gas flow through the second ring end
gap and the ring face. The gas flow spikes near TDC indicate the occurrences of ring collapse, as
gas can also flow past the second ring through the ring face and cylinder bore clearance. This
corresponds to the second land gas pressure fluctuation in Figure 7-11.
In this case, the forces on the ring face were sufficient to collapse the ring before the ring could
be pushed axially downward.

134

0.75

1200

0.6

800

0.45

400

0.3

0

Ring Location

Pressure (KPa)

Inter-ring pressure and ring locations
1600

0.15
90

180

270

360

450

540

630

-400

0

-800

-0.15

CAD
In-cyl

2nd land

top ring

2nd ring

Figure 7-11 Inter-ring pressure and ring locations for second ring lift case

Instantaneous flow through ring 2 gap and ring face
0.006

Gas flow (Kg/s)

0.005
0.004
0.003
0.002
0.001
1.1E-17
-0.001

90

180

270

360

450

540

630

CAD
ring 2 gap

Figure 7-12 Instantaneous flow through second ring end gap and ring face

135

The in-cylinder gas pressure and second land pressure are shown in Figure 7-13 for the large top
ring end gap, small second ring gap case for which a cross-over point is found. It is obvious that
the second land gas pressure is higher than the in-cylinder gas pressure from about 420 DEG to
600 DEG. During this period, the in-cylinder gas pressure decreases faster than the second land
pressure, and the gas in the second land can flow back into the combustion chamber. The top
ring is lifted and seats against the top flank of the groove. Top ring fluttering does not occur
which causes the second land gas pressure to remain higher than the in-cylinder pressure. The
second ring stays bottom seated throughout the cycle. The reverse gas flow that occurs from
about 430 DEG to 600 DEG through the top ring end gap as the top ring seats against the groove
top side is shown in Figure 7-14. Along with this reverse gas flow, lubrication oil carried by the
gas flow travels back into combustion chamber. Thus lubrication oil consumption may increase
[14].

1.65

2400

1.35

1600

1.05

800

0.75

0

0.45
90

180

270

360

450

-800

540

Ring location

Pressure (KPa)

Inter-ring pressures and ring locations
3200

630
0.15

-1600

-0.15

CAD
In-cyl

2nd_land

top ring

2nd ring

Figure 7-13 Inter-ring pressures and ring locations for second ring non-lift case

136

Instantaneous flow through ring 1 gap
1.00E-02
8.00E-03

Gas flow (Kg/s)

6.00E-03
4.00E-03
2.00E-03
0.00E+00
90

180

270

360

450

540

630

-2.00E-03
-4.00E-03

CAD
ring 1 gap

Figure 7-14 Instantaneous flow through top ring end gap for second ring non-lift case

Ring dynamics was discussed using the software CASE with an emphasis on the second ring
fluttering and collapse for a modern diesel engine at full load high speed condition. From this
study, the following conclusions can be made:
Second ring fluttering and collapse occur because the pressure above the ring is not sufficient to
hold the ring down and the ring lifts because of the inertial force. Once the ring is seated on the
top side of the groove, the pressure at the region above the ring will build up and push the ring
down. Inertia will lift the ring back in an unstable or fluttering manner. Ring collapse can also
occur when the lubrication oil hydrodynamic force and gas pressure force on the ring face
surpass the ring tension and back pressure force as the ring stays top seated.
When the second ring flutters or collapses the blowby will generally be higher. This is because
the ring does not seal the gases and the gases flow past the ring. While this can cause high

137

blowby, the pressure in the second land will be very low. This will prevent reverse blowby and
the top ring from lifting.
Conversely, when the second ring is stable, the pressure in the second land will be greater. It is
possible that there is a condition with the cylinder pressure falling below the high second land
pressure, resulting in reverse blowby and/or top ring lifting. This could be bad for oil
consumption as the reverse flow may carry oil back into the combustion chamber.
Second ring flutter can be stopped by increasing the pressure forces acting on the second ring
during the early part of the compression stroke. This can be done by controlling engine factors
such as intake manifold pressure and engine speed. Also it is strongly affected by the top and
second ring end gaps as shown in this study.
The static twist of the second ring will also have an effect on ring flutter and collapse. A negative
static twist second ring will be more likely to flutter than a positive twist ring. However if the
second ring lifts, the positive twist ring will be more likely to collapse than the negative twist
ring.
The ring end gaps will have a significant effect on controlling the second ring fluttering. A large
top ring gap will increase the pressure above the second ring. A small second ring gap will do
the same. Higher pressure above the second ring will reduce the potential for ring flutter.
Second ring fluttering and ring collapse can have a significant effect on both engine blowby and
oil consumption. Therefore it is very important to understand these phenomena and how to
control them.

