calibration of wear and friction models for a heavy-duty

Calibration of wear and friction modelsfor a Heavy-Duty Piston Ring pack

Lucas Wernelind

Mechanical Engineering, master’s level 2020

Department of Engineering Sciences and Mathematics

Lulea University of Technology

Sweden

June 17, 2020

Preface

i

Abstract

All over the world governments and legislators are updating engine regulations on CO2 emissions.Thiscombined with the rising fuel costs are increasing the demand on fuel efficiency, especially in HeavyDuty Diesel Engines (HDDE). A reduction of friction in the piston ring pack will lead to a reductionof CO2 emissions and higher fuel efficiency, helping both customers and the environment. Changesmade to reduce the friction in the ring pack can however not compromise their robustness or increasethe oil consumption. Since doing this will increase the cost for the customer. Using numerical simu-lation models during the development process will reduce the number of physical tests, thus reducingthe development costs. Since the dynamics of the piston ring pack is very complex, some phenomenacan as of now only be studied using simulations.

The focus of this thesis work was a methodology for the development and calibration of numeri-cal models utilizing existing software and test data. The end goal of the numerical models is anaccurate prediction of the friction caused by the ring pack, the wear of the ring pack and the overalllube oil consumption of the system. By studying how these changed with different design deci-sions during development new information and insights can be gained, saving money by reducingthe number of physical tests needed and creating more efficient and robust products for the customer.

The results from the numerical model that has been developed and calibrated during this workshows promise and the methodology developed in this work has the potential to become an au-tomated process, making the increase in workload smaller in comparison to the potential gain inefficiency of the products.

ii

Nomenclature

ρ Lubricant density kg/m3

η Lubricant dynamic viscosity PashT True clearance mh Clearance, distance between the surfaces mp Pressure Pax Space coordinate my Space coordinate mt Time sU Entraining velocity, velocity of the moving surface m/sδ Amplitude of surface roughness mσ Composite surface roughness mΦx x -direction flow factor -Φy y-direction flow factor -Φs Shear flow factor -Φfpx x -direction Poiseuille stress flow factor -Φfs Couette stress flow factor -Φf Shear stress flow factor -Us Relative surface velocity m/sθ Fill ratio -pc Cavitation pressure PaE Elastic/Young’s modulus Paν Poisson’s ratio -β Asperity summit radius mγ Surface density peaks kg/m2

σs Standard deviation of σ mWL Wear load N/mµ Friction coefficient -k Wear rate -H Material hardness Pahv Wear depth mkc Mass transfer number/coefficient m/hD Diffusion coefficient m2/hT Temperature KR Gas constant J/kgKκ Isentropic exponent -ψ Gas flow coefficient -m Mass kgF Force N

iii

ξ Twist angle of the ring ◦

hrel Relative separation -α Thermal expansion coefficient 1/Kτh Hydrodynamical shear stress Paτa Asperity shear stress Paτtot Total shear stress Paφ Crank angle ◦

V Blow-by l/minε0 Lubricant thermal expansion coefficient 1/K

iv

Contents

1 Introduction 11.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Delimitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 The Piston Ring Pack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 42.1 Thin film flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Fluid film friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Hydrodynamic cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Lubricant viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.5 Lubricant density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Surfaces in contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Asperity contact pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Gas flow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Lube Oil Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.1 Oil evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.2 Oil throw off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.3 Oil blow up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Ring dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5.1 Forces acting on the rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5.2 2D modelling of ring twist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.3 3D modelling of ring twist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Method 173.1 Numerical model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 General modelling assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.2 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.3 Solution procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Physical testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.1 Cameron Plint TE-77 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.2 Floating liner rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Calibration of numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.1 Optimization objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

v

4 Results 254.1 Blow-by optimization - Calibration of ring

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Inter-ring pressure optimization - Calibration of gas flow coefficients . . . . . . . . . . 304.3 Friction caused by the ring pack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3.1 Influence of surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Wear of the ring pack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.5 Lube oil consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Discussion 405.1 Calibration of numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Calibration of ring temperature . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1.2 Calibration of inter-ring pressure . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Friction caused by the ring pack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3 Wear of the ring pack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.4 Lube oil consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6 Conclusions 446.1 Conclusion of model calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2 Conclusion of simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

vi

Chapter 1

Introduction

All over the world governments and legislators are updating engine regulations on CO2 emissions.This combined with the rising fuel costs are increasing the demand on fuel efficiency, especially inHeavy Duty Diesel Engines (HDDE). It’s estimated that mechanical losses, almost entirely due tofriction, within the engine account for 15% of total losses [1, 2]. McGeehan [3] stated that upwards of60-75% of the total friction losses comes from the piston assembly and measurements by Richardson[2] shows that upwards of 2-3% from the piston ring pack alone. Based on fuel consumption data byAndersson [4] a 10% reduction in mechanical losses would lead to a potential 1.5% reduction of fuelconsumption. Thus a reduction of friction in the piston ring pack will lead to a reduction of CO2

emissions and higher fuel efficiency, helping both customers and the environment. Changes made toreduce the friction in the ring pack can however not compromise their robustness or increase the oilconsumption. Since doing this will increase the cost for the customer. The focus of this thesis workwill be the development of numerical models that can be used as a tool in the development of futurepiston ring packs.

1.1 Objective

The objective of this thesis is to estimate oil consumption trends and to calibrate friction andwear models for the piston ring to cylinder liner (PRCL) contact taking the dynamics of the pistonring pack into consideration. The developed models should be a useful tool when developing newcomponents. Thus the need to be calibrated in order to make sure that they are representative ofreality. The calibration should be performed using experimental data from physical test with thecorresponding components. A study of the capabilities of a three dimensional tool to study thedynamics of the piston rings should also be performed.

1.2 Delimitation

This thesis work will be limited to the study of the piston ring pack using existing software, thusthe numerical models developed in this work will be limited by the capabilities of the software.Optimization of the PRCL contact, in terms of material choices and combinations, will not beperformed in this work. Optimisation in terms of ring geometry, lubricant selection or combustiondynamics will not be considered in this work.

1

1.3. THE PISTON RING PACK CHAPTER 1. INTRODUCTION

1.3 The Piston Ring Pack

In most internal combustion engines the piston ring pack consists of three different piston rings. Threedifferent rings, each with there own role to fill. A schematic illustration of the PRCL contact canbe found in Figure 1.1. The main goal of the piston ring pack is twofold, preventing the combustiongases from escaping the chamber and stopping oil from entering the combustion chamber [5]. Theyact as a seal for both the combustion gases and the lubricating oil. The distinct roles of the threedifferent piston rings are:

� Upper Compression Ring: Sealing the combustion chamber and preventing gas from escaping

� Lower Compression Ring: Sealing potentially escaping gases and preventing oil from movingfurther up

� Oil Control Ring: Blocking oil flow between the piston ring pack and the piston skirt

Figure 1.1: A schematic illustration of the piston ring pack and the PRCL contact.

It is common that the rings are made from cast iron to receive adequate mechanical propertiessuitable for the task. To reduce the friction and increase the wear resistance surface coatings arecommon. Since the temperature along the length of the cylinder liner can be between approximately90 °C and 200 °C the viscosity of the lubricant will greatly vary. This combined with the varyingvelocity of the piston ring pack and the dynamic contact load applied due to varying gas pressurein the groove volumes the lubrication regime will vary during the cycle. Going from mixed andboundary lubrication at the top and bottom of the stroke to full film hydrodynamic lubrication atmid-stroke [5]. This ads complexity to the system since consideration of multiple lubrication regimesis needed, thus a mixed-lubrication model needs to be used.

2

1.4. PREVIOUS WORK CHAPTER 1. INTRODUCTION

1.4 Previous work

Studies of the piston ring and cylinder liner has been performed for a few decades. Even thoughthe area has been studied for a while only two major commercial softwares exist, Excite Piston andRings [6], a software developed by AVL, an Austrian automotive company and research institute, aswell as RINGPAK [7] developed by Ricardo, a British engineering company.Both of these commercial softwares and most simulation models presented in literature are built onthe same basis. They utilise the Reynolds equation [8] as the description of the lubricant flow in thecontact region. Common approaches in literature is either to solve the equation using the Reynoldsboundary conditions [9, 10] or utilising a cavitation algorithm [11–13]. It’s quite common to useElrod’s universal cavitation algorithm [14], but other algorithms for mass-conserving hydrodynamiccavitation has been successfully applied to the simulation of the PRCL contact. A similar approachis the algorithm developed by Vijayaraghavan and Keith [15, 16], a more rigorously derived modelthat ultimately leads to an algorithm similar to that of Elrod’s. Other models, such as the mass-conserving two-dimensional model by He et al. [17] has been shown to adequately model the problemof cavitation in the lubricated regime.To describe eventual direct contact between asperities, in eventual dry areas of the contact region,the model by Greenwood and Tripp [18] is often utilised, as is the case in Excite Piston and Rings[6].Since no surface is perfectly smooth consideration of the effects of roughness on the hydrodynamicflow of lubricant is needed. The flow factor method, developed by Patir and Cheng [19, 20] is acommon way to account for the surface roughness. This is the method used in this work. Anothermethod to account for the influence of surface roughness is the model by Almqvist [21] which utilisesa homogenization approach. This has been applied to the PRCL contact problem by both Soderfjall[22] and Spencer [5] with great success.Studies accounting for piston ring dynamics are rarer, since this ads immense complexity to analready complex problem. Tian et al. [23] has studied the effects of piston ring dynamics on wearand oil consumption. They concluded that such effects have potential for improving the guidancesimulation models have in the design phase. Liu and Tian [24] studied the effects that ring dynamicshas on the build up of lubrication along the circumference of the PRCL contact using a FEM basednumerical model. Lyubarskyy and Bartel [25] used a two-dimensional CFD approach to modelthe piston assembly, with considerations of the piston ring dynamics, concluding that the staticring twist is an often overlooked, but important parameter that can impact the performance of thePRCL contact. The review performed by Kurbet and Malagi [26] concludes that a three-dimensionalmodelling approach is required to fully understand the complex dynamics and interactions of thepiston ring pack.

