optimizing surface texture for combustion engine cylinder liners989994/fulltext01.pdf · chapter 1...

LICENTIATE T H E S I S

Department of Applied Physics and Mechanical EngineeringDivision of Machine Elements

Optimizing Surface Texture for Combustion Engine Cylinder Liners

Andrew Spencer

ISSN: 1402-1757 ISBN 978-91-7439-178-7

Luleå University of Technology 2010

Andrew

Spencer Optim

izing Surface Texture for Com

bustion Engine C

ylinder Liners

ISSN: 1402-1544 ISBN 978-91-7439-XXX-X Se i listan och fyll i siffror där kryssen är

Optimizing Surface Texture forCombustion Engine Cylinder Liners

Andrew Spencer

Lulea University of TechnologyDepartment of Applied Physics and Mechanical Engineering,

Division of Machine Elements

Printed by Universitetstryckeriet, Luleå 2010

ISSN: 1402-1757 ISBN 978-91-7439-178-7

Luleå 2010

www.ltu.se

‘Engineering is the art of modelling materials we do not wholly understand,

into shapes we cannot precisely analyse so as to withstand forces we cannot

properly assess, in such a way that the public has no reason to suspect the

extent of our ignorance.’

- Dr. A.R. Dykes, Address to the Institute of Structural Engineers(1978)

Abstract

The Piston Ring - Cylinder Liner (PRCL) contact is the single largest con-tributor to frictional losses in an internal combustion (IC) engine, causing20-40% of all mechanical losses. If these mechanical losses can be reducedby 10% then vehicle fuel efficiency could be increased by approximately1.5-2.5%. In todays automotive industry fuel efficiency is one of the mostimportant factors in vehicle design due to increasing concerns about energysecurity, increasing fuel prices and climate change. The objective of thisproject is to optimise the cylinder surface texture, which when referring tocylinder liners in this work means the cross-hatch grooves left by the honingprocess.

This work focuses on simulation techniques that can be used to helpoptimize cylinder liner surface texture to reduce friction while at the sametime minimizing oil consumption and wear. Cylinder liner surface topog-raphy is investigated with a range of measurement techniques in order toreveal all the important features of the existing surface. Different ways ofcharacterizing surface topography based on both traditional height averag-ing parameters and functional parameters calculated for a range of differentsurface measurements are discussed. The different characterization tech-niques are compared to find the most appropriate way of quantitativelydescribing surface topographies.

A full engine cycle simulation of the PRCL contact has been developed.A homogenization technique was implemented for solving the Reynoldsequation. This is a two scale approach where surface roughness is treatedon the local scale and surface texture plus global geometry on the globalscale. A method for generating artificial surface topography based on realsurface measurement data was developed. This allows for the possibility ofsimulating a wide range of new surface topographies in order to investigatetheir potential for reducing friction and minimising oil consumption andwear.

i

Acknowledgements

The work presented in this thesis has been funded by Stiftelsen for Strate-gisk Forskning (SSF) and ProViking through the PROACT project. TheKempe Foundations SMK -2546 is thanked for funding the SPM used forthe measurements of the cylinder liner and piston ring. The assistance ofthe Wolfson School, Loughborough University is gratefully acknowledgedfor performing stylus measurements for this project. Thanks go to ScaniaAB for assisting with their expertise, technical data and providing com-ponent samples. From Scania I would like to thank Hubert Herbst, PeterDaelander, Mattias Berger and Martin Soder.

I would like to thank my supevisor Prof. Roland Larsson for guiding methrough this work and his support and guidance. I would also like to thankDr. Andreas Almqvist with all of his help across a broad range of topics,from Matlab through Homogenization and on to LaTeX!

I am grateful to all my friends and colleagues at the Division of MachineElements for providing a friendly and enjoyable place to work. I would alsolike to thank Illia Dobryden from the Division of Physics for his work withthe AFM measurements.

iii

Contents

Nomenclature 1

I The Thesis 3

1 Introduction 5

1.1 The PRCL contact . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 The Piston Ring Pack . . . . . . . . . . . . . . . . . . 5

1.1.2 The Cylinder Liner . . . . . . . . . . . . . . . . . . . . 6

1.1.3 The Tribology of the PRCL contact . . . . . . . . . . 7

1.2 Optimizing the PRCL contact . . . . . . . . . . . . . . . . . . 7

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.1 Implementation of an All Regime model . . . . . . . . 9

1.3.2 Texture modelling in a PRCL simulation . . . . . . . 10

1.3.3 PRCL Surface Characterization . . . . . . . . . . . . . 10

2 Surface Modelling 13

2.1 Measurement Techniques . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Stylus Profiliometry . . . . . . . . . . . . . . . . . . . 13

2.1.2 White Light Interferometry (WLI) . . . . . . . . . . . 14

2.1.3 Atomic Force Microscopy (AFM) . . . . . . . . . . . . 14

2.1.4 Comparison of Techniques . . . . . . . . . . . . . . . . 15

2.1.5 Scan Size . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.6 Sampling interval . . . . . . . . . . . . . . . . . . . . . 15

2.2 PRCL Measurements . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 SP measurements . . . . . . . . . . . . . . . . . . . . . 18

2.2.2 WLI measurements . . . . . . . . . . . . . . . . . . . . 18

2.2.3 AFM measurements . . . . . . . . . . . . . . . . . . . 20

2.2.4 Data processing of surface measurements . . . . . . . 21

2.3 Artificial Surface Generation . . . . . . . . . . . . . . . . . . 23

v

3 All regime simulation 27

3.1 Global problem and geometry . . . . . . . . . . . . . . . . . . 27

3.2 Full film simulation . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Mixed and Boundary simulation . . . . . . . . . . . . . . . . 30

3.4 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.1 Cavitation Algorithms . . . . . . . . . . . . . . . . . . 31

3.5 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Surface Characterization 37

4.1 Rk parameters - ISO 13565-2 . . . . . . . . . . . . . . . . . . 38

4.2 Rq parameters - ISO 13565-3 . . . . . . . . . . . . . . . . . . 40

4.3 Rk parameters from 2D and 3D measurements . . . . . . . . 40

4.4 Rk parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.5 Flow Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Full engine cycle simulations 47

5.1 Model inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2 Force balance and time dependence . . . . . . . . . . . . . . . 48

6 Conclusion and Future Work 51

6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

II Appended Papers 55

A 57

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.2.1 Surface Texture . . . . . . . . . . . . . . . . . . . . . . 61

A.2.2 Cavitation Algorithm . . . . . . . . . . . . . . . . . . 63

A.2.3 Boundary conditions . . . . . . . . . . . . . . . . . . . 64

A.2.4 Film thickness . . . . . . . . . . . . . . . . . . . . . . 65

A.2.5 Force Balance and Time dependence . . . . . . . . . . 65

A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 68

B 69

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B.2 Model Development . . . . . . . . . . . . . . . . . . . . . . . 73

B.2.1 Geometry and global problem . . . . . . . . . . . . . . 73

B.2.2 Global Surface Texture . . . . . . . . . . . . . . . . . 74B.2.3 Reynolds equation . . . . . . . . . . . . . . . . . . . . 76B.2.4 Flow Factors . . . . . . . . . . . . . . . . . . . . . . . 76B.2.5 Model Input Parameters . . . . . . . . . . . . . . . . . 77B.2.6 Force Balance and Time Dependence . . . . . . . . . . 79B.2.7 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . 80B.2.8 Grid size and convergence . . . . . . . . . . . . . . . . 80

B.3 Texture Investigation . . . . . . . . . . . . . . . . . . . . . . . 80B.4 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 82B.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83B.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 84

C 85C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88C.2 Surface Measurements . . . . . . . . . . . . . . . . . . . . . . 89

C.2.1 WLI Measurements . . . . . . . . . . . . . . . . . . . 89C.2.2 AFM Measurements . . . . . . . . . . . . . . . . . . . 90C.2.3 Data processing of surface measurements . . . . . . . 91

C.3 Rk parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 94C.4 Flow Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 95C.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99C.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 100

List of Appended Papers

Paper A

A numerical model to investigate the effect of honing angle on the

hydrodynamic lubrication between a combustion engine piston ring

and cylinder liner

A. Spencer, A. Almqvist, R. Larsson

(Presented at NordTrib 2010 and submitted to Proceedings of the Institution of

Mechanical Engineers, Part J: Journal of Engineering Tribology - NordTrib

Special Issue)

Paper B

A semi-deterministic texture-roughness model of the piston ring -

cylinder liner contact

A. Spencer, A. Almqvist, R. Larsson

(Presented at Leeds-Lyon 2010 and submitted to Proceedings of the Institution of

Mechanical Engineers, Part J: Journal of Engineering Tribology - Leeds-Lyon

Special Issue)

Paper C

Surface Characterization with Functional Parameters

A. Spencer, I. Dobryden, N. Almqvist, A. Almqvist, R. Larsson

(To be submitted to STLE: Tribology Transactions)

ix

Nomenclature

α Honing Angle ()

β Compressibility factor (Pa)

β∗ Correlation length (m)

η Coefficient of friction

µ Dynamic Viscosity (Pa·s)

h Average film thickness at a given separation (m)

φ Crank Angle ()

ρ Lubricant density (kg/m3)

ρc Cavitation density (kg/m3)

τ Spatial sampling interval (m)

θ Fractional film content

ε Roughness wavelength (m)

a Ratio of connecting rod length to crankshaft radius

A0 Pressure induced flow factor matrix

Ar Real area of contact (m2)

axx Pressure induced flow factor

B0 Shear induced flow factor matrix

bxx Shear induced flow factor

d Bore diameter (m)

E Young’s Modulus (Pa)

1

E∗ Effective Young’s Modulus (Pa)

FT Ring tangential force (N)

g Cavitation switch function

h Film thickness (m)

hmin Minimum film thickness (m)

L Engine Stroke (m)

l Width of contact (piston ring) (m)

N Engine Speed (rpm)

n No. of data points

p Film Pressure (Pa)

p0 Homogenized film pressure (Pa)

R Ring Radius (m)

Rq RMS Roughness (m)

t Time (s)

U Entraining Speed (m/s)

v Poisson’s Ratio

W Load (N)

w Periodic global width (m)

x Direction parallel to entraining motion (m)

y Direction normal to entraining motion (m)

z Height of point on surface (m)

Part I

The Thesis

3

Chapter 1

Introduction

In this chapter the Piston Ring - Cylinder Liner (PRCL) contact is intro-duced. The motivation behind this research is outlined and the overall goal,optimizing cylinder liner surface texture, is divided into several objectives.

1.1 The PRCL contact

Typically for a medium size car over an urban cycle only 12% of the totalpower from the fuel is converted to useful energy at the wheels [1]. Therest of the energy from combustion of the fuel goes into cooling, exhaust,pumping and mechanical losses. The mechanical contribution amounts to17% [1] of the total losses and the friction between the piston assembly andcylinder liner is the single largest contributor; amounting to 20-40% of thetotal mechanical losses [2]. Furthermore, the compression rings typicallycontribute 4-5% of all mechanical losses in a multi-cylinder engine [3]. Ifthese mechanical losses can be reduced by 10% then fuel efficiency couldbe increased by between 1.5-2.5% [1, 3]. Therefore the study of the PRCLcontact is highly important in reducing friction and improving fuel economy,one of the main drivers in engine design today.

1.1.1 The Piston Ring Pack

A typical IC engine has 3 piston rings which form the piston ring pack.Larger diesel engines may have 4 rings. The three piston rings all havedifferent roles and their shape varies because of this, see Fig. 1.1.

• Compression Ring: Seals the combustion chamber

• Scraper Ring: Provides additional sealing, scrapes oil downwards

• Oil Control Ring: Distributes oil onto the liner

5

6 CHAPTER 1. INTRODUCTION

Figure 1.1: Piston Ring Pack

Essentially the piston rings have two tasks; to stop gases leaving the com-bustion chamber and prevent excess oil entering the chamber.

1.1.2 The Cylinder Liner

Cylinder liners are traditionally manufactured from cast iron and are theneither cast or pressed in to the engine block, which is often aluminium. Al-ternatively, if no cylinder liner is used a ceramic particulate phase can becast into the aluminium liner during the manufacturing of the block. Typi-cally a machining process known as honing is used to apply the desired finishto the cylinder liner surface. The grooves that the honing process leaves be-hind are believed to be important in controlling the amount of oil availablein the contact, by both retaining oil on the liner surface and improving thedistribution of oil. Another perceived function of the honing texture is toallow wear debris, generated during boundary lubrication around TDC, tobe channelled away from the conjunction so as to cause only minimal dam-age and scratching to the smooth plateaux which are said to be importantfor fluid film generation. Usually in modern engines three stage, or plateauhoning, is used. The three stages are listed below and illustrated in Fig. 1.2.

1. The liner is honed roughly to size

2. The peaks are removed using a smoother honing tool

3. The material that has become embedded in the crosshatch is removedwith a very smooth honing tool

1.2. OPTIMIZING THE PRCL CONTACT 7

Figure 1.2: 3 stage plateau honing process

The second stage, creating the plateaux, partly replaces the running inprocess as the peaks that would have worn away during initial running ofthe engine are removed.

1.1.3 The Tribology of the PRCL contact

The Stribeck curve is often used to illustrate the different lubrication regimesand corresponding frictional coefficient. As the entraining velocity betweencylinder liner and piston ring pack varies between zero and several metresper second, the lubrication regime will vary from boundary and mixed at thetop and bottom of the stroke to fully hydrodynamic during the midstroke.Therefore when considering optimizing the contact, all regimes must beconsidered.

1.2 Optimizing the PRCL contact

The overall objective of this research is to develop a numerical simulationof the PRCL contact, validated by experiment, that can be used to assistin optimising the contact with a focus on the cylinder liner surface finish.


Figure 1.3: Stribeck Curve

When considering what it means to ‘optimize’ the surface, three thingsshould be considered;

• Frictional Power losses

• Blowby and oil consumption

• Wear

The power losses from the PRCL contact should be minimized in orderto increase the overall efficiency of the engine. It is important to realisethat minimizing power loss is not the same thing as minimizing friction.The highest frictional losses, where the friction coefficient is highest, willoccur around Top Dead Centre (TDC) when boundary lubcrication occurs.However, at this point in the engine cycle the piston is travelling at lowspeeds and is momentarily stationary. Therefore, the power loss, in watts, isminimal. During the midstroke the lubrication regime is fully hydrodynamicand the friction coefficient is much lower, however the piston is travellingat many metres per second leading to high power losses.