7.3

3D Ring Dynamic Simulation Analysis

138

In this section, the ring dynamics is analyzed with the consideration of 3D effect. Examples are
given for a second compression scraper ring. In addition to the constraint loads from the
cylinder liner and groove sides, the ring is also under dynamic load from ring inertia, pressure
load from the piston lands and groove, and friction load at the ring face. The friction load is
calculated as the product of the contact force from the previous CAD and the friction coefficient
as specified by the user (0.01 in this study). The pressure load and inertial load are provided
from the CASE simulation result for the ring. It is assumed that the pressure can only affect the
ring dynamics. However, the ring dynamics and deformation do not affect to the gas flow and
pressure distribution. At each CAD, the contact forces between the ring and cylinder liner,
piston groove sides can be found, together with the ring deformation and twist angle along the
ring circumference. The inter-ring gas pressures for the ring pack can be found in Figure 7-15.

Figure 7-15 Inter-ring gas pressure
139

The focus of this study is the dynamics of the second ring. Thus, the pressure boundary for the
second ring includes the gas pressures in the 2nd land, 2nd groove and 3rd land. The inter-ring gas
pressures are predicted using CASE program.
The ring acceleration plot is shown in Figure 7-16.

Figure 7-16 Ring acceleration

Figure 7-17 and Figure 7-18 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 90 CAD. The ring deformation in the axial direction
is amplified by 10 times.

140

Figure 7-17 Ring twist angle at 90 CAD

Figure 7-18 Deformed ring at 90 CAD

141

Table 7-5 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-5 Contact forces in axial direction at 90 CAD
90 CAD (N)
0°
45°
90°
135°
180°

Node 1
21.0
47.1
16.2
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
13.7
21.7
60.8
74.2
16.3

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-19 and Figure 7-20 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 180 CAD. The ring deformation in the axial
direction is amplified by 10 times.

Figure 7-19 Ring twist angle at 180 CAD

142

Figure 7-20 Deformed ring at 180 CAD

Table 7-6 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-6 Contact forces in axial direction at 180 CAD
180 CAD (N)
0°
45°
90°
135°
180°

Node 1
20.6
43.1
12.3
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
0.8
0.0
33.9
45.2
9.7

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-21and Figure7-22 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 270 CAD. The ring deformation in the axial
direction is amplified by 10 times.

143

Figure 7-21 Ring twist angle at 270 CAD

Figure7-22 Deformed ring at 270 CAD
144

Table 7-7 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-7 Contact forces in axial direction at 270 CAD
270 CAD (N)
0°
45°
90°
135°
180°

Node 1
15.4
31.0
17.0
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
0.0
0.0
17.0
32.8
6.7

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-23 and Figure 7-24 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 360 CAD. The ring deformation in the axial
direction is amplified by 10 times.

Figure 7-23 Ring twist angle at 360 CAD

145

Figure 7-24 Deformed ring at 360 CAD
Table 7-8 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-8 Contact forces in axial direction at 360 CAD
360 CAD (N)
0°
45°
90°
135°
180°

Node 1
24.1
52.8
27.6
1.5
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
49.6
90.0
139.0
157.6
35.2

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-25 and Figure7-26 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 450 CAD. The ring deformation in the axial
direction is amplified by 10 times.

146

Figure 7-25 Ring twist angle at 450 CAD

Figure7-26 Deformed ring at 450 CAD
Table 7-9 lists the contact forces at the four potential contact points as shown in Figure 3-13.
147

Table 7-9 Contact forces in axial direction at 450 CAD
450 CAD (N)
0°
45°
90°
135°
180°

Node 1
26.2
56.6
33.3
6.5
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
70.7
131.2
186.4
204.1
46.4

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-27 and Figure 7-28 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 540 CAD. The ring deformation in the axial
direction is amplified by 10 times.

