Ring Piston

Master's Thesis 2010:06

3D Parameterized FEM Modelling of a Piston Ring in aMarine Diesel Engine

A simulation approach using FEM

Jon Elfridsson

Department of PhysicsMaster of Science programme in Engineering Physics

Umeå UniversityUmeå, Sweden, 2010

3D Parameterized FEM Modelling of a Piston Ring in a Marine Diesel EngineA simulation approach using FEMMaster's ThesisJon Elfridsson

Master's Thesis 2010:06

Department of PhysicsMaster of Science programme in Engineering PhysicsUmeå UniversitySe-901 87 Umeå, Sweden

Author: Jon Elfridsson, Umeå UniversitySupervisor: Hans-Gunnar Qvist, Daros Piston Rings ABExaminer: Mats G Larson, Umeå University

Printed at Umeå UniversityUmeå, Sweden 2010

3D Parameterized FEM Modelling of a Piston Ring in a MarineDiesel Engine

Abstract: The piston ring in a marine two-stroke diesel engine operates in de-manding conditions, involving high temperatures and pressures. Its main purposesare to seal the combustion chamber of the engine, minimize the frictional contactagainst the cylinder liner and transfer heat from the piston. The development ofnew piston ring designs for marine diesel engines is mainly based on engineeringknowledge and expertise but is somewhat unstructured.A new method which may be used to overcome this lack of structure is to simulatethe working conditions for the piston ring. This is the main objective of this thesiswork, to invent a simulation method which allows accurate and distinct results tobe obtained and thereby knowledge about piston ring performance.The simulation method is based on a three-dimensional geometric model of the pis-ton ring, where the radial geometry should be described by the lathe curve fromindustry. It should also be implemented and function automatically as a simulationtool. In short terms, the calculated stresses and strains in the material, the contactpressure against the cylinder liner and the piston ring twist should be evaluated. Thesimulation tool should be able to model two dierent types of piston ring designs,namely straight cut design and CPR design, and both with optional dimensions.Validation of the results are performed with a simulation model which uses fewerdimensions, but also utilizes engineering knowledge from the marine industry. Inaddition to this, some more advanced investigations have been performed in orderto demonstrate the capacity and power of the simulation tool.The simulation method appears to perform well and according to the simple model,but it also shows good prediction in more advanced investigations. For example,piston rings in overheated engines tend to twist more than usual, which could beseen in real investigations, and the behavior is easily recreated with the simulationtool. Also investigations with reduced cross sections, which is well known withinhigh-speed engines, are performed.The method is executed automatically with the developed simulation tool which isbased on ANSYS, a commercial simulation software. This software, that is com-monly used in development work, uses a nite element method to solve the problem.The simulation tool is used as an external input which congures the geometry, -nite element formulation and the result rendering.Keywords: piston ring, nite element method, solid mechanics, contact pressure,twist, temperature eld, three-dimensional

3D Parametriserad FEM Modellering av en Kolvring i en MarinDieselmotor

Sammanfattning: Kolvringen i en marin tvåtaktsmotor arbetar under krävandeförhållanden i form av hög temperatur och högt tryck. Dess huvudsyften är att tätamotorns förbränningskammare, minimera friktion mot cylindern och transporteravärme från kolven. Utvecklingen av nya kolvringsmodeller för marint bruk är hu-vudsakligen baserat på ingenjörskunskap och expertkunnande vilket dock lett till enviss osäkerhet.En modern metod för att bemästra denna osäkerhet är att simulera kolvringenoch dess förhållanden i motorn. Det huvudsakliga målet är att skapa en simuler-ingsmetod som ger noggranna och tydliga resultat och därav kunskap om kolvringenspåfrestningar och egenskaper under drift av motorn.Simuleringsmetoden är skapad för en tredimensionell geometri som är beskrivenav bl.a. den svarvkurva som används inom industrin. Metoden skall även varaimplementerad och fungera automatiskt som ett beräkningsverktyg vilket inom enrimlig tidsrymd skall beräkna intresseområden såsom spänningar, kontakttryck ochtwist. Det skall även vara konstruerat så att två olika kolvringmodeller skall kunnasimuleras, nämligen rakskuren ring och gastät ring, och båda med valbara dimen-sioner.Simuleringsmetoden är bekräftad genom att jämföra med en enklare simuleringsmod-ell samt teknisk kunskap och resonemang. Utöver att bekräfta modellen genomförsäven en del mer avancerade undersökningar för att kunna återge simuleringsverk-tygets verkliga eektivitet.Resultaten återger rätt karaktär och i rätt storleksordning i jämförelse med den en-klare modellen men visar även på sanningenliga resultat vid mer avancerade tester.Exempelvis har överhettade motorer ofta en förstärkt twist, vilket är uppmärksam-mat vid mätningar, och sådana eekter kan återges med simuleringsverktyget. Äventester med förändrade tvärsnittsproler, vilka ofta används inom fordonsindustrin,och vilken eekt dessa proler får på twistningen har genomförts.Metoden och det automatiska simuleringsverktyget är implementerat i den kommer-siella programvaran ANSYS. Programmet använder sig av nita elementmetoden föratt lösa problem och är ett vanligt program inom era olika utvecklingsområden.Verktyget används som en extern inläsning till programmet vilket kongurerar ge-ometrin, nita elementformuleringen och resultatrenderingen.Nyckelord: kolvring, nita elementmetoden, hållfasthetslära, kontakttryck, twist,värmelast, tredimensionell

v

AcknowledgmentsThis master's thesis was performed at Daros Piston Rings AB during the winterand spring of year 2010. Several thanks to the sta members at the department ofresearch and development and particularly to my supervisor Hans-Gunnar Qvist forhis supportive and assets during the period. Beyond these main suppliers I wouldalso like to thank the employees at EDR Engineering Data Resources AB, and es-pecially Chouping Luo, for his guidance through diculties in ANSYS. Finally Iwould like to thank my family and friends for their support.

Mölnlycke, 17th June 2010Jon Elfridsson

Contents

1 Introduction 31.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 The two-stroke diesel engine . . . . . . . . . . . . . . . . . . . 31.1.2 The piston ring . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Piston ring designs . . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.1.5 Daros Piston Rings AB . . . . . . . . . . . . . . . . . . . . . 9

1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Theory 132.1 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Function space . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.2 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.3 Orthogonal projection . . . . . . . . . . . . . . . . . . . . . . 152.1.4 Linear system of equations . . . . . . . . . . . . . . . . . . . . 162.1.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Solid mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Static equilibrium and stress . . . . . . . . . . . . . . . . . . 182.2.2 Displacement and strain . . . . . . . . . . . . . . . . . . . . . 192.2.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 192.2.4 The equations of linear elastostatics . . . . . . . . . . . . . . 202.2.5 Variational formulation . . . . . . . . . . . . . . . . . . . . . 202.2.6 Finite element formulation . . . . . . . . . . . . . . . . . . . . 212.2.7 Engineering notation . . . . . . . . . . . . . . . . . . . . . . . 212.2.8 Non-linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Non-linear contact mechanics . . . . . . . . . . . . . . . . . . . . . . 23

3 Method 273.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Main processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Piston ring geometry . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Contact surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Model limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Parameter description . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4.2 Temperature eld . . . . . . . . . . . . . . . . . . . . . . . . . 34

viii Contents

3.4.3 Applied pressure . . . . . . . . . . . . . . . . . . . . . . . . . 343.5 Convergence criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.6 Analyzing results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Results 414.1 Final conguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.1 Final method . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2 Validation of model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 434.2.2 Rened mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.3 Material stress . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.4 Verication of pretwist . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Dierent piston ring grooves . . . . . . . . . . . . . . . . . . . . . . . 464.3.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 464.3.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 474.4.2 Twist at dierent crank angles . . . . . . . . . . . . . . . . . 484.4.3 Additional temperature gradient . . . . . . . . . . . . . . . . 504.4.4 New cross section . . . . . . . . . . . . . . . . . . . . . . . . . 524.4.5 Counteract of temperature gradient . . . . . . . . . . . . . . . 54

5 Discussion 575.1 The method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.1 Usability and eciency . . . . . . . . . . . . . . . . . . . . . . 585.1.2 Reliability and validation . . . . . . . . . . . . . . . . . . . . 585.1.3 Dierent piston ring designs . . . . . . . . . . . . . . . . . . . 595.1.4 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 60

5.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.2.1 Eects due to temperature gradients . . . . . . . . . . . . . . 615.2.2 Eects due to new inner proles . . . . . . . . . . . . . . . . 62

5.3 Main conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.4 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Bibliography 67

A Algorithm description 69

B Input parameters 71B.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Chapter 1

Introduction

This chapter introduces the background to the problem, the purpose with the solu-tion, limitations to get there and the nal objectives with the thesis work. Declara-tion of the purpose with research within the area of marine two-stroke engines andplace it into a bigger context.

Contents1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 The two-stroke diesel engine . . . . . . . . . . . . . . . . . . . 31.1.2 The piston ring . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Piston ring designs . . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.1.5 Daros Piston Rings AB . . . . . . . . . . . . . . . . . . . . . 9

1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.1 BackgroundThe main features of a piston ring is to seal the combustion chamber of the engine,minimize the frictional contact against the cylinder liner and transfer heat from thepiston. Its working conditions are demanding and it is desirable to minimize thethermal stresses and friction by examining the contact pressure, which arises againstthe dierent surfaces of the piston ring, but also see the behavior in total inside ofa running engine. During this section the marine two-stroke diesel engine will beintroduced, its piston ring pack and dierent kind of piston ring designs.

1.1.1 The two-stroke diesel engineA general denition of the diesel engine is

any internal combustion engine in which air is compressed to a su-ciently high temperature to ignite diesel fuel injected into the cylinder,where combustion and expansion actuate a piston. [Britannica 1990]

4 Chapter 1. Introduction

The piston in a two-stroke diesel engine operates up and downward as in aconventional combustion engine but in dierence from the general two-stroke petrolengine the diesel engine does not use a mixture of air, fuel and oil which transfersthrough the crankcase before ignition. Instead the crankshaft bearings are lubricatedas in a four-stroke engine and the fuel is injected directly into the cylinder via a fuelinjector. The engine cycle of a typical two-stroke diesel engine could be describedin four distinct phases and is graphically illustrated in gure 1.1.

The four phases are

Compression (gure 1.1(a)): The piston is moving upward along the cylinderliner and the crankshaft rotates clockwise. As the piston moves, the air in thecylinder becomes compressed and the temperature increases.

Expansion (gure 1.1(b)): When the piston approaches the top of the cylin-der, often referred to as the top dead center (TDC), the fuel is injected bythe fuel injector. Because of high pressure and high temperature the injectedfuel, which usually appears as tiny droplets, ignites while the piston passes theTDC. The piston is forced downward because of the expanding gas arisen fromthe burning fuel and the translational energy from the movement is convertedinto rotational energy in the crankshaft.

Exhaust (gure 1.1(c)): During the movement of the piston along the cylinderliner the high energy in the combustion gas is rapidly decreasing. Approxi-mately 110 crank angle degrees after TDC the exhaust valves opens and amixture of nitrogen, carbon dioxide, water vapor and unused oxygen escapesfrom the cylinder.

Air intake (gure 1.1(d)): When the piston approaches the bottom deadcenter (BDC), i.e. the lowest position of the piston, the piston uncovers aset of scavenging ports. Pressurized air ows into the cylinder and pushesthe remaining exhaust gases through the exhaust valve. When the piston haspassed the BDC, the scavenging ports and the exhaust valve closes and a newcompression cycle begins.

(a) Compression. (b) Expansion. (c) Exhaust. (d) Air intake.

Figure 1.1: The engine cycle for a two-stroke diesel engine.

