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

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Calibration of wear and friction models

for a Heavy-Duty Piston Ring pack

Lucas Wernelind

Mechanical Engineering, master's level (120 credits) 2020

Luleå University of Technology

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Preface

During the spring term I have conducted my master’s thesis at NMDP, the group for Power Cylinder development at Scania CV AB in S¨odert¨alje. This thesis work concludes my five years at a student at Lule˚a University of Technology, five years of learning and meeting new people, for which I am very grateful.

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Abstract

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 in Heavy Duty Diesel Engines (HDDE). 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 to reduce the friction in the ring pack can however not compromise their robustness or increase the 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 reducing the development costs. Since the dynamics of the piston ring pack is very complex, some phenomena can as of now only be studied using simulations.

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Nomenclature

ρ Lubricant density kg/m3

η Lubricant dynamic viscosity Pas hT True clearance m

h Clearance, distance between the surfaces m

p Pressure Pa

x Space coordinate m y Space coordinate m

t Time s

U Entraining velocity, velocity of the moving surface m/s δ Amplitude of surface roughness m σ Composite surface roughness m Φx x -direction flow factor

-Φy y-direction flow factor

-Φs Shear flow factor

-Φf px x -direction Poiseuille stress flow factor

-Φf s Couette stress flow factor

-Φf Shear stress flow factor

-Us Relative surface velocity m/s

θ Fill ratio

-pc Cavitation pressure Pa

E Elastic/Young’s modulus Pa ν Poisson’s ratio -β Asperity summit radius m γ Surface density peaks kg/m2

σs Standard deviation of σ m WL Wear load N/m µ Friction coefficient -k Wear rate -H Material hardness Pa hv Wear depth m

kc Mass transfer number/coefficient m/h

D Diffusion coefficient m2/h T Temperature K R Gas constant J/kgK κ Isentropic exponent -ψ Gas flow coefficient

-m Mass kg

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ξ Twist angle of the ring ◦ hrel Relative separation

-α Thermal expansion coefficient 1/K τh Hydrodynamical shear stress Pa

τa Asperity shear stress Pa

τtot Total shear stress Pa

φ Crank angle ◦ ˙

V Blow-by l/min

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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 in Heavy Duty Diesel Engines (HDDE). It’s estimated that mechanical losses, almost entirely due to friction, within the engine account for 15% of total losses [1, 2]. McGeehan [3] stated that upwards of 60-75% 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 by Andersson [4] a 10% reduction in mechanical losses would lead to a potential 1.5% reduction of fuel consumption. 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 to reduce the friction in the ring pack can however not compromise their robustness or increase the oil consumption. Since doing this will increase the cost for the customer. The focus of this thesis work will be the development of numerical models that can be used as a tool in the development of future piston ring packs.

1.1 Objective

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

1.2 Delimitation

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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. Three different rings, each with there own role to fill. A schematic illustration of the PRCL contact can be found in Figure 1.1. The main goal of the piston ring pack is twofold, preventing the combustion gases from escaping the chamber and stopping oil from entering the combustion chamber [5]. They act as a seal for both the combustion gases and the lubricating oil. The distinct roles of the three different 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 moving

further 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.

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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 though the area has been studied for a while only two major commercial softwares exist, Excite Piston and Rings [6], a software developed by AVL, an Austrian automotive company and research institute, as well as RINGPAK [7] developed by Ricardo, a British engineering company.

Both of these commercial softwares and most simulation models presented in literature are built on the same basis. They utilise the Reynolds equation [8] as the description of the lubricant flow in the contact region. Common approaches in literature is either to solve the equation using the Reynolds boundary conditions [9, 10] or utilising a cavitation algorithm [11–13]. It’s quite common to use Elrod’s universal cavitation algorithm [14], but other algorithms for mass-conserving hydrodynamic cavitation has been successfully applied to the simulation of the PRCL contact. A similar approach is the algorithm developed by Vijayaraghavan and Keith [15, 16], a more rigorously derived model that 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 problem of 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 hydrodynamic flow of lubricant is needed. The flow factor method, developed by Patir and Cheng [19, 20] is a common way to account for the surface roughness. This is the method used in this work. Another method to account for the influence of surface roughness is the model by Almqvist [21] which utilises a homogenization approach. This has been applied to the PRCL contact problem by both S¨oderfj¨all [22] and Spencer [5] with great success.

