Piston

Lubrication regime transitions at the pistonring–cylinder liner interfaceN W Bolander1�, B D Steenwyk1, F Sadeghi1, and G R Gerber2

1School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA2Caterpillar Inc., Lafayatte, IN, USA

The manuscript was received on 11 March 2004 and was accepted after revision for publication on 24 September 2004.

DOI: 10.1243/135065005X9664

Abstract: An experimental apparatus and an analytical model have been developed to inves-tigate and determine the lubrication condition and frictional losses at the interface between apiston ring and cylinder liner. In order to obtain a solution for the lubrication condition betweenthe piston ring and cylinder liner, the system of Reynolds and film thickness equations subject toboundary conditions were simultaneously solved. The effects of boundary and mixed lubrica-tion conditions were implemented using the Greenwood–Tripp stochastic approach. TheElrod cavitation algorithm was used to investigate the effects of fluid rupture and reformationat the top and bottom dead centres. The experimental results indicate that the piston ringand liner experience all the different lubrication regimes (i.e. boundary, mixed, and hydro-dynamic lubrication) during a stroke. A comparison between experimental and analyticalresults indicated that they are in good agreement and the analytical model developed for thisstudy can capture the different lubrication regimes that the piston ring and liner experience.

Keywords: piston ring, mixed lubrication, friction, lubrication

1 INTRODUCTION

Modern reciprocating engines are expected to con-form to strict efficiency standards. A key factor inachieving these standards is the minimization ofparasitic losses due to friction. The piston ringassembly is one of the main sources of friction inan internal combustion engine, which by someestimates can account for 20–40 per cent of enginefrictional losses [1]. A thorough understanding ofthe lubrication condition at the piston ring–cylinderliner interface is vital in determining the sources offrictional loss. It is well known that the piston ringencounters the entire range of lubrication regimesthrough each stroke (i.e. boundary lubrication,mixed lubrication, elastohydrodynamic lubrication(EHL), and hydrodynamic lubrication). Thus, aninvestigation into frictional losses at the pistonring–cylinder liner contact must take into account

the transitions from a state of full-film lubricationto boundary lubrication.

An early example of modelling and analysis of thefrictional losses at the piston ring–cylinder linercontact is attributed to Rohde et al. [2]. This mixed-friction model was based on the averaged flowReynolds equation with the half-Sommerfeld boun-dary condition obtained by Patir and Cheng [3].Asperity interactions were included through theGreenwood–Tripp [4] model. Dowson et al. [5]used a hydrodynamic lubrication model to studyfilm thickness, lubricant transport, and viscous fric-tion at the piston ring–cylinder liner (PRCL) contact.They used the Reynolds boundary condition in theiranalysis. Later investigations showed strong EHLeffects near top dead centre (TDC). Jeng [1] discussedthe fact that the Sommerfeld-type boundary con-ditions used in many of the previous investigationsare deficient because of the violation of continuityat the cavitation boundary. He developed a one-dimensional model using the Reynolds boundarycondition combined with a system of two non-linear differential equations. This method improvedon the work of Dowson et al. [5] by relaxing the

�Corresponding author: School of Mechanical Engineering,

Purdue University, West Lafayette, IN 47907-1288, USA.

19

J01504 # IMechE 2005 Proc. IMechE Vol. 219 Part J: J. Engineering Tribology

Lubrication regime transitions at the pistonring–cylinder liner interfaceN W Bolander1�, B D Steenwyk1, F Sadeghi1, and G R Gerber2

1School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA2Caterpillar Inc., Lafayatte, IN, USA

The manuscript was received on 11 March 2004 and was accepted after revision for publication on 24 September 2004.

DOI: 10.1243/135065005X9664

Abstract: An experimental apparatus and an analytical model have been developed to inves-tigate and determine the lubrication condition and frictional losses at the interface between apiston ring and cylinder liner. In order to obtain a solution for the lubrication condition betweenthe piston ring and cylinder liner, the system of Reynolds and film thickness equations subject toboundary conditions were simultaneously solved. The effects of boundary and mixed lubrica-tion conditions were implemented using the Greenwood–Tripp stochastic approach. TheElrod cavitation algorithm was used to investigate the effects of fluid rupture and reformationat the top and bottom dead centres. The experimental results indicate that the piston ringand liner experience all the different lubrication regimes (i.e. boundary, mixed, and hydro-dynamic lubrication) during a stroke. A comparison between experimental and analyticalresults indicated that they are in good agreement and the analytical model developed for thisstudy can capture the different lubrication regimes that the piston ring and liner experience.

Keywords: piston ring, mixed lubrication, friction, lubrication

1 INTRODUCTION

Modern reciprocating engines are expected to con-form to strict efficiency standards. A key factor inachieving these standards is the minimization ofparasitic losses due to friction. The piston ringassembly is one of the main sources of friction inan internal combustion engine, which by someestimates can account for 20–40 per cent of enginefrictional losses [1]. A thorough understanding ofthe lubrication condition at the piston ring–cylinderliner interface is vital in determining the sources offrictional loss. It is well known that the piston ringencounters the entire range of lubrication regimesthrough each stroke (i.e. boundary lubrication,mixed lubrication, elastohydrodynamic lubrication(EHL), and hydrodynamic lubrication). Thus, aninvestigation into frictional losses at the pistonring–cylinder liner contact must take into account

the transitions from a state of full-film lubricationto boundary lubrication.

An early example of modelling and analysis of thefrictional losses at the piston ring–cylinder linercontact is attributed to Rohde et al. [2]. This mixed-friction model was based on the averaged flowReynolds equation with the half-Sommerfeld boun-dary condition obtained by Patir and Cheng [3].Asperity interactions were included through theGreenwood–Tripp [4] model. Dowson et al. [5]used a hydrodynamic lubrication model to studyfilm thickness, lubricant transport, and viscous fric-tion at the piston ring–cylinder liner (PRCL) contact.They used the Reynolds boundary condition in theiranalysis. Later investigations showed strong EHLeffects near top dead centre (TDC). Jeng [1] discussedthe fact that the Sommerfeld-type boundary con-ditions used in many of the previous investigationsare deficient because of the violation of continuityat the cavitation boundary. He developed a one-dimensional model using the Reynolds boundarycondition combined with a system of two non-linear differential equations. This method improvedon the work of Dowson et al. [5] by relaxing the

�Corresponding author: School of Mechanical Engineering,

Purdue University, West Lafayette, IN 47907-1288, USA.

19


assumption of a constant flowrate across the ring.The model was used to study film thickness, friction,and starvation conditions for piston ring lubricationthrough the complete engine cycle. Hu et al. [6] app-lied a non-axisymmetrical quasi-two-dimensionalanalysis to the PRCL contact. This model used theaverage flow Reynolds equation and the Reynoldsboundary conditions and employed the Greenwood–Tripp [4] model for asperity contact to solve themixed lubrication problem. Flow in the circum-ferential direction was not permitted in order tosimplify the solution; however, a linear complimen-tary problem was performed in this direction todetermine the deflection of the ring. Yang andKeith [7] indicated that the pressure reformationcannot be accurately predicted by the Reynoldsboundary condition, especially when high pressureexists at the trailing edge of the ring. Proper deter-mination of the reformation boundary is criticalto accurately determining the load capacity of thepiston ring. For this purpose a previously developedcavitation algorithm [8] was modified to include theEHL effects that Dowson et al. [9] had found soimportant in the region near TDC. Later, theirmodel was extended to include flow in the circumfer-ential direction [10, 11]. These models assumedsmooth surfaces and were therefore unable to deter-mine realistically the frictional losses in regionswhere mixed lubrication is dominant. Sawicki andYu [12] applied the Jakobsson–Floberg–Olsson cavi-tation theory to piston ring lubrication in a one-dimensional model similar to that of Jeng [1]. Theynote that Jeng’s model is able to provide a good esti-mation of the film thickness using the Reynoldsboundary condition but will probably underestimatefriction and power loss and overestimate flowrates.Akalin and Newaz [13] developed a one-dimensionalanalytical model based on the average flow Reynoldsequation obtained by Patir and Cheng. Mixedlubrication is enabled through the use of theGreenwood–Tripp asperity contact model in amanner similar to that of Hu et al. [6]. Reynolds(Swift–Stieber) boundary conditions were used andresults from this model were corroborated to experi-mental results [14]. However, Priest et al. [15]suggested that the lack of detailed experimentaldata in the area of piston ring lubrication requiresthat future progress be based upon combinedtheoretical and experimental investigations.