The second parameter to minimize is blowby and oil consumption. Sim-ply put, the combustion gases should stay in the combustion chamber andthe engine oil should stay in the engine. Blowby is defined as the combus-tion gas that flows from the combustion chamber past the piston rings andinto the crankcase, resulting in a loss of power and efficiency. Blowby isa volumetric power loss meaning that minimized blowby is also minimizedpower loss. Blowby can occur through three routes;

1. Through the ring gap

1.3. OBJECTIVES 9

2. Past the face of the ring (i.e. between the piston ring and the liner)

3. Between the flank of the ring and the ring groove

The second and third of these leakage paths are through tribological con-tacts. In particular, the second is the contact that is to be optimized in thisresearch and therefore the effect on blowby of any optimization needs to beconsidered. Similarly, the amount of oil that passes the piston rings shouldbe kept to a minimum. Too much oil entering the combustion chamber isundesirable as it will lead to a substantial increase in exhaust gas hydro-carbon levels. Finally, wear should be kept to a minimum. This is only anissue where asperity contact occurs near TDC.

1.3 Objectives

In this Licentiate, simulations of the PRCL contact have been developedto aid in the optimizing process. The work presented in this licentiate canbe broken down into three separate sub-objectives, in which attempts aremade to address several gaps in existing research.

1.3.1 Implementation of an All Regime model

Throughout this work two terms will be used to describe the different scalesof the cylinder liner surface, ‘texture’ and ‘roughness’. Texture is defined asthe larger scale cross-hatch like pattern left behind by the first stage of thehoning process. Roughness is defined as the smaller scale, smaller amplitudeof the surface between the cross-hatching, the diamond like plateaux. Thesetwo scales are illustrated in Fig. 1.4. In many existing PRCL simulations the

Figure 1.4: Texture and Roughness definitions

surface finish of the cylinder liner is only taken into account when boundarylubrication occurs around TDC. PRCL models by Mishra et al. [3], Maet al. [4] and Liu et al. [5] implement a Greenwood and Tripp [6] typemodel when asperity contact is predicted but do not take into account thesurface finish when the lubrication regime is hydrodynamic. It is proposedthat the cylinder liner honing must have some effect even when asperity


interactions do not take place. Honing is known to be important for theadequate functioning of the contact and asperity interactions only occur fora small percentage of the engine cycle.

Other PRCL simulations such as those by Hu et al. [7] and Akalinand Newaz [8] implement the Patir and Cheng Average Flow model [9, 10],thereby incorporating the effect of surface finish in the mixed and hydrody-namic lubrication regimes. These simulations lump together both textureand roughness into the same set of flow factors and no differentiation ismade between them. One of the issues addressed in this research is whetherthis is an acceptable assumption to make.

In this work the PRCL contact is modelled using an all regime model[11, 12] whereby the homogenization technique is used in place of Patir andCheng flow factors. It is believed that this is the first time this techniquehas been applied to the PRCL contact in published work. The homogeniza-tion technique provides a more rigorously derived means of calculating flowfactors than the Patir and Cheng method [13].

1.3.2 Texture modelling in a PRCL simulation

As discussed in the previous section, the two scales of the cylinder linersurface finish, texture and roughness, have in the past been lumped to-gether and treated as one. However, as discussed in section 1.1.2 the honinggrooves (texture) and plateaux (roughness) perform different functions inthe contact. Therefore it may be beneficial to be able to optimize thesedifferent scales independently and treat them separately in the simulation.

In this work a method of artifically generating surface texture is de-veloped so that the effect of adjusting different texture parameters can beseen individually. This work is then used to investigate the effect of honingangle on the PRCL contact. This was undertaken previously by Michailand Barber [14, 15] who similarly developed an analytical emulation of ahoned surface. Their study used Patir and Cheng flow factors and took thehoned surface to be a combination of cosine waves with the peaks removedto simulate the plateaux. It is suggested that the artificial surface texturepresented in this work could be a more realistic representation of the honedtexture.

1.3.3 PRCL Surface Characterization

The focus of this work described thus far has been on optimizing the cylin-der liner surface finish. However, it is also important to be able to effectivelycharacterize the surfaces involved. If an improved surface is developed, itmust be possible to describe it with some form of surface characterization so

1.3. OBJECTIVES 11

that it can be recorded and reliably manufactured. Without effective sur-face characterization, it would be very difficult to implement any optimizedsurface in production. Traditionally cylinder liners are characterized by ei-ther the ISO-13565-2 or ISO-13565-3 standards for the characterization ofcomponents with surface texture that have stratified functional properties.Although these parameters describe the topography of the surface neitherof them necessarily describe the ability of the surface to carry out its func-tion in a tribological contact. In the case of ISO-13565-2, the Abbott curvebased Rk parameters, it has been noted by Malburg et al. [16] that ‘stud-ies conducted by a major engine manufacturer have shown no correlationbetween these Rk parameters and engine performance’.

In this research the possibility of characterizing surfaces with functional‘flow factors’ is investigated. Characterizing the surfaces with flow factorsshould give better correlation to the performance of the contact and theparameters that are attempting to be optimized. Secondly, the effect ofmeasuring technique on both Rk parameters and flow factors is investigated.

The goal of this third objective is to find the most suitable and reliableway of characterizing the cylinder liner surface so that any surface improve-ments found as a result of simulations can be described in the best possibleway to be implemented in a manufacturing process.

Chapter 2

Measurement and Modellingof Cylinder Liner Surface

This chapter presents cylinder liner surface topography measurements. Threedifferent measurement techniques are introduced, evaluated and used tomeasure the current liner surface. The features of the surface are discussedand methods for artificially generating and simulating the surface are intro-duced.

2.1 Overview of Different Measurement Techniques

In the following sections three different techniques considered as suitablefor surface topography measurements of the cylinder liner surface are intro-duced and evaluated. Some key points about these techniques are mentionedand then a comparison between them is performed. The effect of scan sizeand sample interval is discussed and a method for choosing these parametersis detailed.

2.1.1 Stylus Profiliometry

Stylus profilometry (SP) has been and still is the technique that is mostcommonly used for measuring surfaces. In the past these have only beenperformed in 2D but now 3D measurements are also possible by takingmany 2D measurements side by side. However, these 3D measurementscan take a considerable amount of time. The time is dependent on scansize and can be several hours if measuring an area of similar size to thatachieveable with white light interferometry in less than a minute. Theroughness of the surface profile is typically underestimated with a stylus,especially for a soft surface when compared with a white light interferometry

13

14 CHAPTER 2. SURFACE MODELLING

measurement. This is due to the tip radius and the contact pressure ofthe stylus causing some deformation of the surface. The deformation isquite commonly permanent and it is possible to visually discern the traceof the tip. This implies that elastic deflection influences the recording ofprofile heights. To obtain high resolution measurements a small radius tipis necessary, however Poon and Bhushan [17] found that with a 0.1 µm tip,even with only 1 mg stylus load the surface measured (a glass-ceramic disc)was damaged to a similar amplitude as the underlying surface roughness.Stylus measurements are susceptable to low frequency noise in the timedomain, a longer measuring time can lead to more low frequency noise [17].It is suggested that because of this effect the filter cut-off length, in the timedomain, should be 10% of the total measurement time.

2.1.2 White Light Interferometry (WLI)

White light interferometry (WLI) provides a non-contact method for mea-suring a surface with a range of magnifications in a much shorter time thanthe other techniques discussed here. However, optical artifacts are likely tobe seen in this type of measurements. Steep slopes, such as the sides of hon-ing grooves, can show additional peaks of 0.1-0.5 µm [18]. The occurance ofthese artifacts is dependent on step height, Ohlsson et al. [18] found that atcertain step heights these additional peaks disappeared almost completelyand that they are not entirely predictable. This is something one pay extraattention to when evaluating surfaces, such as the cylinder liner because ofthe steps created by the honing procedure. Another limitation is that lightcan be reflected at too great an angle to be recorded and hence no heightdata can be obtained.

2.1.3 Atomic Force Microscopy (AFM)

AFM measurements can have an extremely high resolution compared tostylus profilometry or white light interferometry measurements, often evenhigher than the scanning electon microscope (SEM) technique [19]. In sev-eral studies AFM measurements of a surface are considered the benchmarkthat other techniques are compared to [17, 18]. Although the lateral reso-lution is much higher than the above-mentioned techniques, the range bothlaterally and vertically is limited (108x108 µm and 6 µm respectively withthe equipment that is available at Lulea University of Technology). Caremust be taken when conducting AFM measurements as external vibrationscan have a severe impact on the measurements, as can improper engagementof the tip onto the sample [17].

2.1. MEASUREMENT TECHNIQUES 15

2.1.4 Comparison of Techniques

Ohlsson et al. [18] compared the three techniques, SP, WLI and AFM,by measuring a range of engineering surfaces, a cylinder liner, steel roller,gear surface and steel sheet. With the AFM measurements as a benchmarkcalculation of roughness parameters, including the Rk set, showed a varia-tion of between 5-20%. Poon and Bhushan [17] conducted a similar study.They investigated the Rq, Rp and Peak to Valley (P-V) parameters andfound that the calculated results were ordered as WLI<SP<AFM, whilethe inverse was true for the correlation length, β∗.

2.1.5 Scan Size

The influence of scan size on roughness parameters was investigated withan AFM by Poon and Bhushan [17]. For the surface investigated, a glass-ceramic disc, the Rq, Rp and P-V parameters increased upto a scan sizeof 16x16 µm where after they stayed reasonably constant. The wavinessof most engineering surfaces will have a longer wavelength than the samplelength suggesting a larger scan size is needed. However, Poon and Bhushan[17] and does show that for a particular surface there is a limit of the requiredscan size at which the roughness parameters become independent of it. Thelong wavelength limit of the surface should be found or somehow estimatedand this should define the scan size. If this limit is found to be longerthan the contact width, then the entire contact width should be measured.The relationship between scan size and sampling interval is also an aspectto be taken into consideration. The reason for this is, as with most opticaltechniques (including the Wyko NT1100 at Lulea University of Technology)increasing the scan size increases the sampling interval as the number ofpoints is fixed at the number of pixels on the CCD.

2.1.6 Sampling interval

If the sampling interval chosen for a measurement is too small then the datapoints collected will be highly correlated and contain redundant information,however with an overly large sampling interval aliasing may occur. Poonand Bhushan [17] found that although Rq, Rp and P-V aren’t too sensitiveto sampling interval. The correlation length, β∗, was shown to increase ontheir surface with a sample interval of greater than 0.5 µm, due to highfrequency features disappearing in the measured data. They found thatthe optimum sampling interval was one sixth of the smallest wavelengthof interest, λ/6. However this depends on many factors, such as whetherelastic or plastic deformation of the surface occurs. In reality there is nonatural limit to the spatial size of features on most engineering surfaces;


finer and finer details are resolved as magnification increases all the waydown to the atomic scale. However, this level of magnification is almostcertainly unnecessary.

The autocorrelation length, β∗, represents the main wavelength struc-ture. It is reasonable to assume that using a fraction of this gives an ap-propriate sampling interval to collect details which are of significance to thecontact, i.e.,

τ = cβ∗, (2.1)

where τ is the sampling interval, β∗ is the correlation length and c is acontant to be found. Onions and Archard [20] derived an expression ofLoad/Area in terms of RMS surface roughness Rq, β∗ and effective Young’smodulus E∗. Using the Greenwood and Williamson approach [21], Poonand Bhushan [17] rearranged this formulation and after some substitution(see Appendix B of their paper) derived;

W

Ar= 0.7245

E∗Rq

τ, (2.2)

where W is Load and Ar is the real area of contact. Rq is defined as,

Rq =

(

1

n

n∑

i=1

z2i

)1

2

, (2.3)

where n is the number of points on the surface and z is the height of eachpoint. The effective Young’s modulus is defined as,

E∗ =1 − v2

1

E1+

1 − v22

E2

−1

, (2.4)

where v and E are the Poissions ratio and Young’s modulus of each materialrespectively. Subsituting Eq. (2.1) into Eq. (2.2) gives;

W

Ar=

0.7245

c

E∗Rq

β∗(2.5)

Poon and Bhushan [17] investigated the constant, c, using a 3D numericalrough surface contact model, described by Tian and Bhushan [22]. Theyfound that, independent of sample or measuring technique (AFM or WLI)a linear relationship between W/Ar and E∗Rq/β∗ could be drawn,

W

Ar= 1.88

E∗Rq

β∗, (2.6)

giving a value of c = 0.4. Therefore a sampling interval as a function of theautocorrelation length should be chosen according to,

τ = 0.4β∗. (2.7)

2.2. PRCL MEASUREMENTS 17

If the measurements are taken with a stylus instrument then the stylussize will limit the sampling interval. However β∗ increases as the stylus sizeincreases and therefore compensates for this effect. As β∗ is affected by thestylus size it is important to first analyse the sample at an interval whereβ∗ is found to be independent of sample interval.

2.2 Cylinder Liner and Piston Ring Surface Mea-surements

The three previously described techniques were used to measure a usedcylinder liner provided by Scania in four different locations. Fig. 2.1 illus-trates where the four samples were taken from on the liner surface. As canbe seen, sample 1 was taken close to TDC at a location where there wasvisible wear. Sample 2 was taken near BDC and Sample 4 was taken atapproximately the midstroke point where the lubrication regime should befully hydrodynamic. Sample 3 was taken close to the bottom of the linerbelow BDC at a location that the piston rings do not come into contactwith. This point should be completely unworn unless there has been anycontact from the piston skirt. Due to the limitations on the size of the

Figure 2.1: Location of samples on liner

sample that can fit in the AFM the four areas highlighted were cut outto produce smaller samples approximately 10x10mm in size. Two samplesfrom a top compression ring were also measured. Sample 5 was taked froma worn top ring (run against the measured cylinder liner) and Sample 6 wastaken from a new, unused top ring. Again, due to the sample size limita-tions in the AFM a small section was cut out from the piston ring oppositethe ring gap, illustrated in Fig. 2.2.


Figure 2.2: Sample cut from piston ring

2.2.1 SP measurements

A Talysurf stylus profilometer (SP) was used at Loughborough Universityto capture 2D line profiles of the surface. Although the measurement is notdirectly comparable with the 3D AFM or WLI measurements the SP wereconsidered for this study because this is the most commonly used methodto measure surfaces in industry. However, the Rk parameter set can becalculated and compared with the Sk parameters calculated from the AFMand WLI measurements (see Section 4.1). With each of the four cylinderliner samples three profiles were taken in the circumferential direction andthree in the axial direction, each 6 mm long. It was not possible to measurethe piston ring samples as these were not available at the time that themeasurements were taken. The standardized ISO 13565 filtering methodwas applied, whereby the first and last 1mm of the sample length werediscarded and the middle 4mm were kept, this being five times the appliedGaussian filter cutoff of 0.8mm.