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Chapter 2 Theory

In the following sections, the theory behind the numerical models developed in this work will be presented. The theory behind the thin film flow, the Reynolds equation governing the pressure in the thin fluid film of lubricant, the friction caused by the fluid film, hydrodynamic cavitation and boundary conditions are presented in Section 2.1. In Section 2.2 the theory behind the contact mechanics in the PRCL contact are presented. The theory behind the gas flow within the piston ring pack 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 ring dynamics are presented in Section 2.5, both for modelling the ring in 2D and 3D. Section 2.6 consist of the theory in the ISO standard for measuring the area surface roughness of components, the different 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 the Reynolds equation. The equation was first derived by Reynolds in 1886 [8] from the Navier-Stokes system of equations, consisting of equations for momentum- and mass-conservation governing the motion of viscous fluids. Under the assumption of a fluid with constant density and viscosity, an incompressible and iso-viscous fluid, and that the surfaces only move in the x -direction, the Reynolds equation 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 lubricants dynamic 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 the equation describes the pressure driven flow, the Poiseuille flow, and the first term on the right hand side describes the shear driven flow, the Couette flow. The second term on the right hand side describes the time dependent flow, often refereed to as the squeeze term.

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2.1. THIN FILM FLOW CHAPTER 2. THEORY in Excite Piston and Rings is on the form

∂ ∂x Φxh3 ∂ ¯p ∂x + ∂ ∂y Φyh3 ∂ ¯p ∂y = 6ηU∂¯hT ∂x + 6ηU σ ∂Φs ∂x + 12η ∂¯hT ∂t , (2.2) where ¯p is the mean hydrodynamic pressure, σ is the composite surface roughness, the RMS average of the surface roughness. The newly introduced ¯hT is the average gap between the piston ring and

the 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 hi operator

refers to the expectation value, the probability-weighted average. For the pressure driven Poiseuille flow the flow factors are expressed as

Φx= h3 T 12η ∂pT ∂x h3 12η∆px , Φy = h3 T 12η ∂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 the

pressure in the thin fluid film, the solution to the Reynolds equation. There are two Poiseuille flow factors since there can exist pressure gradients in two directions. For the shear driven Couette flow there 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 h3 T 12η ∂pT ∂x , (2.5)

where Us= u1− u2, the difference in surface velocity for the two moving surfaces. To understand the

effects 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, meaning that the surface roughness has no effect, and the shear flow factor approaches zero, meaning that the extra term added to equation (2.9) vanishes. This means that for large enough separations surface roughness will have no effect, meaning that the modified Reynolds equation will equal the regular Reynolds equation. The relative separation between the two surfaces can be calculated according to

hrel =

h − ¯δ

σ , (2.6)

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2.1. THIN FILM FLOW CHAPTER 2. THEORY Relative separation [-] Normalised Flo w F actor Φx Φy

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

Relative separation [-] Normalised Flo w F actor 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 Piston and Rings [6] use additional flow factors derived by Patir and Cheng [19, 20]. These three additional flow factors, one connected to the pressure driven Poiseuille flow and two connected to the shear driven Couette flow, are used in the calculation of the friction. Contrary to before the Poiseuille only has one flow factor in the x -direction, due to the restriction in motion. This flow factors can be expressed as Φf px = D_h T η ∂p_∂xT E h η ∆px . (2.7)

For the shear driven Couette flow the two corresponding flow factors are Φf s = − h Usη hT 2 ∂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 flow factors from equation (2.8) as a function of dimensionless separation. Figure 2.2b shows the pressure stress flow factors from equation (2.7) as a function of dimensionless separation.

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2.1. THIN FILM FLOW CHAPTER 2. THEORY Relative separation [-] Normalised Flo w F actor Φf Φf s

(a) The shear stress flow factors.

Relative separation [-] Normalised Flo w F actor Φf px

(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 pressure pc. This cavitation pressure is related to the saturated vapour pressure of the liquid. When the

pressure of the liquid reaches below the cavitation pressure the fluid will vaporize, creating small bubbles of vapour within the fluid. This is often referred to as the fluid film rupturing. When the 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 PRCL contact, Spencer [5] has shown that hydrodynamic cavitation will occur when the contacting surfaces diverge away from each other. In the work performed by S¨oderfj¨all [22] as well as Spencer [5], a multitude of different approaches of treating hydrodynamic cavitation in the PRCL contact have been 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 was the algorithm developed by Giacopini et al. [27], a linear complementary problem (LCP) formulation of the mass-conserving hydrodynamic cavitation. According to Spencer this implementation was incredibly stable but not quite as fast as other methods.