Ting [16, 17] developed a reciprocating test rig tomeasure the friction coefficient between rings andliners taken from actual engines. Friction resultswere obtained using a piezoelectric-type load cell.The results were presented in a Stribeck-type relation-ship. Dearlove and Cheng [18] developed a reciprocat-ing test rig based on an actual single-cylinder engine. Afloating liner segment was instrumented to provide

frictional data. The lubricant film thickness at mid-stroke was measured using the laser fluorescencetechnique. Arcoumanis et al. [19] measured film thick-ness throughout the stroke using a purpose-madecapacitance transducer. Their reciprocating test righad a maximum stroke length of 50 mm. Frictionaldata were obtained using a deflection-based measure-ment. Akalin and Newaz [14] employed a deflection-based force approach to measure friction usingactual engine rings and a cylinder liner.

In this study a model was developed to solve forthe lubrication condition and frictional losses at thepiston ring–cylinder liner interface through a com-plete engine cycle. The two-dimensional cavitation-enabled Reynolds equation is coupled with thestochastic asperity contact model of Greenwoodand Tripp [4] to allow calculation of lubricant filmthickness and friction for a piston ring operating inthe mixed lubrication regime. A test rig has alsobeen developed to correlate with the numericalmodel and to explore further the lubrication condi-tion at the piston ring–cylinder liner interface. Actualpiston rings and cylinder liner segments were usedin the experimental test rig. A piezoelectric-typeforce transducer was employed for fast frequencyresponse to capture the frictional phenomena atthe TDC and bottom dead centre (BDC).

2 TEST RIG DESCRIPTION ANDEXPERIMENTAL PROCEDURE

2.1 Piston ring reciprocating liner test rig

A computer-aided design (CAD) drawing of thepiston ring reciprocating liner test rig designed,developed, and constructed for this study is illus-trated in Fig. 1. Figure 2 depicts a close-up view of

Fig. 1 CAD drawing of the piston ring reciprocating

liner test rig

20 N W Bolander, B D Steenwyk, F Sadeghi, and G R Gerber

Proc. IMechE Vol. 219 Part J: J. Engineering Tribology J01504 # IMechE 2005

assumption of a constant flowrate across the ring.The model was used to study film thickness, friction,and starvation conditions for piston ring lubricationthrough the complete engine cycle. Hu et al. [6] app-lied a non-axisymmetrical quasi-two-dimensionalanalysis to the PRCL contact. This model used theaverage flow Reynolds equation and the Reynoldsboundary conditions and employed the Greenwood–Tripp [4] model for asperity contact to solve themixed lubrication problem. Flow in the circum-ferential direction was not permitted in order tosimplify the solution; however, a linear complimen-tary problem was performed in this direction todetermine the deflection of the ring. Yang andKeith [7] indicated that the pressure reformationcannot be accurately predicted by the Reynoldsboundary condition, especially when high pressureexists at the trailing edge of the ring. Proper deter-mination of the reformation boundary is criticalto accurately determining the load capacity of thepiston ring. For this purpose a previously developedcavitation algorithm [8] was modified to include theEHL effects that Dowson et al. [9] had found soimportant in the region near TDC. Later, theirmodel was extended to include flow in the circumfer-ential direction [10, 11]. These models assumedsmooth surfaces and were therefore unable to deter-mine realistically the frictional losses in regionswhere mixed lubrication is dominant. Sawicki andYu [12] applied the Jakobsson–Floberg–Olsson cavi-tation theory to piston ring lubrication in a one-dimensional model similar to that of Jeng [1]. Theynote that Jeng’s model is able to provide a good esti-mation of the film thickness using the Reynoldsboundary condition but will probably underestimatefriction and power loss and overestimate flowrates.Akalin and Newaz [13] developed a one-dimensionalanalytical model based on the average flow Reynoldsequation obtained by Patir and Cheng. Mixedlubrication is enabled through the use of theGreenwood–Tripp asperity contact model in amanner similar to that of Hu et al. [6]. Reynolds(Swift–Stieber) boundary conditions were used andresults from this model were corroborated to experi-mental results [14]. However, Priest et al. [15]suggested that the lack of detailed experimentaldata in the area of piston ring lubrication requiresthat future progress be based upon combinedtheoretical and experimental investigations.

Ting [16, 17] developed a reciprocating test rig tomeasure the friction coefficient between rings andliners taken from actual engines. Friction resultswere obtained using a piezoelectric-type load cell.The results were presented in a Stribeck-type relation-ship. Dearlove and Cheng [18] developed a reciprocat-ing test rig based on an actual single-cylinder engine. Afloating liner segment was instrumented to provide

frictional data. The lubricant film thickness at mid-stroke was measured using the laser fluorescencetechnique. Arcoumanis et al. [19] measured film thick-ness throughout the stroke using a purpose-madecapacitance transducer. Their reciprocating test righad a maximum stroke length of 50 mm. Frictionaldata were obtained using a deflection-based measure-ment. Akalin and Newaz [14] employed a deflection-based force approach to measure friction usingactual engine rings and a cylinder liner.

In this study a model was developed to solve forthe lubrication condition and frictional losses at thepiston ring–cylinder liner interface through a com-plete engine cycle. The two-dimensional cavitation-enabled Reynolds equation is coupled with thestochastic asperity contact model of Greenwoodand Tripp [4] to allow calculation of lubricant filmthickness and friction for a piston ring operating inthe mixed lubrication regime. A test rig has alsobeen developed to correlate with the numericalmodel and to explore further the lubrication condi-tion at the piston ring–cylinder liner interface. Actualpiston rings and cylinder liner segments were usedin the experimental test rig. A piezoelectric-typeforce transducer was employed for fast frequencyresponse to capture the frictional phenomena atthe TDC and bottom dead centre (BDC).

2 TEST RIG DESCRIPTION ANDEXPERIMENTAL PROCEDURE

2.1 Piston ring reciprocating liner test rig

A computer-aided design (CAD) drawing of thepiston ring reciprocating liner test rig designed,developed, and constructed for this study is illus-trated in Fig. 1. Figure 2 depicts a close-up view of

Fig. 1 CAD drawing of the piston ring reciprocating

liner test rig



the completed reciprocating carriage assembly. Thetest rig was designed to have the cylinder liner reci-procate while keeping the piston ring stationaryand can accommodate a wide range of loads,speeds, and lubricant conditions at the PRCL inter-face. The apparatus can accommodate cylinderbore diameters of 51–140 mm (2.0–5.5 in) with astroke in the range 38–152 mm (1.5–6 in). A 2.2 kW(3 hp) variable-speed d.c. motor is used to turn thecrank between 15 and 300 r/min, which is measuredby a magnetic pick-up. The output shaft of the1750 r/min motor is connected to a 14:3 toothedbelt speed reduction drive system. The crank is con-nected to a Thompson linear carriage, which housesa 608 section of the 137.2 mm (5.402 in) bore cylinderliner. The piston ring is held stationary under thepivot arm above the reciprocating liner segment ina specially designed ring holder (Fig. 3). Load isapplied to the PRCL interface through dead weightsat the end of the arm. A piezoelectric Kistler three-axis force transducer and charge amplifier are usedto measure the normal, tangential, and side loads

generated on the piston ring. The piezoelectricforce transducer was chosen to maximize rigidityand natural frequency, thus allowing high samplingrates and minimum ring motion. The frequencyresponse of this piezoelectric force sensor allowsthe frictional behaviour to be resolved near theends of stroke where the frictional force switchesdirection nearly instantaneously. A Dell workstationwith a National Instruments data acquisition boardand software is used to collect the sensor data andto control the charge amplifier. Data collectedinclude the friction, normal, and tangential loads,as well as the rotational speed of the motor.

2.2 Experimental procedure

For each test the following procedure is followed.First, two rows of 15 drops of SAE 30 oil (1.0 ml) areevenly distributed along the entire stroke of66.7 mm (2 5

8 in) on the axis of the liner segment.The ring is raised above the liner to a repeatableand stable position by lifting the loaded arm upagainst a hard stop. At this point the data acquisitionbegins and the charge amplifier is switched to oper-ate mode which defines the zero frictional force.Immediately, the ring is lowered on to the linernear mid-stroke (crank position of 2708), followedby starting the motor. Friction and speed arerecorded for 16 cycles. The sampling frequency ofthe friction measurement is set such that 1000 datapoints are collected per crank revolution.