1.1. Background 5

In the general two-stroke engine the crankshaft is connected directly to the pistonvia the connecting rod. The involved side thrust, because of the possible angularityof the piston, is transmitted to the cylinder liner by the piston skirts or the trunk.To prevent this side thrust a new type of engine, called the crosshead engine (seegure 1.2), was invented. The principle of this engine is the same but the gain withthe crosshead engine is that it minimizes the side thrust but also prevents crankcaseexplosions occurring in regular engines. Another advantage of the crosshead engineis that it allows longer stroke, which in turn allows a greater quantity of fuel to beignited. Because of this, the crosshead engine also could become more powerful.

Figure 1.2: A schematic overview of the crosshead engine.

The combustion chamber of the engine is bounded by the cylinder liner, thepiston and the cylinder head. Dierently to the general engine, the crankcase isseparated with a diaphragm plate and the alignment of the piston rod is xed by astung box which is mounted on this plate. The stung box also provides a perfectseal between the crankcase and the combustion chamber avoiding oil and gas to passbetween the two spaces. At the bottom of the piston rod the crosshead connect thepiston rod to the crankshaft and transmit the downward force into rotational energy.The crosshead motion is supported by guide shoes to ensure a perfect alignment ofthe piston along the cylinder liner.[Marinediesels 2010]

1.1.2 The piston ringThe piston ring is one of the main components of an internal combustion engine.Its main purposes are to seal the combustion chamber of the engine, minimize thefriction against the cylinder liner but also transfer heat from the piston to the cooledcylinder liner. Another important property of the piston ring is to evenly distribute


oil along the cylinder liner in order to avoid engine seizure. The working conditionsfor the piston ring are very demanding and it is desirable to optimize these factorsby analyzing the behavior of the piston ring.

One cylinder in a modern marine two-stroke diesel engine usually contains fourto ve piston rings referred to as the ring pack and for each of the piston ringsthere is a corresponding piston ring groove at the piston in which the piston ringis mounted. The top ring of the ring pack normally has a base material of highergrade cast iron and sometimes the ring is thicker and higher than the other pistonrings in the ring pack. These design modications are added because the top ringis working under higher thermal and mechanical load compared to the lower rings.

When the engine is turned o the single piston ring is only aected by the contactsurfaces against the cylinder liner and the piston ring groove. But when the engineis running the piston ring pack is also aected by gas pressures and temperatureresulting from compression and combustion. The cylinder pressure acts on the upperpart of the top piston ring and a fraction of the cylinder pressure acts below thetop piston ring. Acting forces of a piston ring, both in ideal state and under realworking conditions, could be viewed in gure 1.3.

(a) Ideal forces. (b) Real working conditions.

Figure 1.3: The pressure conditions for the cross section of the piston ring.

The base material in a marine piston ring is vermicular or ductile cast iron andthere is often an anti-wear or running-in coating on the outer surface of the pistonring. Typical dimensions of a piston ring in a marine two-stroke diesel engine is 500to 1000 mm in diameter, 15 to 30 mm in radial thickness and 10 to 20 mm in axialheight.

When mounting a piston ring it is very common with plastic deformation whenbending the ring over the piston. This could have critical eects on the contactpressure against the cylinder liner but when the ring is mounted in the right way itis, dependent on engine load, expected to last for 30,000 hours. The plasticity dueto mounting is taken into account when designing the lathe curve (circumferentialgeometry) of the piston ring. When the piston ring has been mounted on the pistonit needs to be compressed to t inside the cylinder, as shown in gure 1.4, andthe optimal lathe curve will achieve a circumferentially uniform contact pressure

1.1. Background 7

(a) Compressed and uncompressedshape.

(b) Compressed and mounted intothe cylinder.

Figure 1.4: The radial deformation of the piston ring.

along the outer surface of the piston ring. Beyond the circumferential geometry anasymmetry is designed in the axial height of the piston ring with the purpose toreduce the contact pressure.

A feature of the piston ring shape is that when the piston ring is compressedinto the cylinder liner and under combustion pressure, the piston ring experiencesa twist. The twist is dened as the dierence of location in height for the inner andouter radial prole compared to the initial uncompressed shape. If the outer surfaceis higher than the inner prole the twist is positive, also called inward twist, andif the outer surface is lower than the inner prole the twist is negative or outward.Piston ring twist is further discussed in section 3.6.

There are techniques to prevent and improve twist by changing the inner proleof the cross section. By changing the inner prole an initial twist may be accom-plished and this is commonly used for smaller high-speed engines. The main functionis to prevent the bottom surface of the piston ring to be exposed to the high com-bustion pressure, which is in order to prevent the piston ring from lifting and thusfailing to seal the combustion chamber.[Corbat 1974]

1.1.3 Piston ring designsPiston ring research areas mainly cover geometry, coatings and base materials. Thisthesis involves theoretical and mechanical engineering, and the main focus is thegeometry of the piston ring design.

There are many dierent geometrical ring designs in marine engines but twoof the most common designs are the straight cut design and the CPR (ControlledPressure Release) design. The straight cut design consists of a straight opening inthe piston ring geometry, as in gure 1.4. This opening allows a blow-by ow ofcombustion gases and it is therefore natural to reduce the blow-by ow rate as muchas possible by minimizing the ring gap under extreme conditions. Due to thermalload and wear, the diameter of the cylinder liner is varying along the stroke. This


aects the piston ring gap and with a larger diameter of the cylinder liner the pistonring opening becomes larger and increased blow-by ow follows. A drawback of thestraight cut design is that the thermal load near the opening may become very highbecause of blow-by ow of hot combustion gases.

In order to avoid this problem the CPR design has been introduced. This designinhibits the gas ow around the gap with a gas lock and distributes the blow-by gasesthrough specic grooves, called CPR grooves, instead. There are generally four to sixgrooves around the outer surface of the piston ring for this purpose. Another positiveeect of the CPR design is that the ow past the piston ring is nearly unaected ofthe diameter of the cylinder liner since the gas lock adapts automatically. The maindisadvantage of this design is the more costly manufacturing. A schematic gas lockdesign is depicted in gure 1.5.

(a) View at bottom surface (uncom-pressed shape).

(b) View at outer surface (com-pressed shape).

Figure 1.5: The geometry of the gas lock of a CPR designed piston ring.

1.1.4 Previous work

There is a previously performed thesis work in which the authors performed Com-putational Fluid Dynamics (CFD) simulations of the blow-by ow in the previouslymentioned ring designs. The authors predicted the blow-by ow past the openingand at the CPR grooves of the piston rings and from this they calculated the temper-ature eld of the piston ring. With this temperature eld the authors then calculatedthe contact pressure of the piston ring against the cylinder liner.[Grahn 2009] Gen-eral trends in contact pressure could be predicted with this model, but the localcontact pressure was irregular due to numerical problems. Some previous resultsare presented in gure 1.6.

Piston ring geometries are normally developed by engine designers or pistonring makers and to achieve accurate and meaningful results the geometries usedin the simulations are made according to real lathe curves used in manufacturing.Each geometry is generated to produce a constant contact pressure at a specictemperature of the piston ring.

Important boundary conditions, like radial overdimension of the cylinder linerand gas pressure in the combustion chamber, are provided by an engine manufac-turer. This information is then used in a simulation with the software AVL EXCITEto evaluate the pressure conditions for each piston ring in the ring pack. The radialoverdimension and the pressure conditions for the top ring, in a specic engine, aredeclared in gure 1.7.

1.1. Background 9

(a) Approximation with rst order elements.

(b) Approximation with higher order solid elements.

Figure 1.6: The contact pressure at the outer surface of the piston ring from previ-ously performed work.

(a) Radial overdimension. (b) Pressure.

Figure 1.7: Technical conditions of the piston ring which is investigated in chapter4. Crank angle 0° corresponds to TDC.

1.1.5 Daros Piston Rings ABIt was in the end of the 18th century the young Scot Peter Robertson foundeda smithy in Gothenburg, Sweden. This was in the year of 1792 and sixty yearslater David Robertson's engineering started. It was the rst factory to specialize inpiston rings and later on it turned into Daros Piston Rings AB. The specializationhappened after the development and patent of an automatic hammering machinefor piston rings in year 1899. It was also by this time the new factory in Partille,Gothenburg, opened with the purpose to manufacture piston rings for two-strokemarine engines and power plants.[Daros 2002]

Today, Daros Piston Rings AB is focusing on piston rings for marine two-stroke


diesel engines and it is one of the most established companies worldwide within thisarea. The complete manufacturing process of piston rings is performed inside thenewest factory in Mölnlycke. With expertise in geometry, material, tribology andadvanced coatings the company fullls the requirements on a tough market. Theproduction of piston rings performed by the company involves new engines as wellas services at vessels. The logotype of Daros Piston Rings AB could be viewed ingure 1.8.

Figure 1.8: The logotype of Daros Piston Rings AB.

1.2 PurposeThe development of new piston ring designs is nowadays mainly based on engineeringexperience and expertise. But even though development has progressed during thelast 100 years there is still a need of knowledge about the actual performance andbehavior of the piston rings in an engine. It is dicult to measure relevant quantitiesin a running engine and the accuracy of such measurements is often insucient. Themain purpose of this thesis is to increase the understanding of the piston ring and itsworking conditions through a simulation tool that could be applied to investigate theperformance of a piston ring package. Simulation techniques have been successfullyapplied to many other disciplines of engineering but there is still no established toolfor three-dimensional simulations of the piston ring package in a marine two-strokediesel engine.

The main focus is to work with the straight cut designed piston ring to investigatesubjects which could arise in a three-dimensional model, like for example piston ringtwist. A simulation model for CPR designed piston rings should also be developedto investigate the main dierences in the working conditions for dierent piston ringdesigns.

1.3 LimitationsAn important aim with the thesis is to create a user-friendly simulation environmentthat is easily adaptable to cope with design changes. A typical engine has several

1.4. Objectives 11

piston rings in the ring pack but only the top ring is considered here because it ismost heavily loaded and the one which is working under the harshest conditions.

Because of the ring motion inside the piston ring groove it is dicult to specifyaccurate boundary conditions, i.e. pressures and temperature, on the piston ring.Boundary conditions are also somewhat simplied due to limitations in the meshquality of the nite element model.[Ansys 2007] In the simulations only steady stateloads are considered.

1.4 ObjectivesThe main objective is to design a simulation tool which enables the company toperform three-dimensional calculations and analyzes of a piston ring pack. Analysistools to evaluate the contact pressure, on the surfaces of the piston ring, and the totaldeformation, including twist, will be included. From the results given in simulationsit should be possible to analyze and distinguish the characteristic behavior of thepiston ring in order for it to be useful in future development. The objectives whichshould be performed during the thesis work are

Find a three-dimensional simulation method to predict the behavior of a pistonring in a marine two-stroke diesel engine.

Create an automatic simulation process which enables the rst objective.

Analyze the piston ring twist behavior of a piston ring under dierent workingconditions.

Chapter 2

Theory

This chapter claries the underlying theory in the applied methods in next chapter(chapter 3, Method). The purpose is to get an understanding of the governingequations of the problem and to achieve better insight when analyzing the results.Equations of solid mechanics will be described and the engineering technique tosolve the problem will be declared during the chapter.