2.2.2 WLI measurements

The WLI (White Light Interferometer) at Lulea University of Technology, aWyko NT 1100, is capable of taking measurements at nine different magni-fications depending on the chosen field of view (FOV) and objective (OBJ)lenses. Note that the amount of captured pixels is limited by the size ofthe CCD to 736x480 so the lateral resolution will vary depending on themagnification chosen. Table 2.1 lists the possible magnifications togetherwith the corresponding measurement area and lateral resolution (RES) they


Table 2.1: Wyko magnifications and corresponding resolutions

OBJ LENSE FOV LENSE AREA (µm) RES. (nm)

2.5 0.5 4960x3760 6741.62.5 1.0 2480x1880 3370.82.5 2.0 1240x940 1685.410 0.5 1240x940 1685.410 1.0 620x470 842.7010 2.0 310x235 421.3550 0.5 248x188 337.1650 1.0 124x94 168.5850 2.0 62x47 84.29

produce. In this study all the six samples, at each of the locations indicatedin Fig. 2.1 and Fig. 2.2, were measured with two different magifications, sixtimes each. The lowest magnification, with the 2.5X OBJ and 0.5X FOVlense was used to give a comparable measurement length to the stylus pro-filometer measurements. Secondly, the 50X OBJ and 1.0X FOV lenses wereused to provide a measurement area almost identical to the AFM measure-ments.

An issue that has been previously mentioned in Section 2.1.2 i.e. thatone of measuring samples with steep gradients on the surface, was encoun-tered with the relatively steep sides of the honing grooves. The WLI wasnot able to obtain some of the heights of points on the slope, this issue wasaddressed with the data processing procedure discussed in section 2.2.4 andthe results can be seen in Fig. 2.3.

(a) Before (b) After

Figure 2.3: WLI surface restore


2.2.3 AFM measurements

An Atomic Force Microscope (AFM) was also used to measure the same sixsamples measured with the WLI. The device was an NT MDT Ntegra andwas operated in contact mode with the probe scanner. The measurementscovered an area of 108x108 µm with 1024x1024 data points giving a lateralresolution of 105 nm, compared to 168.5 8nm for the WLI measurements.The scan velocity was 87 µm/s but the varied somewhat for different sam-ples, the rougher the sample the lower the value. On the roughest sample,sample 3 which was unworn cylinder liner, the scan velocity was 50 µm/s.A Silicon Nitride cantilever of type PNP-DB was used with a length of 100µm, force constant of 0.48 N/m and a tip radius of less than 10 nm.

(a) Unworn (b) Worn

Figure 2.4: AFM images of Piston Ring

(a) Unworn (b) Worn

Figure 2.5: AFM images of Cylinder Liner

The measurements took around 45 minutes each, thus taking consid-erably longer than the few seconds required for the WLI measurements.


However the benefits of the AFM technique were that the sides of the hon-ing grooves could be recorded and that the amount of points collected forthe measurements taken at each of the six samples was almost three timesgreater than that of the WLI.

2.2.4 Data processing of surface measurements

The raw data from the SP, WLI and AFM measurements was processedwith series of MATLAB routines developed in house. The procedure isillustrated in Fig. 2.6. Tilt removal fits a 2D linear polynomial to the surface

Figure 2.6: Process for importing raw data

and subtracts its gradient to project the data onto the xy-plane. Thisprocess is necessary for any surface that is imported from raw measurementdata because it is highly unlikely that the sample will have been positionedcompletely horizontally while being measured. However, care should alwaysbe taken when removing tilt from the measurement as it can alter the surfaceprofile. Chiffre et al. [23] demonstrate the effect of removing the slope ofa first order polynomial fitted to a sinusoidal profile. The slope removalcauses an asymmetry in the in the sinusoidal wave, which in turn alters the


Figure 2.7: Effect of tilt removal on a sinusoidal profile

values of the roughness parameters, an issue illustrated in Fig. 2.7. Theeffect of form is always present in a 3D measurement. something that is notalways the case with 2D measurements. Typically form is removed by fittinga polynomial of order n using the least squares method. The order, n, isimportant. The higher the better the fit to the profile but too high and it willcause unwanted changes to the original data. Chiffre et al. [19, 23] suggestthat a quadratic polynomial (n = 2) is used for ‘uni-curved’ surfaces (gears,bored holes). Anything greater than n = 4 makes little difference, howeverthe order chosen will have some effect and being consistent when chosingorder is very important. In this work curvature removal is performed byfitting a quadratic polynomial to the surface and then subtracting it. Thereason for choosing a quadratic polynomial is due to the inherent curvatureof the piston ring and cylinder liner.

With the AFM measurement there will be no missing data because atevery location on the surface a stylus height is recorded, whether it be areal or a false point. However with the WLI technique it is likely thatsome points in the measurement area will not be registered by the CCD.This can occur for a number of reasons, but is often because the surfacehas too high a gradient (such as the side of a honing groove) or there isa deposit on the surface that fails to reflect enough light. Therefore datarestoration is performed on all of the WLI measurements but on none of theAFM measurements. To restore missing points the Delaunay triangulationmethod is employed in combination with linear interpolation [24]. If linearinterpolation fails employing the nearest neighbour method can provide fordata restoration. However, this algorithm is likely to produce unwantedartifacts and one must pay extra attention to the final result.

The next process is to apply a low pass Gaussian filter to the surface

2.3. ARTIFICIAL SURFACE GENERATION 23

with a cut-off length set to four fifths of the sample length as per ISO 11562.This is done to remove any spikes that may be present in the data and isapplied to all measurements from either the SP, WLI or AFM technique.The final process, only necessary for the 3D surfaces, is to mirror the surface

Figure 2.8: Effect of mirring a honed surface showing unrealistic diamond-like patterns

in both the x- and the y- direction. This is done in order to remove theinfluence induced by non periodic boundaries and the effect this may haveon the flow factors computed for the surface under consideration. Care mustbe taken to ensure that the mirrored surface is representative of the originalsurface. If the original surface has a lay in a particular direction then theoperation of mirroring can create a final surface disimilar to the original.For honed finishes this is the case, see Fig. 2.8 for a graphical illustrationof this problem. Due to this difficulty mirroring is not applied to the lowmagnification WLI images but is applied to the higher magnification imagesand to the AFM images that only feature cylinder liner plateau and not thehoning grooves.

2.3 Artificial Surface Generation

To optimise the surface texture of a cylinder liner the performance of manydifferent topographies need to be investigated through simulations. Realsurface topography is only available for the current in-production liner. Ar-tificial liner surfaces will be generated to be able to simulate the performanceof different topographies. Another advantage of using artificial surfaces is


Figure 2.9: Measured Cylinder Liner Surface with WLI

that they can be made periodic, which makes a perfect match with theperiodic boundary conditions implemented in the next chapter.

The WLI surface measurements discussed in Section 2.2.2 were used as abasis for the artificially generated surfaces. An investigation of the surfaceshowed that although while the diamond like pattern on the surface wasnot uniform, the diamonds had a typical, or mean, area of approximately0.048 mm2 as highlighted in Fig. 2.9. In this study, to keep textures with

Figure 2.10: Artificial Honing Groove

different honing angles comparable, the area of each diamond will be keptconstant at this value. To generate a single groove Eq. (2.8) is used (taken

2.3. ARTIFICIAL SURFACE GENERATION 25

from [25]):

hT (x, y) = 10−w(x+ky)2 cos[2π(x + ky)]. (2.8)

In equation Eq. (2.8) two variables should be explained. The width of thehoning groove is set with w, this must be iterated for so that the desiredpercentage of plateau is achieved while the area is kept at the specifiedvalue. The k parameter is related to the desired angle of the honing grooveaccording to,

k =1

tanα, (2.9)

where α is the honing angle. A single diagonal groove is created usingEq. (2.8) as illustrated in Fig. 2.10. This single groove is mirrored in both

Figure 2.11: Artificial Surface

the x- and the y- directions to give one artificial diamond. This single di-amond is tiled to create a complete surface for the ring to slide over, seeFig. 2.11. The surface is long enough for the ring to be able to slide farenough, through enough time steps, for a steady state periodic solution tobe reached. The artificial surface only needs to be one diamond wide inthe circumferential direction since periodic boundary conditions are imple-mented in the solution. The depth of the artificial honing scratches is alsobased on the measured surface. Fig. 2.12 shows a typical cross-section. Itcan be observed that the honing depth has some variation. In this simula-tion a value of 2 µm has been used as a representative depth.

Figure 2.12: Cross Section of the Surface Profile

Chapter 3

All regime simulation of thePRCL contact

As discussed in Section 1.1.3 the PRCL contact goes through all regimes oflubrication, from boundary to full film during a single stroke in the combus-tion cycle. Therefore any simulation of the contact must be able to model allregimes of lubrication. The Lulea model has been adapted for this purposeand has been implemented to provide an all regime lubrication model. Thistechnique incorporates a mixed lubrication and contact mechanics modelusing measured surface topography [11].

3.1 Global problem and geometry

A small portion of the ring is modelled in two dimensions with periodicboundary conditions applied in the circumferential direction. This meansthat the pressure and film thickness at the top edge in Fig. 3.1 is the same asthat on the bottom edge. It is assumed that the ring is symmetric about itsaxis to make this assumption valid. Clearly this is not the case at the ringgap but as the ring has a much greater circumference than width it shouldbe valid for the majority of the contact. The ring geometry is modelledusing the equation:

h = hmin +x2

2R, (3.1)

where h is the film thickness, hmin is the minimum film thickness and R isthe ring radius.

27

28 CHAPTER 3. ALL REGIME SIMULATION

Figure 3.1: Global Geometry

3.2 Full film simulation

When the PRCL contact is in the full film lubrication regime the Reynoldsequation is solved to calculate the hydrodynamically supported load for agiven film thickness. The incompressible, time dependent Reynolds equationused in this model can be written as:

∂

∂x

(

h3 ∂p

∂x

)

+∂

∂y

(

h3 ∂p

∂y

)

= 6µUdh

dx+ 12µ

dh

dt. (3.2)

where p is the film pressure, µ is the lubricant viscosity and U is the en-trainment velocity. In this work the effect of surface roughness on fluid filmformation will also be included. The size of the global problem is approxi-mately 4 mm in the axial direction by 0.5 mm circumferentially. To be ableto resolve the surface roughness over the entire solution domain an extremelylarge grid size is required, in the order of several thousand nodes axially by

3.2. FULL FILM SIMULATION 29

several hundred nodes circumferentially. Solving for a grid size this big,incorporating a force balance and time dependence (discussed further inSection 5.2) is not viable within an acceptable period of time. Therefore,to reduce the grid size and thereby decrease the solution time the Reynoldsequation has been run through a mathematical homogenization procedure.

Homogenization can be regarded as a mathematical averaging techniquethat applied to the Reynolds equation allows the problem to be separatedto and then treated at two distinct scales, a ‘global’ and a ‘local’ scale.The thought behind this is that it allows the surface roughness scale tobe treated separately from the shape, or geometry, of the application andthereby a coarser grid can be used for the global problem. A homogenizedReynolds equation is solved, which incorporates ‘flow factors’ that modifythe solution to the global problem due to the effect of surface roughness.This homogenized Reynolds equation is written as:

∇ · (A0 (x, y)∇p0 (x, y)) = λ∇ · B0 (x, y) + γdh

dt(3.3)

where:

A0 =

(

a11 a12

a21 a22

)

and B0 =

(

b12

b22

)

(3.4)

where p0 is the homogenized film pressure, h is the average film thicknessat a given separation, λ = 6µU and γ = 12µ.

a11 (x) =1

|Y |

∫

Yh3 (x, y)

(

1 +∂ω1

∂y1

)

dy,

a12 (x) =1

|Y |

∫

Yh3 (x, y)

∂ω2

∂y1dy,

a21 (x) =1

|Y |

∫

Yh3 (x, y)

∂ω1

∂y2dy,

a22 (x) =1

|Y |

∫

Yh3 (x, y)

(

1 +∂ω2

∂y2

)

dy,

b12 (x) =1

|Y |

∫

Y

(

h (x, y) − h3 (x, y)∂υ1

∂y1

)

dy,

b22 (x) =1

|Y |

∫

Yh3 (x, y)

∂υ1

∂y2dy.

(3.5)


w1, w2 and v1 solutions to the following (periodic) local problems;

∇y ·(

h3∇yυ1

)

= ∇y · (e1h) on Y,

∇y ·(

h3∇yω1

)

= −∇y ·(

e1h3)

on Y,

∇y ·(

h3∇yω2

)

= −∇y ·(

e2h3)

on Y,

(3.6)

with periodic boundary conditions in both directions, where e1 = (1, 0)T

and e1 = (0, 1)T . The work of Almqvist et al. [26] should be seen for a fullexplanation and derivation. These equations are solved on the local scaleover a representative, periodic section of surface roughness for a range ofdifferent surface separations to produce a set of flow factors. The flow fac-tors are then incorporated into the homogenized Reynolds equation whichis solved on the global scale. The roughness incorporated within the flowfactors should have a wavelength that is sufficiently smaller than the widthof the contact for this approach to be suitable. This is illustrated in Fig. 3.2.The smaller the wavelength (ε) of the surface roughness that is incorporated

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3x 10

7

x/L

Pre

ssur

e (P

a)

SmoothHomogenizedDeterministic

Figure 3.2: Convergence of pressure solution with decreasing ε [26]

into the flow factors, the closer the homogenized solution fits the determin-istic one. It is generally found that the roughness, or local scale, wavelengthshould be at least ten times smaller than the contact width.

3.3 Mixed and Boundary simulation

The mixed lubrication regime begins when the highest peaks of the surfaceasperities start to support some of the load. A contact mechanics model is

3.4. CAVITATION 31

implemented to simulate how the asperities support the load as the surfacesmove closer together. The contact mechanics model implemented is anelasto-plastic Boussinesq type solution as described by Sahlin et al. [11]. Inthe mixed regime the supported load will be shared between the asperityinteractions and the hydrodynamically supported load. This hydrodynamiccontribution is calculated as previously discussed in Section 3.2. By solvingthe Reynolds equation in the regions where the surfaces are not in contact.

3.4 Cavitation

Cavitation in an oil film occurs when the fluid is unable to sustain largeand continuous negative pressures. A cavity, or cavities, of gas form withinthe body of the fluid. In this section experimental evidence for cavitationoccuring in the PRCL contact is discussed and then the cavitation algo-rithms used in Paper A and Paper B are introduced. In all the simulationspresented in this work cavitation is considered on the global scale but noton the local scale within the flow factor calculations, i.e., inter-asperitycavitation is not considered.

3.4.1 Cavitation Algorithms

The two cavitation algorithms presented here are both solutions for approx-imating cavitation when solving the Reynolds equation with finite differ-ences. Both algorithms are based on the same general principle, which willbe introduced here and in the following subsections the differences betweenthe two techniques are detailed. The algorithms allow the film pressure tobe modelled with a single ‘universal’ differential equation. Terming it uni-versal is due to it applying not only in the region where a full film is presentbut also in the cavitated region with mass conservation at the boundarybetween zones. These two zones are defined as follows:

• Full Film zone - Where the standard Reynolds equation applies. Thelubricant pressure varies above the cavity pressure.

• Cavitated zone - Only a fraction of the conjunction is filled with lubri-cant and striations may occur [27]. The lubricant pressure is constantat the cavity gas pressure. The striations have the linear velocity pro-file of Couette flow. It is acknowledged that some oil will attach tothe moving surface in the gas filled area, but this is neglected.