In order to study the effects of load and speed onfriction and the lubrication at the PRCL interface,the load and crank rotational speed were variedfrom 1 to 8 kgf and from 30 to 300 r/min respectively.Table 1 contains the load and speed conditionstested. In all cases, the same amount, type, andarrangement of oil is used. The stroke was heldconstant at 66.7 mm (2 5

8 in). Speeds were chosen toillustrate the various lubrication regimes.

Table 2 contains the resulting pressure betweenthe piston ring and liner. This nominal contact pres-sure can be thought of as the sum of the ring elasticpressure and cylinder gas pressure acting on the backside of the ring. A typical installation pressure forthe original equipment manufacturer (OEM) ringused in this investigation is 0.24 MPa, a typicalpeak engine compression pressure is 1.0 Mpa, anda typical peak combustion pressure is 2.0–4.0 MPafor gasoline engines.

The ring and liner surfaces were characterized usingan optical surface profilometer. Table 3 contains the

Table 1 Load and speed conditions

Load (kgf) 1, 2, 3, 4, 6, 8Speed (r/min) 30, 60, 90, 120, 180, 240, 300

Fig. 2 Completed bench-scale piston ring reciprocating

liner test rig

Fig. 3 Ring holder and force sensor assembly

Lubrication regime transitions at the piston ring–cylinder liner interface 21


the completed reciprocating carriage assembly. Thetest rig was designed to have the cylinder liner reci-procate while keeping the piston ring stationaryand can accommodate a wide range of loads,speeds, and lubricant conditions at the PRCL inter-face. The apparatus can accommodate cylinderbore diameters of 51–140 mm (2.0–5.5 in) with astroke in the range 38–152 mm (1.5–6 in). A 2.2 kW(3 hp) variable-speed d.c. motor is used to turn thecrank between 15 and 300 r/min, which is measuredby a magnetic pick-up. The output shaft of the1750 r/min motor is connected to a 14:3 toothedbelt speed reduction drive system. The crank is con-nected to a Thompson linear carriage, which housesa 608 section of the 137.2 mm (5.402 in) bore cylinderliner. The piston ring is held stationary under thepivot arm above the reciprocating liner segment ina specially designed ring holder (Fig. 3). Load isapplied to the PRCL interface through dead weightsat the end of the arm. A piezoelectric Kistler three-axis force transducer and charge amplifier are usedto measure the normal, tangential, and side loads

generated on the piston ring. The piezoelectricforce transducer was chosen to maximize rigidityand natural frequency, thus allowing high samplingrates and minimum ring motion. The frequencyresponse of this piezoelectric force sensor allowsthe frictional behaviour to be resolved near theends of stroke where the frictional force switchesdirection nearly instantaneously. A Dell workstationwith a National Instruments data acquisition boardand software is used to collect the sensor data andto control the charge amplifier. Data collectedinclude the friction, normal, and tangential loads,as well as the rotational speed of the motor.

2.2 Experimental procedure

For each test the following procedure is followed.First, two rows of 15 drops of SAE 30 oil (1.0 ml) areevenly distributed along the entire stroke of66.7 mm (2 5

8 in) on the axis of the liner segment.The ring is raised above the liner to a repeatableand stable position by lifting the loaded arm upagainst a hard stop. At this point the data acquisitionbegins and the charge amplifier is switched to oper-ate mode which defines the zero frictional force.Immediately, the ring is lowered on to the linernear mid-stroke (crank position of 2708), followedby starting the motor. Friction and speed arerecorded for 16 cycles. The sampling frequency ofthe friction measurement is set such that 1000 datapoints are collected per crank revolution.

In order to study the effects of load and speed onfriction and the lubrication at the PRCL interface,the load and crank rotational speed were variedfrom 1 to 8 kgf and from 30 to 300 r/min respectively.Table 1 contains the load and speed conditionstested. In all cases, the same amount, type, andarrangement of oil is used. The stroke was heldconstant at 66.7 mm (2 5

8 in). Speeds were chosen toillustrate the various lubrication regimes.

Table 2 contains the resulting pressure betweenthe piston ring and liner. This nominal contact pres-sure can be thought of as the sum of the ring elasticpressure and cylinder gas pressure acting on the backside of the ring. A typical installation pressure forthe original equipment manufacturer (OEM) ringused in this investigation is 0.24 MPa, a typicalpeak engine compression pressure is 1.0 Mpa, anda typical peak combustion pressure is 2.0–4.0 MPafor gasoline engines.

The ring and liner surfaces were characterized usingan optical surface profilometer. Table 3 contains the

Table 1 Load and speed conditions

Load (kgf) 1, 2, 3, 4, 6, 8Speed (r/min) 30, 60, 90, 120, 180, 240, 300

Fig. 2 Completed bench-scale piston ring reciprocating

liner test rig

Fig. 3 Ring holder and force sensor assembly



arithmetic mean roughness Ra, r.m.s roughness Rq,and skewness Rsk for the ring and liner.

3 NUMERICAL MODEL DESCRIPTION

In this study, a model was developed to investigatethe lubrication condition between a piston ringand cylinder liner. It is assumed that the contactoperates under fully flooded conditions throughoutthe stroke and the mode of cavitation is closedform [12]. The following assumptions were madein the derivation of the fluid momentum (Reynolds)equation.

1. The lubricant is Newtonian.2. The pressure is constant across the film.3. The flow is laminar and viscous dominant.4. The body forces and inertial effects are

neglected.5. The lubricant viscosity is constant.6. The lubricant cavitates when the film pressure

falls below the lubricant vapour pressure.

3.1 Reynolds equation

The non-dimensional isothermal two-dimensionaltime-dependent Reynolds equation including thecavitation algorithm is given by [20]

@

@XH3 @(Ff)

@X

� �þ@

@YH3 @(Ff)

@Y

� �

¼ g@

@X{½1þ (1� F)f�H}

þ s@

@T{½(1þ (1� F)f�H} (1)

The function f and cavitation index F are defined by

p� pc

pa � pc

¼ Ff in the full-film region (2)

r

rc

¼ 1þ (1� F)f in the cavitation zone (3)

F(x, y) ¼1 forf 5 0

0 forf , 0

�(4)

The dimensionless boundary conditions are given by

Ff ¼

pL�pc

pa�pcat the leading edge of the ring

pT�pc

pa�pcat the trailing edge of the ring

((5)

@(Ff)

@Y

��Y¼�1/2

¼@(Ff)

@Y

��Y¼1/2

¼ 0 (6)

The first boundary condition sets the pressure at theleading and trailing edges of the ring equal to the localambient conditions in the cylinder or ring gap. Thesecond boundary condition enforces the axisymmetryof the piston ring section. Although the model pre-sented here assumes that the piston ring is operatingunder axisymmetry conditions, the underlying dis-cretization of the governing equations remains twodimensional. Thus, extension and inclusion of non-axisymmetric effects and/or circumferential flow caneasily be accommodated.

3.2 Film thickness equation

Figure 4 illustrates the geometry of the piston ringand the cylinder wall lubricated contact as modelledin this study. The lubricant film thickness for apiston ring with a symmetric parabolic face can beexpressed in terms of the minimum film thicknesshmin(t) as

h(x, y) ¼ hmin(t)þd

(b/2)2x2 (7)

Table 2 Load and nominal pressure

conditions over the ring

Normal force (kgf) Nominal pressure (MPa)

1 0.142 0.293 0.434 0.586 0.878 1.15

Table 3 Surface roughnesses of the piston ring and

cylinder liner

Ra(mm) Rq(mm) Rsk

Piston ring 0.55 0.90 23.04Cylinder liner 0.86 1.10 20.55

Fig. 4 The physical geometry of the axisymmetric ring

and cylinder liner section used in the numerical

model



arithmetic mean roughness Ra, r.m.s roughness Rq,and skewness Rsk for the ring and liner.

3 NUMERICAL MODEL DESCRIPTION

In this study, a model was developed to investigatethe lubrication condition between a piston ringand cylinder liner. It is assumed that the contactoperates under fully flooded conditions throughoutthe stroke and the mode of cavitation is closedform [12]. The following assumptions were madein the derivation of the fluid momentum (Reynolds)equation.

1. The lubricant is Newtonian.2. The pressure is constant across the film.3. The flow is laminar and viscous dominant.4. The body forces and inertial effects are

neglected.5. The lubricant viscosity is constant.6. The lubricant cavitates when the film pressure

falls below the lubricant vapour pressure.