Contents2.1 Finite element method . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Function space . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.2 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.3 Orthogonal projection . . . . . . . . . . . . . . . . . . . . . . 152.1.4 Linear system of equations . . . . . . . . . . . . . . . . . . . 162.1.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Solid mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Static equilibrium and stress . . . . . . . . . . . . . . . . . . 182.2.2 Displacement and strain . . . . . . . . . . . . . . . . . . . . . 192.2.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 192.2.4 The equations of linear elastostatics . . . . . . . . . . . . . . 202.2.5 Variational formulation . . . . . . . . . . . . . . . . . . . . . 202.2.6 Finite element formulation . . . . . . . . . . . . . . . . . . . 212.2.7 Engineering notation . . . . . . . . . . . . . . . . . . . . . . . 212.2.8 Non-linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Non-linear contact mechanics . . . . . . . . . . . . . . . . . . 23

2.1 Finite element methodThe nite element method is an approximative approach of modeling natural phe-nomena described by partial dierential equations. It is straightly developed fromthe laws of mathematics and often applied on physical problems such as solid me-chanics. The basic concepts of the nite element method applied on a physicalproblem are

Divide the domain into smaller subdomains which are dened as the niteelements.

14 Chapter 2. Theory

For each element, formulate intuitive relations among the physical variablessuch as mechanical forces, displacements and temperature.

Combine the elements with given relationships and obtain the variables ofinterest for each discrete element and by that, the whole system.

To clarify for the nite element method rst of all the used function space andthe approximation methods are needed to be declared. Then, the linear system ofequations and how the problem nally could be solved, is described.

2.1.1 Function spaceIf I = [a, b] is an one-dimensional interval with N + 1 distinct node points denotedby xiN

i=0 the interval I could be divided into N subintervals Ii = [xi−1, xi], fori = 1, 2, ..., N , and each with the individual length hi = xi − xi−1. In the niteelement method this partition of subintervals is referred to as the mesh of the domainand each subinterval as an element. The nodes contain the information of the model.

Introduce the function space Vh of continuous piecewise linear functions over theclosed interval I as

Vh = v : v ∈ C(I), v|Ii ∈ P1(Ii) (2.1)

with the space C(I) of continuous functions on I and the space P1(Ii) of linearfunctions on Ii. The functions in Vh thus become linear on each subinterval Ii

and continuous on I. For each set of nodal values in the interval I there exists afunction v ∈ Vh with exactly these nodal values. With this knowledge the new basisϕjN

j=0 ⊂ Vh is introduced where

ϕj(xi) =

1 if i = j

0 if i 6= j, for i, j = 0, 1,..., N (2.2)

The shape of the basis functions are displayed in gure 2.1.

Figure 2.1: The basis functions ϕ0(x) and ϕi(x).

Each one of the hat functions is continuous piecewise linear and have the value oneat the corresponding node point and zero at all other. The interval where the hatfunction is nonzero is called the support of the function and the support of ϕi istherefore Ii ∪ Ii+1. With this basis consisting of hat functions, all functions v ∈ Vh

2.1. Finite element method 15

could be described as a linear combination

v(x) =N∑

i=0

aiϕi(x) (2.3)

where ai is the value of the function v at each corresponding node. Observe that ϕ0

and ϕN are dierent in shape compared to the other basis functions since they arelocated at the boundaries of the interval.

Higher order basis functionsThis basis of hat functions could actually be any function which achieves a unit valueat the corresponding node and zero at all other nodes. The function space could forexample contain second order polynomials P2 and the hat functions could therebybe more smooth. This could have a big inuence in eciency and less node pointsare often needed if v is a smooth function which could be described by higher orderpolynomials over discrete subintervals. A important notice though, when describinga second order polynomial, is that it is necessary with three node points for eachfunction instead of two for a linear description.

2.1.2 InterpolationThe linear interpolation of a continuous function f is by denition given by

πf = f(x0)ϕ0 + f(x1)ϕ1 (2.4)

where the interpolation πf and the function f achieve the same values at the nodesx0 and x1. By extending the interpolation to the more useful case with continuouspiecewise linear functions the interpolant is dened as

πf =N∑

i=0

f(xi)ϕi (2.5)

and an example of a linear interpolation is shown in gure 2.2(a).

2.1.3 Orthogonal projectionAnother alternative approximation of a continuous function is orthogonal projection.In comparison with interpolation the projection method gives a good approximationon average instead of exact values at the node points. A big advantage of using themethod of orthogonal projection is also that it does not require continuous functions.Start by dening the space L2(I) by square integrable functions over the interval I

asL2(I) = v :

∫

Iv2dx < ∞ (2.6)

with the scalar product

(v, w) =∫

Ivw dx, ∀v, w ∈ L2 (2.7)


and norm‖v‖ = ‖v‖L2 =

√(v, v) (2.8)

If the scalar product (v, w) = 0 the two functions v and w are orthogonal to eachother.

The projection Phf of the function f ∈ L2(I) onto the space Vh is described by∫

I(f − Phf)v dx = 0, ∀v ∈ Vh (2.9)

and an orthogonal projection is showed and compared to the corresponding linearinterpolation in gure 2.2. For both methods the same mesh is used and the dif-ference between interpolation and orthogonal projection is clear from the gure.The interpolation approximate the original function exact on the nodes and theprojection approximate on the average over the whole interval.

(a) Interpolation. (b) Orthogonal projection.

Figure 2.2: Two dierent approximations with a uniform mesh over the closed in-terval I = [0, 1] and with f(x) = x · cos(πx).

2.1.4 Linear system of equationsBecause equation 2.9 is satised for every choice of function v ∈ Vh, the equation willalso be valid for a linear combination of functions v ∈ Vh. Therefore the equationcould be expressed as

∫

I(f − Phf)ϕi dx = 0, for i = 0, 1,..., N (2.10)

The projection Phf could be written as a linear combination of hat functions becausethe denition is made up from the continuous piecewise linear functions. It couldwith the unknown coecients ξj , for j=0,1,..,N, be expressed as

Phf =N∑

j=0

ξjϕj (2.11)

2.2. Solid mechanics 17

Equation 2.10 could be rewritten as∫

Ifϕi dx =

∫

I

N∑

j=0

ξjϕj(x)

ϕi dx

=N∑

j=0

ξj

∫

Iϕjϕi dx, for i = 0, 1,..., N (2.12)

and by dening

mij =∫

Iϕjϕi dx, for i, j = 0, 1,..., N (2.13)

bi =∫

Ifϕi dx, for i = 0, 1,..., N (2.14)

equation 2.12 is simplied to

bi =N∑

j=0

mijξj , for i=0,1,...,N (2.15)

This is a system of linear equations with the unknown coecients ξj and in matrixform equation 2.15 is expressed as

b = Mξ (2.16)

The matrix M and the vector b is called the mass matrix and load vector respec-tively, and the orthogonal projection of the function f is found by linear algebra

ξ = M−1b (2.17)

2.1.5 ImplementationTo calculate the mass matrix and the load vector a numerical integration method isneeded to be introduced. There are dierent types of numerical methods to performcalculations of integrals where the midpoint rule, trapezoidal rule, Simpson's Ruleand Gauss quadrature are the most common. The basic feature of these quadraturerules are that they all could be described by

QI(f) =n∑

j=1

ωjf(qj) (2.18)

where wj is the weight of the quadrature and qj the quadrature point.[Larson 2007]

2.2 Solid mechanicsThe basic feature of solid mechanics is to describe the motion and deformation ofa solid volume under external loads. It is a part of continuum mechanics and a bigbranch in both mechanics, physics and mathematics. In this section the governingequations will be declared and how these are applied with the nite element methodwill be shown.


2.2.1 Static equilibrium and stressThe basic concept with solid mechanics is that the net force acting on any solidvolume must vanish in the equilibrium state. There are two dierent kinds of forceswhich acts on a volume and these are volume forces and contact forces. The volumeforces penetrates the whole volume and could be described by a force density f .An example of a typical volume force is the gravity acting on a solid body. Thecontact force on the other hand acts on the surface of the solid volume. Althoughthe force only act directly on the surface it is described by vector elds that existin the whole volume. One simple intuitive example of a contact force is appliedpressure, for example from a gas, with forces acting normal to the surface. Thecontact forces are described by the stress tensor σ, which in fact is a 3× 3 matrix,where each element σij describe the force per unit area acting in the direction xi ona surface with normal direction xj . Total force acting on a volume V with surfaceS is then the combination of volume and surface contributions

F =∫

Vf dV +

∫

Sσ · n dS (2.19)

The surface integral could be converted into a volume integral with the divergencetheorem and the result become

F =∫

V(f +∇ · σ) dV (2.20)

where the following notation is used

(∇ · σ)i =3∑

j=1

∂σij

∂xj, for i = 1, 2, 3 (2.21)

To achieve force equilibrium within the solid volume the total force F must be equalto zero, which will be achieved when

f +∇ · σ = 0 (2.22)

This equation is also called Cauchy's equation of equilibrium. The important mean-ing of the equation is that the net force of every individual particle in a materialthroughout the volume V vanishes. This result could also be compared and showedto be consistent with Newton's second law of nature.[Larson 2009]

In addition to equation 2.22, the fundamental equation for isotropic linear elasticsolids needs to be described. This equation describe the local relations between thestresses and the local state of matter of the solid. By enforcing conservation ofthe angular momentum the stress tensor could be shown to be symmetric and thisreduces the tensor to six independent components

σ = σT (2.23)


2.2.2 Displacement and strainBy describing how each individual particle in a volume is displaced from its ini-tial position (u = x − x0) the total deformation of the body could be evaluated.The individual deformations are described by the strain tensor which under smalldisplacements could be dened as the 3× 3 matrix

ε =12

(∇u +∇uT)

(2.24)

Any deformation in the solid body is caused by the displacement u, and thereforethe strain tensor does not vanish if u 6= 0. This could be compared with classicalrigid body translations and rotations which enforce ε = 0. The diagonal componentεii of the strain tensor describes the relative change in length along the xi-axis andthe o-diagonal element εij describes the change in the direction initially orthogonalto the axes xi and xj . With knowledge that solely translations and rotations couldnot eect the body stresses, the stresses only depend on the local strains. In fact,when the strains are small, the relation between the stress tensor and the straintensor could be assumed to be approximately linear. This is not a law of nature butinstead deduced from empirical measurements and experiments, and the relationis often referred to as Hooke's law. By symmetry reasons in an isotropic material(independent of spatial direction) and assuming that there are no stresses in theinitial uncompressed body, the relationship between the two tensors is

σ = 2µε(u) + λ(∇ · u)I (2.25)

where I is the 3× 3 identity matrix. The elastic moduli, µ and λ, called the Laméparameters are dened by

µ = E2(1+ν) λ = Eν

(1+ν)(1−2ν) (2.26)

where E, Young's elastic modulus, describe the stiness of the material and ν,Poisson's ratio, measure the tendency to narrow the cross section of the materialwhen it is stretched. Combine the equation of force equilibrium (equation 2.22)with the linear relationship (equation 2.25), the result consist of a two vector valuedpartial dierential equation which govern the displacement vector u by

−∇ · σ = f (2.27a)σ = 2µε(u) + λ(∇ · u)I (2.27b)

2.2.3 Boundary conditionsThe boundary conditions of the physical problem are very important in order toachieve results of importance and the specic boundary conditions correspond tothe unique solution u of the problem. There are two dierent types of boundary


conditions in solid mechanics, namely, Dirichlet's and Neumann's boundary condi-tions. Dirichlet's is directly constrained on the displacement vector u and normallytake the form u = gD. Neumann's boundary conditions control the normal stressesand take the form σ ·n = gN . Both gD and gN should be given from the formulationof the problem.