3

Chapter 2

Theory

In the following sections, the theory behind the numerical models developed in this work will bepresented. The theory behind the thin film flow, the Reynolds equation governing the pressure inthe thin fluid film of lubricant, the friction caused by the fluid film, hydrodynamic cavitation andboundary conditions are presented in Section 2.1. In Section 2.2 the theory behind the contactmechanics in the PRCL contact are presented. The theory behind the gas flow within the piston ringpack is presented in Section 2.3. The phenomena affecting the lube oil consumption, evaporation,throw off and blow up, are presented in Section 2.4. The theory behind the calculations of ringdynamics are presented in Section 2.5, both for modelling the ring in 2D and 3D. Section 2.6 consistof the theory in the ISO standard for measuring the area surface roughness of components, thedifferent parameters used in this work are explained.

2.1 Thin film flow

Thin film flow in a lubricated contact, such as in the PRCL contact region, is governed by theReynolds equation. The equation was first derived by Reynolds in 1886 [8] from the Navier-Stokessystem of equations, consisting of equations for momentum- and mass-conservation governing themotion of viscous fluids. Under the assumption of a fluid with constant density and viscosity, anincompressible and iso-viscous fluid, and that the surfaces only move in the x -direction, the Reynoldsequation can be written as

∂

∂x

(ρh3

12η

∂p

∂x

)+

∂

∂y

(ρh3

12η

∂p

∂y

)=U

2

(∂ρh)

∂x+

(∂ρh)

∂t, (2.1)

where x and y represent the spacial coordinates, t is time, ρ is the lubricant density, η is the lubricantsdynamic viscosity, p is the pressure in the fluid film and h is the separation between the surfaces.U is the entraining velocity in the x -direction, the speed of the piston. The left hand side of theequation describes the pressure driven flow, the Poiseuille flow, and the first term on the right handside describes the shear driven flow, the Couette flow. The second term on the right hand sidedescribes the time dependent flow, often refereed to as the squeeze term.Since no surface is perfectly smooth, consideration of the effects the surface roughness has on theflow of lubricant is needed. Excite Piston and Rings [6] has implemented the aforementioned flowfactor method by Patir and Cheng [19, 20]. This averaged Reynolds equation is capable of modelingmixed lubrication conditions, suitable for the PRCL contact. The averaged Reynolds equation solved

4

2.1. THIN FILM FLOW CHAPTER 2. THEORY

in Excite Piston and Rings is on the form

∂

∂x

(Φxh

3 ∂p

∂x

)+

∂

∂y

(Φyh

3∂p

∂y

)= 6ηU

∂hT∂x

+ 6ηUσ∂Φs

∂x+ 12η

∂hT∂t

, (2.2)

where p is the mean hydrodynamic pressure, σ is the composite surface roughness, the RMS averageof the surface roughness. The newly introduced hT is the average gap between the piston ring andthe cylinder liner, the average of the true clearance hT that can be expressed as

hT = h+ δ1 + δ2, (2.3)

where h is the nominal clearance and δi is the amplitude of the roughness of each surface in contact.The true clearance is the distance between the surfaces with the surface roughness taken into account.In equation (2.2) Φi denotes the flow factors derived by Patir and Cheng [19, 20]. The 〈〉 operatorrefers to the expectation value, the probability-weighted average. For the pressure driven Poiseuilleflow the flow factors are expressed as

Φx =

⟨h3T12η

∂pT∂x

⟩h3

12η∆px

, Φy =

⟨h3T12η

∂pT∂y

⟩h3

12η∆py

, (2.4)

where ∆px and ∆py are the pressure gradients in the x - and y-directions respectively and pT is thepressure in the thin fluid film, the solution to the Reynolds equation. There are two Poiseuille flowfactors since there can exist pressure gradients in two directions. For the shear driven Couette flowthere is however only one flow factor, this since the model only considers movement in one direction,the x -direction. Thus shearing only occurs in one direction, the same direction as the movement.This shear flow factor is expressed as

Φs = − 2

Usσ

⟨h3T12η

∂pT∂x

⟩, (2.5)

where Us = u1−u2, the difference in surface velocity for the two moving surfaces. To understand theeffects these flow factors have Figure 2.1a shows the x - and y-direction flow factors from equation(2.4) as a function of dimensionless separation. The effects of the shear flow factor from equation(2.5) are shown in Figure 2.1b.

Where both Figure 2.1a and 2.1b show that the closer the surfaces are the more effect the factors have.The x - and y-direction flow factors approach one for larger separation between the surfaces, meaningthat the surface roughness has no effect, and the shear flow factor approaches zero, meaning that theextra term added to equation (2.9) vanishes. This means that for large enough separations surfaceroughness will have no effect, meaning that the modified Reynolds equation will equal the regularReynolds equation. The relative separation between the two surfaces can be calculated accordingto

hrel =h− δσ

, (2.6)

where h is the nominal separation between the surfaces, δ is the mean amplitude of the surfaceroughness and σ is the composite surface roughness, the RMS average of the surface roughness.

5


Relative separation [-]

Nor

mal

ised

Flo

wF

acto

r

Φx

Φy

(a) The x - and y-direction flow factors.


Nor

mal

ised

Flo

wF

acto

r

Φs

(b) The shear flow factor.

Figure 2.1: Normalised Flow Factors as a function of dimensionless separation.

2.1.1 Fluid film friction

To calculate the friction due to the surfaces interacting with the thin film of lubricant Excite Pistonand Rings [6] use additional flow factors derived by Patir and Cheng [19, 20]. These three additionalflow factors, one connected to the pressure driven Poiseuille flow and two connected to the sheardriven Couette flow, are used in the calculation of the friction. Contrary to before the Poiseuilleonly has one flow factor in the x -direction, due to the restriction in motion. This flow factors can beexpressed as

Φfpx =

⟨hTη∂pT∂x

⟩hη∆px

. (2.7)

For the shear driven Couette flow the two corresponding flow factors are

Φfs = − h

Usη

⟨hT2

∂pT∂x

⟩,

Φf = h

⟨1

hT

⟩for hT = h+ δ1 + δ2 ∧ hT ≥ 0.

(2.8)

To understand the effects these flow factors have Figure 2.2a shows the effect of the shear stress flowfactors from equation (2.8) as a function of dimensionless separation. Figure 2.2b shows the pressurestress flow factors from equation (2.7) as a function of dimensionless separation.

Where for an increasing relative separation between the surfaces these stress flow factors approacheither zero or one, meaning that the influence of the surface roughness will vanish. This means thatthe solution will approach that of smooth surfaces.

6



Nor

mal

ised

Flo

wF

acto

r

Φf

Φfs

(a) The shear stress flow factors.


Nor

mal

ised

Flo

wF

acto

r

Φfpx

(b) The pressure stress flow factor.

Figure 2.2: Normalised Flow Factors as a function of dimensionless separation.

2.1.2 Hydrodynamic cavitation

Hydrodynamic cavitation occurs when the pressure of the lubricant falls below the cavitation pressurepc. This cavitation pressure is related to the saturated vapour pressure of the liquid. When thepressure of the liquid reaches below the cavitation pressure the fluid will vaporize, creating smallbubbles of vapour within the fluid. This is often referred to as the fluid film rupturing. Whenthe pressure in the fluid film increases again theses bubbles collapses and generates a shock wave.This film reformation is a cause of extra wear in the contact region. When studying the PRCLcontact, Spencer [5] has shown that hydrodynamic cavitation will occur when the contacting surfacesdiverge away from each other. In the work performed by Soderfjall [22] as well as Spencer [5], amultitude of different approaches of treating hydrodynamic cavitation in the PRCL contact havebeen studied. Implementations based on the work of both Vijayaraghavan and Keith [15] and Elrod[14] are commonly found in the literature. Spencer [5] found that the most effective approach wasthe algorithm developed by Giacopini et al. [27], a linear complementary problem (LCP) formulationof the mass-conserving hydrodynamic cavitation. According to Spencer this implementation wasincredibly stable but not quite as fast as other methods.

2.1.3 Boundary conditions

To solve the Reynolds equation boundary conditions are needed. In Excite Piston and Rings [6]the Jacobson-Floberg-Olsen (JFO) boundary conditions [28–31] are used. These boundary condi-tions ensures mass-conservation within the hydrodynamic contact area by modifying the Reynoldsequation. This modification introduces a fill ratio θ, to define the modified Reynolds equation, fromequation (2.2), as

∂

∂x

(Φxh

3 ∂p

∂x

)+

∂

∂y

(Φyh

3∂p

∂y

)= 6ηU

∂(θhT

)∂x

+ 6ηUσ∂ (θΦs)

∂x+ 12η

∂(θhT

)∂t

. (2.9)

This modified Reynolds equation insures that both the rupture and reformation boundary conditionsare fulfilled. The theory is based on the assumption that the fluid is either fully saturated, meaningthat the fill ratio θ = 1 and that the pressure in the fluid exceeds the cavitation pressure, p > pc, or

7


that the film has ruptured and that the fluid is cavitated, meaning that θ < 1 and that the pressureis equal to the cavitation pressure, p = pc, [32]. This was mathematically formulated as a boundarycondition for the rupture point, the point at which the cavitation starts xc, and the reformationpoint, the point at which the fluid film reforms xr. The boundary conditions for xc are

p(xc) = pc,∂p

∂n

∣∣∣∣x=xc

= 0, (2.10)

and the boundary condition for xr is

h3

12η

∂p

∂n

∣∣∣∣x=xr

=Vn2

(1− θ)∣∣∣∣x=xr

. (2.11)

Meaning that Excite Piston and Rings [6] handles eventual cavitation occurring in the fluid film bysolving the modified Reynolds equation, equation (2.9), with the rupture and reformation boundaryconditions, (2.10) and (2.11) respectively, [32]. This fill ratio, describing the saturation of the fluid,can be calculated as

θ(x) =ρ(p(x))

ρc, (2.12)

where ρc = ρ(pc), the density of the lubricant at cavitation pressure. This quantity can be referredto as the dimensionless density [32].