2.1.3 Boundary conditions

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2.1. THIN FILM FLOW CHAPTER 2. THEORY that the film has ruptured and that the fluid is cavitated, meaning that θ < 1 and that the pressure is equal to the cavitation pressure, p = pc, [32]. This was mathematically formulated as a boundary

condition for the rupture point, the point at which the cavitation starts xc, and the reformation

point, 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 = Vn 2 (1 − θ) x=xr . (2.11)

Meaning that Excite Piston and Rings [6] handles eventual cavitation occurring in the fluid film by solving the modified Reynolds equation, equation (2.9), with the rupture and reformation boundary conditions, (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 referred

to 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 between atmospheric pressure and tens of MPa. With temperature and pressure variations of this size the assumption 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) = ¯η0exp B T + C | {z } V ogel exp (αRp) | {z } Roelands , (2.13) where ¯η0, B and C are constants in the Vogel equation, η is the dynamic viscosity of the lubricant

and T is the temperature. αR is the Roelands pressure coefficient and p is the pressure where the

former can be calculated as

αRp = (ln (η0(T )) + 9.67) −1 + (1 + 5.1e−9p)z(T ), (2.14a) z(T ) = Dz+ Czlog 1 + T 135 . (2.14b) Where z(T ) is the temperature dependent exponent, T is the temperature of the oil and Dz and

Cz are material constants reflecting the molecular weight and bonding structure of the lubricant

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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 Unit ¯ η0 mPas B °C C °C Dz − Cz −

2.1.5 Lubricant density

In order to model the the pressure in the thin fluid film of lubricant using the Reynolds equation the 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. The aforementioned temperature variations [5] are large, thus the density of the fluid can greatly vary during 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 ε0is the thermal expansion

coefficient 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 asperities might occur. This contact will create contact pressure which in turn will cause material to be worn off 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 calculate the contact pressure between asperities. The elastic behaviour of the two contacting surfaces is combined into a reference elastic modulus as

E∗ = 1 1 − ν2 1 E1 +1 − ν 2 2 E2 , (2.16) where E is the elastic modulus of the surface and ν is Poisson’s ratio. Using this expression the nominal pressure generated by asperities in contact can be calculated as

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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 the surfaces in contact, σsis the standard deviation of the composite surface roughness, pais the asperity

pressure, the contact pressure between asperities. The model is based on the assumption that the height 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 in contact. In Figure 2.3 a schematic example of the mean asperity contact pressure and the contact ratio are presented as a function of dimensionless separation between the two surfaces. These are calculated using the Greenwood and Tripp model (2.17). As expected the contact pressure increases when the surfaces are closer to each other, that is when the contact ratio increases, and when the surfaces are far enough apart they are not in contact, thus the contact pressure is zero.

Relative separation [-] Mean Pressure [MP a] Relative separation [-] Con tact ratio [-]

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

2.2.2 Wear

When direct contact between asperities occur, as is the case in the mixed- and boundary-lubrication regions of the PRCL contact, wear will occur. Material from the softer surface will be worn off due to the contact pressure and relative motion of the surfaces. Using the calculated contact pressure from 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 Z 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 on

the wear load the wear depth can be calculated according to hv =

k

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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 translate into extra contact forces between the piston rings and the cylinder liner. A schematic picture of the piston ring pack used in the gas flow model can be seen in Figure 2.4. High pressure gas will flow from the combustion chamber, through the throttling points located between the rings and the bodies into the 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 in the piston ring pack, p∞ is the pressure in the combustion chamber and pa is the ambient pressure, the

pressure in the crankcase. TCR is the top compression ring, LCR is the 2nd compression ring and OCR is the oil control ring.