2.2.4 The equations of linear elastostatics

Consider the following problem formulation. Find the stress tensor σ and the dis-placement vector u for the homogeneous isotropic linear elastic solid described bythe domain Ω, such that

−∇ · σ = f x ∈ Ω (2.28a)σ = 2µε(u) + λ(∇ · u)I x ∈ Ω (2.28b)u = gD x ∈ ΓD (2.28c)

σ · n = gN x ∈ ΓN (2.28d)

where ΓD and ΓN are boundary segments such that the union ΓD ∪ ΓN = ∂Ω andthe intersection ΓD ∩ ΓN = ®. The combination of these equations is referred asthe equations of linear elastostatics.[Larson 2009]

2.2.5 Variational formulation

Dene the subspaceV = v ∈ [H1(Ω)]3 (2.29)

where H1(Ω) = v : ‖∇v‖ + ‖v‖ < ∞. Multiply equation 2.28a with the testfunction v ∈ V and integrate by parts which give

(−∇ · σ, v)Ω =3∑

i,j=1

(−∂σij

∂xj, vi

)

Ω

=3∑

i,j=1

−(σij , njvi)∂Ω +(

σij ,∂vi

∂xj

)

Ω

= (f , v)Ω (2.30)

Rewrite the expression and the variational formulation could with the introducedcontraction operator be written

Find u ∈ V such that

(σ : ∇u)Ω − (σ · n, v)∂Ω = (f , v)Ω, ∀v ∈ V (2.31)


2.2.6 Finite element formulationDene the space

V h = v ∈ [Vh]3 (2.32)

with Vh dened in equation 2.1. The nite element formulation is

Find U ∈ V h such that

(σ : ∇U)Ω − (σ · n, v)∂Ω = (f , v)Ω, ∀v ∈ Vh (2.33)

2.2.7 Engineering notationFor technical engineering the formulation of the relationships are customary rewrit-ten as the product of a couple of matrices. By rearranging the independent nonzerocomponents of the stress tensor and the strain tensor into vectors, this induce

σ =[σ11 σ22 σ33 σ12 σ23 σ31

]T (2.34)

ε =[ε11 ε22 ε33 2ε12 2ε23 2ε31

]T (2.35)

The relation between stresses and strains are still described by Hooke's law (equation2.25) but now expressed with vector notations as

σ = Dε (2.36)

where D is the elastic stiness modulus matrix for tree dimensions

D =

λ + 2µ λ λ 0 0 0λ λ + 2µ λ 0 0 0λ λ λ + 2µ 0 0 00 0 0 µ 0 00 0 0 0 µ 00 0 0 0 0 µ

(2.37)

In addition to this the solid material could have internal strains caused by thermalexpansion. These thermal strains are subtracted from the right hand side of equation2.36 and result in

σ = Dε−Dε0 (2.38)

The thermal strain tensor is described by

ε0 = α∆T[1 1 1 0 0 0

]T (2.39)

where α is the coecient of thermal expansion and ∆T the dierence in temperaturebetween two dierent states.[Grahn 2009]

In engineering notations, the nite element ansatz U ∈ V h, could be written as


U =

U1

U2

U3

=

ϕ1 0 0 ϕ2 0 0 · · · ϕN 0 00 ϕ1 0 0 ϕ2 0 · · · 0 ϕN 00 0 ϕ1 0 0 ϕ2 · · · 0 0 ϕN

d11

d12

d13

d21

d22

d23...

dN1

dN2

dN3

=

= ϕd (2.40)

where ϕi, for i = 1 ,..., N, are the hat functions dened in equation 2.2. Vector d

contain the displacements of the nodes and for a three-dimensional problem thereare three vector elements for each node, each representing the displacement for eachdirection in the coordinate system. Displacements of the nodes and the strain eldare related by equation 2.24 or in engineering notations

ε =

ε11

ε22

ε33

2ε12

2ε23

2ε31

=

∂∂x1

0 00 ∂

∂x20

0 0 ∂∂x3

∂∂x2

∂∂x1

00 ∂

∂x3

∂∂x2

∂∂x3

0 ∂∂x1

u1

u2

u3

=

= ∇u (2.41)

This leads to the introducing of the strain matrix B which is given by

B =

∂∂x1

0 00 ∂

∂x20

0 0 ∂∂x3

∂∂x2

∂∂x1

00 ∂

∂x3

∂∂x2

∂∂x3

0 ∂∂x1

ϕ1 0 0 ϕ2 0 0 · · · ϕN 0 00 ϕ1 0 0 ϕ2 0 · · · 0 ϕN 00 0 ϕ1 0 0 ϕ2 · · · 0 0 ϕN

=

= ∇ϕ (2.42)

and the discrete strains and stresses could with the new notations be expressed as

ε = Bd (2.43)σ = DBd (2.44)

The nite element formulation of the problem could then be written as(∫

ΩBT DB dΩ

)d =

(∫

ΩϕT f dΩ

)+

(∫

∂ΩϕT g ∂(∂Ω)

)+

(∫

ΩBT Dε0 dΩ

)

(2.45)

2.3. Non-linear contact mechanics 23

where g correspond to the combination of both Dirichlet's and Neumann's boundaryconditions. Equation 2.45 could in vector and matrix notations be written

Kd = F (2.46)

and the displacements are given with linear algebra

d = K−1F (2.47)

2.2.8 Non-linearityThe governing of solid mechanics is the observation of small displacements and alinear relationship for the model. In many cases the linear relationship is not trueif large displacements occur in the model but non-linearities could also arise in thematerial stability or with the specied boundary conditions. To avoid non-linearproblems an iterative solver is often used during the solution process, which per-form linearly approximated calculations step by step. One of the most commonmethods is Newton's iteration method and this method rely on calculating the er-ror δ of an initial guess of the displacements. Then, in an iterative manner, thedisplacement vector updates with the calculated error, and so on, until the errorbecomes condentially small. By putting d = d0 + δ in equation 2.47 the error δ ofthe guess d0 could be calculated as

δ = K−1F − d0 (2.48)

The updating scheme for Newton's iteration method would look like

Make an initial guess d0 of the displacements.

Calculate the error δ.

Update the displacements with d = d0 + δ. Then put d0 = d as a new guess.

Repeat step two and three until the displacement error δ get small enough.

2.3 Non-linear contact mechanicsA special feature of non-linear solid mechanics appears at the boundary of the solid,or more precisely where there is contact against any other object and penetrationoccur. The penetration of a contact surface is generally composed by a surfaceloaded with springs which enforce the solid to strike against any other collidingsurface. There are many dierent methods for this purpose but two of the mostcommon are the pure penalty method and augmented Lagrange method.

The pure penalty method require normal and tangential contact stiness of thesurface and the actual penetration of a surface depends on the stiness of the springs.An introduced contact traction vector is expressed as

[P τ 1 τ 2

]T (2.49)


where P is the normal contact pressure and τ 1 and τ 2 the frictional stress in twodierent directions. The contact pressure at each spring could be written

P =

0 if un > 0Knun if un ≤ 0

(2.50)

where Kn is the contact normal stiness and un the contact gap size (compare withthe force in a physical spring). Frictional stress for each node is given by

τi =

Ksui if ‖τ‖ =

√τ21 + τ2

2 − µisoP < 0 (sticking)µisoKnun if ‖τ‖ =

√τ21 + τ2

2 − µisoP = 0 (sliding) (2.51)

where Ks is the tangential contact stiness, µiso the coecient of friction and ui

the contact slip distance in direction i.The augmented Lagrange method is an iterative method of evaluating the penalty

updates involved in the pure penalty method. For the augmented Lagrange methodthe contact pressure is dened by

P =

0 if un > 0Knun + λi+1 if un ≤ 0

(2.52)

where λi+1 is the Lagrange multiplier. Its denition is

λi+1 =

λi + Knun if |un| > ε

λi if |un| ≤ ε(2.53)

where ε is a compatibility tolerance for the method. The multiplier λi, at iteration i,is calculated locally for each element and iteratively. Augmented Lagrange methodis a more expensive method but commonly recommended because it has shown goodperformance in most types of problems and especially problems with large and rapiddeformations.[Ansys 2007]

Chapter 3

Method

This chapter describes the systematic work ow, the used methods during the con-guration and the execution of the automatic simulation tool. The chapter includeinformation about how the piston ring geometry is congured, how the surroundingenvironment is generated and how the loads are applied on the piston ring. Further,information about how to evaluate the results and how to counteract convergenceproblems will be discussed.

Contents3.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Main processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Piston ring geometry . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Contact surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Model limitations . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Parameter description . . . . . . . . . . . . . . . . . . . . . . 34

3.4.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4.2 Temperature eld . . . . . . . . . . . . . . . . . . . . . . . . 343.4.3 Applied pressure . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5 Convergence criteria . . . . . . . . . . . . . . . . . . . . . . . . 363.6 Analyzing results . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 ApproachSome main challenges with the simulations are the conguration of the piston ringgeometry, the large deformations which are involved when the piston ring is mountedinto the cylinder and also advanced surface interactions. The piston ring geometryis implemented as uncompressed but when mounted into the cylinder it becomescompressed, thus generating a circumferential contact pressure against the cylinderliner. Also the temperature eld has a very important eect on the simulation resultbecause this eld will induce thermal stresses in the ring due to thermal expansion.

Because of the cyclic behavior of the diesel engine (described in section 1.1.1)it is unavoidable to neglect the temporal dimension. But since the time scale for

28 Chapter 3. Method

cyclic motion in the engine is assumed to be much longer than the time scale for thepiston ring boundary conditions (the gas ow passing the piston ring, twist, rotationetcetera) the problem is discretized into a series of steady state simulations. For eachinstant crank angle the corresponding cylinder liner diameter and pressures are usedfor prediction of the piston ring behavior.

The simulation tool is set up with the commercial engineering software ANSYS.ANSYS is a simulation software based on the technology of nite elements withapplications for solid mechanics and advanced non-linear contact mechanics. Allsimulations are performed on a workstation PC with a dual core 3.16 GHz CPU, 8Gb RAM and a 64-bit Windows 7 operating system.

3.2 Main processesThis section describes the procedure in each step of the simulation work ow. Thegeometry of the piston ring and the boundary conditions may easily be modiedin the simulation environment and it is also possible to adapt specic simulationwork ows. For the advanced user it is recommended to analyze the simulation toolthoroughly to obtain a deeper understanding with help of the reference manual forADPL (ANSYS Parametric Design Language) commands, which is the programminglanguage in ANSYS. During a simulation there are mainly four dierent processeswhich are executed and these are

Design of the piston ring geometry.

Solid element mesh generation.

Generation of contact surfaces.

Application of the specic boundary conditions.

3.2.1 Piston ring geometryThe piston ring geometry is implemented in the uncompressed shape in order toachieve the correct contact pressure when the piston ring is mounted, i.e. in contactwith and inside the cylinder liner. This is achieved with the outer radial prolegenerated with the lathe curve generator, which is a software used at the companywhen designing the lathe curves for the production of new piston rings. The maindierence between the lathe curve generator and the newly developed tool is theneglected dimension of axial height. For example, the crowned running surfaceagainst the cylinder liner on the piston ring cannot be handled with the lathe curvegenerator. However, the running surface has an important inuence on the dynamicbehavior of the piston ring.

The generation of the piston ring geometry is automatically executed by the sim-ulation tool with help of input les, containing geometrical specications, combinedwith the corresponding dimensions. If the piston ring is of the CPR type, dimen-sions for gas lock and CPR grooves are also needed. Normally, the most dicult

3.2. Main processes 29

step during the geometry generation is the generation of the gas lock, because thereare some tolerances that may need adjustment in order for the geometry to becomeaccurate.

ANSYS geometry operators, called booleans, have been used to generate parts ofthe geometry and they work in the background of the simulation work ow during thegeometry setup. A proposal after setting up a new geometry is to check the resultsgraphically before applying boundary conditions and, if required, adjust tolerancesfor booleans. Resulting geometries from the generation process are presented ingure 3.1.

(a) Straight cut design. (b) CPR design.

Figure 3.1: The automatically generated geometry of the two dierent piston ringdesigns.

3.2.2 Mesh generationThe nite element mesh of the piston ring is implemented with higher order elements,i.e. the basis of hat functions consist of polynomials of second order. This methodis chosen because the geometry is smooth and curved over most of the surfaces andlower order elements would then negatively aect the results. The model is madeup of 20-node hexahedrons and 10-node tetrahedrons, see gure 3.2, where the

(a) 10-node tetrahedron. (b) 20-node hexahedron.