2.1.4 Lubricant viscosity

As mentioned earlier the temperature of the domain will greatly vary during the engines cycle, be-tween approximately 90 °C and 200 °C [5]. The pressure during the engines cycle can vary betweenatmospheric pressure and tens of MPa. With temperature and pressure variations of this size theassumption of constant lubricant viscosity is hard to motivate. Thus the dynamic viscosity is calcu-lated using a viscosity-temperature equation, the Vogel equation, and a viscosity-pressure equation,the Roelands equation. By combining these equations the relation for the viscosity becomes

η(T, p) = η0 exp

(B

T + C

)︸︷︷︸

V ogel

exp (αRp)︸︷︷︸Roelands

, (2.13)

where η0, B and C are constants in the Vogel equation, η is the dynamic viscosity of the lubricantand T is the temperature. αR is the Roelands pressure coefficient and p is the pressure where theformer can be calculated as

αRp = (ln (η0(T )) + 9.67)(−1 + (1 + 5.1e−9p)z(T )

), (2.14a)

z(T ) = Dz + Cz log

(1 +

T

135

). (2.14b)

Where z(T ) is the temperature dependent exponent, T is the temperature of the oil and Dz andCz are material constants reflecting the molecular weight and bonding structure of the lubricantrespectively. All of the constants present in these equations are experimentally determined for aspecific lubricant oil, the units of these coefficients are presented in Table 2.1.

8

2.2. SURFACES IN CONTACT CHAPTER 2. THEORY

Table 2.1: The units of the constants present in equations (2.13) and (2.14).

Constants Unitη0 mPasB °CC °CDz −Cz −

2.1.5 Lubricant density

In order to model the the pressure in the thin fluid film of lubricant using the Reynolds equationthe lubricant is assumed to be incompressible, the density of the fluid is not dependent on pressure.In this work the density of the fluid is however assumed to be dependent on the temperature. Theaforementioned temperature variations [5] are large, thus the density of the fluid can greatly varyduring engine cycle. To model this thermal expansion of the lubricant the model after Dowson-Higginson is used

ρ (T ) = ρ0 (1− ε0(T − 15)) , (2.15)

where ρ0 is the density of the lubricant at 15 °C, T is the temperature and ε0 is the thermal expansioncoefficient of the lubricant, this constant has the dimensions (1/K).

2.2 Surfaces in contact

In the mixed- and boundary-lubrication regions of the PRCL contact direct contact between asperitiesmight occur. This contact will create contact pressure witch in turn will cause material to be wornoff during the engine cycle.

2.2.1 Asperity contact pressure

In Exicte Piston and Rings [6] the model derived by Greenwood and Tripp [18] is applied to calculatethe contact pressure between asperities. The elastic behaviour of the two contacting surfaces iscombined into a reference elastic modulus as

E∗ =1(

1− ν21E1

+1− ν22E2

) , (2.16)

where E is the elastic modulus of the surface and ν is Poisson’s ratio. Using this expression thenominal pressure generated by asperities in contact can be calculated as

pa =16√

2π

15(σsβγ)2E∗

√σsβF 5

2

(h

σs

), (2.17a)

F 52

=

4.4086 · 10−5

(4− h

σs

)6.804

,h

σs< 4

0,h

σs≥ 4

(2.17b)

9

2.2. SURFACES IN CONTACT CHAPTER 2. THEORY

where β is the radius of the asperity at its summit, γ is the surface density peaks on each of thesurfaces in contact, σs is the standard deviation of the composite surface roughness, pa is the asperitypressure, the contact pressure between asperities. The model is based on the assumption that theheight of the asperities vary randomly within a Gaussian distribution.

As input to the Excite Piston and Rings simulation model are the stiffness curves of the surfaces incontact. In Figure 2.3 a schematic example of the mean asperity contact pressure and the contactratio are presented as a function of dimensionless separation between the two surfaces. These arecalculated using the Greenwood and Tripp model (2.17). As expected the contact pressure increaseswhen the surfaces are closer to each other, that is when the contact ratio increases, and when thesurfaces are far enough apart they are not in contact, thus the contact pressure is zero.


Mea

nP

ress

ure

[MP

a]


Con

tact

rati

o[-

]

Figure 2.3: Contact pressure and contact ratio as a function of dimensionless separation between thesurfaces in contact.

2.2.2 Wear

When direct contact between asperities occur, as is the case in the mixed- and boundary-lubricationregions of the PRCL contact, wear will occur. Material from the softer surface will be worn off dueto the contact pressure and relative motion of the surfaces. Using the calculated contact pressurefrom equation (2.17) Excite Piston and Rings [6] computes the wear based on Archard’s wear model.The wear load is calculated based on the contact pressure between asperities as

WL =1

tcycl

∫ tcycl

0

paµ |US| dt, (2.18)

where µ is the friction coefficient in the asperity contact and tcycl is the engine cycle time. Based onthe wear load the wear depth can be calculated according to

hv =k

HWLtacc, (2.19)

where k is the wear rate, sometimes referred to as the wear coefficient, H is the material hardness ofthe softer surface and tacc is the accumulated time for the wear.

10

2.3. GAS FLOW MODEL CHAPTER 2. THEORY

2.3 Gas flow model

Gas flow within piston ring pack leads to gas forces acting on the rings, these gas forces will translateinto extra contact forces between the piston rings and the cylinder liner. A schematic picture of thepiston ring pack used in the gas flow model can be seen in Figure 2.4. High pressure gas will flow fromthe combustion chamber, through the throttling points located between the rings and the bodies intothe chambers, denoted with c. Each of these chambers are connected with a throttle.

Figure 2.4: Gas flow model for the entire piston ring pack. Here c denotes the chambers, the volumes inthe piston ring pack, p∞ is the pressure in the combustion chamber and pa is the ambient pressure, thepressure in the crankcase. TCR is the top compression ring, LCR is the 2nd compression ring and OCR isthe oil control ring.

To calculate the gas forces acting on the rings the mass flow between the chambers needs to becalculated. This flow process is assumed to have an isothermal change of state and the maximumallowed velocity is limited to the speed of sound [33]. The mass flow of gas between chambers canbe calculated according to

m = Aψpc

√2

RcTc

√√√√√√ κ

κ− 1

(p0pc

)2

κ −(p0pc

)κ+ 1

κ

, (2.20)

where κ is the isentropic exponent of the combustion gas, A is the area of the throttle and ψ isthe gas flow coefficient of the throttle. p0 denotes the pressure before the throttle, the pressure inthe chamber where the flow is coming from. Rc is the gas constant of the combustion gas, Tc is thetemperature of the gas in the chamber and pc is the pressure of the gas in the chamber. This pressureis calculated according to

pc =RcTcVc

(m+ ∆m) , (2.21)

11

2.4. LUBE OIL CONSUMPTION CHAPTER 2. THEORY

where Vc is the volume of the chamber, m is the mass of gas currently in the chamber and ∆m isthe mass of gas flowing into the chamber, simply ∆m = m∆t where ∆t is the time-step used inthe calculation. The gas pressures in the chambers are determined in a quasi stationary way usingstep-by-step calculations. Starting from the top the mass flows and chamber pressures are computedfor every throttle and chamber in the entire piston ring pack [33]. Once the gas pressure in thechambers are known they can be transformed to the gas forces acting on the rings.

2.4 Lube Oil Consumption

The Lube Oil Consumption (LOC) is an important quantity to minimize, since a minimisation of oilconsumption will decrease the cost for the customer and reduce emissions. Eventual oil that leaksinto the combustion chamber will lead more particles in the exhaust gases after combustion. It ishowever important to make sure that the lubrication of the piston ring pack is sufficient, since tolittle lubrication will lead less full-film hydrodynamic lubrication and thus to more wear and higherfriction. In the model developed in this work three main components of LOC will be considered,these are evaporation, throw off and blow up.

2.4.1 Oil evaporation

Evaporation of the lubrication oil occurs wherever the oil layer on the cylinder liner wall comes incontact with the combustion gases. When this occurs mass transfer over the phase boundary in themedium of combustion gas starts. Excite Piston and Rings [6] uses the steady state convective masstransfer model similar to the one presented by Hubert M. and Hans H [34]. Thus the evaporationrate is given as

kcRfTf

(p− p∞) = − D

RfTf

dp

dx= m, (2.22)

where kc is the material transmission coefficient, the mass transfer coefficient or mass transfer number,D is the diffusion coefficient, p is the pressure in the fluid film, p∞ is the combustion pressure, Rf

is the gas constant of the oil vapour and Tf is the temperature of the oil film. m is the mass flowrate occurring due to evaporation of the thin fluid film. It has been shown that the evaporation rateis influenced considerably by the velocity of the combustion gas, the pressure and the temperature[34].

2.4.2 Oil throw off

To calculate the mass of oil throw-off from the total mass of oil accumulated above the top ring, amodel based of the equilibrium of forces is used. By dividing the entire oil film into discrete layers,and assuming that each layer has a distinct constant acceleration, the velocity of each layer can bedetermined [33]. The model, the assumptions and the consequences of this model is explained furtherby Hubert M. and Hans H [34]. The mass flow of oil throw off can be calculated as

mthrw−off = fthrw

{ρ∆u∆rπD, mthrw−off∆t ≤ macc,macc∆t otherwise,

(2.23)

where fthrw is an empirical scaling factor, ρ is the density of the lubricant, D is the cylinder diameter,∆r is the piston top land to liner clearance, ∆u is the mean difference velocity of the oil film, ∆tis the time step and macc is the mass of accumulated oil between the top land and the liner wall[33].

12

2.5. RING DYNAMICS CHAPTER 2. THEORY

2.4.3 Oil blow up

At certain times during the engines cycle the pressure in the first inter-ring volume, the volumebetween the top and second compression rings, can be greater than the pressure in the combustionchamber. When this occurs oil will flow up through the ring gap of the top ring, transporting oilinto the combustion chamber. For this Excite Piston and Rings [6] uses the following empiricalexpression

mblw−up = fblwρa2

8πbηmax

[(p1/2 − p∞), 0

], (2.24)

where b is the width of the rings running face, p1/2 is the pressure in the inter-ring volume, p∞ is thepressure in the combustion chamber, η is the viscosity of the lubricant, a is the area of the ring gap,ρ is the density of the lubricant and fblw is an empirical scaling factor [33]. As the equation shows,if the pressure in the combustion chamber is higher than the pressure in the inter-ring volume, nooil transport due to blow up will occur.