Cavitation can either be ‘open’ or ‘closed’ depending on whether reformationoccurs, see Fig. 3.3. The oil film will rupture and switch between being in the


(a) Open (b) Closed

Figure 3.3: Cavitation types

full film zone and the cavitated zone at the Reynolds boundary condition:

p = 0,∂p

∂x= 0. (3.7)

If film reformation occurs and the cavitated zone becomes full film againthis will occur at the JFO [28] boundary condition:

h2

12µ

∂p

∂n=

Vn

2(1 − θ) , (3.8)

where Vn is the lubricant entrainment speed and θ is the fractional filmcontent, defined as;

θ =ρ

ρc, (3.9)

where ρ is the lubricant density and ρc is the density of the lubricant atthe cavitation pressure. From here the derivations of the two algorithmsdiffer. They are described separately in the following sections along withthe advantages and disadvantages of using them in simulations of the PRCLcontact.

Vijayaraghaven - Paper A

In Paper A the Vijayaraghaven and Keith [29] algorithm is used when solv-ing the Reynolds equation to implement boundary conditions at film rup-ture and reformation. The approach is similar to the Elrod algorithm [30]but with two advantages; compressibility is considered in the full film zoneand the discretisation is rigorously derived, rather than being the result ofconsiderable experimentation. The Reynolds equation is written as;

d

dt(ρchθ) +

d

dx

(

ρchU

2θ −

ρcβh3g

12µ

dθ

dx

)

+d

dy

(

−ρcβh3g

12µ

dθ

dy

)

= 0, (3.10)

3.4. CAVITATION 33

where g is a switch function becoming 1 in the full-film zone and 0 in thecavitated zone and β is the compressibility factor. The type of zone iscalculated from the value of θ, above 1 the region is full-film and below 1the region is cavitated. The film pressure is found from θ;

p = pc + gβlnθ (3.11)

Once the discretization has been applied Eq. (3.10) can be written in theform:

awθi−1,j + aeθi+1,j + anθi,j−1 + asθi,j+1 + apθi, j = rhs, (3.12)

where;

aw = U(chi−1,j)

4∆x− C1 (hwgw)

ae = U(ahi+1,j)

4∆x− C1 (hege)

an = −C2 (hngn)

as = −C2 (hsgs)

ap = U(bhi,j)

4∆x+ C1 [(he + hw) gp] + C2 [(hn + hs) gp] −

hp

∆t

rhs = −C1 [hege − (he + hw) gp + hwgw] − C12 [hsgs

− (hn + hs) gp + hngn] −h∗

pθ∗

i,j

∆t

(3.13)

with the Couette flow coefficients;

a =gi+1,j + gi+1,j

2

b = 2 −gi+1,j + gi+1,j

2

c =gi+1,j + gi+1,j

2

(3.14)

Poiseuille flow coefficients;

C1 =β

12µ∆x2

C2 =β

12µ∆y2

(3.15)


A linear system of equations is formed and θ is solved for directly. Once θhas been found the switch function, g, is updated at every node based on thecalculated value of θ. If θ is greater than 1 then g is set to 1, if θ is less than 1g is set to zero. This process is repeated, θ is solved for and the value of g isupdated based on the new result, until convergence is reached. Convergenceis assumed to have been reached when the change in θ at any node was lessthan 10−4 and there were no changes in g. As the solution to θ is founddirectly this cavitation algorithm was found to be several times quicker thanthe Ausas solution (described in section 3.4.1). However, when the nominalfilm thickness between the piston ring and cylinder becomes smaller than1 µm, spikes begin to appear at the boundary between the full film andcavitated zones, see Fig. 3.4. This problem was not encountered with theAusas algorithm.

Figure 3.4: Spikes in the Vijayaraghaven solution

Ausas - Paper B

In work by Ausas et al. [31, 32] the Reynolds equation is written as;

h3

(

∂p

∂n

)

= h (1 − θ+) e1 · n ≥ 0 (3.16)

and then discretized to give:

si,jpi+1,j − (si,j + si−1,j) pi,j + si−1,jpi−1,j + q2 (si,j+1pi,j+1

− (si,j+1 + si,j) pi,j + si,jpi,j−1) = (ci,j − ci−1,j) ∆x1

(3.17)

where;

si,j = θi,j (hi,j)3 , ci,j = θi,jhi,j , q =

∆x1

∆x2(3.18)

3.5. FRICTION 35

where the following has been assumed;

∂p

∂x1

∣

∣

∣

∣

i,j

=pi+1,j − pi,j

∆x1,

∂p

∂x2

∣

∣

∣

∣

i,j

=pi,j − pi,j−1

∆x2(3.19)

To solve the problem a Gauss-Seidel iterative process is used in which nosystem of linear equations is needed. When implemented in Matlab, thiscavitation algorithm is slower than the Vijayaraghaven approach, howeverno stability issues are encountered. Therefore it is used in the full enginecycle models presented in Paper B where thin films are encountered. TheVijayaraghaven algorithm is found to be unsuitable for full engine cyclemodels due to the spikes encountered with thin films.

3.5 Friction

The calculated friction force is comprised of two elements, viscous full filmfriction and boundary contact friction. The boundary friction is calculatedfrom:

Fbound = η

∫

ΩPcpdA (3.20)

Pcp is the mean contact pressure which is found from the contact mechanicsmodel described in [33, 11]. The viscous full film friction is calculated withadditional flow factors c11, c11 and d12 using [11]:

F0 = −

∫

ΩµU

(

1

h+ 6c11

)

−

((

−h

2+ d11

)

∂p0

dx+ d12

∂p0

dy

)

dxdy (3.21)

Where h is the average film thickness at a given separation.

Chapter 4

Characterization of SurfaceTopography

Typically, engineering surfaces are characterized with traditional roughnessparameters that perform some type of height averaging across the surface.Two of these groups, the Rk and Rq parameter sets (designated Sk and Sq

when applied to 3D surfaces rather than 2D profiles) are designed for sur-faces with stratified functional properties and are often used to characterizecylinder liner topography. Although these parameters describe the topog-raphy of the surface, neither of them necessarily describe the ability of thesurface to carry out its function in a tribological contact. They also ignoreadditional information that can be provided by a 3D data set [34] comparedto a 2D one.

Care should also be taken when using roughness parameters that wereoriginally used for 2D measurements and applying them to 3D surfaces,especially when making comparisons. For example, with a random Gaussiandistributed surface Rp < Sp [17]. Generally, 2D parameters are smaller than3D parameters. Pawlus et al. [35] found that Rk was 25% smaller on averagethan Sk for the surfaces that they investigated. There are several reasonsfor these differences, including different places of measurement, scan length,filtering and measurement technique.

In this section, the traditional Rk parameters (based on the Abbottcurve) have been calculated as well as functional ‘flow factors’ which modifythe Reynolds equation to incorporate the effects of surface topography. Tocalculate flow factors the homogenization technique has been implementedand a full 3D contact mechanics model has been incorporated. By doingso, surface functionality in mixed lubrication can be studied, as discussedin Chapter 3. Furthermore, the Rk parameters and flow factors have beencalculated for both WLI and AFM surface measurements (as discussed in

37

38 CHAPTER 4. SURFACE CHARACTERIZATION

Section 2.2) so that the effect of measuring technique on roughness andfunctional parameters can be investigated. Rk parameters have also beencalculated from 2D stylus measurements so that a comparison between 2Dprofile and 3D surface results can be made.

4.1 Rk parameters - ISO 13565-2

The Rk parameters are based on the Abbott curve and attempt to indi-vidually define the peaks, valleys and plateaux of a surface with differentnumerical parameters. The red line in Fig. 4.1 illustrates a typical Abbott

Figure 4.1: Abbott curve parameters

curve. To obtain the Abbott curve for a 2D profile or a 3D surface theheight range is first divided into ‘bins’ and the percentage of material thatfalls into each of these bins is plotted against the bin height. This yields theheight distribution of the surface. The Abbott curve is related to the cu-mulative distribution of surface heights and hence can be obtained from theheight distribution. To calculate the numerical parameters, a straight linemust be plotted through the 40% of the curve with the shallowest gradient,giving the green line in Fig. 4.1. Rk is defined as the change in height ofthis green line across the width of the graph, between 0% and 100% asperityheight distribution. Rpk is the difference between the highest point on thesurface minus the height of the green line at 0% asperity height distribu-tion. Similarly, Rvk is the difference between the height of the green lineat 100% asperity height distribution minus the height of the lowest pointon the surface. Mr1 is the percentage of surface heights classified as peaks

4.1. RK PARAMETERS - ISO 13565-2 39

Table 4.1: Rk parameter definitions

SYMBOL DEFINITION

A1

∫ A−1(c1)

0(A(x) − c1)dx

A2

∫ 100

A−1(c2)(A(x) − A(100))dx

Mr1 A−1(c1)

Mr2 A−1(c2)

Rk c1 − c2

Rpk A(0) − c1

Rvk c2 − A(100)

by Rpk. In other words, Mr1 is a material ratio that defines the ratio ofmaterial that counts as peaks. At the other end of the scale, Mr2 is thepercentage of surface heights classified as valleys by Rvk. Finally A1 is thearea enclosed by the Abbott curve in the Rpk region and A2 is the areaenclosed by the Abbott curve in the Rvk region. Mathematically, these pa-rameters are defined in Table 4.1. For a cylinder liner Rk can be used todescribe the roughness height after the running in process and Rvk the oilaccumulation in the honing grooves. Weidner et al. [36] have developed‘structural’ parameters. Using the Abbott curve, they separate the peakand valley regions into a number of different structural parameters. Theyalso found that by setting the mean reference line, the zero point, to thepoint of highest material density the core region to calculate Rk was ap-proximated best. This was achieved by using Gaussian regression filtersand alignment operators. An algorithm was implemented to not only cal-culate the Rk group but to detect honing angle, volume, orientation andorientation affinity (round or rectangular). Bigerelle and Iost [37] clearlydescribed an algorithm to calculate the Rk parameters. They found withmost engineering surfaces anything more than 250 intercept lines (the binsused to produce the Abbott curve) was enough to be independent of the


calculated roughness parameters. It is important that the outcome of thehoning process, or any other surface finishing process, is represented by theroughness parameters. In regard to the Rk parameters, Malburg et al. [16]state ‘Studies conducted by a major engine manufacturer have shown nocorrelation between these Rk parameters and engine performance’. A singlehoning process produces a gaussian distribution, which leads to an Abbottcurve with a point of inflection at the 50% mark. There are no distinguish-ing points along it. Zipin [38] highlights that most manufacturing processesproduce a surface that is approximately normally distributed. When thesesurfaces are plotted as an Abbott curve, distinct peak and valley regionsare apparent even though they represent portions of the surface profile thatcome from the same height distribution. Zipin derives that for a normallydistributed surface a direct relation Rpk = Rvk = 2.189Ra exists. Rpk

becomes very unstable when applied to 3D measurements [35].

It is suggested that the Rq parameter set, described in the next section,with normal probability coordinates on the x-axis, is a better representationof the surface. This is because in the case of a normally distributed surfaceas investigated by Zipin, the Abbott curve becomes a straight line whenplotted with normal probability coordinates, i.e., evidence that you cannot split the surface into distinct peak and valley regions. Also, a cleardistinction in gradient is shown for each honing process. However, in thisstudy the Rk set was chosen to be investigated further as this is commonpractice in the European automotive industry.

4.2 Rq parameters - ISO 13565-3

Several authors suggest that the Rq parameter set is a better alternativeto the Rk group for describing surfaces [35, 39]. For a honed surface, eachmachining step, first the coarse and then the fine grit, give two distinctslopes on the Rq graph. There is a better link to multiple processes andtherefore better process control, as well as correlation with the physicalhoning parameters. Rvq is affected by coarse grit size, Rpq by plateau gritsize and Rmq by plateau honing time. Pawlus et al. [35] found that with a2D analysis of the surface neither the Rq or Rk family of parameters weremore stable with respect to repeatability, however with a 3D analysis theRq parameters were more stable.

4.3 Rk parameters from 2D and 3D measurements

In the previous section it was suggested that there can be a difference be-tween the Rk parameters when calculated by different means and in either

4.4. RK PARAMETERS 41

Table 4.2: Comparison of Rk and Sk parameters

Sample Ra Rk Rpk Rvk Mr1 Mr2

1 2D 0.28 0.61 0.14 3.23 6.86 80.653D 0.15 0.36 1.20 3.76 9.72 83.59

2 2D 0.63 0.52 0.09 5.42 2.43 61.353D 0.40 0.47 1.10 5.00 6.39 72.96

3 2D 0.51 0.68 0.81 5.95 6.93 77.183D 0.31 0.62 1.64 5.83 8.26 81.38

4 2D 0.56 0.79 0.07 3.74 1.69 67.203D 0.45 0.67 1.11 5.13 4.84 71.93

2D or 3D. This will now be investigated. For the 2D SP and 3D WLI mea-surement techniques described in Section 2.2 the Rk and the Sk parametersets have been calculated. WLI measurements with a 2.5X OBJ and 0.5XFOV lense were used to give a sample area of 5.0 × 3.8 mm to comparewith the SP measurement length of 6 mm. All surfaces had tilt and cur-vature removed and a Gaussian filter applied and the WLI measurementshad the missing data restored by means of the method described in Section2.2.4. The results are presented in Table 4.2. Each sample was measuredsix times with each technique and the results presented in the table are theaverage the six measurements for each sample. It can be seen in Table 4.2that there can be a large variation between the 2D and 3D measurements.In the case of Ra and Rk values the 2D stylus measurements always givea higher value. However the inverse is true with the Rpk values where thestylus values are significantly lower to a different order of magnitude. Itis suggested that this could be caused by the stylus deforming some of thepeaks that it passes over leading to a somewhat flattened profile. The Rvk

values for both measurement techniques are rather similar.

4.4 Rk parameters from AFM and WLI measure-ments

A second comparison was made between the AFM and WLI measurements.For this purpose, a magnification was chosen for the WLI measurements togive an almost identical area to the AFM measurements. However the res-olution was considerably higher with the AFM measurement having almostthree times as many data points across the sample area. Fig. 4.2 illustratesthe two different measurement areas. In this study the piston ring sam-ples, worn and unworn, were measured along with Sample 1 and Sample


Figure 4.2: Comparison of measurement areas with WLI and AFM tech-niques.