To calculate the gas forces acting on the rings the mass flow between the chambers needs to be calculated. This flow process is assumed to have an isothermal change of state and the maximum allowed velocity is limited to the speed of sound [33]. The mass flow of gas between chambers can be calculated according to ˙ m = Aψpc r 2 RcTc v u u u u t κ κ − 1    p0 pc 2 κ ₋ p0 pc κ + 1 κ   , (2.20) where κ is the isentropic exponent of the combustion gas, A is the area of the throttle and ψ is the gas flow coefficient of the throttle. p0 denotes the pressure before the throttle, the pressure in

the chamber where the flow is coming from. Rc is the gas constant of the combustion gas, Tc is the

temperature of the gas in the chamber and pcis the pressure of the gas in the chamber. This pressure

is calculated according to

pc =

RcTc

Vc

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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 is

the mass of gas flowing into the chamber, simply ∆m = ˙m∆t where ∆t is the time-step used in the calculation. The gas pressures in the chambers are determined in a quasi stationary way using step-by-step calculations. Starting from the top the mass flows and chamber pressures are computed for every throttle and chamber in the entire piston ring pack [33]. Once the gas pressure in the chambers 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 oil consumption will decrease the cost for the customer and reduce emissions. Eventual oil that leaks into the combustion chamber will lead more particles in the exhaust gases after combustion. It is however important to make sure that the lubrication of the piston ring pack is sufficient, since too little lubrication will lead less full-film hydrodynamic lubrication and thus to more wear and higher friction. 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 in contact with the combustion gases. When this heating occurs mass transfer over the phase boundary in the medium of combustion gas starts. Excite Piston and Rings [6] uses the steady state convective mass transfer model similar to the one presented by Hubert M. and Hans H [34]. Thus the evaporation rate is given as kc RfTf (p − p∞) = − D RfTf dp dx = ˙m, (2.22) where kcis 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 flow

rate occurring due to evaporation of the thin fluid film. It has been shown that the evaporation rate is 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, a model 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 be determined [33]. The model, the assumptions and the consequences of this model is explained further by Hubert M. and Hans H [34]. The mass flow of oil throw off can be calculated as

˙

mthrw−of f = fthrw

(

ρ∆¯u∆rπD, mthrw−of f∆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, ∆t is the time step and macc is the mass of accumulated oil between the top land and the liner wall

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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 volume between the top and second compression rings, can be greater than the pressure in the combustion chamber. When this occurs oil will flow up through the ring gap of the top ring, transporting oil into the combustion chamber. For this Excite Piston and Rings [6] uses the following empirical expression

˙

mblw−up = fblw

ρa2

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 the

pressure 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, no oil 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, friction forces, mass forces and damping forces. Gas and oil in the ring grooves will cause gas forces and damping forces respectively, contact between the piston ring and the cylinder liner will cause friction forces and gravity and inertia will cause mass forces. In the following subsections the important forces used in the modelling of the piston ring dynamics will be presented, along the the modelling of 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 pressure in the thin fluid film of lubricant, to gas forces due to high pressure gas in the ring groove. A brief explanation 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= mRx¨R, (2.25)

where mR is the mass of the ring and ¨xR is the acceleration of the ring, both due to gravity and the

movement of the piston. Gas force

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2.5. RING DYNAMICS CHAPTER 2. THEORY Friction force

The friction forces acting of the piston ring can be calculated when the contact pressure between asperities is known, this contact pressure is calculated according to equation (2.17). Knowing the contact pressure, the friction force due to direct contact between the surfaces can be calculated. The friction 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 between the surfaces and the friction caused by the thin fluid film. In the work by Kalliorinne [35] this shear stress due to friction caused by the fluid film, the hydrodynamical shear stress, was expressed as

τh = η Us h (Φf ± Φf s) ± Φf px h 2 ∂p ∂x ∓ σs σ Φf pxh − ¯hT ∂ p ∂x − 2η Us h Φf s , (2.26) where the different signs are coupled to different surfaces and they depend on how the problem is stated [35]. η is the viscosity of the lubricant, h is the clearance between the surfaces, p is the pressure in the fluid film, Us is the relative velocity of the surfaces, σ is the composite surface roughness and

σs is the standard deviation of σ, ¯hT is the average true clearance between the surfaces and Φi are

the different flow factors from equation (2.7) and (2.8). The total shear stress is simply the sum of the hydrodynamical shear stress and the shear stress due to asperity contact, where the latter can be expressed as

τa= paµ, (2.27)

where µ is the friction coefficient and pa is the contact pressure between asperities. Thus the total

shear 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 the Reynolds equation for an infinitely long slider. By neglecting any periphery flow the equation reduces down 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 can be 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 center of the cross section is calculated. This momentum utilises every force acting on the ring and is calculated as

X

M =X(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 of

the ring. The elastic moment against ring twisting, Melastic, can be calculated according to

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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 ring and 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 mass to be lumped, all of the mass is concentrated in the center of each element, and these mass lumps are connected by beam elements. Since the model considers three dimensions each element has six degrees of freedom, three translational and three rotational [33]. These elements are assembled into global matrices before the equation of motion of the rings are solved. The dynamic forced response of the ring is formulated as

M ¨x + C ˙x + 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 stiffness matrix of the ring. ¨x, ˙x and x is the acceleration-, velocity- and displacement-vector of the ring respectively. 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 are of the size (6N×6N) and (6N×1) respectively, where N denotes the number of elements that the ring is divided into [33]. The nodal displacements, x, are obtained from an iterative solution to the equation 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.