Figure 3.2: The shape of the nite elements used in the model.


main sections of the piston ring consist of hexahedrons while the more complicatedgeometries, i.e. the gas lock and the CPR-grooves, are generated with tetrahedrons.Usage of hexahedrons reduces the total number of nodes needed to describe thering geometry and thereby the total number of degrees of freedom for the completemodel. For piston rings with straight cut openings solely hexahedrons are used todescribe the complete piston ring geometry.

The mesh quality is furthermore also easily adaptable. This may be useful whenlower order elements are wanted or when the complete ring should be meshed inmore detail. Some examples of the mesh generation performed by the automaticsimulation tool could be viewed in gure 3.3.

(a) Straight cut design. (b) CPR design.

Figure 3.3: The automatically generated nite element mesh of the two dierentpiston ring designs.

3.2.3 Contact surfacesANSYS is a powerful software when dealing with solid-to-solid contacts but also,as in this case, solid-to-rigid-surface contacts. Main contact surfaces of the pistonring are against the cylinder liner and the piston ring groove but there is also acontact surface inside the gas lock when dealing with the CPR designed pistonring. The contact analysis is invoked within the code and the contact and targetelements are adapted at the relevant surfaces with specic contact properties suchas contact algorithm and tolerances. Because of multiple contact surfaces and animpressive set of contact parameters for each one of them a need of several attemptsto get a good understanding between truthful results and an eective time-scale isof importance. The contact algorithm which is used for all the contact elementsis augmented Lagrange method which is a stable method for problems with largedeections.[Ansys 2007] To enforce better convergence of the problem low contactspring stiness is used, but in this case it should only slightly aect the results andonly small penetrations are involved due to smooth contact surfaces and a uniformlydistributed contact pressure. For this specic problem, frictionless support is used atthe contact surfaces. This is a simplication but the friction force is negligibly smallcompared to the tension in the piston ring and the acting pressures. The contactsurfaces are automatically generated but may become erroneous if the geometry is

3.2. Main processes 31

changed in an unpredicted way.Interaction between two surfaces is implemented in ANSYS by generating con-

tact and target elements. The contact elements, which contain the nodal results, aremodeled on the surface of the piston ring while the target elements are generatedon the corresponding surface at the cylinder liner or piston ring groove. It is thebasic method to implement the target element on the xed surfaces without under-lying solid elements, i.e. rigid surfaces. In the gas lock the results are achieved atthe contact surface at the female part and the male part is congured as a targetsurface.

The contact interactions which the piston ring experiences is inward in radialdirection from the cylinder liner and upward from the piston ring groove at thebottom area of the piston ring. Therefore correct geometries of the cylinder and thepiston are of big importance in order to represent real running conditions in marinetwo-stroke diesel engines. In addition, the contact in the gas lock has an inuenceon the strains and stresses in that area. These three pairs of contact and targetelements in the model are shown in gure 3.4.

(a) Against cylinder liner. (b) Against piston ring groove. (c) Inside gas lock.

Figure 3.4: The automatically generated contact surfaces on the piston ring.

3.2.4 Boundary conditionsThe boundary conditions of a model are implemented as realistic as possible with abalance between precision and calculation time, where the level of precision shouldenable results close to reality which are interesting from a commercial point ofview. They have been chosen carefully but some simplications are made to simplifyimplementation and improve convergence.

The boundary conditions are indirectly applied to the nodes of the nite elementmodel via the surfaces and volume belonging to the piston ring. Therefore, for atypical mesh shown in gure 3.3, some simplications are applied. If a certain con-dition is dened for one node and another condition is dened for another node nextto the rst one, then the conditions will vary approximately between these nodes.There are dierent types of boundary conditions implemented in the model andthese are geometrical constraints, applied temperature eld, pressures and nallycomplicated contact interactions.


ConstraintsWhen solving a problem of this type the model has to be suciently constrained orthe solution will not converge. An example of this is when the piston ring is forcedinto and against the cylinder liner and the piston ring is constrained not to movealong the axial height or rotate inside the cylinder liner.

Temperature eldThe distributed temperature in the piston ring is applied to each node of the niteelement model in the initial phase of the simulation. This is a very important featureof the simulation and an intuitive way of controlling the performance of the pistonring under dierent running temperatures followed by varying loads of the engine.

Figure 3.5: A typical temperature eld with a temperature gradient in axial heightapplied to the piston ring.

Normally, the temperature eld is dierent for a straight cut ring compared toa CPR ring. The default temperature eld used correspond to the one in the lathecurve generator, which is approximately as it should be for a straight cut designedpiston ring. This feature is important in order to validate the results in a fair way butthe application is also eective if the model should be tested for other temperatureelds with the same character. The only addition to the two-dimensional temper-ature eld specied in the lathe curve generator is that the temperature also couldbe adjusted in axial height in this application, see gure 3.5. Another preconguredtemperature eld is designed to imitate the temperature eld in a typical CPR pis-ton ring. But this is developed from large presumptions and is not recommended tobe used before a proper review. Probably, the temperature eld for the straight cutdesign is a good approximation and it is, with small modications, also used in thelathe curve generator when developing CPR piston rings. All temperatures will belinear between the nodes and this is, as mentioned, because no information couldbe stored in the space between nodes.

3.3. Model limitations 33

ForcesAll transformations and displacements of the piston ring are enforced by forces arisenfrom dierent types of loads. The piston ring is forced into the cylinder throughcontact elements on the piston ring which are forced to come in contact with targetelements on the cylinder liner.

Pressure loads are applied to all surfaces of the piston ring. For the inner and topsurface the pressure is designed to be uniformly distributed at a specic magnitude,but for the outer and bottom surface the pressure is distributed dierently over thenodes of the nite element model, see gure 3.6. Similarly to the temperature con-ditions, the pressure conditions are applied at the nodes and become approximatedbetween the nodes.

Figure 3.6: Typical pressures applied to the piston ring in the nite element model.This condition corresponds to a negative slope of the piston ring groove.

SymmetryTo achieve a more eective model, the straight cut geometry is modeled with bound-ary conditions which describe the symmetry at the piston ring back. The symmetrycondition results in a lower total number of nodes, thereby fewer degrees of freedom,and the problem will become less computationally expensive.

3.3 Model limitationsThe model has fairly few simplications and hopefully they do not signicantlyinuence the results. Most salience are probably the implementation of loads, espe-cially temperature and pressures, which arise from diculties with the piston ringgeometry and the nite element mesh. All boundary conditions are also conguredas they should be in the static initial state and they are not updated during thesimulation process. Even though the problem is not a typical non-linear problemthe main simulation setup becomes non-linear, because of large deections and thecontact surfaces, and therefore an iterative solving process is used. Another pistonring feature which is not taken into account are the internal stresses from plasticityarisen in the mounting of the piston ring on the piston.


3.4 Parameter descriptionThis section describes how dierent input parameters change the simulation modeland how the user is able to manage them. The user may easily change the dimensionsof the piston ring, cylinder liner and piston but also magnitudes of pressures andtemperature etcetera.

3.4.1 GeometryThis section describes the input parameters which modify the geometry of the pistonring but also the environment such as the cylinder liner and the piston ring groove.The typical shape of the piston ring is loaded from two input les, one for the outerradial prole generated with the lathe curve generator and one with the shape ofthe crowned outer surface. But some additional parameters are also needed, such asradial thickness, axial height, piston ring gap and dimensions of the inner asymme-try. Also dimensions of the gas lock and the CPR-grooves are needed for the morecomplicated geometry. The cylinder liner diameter may be changed to account foroverdimension resulting from thermal expansion and wear and the dimensions of thepiston and the slope of the piston ring groove may also be adjusted. Congurationparameters are shown in gure 3.7 for the overall geometry and in gure 3.8 for apiston ring with gas lock and CPR grooves.

3.4.2 Temperature eldAn important feature of the simulation tool is to be able to analyze a piston ringrunning apart from the temperature eld corresponding to the lathe curve genera-tor. The temperature eld boundary condition allows a basic reference temperaturein the piston ring, then for some angle from the back the temperature increases ina specic order over the angle and against the opening, see gure 3.5. This typeof gradient is congured for both inner and outer radius of the piston ring, eachgradient with a specic temperature and start angle. In addition, the temperatureeld may also vary in axial height. For a specic angle around the opening the tem-perature increases linearly in axial height and quadratically over the angle againstthe opening. All parameters are schematically shown in gure 3.9.

Also for the CPR designed piston ring an application for the temperature eldis available. For each CPR groove a surrounding interval is specied in which thetemperature is increased exponentially. The temperature is also increased aroundthe opening which is experienced in combination with leakage in the gas lock.

3.4.3 Applied pressureThe pressure conditions for the piston ring represent the combustion pressure andthe reduced pressure below the piston ring, and these are declared in gure 1.7(b).Pressure conditions are applied at every surface of the piston ring at the initial stateand this because the model would be much more computationally expensive with

3.4. Parameter description 35

(a) Piston ring cross section. (b) Radial dimensions.

Figure 3.7: Dimensions of the piston ring geometry. OPSHAPE360 and RPF areinput les for the conguration.

(a) Gas lock. (b) CPR-groove.

Figure 3.8: Dimensions of the gas lock and the CPR-grooves.

Figure 3.9: Parameters for the temperature eld of a straight cut designed pistonring.


time-dependent pressure conditions. Another detail is that a more improved meshgeneration is needed at the surfaces to get any eect from a dynamical applicationof the pressure. This approximation from dynamical to static is the case both atthe outer and the bottom surface of the piston ring, where the pressure conditionsare congured to change at a dividing line. The pressure is applied as in gure 3.10for dierent angles of the piston ring groove and if the piston ring groove is in anglewith the piston ring in the initial state the surface under the piston ring, which nowis in contact with the piston ring groove, should not be loaded by any pressure. Thisconguration of the pressure conditions is though applied manually in order to beable to investigate the behavior of a dynamical application.

(a) Positive angle. (b) Negative angle.

Figure 3.10: Pressure conditions for the cross section of the piston ring for dierentangles of the piston ring groove.

The dividing line for the pressure application at the outer surface is at the axialheight of the apex of the crowned surface. For the bottom surface the dividing lineis located at the radius of the piston or the inner radius of the piston ring for apositive and a negative slope of the piston ring groove respectively. The surfaces inthe piston ring gap is exposed by the higher pressure for the straight cut design andfor the CPR design a more advanced pressure application is designed to imitate thereality for the gas lock in a better manner.

3.5 Convergence criteriaThe simulation model is complex and because the solving process should be suf-ciently eective, problems with convergence could occur only when changing thegeometry or loads slightly. It could be more reliable but the drawback would belonger computational time to solve the problem. The purpose of this section isto get a better understanding of the complications involved in the model and howto manage these to overcome convergence problems but also in order to adjust forshorter computational time.

3.6. Analyzing results 37

Alignment against pistonIn an initial step of the simulation a convergence problem occurs when the pistonring is aligned against the piston ring groove. This problem is handled by applyingpressure on the top of the piston ring during this load step, which is in addition tothe default setting with forced contact between the contact and target elements atthe interacting surfaces.

Time stepIf there are problems with convergence the rst modication is to decrease the initialtime step for the specic load step in the solution manager. Another method maybe to apply loads stepwise over multiple load steps.

MeshIn some cases there could be convergence problems which arise from a bad nite ele-ment mesh of the model. This may occur when the geometrical dimensions becomenon-comparable with the standard conguration, as for the case when modeling asmaller high-speed engine piston ring and the element size becomes too large to de-scribe the geometry suciently. In order to overcome this problem, rene the meshand evaluate the new mesh generation until it becomes comparable with gure 3.3.