0 50 100−2

−1

0

1

2

Asperity height distribution (%)

Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(a) Unworn

0 50 100−1.5

−1

−0.5

0

0.5

1


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(b) Worn

Figure 4.3: Cylinder Liner Abbott Curves

3 of the cylinder liner, the most and least worn respectively. Each samplewas measured six times with each measurement technique and the averagevalues are presented in Table 4.3. The Abbott curves have been plotted forall four samples so that a comparison can be made between the curves pro-duced from the AFM measurements and those from the WLI measurements.All four Abbott curve plots exhibit a similar difference in profile between

the AFM and WLI measurements. The WLI measurements have a steepergradient and a larger amplitude range than the AFM measurements. Onthe left side of the graphs, in the peaks region, the WLI measurements cancreate anomalous peaks around the honing grooves as discussed in Section2.1.2. This leads to a steeper Abbott curve in this region than is actuallythe case. Also, the AFM, with its contacting stylus, can flatten the surface

4.5. FLOW FACTORS 43

0 50 100−1.5

−1

−0.5

0

0.5

1


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(a) Unworn

0 50 100−1.5

−1

−0.5

0

0.5

1


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(b) Worn

Figure 4.4: Piston Ring Abbott Curves

Table 4.3: Rk values


Worn Liner AFM 0.05 0.15 0.21 0.43 13.78 92.25WLI 0.17 0.50 0.57 0.84 8.25 85.99

Unworn Liner AFM 0.11 0.33 0.30 0.34 6.20 85.89WLI 0.21 0.68 0.78 0.78 9.33 88.81

Worn Ring AFM 0.05 0.16 0.21 0.15 12.86 91.33WLI 0.16 0.43 0.49 1.02 6.46 82.23

Unworn Ring AFM 0.02 0.05 0.12 0.14 14.89 89.97WLI 0.10 0.27 0.38 0.97 7.61 84.24

leading to a flattened curve in the peaks region. These two reasons go to-wards explaining the difference between the AFM and WLI measurementson the left side of the Abbott curves. On the right side of the Abbott curves,in the valleys region, the WLI again exhibits a steeper gradient than theAFM. This could be because the AFM stylus is not reaching the bottom ofsome of the honing grooves, a problem that is not apparent with the WLImeasurements. The Rk numerical parameters for these Abbott curves aresummarised in Table 4.3.

4.5 Flow Factors

For the surface measurements of the four samples discussed in Section 4.4,flow factors have also been calculated using the homogenization methodincluding contact mechanics for the mixed lubrication regime as outlinedin Chapter 3. The results are presented in Fig. 4.5 and Fig. 4.6 for the


−2 −1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

α / αc

Nor

mal

ized

flow

fact

or

AFM − Worn C.L.WLI − Worn C.L.AFM − Unworn C.L.WLI − Unworn C.L.AFM − Worn P.R.WLI − Worn P.R.AFM − Unworn P.R.WLI − Unworn P.R.

Figure 4.5: a11 flow factors

−2 −1 0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

α / αc

Nor

mal

ized

flow

fact

or


Figure 4.6: a22 flow factors

pressure flow factors, Fig. 4.7 for the shear flow factors and Fig. 4.8 forthe asperity contact pressures. Flow factors have been calculated for 55different separations, 30 in the hydrodynamic regime and 25 in the mixedregime. The flow factors presented here are normalized when plotted on the

4.5. FLOW FACTORS 45

−2 −1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

α / αc

Nor

mal

ized

flow

fact

or


Figure 4.7: b22 flow factors

0 0.2 0.4 0.6 0.8 1

x 10−6

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

8

h / hc

Uni

t Con

tact

Pre

ssur

e (P

a)


Figure 4.8: Contact Pressures

graphs. The pressure induced flow factors are normalised against h3 andthe shear induced flow factors normalised against h. The normalized flowfactors are plotted against α/αc, where α is the rigid body global separationand αc is the value of α where the first asperity contact occurs. Therefore avalue of 1 on the x- axis marks the point between mixed and hydrodynamic


lubrication.In Fig. 4.5, Fig. 4.6 and Fig. 4.7, a clear difference in behaviour can be

seen between the red curves of the unworn cylinder liner and the blue curvesof the worn cylinder liner for the pressure and shear flow factors, showingthat flow factors can clearly differentiate between surfaces with differentlevels of wear. There is also a differentiation, but much smaller, betweenthe black lines of the unworn ring and the green lines of the worn ring.However, it was to be expected that less difference would be seen with thering samples, as they are hard chromium and suffer only minimal wear.

The flow factors presented here also show good correlation between thosecurves calculated from AFM measurements and those from WLI measure-ments. Each of the four surfaces are clearly separable from each otherdespite whether the WLI or AFM measurement is considered. This is notthe case with the Rk parameters in Table 4.3 which show more deviationbetween measuring technique than they do between different samples.

Therefore, it is suggested that flow factors may prove a more repeatabletechnique for charaterising surfaces that is much more independent of mea-suring technique than the Rk parameter set. Furthermore, flow factors bytheir very definition correlate directly to the functional performance of thetribological contact which is not the case for the Rk parameters.

Chapter 5

Full engine cycle simulations

In this chapter simulations of the full four stroke engle cycle are described,which utilise the all regime model presented in Chapter 3. The cylinderliner surface texture is described on the global scale with the artificial sur-face texture generated in Section 2.3. The roughness of the cylinder lineris described using flow factors calculated from WLI measurements of thecylinder liner plateaux.

5.1 Model inputs

To simulate the PRCL contact several inputs describing the running condi-tions of the engine are required. The entraining motion of the piston ringis related to the engine speed by:

U =πLNsinφ

60

1 +

cosφ(

(

2aL

)2− sin2 φ

)1/2

, (5.1)

where L is the engine stroke, N is the engine speed in RPM, φ is thecrank angle and a is the ratio of connecting rod length to crankshaft radius.As described in Section 3.1, the combustion chamber and first land gaspressures are required as the boundary conditions for solving the Reynoldsequation across the global geometry problem. They are also required tosolve the force balance described in the next section. The gas pressures forthree different engine speeds at full load were provided by Scania from aseparate numerical model they have developed with the commercial AVLRingPack software, shown in Fig. 5.1.

47

48 CHAPTER 5. FULL ENGINE CYCLE SIMULATIONS

0 100 200 300 400 500 600 7000

50

100

150

200

250

Crank Angle (°)

Pre

ssur

e (B

ar)

1200RPM Combustion Chamber1200RPM Inter−ring1600RPM Combustion Chamber1600RPM Inter−ring1900RPM Combustion Chamber1900RPM Inter−ring

Figure 5.1: Gas pressure variation with crank angle.

5.2 Force balance and time dependence

An iterative procedure is used to calculate the value of hmin required for thelubricant film pressure to support the opposing load, a combination of thegas pressure acting on the back of the ring and ring tension. This balanceis defined as:

∫

Ω

∫

Ωpdxdy = max (pin, pout)wl +

2Ftw

d(5.2)

The fzero algorithm in Matlab is used to find the required hmin to balancethese forces. This is a combination of the bisection, secant, and inversequadratic interpolation methods. Once the force balance has been satisfiedthe solution increments one time step, equating approximately 0.5 crankangle depending on engine speed. A new gas pressure, piston speed and tem-perature are found and the force balance is solved again. As the Reynoldsequation implemented is time dependent, more than one complete enginecycle must be simulated for the entire solution to converge. The discretizedtime dependent term needs a solution from the previous time step. For thefirst crank angle solved for this information is not available. An initial filmthickness must be guessed; in the simulations presented here a guess of 1µm is made at 360 crank angle. After one complete engine cycle the film

5.2. FORCE BALANCE AND TIME DEPENDENCE 49

thickness and change in film thickness with time (gradient) are compared tothat found on the previous cycle and the simulation is stopped when theseare within a specified tolerance. Typically this requires 1.1 engine cycles.The results for minimum film thickness and friction as a function of crankangle are presented in Fig. 5.2 and Fig. 5.3.

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

Crank Angle (°)

Film

Thi

ckne

ss (µ

m)

1200RPM1600RPM1900RPM

Figure 5.2: Minimum film thickness variation with crank angle.

Shortly after TDC and peak combustion pressure, the film thicknessreaches a minimum of 0.05 µm at a crank angle of 14. Approximatelyhalfway down the intake stroke, at a crank angle of 445, the film thicknessreaches a maximum of 5.22 µm. With a measured plateau Ra value of 0.05-0.21 µm this proves the earlier stated assumption that the PRCL contactoperates throughout all lubrication regimes. At full load with a lower enginespeed the oil film becomes thinner. This is due to a lower entraining speedand higher combustion pressure (see Fig. 5.1), as predicted by Fig. 1.3.

When running these simulations it has been assumed that the inlet tothe contact is always fully flooded. This means that it is assumed that at allparts of the stroke there is always enough oil present on the cylinder linerto fully flood the inlet. This may be a valid assumption at the ends of thestroke where an oil film a fraction of a micro thick is predicted, but in themidstroke with a > 5 µm predicted minimum film thickness it is unrealisticto assume that there will be this volume of oil available.

The friction data presented as a function of crank angle in Fig. 5.3 is a

50 CHAPTER 5. FULL ENGINE CYCLE SIMULATIONS

0 100 200 300 400 500 600 7000

200

400

600

800

1000

1200

1400

Fric

tion

(N)

Crank Angle (°)


Figure 5.3: Friction variation with crank angle.

combination of boundary and viscous friction. There is an extremely largepeak at 18-20 crank angle soon after where combustion occurs. The bound-ary friction is predominant however the piston is travelling at a reasonablespeed and so there is also a notable viscous contribution. The viscous fric-tion is at its highest just past the centre of the engine stroke, obviouslywhen the film thickness is highest. At BDC and TDC between the exhaustand intake stroke friction is negligible. The piston velocity is zero so thereis no viscous contribution and the time dependent squeeze effect keeps thelubrication regime hydrodynamic as the combustion gas pressure is low.

It should be recalled that the real factor in increasing engine effeciencyis to minimise power losses from the engine, not friction. Power losses arecalculated from friction multiplied by piston velocity. Although there arevery high values of friction just after TDC on the expansion stroke thepiston has a low velocity compared to the midstroke. During the midstrokethe friction is much lower but the piston speed is much higher. Reducingfriction is always desirable, however to meet the end goal of increased engineefficiency it is important to minimise power losses, not friction.

Chapter 6

Conclusion and Future Work

In this Chapter the results of the research presented in this licentiate the-sis are summarised. Future work, to continue with the development of asimulation tool, to assist in optimising cylinder liner surface texture is alsodiscussed.

6.1 Conclusion

The work presented here had three objectives, to implement an all-regimehomogenization based model in a PRCL simulation, develop a process formodelling cylinder liner surface texture with adjustable geometric param-eters and investigate functional methods of characterizing surface topogra-phy.

The Lulea all-regime model has been implemented in a time dependentfull engine cycle simulation with periodic boundary conditions and textureand roughness modelled on separate scales. It was found that it is moreaccurate to include the surface texture in the global scale with a deter-ministic solution rather than within flow factors. This is contrary to themethod employed in many existing simulations, which lump together tex-ture and roughness in one set of flow factors. This approach also allowsthe effect of texture and roughness to be investigated independently, and asthey are each products of a different stage of the honing process this maybe beneficial in optimizing surface texture.

A solution has been developed to generate artificial surface texture basedon real honing geometry. Honing angle, depth, width and surface coveragecan all be adjusted. Furthermore, the artificially generated surface is peri-odic and so can be used with the periodic boundary conditions implementedto solve the global problem. This solves another problem with using real,measured surface topography that is not naturally periodic and becomes un-

51

52 CHAPTER 6. CONCLUSION AND FUTURE WORK

representative if mirrored to create periodicity. Using this artificial surfacetopography allows for individual honing parameters to be adjusted indepen-dent of anything else.

Flow factors have been investigated as a means of characterizing an en-gineering surface based on its functionality or performance. It was foundthat, not only can surfaces with different levels of wear be clearly differenti-ated between with flow factors, but that the result was almost independentof measuring technique, AFM or WLI. This was not found to be the casewith the traditional Rk parameter set, which varied significantly betweenSP, WLI and AFM measurements.

6.2 Future Work

One of the main purposes of applying honing to the cylinder liner is to retainand distribute oil on the surface. Without an oil availability model such asthat presented by Tian [40], these benefits and the effect changing honingparameters has on them, cannot be studied. Another reason for developingan oil availability model, is so that the inlet condition can be adjusted fromfully flooded to a level dependent on how much oil is available on the liner.To be able to model the quantities of oil on the liner the full ring pack willneed to be simulated.

Another important task for the future is to perform Cameron Plint re-ciprocating test using liner and ring samples as a first step to fully validatingthe model. Scania will provide cylinder liners with different honing texturesand these will be simulated using the Lulea model and then, tested in therig in order to validate the model.

Figure 6.1: Comsol Compression Ring model

6.2. FUTURE WORK 53

The global scale of the problem will also be investigated. Rather thanjust investigating a small periodic segment of the contact, the entire ringgeometry will be simulated to investigate the effect implementing a non-axisymmetric solution will have. Fig. 6.1 illustrates work in progress on aComsol Multiphysics model of the top compression ring. Fluid film pressureis found by solving the Reynolds equation and the film thickness is coupledwith the global deformation of the ring caused by the combustion gas andhydrodynamic film pressures.

54 CHAPTER 6. CONCLUSION AND FUTURE WORK

Part II

Appended Papers

55

Paper A

57

59

Submitted to Proceedings of the Institution of Mechanical Engineers,

Part J: Journal of Engineering Tribology - NordTrib Special Issue

A numerical model to investigate the effect of honingangle on the hydrodynamic lubrication between acombustion engine piston ring and cylinder liner

A. Spencer1, A. Almqvist, R. Larsson

Lulea University of Technology, Department of Mechanical Engineering, Division

of Machine Elements, Lulea SE-971 87 Sweden

Received 4 October 2010

AbstractA numerical model has been developed to investigate the effect of cylin-der liner honing angle on hydrodynamic lubrication between piston ringand cylinder liner. The Reynolds equation was solved in 2D with periodicboundary conditions. An artificial surface texture was generated, based on areal surface measured with white light interferometry. Cavitation was mod-elled with the Vijayaraghavan and Keith algorithm. Honing angles between25−75 were investigated to find the effect of honing angle on film thickness.

Keywords: Cylinder Liner, Honing, Texture

1Corresponding author.E-mail address: [email protected]

60 PAPER A.

A.1 Introduction

Typically for a medium size car over an urban cycle only 12% of the totalpower from the fuel is converted to useful energy at the wheels [1]. Therest of the energy from combustion of the fuel goes into cooling, exhaust,pumping and mechanical losses. The mechanical contribution amounts to17% [1] of the total losses and the friction between the piston assembly andcylinder liner is the single largest contributor; amounting to 20-40% of thetotal mechanical losses [2]. Furthermore, the compression rings typicallycontribute 4-5% of all mechanical losses in a multi-cylinder engine [3]. Ifthese mechanical losses can be reduced by 10% then fuel efficiency could beincreased by between 1.5-2.5% [1, 3]. Therefore the study of the piston ringcylinder liner conjunction (PRCL) is highly important in reducing frictionand improving fuel economy, one of the main drivers in engine design today.