2.5 Ring dynamics

during the engine cycle forces will act on the piston ring. Examples of these being, gas forces, frictionforces, mass forces and damping forces. Gas and oil in the ring grooves will cause gas forces anddamping forces respectively, contact between the piston ring and the cylinder liner will cause frictionforces and gravity and inertia will cause mass forces. In the following subsections the importantforces used in the modelling of the piston ring dynamics will be presented, along the the modellingof ring twisting, both in two- and three-dimensional models.

2.5.1 Forces acting on the rings

The forces acting on the ring comes in various forms, from hydrodynamic force due to the pressurein the thin fluid film of lubricant, to gas forces due to high pressure gas in the ring groove. A briefexplanation of the different forces acting on the ring will now be presented.

Mass force

The mass force acting on the ring can simply be expressed as

Fmass = mRxR, (2.25)

where mR is the mass of the ring and xR is the acceleration of the ring, both due to gravity and themovement of the piston.

Gas force

The gas force acting on the ring, both from the top of the ring, the bottom of the ring and fromthe ring groove, is simply the pressure of the gas at one side of the ring multiplied with the areaof that side. The pressure can be calculated from equation (2.21) when the mass is the chamber isknown.

13

2.5. RING DYNAMICS CHAPTER 2. THEORY

Friction force

The friction forces acting of the piston ring can be calculated when the contact pressure betweenasperities is known, this contact pressure is calculated according to equation (2.17). Knowing thecontact pressure, the friction force due to direct contact between the surfaces can be calculated. Thefriction cause by the thin fluid film can be calculated using the flow factor in equation (2.7) and (2.8).The total force cause by friction is the summation of the friction caused by direct contact betweenthe surfaces and the friction caused by the thin fluid film. In the work by Kalliorinne [35] this shearstress due to friction caused by the fluid film, the hydrodynamical shear stress, was expressed as

τh = ηUs

h(Φf ± Φfs)± Φfpx

h

2

∂p

∂x∓ σsσ

[(Φfpxh− hT

) ∂p∂x− 2η

Us

hΦfs

], (2.26)

where the different signs are coupled to different surfaces and they depend on how the problem isstated [35]. η is the viscosity of the lubricant, h is the clearance between the surfaces, p is the pressurein the fluid film, Us is the relative velocity of the surfaces, σ is the composite surface roughness andσs is the standard deviation of σ, hT is the average true clearance between the surfaces and Φi arethe different flow factors from equation (2.7) and (2.8). The total shear stress is simply the sum ofthe hydrodynamical shear stress and the shear stress due to asperity contact, where the latter canbe expressed as

τa = paµ, (2.27)

where µ is the friction coefficient and pa is the contact pressure between asperities. Thus the totalshear stress can be expressed as

τtot = τh + τa. (2.28)

Damping force

The damping force caused by eventual oil filling in the ring groove can be calculated using theReynolds equation for an infinitely long slider. By neglecting any periphery flow the equation reducesdown to a ordinary differential equation on the form

∂

∂x

(h3∂p

∂x

)= 6ηU

∂h

∂x+ 12η

∂h

∂t, (2.29)

where the pressure acting as a damper is solved for. Knowing this pressure the damping force canbe calculated [33].

2.5.2 2D modelling of ring twist

To calculate the ring twist in the two-dimensional model, the angular momentum around the centerof the cross section is calculated. This momentum utilises every force acting on the ring and iscalculated as ∑

M =∑

(Fihi) +Mpre−twist = Melasticξ, (2.30)

where Fi is the force acting on the ring, hi is the distance between the force and the center of mass,Mpre−twist is the eventual twist angle of the ring present from mounting and ξ is the twist angle ofthe ring. The elastic moment against ring twisting, Melastic, can be calculated according to

Melastic = πBEH3

6(B −W )ln

(B

B − 2W

), (2.31)

14

2.6. SURFACE ROUGHNESS CHAPTER 2. THEORY

where B is the cylinder bore, H is the height of the piston ring, W is the width of the piston ringand E is the Young’s modulus [33].

2.5.3 3D modelling of ring twist

To simulate the ring dynamics in three dimensions a finite-element (FE) based formulation is used.The ring is divided into elements along the circumferential direction. The model considers the massto be lumped, all of the mass is concentrated in the center of each element, and these mass lumpsare connected by beam elements. Since the model considers three dimensions each element has sixdegrees of freedom, three translational and three rotational [33]. These elements are assembled intoglobal matrices before the equation of motion of the rings are solved. The dynamic forced responseof the ring is formulated as

Mx + Cx + Kx = f , (2.32)

where M is the mass matrix of the ring, C is the damping matrix of the ring and K is the stiffnessmatrix of the ring. x, x and x is the acceleration-, velocity- and displacement-vector of the ringrespectively. f is the vector containing externally applied force acting on the ring, the load vector.Since every node of the ring has six degrees of freedom the sizes of these matrices and vector areof the size (6N×6N) and (6N×1) respectively, where N denotes the number of elements that thering is divided into [33]. The nodal displacements, x, are obtained from an iterative solution to theequation of motion, equation (2.32).

2.6 Surface roughness

This section contains the needed theory behind the different parameters that describe the area sur-face roughness of a measured component. These parameters are defined in the ISO-25178 standard[36] and thus will only be briefly explained in this report for clarity.

The first parameter used is Sa, describing the arithmetical mean height of the surface, on theform

Sa =1

A

∫∫A

|z(x, y)| dxdy, (2.33)

where A is the are of the measurement and z(x, y) is the height of the surface at a given x- andy-coordinate.

15

2.6. SURFACE ROUGHNESS CHAPTER 2. THEORY

The next parameter used in this work is Sk, defined as the distance between the highest and lowestlevel of the core surface, this is explained in Figure 2.5.

Figure 2.5: The definition of the core surface height Sk, the figure shows a profile instead of a surface areafor ease of illustration. The principle is the same for a surface area. Figure from [36].

From the definition of the height of the core surface comes the definition of the last two parameters,Spk and Svk, describing the average height of the protruding peaks above the core surface and theaverage height of the protruding dales below the core surface respectively [36].

16

Chapter 3

Method

In this chapter of the thesis the methods used, both in the numerical simulation and the physicaltesting of components, is presented. In Section 3.1 the modelled components and the numericalsolution procedure of the simulation models is presented, both for the two- and three-dimensionalmodels developed in this work. In Section 3.2 the test equipment used in the testing of componentsis presented, how they work and how they are used in order to perform the testing. In Section 3.3the calibration procedure of the numerical models to available experimental data is described.

3.1 Numerical model development

The dynamics of the piston ring pack are affected by many different phenomena and loads. Inorder to account for everything the solution procedure and assumptions of the simulation modelare important. In the following subsections said assumptions and numerical solution procedure arepresented, both for the two- and three-dimensional model.

3.1.1 General modelling assumptions

The assumptions for both the two- and three-dimensional models, the general assumptions are pre-sented below [33].

� Rings are considered to be single masses and their radial mass forces is neglected

� Calculation of the gas flow and gas pressures is quasi stationary and only done in the chambersand throttles for an isothermal and subsonic flow

� Calculations are performed at thrust side (TS, intake manifold side) and anti-thrust side (ATS,exhaust port side) with their mutual influence taken into account. Along the circumferenceconditions are assumed to be constant

3.1.2 Numerical model

The two-dimensional model is the baseline for these types of numerical simulations. Under theseassumptions the ring can move in radial and axial directions. Only two points are considered alongthe circumference of the piston ring, at TS and ATS. The modelling procedure of the model in twodimensions will be presented. The preprocessing step presented in Figure 3.1 is performed to accountfor the effects that surface roughness has on both the contact mechanics and the hydrodynamic flow

17

3.1. NUMERICAL MODEL DEVELOPMENT CHAPTER 3. METHOD

of lubricant in the PRCL contact. The calculations of the flow factors and the contact pressure andratio are performed using in-house code available at Scania. The code for the flow factors is basedon models presented by Almqvist [21] and implemented by both Spencer [5] and Soderfjall [22] andthe contact pressure and contact ratio is based on the Greenwood and Tripp [18] model.

Measure the sur-face topography

Calculate flow factorsfrom (2.4)-(2.8)

Calculate contactpressure and contact

ratio as in 2.3

Store in files forinput in Excite

Piston and Rings

Figure 3.1: Preprocessing step for the simulation models in order to model the effects of surfaceroughness.

Using the calculated flow factors, contact pressure and contact ratio as a function of relative sep-aration the effects of surface roughness can be introduced into the simulation model. The surfacetopography measurement is taken on the cylinder liner since it has more surface roughness in com-parison to the piston rings. Using these factors the rest of the simulation setup can be performed.This process is schematically illustrated in Figure 3.2.

Define generalengine data

Define load case

Define geome-try of piston

and piston rings

Define material data

Define mean tem-perature of rings

and grooves

Define linerdeformation

Define contactsusing files from 3.1

Define combus-tion gas data

Define param-eters for wear

Figure 3.2: Work-flow for building the simulation model.

To better understand all of the inputs needed in the building of the simulation model they will bebriefly explained.

� General engine data consist of cylinder bore, engine stroke and conrod length

18


� The load case consist of engine speed and combustion pressure as a function of crank angle.By defining these two parameters different driving cycles can be simulated

� When defining the geometry of the piston rings the gas flow coefficients ψ are defined in orderto correctly model the flow losses introduced by the rings. The weights, tension forces andeventual twist angle present during assembly are also defined

� Material data is defined for the piston rings, so that their dynamics can be modelled properly.The elastic modulus E, Poisson’s ratio ν and the thermal expansion coefficient α are defined

� Mean temperature of the rings and grooves are defined, these are important parameters sincethey greatly affect deformations and lubricant viscosity thus changing the lubrication regime.Knowing the temperature of the rings and grooves and the pressure in the different volumesthe viscosity of the lubricant can be calculated via (2.13)

� Liner deformation consists of two parts, assembly load and thermal deformation, the thermaldeformation occurs at a certain temperature corresponding to a certain load

� Contact and flow factors from the pre processing step, Figure 3.1, are introduced to capturethe effects of surface roughness of the contacting geometries

� Data for the combustion gas, temperature T, the heat transfer coefficient (HTC) h and theSwirl/Tumble numbers are important to introduce for the LOC model. The Swirl number ofthe air flowing into the cylinder is the ratio of tangential momentum flux to axial momentumflux of said air, this describes rotation parallel to the cylinder axis. Tumble instead describesflow about the circumferential axis of cylinder. Combined they help describe the overall flowfield of the gases inside the combustion chamber

� The parameters defined to perform the wear simulation is the wear coefficient k and the materialhardness H of the surfaces in contact

Many of the inputs related to the simulation model are results from other simulations, an examplebeing pressure and temperature in the cylinder, Swirl/Tumble numbers of the gases in the cylinderand HTC of the combustion gases. These parameters are results from CFD simulations of thecombustion process, while the thermal deformation of the cylinder liner comes from FEM simulations.The definition of combustion gas data is only needed in case a LOC model is run. These modelsare decoupled since the input to the LOC model, the film thickness on TS and ATS, are outputsfrom the ring dynamics model. When the oil film thickness is known it can be used to calculatethe evaporation of oil from equation (2.22). These parameters are assumed to only affect the LOCmodel.With the engine speed and dimensions of the crank train defined the velocity of the piston can becalculated according to

U =πLN sin (φ)

60

1 +cos (φ)((

2k

L

)2

− sin2 (φ)

)1/2

, (3.1)

where N is the engine speed, L is the stroke length of the engine, k is the length of the conrod andφ is the crank angle [5].