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2.6. SURFACE ROUGHNESS CHAPTER 2. THEORY The next parameter used in this work is Sk, defined as the distance between the highest and lowest level 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 area for ease of illustration. The principle is the same for a surface area. Figure from [36].

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Chapter 3 Method

In this chapter of the thesis the methods used, both in the numerical simulation and the physical testing of components, is presented. In Section 3.1 the modelled components and the numerical solution procedure of the simulation models is presented, both for the two- and three-dimensional models developed in this work. In Section 3.2 the test equipment used in the testing of components is presented, how they work and how they are used in order to perform the testing. In Section 3.3 the 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. In order to account for everything the solution procedure and assumptions of the simulation model are important. In the following subsections said assumptions and numerical solution procedure are presented, 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 chambers and 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 circumference conditions are assumed to be constant

3.1.2 Numerical model

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3.1. NUMERICAL MODEL DEVELOPMENT CHAPTER 3. METHOD of lubricant in the PRCL contact. The calculations of the flow factors and the contact pressure and ratio are performed using in-house code available at Scania. The code for the flow factors is based on models presented by Almqvist [21] and implemented by both Spencer [5] and S¨oderfj¨all [22] and the contact pressure and contact ratio is based on the Greenwood and Tripp [18] model.

Measure the sur-face topography Calculate flow factors

from (2.4)-(2.8)

Calculate contact pressure and contact

ratio as in 2.3 Store in files for

input in Excite Piston and Rings

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

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 surface topography 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 general

engine data Define load case

Define geome-try of piston and piston rings Define material data Define mean

tem-perature of rings and grooves Define liner

deformation Define contacts using 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 be briefly explained.

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3.1. NUMERICAL MODEL DEVELOPMENT CHAPTER 3. METHOD 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 order to correctly model the flow losses introduced by the rings. The weights, tension forces and eventual 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 since

they 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 volumes the viscosity of the lubricant can be calculated via (2.13)

Liner deformation consists of two parts, assembly load and thermal deformation, the thermal deformation 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 capture the effects of surface roughness of the contacting geometries

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

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

Many of the inputs related to the simulation model are results from other simulations, an example being pressure and temperature in the cylinder, Swirl/Tumble numbers of the gases in the cylinder and HTC of the combustion gases. These parameters are results from CFD simulations of the combustion 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 models are decoupled since the input to the LOC model, the film thickness on TS and ATS, are outputs from the ring dynamics model. When the oil film thickness is known it can be used to calculate the evaporation of oil from equation (2.22). These parameters are assumed to only affect the LOC model.

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3.1. NUMERICAL MODEL DEVELOPMENT CHAPTER 3. METHOD

3.1.3 Solution procedure

The solution procedure for the entire model, concerning both the ring dynamics and the LOC, can be seen in Figure 3.3. Since the input to the LOC model is the film thickness of the lubricant as a function of crank angle, the ring dynamics model needs to be solved before. This means that the LOC model can be considered a post-processing step to the ring dynamics model, the same can be said for the computation of the wear. This means that the entire ring dynamics simulation is run before the LOC model is started. A more in depth explanation of the solution procedure found in Figure 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 for the crank angle. The step size ∆φ is defined and during the simulation the current crank angle is calculated as φi = i∆φ where i is the current iteration. Here the viscosity of the lubricant

is calculated according to the Vogel/Roelands equation (2.13) and the velocity of the piston is evaluated according to (3.1). Every calculation is performed for every step of the crank angle and 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 are

presented in Section 2.5.1.

i) The modified Reynolds equation (2.9) in order to receive the pressure in the lubricant film, 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 the pressure 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 explicit integration 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 based formulation

Once the ring dynamics model has completed every step in the discretization the LOC model will 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 angle resolved 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 asperity contact pressure known from the ring dynamics model the wear load from equation (2.18) can be used to compute the wear depth (2.19)