Usually a cylinder liner is honed to apply the desired surface finish.With modern plateau honing [41] the finished surface consists of relativelysmooth plateaux separated by grooves that lie at two opposing angles toform a crosshatch pattern. The flat plateaux provide a smooth surfaceto allow for hydrodynamic film build up between the piston rings and thecylinder liner surface. The grooves serve two purposes; primarily they actas an oil reservoir. The only available oil for lubrication is supplied to thecontact by the movement of the piston rings on the upstroke; this oil isretained in the grooves to lubricate the contact on the piston downstroke.A secondary reason for the grooves is to transport wear debris away fromthe contact. Small particles can be swept downwards in the grooves towardsthe crankcase and hopefully cause only minimal scratching to the smoothplateau surfaces.

Very few numerical studies have investigated the effect of honing param-eters, and in particular honing angle, on lubrication performance. Thereforethis may be an area that has great potential for optimisation, and changinga parameter such as honing angle should not add any significant costs tocylinder liner manufacture. Also many existing PRCL models do not con-sider non-Gaussian roughness patterns which are typical of a honed surface.

A similar study, investigating the effect of honing angle on lubricationperformance, was undertaken by Michail and Barber [14, 15]. They tooimplemented an analytical emulation of a honed surface and used flow fac-tors calculated with the Patir and Cheng [9] Average Flow model in theirsolution of the Reynolds equation. However their surface representationconsisted of a combination of cosine waves to form a surface with the peaksof the waves removed to resemble the plateaux. It is suggested that themethod developed in this paper to resemble the honing pattern is a moreaccurate representation of a real honed surface and in particular the sides

A.2. THEORY 61

of the grooves.

A.2 Theory

In this section the theory behind the model developed will be outlined.

A.2.1 Surface Texture

This study aims to investigate the effect of different honing angles on PRCLlubrication. Real surface topography was only available for a single exist-ing honing angle and so to make the study of different angles possible anartificial surface texture is generated and used. Another advantage of usingan artificial surface is that it can be made periodic, a requirement for theboundary conditions implemented. The surface of a real cylinder liner wasmeasured with a Wyko NT 1100 white light interferometer and this wasused as a basis for the artificially generated surfaces. An investigation ofthe surface showed that although while the diamond like pattern on thesurface was not uniform, the diamonds had a typical, or mean, area of 0.048mm2 as highlighted in Fig. A.1. In this study, to keep textures with different

Figure A.1: Measured Cylinder Liner Surface with WLI

honing angles comparable, the area of each diamond will be kept constantat this value. To generate a single groove equation Eq. (A.1) is used (takenfrom [25]):

hT (x, y) = 10−w(x+ky)2cos[2π(x + ky)]. (A.1)

In Eq. (A.1) two variables should be explained. The width of the honinggroove is set with w, this must be iterated for so that the desired percentageof plateau is achieved and the area is kept to the specified value. The

62 PAPER A.

k parameter is dependent on the desired angle of the honing groove asdescribed by Eq. (A.2):

k =1

tanα(A.2)

A single diagonal groove is created using Eq. (A.1) as illustrated in Fig. A.2.This single groove is mirrored in both the x and y planes to give one artificial

Figure A.2: Artificial Honing Groove

diamond. This single diamond is tiled to create a complete surface for thering to slide over Fig. A.3. The surface is long enough for the ring to

Figure A.3: Artificial Surface

be able to slide far enough, through enough time steps, for a steady stateperiodic solution to be reached. The artificial surface only needs to be onediamond wide in the circumferential direction; periodic boundary conditionsare implemented in the solution so this is all that is required. The depthof the artificial honing scratches is also based on the real measured surface.Fig. A.4 shows a typical cross-section. It can be observed that the honingdepth has some variation. In this simulation a value of 2 µm has been usedas a representative depth.

A.2. THEORY 63

Figure A.4: Cross Section of the Surface Profile

A.2.2 Cavitation Algorithm

The Vijayaraghavan and Keith [29] cavitation algorithm was used to solvethe Reynolds equation, implementing cavitation boundary conditions at filmrupture and reformation. The approach is similar to the Elrod algorithm[30] but with two advantages; compressibility is considered in the full filmzone and the discretisation is rigorously derived, rather than being the resultof considerable experimentation. The Reynolds equation is written as;

dρchθ

dt+

d

dx

(

ρchU

2θ −

ρcβh3g

12µ

dθ

dx

)

+d

dy

(

−ρcβh3g

12µ

dθ

dy

)

= 0. (A.3)

where g is a switch function becoming 1 in the full-film zone and 0 in thecavitated zone. The type of zone is calculated from the value of θ, above 1the region is full-film and below 1 the region is cavitated. The film pressureis found from θ;

P = P + gβlnθ (A.4)

Once the discretization has been applied Eq. (A.3) can be written in theform;

awθi−1,j + aeθi+1,j + anθi,j−1 + asθi,j+1 + apθi, j = rhs, (A.5)

64 PAPER A.

where,

aw = U(chi−1,j)

4∆x− C1 (hwgw)

ae = U(ahi+1,j)

4∆x− C1 (hege)

an = −C2 (hngn)

as = −C2 (hsgs)

ap = U(bhi,j)

4∆x+ C1 [(he + hw) gp] + C2 [(hn + hs) gp] −

hp

∆t

rhs = −C1 [hege − (he + hw) gp + hwgw] − C12 [hsgs

− (hn + hs) gp + hngn] −h∗

pθ∗

i,j

∆t

(A.6)

with the Couette flow coefficients;

a =gi+1,j + gi+1,j

2

b = 2 −gi+1,j + gi+1,j

2

c =gi+1,j + gi+1,j

2

(A.7)

Poiseuille flow coefficients;

C1 =β

12µ∆x2

C2 =β

12µ∆y2

(A.8)

A.2.3 Boundary conditions

A pressure is specified at the inlet and outlet points based on typical gaspressures encountered (see Eq. (A.1)). Periodic boundary conditions areimplemented in the circumferential (perpendicular to entraining motion)direction. The inlet is assumed to be in the fully flooded condition.

A.2. THEORY 65

A.2.4 Film thickness

The ring is assumed to have a parabolic shape. The total film thickness isa combination of this shape, the contribution from the surface texture anda minimum film thickness, given by Eq. (A.9).

h = hmin + ax2 + hT . (A.9)

An iterative procedure is used to solve the system of equations. The problemis solved over a grid of 1000x50 nodes. Initially g is assumed to equal 1everywhere. The values of θ are then calculated at all grid points usingGaussian elimination and g is updated based on these new values. Thisprocess is repeated until convergence is reached, which is assumed to bewhen the following becomes true:

∫ ∫

Pdxdy −∫ ∫

PPREV dxdy∫ ∫

PPREV dxdy< 10−5. (A.10)

A.2.5 Force Balance and Time dependence

To balance the forces (or pressures) that the piston ring is subjected to aniterative procedure is used. The procedure finds the value of hmin requiredfor equation (8) to be true. Everything on the right hand side is known andthe mean hydrodynamic pressure on the left hand side is a function of hminin Eq. (A.9).

∫

Ω

∫


2Ftw

d(A.11)

The fzero algorithm in Matlab is used to find the required hmin to bal-ance the forces. This is a combination of the bisection, secant, and inversequadratic interpolation methods. Once the force balance has been satisfiedthe solution increments one time step. A new surface texture is calculatedas the ring has slid over a proportion of the texture pattern and the forcebalance is then solved again. The time is incremented until the ring hasslid over five full texture diamonds, enough for a periodic value of hmin tobecome apparent. Fig. A.1 lists all of the parameters used in the solution.The simulation is run with parameters that represent typical conditions atthe mid-stroke of the engine cycle. The speed is kept constant and thusthe result is at a stationary condition. The repeating pattern is, however,necessary so that a time dependent solution can be solved. The condi-tions used were chosen as the model presented is currently only capable ofsimulating hydrodynamic lubrication; the mixed and boundary lubricationregimes at Top Dead Centre (TDC) and Bottom Dead Centre (BDC) wereintentionally avoided.

66 PAPER A.

A.3 Results

The honing angle of the cylinder liner measured with white light interefer-ometry Fig. A.1 was 50. Honing angles of ±25 from this existing casehave been investigated, in increments of 5. A typical pressure distributionis illustrated in Fig. A.5. The simulation shows that a steady state solution

Figure A.5: Calculated lubricant pressure across ring width

is obtained after the ring has transversed approximately two complete tex-ture patterns, or 20 time steps. Fig. A.6 shows the minimum film thickness,hmin, as a function of time as the ring slides over the diamond texture.From Fig. A.6 it can be seen that a fairly steady state of film thickness

Figure A.6: Minimum Film Thickness as a function of time steps

occurs after 20 time steps, with oscillations occurring periodically as thering passes over each honing diamond. This pattern was observed for all ofthe honing angles investigated. Therefore in Fig. A.7 the average minimum

A.4. DISCUSSION 67

film thickness is calculated for each honing angle from the 20th time steponwards; so that only the steady state points are considered.

Figure A.7: Average Film Thickness verses Honing Angle

A.4 Discussion

The first issue to highlight is that the variation in film thickness with honingangle is minimal. A 20 nm variation was observed across the range of honingangles. 0.4% of the total minimum film thickness of ≈ 5µm. A curve hasbeen fitted to the calculated average results however the values for 45 and50 deviate significantly from this. However the results generally show thatthe film thickness is greater with a smaller honing angle. This is supportedby the conclusions in [15] which also show that a smaller angle leads to agreater oil film thickness.

A.5 Conclusion

It has been shown that the effect of the honing angle in the middle of thepiston stroke is negligible compared to the large hydrodynamic film alreadydeveloped. A simulation run closer to TDC or BDC, thereby running atconditions closer to mixed lubrication, might yield a greater effect from thehoning angle parameter as the surface grooves become a bigger percentage ofthe total film thickness. It would be also be of value to investigate angles faraway from 50, such as 140, which can be machined as a product of helicalslide honing. Such an angle has been shown to reduce oil consumptionduring bench tests [41].

68 PAPER A.

Table A.1: Solution Parameters

Parameter Units Value

Plateau depth µ m 2Area of one diamond texture mm2 0.048

Compressibility Factor Pa 6.9x107

Dynamic Viscosity Pa·s 0.04Inlet Pressure kPa 437.5

Outlet Pressure kPa 357Simulation Time s 1.5x10−4

No. of time steps 50Ring width mm 4

Ring effective width mm 2.7Piston Speed m/s 5

Tangential Ring Force N 10Bore Diameter m 0.05

A.6 Acknowledgements

The authors would like to thank Stiftelsen for Strategisk Forskning (SSF)and ProViking for funding this work and Scania AB for discussions and forproviding technical data.

Paper B

69

71

Submitted to Proceedings of the Institution of Mechanical Engineers,

Part J: Journal of Engineering Tribology - Leeds-Lyon Special Issue

A semi-deterministic texture-roughness model of thepiston ring - cylinder liner contact

A. Spencer1, A. Almqvist, R. Larsson


of Machine Elements, Lulea SE-971 87 Sweden

Received 21st July 2010

AbstractMany simulations already exist to model the piston ring - cylinder liner con-tact, however very few models have been used to investigate the optimumsurface texture. An axi-symmetric, timedependent 2D semi-deterministictexture-roughness model of the piston ring to cylinder liner contact with pe-riodic boundary conditions and mass preserving global cavitation has beendeveloped. The cylinder liner texture, generated by honing, was consid-ered deterministically on the global scale, after an investigation comparingdeterministic and homogenized solutions.

The surface texture of a real cylinder liner was measured with whitelight interferometry and an algorithm developed to generate an artificialperiodic texture representative of the real surface. The effect of cylinderliner plateau roughness has been incorporated on the local scale by homog-enization of the Reynolds equation and calculation of flow factors from realsurface topography. The lubricant boundary pressures have been calculatedusing results from a numerical ring-pack model and the lubricant viscosityhas been adjusted based on the cylinder liner wall temperature.

It was found from the result of a comparison between deterministic andhomogenized solutions that surface texture should be modelled on the globaland not on the averaged roughness scale as is the case with many previousinvestigations.

Keywords: Honing, Cylinder Liner, Piston Ring, Texture, Homogenization


72 PAPER B.

B.1 Introduction

Power losses from an internal combustion engine can account for a largepercentage of the total power output of the engine, varying from 10% at fullload to 100% at idle [42]. Frictional losses account for a large percentage ofthese and the piston ring - cylinder liner (PRCL) conjunction is the singlelargest contributor to frictional losses in an IC engine, accounting for 20-40% of the total frictional losses [2]. The compression rings are responsiblefor 4-5% of all losses in a multi-cylinder engine [3]. If parasitic losses canbe reduced by 4% then a fuel efficiency increase of 1% can be realised [3].Therefore studying this tribological contact has great potential for reducingfriction and improving fuel economy in an engine, something that is at theforefront of engine design today.

Typically a machining process known as honing is used to apply the de-sired finish to the cylinder liner surface. The grooves that the honing pro-cess leaves behind are believed to be important in controlling the amountof oil available in the contact, by both retaining oil on the liner surface andimproving the distribution of oil. Another perceived function of the hon-ing texture is to allow wear debris, generated during boundary lubricationaround TDC, to be channelled away from the conjunction so as to causeonly minimal damage and scratching to the smooth plateaux which are saidto be important for fluid film generation. In this study the effect of applyingthe honing to hydrodynamic lubrication is investigated.

Most existing PRCL models do not consider the effect on lubrication ofnon-Gaussian roughness patterns typical of a honed surface. Several existingsimulations [7, 8], implement the Patir and Cheng Average Flow model [9] tosimulate the effect of the surface finish on hydrodynamic lubrication. Thesesimulations lump together both surface texture generated by honing andplateau roughness in the same set of flow factors. This paper investigateswhether this is a valid approach to take or whether these scales should beseparated.

Very few numerical studies have investigated the effect of honing textureon lubrication performance in isolation. One which has, undertaken byMichail and Barber [14, 15], implemented an analytical emulation of a honedsurface. Their study used Patir and Cheng flow factors and took the honedsurface to be a combination of cosine waves with the peaks removed tosimulate the plateaux. It is suggested that the artificial surface texturepresented in this paper could be a more realistic representation of a honedsurface than their approach.

The limited work undertaken in modelling the geometry of the surfacetexture means that this is an area that has great potential for optimisation,and changing the details of the honing texture should not add any significant

B.2. MODEL DEVELOPMENT 73

costs to cylinder liner manufacture.

B.2 Model Development

In this section the development of the numerical model is described.

B.2.1 Geometry and global problem

A small portion of the ring is modelled in two dimensions with periodicboundary conditions applied in the circumferential direction. This meansthat the pressure and film thickness at the top edge in Fig. B.1 is the sameas that on the bottom edge.

Figure B.1: Global Geometry

It is assumed that the ring is symmetric about its axis to make thisassumption valid. Clearly this is not the case at the ring gap but as the

74 PAPER B.

ring has a much greater circumference than width it should be valid for themajority of the contact. The ring geometry is modelled using the equation:

h = hmin +x2

2R. (B.1)

B.2.2 Global Surface Texture

An artificial cylinder liner surface texture was generated based on real cylin-der liner surface topography. The surface texture of a cylinder liner wassampled using white light interferometry with a Wyko NT1100 to investi-gate the typical honing pattern, illustrated in Fig. B.2. The direction ofentraining motion in the figure is left-right. The honing angle is 50.