3.6 Analyzing resultsThe results from the simulations may all be viewed within the interface of ANSYSand some of the main results within these types of problems are deformations,strains and stresses for the solid model and contact pressures at the contact surfaces.These results give a fast and eective intuition of the accuracy and the value of thesimulation.

In addition, some analysis tools are designed to reveal less intuitive results andplot them in two-dimensional graphs. Examples of such results are the contact pres-sure integrated over axial height and the twist of the piston ring. These results arewritten to external les which could be investigated within the software MATLABor with the open source software GNU Octave. The basic representation of the

Figure 3.11: The results in chapter 4 are represented from the back of the pistonring and in degrees corresponding to the uncompressed geometry.


results in chapter 4 is for the angle from the back of the piston ring, see gure 3.11.In the presentation of the results all evaluated points are marked with circles andthe curve represent an interpolation between these.

Contact pressure of the outer surface is evaluated as the integral over axial heightand calculated around the whole piston ring. This is in order to evaluate the resultin a powerful manner and to get a more intuitive presentation and understandingof the contact pressure distribution, but also for ability to compare it with thetwo-dimensional simulation.

The twist of the piston ring is measured at every 45 degree from the back to theopening. For the straight cut design a last measurement is performed at the openingand for the CPR designed directly next to the gas lock. The twist is measuredat both the bottom surface and the outer surface of the piston ring, where themeasurement which is performed at the bottom surface gives a good comparisonof the twist compared to the slope of the piston ring groove. This feature is inorder to see if the surfaces are aligned or not, and how the pressures should acton the surfaces. If the thermal expansion in the material should be included themeasurement of the outer surface is used instead. This measurement will give abetter approximation of the angle corresponding to the wear of the outer surface ofa piston ring and this is especially important when a thermal gradient is includedin axial height. The twist is evaluated from two points for each surface, see gure3.12.

Figure 3.12: Measurements of the twist are performed at two surfaces. The picturedmeasurements are referred to as the negative twist.

Chapter 4

Results

This chapter declares and validates the nal method of the automatic simulationtool, but it also include results from some specic areas of use. Validation is intendedto ensure the functionality and reliability of the simulation method, and the investi-gations with dierent pressures, temperature gradients and modied geometries areapplied in order to establish the value of the tool in development work.

The simpler straight cut designed piston ring is mostly used in the chapter,due to faster convergence and reduced discussion of the results since they are moreintuitive. There will still be an investigation with CPR designed piston rings andthe functionality of the corresponding simulation method. The central idea is toinvestigate the three-dimensional eects and thereof mainly the twist of the pistonring. Contact pressure results are only evaluated in order to validate the simulationmethod since investigations of the radial eects are more eective in a simpler two-dimensional simulation model.

Contents4.1 Final conguration . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.1 Final method . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2 Validation of model . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 434.2.2 Rened mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.3 Material stress . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.4 Verication of pretwist . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Dierent piston ring grooves . . . . . . . . . . . . . . . . . . . 464.3.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 464.3.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.1 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 474.4.2 Twist at dierent crank angles . . . . . . . . . . . . . . . . . 484.4.3 Additional temperature gradient . . . . . . . . . . . . . . . . 504.4.4 New cross section . . . . . . . . . . . . . . . . . . . . . . . . . 524.4.5 Counteract of temperature gradient . . . . . . . . . . . . . . 54

42 Chapter 4. Results

4.1 Final congurationThis is a description of the basic conguration of the simulation tool and the cor-responding results for each specic case is presented later in the chapter. Thecalculations are performed with a cylinder diameter of 900 mm in the basic geo-metrical conguration. This is without the inuence of temperature and wear andthe piston land clearance, i.e. the gap between a centered piston and the cylinderliner, is 1.25 mm measured from this cylinder diameter. The piston ring grooveis congured with either a slope of 0.16 degrees inward or 0.05 degrees outward.Typical height of the piston ring is 19.4 mm, radial thickness 28 mm, the base ma-terial consists of a specic grade of cast iron and the mesh of the model is generatedas described during chapter 3. For a simulation the setup is congured with therunning diameter of the cylinder (overdimensional measurement) and pressure con-ditions for the corresponding crank angle declared in gure 1.7. The temperatureeld is implemented in a more intuitive way with help from actual measurementsand engineering knowledge but also the previous thesis work [Grahn 2009], see sec-tion 1.1.4. One important feature of the model setup, which also is mentioned inchapter 3, is that the pressure is applied as it should be in the initial state and it isnot updated later on during the simulation. The pressure alignment on the pistonring is congured for the two dierent piston ring grooves as in gure 3.10, but it isimportant to understand the motion of the piston ring and the way this aects theapproximation of the pressure application.

4.1.1 Final method

The nal method and the processes within the simulation tool are summarized ingure 4.1. Main processes of the simulation method are declared and informationneeded to execute the automatic simulation is pictured. The steps of the processeswhere the specic input conguration is used should also become clear, includingwhere the so called automatic additives are inserted to achieve good performanceand accurate results. Read gure 4.1 through the column of procedures and rec-ognize the parameter specications needed from the user and the additives whichare automatically added to the processes in order to generate and analyze the -nite element model. A simplied version of the nal algorithm description for theautomatic simulation tool is presented in appendix A.

4.2 Validation of modelThis section is intended to verify that the results from the simulation model appearto be good in comparison with actual measurements, knowledge and another sim-pler simulation software. The simulations are done in a simple manner and withreasonable simplications, in order to achieve results in a short time but still giveenough accuracy to validate the simulation method.

4.2. Validation of model 43

Figure 4.1: A schematic overview of the simulation method.

4.2.1 Model congurationInstallation of the piston ring in the cylinder is simulated and compared with asimpler simulation model in two dimensions to investigate the reliability of thethree-dimensional automatic simulation tool. The investigation is made with thestandard cylinder diameter (900 mm) for a cold and newly manufactured cylinderliner, a piston ring with a total piston ring opening of 16° and the lathe curve forthe specic piston ring is generated in order to achieve good contact pressure at zerodegrees Celsius. This is mainly to avoid the eect from the element approximationin the temperature eld when the results are validated. A symmetrical crownedouter surface is used for the evaluation of the contact pressures and a constraintagainst movement of the bottom surface of the piston ring in the axial direction isalso applied. This to constrain against twist of the piston ring and the followingeects on the results. In another case, the measurement of the twist is investigatedand an asymmetrical crowned outer surface is used in order to enforce an initialtwist when the piston ring is installed.

4.2.2 Rened meshOne of the main methods in the evaluation of the results is by comparing the contactpressure of an installed piston ring with a simpler model without axial height, andthus no running prole on the outer surface and no twist eects. This simpler


method, which was developed earlier, is also conrmed to be accurate according toreal measurements and investigations in, at least, the matter of contact pressureanalyzes.

The evaluated contact pressure is the pressure integrated across the axial height,as described in section 3.6, and the validation results can be seen in gure 4.2(a).Two dierent nite element mesh generations are declared for the three-dimensionalmodel, and compared with the simpler model. Validation of the piston ring twisteect is also done by evaluating the twist for two dierent mesh generations, withthe results declared in gure 4.2(b).

(a) Contact pressure. (b) Piston ring twist.

Figure 4.2: Validation of the model. The results are evaluated with dierent meshgenerations and compared with a two-dimensional simulation method.

The contact pressure which is evaluated with the two-dimensional simulationmodel is evenly distributed along the outer surface of the piston, increasing nearthe opening and falls toward zero at the opening. It is clear that the new simula-tion model reproduces the result when the magnitude is compared, but the contactpressure around the opening is not perfectly equivalent. This is probably a typicalerror arising from dierent mesh generations while the ner mesh achieves resultwith less error. The results in gure 4.2(b) correspond to a simulation of a pistonring with an asymmetrical outer surface when it is forced into the cylinder. It isxed in axial height at the back and at the opening, and the twist is measured atboth the bottom and the outer surface. It is clear that the mesh generation doesnot eect the piston ring twist as much as it aects the contact pressure. Furtheron during the chapter the model is congured with the coarser mesh, in order toachieve shorter calculation time, when only the twist is of interest.

4.2.3 Material stressThis is a more intuitive validation of the model. The visualized stresses in gure 4.3are the von Mises total stresses for the piston ring with the asymmetrical crownedouter surface. In the gure the stresses shows a smooth transition across the pistonring, with high stresses at the back and almost zero at the opening. The stresses

4.2. Validation of model 45

are higher on the inner and outer surfaces and the stresses approaches zero in themiddle of the radial thickness.

Figure 4.3: The von Mises stresses of the piston ring in compressed state. Left inthe gure corresponds to the back of the piston ring.

4.2.4 Verication of pretwistIn this section the behavior of a piston ring with a new inner cross section is investi-gated, and the results are hopefully intended to correspond with earlier results foundusing beam theory, see [Corbat 1974]. All simulations are performed with a pistonring of height 5.5 mm, radial thickness 9 mm and three dierent inner asymmetries,A1=A2=2, 3, 4 mm, are examined, see gure 3.7(a). The piston ring has a cylinderdiameter of 240 mm, a symmetrical crowned outer surface and a radial prole foran evenly distributed contact pressure at 0°C.

(a) From the simulation method. (b) Calculated with beam theory(gure courtesy of [Corbat 1974]).

Figure 4.4: The twist of the piston ring in compressed mode. Constraints againstmovement in the axial direction at the back and at the opening of the piston ring.

If the case of A1=A2=2 is disregarded, the twist behavior of the piston ring couldbe validated. From the simulation results, gure 4.4(a), the maximum value of thetwist is located between 110° and 120° and this corresponds to the results evaluatedfrom beam theory, gure 4.4(b). The magnitude of the twist is also comparablewith consideration of the dierent assumptions in the two models.


4.3 Dierent piston ring grooves

The CPR designed piston ring is considered in this investigation. This design usesmore calculation time and it is therefore only used in this intuitively simpler simu-lation test. The main focus of the investigation considers the eects on piston ringperformance due to two dierent slopes of the piston ring groove.

4.3.1 Model conguration

All dimensions of the gas lock and the CPR grooves are presented in table B.1 inappendix B, the cylinder diameter is 900 mm and the pressures are 140 MPa aboveand 70 MPa below the piston ring. The conguration of the CPR designed pistonring is more demanding and convergence is harder to enforce so the pressures areapplied in multiple load steps. As in the lathe curve generator the temperature eldof the piston ring is set to 0°C. This conguration is mainly due to a more time-eective simulation model without an additional temperature eld. The piston ringalso have an asymmetrical outer surface, which is how it is manufactured.

Two dierent slopes of the piston ring groove were investigated. The rst slopeis 0.16 degrees inward, which is typical for engines with CPR designed piston rings,and the second is 0.05 degrees outward, which is an experimental part of the inves-tigation. Temperature and wear eects which are hard to investigate with precisionalso eect the slopes, but these values should be accurate in magnitude. The resultsfrom the simulations are presented in gure 4.6 and the compressed geometry canbe seen in gure 4.5. A measurement of the contact pressure is performed along thepiston ring, but not at the locations for the gas lock and the CPR grooves.

(a) Piston ring. (b) Gas lock from outside. (c) Gas lock from inside.

Figure 4.5: The CPR designed piston ring in compressed shape and under combus-tion pressure.

4.3.2 Evaluation

The corresponding contact pressures for the two piston ring slopes are declared ingure 4.6(a). They are smooth around the outer surface of the piston ring andincrease around the CPR grooves. It is though clear that the contact pressurediers in magnitude and becomes larger for the piston ring groove with slope 0.05°outward. The twist is also measured and the piston ring is aligned against the pistonring groove in booth cases, see gure 4.6(b).

4.4. Application 47

(a) Contact pressure. (b) Piston ring twist.