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3.1. NUMERICAL MODEL DEVELOPMENT CHAPTER 3. METHOD

Initialize crank angle, φi = i∆φ

Iterativly solve the forces act-ing on the ract-ings Solve the equations of

motion using explicit integration in time

Store results for current crank angle Ring dynamics model

Initialize crank angle, φi = i∆φ

Calculate oil con-sumption components

using (2.22)-(2.24) Sum all the components Store results for current crank angle

LOC model Initialize the model

Preprocess the model

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

Iterate until φi = φend Iterate until φi = φend Set i = 0 φ = 0

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3.2. PHYSICAL TESTING CHAPTER 3. METHOD

3.2 Physical testing

Many parameters affect the tribological behaviour of the PRCL contact, one important thing to understand 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 biggest impact on the PRCL contact are the friction coefficient and the wear rate, µ and k respectively. To perform these tests two different experimental rigs where used, a Cameron Plint TE-77 tribometer and 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, utilised by Spencer [5] to test components in the PRCL contact, is a flexible tribometer schematically shown in Figure 3.4.

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

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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 S¨oderfj¨all [22, 38] is used. Here the PRCL contact is run a lower but realistic speeds and the 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 numerical models easier and more flexible. A thorough explanation about the test rig and the processing of the results 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 testing perform 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 that the parameters outside the scope of the physical tests performed in this thesis are accurate. The physical test performed in this work covers the most interesting material parameters of the PRCL contact, the friction coefficient µ and the wear rate k, in the tribological interface of the piston ring and the cylinder liner. In order to receive values of the remaining parameters a reverse parameter identification is performed, an optimization scheme to fit numerical data to available test data. These calibrations are performed for numerical models where the ring dynamics are modelled in 2D. In this work, HEEDS, a software designed to optimize engineering designs, is connected to Excite Piston and Rings to perform the parameter optimization.

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 between the numerical results and the experimental data, to goal is often to minimize or maximize this function under some defined constrains. In this work the optimization is performed in order to receive pa-rameters that can not be measured during any type of test currently available, the ring temperatures 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 gov-erning the flow area for both the lubricant and the combustion gas. The flow coefficients ψ governs 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 the available data the objective function, denoted E1, was defined as

E1 Tring = v u u t 1 n n X i ˙Vm,iζ − ˙Ve,i 2 , (3.2)

where Tring is the mean temperature of the ring, ˙Vm,i is the blow-by from the model for a specific

case i, ˙Ve is the blow-by from experiments, n is the number of cases and ζ is a parameter for scaling

the data to match the conditions of the experiments. E1 is a function of the mean ring temperature

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3.3. CALIBRATION OF NUMERICAL MODELS CHAPTER 3. METHOD minimization problem can be formulated as

min E1 Tring

s.t Tliner ≤ Tring ≤ Tpiston

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 ring

index i, Tliner is the mean temperature of the cylinder liner and Tpiston is the mean temperature of

the piston, more precisely the mean temperature of the ring groove. The constrains on the problem corresponds to that the temperature of the piston ring is bounded between the temperatures of the piston 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 the test data used in the optimization has ring groove temperature. The relationship between the ring temperature and the groove temperature is assumed to be linear on the form Tring = zTpiston, thus

the 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. The inter-ring pressures are the pressures in the chambers in Figure 2.4 and these pressure affect the blow-by and the forces acting on the rings. The chambers in the model are located both in the ring grooves and the 2nd and 3rd piston lands, the chambers between the TCR and LCR and LCR and OCR respectively. As can be seen in the gas flow model presented in Section 2.3 the pressure in the chambers 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}) = v u u t 1 n n X 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 coefcoef-ficients govern the gas flow at three different locations, in the throttle at the top of the ring, the throttle at the bottom of the ring and the throttle at the ring gap. p∗_2ndL denotes the pressure in 2nd piston land from the numerical model, p2ndL is the pressure in 2nd piston land from experimental measurements and n is the number

of cases. The goal is to minimize the RMS objective function or the peak pressure function, since as 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 problem can 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 elements

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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 simulated blow-by is presented. In Section 4.2 the results from the calibration of the inter-ring pressure are presented. Section 4.3 covers the results from the friction caused by the ring pack, and how the overall 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 study of the affect of surface topography measurements and the ring dynamics modelling will be done for the wear of the ring pack and the oil consumption during the engines cycle, in Section 4.4 and 4.5 respectively.