Figure B.2: Measured Cylinder Liner Surface with WLI

Although the diamond patterns generated on the surface by the honingoperation are not uniform, a typical diamond, as highlighted in the image,has an area of 0.048 mm2. An algorithm was generated to produce an artifi-cial surface texture with variable honing angle, groove depth and percentageof plateau while keeping the diamond area constant at 0.048 mm2. The areawas held constant so that different artificial textures are comparable and re-alistic. To generate a texture groove in the surface, the following equationwas used:

hT (x, y) = 10−w(x+ky)2cos[2π(x + ky)]. (B.2)

Two variables require some explanation. The w coefficient is used to adjustthe width of the honing groove. This is done iteratively to achieve thedesired percentage of plateau. The parameter k is a function of the angleof the honing groove, and is derived as:

k =1

tanα(B.3)


Eq. (B.2) is used to create one diagonal groove, illustrated in Fig. B.3.

Figure B.3: Artificial Honing Groove

To create the diamond shape as seen on the real surface this single grooveis mirrored in the x direction and then y direction. This single diamondis tiled to create a complete surface that has the same width as the pistonring (Fig. B.4). The surface is only one diamond wide in the circumferential

Figure B.4: Artificial Surface

direction. Periodic boundary conditions are implemented in the solution asillustrated in Fig. B.1; in effect the strip in Fig. B.4 repeats infinitely in thecircumferential direction.

Information regarding the depth of the honing scratches was also ob-tained from the Wyko measurements. It was observed that the honingdepth has some variation but had an average of 2 µm was found which wastherefore chosen as a representative depth. The honing angle in the cylinderliner measured was 50 which was also chosen for use in these simulations.

76 PAPER B.

B.2.3 Reynolds equation

The homogenized, iso-viscous, time dependent Reynolds equation is solveto model the lubrication in the PRCL conjunction:

∇ (A0 (x, y)∇p0 (x, y)) = λ∇B0 (x, y) + γdh

dt, (B.4)

where A0 and B0 are the flow factors:

A0 =

(

a11 a12

a21 a22

)

and B0 =

(

b12

b22

)

(B.5)

These are described in detail by Almqvist et al. [25]. The factors a12

and a21 are the cross-flow terms, describing the magnitude of the pressureinduced flow in the direction perpendicular to the entraining motion. Dueto the symmetry in the problem (seen in Fig. B.1 and Fig. B.4) it shouldbe possible to neglect these terms. This assumption is validated in sectionB.2.4 when the flow factors are calculated and the cross flow terms are foundto be many orders of magnitude smaller than the other terms.

To model cavitation in the contact the Ausas et al. algorithm is used [31].The Vijayaraghaven [29] and Elrod [30] algorithms were also tested but werefound to be unstable around the honing grooves in the cavitated regions. Nosuch difficulties were encountered with the Ausas et al. technique. Eq. (B.4)can be written as:

∇ (A0∇p0) = α∇ (B0 (x) θ) + γd(

hθ)

dt(B.6)

where:p ≥ 0 θ = 1 (Full Film region)p = 0 θ < 1 (Cavitated region)

(B.7)

The problem is non-dimensionalized and discretized as is described by Ausaset al. [32]. The solution procedure, a Gauss-Seidel relaxation scheme, is thesame as is described in [32] and so will not be repeated here.

The inlet and outlet pressure are set to the inlet and outlet gas pressuresrespectively; these are the pressure in the combustion chamber and the inter-ring gas pressure. The contact is assumed to be fully flooded at all times asan oil availability model has not been used in this study.

B.2.4 Flow Factors

Two sets of flow factors have been calculated. One set for a single artificialdiamond of the artificial surface texture, as illustrated in section B.2.2, and


Figure B.5: Plateau surface roughness

another for a real measured area of plateau roughness as measured with aWyko NT1100 and illustrated in Fig. B.5.

The flow factors A0 for the surface shown in Fig. B.5 are illustrated inFig. B.6. The value of the flow factor (y axis) is plotted against the surfaceseparation divided by the separation at which mechanical contact occurs; i.e.a value of 1 on the x-axis is where mechanical contact occurs. It is observedthat the cross flow terms, a12 and a21, are miniscule in comparison to thea11 and a22 terms especially in the full film region and so the assumption insection B.2.3 is valid.

The flow factors are calculated for 55 different separations, from contactto a mean separation of 8 µm and then for any given separation the flowfactor is interpolated for using a cubic spline. The calculation process andcontact mechanics model used is well described in [11, 12] and is not repeatedhere.

B.2.5 Model Input Parameters

The engine simulated in this paper is a heavy duty truck engine. Two impor-tant input conditions for the model are provided from a separate simulationdeveloped with the commercial AVL Piston and Rings software; these arethe cylinder liner temperature and combustion chamber and inter-ring gaspressures. The cylinder liner temperature is used to calculate the viscosityof the oil on the liner. It is assumed that the temperature of the lubricantin the contact is the same as the liner temperature at that point and theReynolds temperature-viscosity relationship is used:

η = η0e−β(T−T0). (B.8)

78 PAPER B.

0 1 2 3 40

0.5

1

1.5F

low

Fac

tors

α/h1

a11a12a21a22

Figure B.6: Flow factors for plateau surface roughness

The gas pressures are required for two purposes. Firstly gas pressure actson the back of the ring, producing a force radially onwards which mustbe supported by the lubricant film or asperity contact. It is assumed thatat any point in the cycle the highest of either the combustion or inter-ringpressure acts on the back of the ring. This assumption is made as, neglectinginertial forces; the ring will be forced against either the top or bottom edgeof its groove by the highest pressure sealing it and preventing the lowerpressure from acting upon it. The other requirement for the gas pressuresare the Reynolds equation boundary conditions. It is assumed that the inletand outlet lubricant pressures are the combustion chamber and inter-ringgas pressure. Fig. B.7 shows the gas pressures for three different enginerunning speeds, all at full load.

The piston speed, and hence the entraining motion of the contact ismodelled with Eq. (B.9):

U =πLNsinφ

60

1 +

cosφ(

(

2aL

)2− sin2φ

)1/2

(B.9)


0 100 200 300 400 500 600 7000

50

100

150

200

250

Crank Angle (°)

Pre

ssur

e (B

ar)

1200RPM Combustion Chamber1200RPM Inter−ring1600RPM Combustion Chamber1600RPM Inter−ring1900RPM Combustion Chamber1900RPM Inter−ring

Figure B.7: Gas pressure vs crank angle

B.2.6 Force Balance and Time Dependence

An iterative procedure is used to calculate the value of hmin required for thelubricant film pressure to support the opposing load, a combination of thegas pressure acting on the back of the ring and ring tension. This balanceis defined as:

∫

Ω

∫


2Ftw

d(B.10)

The fzero algorithm in Matlab is used to find the required hmin to balancethese forces. This is a combination of the bisection, secant, and inversequadratic interpolation methods. Once the force balance has been satisfiedthe solution increments one time step, equating approximately 0.5 crankangle depending on engine speed. A new gas pressure, piston speed and tem-perature are found and the force balance is solved again. As the Reynoldsequation implemented is time dependent more than one complete enginecycle must be simulated for the entire solution to converge. The discretizedtime dependent term needs a solution from the previous time step. For thefirst crank angle solved for this information is not available. An initial filmthickness must be guessed; in the simulations presented here a guess of 1µm is made at 360 crank angle. After one complete engine cycle the filmthickness and change in film thickness with time (gradient) are compared to

80 PAPER B.

that found on the previous cycle and the simulation is stopped when theseare within a specified tolerance. Typically this requires 1.1 engine cycles.

B.2.7 Friction

Friction is calculated for the entire engine cycle. The friction is composedof two components, the viscous full film friction and the boundary contactfriction. The boundary friction is calculated by:

Fbound = η

∫

ΩPcpdA (B.11)

In this simulation the coefficient of friction between the piston ring andcylinder liner is taken as 0.1. PCP is the mean contact pressure which isfound from the contact mechanics model. The hydrodynamic friction iscalculated with additional flow factors c11, d11 and d12 using [11]:

F0 = −

∫

ΩµU

(

1

h+ 6c11

)

−

((

−h

2+ d11

)

∂p0

dx+ d12

∂p0

dy

)

dx (B.12)

Where h is the average film thickness at a given separation.

B.2.8 Grid size and convergence

The effect of number of nodes on the solution was investigated. With surfacetexture described on the global scale Fig. B.4 the number of nodes must bebig enough to describe it in sufficient detail. A large number of nodes wasfirst chosen (1200x60) and then was reduced until the results produced wereno longer considered acceptable. It was found that 242x12 nodes produceda supported load within 0.6% and a maximum pressure within 0.1% of the1200x60 solution. This was considered an acceptable error, and the solutiontime with the smaller number of nodes was almost two orders of magnitudesmaller.

B.3 Texture Investigation

A model has been described in section B.2 that has the capability to modelsurface texture, the honing grooves, both deterministically and with flowfactors. Surface roughness can also be modelled with flow factors, howevernot deterministically as the number of nodes to resolve surface roughnessacross the contact would become so large that the solution time wouldbecome too great.

Existing simulations often treat surface roughness and texture on thesame scale with Patir and Cheng flow factors. However the conjunction

B.3. TEXTURE INVESTIGATION 81

includes many scales, the biggest of which (the texture) is reasonably closein magnitude to the contact width. In the specific contact investigated thereare approximately 20 repetitions of the texture pattern across the contactwidth. An investigation has been carried out to see whether it is acceptableto include the effect of texture within the flow factors.

For a fixed minimum film thickness (1 µm) the stationary case problemis solved with a deterministic texture (section B.2.2) and a homogenizedtexture (section B.2.4). A smooth surface, with neither deterministic norhomogenized texture, is also solved for comparison. Fig. B.8 shows theresults of this study. As the pressure profile varies slightly across the periodicwidth of the deterministic contact several different cross sections are plottedfor the deterministic case.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3x 10

7

x/L

Pre

ssur

e (P

a)

SmoothHomogenizedDeterministic

Figure B.8: Comparison of homogenized, deterministic and smooth solu-tions

It can be seen that while the homogenized profile is close to the deter-ministic profile when compared to the smooth solution, the homogenizedsolution is generally of a smaller magnitude than the deterministic solution.The predicted supported load for the deterministic case is 4.8% higher thanfor the homogenized case.

This can be explained because the homogenized solution assumes thatthe texture repeats an infinite amount of times across the contact width,however in reality it only repeats 20 times. Therefore the homogenizedsolution underestimates the pressure build up. It is suggested that whileit is acceptable to homogenize surface roughness that has a much smallerwavelength than the contact width, the same is not true for the honedsurface texture which has a much larger wavelength.

82 PAPER B.

B.4 Model Results

Due to the result found in section B.3 the model presented includes surfacetexture on the global scale and plateau roughness (Fig. B.5) is incorporatedwith flow factors on the local scale. The top compression ring is modelledfor the entire engine cycle for three different running conditions, 1200, 1600and 1900 RPM at full load.

The results for minimum film thickness and friction as a function ofcrank angle are presented in Fig. B.9 and Fig. B.10 respectively.

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

Crank Angle (°)

Film

Thi

ckne

ss (µ

m)


Figure B.9: Film thickness vs crank angle

It can be seen that with a lower engine speed the film thickness is reducedand the friction increases. This is to be expected with lower engine speedsthe gas pressure is higher, the temperature is higher, lubricant viscositylower and entraining motion speed reduced.

A period of boundary lubrication occurs, with large increase in friction,shortly after combustion at TDC due to the very large increase in com-bustion chamber pressure (Fig. B.9). It is crucial to incorporate plateauroughness in the model in order to implement the boundary lubricationmodel. If the plateaux were considered smooth then almost no contactwould occur.

It should be noted that fully flooded conditions are always assumed. Inreality this is unlikely to be the case, particularly around TDC and dur-

B.5. CONCLUSION 83

0 100 200 300 400 500 600 7000

200

400

600

800

1000

1200

1400

Fric

tion

(N)

Crank Angle (°)


Figure B.10: Friction vs crank angle

ing the mid-stroke when a large film thickness is predicted. With an oilavailability model the film thicknesses would be reduced and the frictionincreased however for the purposes of comparing deterministic and homog-enized texture models fully flooded conditions were considered adequate.

B.5 Conclusion

An investigation in to modelling surface texture in the PRCL conjunctionhas been carried out. Two dimensions, contact, roughness, texture and timedependence were included in the model. It was found that it is more accurateto include the surface texture in the global scale with a deterministic solutionrather than within flow factors, and in doing so separate out the effect ofroughness and texture. This is contrary to the method employed in manyexisting simulations, which lump together texture and roughness in one setof flow factors.

This approach also allows the effect of texture and roughness to beinvestigated independently, and as they are each products of a differentstage of the honing process this may be beneficial in optimizing surfacetexture.

84 PAPER B.

B.6 Acknowledgements

The authors would like to thank Stiftelsen for Strategisk Forskning (SSF)and ProViking for funding this work and Scania AB for discussions and forproviding technical data.

Paper C

85

87

To be submitted to STLE: Tribology Transactions

Surface Characterization with Functional Parameters

A. Spencer1, I. Dobryden, N. Almqvist, A. Almqvist, R. Larsson


of Machine Elements and the Division of Physics, Lulea SE-971 87 Sweden

AbstractTypically engineering surfaces are characterized with traditional roughnessparameters that perform some type of height averaging over the surface.Although these parameters describe the topography of the surface none ofthem necessarily describe the ability of the surface to carry out its func-tion in a tribological contact. In this study an ICE cylinder liner has beeninvestigated. The traditional Rk parameters (based on the Abbott curve)have been calculated as well as functional ‘flow factors’ which modify theReynolds equation to incorporate the effects of surface topography. To cal-culate flow factors the homogenization technique has been implemented anda full 3D contact mechanics model has been incorporated so that surfacefunctionality in mixed lubrication can be studied. Furthermore, the cylin-der liner surface has been measured with both white light interferometeryand an AFM so that the effect of measuring technique on roughness andfunctional parameters can be investigated.

Keywords: Roughness Effects in Hydrodynamics, AFM, Surface Roughness Analy-

sis and Models


88 PAPER C.

C.1 Introduction

It is necessary to characterize engineering surface topography to make surethat any component leaving a manufacturing process will function to therequired performance level in the tribological contact that it is subjectedto. In this study the components investigated are the combustion enginecylinder liner and top compression ring and the tribological contact is thatbetween them.

Traditionally the surface topography of cylinder liners is characterizedby the ISO-13565-2 or ISO-13565-3 standards for the characterization ofcomponents with surface texture that have stratified functional properties.ISO 13565-2 characterizes the height of the surface topography with thelinear material ratio curve (the Abbott curve), known as the Rk group ofparameters, and ISO 13565-3 characterizes the height with the materialprobability curve, known as the Rq group of parameters. Traditionally theRk parameters are used in the European automotive industry and the Rq

parameters used in the US automotive industry. In this study it is the Rk

group of parameters that will be evaluated.