Figure 7-27 Ring twist angle at 540 CAD

148

Figure 7-28 Deformed ring at 540 CAD

Table 7-10 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-10 Contact forces in axial direction at 540 CAD
540 CAD (N)
0°
45°
90°
135°
180°

Node 1
23.0
50.7
23.9
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
35.3
63.3
107.6
125.6
28.0

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-29 and Figure 7-30 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 630 CAD. The ring deformation in the axial
direction is amplified by 10 times.

149

Figure 7-29 Ring twist angle at 630 CAD

Figure 7-30 Deformed ring at 630 CAD
150

Table 7-11 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-11 Contact forces in axial direction at 630 CAD
630 CAD (N)
0°
45°
90°
135°
180°

Node 1
20.9
40.7
16.0
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
13.5
20.6
60.4
73.3
16.0

Node 4
0.0
0.0
0.0
0.0
0.0

Figure 7-31 and Figure 7-32 show the ring twist angle along the ring circumference for half ring
and the deformed ring shape respectively at 720 CAD. The ring deformation in the axial
direction is amplified by 10 times.

Figure 7-31 Ring twist angle at 720 CAD

151

Figure 7-32 Deformed ring at 720 CAD

Table 7-12 lists the contact forces at the four potential contact points as shown in Figure 3-13.
Table 7-12 Contact forces in axial direction at 720 CAD
720 CAD (N)
0°
45°
90°
135°
180°

Node 1
21.6
48.2
18.6
0.0
0.0

Node 2
0.0
0.0
0.0
0.0
0.0

Node 3
23.0
38.9
81.1
95.5
21.0

Node 4
0.0
0.0
0.0
0.0
0.0

From Table 7-5 to Table 7-12, the contact force results clearly show that the ring stays bottom
seated, since no contact forces are found at the ring top side at node 2 and node 4. However,
the ring bottom side contact pattern varies from crank angle to crank angle depending on the
pressure load and the inertial load.
In this study, the ring is constrained in 9 locations in both radial and axial directions. And due to
the symmetric boundary condition about the ring back, the two parts of the ring have the same
152

behavior regarding to the constraint forces, axial movement, twisting angle, etc. The radial and
axial constraint forces over the engine cycle shown in Figure 7-15 for one half of the ring (5
locations) are plotted from Figure 7-33 to Figure 7-42. In these plots, the upper and lower
nodes for the radial constraints refer to the nodes in Figure 3-8 and the nodes 1, 2, 3 and 4 for
the axial constraints refer to those in Figure 3-13.
Figure 7-33 and Figure 7-34 show the radial constraint force and axial constraint force at the
ring back (0 DEG) over a cycle respectively.

Figure 7-33 Radial Constraint Force at 0 DEG over a Cycle

153

Figure 7-34 Axial Constraint Force at 0 DEG over a Cycle

Figure 7-35 and Figure 7-36 show the radial constraint force and axial constraint force at 45
DEG away from ring back over a cycle respectively.

154

Figure 7-35 Radial Constraint Force at 45 DEG over a Cycle

155

Figure 7-36 Axial Constraint Force at 45 DEG over a Cycle

Figure 7-37 and Figure 7-38 show the radial constraint force and axial constraint force at 90 DEG
away from the ring back over a cycle respectively.

156

Figure 7-37 Radial Constraint Force at 90 DEG over a Cycle

157

Figure 7-38 Axial Constraint Force at 90 DEG over a Cycle

Figure 7-39 and Figure 7-40 show the radial constraint force and axial constraint force at 135
DEG away from the ring back over a cycle respectively.

158

Figure 7-39 Radial Constraint Force at 135 DEG over a Cycle

159

Figure 7-40 Axial Constraint Force at 135 DEG over a Cycle

Figure 7-41 and Figure 7-42 show the radial constraint force and axial constraint force at the
ring end tip (near 180 DEG away from the ring back) over a cycle respectively.

160

Figure 7-41 Radial Constraint Force at 180 DEG over a Cycle

161

Figure 7-42 Axial Constraint Force at 180 DEG over a Cycle

The ring twist angle at each circumferential location along the ring circumference over a cycle is
shown in Figure 7-43.

162

Figure 7-43 Ring Twist Angle over a Cycle

It is found from the ring twist angle plot that the ring twist varies from cross-section to crosssection and from crank angle to crank angle over the cycle. The ring undergoes the highest
positive twist for the part less than ± 90° away from the ring back from about 250 CAD to 320
CAD due to the lower pressure load on the ring during that time. And the highest negative twist
is found for the part about ± 120° away from the ring back from 360 CAD to 510 CAD.