3.1 Reynolds equation

The non-dimensional isothermal two-dimensionaltime-dependent Reynolds equation including thecavitation algorithm is given by [20]

@

@XH3 @(Ff)

@X

� �þ@

@YH3 @(Ff)

@Y

� �

¼ g@

@X{½1þ (1� F)f�H}

þ s@

@T{½(1þ (1� F)f�H} (1)

The function f and cavitation index F are defined by

p� pc

pa � pc

¼ Ff in the full-film region (2)

r

rc

¼ 1þ (1� F)f in the cavitation zone (3)

F(x, y) ¼1 forf 5 0

0 forf , 0

�(4)

The dimensionless boundary conditions are given by

Ff ¼

pL�pc

pa�pcat the leading edge of the ring

pT�pc

pa�pcat the trailing edge of the ring

((5)

@(Ff)

@Y

��Y¼�1/2

¼@(Ff)

@Y

��Y¼1/2

¼ 0 (6)

The first boundary condition sets the pressure at theleading and trailing edges of the ring equal to the localambient conditions in the cylinder or ring gap. Thesecond boundary condition enforces the axisymmetryof the piston ring section. Although the model pre-sented here assumes that the piston ring is operatingunder axisymmetry conditions, the underlying dis-cretization of the governing equations remains twodimensional. Thus, extension and inclusion of non-axisymmetric effects and/or circumferential flow caneasily be accommodated.

3.2 Film thickness equation

Figure 4 illustrates the geometry of the piston ringand the cylinder wall lubricated contact as modelledin this study. The lubricant film thickness for apiston ring with a symmetric parabolic face can beexpressed in terms of the minimum film thicknesshmin(t) as

h(x, y) ¼ hmin(t)þd

(b/2)2x2 (7)

Table 2 Load and nominal pressure

conditions over the ring

Normal force (kgf) Nominal pressure (MPa)

1 0.142 0.293 0.434 0.586 0.878 1.15

Table 3 Surface roughnesses of the piston ring and

cylinder liner

Ra(mm) Rq(mm) Rsk

Piston ring 0.55 0.90 23.04Cylinder liner 0.86 1.10 20.55

Fig. 4 The physical geometry of the axisymmetric ring

and cylinder liner section used in the numerical

model



where d is the crown height and b is the width ofthe ring. For the OEM piston rings used in thisstudy, d ¼ 13 mm and b ¼ 3.79 mm.

3.3 Force balance equation

At any instant the forces acting on the ring can bebroken down into four components:

(a) hydrodynamic pressure ph acting on the ring face;(b) asperity contact pressure ps acting on the ring

face;(c) ring elastic pressure pel for the segment;(d) gas pressure pg acting on the back of the ring.

The velocity of the piston ring varies constantlythroughout the stroke, reaching zero momentarilyat TDC and BDC. The time-dependent form of theReynolds equation used in this study includes thesqueeze-film effect to handle the conditions atthe TDC and BDC, as well as accurately capturingthe cavitation rupture and reformation boundaries.As described in reference [12] the pressure contri-bution from the reformed lubricant film and thetrailing-edge pressure may contribute substantiallyto the overall load support.

The asperity contact pressure for the ring segmentcan be calculated using the Greenwood–Tripp [4]asperity contact model. The form of the contactmodel used in this study is based on a simplifyingcurve fit employed by Hu et al. [6] and Akalin andNewaz [13]. The same parameters used by these inves-tigators have been maintained in the current work.

The ring elastic pressure can be calculated as

pel ¼2Tr

bB(8)

where Tr is the ring tension and B is the cylinder borediameter [1]. The pressure acting on the back ofthe ring is assumed to be the larger of pL and pT.The force balance equation can then be expressedas a summation of the forces acting on the ringsegment according to

ða/2

�a/2

ðb/2

�b/2

(pel þ pg) dx dy

�

ða/2

�a/2

ðb/2

�b/2

(ph þ ps) dx dy ¼ 0 (9)

3.4 Frictional force equations

The frictional force acting between the piston ringsegment and the cylinder wall consists of a viscousshear force in the lubricant film and friction bet-ween the asperities in contact. An experimentallymeasured value of 0.14 is used for the dynamic

asperity coefficient of friction ma. The resultingexpression for total frictional force on the segment is

Ff ¼

ða=2

�a=2

ðb=2

�b=2

�h

2

@p

@x�hU

h

� �þ mapa

� �dx dy

(10)

3.5 Solution method

Integration of the modified non-dimensional Reynoldsequation (1) over a control volume [21] yields

ðe

w

ðn

s

@

@XH3 @(Ff)

@X

� �þ@

@YH3 @(Ff)

@Y

� �� dY dX

¼

ðe

w

ðn

s

g@

@X{½1þ (1� F)f�H}

� �dY dX

þ

ðe

w

ðn

s

s@

@T{½1þ (1� F)f�H}

� �dY dX

(11)

The discretized form of equation (11) takes on theform

H3 @(Ff)

@X

� �e

DY � H3 @(Ff)

@X

� ��

w

DY þ H3 @(Ff)

@Y

� �n

�� DX � H3 @(Ff)

@Y

� ��s

DX

¼ g{½1þ (1� F)f�H} eDYj

� g{½1þ (1� F)f�H}��

wDY

þ

sDXDY ({½1þ (1� F)f�H}n

� {½1þ (1� F)f�H}n�1)

DT(12)

The discretization shown in equation (12) results ina system of linear equations that are solved using theGauss–Siedel relaxation scheme. In order to ensure astable convergence, both F and f are relaxed afterevery Gauss–Seidel sweep according to

frelaxed ¼ affnew þ (1� af)fold

Frelaxed ¼ aF Fnew þ (1� aF )Fold

(13)

where

Fnew ¼1 if frelaxed 5 0

0 if frelaxed , 0

�

According to Payvar and Salant [20] the key tostability is in the proper selection of the relaxationcoefficients. Following their recommendation, relax-ation coefficients of af ¼ 0.2 and aF ¼ 0.01 werechosen. A mesh size of 100 � 50 was found to providea grid-independent pressure solution. Iteration



where d is the crown height and b is the width ofthe ring. For the OEM piston rings used in thisstudy, d ¼ 13 mm and b ¼ 3.79 mm.

3.3 Force balance equation

At any instant the forces acting on the ring can bebroken down into four components:

(a) hydrodynamic pressure ph acting on the ring face;(b) asperity contact pressure ps acting on the ring

face;(c) ring elastic pressure pel for the segment;(d) gas pressure pg acting on the back of the ring.

The velocity of the piston ring varies constantlythroughout the stroke, reaching zero momentarilyat TDC and BDC. The time-dependent form of theReynolds equation used in this study includes thesqueeze-film effect to handle the conditions atthe TDC and BDC, as well as accurately capturingthe cavitation rupture and reformation boundaries.As described in reference [12] the pressure contri-bution from the reformed lubricant film and thetrailing-edge pressure may contribute substantiallyto the overall load support.

The asperity contact pressure for the ring segmentcan be calculated using the Greenwood–Tripp [4]asperity contact model. The form of the contactmodel used in this study is based on a simplifyingcurve fit employed by Hu et al. [6] and Akalin andNewaz [13]. The same parameters used by these inves-tigators have been maintained in the current work.

The ring elastic pressure can be calculated as

pel ¼2Tr

bB(8)

where Tr is the ring tension and B is the cylinder borediameter [1]. The pressure acting on the back ofthe ring is assumed to be the larger of pL and pT.The force balance equation can then be expressedas a summation of the forces acting on the ringsegment according to

ða/2

�a/2

ðb/2

�b/2

(pel þ pg) dx dy

�

ða/2

�a/2

ðb/2

�b/2

(ph þ ps) dx dy ¼ 0 (9)

3.4 Frictional force equations

The frictional force acting between the piston ringsegment and the cylinder wall consists of a viscousshear force in the lubricant film and friction bet-ween the asperities in contact. An experimentallymeasured value of 0.14 is used for the dynamic

asperity coefficient of friction ma. The resultingexpression for total frictional force on the segment is

Ff ¼

ða=2

�a=2

ðb=2

�b=2

�h

2

@p

@x�hU

h

� �þ mapa

� �dx dy

(10)

3.5 Solution method

Integration of the modified non-dimensional Reynoldsequation (1) over a control volume [21] yields

ðe

w

ðn

s

@

@XH3 @(Ff)

@X

� �þ@

@YH3 @(Ff)

@Y

� �� dY dX

¼

ðe

w

ðn

s

g@

@X{½1þ (1� F)f�H}

� �dY dX

þ

ðe

w

ðn

s

s@

@T{½1þ (1� F)f�H}

� �dY dX

(11)