Figure 4.6: Simulations with CPR designed piston rings under combustion pressure.The simulations are congured with two dierent slopes of the piston ring groove.

4.4 ApplicationIn this section the powerfulness of the simulation tool is evaluated with typical prob-lems in the development area. The main focus in all the dierent investigations ison the three-dimensional behavior under working conditions inside a typical runningengine.

First, an investigation of piston ring motion during an engine cycle is done toacquire knowledge about the varying conditions and the corresponding eect on thepiston ring. Then an overheated engine is considered by implementing an extrathermal gradient in axial height of the piston ring, which forces the upper surface ofthe piston ring to become warmer. The asymmetrical inner prole, which is typicallyused in smaller high-speed engines, is also investigated to observe the desirable so-called pretwist which occurs in the compressed shape inside the cylinder.

The goal, after the engine cycle is investigated, is to investigate how the tempera-ture gradient and dierent proles change the twist individually, but also investigateif there is any possibility of overcoming a twist due to increased temperature, byusing a piston ring geometry that gives an enforced pretwist.

4.4.1 Model congurationThe slope of the piston ring groove is 0.05° outward and therefore the lower pressurebelow the piston is applied to the bottom surface of the piston ring, see gure 3.10(b).Temperature eld from the lathe curve generator is applied, the dimensions are thesame as specied in section 4.1 (height = 19.4, thickness = 28 mm), the piston ringopening in uncompressed shape is 14° and it is modeled with an asymmetrical outersurface. All the dierent congurations are declared for each investigation duringthe following sections.


4.4.2 Twist at dierent crank anglesThe investigated crank angles are simulated with the corresponding overdimensionaldiameter of the cylinder liner and acting pressures, all declared in gure 1.7. It isimportant to understand the motion of the piston ring through the engine cycle andthis is a system to evaluate a relationship between piston ring twist and the physicalenvironment, with corresponding loads for each static crank angle. The static stateswhich are evaluated are declared in table 4.1 and the results can be viewed in gures4.7 and 4.8. Measurements of the twist are performed at both the bottom and theouter surface of the piston ring in order to achieve a better understanding of thedierence. The results are also interpolated between the evaluated crank angles, foran intuitive understanding of the dynamic motion.

Angle Roverdimension P1 (MPa) P2 (MPa)-90 0.709937652 4.794 3.914751-75 0.590921591 6.544 4.944093-45 0.612668828 18.205 6.92941-15 0.866582951 82.668 20.515770 0.942841328 126.57 35.4866915 0.866582951 140.59 50.7029145 0.612668828 51.584 51.31673135 0.627996152 4.358 4.093824195 0.602932191 3.674 3.661374270 0.709937652 4.794 3.914751

Table 4.1: The conguration for the analyzed crank angles.

It becomes clear that the twist of the piston ring appears dierently duringthe engine cycle due to dierent pressure conditions and cylinder liner diameters.But also the measurements along the piston ring, according to gure 3.11, are non-planar. The maximum absolute twist of the piston ring occurs when the crankangle is approximately equal to -15°, and it is measured at 135° from the back wheninvestigating the bottom twist. Alignment against the piston ring groove could besaid to be approximately correct between -45° and 15° because some dierences couldoccur due to deformations in the material. At the bottom surface the absolute twistincreases along the piston ring from the back to the opening but measurements atthe outer surface result in a decreasing absolute twist. This could be reinforced bythe dierences in radial thermal expansion due to the outer asymmetrical surfaceand deformations in the material. The absolute twist decreases fairly around crankangle 195°, which is when the total net force from the gases, acting on the pistonring, is very small in magnitude compared to the other states. At this crank anglealso the radial overdimension of the cylinder compared to the other evaluated statesis very small. The absolute twist always seems to be larger on the outer surfacecompared with the bottom surface and this is probably due to a combination ofthermal expansion and deformations in the material.

4.4. Application 49

(a) View at the top of the piston ring. (b) View at the cross section in the back ofthe piston ring.

Figure 4.7: The von Mises stresses in the piston ring at crank angle 15°.

(a) Measured at the bottom surface along thepiston ring.

(b) Measured at the bottom surface for eachcrank angle.

(c) Measured at the outer surface along thepiston ring.

(d) Measured at the outer surface for eachcrank angle.

Figure 4.8: Twist of the piston ring during an engine cycle.


4.4.3 Additional temperature gradientAll simulations with temperature elds which not conform with the lathe curvegenerator are calculated in the static state with crank angle 15° after TDC (topdead center). This is the crank angle where the pressure conditions probably aremost demanding, i.e. highest combustion pressure and a high net force, during theengine cycle. Engines which are working under high loads and become overheatedcould be investigated by adding an extra temperature gradient. Such engines aretypically described, from engineering reasoning, by an extra temperature gradientin axial height around the opening.

The main subject of the investigation is because extreme wear are experiencedon piston rings in engines which regularly work under high loads. Important mea-surement is the piston ring twist on the outer surface against the cylinder liner.This measurement is especially important near the piston ring opening where dam-age has occurred in earlier real life investigations, probably because of temperatureand wear. The parameters used, please refer to gures and 3.9, are printed in tableB.2 apart from FITZ=45+7 (extension + ring gap), and DTZ = 0, 50, 150, 250 and500°C. These parameters result in a temperature eld according to gure 4.9.

Figure 4.9: A piston ring with an additional temperature gradient near the opening.Blue corresponds to the reference temperature in the piston ring and red to thewarmest location.

The piston rings which are overheated with an extra temperature gradient inaxial height, are aected by an increased absolute twist outward compared with thegeneral temperature eld. It is obvious that the temperature gradient inuences thetwist of the piston ring. The absolute twist is drastically increased near the openingof the piston ring, which can be seen in gure 4.11. It is also clear that the twisthas an approximately linear relationship with the magnitude of the temperaturegradient, which probably could be deduced from the linear thermal expansion. Whenthe twist of the two surfaces is compared, there is approximately 50 percent moretwist on the outer surface compared to the surface at the bottom, which is mainlybecause of thermal expansion, but also deformations, in the piston ring material.The von Mises stresses in the piston ring are visualized in gure 4.10.

4.4. Application 51

(a) View at the top of the piston ring. (b) View of the cross section at the back of thepiston ring.

Figure 4.10: The von Mises stresses in the piston ring at crank angle 15°. Thetemperature eld is congured with DTZ = 250°C and FITZ = 45+7°.

(a) Measured on the bottom surface along thepiston ring.

(b) Measured on the bottom surface for eachapplied temperature eld.

(c) Measured on the outer surface along thepiston ring.

(d) Measured on the outer surface for each ap-plied temperature eld.

Figure 4.11: Twist with an additional temperature gradient at crank angle 15°.


4.4.4 New cross sectionThe relationship between the twist eect and dierent cross sections should be in-vestigated. It is common in the vehicle industry to change the geometry in order toenforce a so called pretwist in the piston ring. The inner prole of the piston ringis changed in the geometry conguration, see gure 3.7(a), with two dierent innerupper corner, namely A1=A2=5≈B/4 and A1=A2=10≈B/2, see gure 4.13. Anexample with A1=A2=10≈B/2 is also visualized in gure 4.12. As in earlier inves-tigation the temperature eld in the piston ring is congured as default accordingto the lathe curve generator and the investigated crank angle is 15°.

Figure 4.12: A piston ring with a modied cross section and with the default tem-perature eld. Blue corresponds to 100°C and red to 200°C.

(a) A1 = A2 = 0 mm. (b) A1 = A2 = 5 mm. (c) A1 = A2 = 10 mm.

Figure 4.13: Three dierent cross sections which are examined.

According to dierent cross sections the twist of the piston ring changes as couldbe seen in gure 4.15. The stresses near the inner surface is transformed when theprole is changed, see gure 4.14, and a change in the twist is enforced. Nearthe opening the twist does not change much, but in the back of the piston ring theabsolute twist is drastically reduced. For this case it results in the piston ring leavingthe state where it had an almost perfect alignment with the piston ring groove.

4.4. Application 53

(a) View on top of the piston ring. (b) View at the cross section in the back ofthe piston ring.

Figure 4.14: The von Mises stresses in the piston ring at crank angle 15°. The newcross section is dened by A1 = A2 = 10 mm.


(b) Measured at the bottom surface for eachcross section.


(d) Measured at the outer surface for eachcross section.

Figure 4.15: Twist with dierent cross sections at crank angle 15°.


4.4.5 Counteract of temperature gradientThis section is intended to investigate if it is possible to compensate the twist inoverheated engines by a pretwist caused by a modied inner cross section prole.Implement the general temperature eld but with a temperature gradient aroundthe opening, dened as the temperature eld in section 4.4.3 but with DTZ=25°Cand FITZ=45+7°. In addition to this, the temperature increases an additional 25°Cin axial height (TKZ=25°C) around the whole piston ring. Resulting temperatureeld is visualized in gure 4.16. The twist is reduced by the two dierent crosssections dened in section 4.4.4 and the results are presented in gure 4.18.

Figure 4.16: A piston ring with an intuitive temperature eld and a new crosssection.

In gure 4.18, it is clear that the implemented temperature eld increases theoutward twist of the piston ring, especially close to the opening. The absolute twistof the piston ring, depended on the temperature, is reduced by introducing the newinner prole. Around the opening the twist is not aected much, but the backof the piston ring is aected and the absolute twist is drastically decreased in thatlocation of the piston ring. When A1=A2=10 approximately one-third of the pistonring have less absolute twist than the slope of the piston ring groove. In gure 4.17 itis visible how the temperature eld redistribute the von Mises stresses in the pistonring.

4.4. Application 55

(a) View at the top of the piston ring. (b) View at the cross section in the back ofthe piston ring.

Figure 4.17: The von Mises stresses in the piston ring at crank angle 15°. The crosssection is dened by A1 = A2 = 10 mm and the temperature eld by TKZ = DTZ= 25°C and FITZ = 45+7°.


(b) Measured at the bottom surface for eachcross section.


(d) Measured at the outer surface for eachcross section.

Figure 4.18: Twist with dierent cross sections and with an additional temperatureeld. The temperature eld is congured with DTZ = 25°C and TKZ = 25°C.Analyzed cross sections are described by A1 = A2 = 0, A1 = A2 = 5 and A1 =A2 = 10.

Chapter 5

Discussion

The discussion of the results in this kind of thesis work is of great importance.One important question which arises is if the used method is accurate and if theautomatic simulation tool could be relied on in the development and manufacturingof piston rings. First, the method is studied and then the simulations which are donein order to validate the approach are analyzed and discussed. Interesting resultswithin the development area are investigated and nally, some discussion about thepossible improvements of the simulation method, in order to achieve more accurateand reliable results, is included.

Contents5.1 The method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.1 Usability and eciency . . . . . . . . . . . . . . . . . . . . . 585.1.2 Reliability and validation . . . . . . . . . . . . . . . . . . . . 585.1.3 Dierent piston ring designs . . . . . . . . . . . . . . . . . . . 595.1.4 Model conguration . . . . . . . . . . . . . . . . . . . . . . . 60

5.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.2.1 Eects due to temperature gradients . . . . . . . . . . . . . . 615.2.2 Eects due to new inner proles . . . . . . . . . . . . . . . . 62

5.3 Main conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 635.4 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.1 The methodThe main feature of the simulation method is that the piston ring could be analyzedunder working conditions and oer results such as contact pressure, material stressand piston ring twist. There are still details in the processes which need to be at-tended to in order to optimize the simulation method, but nevertheless the behaviorof the piston ring seems to correspond with reality. One of the main diculties as-sociated with simulations and the involved approximations, when the solution timehas to be optimized, is that the model needs to relate to reality and be accurateenough. If the time aspect was neglected and a more detailed model was analyzed,results from simulations could be much more accurate.