19


3.1.3 Solution procedure

The solution procedure for the entire model, concerning both the ring dynamics and the LOC, canbe seen in Figure 3.3. Since the input to the LOC model is the film thickness of the lubricant as afunction of crank angle, the ring dynamics model needs to be solved before. This means that theLOC model can be considered a post-processing step to the ring dynamics model, the same can besaid for the computation of the wear. This means that the entire ring dynamics simulation is runbefore the LOC model is started. A more in depth explanation of the solution procedure found inFigure 3.3 will now be presented.

� Preprocessing of the model concerns the steps explained in Figure 3.1 and 3.2

� The simulation is run for a given number of engine cycles, the discretization is performed forthe crank angle. The step size ∆φ is defined and during the simulation the current crank angleis calculated as φi = i∆φ where i is the current iteration. Here the viscosity of the lubricantis calculated according to the Vogel/Roelands equation (2.13) and the velocity of the piston isevaluated according to (3.1). Every calculation is performed for every step of the crank angleand the initialization step is the same both for the ring dynamics model and the LOC model

� The forces acting on the ring are iteratively solved. All of the forces acting on the ring arepresented in Section 2.5.1.

i) The modified Reynolds equation (2.9) in order to receive the pressure in the lubricantfilm, since the dimensions of the ring are known this pressure can be converted to a force

ii) Eventual oil present in the groove applies a damping force on the ring, this force is com-puted via the one-dimensional Reynolds equation (2.29)

iii) To compute the gas forces acting on the ring equation (2.20) and (2.21) are used and thepressure of the combustion gas in the chamber is converted into a force

iv) The mass force of the ring is calculated via (2.25)

v) The friction forces, both from the contact between asperities and from the lubricant film,are calculated according to equation (2.26) and (2.27)

� When all of the forces acting on the ring are known the equations of motion using an explicitintegration scheme. For a two-dimensional model equation (2.30) is solved and for the three-dimensional model the dynamic forced response in equation (2.32) is solved using a FE basedformulation

� Once the ring dynamics model has completed every step in the discretization the LOC modelwill run. Both model runs the defined amount of iteration, thus an internal reset is performed

� The components of the LOC model, evaporation, throw-off and blow-up are individually calcu-lated using the now known film thickness of lubricant, one result from the ring dynamics model.Since the evaporation rate in equation (2.22) is heavily dependent on temperature, crank angleresolved gas temperature and HTC are important in order to get reliable results

� Once both the ring dynamics and the LOC are done the wear is computed. With the asperitycontact pressure known from the ring dynamics model the wear load from equation (2.18) canbe used to compute the wear depth (2.19)

The results from the model are stored for each step of the crank angle and can be evaluated as afunction of the crank angle.

20


Initialize crankangle, φi = i∆φ

Iterativly solvethe forces act-

ing on the rings

Solve the equations ofmotion using explicitintegration in time

Store results forcurrent crank angle

Ring dynamics model

Initialize crankangle, φi = i∆φ

Calculate oil con-sumption components

using (2.22)-(2.24)

Sum all thecomponents

Store results forcurrent crank angle

LOC model

Initialize the modelPreprocess the model

Calculate the wear us-ing (2.18) and (2.19)Store all the results

Iterate untilφi = φend

Iterate untilφi = φend

Seti = 0φ = 0

Figure 3.3: Solution procedure for the Excite Piston and Rings model.

21

3.2. PHYSICAL TESTING CHAPTER 3. METHOD

3.2 Physical testing

Many parameters affect the tribological behaviour of the PRCL contact, one important thing tounderstand is the behaviour of the materials in contact. By performing physical tests of the compo-nents a greater insight in there physical properties can be achieved. The parameters with the biggestimpact on the PRCL contact are the friction coefficient and the wear rate, µ and k respectively. Toperform these tests two different experimental rigs where used, a Cameron Plint TE-77 tribometerand a floating liner rig.

3.2.1 Cameron Plint TE-77

A Cameron Plint TE-77 high frequency reciprocating tribometer was used to experimentally deter-mine the friction coefficient and the wear rate of the materials in the PRCL contact. The rig, utilisedby Spencer [5] to test components in the PRCL contact, is a flexible tribometer schematically shownin Figure 3.4.

Figure 3.4: A schematic illustration of the Cameron Plint TE-77 tribometer. Illustration from [5].

During testing a specimen of the cylinder liner is held stationary in a bath of lubricant with a pistonring mounted such that it is pushed onto the cylinder liner. The bath of lubricant is fixed in bothaxial and lateral direction on a flexible support that is allowed to move in the horizontal directions.This support is fixed to a force transducer that measures the frictional force in the contact. A moredetailed explanation of the test rig can be found in [5, 37]. In this work coefficients determinedduring in-house measurements at Scania using the Cameron Plint TE-77 tribometer is used in thenumerical modelling.

22

3.3. CALIBRATION OF NUMERICAL MODELS CHAPTER 3. METHOD

3.2.2 Floating liner rig

To compare the numerical results to crank angle resolved friction results the experimental rig devel-oped by Soderfjall [22, 38] is used. Here the PRCL contact is run a lower but realistic speeds andthe results, such as overall friction force caused by the ring pack, is obtained as crank angle resolved.Thus comparisons can be made over the entire engines cycle, making the analysis of the numericalmodels easier and more flexible. A thorough explanation about the test rig and the processing of theresults that are performed before comparison to the numerical results can be found in [22, 38].

3.3 Calibration of numerical models

In order to verify the accuracy of the numerical model calibration is needed. The physical testingperform in this work, on a component level, means that some of the material parameters are cal-ibrated. In order to further this calibration an optimization scheme is needed to make sure thatthe parameters outside the scope of the physical tests performed in this thesis are accurate. Thephysical test performed in this work covers the most interesting material parameters of the PRCLcontact, the friction coefficient µ and the wear rate k, in the tribological interface of the piston ringand the cylinder liner. In order to receive values of the remaining parameters a reverse parameteridentification is performed, an optimization scheme to fit numerical data to available test data. Thesecalibrations are performed for numerical models where the ring dynamics are modelled in 2D.

3.3.1 Optimization objectives

In order to perform a reverse parameter identification a three things are needed. An objective,numerical results and experimental data. The objective function describes the relation betweenthe numerical results and the experimental data, to goal is often to minimize or maximize thisfunction under some defined constrains. In this work the optimization is performed in order toreceive parameters that can not be measured during any type of test currently available, the ringtemperatures and the flow coefficients ψ. These parameters greatly affect the behaviour of the system,mainly the behaviour of the fluids. The ring temperature governs the thermal expansion of the ring,thus governing the flow area for both the lubricant and the combustion gas. The flow coefficients ψgoverns the losses present in the throttles, thus affecting the gas forces and flows.

Calibration of ring temperature

To calibrate the ring temperature in order to match the blow-by of the numerical model with theavailable data the objective function, denoted E1, was defined as

E1

(T ring

)=

√√√√ 1

n

n∑i

(Vm,iζ − Ve,i

)2, (3.2)

where T ring is the mean temperature of the ring, Vm,i is the blow-by from the model for a specificcase i, Ve is the blow-by from experiments, n is the number of cases and ζ is a parameter for scalingthe data to match the conditions of the experiments. E1 is a function of the mean ring temperaturesince the temperature will affect the thermal expansion of the ring thus affecting the flow area of gas.As E1 → 0 the numerical results will better match the experimental results of the blow-by. Thus a

23

3.3. CALIBRATION OF NUMERICAL MODELS CHAPTER 3. METHOD

minimization problem can be formulated as

min E1

(T ring

)s.t T liner ≤ T ring ≤ T piston

gring,i > 0

(3.3)

where the goal is to minimize the objective function E1. Here gring,i is the ring gap for a specific ringindex i, T liner is the mean temperature of the cylinder liner and T piston is the mean temperature ofthe piston, more precisely the mean temperature of the ring groove. The constrains on the problemcorresponds to that the temperature of the piston ring is bounded between the temperatures of thepiston ring groove and the cylinder liner and the the ring gap can not close during the engines cycle.The changing of the ring temperature is done through the temperature of the ring groove, since thetest data used in the optimization has ring groove temperature. The relationship between the ringtemperature and the groove temperature is assumed to be linear on the form T ring = zT piston, thusthe value of a scalar multiplier z is changed during the optimization routine to minimize equation(3.2).