The discretized form of equation (11) takes on theform

H3 @(Ff)

@X

� �e

DY � H3 @(Ff)

@X

� ��

w

DY þ H3 @(Ff)

@Y

� �n

�� DX � H3 @(Ff)

@Y

� ��s

DX

¼ g{½1þ (1� F)f�H} eDYj

� g{½1þ (1� F)f�H}��

wDY

þ

sDXDY ({½1þ (1� F)f�H}n

� {½1þ (1� F)f�H}n�1)

DT(12)

The discretization shown in equation (12) results ina system of linear equations that are solved using theGauss–Siedel relaxation scheme. In order to ensure astable convergence, both F and f are relaxed afterevery Gauss–Seidel sweep according to

frelaxed ¼ affnew þ (1� af)fold

Frelaxed ¼ aF Fnew þ (1� aF )Fold

(13)

where

Fnew ¼1 if frelaxed 5 0

0 if frelaxed , 0

�

According to Payvar and Salant [20] the key tostability is in the proper selection of the relaxationcoefficients. Following their recommendation, relax-ation coefficients of af ¼ 0.2 and aF ¼ 0.01 werechosen. A mesh size of 100 � 50 was found to providea grid-independent pressure solution. Iteration



continues through the grid points until the solutionreaches convergence, defined as

maxfnew � fold

fnew

��

� �i,j

, 10�5 (15)

Since the piston ring lubrication condition ishighly transient, the force balance equation (9)must also be satisfied at each time step according to

ða=2

�a=2

ðb=2

�b=2

(pel þ pg) dx dy

�

ða=2

�a=2

ðb=2

�b=2

(ph þ pa) dx dy 4 0:001 (16)

4 RESULTS AND DISCUSSION

The experimental test rig was designed and deve-loped to operate under ambient conditions and tomaintain a constant load throughout the stroke.Note that in a real engine the combustion chamberpressure would lead to much higher loading of thepiston ring at TDC than near BDC, with correspond-ingly greater frictional loss. In order to corroboratethe experimental and numerical model results theleading- and trailing-edge pressures in equation (5)were set to the ambient pressure and the dynamiccomponents of the force balance equation (pg and

pel) in equation (9) were set to the constant appliednormal load. Measured surface roughness valueswere used in the asperity contact model. Exper-iments were conducted at room temperature usingSAE 30 oil. In the numerical modelling a viscosityof 0.20 Pa s was chosen for all the numerical analysis.Figure 5 shows a typical result for the measured andpredicted values of coefficient of friction Cf as thepiston ring travels from TDC (08) to BDC (1808) andback again to TDC (3608). TDC and BDC refer tothe crank position and not to the position of thering on the liner. The ring position is opposite fromthat of an engine because here it is the liner that ismoving and not the ring. The sign of Cf indicatesthe direction of travel. In general, the measuredand predicted values correlate well throughout therange of operating conditions tested.

4.1 Lubrication regime transition

For a full rotation of the crank, the piston ringtransitions through different regimes of lubrication.Figure 6 illustrates the transitions over an expansionstroke (0–1808). At the beginning of the stroke(08, TDC) the contact is dominated by asperity–asperity interaction. As evidenced by the large spikein Cf, this portion of the stroke is in the boundarylubrication region, which is defined here as pureasperity-to-asperity solid contact. Note that themaximum value of the friction spike does not exceed

Fig. 5 Friction results exhibiting all three lubrication regimes (120 r/min; 3 kgf)



continues through the grid points until the solutionreaches convergence, defined as

maxfnew � fold

fnew

��

� �i,j

, 10�5 (15)

Since the piston ring lubrication condition ishighly transient, the force balance equation (9)must also be satisfied at each time step according to

ða=2

�a=2

ðb=2

�b=2

(pel þ pg) dx dy

�

ða=2

�a=2

ðb=2

�b=2

(ph þ pa) dx dy 4 0:001 (16)

4 RESULTS AND DISCUSSION

The experimental test rig was designed and deve-loped to operate under ambient conditions and tomaintain a constant load throughout the stroke.Note that in a real engine the combustion chamberpressure would lead to much higher loading of thepiston ring at TDC than near BDC, with correspond-ingly greater frictional loss. In order to corroboratethe experimental and numerical model results theleading- and trailing-edge pressures in equation (5)were set to the ambient pressure and the dynamiccomponents of the force balance equation (pg and

pel) in equation (9) were set to the constant appliednormal load. Measured surface roughness valueswere used in the asperity contact model. Exper-iments were conducted at room temperature usingSAE 30 oil. In the numerical modelling a viscosityof 0.20 Pa s was chosen for all the numerical analysis.Figure 5 shows a typical result for the measured andpredicted values of coefficient of friction Cf as thepiston ring travels from TDC (08) to BDC (1808) andback again to TDC (3608). TDC and BDC refer tothe crank position and not to the position of thering on the liner. The ring position is opposite fromthat of an engine because here it is the liner that ismoving and not the ring. The sign of Cf indicatesthe direction of travel. In general, the measuredand predicted values correlate well throughout therange of operating conditions tested.

4.1 Lubrication regime transition

For a full rotation of the crank, the piston ringtransitions through different regimes of lubrication.Figure 6 illustrates the transitions over an expansionstroke (0–1808). At the beginning of the stroke(08, TDC) the contact is dominated by asperity–asperity interaction. As evidenced by the large spikein Cf, this portion of the stroke is in the boundarylubrication region, which is defined here as pureasperity-to-asperity solid contact. Note that themaximum value of the friction spike does not exceed

Fig. 5 Friction results exhibiting all three lubrication regimes (120 r/min; 3 kgf)



the experimentally measured dry coefficient of fric-tion. As the piston ring accelerates away from TDC,a lubricant film separating the two contactingbodies begins to develop. Here asperity–asperityinteraction remains significant; however, the load issupported partly by the asperity-to-asperity solidcontact and partly by the lubricant present in thecontact. This portion of the stroke is considered tobe the mixed lubrication regime. As the velocityincreases, the load balance shifts further towardsthe lubricant as the surfaces separate and asperityinteraction decreases. As illustrated in Fig. 7a thefrictional force at the contact is due to asperity con-tact and viscous losses. The frictional force due toasperity interaction (when present) is generallymuch larger than the viscous losses, resulting in apoint of minimum Cf as the ring makes a transitionfrom mixed lubrication to full-film lubrication.Through the full-film region the lubricant film isthick enough to prevent asperity interaction; thusall frictional losses during this section of the strokeare due to viscous drag. Since viscous shear is pro-portional to the relative velocity of the ring a localmaximum in the friction curve is observed nearmid-stroke. The presence of this viscous ‘hump’ inthe friction trace is evidence that the ring hasreached a state of full-film lubrication. From nearmid-stroke to BDC the opposite chain of events tran-spires. As the ring decelerates, the hydrodynamic

action of the ring is decreased, which in turn leadsto smaller film thickness. The velocity continues todecrease until it is no longer sufficient to build athick film to separate the surfaces completely, andthe ring returns to a state of mixed lubrication.Asperity interaction and frictional losses continueto increase until the ring reaches BDC. Note thatthe friction trace is not perfectly symmetric due tovariation in acceleration and deceleration near TDCand BDC.

Figures 7a and b illustrate the relationshipbetween the onset of asperity contact at the ends ofstroke and the minimum film thickness. While theminimum film thickness remains greater than theeffective surface roughness sc, the surfaces are com-pletely separated and the only contribution to thecoefficient of friction is from the viscous shear.When the minimum film thickness falls below sc,the asperities begin to come into contact.