The goal of this work is to investigate whether the Rk parameters (des-ignated Sk when applied to a 3D surface rather than a 2D profile) are themost suitable means for characterizing the cylinder liner or piston ring sur-face and to propose an alternative functional solution. Although the Rk

parameters are widely used in industry, Malburg et al. [16] state that ‘stud-ies conducted by a major engine manufacturer have shown no correlationbetween these Rk parameters and engine performance’. Although these pa-rameters describe the topography of the surface neither of them necessarilydescribe the ability of the surface to carry out its function in a tribologicalcontact. Also, the Rk parameters were initially designed to be applied to a2D line profile measurement, if a 3D surface measurement is evaluated thenthey do not utilise any of the additional information that could be extractedfrom a surface.

It is suggested that surfaces may be better characterized by performancewith functional ‘flow factors’ calculated from 3D surface topography mea-surements. Flow factors are used to modify the Reynolds equation to takeinto account surface roughness which can be used to simulate film thick-ness in the contact. Other flow factors can be used to describe how surfaceroughness affects viscous friction across the contact. In this work flow fac-tors have been calculated using homogenization, a mathematical averagingtechnique. Furthermore, to incorporate the mixed lubrication regime a full3D Boussinesq type contact mechanics model is employed. The process isexplained by Sahlin et al. [11, 12].

In this study a worn and unworn section of cylinder liner and piston

C.2. SURFACE MEASUREMENTS 89

ring are measured both with an Atomic Force Microscope (AFM) and WykoNT1100 White Light Interferometer (WLI). Two different techniques wereemployed so that the the effect of measuring technique on the results canbe assessed. From these parameters the Rk parameters and flow factors arecalculated and a comparison made.

C.2 Surface Measurements

The surface of the cylinder liner and piston ring have been measured withtwo different methods; an Atomic Force Microscope (AFM) and a WhiteLight Interferometer (WLI). Four different regions were investigated, twodifferent sections of a cylinder liner, worn and unworn, and two differentpiston rings, new and used. The area measured with the two techniqueswas virtually identical, but with the AFM imaging a square area and theWLI a rectangular area, as illustrated in Fig. C.1. However the AFM hasa higher lateral resolution and sampled almost three times as many datapoints per measurement across the surface compared to the WLI.

Figure C.1: Comparison of measurement areas with WLI and AFM tech-niques

C.2.1 WLI Measurements

A White Light Interferometer (Wyko NT 1100) was used to measure eachof the four samples. Each sample was measured twelve times so that anyvariation between measurements could be observed. The location on thesurface of the sample where the measurement was taken was chosen atrandom. A 50X objective lense and 1X Field of View lense were used to

90 PAPER C.

give a measurement area of 124x94 µm with 736x480 data points giving alateral resolution of 169 nm. Each measurement with the WLI techniquetook a handful of seconds, many times quicker than with the AFM techniquediscussed in section C.2.2. Typical measurements for the four surfaces areshown in Fig. C.2 and Fig. C.3. The sliding motion in these images is in the

Figure C.2: Piston Ring WLI images (unworn left, worn right)

Figure C.3: Cylinder Liner WLI images (unworn left, worn right)

vertical direction. The piston ring is chromium coated and exhibits littlewear apart from some minor scratching and smoothing in the direction ofsliding. The cylinder liner is a much softer cast iron and becomes markedlydifferent after having been worn in the engine. The plateaux have beenmassively smoothed leaving the deep honing grooves clearly visible.

C.2.2 AFM Measurements

An Atomic Force Microscope (AFM) was also used to measure the same foursamples measured with the WLI. The device was an NT MDT Ntegra andwas operated in contact mode with the probe scanner. The measurementscovered an area of 108x108 µm with 1024x1024 data points giving a lateralresolution of 105 nm, compared to 168.5 8nm for the WLI measurements.


(a) Unworn (b) Worn

Figure C.4: AFM images of Piston Ring

(a) Unworn (b) Worn

Figure C.5: AFM images of Cylinder Liner

The scan velocity was 87 µm/s but the varied somewhat for different sam-ples, the rougher the sample the lower the value. On the roughest sample,sample 3 which was unworn cylinder liner, the scan velocity was 50 µm/s.A Silicon Nitride cantilever of type PNP-DB was used with a length of 100µm, force constant of 0.48 N/m and a tip radius of less than 10 nm. Typicalmeasurements for the four surfaces are shown in Fig. C.4 and Fig. C.5.

A similar trend of wear can be visually observed in the AFM measure-ments as for the WLI measurements.

C.2.3 Data processing of surface measurements

The raw data from the SP, WLI and AFM measurements was processedwith series of MATLAB routines developed in house. The procedure isillustrated in Fig. C.6. Tilt removal fits a 2D linear polynomial to the surface

92 PAPER C.

Figure C.6: Process for importing raw data

and subtracts its gradient to project the data onto the xy-plane. Thisprocess is necessary for any surface that is imported from raw measurementdata because it is highly unlikely that the sample will have been positionedcompletely horizontally while being measured. However, care should alwaysbe taken when removing tilt from the measurement as it can alter the surfaceprofile. Chiffre et al. [23] demonstrate the effect of removing the slope ofa first order polynomial fitted to a sinusoidal profile. The slope removalcauses an asymmetry in the in the sinusoidal wave, which in turn alters thevalues of the roughness parameters, an issue illustrated in Fig. C.7. Theeffect of form is always present in a 3D measurement. something that is notalways the case with 2D measurements. Typically form is removed by fittinga polynomial of order n using the least squares method. The order, n, isimportant. The higher the better the fit to the profile but too high and it willcause unwanted changes to the original data. Chiffre et al. [19, 23] suggestthat a quadratic polynomial (n = 2) is used for ‘uni-curved’ surfaces (gears,bored holes). Anything greater than n = 4 makes little difference, howeverthe order chosen will have some effect and being consistent when chosingorder is very important. In this work curvature removal is performed by


Figure C.7: Effect of tilt removal on a sinusoidal profile

fitting a quadratic polynomial to the surface and then subtracting it. Thereason for choosing a quadratic polynomial is due to the inherent curvatureof the piston ring and cylinder liner.

With the AFM measurement there will be no missing data because atevery location on the surface a stylus height is recorded, whether it be areal or a false point. However with the WLI technique it is likely thatsome points in the measurement area will not be registered by the CCD.This can occur for a number of reasons, but is often because the surfacehas too high a gradient (such as the side of a honing groove) or there isa deposit on the surface that fails to reflect enough light. Therefore datarestoration is performed on all of the WLI measurements but on none of theAFM measurements. To restore missing points the Delaunay triangulationmethod is employed in combination with linear interpolation [24]. If linearinterpolation fails employing the nearest neighbour method can provide fordata restoration. However, this algorithm is likely to produce unwantedartifacts and one must pay extra attention to the final result.

The next process is to apply a low pass Gaussian filter to the surfacewith a cut-off length set to four fifths of the sample length as per ISO 11562.This is done to remove any spikes that may be present in the data and isapplied to all measurements from either the SP, WLI or AFM technique.The final process, only necessary for the 3D surfaces, is to mirror the surfacein both the x- and the y- direction. This is done in order to remove theinfluence induced by non periodic boundaries and the effect this may haveon the flow factors computed for the surface under consideration. Care mustbe taken to ensure that the mirrored surface is representative of the originalsurface. If the original surface has a lay in a particular direction then theoperation of mirroring can create a final surface disimilar to the original.

94 PAPER C.

Figure C.8: Effect of mirring a honed surface showing unrealistic diamond-like patterns

For honed finishes this is the case, see Fig. C.8 for a graphical illustrationof this problem. Due to this difficulty mirroring is not applied to the lowmagnification WLI images but is applied to the higher magnification imagesand to the AFM images that only feature cylinder liner plateau and not thehoning grooves.

C.3 Rk parameters

The Rk parameters are based on the Abbott curve and attempt to indi-vidually define the peaks, valleys and plateaux of a surface with differentnumerical parameters. The red line in Fig. C.9 illustrates a typical Abbottcurve. To obtain the Abbott curve for a 2D profile or a 3D surface theheight range is first divided into ‘bins’ and the percentage of material thatfalls into each of these bins is plotted against the bin height. This yields theheight distribution of the surface. The Abbott curve is related to the cu-mulative distribution of surface heights and hence can be obtained from theheight distribution. To calculate the numerical parameters, a straight linemust be plotted through the 40% of the curve with the shallowest gradient,giving the green line in Fig. C.9. Rk is defined as the change in height ofthis green line across the width of the graph, between 0% and 100% asperityheight distribution. Rpk is the difference between the highest point on thesurface minus the height of the green line at 0% asperity height distribu-tion. Similarly, Rvk is the difference between the height of the green line

C.4. FLOW FACTORS 95

Figure C.9: Abbott curve parameters

at 100% asperity height distribution minus the height of the lowest pointon the surface. Mr1 is the percentage of surface heights classified as peaksby Rpk. In other words, Mr1 is a material ratio that defines the ratio ofmaterial that counts as peaks. At the other end of the scale, Mr2 is thepercentage of surface heights classified as valleys by Rvk. Finally A1 is thearea enclosed by the Abbott curve in the Rpk region and A2 is the areaenclosed by the Abbott curve in the Rvk region. Mathematically, these pa-rameters are defined in Table C.1. For a cylinder liner Rk can be used todescribe the roughness height after the running in process and Rvk the oilaccumulation in the honing grooves.

C.4 Flow Factors

For the surface measurements of the four samples discussed in Section C.2,flow factors have also been calculated using the homogenization methodincluding contact mechanics for the mixed lubrication regime as outlinedin Chapter 3 of the Thesis. The results are presented in Fig. C.12 andFig. C.13 for the pressure flow factors, Fig. C.14 for the shear flow factorsand Fig. C.15 for the asperity contact pressures. Flow factors have beencalculated for 55 different separations, 30 in the hydrodynamic regime and25 in the mixed regime. The flow factors presented here are normalized whenplotted on the graphs. The pressure induced flow factors are normalisedagainst h3 and the shear induced flow factors normalised against h. Thenormalized flow factors are plotted against α/αc, where α is the rigid body

96 PAPER C.

Table C.1: Rk parameter definitions

SYMBOL DEFINITION

A1

∫ A−1(c1)

0(A(x) − c1)dx

A2

∫ 100

A−1(c2)(A(x) − A(100))dx

Mr1 A−1(c1)

Mr2 A−1(c2)

Rk c1 − c2

Rpk A(0) − c1

Rvk c2 − A(100)

0 50 100−2

−1

0

1

2


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(a) Unworn

0 50 100−1.5

−1

−0.5

0

0.5

1


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(b) Worn

Figure C.10: Cylinder Liner Abbott Curves

C.4. FLOW FACTORS 97

0 50 100−1.5

−1

−0.5

0

0.5

1


Rou

ghne

ss A

mpl

itude

(µm

)

AFMWLI

(a) Unworn

0 50 100−1.5

−1

−0.5

0

0.5

1

Asperity height distribution (%)R

ough

ness

Am

plitu

de (

µm)

AFMWLI

(b) Worn

Figure C.11: Piston Ring Abbott Curves

Table C.2: Rk values


Worn Liner AFM 0.05 0.15 0.21 0.43 13.78 92.25WLI 0.17 0.50 0.57 0.84 8.25 85.99

Unworn Liner AFM 0.11 0.33 0.30 0.34 6.20 85.89WLI 0.21 0.68 0.78 0.78 9.33 88.81

Worn Ring AFM 0.05 0.16 0.21 0.15 12.86 91.33WLI 0.16 0.43 0.49 1.02 6.46 82.23

Unworn Ring AFM 0.02 0.05 0.12 0.14 14.89 89.97WLI 0.10 0.27 0.38 0.97 7.61 84.24

98 PAPER C.

−2 −1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

α / αc

Nor

mal

ized

flow

fact

or


Figure C.12: a11 flow factors

−2 −1 0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

α / αc

Nor

mal

ized

flow

fact

or


Figure C.13: a22 flow factors

global separation and αc is the value of α where the first asperity contactoccurs. Therefore a value of 1 on the x- axis marks the point between mixedand hydrodynamic lubrication.

C.5. DISCUSSION 99

−2 −1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

α / αc

Nor

mal

ized

flow

fact

or


Figure C.14: b22 flow factors

0 0.2 0.4 0.6 0.8 1

x 10−6

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

8

h / hc

Uni

t Con

tact

Pre

ssur

e (P

a)


Figure C.15: Contact Pressures

C.5 Discussion

All four Abbott curve plots exhibit a similar difference in profile betweenthe AFM and WLI measurements. The WLI measurements have a steepergradient and a larger amplitude range than the AFM measurements. On the

100 PAPER C.

left side of the graphs, in the peaks region, the WLI measurements can createanomalous peaks around the honing grooves as discussed in Section 2.1.2.This leads to a steeper Abbott curve in this region than is actually the case.Also, the AFM, with its contacting stylus, can flatten the surface leadingto a flattened curve in the peaks region. These two reasons go towardsexplaining the difference between the AFM and WLI measurements on theleft side of the Abbott curves. On the right side of the Abbott curves,in the valleys region, the WLI again exhibits a steeper gradient than theAFM. This could be because the AFM stylus is not reaching the bottom ofsome of the honing grooves, a problem that is not apparent with the WLImeasurements. The Rk numerical parameters for these Abbott curves aresummarised in Table C.2.

With regard to the flow factors, Fig. C.12, Fig. C.13 and Fig. C.14,a clear difference in behaviour can be seen between the red curves of theunworn cylinder liner and the blue curves of the worn cylinder liner forthe pressure and shear flow factors, showing that flow factors can clearlydifferentiate between surfaces with different levels of wear. There is alsoa differentiation, but much smaller, between the black lines of the unwornring and the green lines of the worn ring. However, it was to be expectedthat less difference would be seen with the ring samples, as they are hardchromium and suffer only minimal wear.

The flow factors presented here also show good correlation between thosecurves calculated from AFM measurements and those from WLI measure-ments. Each of the four surfaces are clearly separable from each otherdespite whether the WLI or AFM measurement is considered. This is notthe case with the Rk parameters in Table 4.3 which show more deviationbetween measuring technique than they do between different samples.

Therefore, it is suggested that flow factors may prove a more repeatabletechnique for charaterising surfaces that is much more independent of mea-suring technique than the Rk parameter set. Furthermore, flow factors bytheir very definition correlate directly to the functional performance of thetribological contact which is not the case for the Rk parameters.

C.6 Acknowledgements

The authors would like to thank Stiftelsen for Strategisk Forskning (SSF)and ProViking for funding this work and Scania AB for discussions andfor providing technical data. Also The Kempe Foundations SMK -2546 isthanked for funding the SPM used to take the measurements.

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