Calibration of inter-ring pressure

Other than the ring temperature the inter-ring pressure is an important quantity to calibrate. Theinter-ring pressures are the pressures in the chambers in Figure 2.4 and these pressure affect theblow-by and the forces acting on the rings. The chambers in the model are located both in the ringgrooves and the 2nd and 3rd piston lands, the chambers between the TCR and LCR and LCR andOCR respectively. As can be seen in the gas flow model presented in Section 2.3 the pressure in thechambers are influenced by the gas flow coefficients ψ presents in the throttles between the chambers.To perform this optimization two different objective functions, denoted E2, was defined as

E2 ({ψ}) =

√√√√ 1

n

n∑i

(p∗2ndL − p2ndL)2, (3.4a)

E2 ({ψ}) = abs (max (p∗2ndL)−max (p2ndL)) , (3.4b)

where {ψ} denotes the vector of gas flow coefficients in the throttles between chambers, three coef-ficients for the ring above and below the chamber. These three coefficients govern the gas flow atthree different locations, in the throttle at the top of the ring, the throttle at the bottom of the ringand the throttle at the ring gap. p∗2ndL denotes the pressure in 2nd piston land from the numericalmodel, p2ndL is the pressure in 2nd piston land from experimental measurements and n is the numberof cases. The goal is to minimize the RMS objective function or the peak pressure function, sinceas this function approaches zero the numerical results approaches the experimental measurements,either for the entire curve or for the maximum measured pressure. Thus the minimization problemcan be formulated as

min E2 ({ψ})s.t 0.2 ≤ ψi ≤ 1,

(3.5)

where ψi denotes an elements in the vector containing the gas flow coefficients, all of the elementsneeds to be bounded between 0.2 and 1. It’s assumed that all of the six different gas flow coefficientsaffect the inter-ring pressure equally, the coefficients are of equal weight.

24

Chapter 4

Results

In this chapter the results obtained from both the numerical models and the experimental test per-formed during this work is presented. In Section 4.1 the effects of ring temperatures on the simulatedblow-by is presented. In Section 4.2 the results from the calibration of the inter-ring pressure arepresented. Section 4.3 covers the results from the friction caused by the ring pack, and how theoverall friction is affected by the surface topography measurement and the ring dynamics modelling.This friction can be compared to measurements taken with the floating liner rig. The same studyof the affect of surface topography measurements and the ring dynamics modelling will be done forthe wear of the ring pack and the oil consumption during the engines cycle, in Section 4.4 and 4.5respectively.

The results presented in this work will be presented as dimensionless, this is done in order to easecomparison between numerical and experimental results and to make it possible to easily comparethese results to results using different hardware in the future.

4.1 Blow-by optimization - Calibration of ring

temperature

To match the blow-by from the numerical model with the measured blow-by during experimentsthe temperature of the ring was optimized according to (3.3). This was done two times for twodifferent cases, one run containing four different load cases and one run containing eight differentload cases.

Smaller calibration set

In Figure 4.1 the blow-by from the experimental data, the original model and the calibrated modelare compared as a function of upper groove temperature, the TCR groove temperature. These resultsare for a run on 1800RPM with full load on the engine with four different piston temperatures.

25

4.1. BLOW-BY OPTIMIZATION - CALIBRATION OF RINGTEMPERATURE CHAPTER 4. RESULTS

180 182 184 186 188 190 192 194 196 198 200

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

TCR groove temperature [°C]

Dim

ensi

onle

ssblo

w-b

y[-

]

ExperimentalBaseline

Calibrated

Figure 4.1: Comparison of the measured and simulated blow-by from two different numerical models withtwo different assumptions of ring temperature.

The baseline numerical model is built on the assumption that the temperature of the piston ring isthe mean temperature of the cylinder liner and the piston ring groove. The calibrated numericalmodel is the results of the optimization, here the ring temperature is set as a linear function of thegroove temperature to match the experimental data. To further show the effect of the calibration ofthe numerical model the difference |Vm,iζ − Ve| is shown as a function of the top compression ringgroove temperature, this difference can be found in Figure 4.2.

The baseline numerical model has a RMS value for all four cases of 111 compared to 7.5 for thecalibrated numerical model.

26


180.8 184.3 187.0 198.60

0.1

0.2

0.3

0.4

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0.6


Diff

eren

cein

dim

ensi

onle

ssblo

w-b

y[-

] BaselineCalibrated

Figure 4.2: Difference in blow-by between the two different numerical models and the measured data forfour different temperatures of the TCR groove.

In order to validate this assumption a linear regression of the measured data is compared to thenumerical results from the assumption of a linear relationship between the ring groove temperatureand the ring temperature. This comparison can be found in Figure 4.3.

180 182 184 186 188 190 192 194 196 198 200

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06


Dim

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w-b

y[-

]

ExperimentalExperimental fit

CalibratedNumerical fit

Figure 4.3: Comparison of the numerical response to a linear regression of the relationship between blow-byand ring groove temperature.

27


Where the linear regression line of the measured data has a R2 value of 0.96 while the linear regressionline for the numerical data has a R2 value of 0.95.

Larger calibration set

In order to generalize the calibration of the ring temperature a larger map of load points was used.This set contained eight load points with different engine speeds and different loads on the engine.These different load points are shown in Table 4.1.

Table 4.1: The different load points for the larger calibration dataset.

Engine speed (RPM) Engine load (%)1200 251200 501200 1001200 1101600 1101800 251800 1001800 110

In order to full-fill the entire map a shape-preserving piecewise cubic spline interpolation scheme wasutilised on the calibrated results. For the four different engine loads, 25%, 50%, 100% and 110% theassumptions of a linear relation between ring temperature and groove temperature differs, but theoverall assumption still has a R2 high enough to be considered valid, although lower for the largerdataset than for the smaller one.

In Figure 4.4 the complete experimental map for the blow-by as a function of engine speed andengine load is presented.

25 50 100 1101200

1600

1800

Engine load [%]

Engi

ne

spee

d[R

PM

]

0.8

0.85

0.9

0.95

1

Dim

ensi

onle

ssblo

w-b

y[-

]

Figure 4.4: The experimental blow-by map, here the measured blow-by is presented as a function of bothengine speed and engine load for the eight different load points presented in Table 4.1.

28


After the numerical model is calibrated the blow-by map can be studied, this map is presented inFigure 4.5.

25 50 100 1101200

1600

1800

Engine load [%]

Engi

ne

spee

d[R

PM

]

0.85

0.9

0.95

1

1.05

1.1

1.15

Dim

ensi

onle

ssblo

w-b

y[-

]

Figure 4.5: The numerical blow-by map, here the simulated blow-by is presented as a function of bothengine speed and engine load for the eight different load points presented in Table 4.1.

In order to better understand the difference between the measured blow-by Figure 4.6 shows thedifference between the two maps as a function of engine speed and engine load.

2550

1001101200

1600

1800

−0.2

0

0.2

Engine load [%]Engine speed [RPM]

−0.1

0

0.1

0.2

Dim

ensi

onle

ssblo

w-b

y[-

]

Figure 4.6: The difference between numerical and measured blow-by, here the difference is presented as afunction of both engine speed and engine load for the eight different load points presented in Table 4.1.

Where the difference between the numerical model and the measured blow-by can be seen to be bothpositive and negative, the numerical model predicts both lower and higher blow-by, depending onthe load point.

29

4.2. INTER-RING PRESSURE OPTIMIZATION - CALIBRATION OF GAS FLOWCOEFFICIENTS CHAPTER 4. RESULTS

4.2 Inter-ring pressure optimization - Calibration of gas flow

coefficients

Once the ring temperature is calibrated in order to match the blow-by during the engines cycle, theinter-ring pressure in the 2nd piston land is optimized according to (3.5). In Figure 4.7 the inter-ringpressure from the measurement is compared to the numerical models, both the original and thecalibrated ones. The figure also contains the combustion pressure and the pressure in the top ringgroove, these are shown in order to better understand the forces on the ring during the engines cycleand to easier see if the calibration is realistic.

−90 0 90 180 270 360 450 540 6300

0.02

0.04

0.06

0.08

0.1

Crank angle [◦]

Dim

ensi

onle

sspre

ssure

[-]

Combustion pressureTCR groove

Experimental 2nd land

Original 2nd land

Pmax calibrated 2nd land

Curvefit calibrated 2nd land

Figure 4.7: Comparison between the 2nd land pressure from the numerical models to the measured pressure.For clarity the figure contains the combustion pressure and the pressure in the top compression ring groove,the TCR groove.

Where the calibrated numerical model shows great correspondence with the measured 2nd land pres-sure. The difference between the original model and the measured data has a RMS value 0.3% andthe difference at peak pressure is 3%. The overall RMS value of the difference between the measuredpressure and the numerical pressure is 0.2% and the difference at peak pressure is 0.9�for the Pmax

calibrated model. The overall RMS value of the difference between the measured pressure and thenumerical pressure is 0.6�and the difference at peak pressure is 0.2% for the curvefit calibratedmodel.

30

4.2. INTER-RING PRESSURE OPTIMIZATION - CALIBRATION OF GAS FLOWCOEFFICIENTS CHAPTER 4. RESULTS

One interesting finding from Figure 4.7 is the part where the 2nd land pressure rises above the pressurein the TCR groove. Figure 4.8 shows a zoomed in version of the interesting region.

180 185 190 195 200 205 210

0.016

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Crank angle [◦]

Dim

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[-]

Combustion pressureTCR groove

Experimental 2nd land

Original 2nd land

Pmax calibrated 2nd land

Curvefit calibrated 2nd land

Figure 4.8: Comparison between the 2nd land pressure from the numerical model to the measured pressurein the region where the pressure in the 2nd land is higher than the TCR groove.

Where the figure shows that the measured pressure in the 2nd land rises above the measured pressurein the TCR groove at a certain period during the engine cycle. During this period the gas forcesacting on the ring will lift the ring, a phenomena that the numerical model can’t capture, even aftercalibration.

31

4.3. FRICTION CAUSED BY THE RING PACK CHAPTER 4. RESULTS

4.3 Friction caused by the ring pack

Once a calibrated numerical model of the PRCL contact has been developed studies of the frictioncaused by the ring pack can be performed. Studies comparing the influence of the surface topogra-phy measurement, the measurement on which the pre-calculated flow factors and contact pressuresfound in Figure 2.1, 2.2 and 2.3 respectively, are based. Studies of the effects of the ring dynamicsmodelling, the choice of modelling the ring twist in either 2D or 3D, are performed.

In Figure 4.9 the overall friction force over the entire engine cycle is presented for the 15 differ-ent surface measurements. The ring dynamics is modelled in 2D and the engine speed is 1200 RPM.These results are from a calibrated numerical model meant to represent the floating liner rig from[22, 38].

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Rig

0.5

1

1.5

2

2.5

3

3.5

Surface measurement [#]

Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

NumericalMeasured

Figure 4.9: The dimensionless friction force caused by the ring pack for the 15 different surface measurementsand the measured friction force in the floating liner rig. These surface measurements are taken at differentcircumferential and axial positions of the cylinder liner.