Figure 8 depicts the variation in pressure over thewidth of the ring section (20.5 , X , 0.5 andY ¼ 0). Beginning at TDC (08) the load is almostentirely supported by asperity contact pressure sym-metric about the centre-line. Note that, since theasperity contact occurs over a relatively small con-tact area, the pressures must be large in order to sup-port the load. These high asperity contact pressuresare the cause of the friction spikes at the ends ofstroke as is shown in Fig. 7. As the ring accelerates

Fig. 6 Different lubrication regimes encountered during an expansion stroke at 120 r/min

and 3 kgf



the experimentally measured dry coefficient of fric-tion. As the piston ring accelerates away from TDC,a lubricant film separating the two contactingbodies begins to develop. Here asperity–asperityinteraction remains significant; however, the load issupported partly by the asperity-to-asperity solidcontact and partly by the lubricant present in thecontact. This portion of the stroke is considered tobe the mixed lubrication regime. As the velocityincreases, the load balance shifts further towardsthe lubricant as the surfaces separate and asperityinteraction decreases. As illustrated in Fig. 7a thefrictional force at the contact is due to asperity con-tact and viscous losses. The frictional force due toasperity interaction (when present) is generallymuch larger than the viscous losses, resulting in apoint of minimum Cf as the ring makes a transitionfrom mixed lubrication to full-film lubrication.Through the full-film region the lubricant film isthick enough to prevent asperity interaction; thusall frictional losses during this section of the strokeare due to viscous drag. Since viscous shear is pro-portional to the relative velocity of the ring a localmaximum in the friction curve is observed nearmid-stroke. The presence of this viscous ‘hump’ inthe friction trace is evidence that the ring hasreached a state of full-film lubrication. From nearmid-stroke to BDC the opposite chain of events tran-spires. As the ring decelerates, the hydrodynamic

action of the ring is decreased, which in turn leadsto smaller film thickness. The velocity continues todecrease until it is no longer sufficient to build athick film to separate the surfaces completely, andthe ring returns to a state of mixed lubrication.Asperity interaction and frictional losses continueto increase until the ring reaches BDC. Note thatthe friction trace is not perfectly symmetric due tovariation in acceleration and deceleration near TDCand BDC.

Figures 7a and b illustrate the relationshipbetween the onset of asperity contact at the ends ofstroke and the minimum film thickness. While theminimum film thickness remains greater than theeffective surface roughness sc, the surfaces are com-pletely separated and the only contribution to thecoefficient of friction is from the viscous shear.When the minimum film thickness falls below sc,the asperities begin to come into contact.

Figure 8 depicts the variation in pressure over thewidth of the ring section (20.5 , X , 0.5 andY ¼ 0). Beginning at TDC (08) the load is almostentirely supported by asperity contact pressure sym-metric about the centre-line. Note that, since theasperity contact occurs over a relatively small con-tact area, the pressures must be large in order to sup-port the load. These high asperity contact pressuresare the cause of the friction spikes at the ends ofstroke as is shown in Fig. 7. As the ring accelerates

Fig. 6 Different lubrication regimes encountered during an expansion stroke at 120 r/min

and 3 kgf



away from the TDC position, hydrodynamic pressurebegins to build in the converging section of the ringface. The transition of the load support from asperitycontact to hydrodynamic pressures is seen as the

peak pressure reduces, spreads out, and shifts awayfrom the centre-line to the converging section ofthe ring face. The ring again decelerates as itapproaches BDC (1808). At these lower velocities

Fig. 7 (a) Relative contributions of the asperity contact and viscous shear components to the total coefficient of

friction (predicted) (120 r/min; 3 kgf); (b) relationship between the onset of asperity contact, minimum film

thickness, and effective surface roughness sc

Fig. 8 Pressure acting over the width of the ring face as a function of crank angle



away from the TDC position, hydrodynamic pressurebegins to build in the converging section of the ringface. The transition of the load support from asperitycontact to hydrodynamic pressures is seen as the

peak pressure reduces, spreads out, and shifts awayfrom the centre-line to the converging section ofthe ring face. The ring again decelerates as itapproaches BDC (1808). At these lower velocities

Fig. 7 (a) Relative contributions of the asperity contact and viscous shear components to the total coefficient of

friction (predicted) (120 r/min; 3 kgf); (b) relationship between the onset of asperity contact, minimum film

thickness, and effective surface roughness sc

Fig. 8 Pressure acting over the width of the ring face as a function of crank angle



the hydrodynamic action is not sufficient to sustainthe thick film; thus the lubricant begins to squeezeout of the contact as the surfaces move closertogether. Pressure generated through this squeezingmotion shifts the profile towards the centre-line.Note that the squeeze pressure is independent ofthe asperity contact pressure that begins to increaseas the lubricant film continues to drop.

4.2 Effect of speed

Figure 9 presents the effect of operating speedon the coefficient of friction under a constant load.

Hydrodynamic action in the converging section ofthe ring is responsible for generating the load-supporting pressure in the lubricant film. Anincrease in the sliding speed enhances the wedgingaction of the converging ring profile, providing abetter load capacity with a larger lubricant film thick-ness. Hence, the increased surface separationdecreases the amount of asperity–asperity contact,which is manifest as a lowering of the friction spikeat the ends of stroke. In the extreme, the lubricantfilm is sufficiently thick to maintain the surfaces inthe full-film regime through the entirety of thestroke. Since the viscous shear is proportional to

Fig. 9 Effect of speed on coefficient of friction: (a) measured using piston ring reciprocating liner test rig;

(b) predicted from analysis



the hydrodynamic action is not sufficient to sustainthe thick film; thus the lubricant begins to squeezeout of the contact as the surfaces move closertogether. Pressure generated through this squeezingmotion shifts the profile towards the centre-line.Note that the squeeze pressure is independent ofthe asperity contact pressure that begins to increaseas the lubricant film continues to drop.

4.2 Effect of speed

Figure 9 presents the effect of operating speedon the coefficient of friction under a constant load.

Hydrodynamic action in the converging section ofthe ring is responsible for generating the load-supporting pressure in the lubricant film. Anincrease in the sliding speed enhances the wedgingaction of the converging ring profile, providing abetter load capacity with a larger lubricant film thick-ness. Hence, the increased surface separationdecreases the amount of asperity–asperity contact,which is manifest as a lowering of the friction spikeat the ends of stroke. In the extreme, the lubricantfilm is sufficiently thick to maintain the surfaces inthe full-film regime through the entirety of thestroke. Since the viscous shear is proportional to

Fig. 9 Effect of speed on coefficient of friction: (a) measured using piston ring reciprocating liner test rig;

(b) predicted from analysis



velocity, a more pronounced rise in the mid-stroke‘hump’ is seen with increased speed.

Figure 10 shows the effect of speed on the mini-mum film thickness under a constant load aspredicted by the numerical model. The effective sur-face roughness sc is used in this figure to denote theonset of asperity interaction. As noted previously, atlow speeds the hydrodynamic action of the conver-ging ring profile is not as strong. Accordingly, inthe 60 r/min case the piston ring remains in mixedlubrication throughout the entire cycle. However, asthe sliding speed increases, the minimum lubricantfilm thickness also rises, until in the 300 r/min case,only very light asperity contact occurs near the endsof stroke. Note that the minimum film thicknessprofile is not symmetric. The point of absolute mini-mum is shifted a few degrees from the TDC and BDCdue to the squeeze-film effect. This effect is also seenin the friction traces of Fig. 9, causing an asymmetryin the friction spikes at the ends of stroke. The pointof maximum solid–solid friction corresponds to thepoint of absolute minimum film thickness along thestroke.

4.3 Effect of load

Figure 11 illustrates the effect of load on the coeffi-cient of friction at a constant speed (120 r/min).Figure 12 shows the corresponding predicted mini-mum film thickness. As expected, increasing the

load decreases the lubricant film thickness. Conse-quently, the regions where asperity interaction is sig-nificant are increased. This is easily seen in thehighest loading case (8 kgf) where the piston ringremains in the mixed-lubrication regime throughoutthe cycle. Not only are the friction spikes at the endsof stroke much wider than for the lower loadingcases, but the friction remains high through themid-stroke region as well. Recall that, if the ringmakes a transition from mixed lubrication to full-film lubrication, a viscous ‘hump’ will be produced.It is also noted that the minimum film thicknessremains below sc through virtually the entirestroke, again indicating the mixed-lubrication con-dition through the entire cycle. Contrast this withthe lightest load case of 2 kgf. In this case, the hydro-dynamic pressure generated in the convergingsection of the ring profile is able to produce amuch thicker lubricant film. This results in smallernarrower friction spikes near the ends of stroke.

5 CONCLUSIONS

A numerical model and experimental test apparatushave been developed to investigate the lubricationand friction condition at the PRCL interface. Goodcorrelation was found between the experimentaland numerical results. The results presented hereencompass the entire range of lubrication regimes

Fig. 10 Effect of speed on minimum film thickness under a constant 3 kgf load (predicted)



velocity, a more pronounced rise in the mid-stroke‘hump’ is seen with increased speed.