The results presented in this work will be presented as dimensionless, this is done in order to ease comparison between numerical and experimental results and to make it possible to easily compare these 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 experiments the temperature of the ring was optimized according to (3.3). This was done two times for two different cases, one run containing four different load cases and one run containing eight different load cases.

Smaller calibration set

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4.1. BLOW-BY OPTIMIZATION - CALIBRATION OF RING

TEMPERATURE 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] Dimensionless blo w-b y [-] Experimental Baseline Calibrated

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

The baseline numerical model is built on the assumption that the temperature of the piston ring is the mean temperature of the cylinder liner and the piston ring groove. The calibrated numerical model is the results of the optimization, here the ring temperature is set as a linear function of the groove temperature to match the experimental data. To further show the effect of the calibration of the numerical model the difference | ˙Vm,iζ − ˙Ve| is shown as a function of the top compression ring

groove temperature, this difference can be found in Figure 4.2.

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TEMPERATURE CHAPTER 4. RESULTS

180.8 184.3 187.0 198.6 0 0.1 0.2 0.3 0.4 0.5 0.6 TCR groove temperature [°C] Difference in dimen sionless blo w-b y [-] _CalibratedBaseline

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

In order to validate this assumption a linear regression of the measured data is compared to the numerical results from the assumption of a linear relationship between the ring groove temperature and 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 TCR groove temperature [°C] Dimensionless blo w-b y [-] Experimental Experimental fit Calibrated Numerical fit

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TEMPERATURE CHAPTER 4. RESULTS Where the linear regression line of the measured data has a R2 _{value of 0.96 while the linear regression}

line 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 25 1200 50 1200 100 1200 110 1600 110 1800 25 1800 100 1800 110

In order to full-fill the entire map a shape-preserving piecewise cubic spline interpolation scheme was utilised on the calibrated results. For the four different engine loads, 25%, 50%, 100% and 110% the assumptions of a linear relation between ring temperature and groove temperature differs, but the overall assumption still has a R2 _{high enough to be considered valid, although lower for the larger}

dataset than for the smaller one.

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

25 50 100 110 1200 1600 1800 Engine load [%] Engine sp eed [RPM] 0.8 0.85 0.9 0.95 1 Dimensionless blo w-b y [-]

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TEMPERATURE CHAPTER 4. RESULTS After the numerical model is calibrated the blow-by map can be studied, this map is presented in Figure 4.5. 25 50 100 110 1200 1600 1800 Engine load [%] Engine sp eed [RPM] 0.85 0.9 0.95 1 1.05 1.1 1.15 Dimensionless blo w-b y [-]

Figure 4.5: The numerical blow-by map, here the simulated blow-by is presented as a function of both engine 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 the difference between the two maps as a function of engine speed and engine load.

25 50 100 110₁₂₀₀ 1600 1800 −0.2 0 0.2 Engine load [%] Engine speed [RPM] −0.1 0 0.1 0.2 Dimensionless blo w-b y [-]

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

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4.2. INTER-RING PRESSURE OPTIMIZATION - CALIBRATION OF GAS FLOW

COEFFICIENTS 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, the inter-ring pressure in the 2nd _{piston land is optimized according to (3.5). In Figure 4.7 the inter-ring}

pressure from the measurement is compared to the numerical models, both the original and the calibrated ones. The figure also contains the combustion pressure and the pressure in the top ring groove, these are shown in order to better understand the forces on the ring during the engines cycle and to easier see if the calibration is realistic.

−900 0 90 180 270 360 450 540 630 0.02 0.04 0.06 0.08 0.1 Crank angle [◦] Dimensionless pressure [-] Combustion pressure TCR 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% and the difference at peak pressure is 3%. The overall RMS value of the difference between the measured pressure and the numerical pressure is 0.2% and the difference at peak pressure is 0.9for the Pmax

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4.2. INTER-RING PRESSURE OPTIMIZATION - CALIBRATION OF GAS FLOW

COEFFICIENTS CHAPTER 4. RESULTS One interesting finding from Figure 4.7 is the part where the 2nd_{land pressure rises above the pressure}

in the TCR groove. Figure 4.8 shows a zoomed in version of the interesting region.

180 185 190 195 200 205 210 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03 Crank angle [◦] Dimensionless pressure [-] Combustion pressure TCR 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 pressure in the region where the pressure in the 2nd land is higher than the TCR groove.