Figure 4.9 shows the dimensionless friction force caused by the ring pack over the engines cycle, theintegral mean of the friction, non-dimenionalized with respect to the measured friction force fromthe floating liner rig. The 15 different surface measurements of the cylinder liner are each comparedto the measurement.

32


To better understand the effects of the ring dynamics modelling an internal comparison between the2D and 3D modelling of the ring dynamics is done. This comparison is shown in Figure 4.10.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.5

0.6

0.7

0.8

0.9

1


Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

2D3D

Figure 4.10: The dimensionless friction force caused by the ring pack for the 15 different surface mea-surements with 2D and 3D modelling of the ring dynamics. This is an internal comparison between thenumerical results and thus no measurement data is presented.

Here the overall dimensionless friction force of the ring pack is presented for each of the 15 differentsurface measurements from calibrated numerical models utilizing both 2D and 3D modelling of thering dynamics. As the figure shows the numerical results shows quite a lot of variance in the predictedfriction for each of the different surfaces. The variance of the results from the 2D modelling of thering dynamics is 0.0066 while the variance for the results of the 3D modelling of ring dynamics is0.0173.

33


4.3.1 Influence of surface roughness

To gain further understanding of the influence of the different surface measurements, more specificallythe roughness parameters of each measurement, described in Section 2.6 from ISO25178, are studied.Here the overall friction caused by the ring pack is presented as a function of the different parameters,Sa, Sk, Spk and Svk. The predicted friction comes from the calibrated numerical model with the ringdynamics modelled in 2D. In these figures trend lines will also be presented, in order to study theeffects of the surface roughness measured by the different parameters on the total calculated friction.These results are from a calibrated numerical model meant to represent the floating liner rig from[22, 38]. In Figure 4.11 the overall friction of the ring pack is presented as a function of Sa, thearithmetic mean of the surface.

0.1 0.2 0.3 0.4 0.5 0.6

0.5

1

1.5

2

2.5

3

3.5

Sa [-]

Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

Figure 4.11: The dimensionless friction force as a function of Sa, the arithmetic mean of the surface,presented in (2.33).

Figure 4.11 shows the influence of Sa on the overall friction force of the ring pack by the numericalmodel. The trend line shows that the overall friction of the ring pack is quite constants with re-gards to Sa, even the higher measured arithmetic mean of the surface shows little difference in thedimensionless friction force predicted by the calibrated numerical model. Since Sa seems to showlittle effect on the friction Sk, the distance between the highest and lowest level of the core surface,explained in Figure 2.5, is studied. Figure 4.12 shows the effect of Sk on the numerical friction ofthe ring pack.

Figure 4.12 shows the influence of Sk on the overall friction force of the ring pack by the numericalmodel. The same trend can be seen for Sk and Sa, that the friction seems rather constant withregards to the roughness parameter. The overall effect of the parameter seems to not effect theoverall friction of the ring pack in such a big way.

The influence of the two last parameters, Spk and Svk, describing the average height of the pro-truding peaks above the core surface and the average height of the protruding dales below the coresurface respectively, are shown in Figure 4.13 and Figure 4.14.

34


0.2 0.4 0.6 0.8 1

0.5

1

1.5

2

2.5

3

3.5

Sk [-]

Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

Figure 4.12: The dimensionless friction force as a function of Sk, the distance between the highest andlowest level of the core surface, explained in Figure 2.5.

0.05 0.1 0.15 0.2 0.25 0.3

0.5

1

1.5

2

2.5

3

3.5

Spk [-]

Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

Figure 4.13: The dimensionless friction force as a function of Spk, the average height of the protrudingpeaks above the core surface, explained in Section 2.6.

The influence of Spk on the friction can be seen to have a larger effect than Sa and Sk. Higher Spkvalues gives higher friction predicted by the calibrated numerical model, a pattern not seen by theother roughness parameters.

35


0 0.5 1 1.5 2 2.5

0.5

1

1.5

2

2.5

3

3.5

Svk [-]

Dim

ensi

onle

ssfr

icti

onfo

rce

[-]

Figure 4.14: The dimensionless friction force as a function of Spk, the average height of the protrudingdales below the core surface, explained in Section 2.6.

Figure 4.14 shows the influence of Svk on the friction, like Sa and Sk the friction from the modelseems to be rather constant with regards to this parameter.

36

4.4. WEAR OF THE RING PACK CHAPTER 4. RESULTS

4.4 Wear of the ring pack

Once the friction forces and the asperity contacts are known, the wear of the piston ring pack canbe calculated. Using Archard’s wear model (2.19) the results in Figure 4.15 are obtained. Here theresults, the wear volume over one engine cycle, are presented for each of the 15 different surfacemeasurements and for each individual ring in the ring pack, the top compression ring, the lowercompression ring and the oil control ring. These results are from a calibrated numerical modelmeant to represent the floating liner rig from [22, 38].

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.2

0.4

0.6

0.8

1


Dim

ensi

onle

ssw

ear

volu

me

[-]

TCRLCROCR

Figure 4.15: The dimensionless wear volume of the ring pack during the engines cycle for the 15 differentsurface measurements. These surface measurements are taken at different circumferential and axial positionsof the cylinder liner.

To better understand the effects of the ring dynamics modelling an internal comparison between the2D and 3D modelling of the ring dynamics is done. This comparison is shown in Figure 4.16. Dueto this being an internal comparison there is no experimental data available for comparison. Thisinternal comparison is from calibrated numerical models.

The 2D and 3D modelling of the ring dynamics both show variance over the 15 different surfacemeasurements, with an arguably larger variance present in the 3D ring dynamics modelling.

37

4.5. LUBE OIL CONSUMPTION CHAPTER 4. RESULTS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.2

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0.8

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Dim

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ear

volu

me

[-]

TCRLCROCR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.2

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0.6

0.8

1


Dim

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ssw

ear

volu

me

[-]

TCRLCROCR

Figure 4.16: Total dimensionless wear volume over the engine cycle for the 15 different surface measure-ments, here 2D and 3D modelling of the ring dynamics are compared, the top figure showing the modellingof the ring dynamics in 2D and the bottom figure showing the modelling of the ring dynamics in 3D.

4.5 Lube oil consumption

The total lube oil consumption during the cycle is compared in this section. Here the three maincomponents, the evaporation, the blow-up and the throw-off of oil are all summed to get the overallconsumption. Figure 4.17 shows the overall LOC of the ring pack over the cycle.

It can be seen that there is variance within the 15 different surface measurements, something thatcan be expected since the dynamics of the ring are different. Figure 4.18 shows the overall LOC over

38

4.5. LUBE OIL CONSUMPTION CHAPTER 4. RESULTS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.2

0.4

0.6

0.8

1


Dim

ensi

onle

sslu

be

oil

consu

mpti

on[-

] EvaporationBlow-up

Throw-off

Figure 4.17: Total dimensionless lube oil consumption for the 15 surface measurements with the ringdynamics modelled in 2D. Here the LOC for each of the three components are presented separately.

the engine cycle for 3D modelling of ring dynamics.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.2

0.4

0.6

0.8

1


Dim

ensi

onle

sslu

be

oil

consu

mpti

on[-

] EvaporationBlow-up

Throw-off

Figure 4.18: Total dimensionless lube oil consumption for the 15 surface measurements with the ringdynamics modelled in 3D. Here the LOC for each of the three components are presented separately.

The figure shows the same as for the 2D results in Figure 4.17, there is a variance between thesurfaces due to differing ring dynamics. The variance for the results from the 2D modelling is 0.0025while the variance for the 3D modelling is 0.0016.

39

Chapter 5

Discussion

In this chapter of the report the discussion concerning the results of the work will be conducted.Section 5.1 will cover discussion of results of the calibration of the numerical models in this work,covering both ring temperature and inter-ring pressure. Discussion concerning the results of thesimulation of the friction caused by the ring pack in covered in Section 5.2. Section 5.3 coversthe discussion of the numerical results from the simulation of the wear predicted by the numericalmodels. Discussion of the results covering the lube oil consumption is performed in Section 5.4 ofthis chapter.

5.1 Calibration of numerical models

In the following section of the report the results from the calibration of the numerical models, boththe calibration of ring temperature and the calibration of inter-ring pressure, will be discussed.

5.1.1 Calibration of ring temperature

Calibration of the ring temperature in order to match the blow-by predicted by the numerical modelwas the first thing performed. The calibration was performed via the usage of (3.3) where two dif-ferent datasets where used. One of the dataset contained a singe load point, 1800 RPM 100% load,with four different runs and the other dataset containing eight different load points varying from1200-1800 RPM and 25-110% load on the engine.

Figure 4.1 and 4.2 shows the results of the calibration with the smaller dataset, where the blow-by has been nondimensionalized. As can be seen in the figures the absolute difference between thecalibration model and the measured data is significantly smaller than the difference between thebaseline model and the measurement. In order to validate the linear assumption at the base of thecalibration the measured and numerical blow-by points with their corresponding linear regressionlines are shown in Figure 4.3. Since the regression lines have a R2 value of 0.96 and 0.95 for theexperimental and numerical fit respectively, the linear assumption is clearly valid. A noteworthypoint is however that the calibrated numerical model predicts a larger slope, as the temperaturein the TCR groove increases the model predicts less blow-by that the measurements shows. Thiscould be explained as the model predicting more thermal expansion of the ring than what is actuallypresent during the engine tests, the smaller flow area in the ring gap will thus decrease the blow-by.

40

5.1. CALIBRATION OF NUMERICAL MODELS CHAPTER 5. DISCUSSION

Performing the calibration of the model with the larger dataset, containing eight different load points,the results found in Figure 4.5-4.6, where 4.6 shows the absolute difference between the model andthe experimental measurement. While the overall difference between some of the load points arehigher, the model predicts the blow-by adequately when the difference between all of the points areconsidered. The model captures some trends when the larger dataset is used in the calibration, thedifference between the model and the measurement is larger for higher engine speeds and is lowerfor higher engine loads. These two phenomena might be connected to something that the numeri-cal model can not capture and that becomes clear when the larger calibration set it utilised. Thenumerical model might predict a larger amount of the blow-by to be through the ring end gap thanwhere actually is, thus the thermal expansion of the ring affects the blow-by more.