Figure 10 shows the effect of speed on the mini-mum film thickness under a constant load aspredicted by the numerical model. The effective sur-face roughness sc is used in this figure to denote theonset of asperity interaction. As noted previously, atlow speeds the hydrodynamic action of the conver-ging ring profile is not as strong. Accordingly, inthe 60 r/min case the piston ring remains in mixedlubrication throughout the entire cycle. However, asthe sliding speed increases, the minimum lubricantfilm thickness also rises, until in the 300 r/min case,only very light asperity contact occurs near the endsof stroke. Note that the minimum film thicknessprofile is not symmetric. The point of absolute mini-mum is shifted a few degrees from the TDC and BDCdue to the squeeze-film effect. This effect is also seenin the friction traces of Fig. 9, causing an asymmetryin the friction spikes at the ends of stroke. The pointof maximum solid–solid friction corresponds to thepoint of absolute minimum film thickness along thestroke.

4.3 Effect of load

Figure 11 illustrates the effect of load on the coeffi-cient of friction at a constant speed (120 r/min).Figure 12 shows the corresponding predicted mini-mum film thickness. As expected, increasing the

load decreases the lubricant film thickness. Conse-quently, the regions where asperity interaction is sig-nificant are increased. This is easily seen in thehighest loading case (8 kgf) where the piston ringremains in the mixed-lubrication regime throughoutthe cycle. Not only are the friction spikes at the endsof stroke much wider than for the lower loadingcases, but the friction remains high through themid-stroke region as well. Recall that, if the ringmakes a transition from mixed lubrication to full-film lubrication, a viscous ‘hump’ will be produced.It is also noted that the minimum film thicknessremains below sc through virtually the entirestroke, again indicating the mixed-lubrication con-dition through the entire cycle. Contrast this withthe lightest load case of 2 kgf. In this case, the hydro-dynamic pressure generated in the convergingsection of the ring profile is able to produce amuch thicker lubricant film. This results in smallernarrower friction spikes near the ends of stroke.

5 CONCLUSIONS

A numerical model and experimental test apparatushave been developed to investigate the lubricationand friction condition at the PRCL interface. Goodcorrelation was found between the experimentaland numerical results. The results presented hereencompass the entire range of lubrication regimes

Fig. 10 Effect of speed on minimum film thickness under a constant 3 kgf load (predicted)



experienced by the piston ring, from boundary tofull-film hydrodynamic lubrication. Measured andpredicted values for coefficient of friction and lubri-cant film thickness are used to investigate the lubri-cation condition throughout the stroke. The effectof operating speed and load are described. Depend-ing on operating conditions, all three lubricationregimes can occur at different points in the stroke.As expected, friction is highest in the mixed lubrica-tion and boundary lubrication regimes that occurnear TDC and BDC.

This study has provided the details of thetransition of the piston ring through the various

lubrication regimes and has identified areas withpotential for improvement. The transitions and thelubrication condition throughout the stroke havebeen examined. The results presented here havealso shown that the numerical model is capable ofpredicting the frictional loss and lubricant film thick-ness for a given piston ring geometry. In a designsetting, the numerical model could be used to evalu-ate potential piston ring behaviour by specifyingthe piston velocity, ring tension, cylinder pressurehistory, pressure history between piston rings, ringcrown height, ring width, effective surface rough-ness, and viscosity.

Fig. 11 Effect of load on coefficient of friction at a constant speed of 120 r/min; (a) measured using piston ring

reciprocating liner test rig; (b) predicted from analysis



experienced by the piston ring, from boundary tofull-film hydrodynamic lubrication. Measured andpredicted values for coefficient of friction and lubri-cant film thickness are used to investigate the lubri-cation condition throughout the stroke. The effectof operating speed and load are described. Depend-ing on operating conditions, all three lubricationregimes can occur at different points in the stroke.As expected, friction is highest in the mixed lubrica-tion and boundary lubrication regimes that occurnear TDC and BDC.

This study has provided the details of thetransition of the piston ring through the various

lubrication regimes and has identified areas withpotential for improvement. The transitions and thelubrication condition throughout the stroke havebeen examined. The results presented here havealso shown that the numerical model is capable ofpredicting the frictional loss and lubricant film thick-ness for a given piston ring geometry. In a designsetting, the numerical model could be used to evalu-ate potential piston ring behaviour by specifyingthe piston velocity, ring tension, cylinder pressurehistory, pressure history between piston rings, ringcrown height, ring width, effective surface rough-ness, and viscosity.

Fig. 11 Effect of load on coefficient of friction at a constant speed of 120 r/min; (a) measured using piston ring

reciprocating liner test rig; (b) predicted from analysis



ACKNOWLEDGEMENT

The authors would like to extend their deepestappreciation to the US Department of Energy fortheir support of this project.

REFERENCES

1 Jeng, Y. Theoretical analysis of piston-ring lubrication.Part 1: fully flooded lubrication. STLE Tribology Trans.,1992, 35, 696–706.

2 Rohde, S. M., Whitaker, K. W., and McAllister, G. T. Amixed friction model for dynamically loaded contactswith application to piston ring lubrication. In SurfaceRoughness Effects in Hydrodynamic and Mixed Lubrica-tion, Proceedings of the ASME Winter Annual Meeting,1980, pp. 19–50.

3 Patir, N. and Cheng, H. S. An average flow model fordetermining effects of three-dimensional roughness onpartial hydrodynamic lubrication. Trans. ASME,J. Lubric. Technol., 1978, 100, 12–17.

4 Greenwood, J. A. and Tripp, J. H. The contact of twonominally flat rough surfaces. Proc. Inst. Mech. Engrs1971, 185, 625–633.

5 Dowson, D., Economou, P. N., Ruddy, B. L.,Strachan, P. J., and Baker, A. J. Piston ring lubrication.Part II: theoretical analysis of a single ring and a com-plete ring pack. In Energy Conservation Through FluidFilm Lubrication Technology: Frontiers in Research and

Design, Proceedings of the ASME Winter Annual Meet-ing, 1979, pp. 23–52.

6 Hu, Y., Cheng, H. S., Arai, T., Kobayashi, Y., andAoyama, S. Numerical simulation of piston ring inmixed lubrication – a non-axisymmetrical analysis.Trans. ASME, J. Tribology, 1994, 116, 470–478.

7 Yang, Q. and Keith, T. G., An elasto-hydrodynamic cavi-tation algorithm for piston ring lubrication. STLE Tribol-ogy Trans., 1995, 38, 97–107.

8 Vijayaraghavan, D. and Keith, T. G. Development andevaluation of a cavitation algorithm. STLE TribologyTrans., 1989, 32, 225–233.

9 Dowson, D., Ruddy, B. L., and Economou, P. N.The elastohydrodynamic lubrication of piston rings.Proc. R. Soc. Lond. A, 1983, 386, 409–430.

10 Yang, Q. and Keith, T. G. Two-dimensional piston ringlubrication. Part 1: rigid ring and liner solution. STLETribology Trans., 1996, 39, 757–768.

11 Yang, Q. and Keith, T. G. Two-dimensional piston ringlubrication. Part 2: elastic ring consideration. STLETribology Trans., 1996, 39, 870–880.

12 Sawicki, J. and Yu, B. Analytical solution of piston ringlubrication using mass conserving cavitation algor-ithm. STLE Tribology Trans., 2000, 43, 587–594.

13 Akalin, O. and Newaz, G. M. Piston ring–cylinderbore friction modeling in mixed lubrication regime.Part I: analytical results. Trans. ASME, J. Tribology,2001, 123, 211–218.

14 Akalin, O. and Newaz, G. M. Piston ring–cylinderbore friction modeling in mixed lubricationregime. Part II: correlation with bench test data.Trans. ASME, J. Tribology, 2001, 123, 219–223.

Fig. 12 Effect of load on minimum film thickness at a constant speed of 120 r/min (predicted)



ACKNOWLEDGEMENT

The authors would like to extend their deepestappreciation to the US Department of Energy fortheir support of this project.

REFERENCES

1 Jeng, Y. Theoretical analysis of piston-ring lubrication.Part 1: fully flooded lubrication. STLE Tribology Trans.,1992, 35, 696–706.

2 Rohde, S. M., Whitaker, K. W., and McAllister, G. T. Amixed friction model for dynamically loaded contactswith application to piston ring lubrication. In SurfaceRoughness Effects in Hydrodynamic and Mixed Lubrica-tion, Proceedings of the ASME Winter Annual Meeting,1980, pp. 19–50.

3 Patir, N. and Cheng, H. S. An average flow model fordetermining effects of three-dimensional roughness onpartial hydrodynamic lubrication. Trans. ASME,J. Lubric. Technol., 1978, 100, 12–17.