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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 friction caused 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 pressures found in Figure 2.1, 2.2 and 2.3 respectively, are based. Studies of the effects of the ring dynamics modelling, 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 measuremdiffer-ents. 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 [#] Dimensionless friction force [-] Numerical Measured

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

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4.3. FRICTION CAUSED BY THE RING PACK CHAPTER 4. RESULTS To better understand the effects of the ring dynamics modelling an internal comparison between the 2D 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 15 0.5 0.6 0.7 0.8 0.9 1 Surface measurement [#] Dimensionless friction force [-] 2D 3D

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 the numerical results and thus no measurement data is presented.

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4.3. FRICTION CAUSED BY THE RING PACK CHAPTER 4. RESULTS To gain further understanding of the influence of the different surface measurements, more specifically the 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 ring dynamics modelled in 2D. In these figures trend lines will also be presented, in order to study the effects 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, the arithmetic 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 [-] Dimensionless friction fo 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 numerical model. 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 the dimensionless friction force predicted by the calibrated numerical model. Since Sa seems to show little 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 of the ring pack.

Figure 4.12 shows the influence of Sk on the overall friction force of the ring pack by the numerical model. The same trend can be seen for Sk and Sa, that the friction seems rather constant with regards to the roughness parameter. The overall effect of the parameter seems to not effect the overall 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 propro-truding dales below the core surface respectively, are shown in Figure 4.13 and Figure 4.14.

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4.3. FRICTION CAUSED BY THE RING PACK CHAPTER 4. RESULTS 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 3 3.5 Sk [-] Dimensionless friction force [-]

Figure 4.12: The dimensionless friction force as a function of Sk, the distance between the highest and lowest 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 [-] Dimensionless friction force [-]

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

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4.3. FRICTION CAUSED BY THE RING PACK CHAPTER 4. RESULTS 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 3 3.5 Svk [-] Dimensionless friction force [-]

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

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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 can be calculated. Using Archard’s wear model (2.19) the results in Figure 4.15 are obtained. Here the results, the wear volume over one engine cycle, are presented for each of the 15 different surface measurements and for each individual ring in the ring pack, the top compression ring, the lower compression ring and the oil control ring. 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 0 0.2 0.4 0.6 0.8 1 Surface measurement [#] Dimensionless w ear v olume [-] TCR LCR OCR

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

To better understand the effects of the ring dynamics modelling an internal comparison between the 2D and 3D modelling of the ring dynamics is done. This comparison is shown in Figure 4.16. Due to this being an internal comparison there is no experimental data available for comparison. This internal comparison is from calibrated numerical models.

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4.5. LUBE OIL CONSUMPTION CHAPTER 4. RESULTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0.2 0.4 0.6 0.8 1 Surface measurement [#] Dimensionless w ear v olume [-] TCR LCR OCR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0.2 0.4 0.6 0.8 1 Surface measurement [#] Dimensionless w ear v olume [-] TCR LCR OCR

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 modelling of 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 main components, the evaporation, the blow-up and the throw-off of oil are all summed to get the overall consumption. Figure 4.17 shows the overall LOC of the ring pack over the cycle.

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4.5. LUBE OIL CONSUMPTION CHAPTER 4. RESULTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0.2 0.4 0.6 0.8 1 Surface measurement [#] Dimensionless lub e oil consumption [-] Evaporation_Blow-up Throw-off

Figure 4.17: Total dimensionless lube oil consumption for the 15 surface measurements with the ring dynamics 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 15 0 0.2 0.4 0.6 0.8 1 Surface measurement [#] Dimensionless lub e oil consumption [-] Evaporation_Blow-up Throw-off

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

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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 the simulation of the friction caused by the ring pack in covered in Section 5.2. Section 5.3 covers the discussion of the numerical results from the simulation of the wear predicted by the numerical models. Discussion of the results covering the lube oil consumption is performed in Section 5.4 of this chapter.

5.1 Calibration of numerical models

In the following section of the report the results from the calibration of the numerical models, both the 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 model was 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 from 1200-1800 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 the calibration model and the measured data is significantly smaller than the difference between the baseline model and the measurement. In order to validate the linear assumption at the base of the calibration the measured and numerical blow-by points with their corresponding linear regression lines are shown in Figure 4.3. Since the regression lines have a R2 _{value of 0.96 and 0.95 for the}

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