Comparing the overall results from the usage of the smaller and larger datasets in order to cali-brate the model, it can be seen that the linear assumption holds. The smaller dataset performsbetter when analysed on the same load points, but when predicting something not present in thedataset, the larger dataset generalizes better.

5.1.2 Calibration of inter-ring pressure

Calibration of the inter-ring pressure in this work has been solely focused on the 2nd land, the cham-ber between the top compression ring and the lower compression ring. Previous studies and researchhave shown that this chamber heavily governs the dynamics of the top two piston rings, thus affectingfriction, wear and oil consumption in the entire ring pack.

In order to calibrate the inter-ring pressure, measured in the 2nd land during engine tests, the flowcoefficients in (2.20) are changed. These govern the losses in the throttles between the chambers,affecting the mass of combustion gas and thus the pressure. Since only a single dataset was usedfor the calibration, two different optimization objectives was used in (3.5), a RMS error and a peakpressure matching. The results of these different optimization objectives can be seen in Figure 4.7,where both are compared to the baseline numerical model and the measured pressure. The compar-ison shows that the two different optimization functions perform differently, calibration with (3.4b)makes the numerical model predict the maximum measured pressure better while calibration with(3.4a) matches the overall pressure curve better.

As Figure 4.7 shows the difference between the original uncalibrated model using the baseline valuesfor the gas flow coefficients predicts a pressure much higher than the measured 2nd land pressure.This means that the original values of the gas flow coefficients where to high, the gas flowing in tothe 2nd land did not flow out fast enough, thus the pressure build up was too high. Utilization of anyof the objective function, (3.4a) or (3.4b), yields significant improvements to the inter-ring pressurewhen compared to the baseline model. In order to choose the objective function that is deemedbest, the most important factor needs to be determined. Is the overall curve shape more importantthan the peak pressure. Is the release of the pressure and the region presented in Figure 4.8 moreimportant to get a better matching of, if so the curve fitting with the RMS error is the way forward.If instead the highest pressure, and thus the highest measured ring force, is deemed more important,the minimization of the difference in peak pressures is the way to go.

The ”uplift region”, shown in Figure 4.8, is an interesting region that none of the numerical models isable to predict. In this region the overall gas forces acting on the ring pushed the ring more upwardsthan into the cylinder liner. During this ”up lift” the ring movement pushes oil into the combustion

41

5.2. FRICTION CAUSED BY THE RING PACK CHAPTER 5. DISCUSSION

chamber, thus a minimization or complete removal of this phenomena will decrease the reverse flowin the system.

5.2 Friction caused by the ring pack

With the numerical models calibrated simulations to predict the friction caused by the ring packwere performed. The main goal of these simulations was to study the performance of the calibrationcompared to measurements of the friction in the floating liner rig [38]. As well as to investigate theinfluence of the position of the surface measurement on which the flow factors and asperity stiffnesscurves, Figure 2.1 - 2.2 and 2.3 respectively. These surface topography measurements are small butyet considered to represent the overall roughness of the surface.

The overall friction force caused by the ring pack over the engine cycle, both from the measurementin the floating liner rig and the numerical prediction based on 15 different surface measurements canbe seen in Figure 4.9. The model from which these results come the ring dynamics are modelled in2D, based on (2.31) and (2.30). It can be seen that the predicted friction caused by the ring packgreatly varies between the different surface measurements, and that only a few of them are close tothe measured friction from the rig. Looking at these results the choice of one surface measurementto be considered representative is hard to motivate, there is simply too much variance between thesurfaces when studying the friction of the ring pack.

Since there are two main ways to model the ring dynamics, 2D and 3D, these different modellingtechniques are compared. Figure 4.10 shows a comparison between the overall friction caused bythe ring pack for 2D and 3D modelling of the ring dynamics. These results seem to show a pattern,the friction predicted by 3D modelling of the ring dynamics is lower for a majority of the surfaces.The 3D ring dynamics however predicts the overall highest friction making the variance between thesurfaces larger than for the 2D modelling. This might be due to the fact that the calibration ofthe numerical models have been performed with 2D modelling of the ring dynamics, thus eventualphenomenons present only in the models with 3D ring dynamics are not considered in the calibration.This might be one of the reasons for the variance to be larger for the 3D case.

During the design and manufacturing of the components in the PRCL contact the acceptable surfaceroughness is defined using for distinct parameters, Sa, Sk, Spk and Svk, defined in the ISO-25178standard [36] and explained further in Section 2.6 in this work. The influence of these parameterson the overall friction of the ring pack are studied in Figure 4.11 - 4.14. Where the variation ofthree of the four parameters, Sa, Sk and Svk, have seemingly little impact on the overall friction.For all 15 surface measurements the trend of the friction is quite constant. This is however not thecase for Spk, where a larger value of this parameter, a higher average height of the protruding peaksabove the core surface, gives a higher friction from the numerical models. These results reinforcesthe problem that one surface is to be considered representative of the overall surface roughness ofthe entire cylinder liner, since the friction shown in the figures have a large variance even though thetrend-line is quite constant.

5.3 Wear of the ring pack

The predicted wear of the ring pack, governed by Archard’s wear equation (2.19) for the calibratednumerical model of the floating liner rig [22, 38] with 2D modelling of ring dynamics can be found

42

5.4. LUBE OIL CONSUMPTION CHAPTER 5. DISCUSSION

in Figure 4.15. Here the results are presented as the wear volume of each individual ring, the topcompression ring, the lower compression ring and the oil control ring, over the course of the enginecycle. These results shows that when predicting the wear that occurs on the ring pack the surfacemeasurement is of great importance, some surface show barely any wear compared to others. Basedon the flow factors and asperity stiffness curves calculated from the surface topography measurementssome of the surfaces shows a larger asperity contact and thus a greater amount of wear. Comparingthis to the friction results in Figure 4.9 and the influence of Sa, Sk, Spk and Svk in Figure 4.11 - 4.14a set of conclusions can be drawn. The wear of the ring pack is exclusively based on the occurrenceof asperity contact in the mixed lubrication region and the friction of the ring pack is based on thefriction from asperity contact as well as the thin film flow of the lubricant. Since the wear is morevaried across the 15 different surfaces than the friction is this tells us that the asperity stiffness curvesare more affected by these topography measurements than the flow factors. This is assumed sincethe wear is more affected than the friction, the former of which that is entirely based on the asperitystiffness and contact ratio curves.

Figure 4.16 shows the comparison between the predicted wear for each ring when the ring dynamicsare modelled in 2D and 3D. These results show that the wear of each piston ring is more constantwhen modelling the piston ring dynamics in 3D, something that is most clear for the lower two rings,the LCR and the OCR. The 2D results for some of the surfaces predicts close to zero wear for thebottom two rings, something that can not be seen when modelling the same thing in 3D. This couldbe interpreted as one single surface topography measurement being more representative of the wearcaused on the ring pack when modelling the dynamics in 3D when compared to 2D. Something thattells us that the calibration should be performed when modelling the ring dynamics in 3D, mainlyto test this idea and to gain further understanding of this.

5.4 Lube oil consumption

The overall lube oil consumption, covering all three components from Section 2.4, oil throw-off, oilblow-up and oil evaporation, over the engine cycle is presented in Figure 4.17 and 4.18, for modellingof the ring dynamics in 2D and 3D respectively. Both of these numerical results are presented for allof the 15 different surface measurements. By modelling the ring dynamics in 3D, on more of the oilconsumption parts appear, the numerical model now predicts LOC due to throw-off, something thatrounds to zero in the 2D model. Thus by a more complex modelling of the ring dynamics the oilconsumption component most related to the dynamics of the ring becomes numerically large enoughnot to be rounded to zero. This suggests that 3D modelling of the ring dynamics is the most accurateway to predict lube oil consumption of the piston ring pack. The third oil consumption component,oil blow-up, is not present in any of the numerical models, this tells us that the calibrated modelpredicts that no oil is being moved into the combustion chamber with the gas, something that needsto be validated in the future to see if that is actually the case.

43

Chapter 6

Conclusions

This chapter of the report contains the conclusions of the work performed. Section 6.1 contains theconclusions of the calibration of the developed numerical models, both the calibration of the ringtemperature and the calibration of inter-ring pressure. Section 6.2 covers the conclusions from theresults and discussion of the numerical simulations performed in this work, the predictions of friction,lube oil consumption and wear of the ring pack. Section 6.3 contains suggestions on future work thatcan be built on this work, covering both parts of the work that can be expanded and further studiesthat could lead to more information and further insights.

6.1 Conclusion of model calibrations

The performed calibrations of the numerical models, both the calibration of ring temperature bymeans of matching blow-by and the calibration of inter-ring pressure, shows promise in improvingthe model. Utilization of measurements already available at Scania, simple optimization problemand HEEDS has been shown to greatly improve the studied parameters. The suggested methodologyand the data utilized in this work has thus been shown to be capable of calibrating the overall forcesand dynamics of the piston rings during the engines cycle.

6.2 Conclusion of simulations

Using the calibrated numerical models the effect of different modelling techniques, modelling of thepiston ring equations of motion in either 2D or 3D, and the significance of the surface topographymeasurement on which the asperity stiffness curves and the flow factors are based, can be studied.The modelling of the ring dynamics have been shown to impact all three major things, the frictioncaused by the ring pack, the lube oil consumption of the ring pack and the wear of the rings. Theresults show that in order to get the numerical model to predict wear on the lower two piston rings,the equations of motion needs to be modelled in 3D.

The surface topography measurement have shown to impact the entire numerical model, whereall three major results tells us that one such small segment is often not representative of the entireroughness. Thus this assumption should be revised and future numerical models built in anotherway.

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6.3 Future work

This methodology and these numerical models shows promise and is one step forward to starting touse simulation as a a larger part in the development of the power cylinder system. The assumptionson which the calibration has been performed needs to be investigated further, to get a more generalmethod and model these assumption might need to be revised. The effect of performing the cali-brations while modelling the ring dynamics in 3D instead of 2D should be studied, does this createmore accurate numerical models. Is that then worth the extra computational time that comes withit. This work has only scratched the surface of this very complex system and opens up the possibilityfor future work in order to get a more thorough understanding.

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calibration of wear and friction models for a heavy-duty

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