163

Chapter 8 CONCLUSION AND RECOMMENDATION
8.1

Conclusion

In this dissertation, two major works have been accomplished: one is the further development
of the cylinder-kit analysis tool, CASE-RING program; the other is the development of a threedimensional piston ring model.
The ring lubrication model has been modified using the average Reynolds equation proposed by
Patir and Cheng [69] considering the influence of surface roughness on hydrodynamic
pressures. The contact between the ring face and the cylinder liner has been modified
considering the cam-shape pressure distribution for the compression rings along their
peripheries. This cam-shape profile in the ring face-cylinder liner interface can be obtained
from the 3D ring analysis. Other minor modifications were also completed due to the request
from the clients of CASE program.
A new 3D piston ring model has been developed. This model differs from the current 2D model
as it calculates the variation in one more dimension: along the ring circumference. These
variations include the ring axial movements, twist angles, contact pressure/force in the radial
from the cylinder liner and axial directions from the groove sides. The model is used to evaluate
the performance of the piston ring pack. Dynamic loadings, including the ring inertial load and
the distributed pressure load, are also considered for dynamic analysis of the ring.
A numerical simulation was performed for a two-stroke engine piston top compression ring,
predicting the piston ring contact and protrusion with the cylinder bridges and ports

164

respectively. It was found the ring free shape is important in determining the ring contact
pattern.
It was found that thermal load has significant influence on the ring performance. As the ring
free shape with the temperature influence could change significantly, especially for the top
compression ring, which is under the most severe thermal load condition. The thermal load
influence needs to be considered in piston ring design.
Experiment measurements were conducted to verify the numerical model with two
approaches. One approach was comparing the measured contact force with the predicted and
good agreement was found. The other approach was using the light-tightness method and the
separation gap near the ring end tips were verified by this experiment.
Ring twists and ring end gap sizes were found having a significant influence on the dynamics of
the second compression ring, including the ring fluttering and the radial collapse. The key for
eliminating the second ring fluttering and collapse is to hold the ring to stay bottom seated at
around 90° before firing TDC when the ring inertial load changes its direction. As long as the
second ring stays bottom seated at this specific location, the ring will not undergo the unstable
motions.
The twist of the ring was also investigated using the 3D model and it was found for a scraper
second ring, the ring twist varies from the ring back to the ring end tip. The variation in the ring
twist can result in different pressure distribution boundary condition for the ring along the
circumference as port of the ring may be exposed to the groove gas while some part may be
exposed to the land gas.

165

8.2

Limitations and Recommendations

The limitations of this numerical model are identified in order to improve it in the future
followed by the recommendations.
The 3D ring model is formulated from the minimum potential energy point of view and has
been proven capable to predict the interactions between the ring and cylinder bore and the
ring and piston groove sides. However, the boundary condition has been set such that the ring
would not rotate in the circumferential direction. It works fine for the static condition and
dynamic condition considering only the piston primary motion, which is along the cylinder axial
direction. The piston second motions and the bore distortions, which are recognized as the
cause of the ring rotation, have not been considered. In the future, these two influences need
to be considered.
Another limitation of this model is that the gas pressures at each crank angle for the dynamic
analysis are obtained from the 1D model and the gas pressure is identical around the ring
circumference. In order to improve the accuracy of the model, the ring dynamics needs to be
coupled with a 3D gas dynamic model in an iterative manner. This means not only the ring
motion will be affected by the pressure distribution; the local gas pressures will also be
influenced by the ring motion.
With the 3D interaction between the ring and cylinder bore, as well as between the ring and
the groove sides, the friction and wear model can be improved accounting for the local
tribological behavior. This needs to be accomplished in a progressive manner as the ring,
groove, and cylinder liner need to be resurfaced after each wear stop. As it has been found
from experiment, the piston rings wear show variation in the circumference direction. It will
166

also be interesting to consider the 3D ring behavior in the lubrication oil film calculation since
the oil film is significantly influenced by the ring twist. It will also be worth to take into
consideration the different oil transportation mechanisms, including the oil throw-off, influence
of engine blowback in addition to oil evaporation which is the only cause of oil consumption for
the current model.

167

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