4 Greenwood, J. A. and Tripp, J. H. The contact of twonominally flat rough surfaces. Proc. Inst. Mech. Engrs1971, 185, 625–633.

5 Dowson, D., Economou, P. N., Ruddy, B. L.,Strachan, P. J., and Baker, A. J. Piston ring lubrication.Part II: theoretical analysis of a single ring and a com-plete ring pack. In Energy Conservation Through FluidFilm Lubrication Technology: Frontiers in Research and

Design, Proceedings of the ASME Winter Annual Meet-ing, 1979, pp. 23–52.

6 Hu, Y., Cheng, H. S., Arai, T., Kobayashi, Y., andAoyama, S. Numerical simulation of piston ring inmixed lubrication – a non-axisymmetrical analysis.Trans. ASME, J. Tribology, 1994, 116, 470–478.

7 Yang, Q. and Keith, T. G., An elasto-hydrodynamic cavi-tation algorithm for piston ring lubrication. STLE Tribol-ogy Trans., 1995, 38, 97–107.

8 Vijayaraghavan, D. and Keith, T. G. Development andevaluation of a cavitation algorithm. STLE TribologyTrans., 1989, 32, 225–233.

9 Dowson, D., Ruddy, B. L., and Economou, P. N.The elastohydrodynamic lubrication of piston rings.Proc. R. Soc. Lond. A, 1983, 386, 409–430.

10 Yang, Q. and Keith, T. G. Two-dimensional piston ringlubrication. Part 1: rigid ring and liner solution. STLETribology Trans., 1996, 39, 757–768.

11 Yang, Q. and Keith, T. G. Two-dimensional piston ringlubrication. Part 2: elastic ring consideration. STLETribology Trans., 1996, 39, 870–880.

12 Sawicki, J. and Yu, B. Analytical solution of piston ringlubrication using mass conserving cavitation algor-ithm. STLE Tribology Trans., 2000, 43, 587–594.

13 Akalin, O. and Newaz, G. M. Piston ring–cylinderbore friction modeling in mixed lubrication regime.Part I: analytical results. Trans. ASME, J. Tribology,2001, 123, 211–218.

14 Akalin, O. and Newaz, G. M. Piston ring–cylinderbore friction modeling in mixed lubricationregime. Part II: correlation with bench test data.Trans. ASME, J. Tribology, 2001, 123, 219–223.

Fig. 12 Effect of load on minimum film thickness at a constant speed of 120 r/min (predicted)



15 Priest, M., Dowson, D., and Taylor, C. M. Theoreticalmodeling of cavitation in piston ring lubrication. Proc.Instn. Mech. Engrs, Part C: J. Mechanical EngineeringScience, 2000, 214, 435–447.

16 Ting, L. L. Development of a reciprocating test rig fortribological studies of piston engine moving com-ponents. Part 1: rig design and piston ring frictioncoefficients measuring method. SAE paper 930685,1993.

17 Ting, L. L. Development of a reciprocating test rigfor tribological studies of piston engine moving com-ponents: Part 2: measurements of piston ring coeffi-cients and rig test confirmation. SAE paper 930686,1993.

18 Dearlove, J. and Cheng, W. K. Simultaneous piston ringfriction and oil film thickness measurements in a reci-procating test rig. SAE paper 952470, 1995.

19 Arcoumanis, C., Duszynski, M., Flora, H., andOstovar, P. Development of a piston-ring lubricationtest-rig and investigation of boundary conditions formodeling lubrication film properties. SAE paper952468, 1995.

20 Payvar, P. and Salant, R. F. A computational methodfor cavitation in wavy mechanical seal. Trans. ASME,J. Tribology, 1992, 114, 199–204.

21 Patankar, S. V. Numerical Heat Transfer and FluidFlow, 1980 (Hemisphere, Washington, DC).

APPENDIX

Notation

a width of ring section across the slidingdirection (m)

b ring thickness in the sliding direction (m)B cylinder bore diameter (m)F cavitation indexFf frictional force (N)h film thickness (m)hmin minimum film thickness (m)href reference film thickness (m)H dimensionless film thickness ¼ h/href

p pressure (MPa)pa ambient pressure (MPa)pc cavitation pressure (MPa)pel ring elastic pressure (MPa)pg gas pressure acting on the back of the ring

(MPa)

ph hydrodynamic pressure (MPa)pL pressure at the leading edge of the

ring (MPa)pT pressure at the trailing edge of the

ring (MPa)ps asperity contact pressure (MPa)t time (s)tref reference time (s)T dimensionless time ¼ t/tref

Tr ring tension (N)U sliding velocity (m/s)x coordinate in the sliding direction (m)X dimensionless coordinate in the sliding

direction ¼ x/by coordinate across the sliding direction (m)Y dimensionless coordinate across the

sliding direction ¼ y/a

a relaxation factor for pressureg characteristic number ¼ 6hUb/href

2�

(pa 2 pc)d crown height of the ring profile (m)h lubricant viscosity (Pa s)ma dynamic asperity coefficient of frictionr lubricant density (kg/m3)rc lubricant density at cavitation pressure

(kg/m3)s squeeze number ¼ 12hb 2/tref(pa 2 pc)href

2

sc effective surface roughness (mm)f dimensionless dependent variable defined

by equations (4) and (5)

Subscripts

e east boundary surface of the controlvolume

i index for the grid number in thex direction

j index for the grid number in the y directionn north boundary surface of the control

volumes south boundary surface of the control

volumew west boundary surface of the control

volume



15 Priest, M., Dowson, D., and Taylor, C. M. Theoreticalmodeling of cavitation in piston ring lubrication. Proc.Instn. Mech. Engrs, Part C: J. Mechanical EngineeringScience, 2000, 214, 435–447.

16 Ting, L. L. Development of a reciprocating test rig fortribological studies of piston engine moving com-ponents. Part 1: rig design and piston ring frictioncoefficients measuring method. SAE paper 930685,1993.

17 Ting, L. L. Development of a reciprocating test rigfor tribological studies of piston engine moving com-ponents: Part 2: measurements of piston ring coeffi-cients and rig test confirmation. SAE paper 930686,1993.

18 Dearlove, J. and Cheng, W. K. Simultaneous piston ringfriction and oil film thickness measurements in a reci-procating test rig. SAE paper 952470, 1995.

19 Arcoumanis, C., Duszynski, M., Flora, H., andOstovar, P. Development of a piston-ring lubricationtest-rig and investigation of boundary conditions formodeling lubrication film properties. SAE paper952468, 1995.

20 Payvar, P. and Salant, R. F. A computational methodfor cavitation in wavy mechanical seal. Trans. ASME,J. Tribology, 1992, 114, 199–204.

21 Patankar, S. V. Numerical Heat Transfer and FluidFlow, 1980 (Hemisphere, Washington, DC).

APPENDIX

Notation

a width of ring section across the slidingdirection (m)

b ring thickness in the sliding direction (m)B cylinder bore diameter (m)F cavitation indexFf frictional force (N)h film thickness (m)hmin minimum film thickness (m)href reference film thickness (m)H dimensionless film thickness ¼ h/href

p pressure (MPa)pa ambient pressure (MPa)pc cavitation pressure (MPa)pel ring elastic pressure (MPa)pg gas pressure acting on the back of the ring

(MPa)

ph hydrodynamic pressure (MPa)pL pressure at the leading edge of the

ring (MPa)pT pressure at the trailing edge of the

ring (MPa)ps asperity contact pressure (MPa)t time (s)tref reference time (s)T dimensionless time ¼ t/tref

Tr ring tension (N)U sliding velocity (m/s)x coordinate in the sliding direction (m)X dimensionless coordinate in the sliding

direction ¼ x/by coordinate across the sliding direction (m)Y dimensionless coordinate across the

sliding direction ¼ y/a

a relaxation factor for pressureg characteristic number ¼ 6hUb/href

2�

(pa 2 pc)d crown height of the ring profile (m)h lubricant viscosity (Pa s)ma dynamic asperity coefficient of frictionr lubricant density (kg/m3)rc lubricant density at cavitation pressure

(kg/m3)s squeeze number ¼ 12hb 2/tref(pa 2 pc)href

2

sc effective surface roughness (mm)f dimensionless dependent variable defined

by equations (4) and (5)

Subscripts

e east boundary surface of the controlvolume

i index for the grid number in thex direction

j index for the grid number in the y directionn north boundary surface of the control

volumes south boundary surface of the control

volumew west boundary surface of the control

volume



Piston

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