58 Chapter 5. Discussion

5.1.1 Usability and eciency

The main objective of the thesis work, see section 1.4, was to develop a simulationmethod which imitates the behavior of a piston ring in a marine two-stroke dieselengine under working conditions, and the second objective was to implement themethod so that it would work in an automatic process. Results from the developedmethod can be said to be reliable and the whole simulation process is automati-cally executed using a commercial software package, so the two rst objectives aresatised. It is also very easy to vary the model for dierent types of geometriesand temperature elds, or a totally dierent investigation could also be set up andanalyzed in a relatively simple manner if wanted, which is the focus of the thirdobjective. The model is an intuitive simulation tool, with its underlying processes,and the time needed for a basic investigation of a static state is approximately lessthan two hours for the straight cut design. For more advanced experiments withimproved temperature elds or geometries, the time can be doubled. Comparedwith a full scale experimental test in an engine, this is an impressive result and evenwhen simulating CPR designed piston rings which could need up to one day to becompleted, it is very eective and time saving. Simulating features does not onlysave time but also reduces the cost by a large margin compared to earlier methodsof marine piston ring development. Another good feature of the automatic simula-tion tool is that it is congured to work eectively on a regular personal computerworkstation.

To evaluate the model, a broad range of information about the piston ring isrequired. The piston ring geometry, temperature eld and working conditions suchas combustion pressure and pressure drop across the piston ring are some of themost typical parameters. Also the computation software ANSYS is required toexecute the automatic simulation tool, but the simulation method could also beimplemented in similar softwares. ANSYS could be very expensive for a smallercompany, especially if this model is the only thing that the program is used for,but the competence and eectiveness of simulations are often emphasized. Eventhough most of the simulations done in chapter 4 (Results) uses one specic set ofparameters for the piston ring, the automatic simulation tool also works for otherdimensions and geometries but with varying eectiveness.

5.1.2 Reliability and validation

The simulations performed in section 4.2 can be conrmed and the achieved resultsare suciently accurate. In gure 4.2(a) the contact pressure is retailed and thebehavior is approximately equal to the two-dimensional simulation model. Thevariations around the opening probably depend mostly on the method of integratingthe contact pressure, but also partly on the nite element approximation itself. Alinear integration method, which is used, involves extreme approximations followedby the bad mesh on the outer surface of the piston ring and an improved mesh hasbeen shown to give more detailed and reliable results. It is a compromise between

5.1. The method 59

eectiveness and accuracy in achieving the results. If the result is to be nearlyperfect, the mesh needs to be made ner, but the evaluation time also becomeslonger.

The contact pressure is smooth and even around the piston ring, increasingaround the opening and goes toward zero at the opening which is the basic featurewanted in a piston ring. One conclusion is that the method is fully acceptable forprediction of the contact pressure if the mesh is made ner, but probably still goodenough if a more improved integration method is used with the coarser mesh. Forthe main feature of this simulation method, such as twist eects and behavior, thesimulation method is a good predictor with the unrened mesh as well, please referto gure 4.2(b). From this fact the integration method is also pointed out to be anerror source to the contact pressure. If the ner mesh was used instead it is possiblethat the accuracy of the twist eect could be improved, but the relevant informationis the behavior and not the details. In gure 4.3, the von Mises stresses are declaredand the distribution behaves as it should, with high stresses at the piston ring backand almost zero at the opening.

An important conclusion when considering the dierent inner proles is thatwhen such a piston ring is installed in the cylinder line, a typical so called pretwistalready occurs in the piston ring, please refer to gure 4.4(a). Beam theory conrmthe behavior of the piston ring, see gure 4.4(b), and it also becomes clear thatthe purpose with dierent inner proles is justied. The tension in the piston ringcontributes to an initial twist and the objective of regulating and enforcing thepressure conditions seems to be fullled with this type of geometry modications.

5.1.3 Dierent piston ring designsThe automatic simulation tool is congured to work with both the straight cut de-sign and with the CPR design. For the details in the CPR design a higher numberof nodes are though needed, which results in a model which requires longer com-putational time to be solved. Another main drawback from this design is problemwith convergence. But this tool is still a good predictor of the behavior and fornding weaknesses in the design. In the simulation model, the main diculty aftergenerating the geometry, is the way the pressures are distributed across the gas lockand how they should be applied. The pressure conditions will change dynamicallywhen the piston ring is installed in the cylinder and moving along the cylinder liner,due to irregularities in the diameter.

Two main disadvantages which occurred with the simulation tool, which arealso according to investigations of real piston rings, are ring collapse and gas lockimbalance. Ring collapse is the case when the opening of the piston ring closes,i.e. collapses.[Tian 2002] This is actually also found in real engines for both straightcut and CPR designed piston rings, but it could be shown by calculating the radialnet forces of the piston rings that it would be more common for the CPR design.The other eect, which leads to imbalance, is a disadvantage in the simulations. Itoccurs mainly because of the diculties when applying the pressures around the


gas lock, but this weakness could in fact also be possible in the case of a real pistonring. The drawback is that the gas lock not seal perfectly and the increased gas owaround the leakage increases the piston ring temperature.

When the eect of dierent piston ring grooves is investigated, it is clear thatthe contact pressure against the cylinder liner is higher, if the slope of the pistonring groove is 0.05° outward. This could be a better condition for the CPR designedpiston ring because it usually experiences ring collapse which could be prevented bya higher radial net force. It is though not the only aspect needed in this investigationand there is probably more to be said about the engineering within this subject.

The magnitude of the contact pressure is increased around the CPR grooveswhich is a consequence of the sharp edges in the geometry adjacent to the grooves.This is a typical problem when contact pressures are evaluated on sharp edges andis usually prevented by using a radius, as on the outer surface of the piston ringwhere the crowned prole distributes the pressure in a more intuitive situation. Fora real piston ring, these sharp edges rapidly become smooth because of wear actingdirectly on the edges where the contact pressure is the highest.

The model of the straight cut designed piston ring is more intuitive and couldrepresent the typical behavior of a piston ring in a more eective and time-savingmanner than the model for the CPR designed piston ring. It is also conrmedto be suciently good when evaluating the twist in the piston ring and the meshgeneration could of course also be rened for more precise results. This model is aperfect tool for development work and the typical behavior of a piston ring, workingunder specic conditions, is easily investigated.

5.1.4 Model conguration

The conguration of the simulation method seems to be reliable, but it is importantto be aware of the main disadvantages. Main drawbacks of the model is related tothe mesh generation which is declared in gure 4.2. If the mesh of the geometryin the model is made ner, this would give more reliable results from the calcula-tions and when investigating some of the outputs from the model. One exampleof these outputs is integration of contact pressure, where a major approximation isinvolved in the calculation. If a much ner mesh is used, also a more systematicand dynamic application of pressures could be applied. Dynamic pressures could bea big improvement of the model, but from the engineering perspective, the resultswould not be drastically changed and when the advantages are compared with thedisadvantages, the simpler mesh of the model is found to be more eective in theseinvestigations. This is mainly because of the ability to show the typical behavior ofthe piston ring in a relatively short calculation time. The behavior of the piston ringalso correlates suciently with expected results, which are based on measurementsin real investigations, engineering knowledge and expertise.

5.2. Application 61

5.2 ApplicationThe power and eectiveness of the automatic simulation tool is clearly motivatedfrom the results presented in section 4.4. They give a direction of the piston ringfeatures but also encounter new subjects into the development area. In gure 4.8 thetypical twist behavior of the piston ring during a complete engine cycle is presented.At each crank angle the piston ring is aected by the radial overdimension of thecylinder, caused by temperature and wear, and the corresponding pressures aboveand below the piston ring. It becomes clear from the results that the piston ringchanges its geometry and physical capacity, as a function of the piston ring twist,during the whole engine cycle. The corresponding contact pressure, which probablygives good sealing of the combustion chamber against the cylinder liner, probablyalso varies but is not investigated in this thesis work. When the crankshaft is locatedaround 195° the absolute twist of the piston ring decreases. This is because the netforce from gas pressures acting on the piston for the corresponding crank anglebecomes negligible compared to the contact pressure in the radial direction, directlyacting from the cylinder liner. For the interval of crank angles between 50° and 110°the net force is directed upward, see gure 1.7(b), and it is possible to experienceso called ring utter where the piston ring moves freely in the piston ring groove.

Typically, under conditions of high pressure net force against the piston ringgroove, the piston ring becomes aligned with the groove and seal the combustionchamber eectively. This is totally clear between crank angles from -15 to 15° andapproximately true between -45 and 15°. The absolute twist of the piston ringduring the rest of the engine cycle is smaller compared to the slope of the pistonring groove and the reduced pressure should act on the bottom surface of the pistonring as modeled in the simulation. Another tendency from the results is that thepiston ring is always more aligned against the piston ring groove near the openingthan in the back of the piston ring.

5.2.1 Eects due to temperature gradientsWhen a specic temperature eld (described in 4.4.3) is applied to the piston ringthe absolute twist becomes aected, and especially around the opening where thetemperature gradient is most intense. Compare this with the earlier results wherethe piston ring was perfectly aligned to the piston under the high pressures at crankangle 15°. It is clear from the results that the thermal expansion has a large inuencewhen the twist on the bottom surface is compared with the outer surface. Anotherconclusion is that the twist varies in a linear manner with the magnitude of the tem-perature gradient. The temperature gradients which are involved in the analyzesare probably too large compared to reality, but the behavior for smaller gradientsshould have the same tendency as in these cases. Measurements which correspondto an increased twist at the opening have been recovered from real investigationby evaluating the wear of used piston rings. An example from these measurementsis presented in gure 5.1 where the piston ring has a scued prole after 11,000


running hours, which corresponds to a temperature gradient of 500°C in gure 4.11.This temperature gradient is probably not realistic in reality, but the characteristicbehavior has been observed in the simulation method. The reason why the temper-ature gradient need to be so high is probably because the real temperature eld isformed in another way, but also because the wear of real piston rings could inducefurther and increased twist as time goes by. Occurrence of high wear of real pistonrings is also conrmed by measuring the radius of the prole which gives a radius ofnearly 2900 mm, see gure 5.1(b), compared with the initial radius of approximately600 mm. The prole is smoother and it is probably easier to move the actual contactsurface and the twist could probably be more expressed. Stresses in the piston ringis also drastically aected when a high temperature gradient is loaded on the pistonring. This could be seen when gure 4.10 is compared with 4.7. Another importantthought is that the behavior should be investigated during the whole engine cycle toexamine where the twist eect, followed by increased temperature, becomes largest.

(a) The slope of the wear. (b) Radius of the outer prole.

Figure 5.1: Measurement of the wear on the crowned outer prole of a straight cutdesigned piston ring. The prole is measured near the opening after 11,000 runninghours.

5.2.2 Eects due to new inner prolesThe main purpose of using piston rings with dierent cross sections is that a reducedinner upper corner induces a positive twist inward. This function is also validatedin the compressed state during section 4.2.4 and should intuitively be a good designto prevent piston ring uttering, which usually occurs when the bottom surface ofthe piston ring is directly aected by the combustion pressure and the net forcebecomes negligible.

When the twist is evaluated under harsh pressure conditions and at the crankangle of 15°, the desired pretwist becomes irrelevant. Under the high pressure con-ditions, the twist mainly changes at the back of the piston ring. This is probablybecause the stresses at the back of the piston ring are large compared to the stressesaround the opening, see gure 4.14(a). It also becomes clear from this gure thatthe stresses on the inside of the piston ring increase, compared to the general geom-etry, see gure 4.7(a). If the results are compared to the main purpose of the newgeometry, to achieve a twist less than the slope of the piston ring groove, it becomesclear that the functionality partly fails. The twist in the back is reduced and thelower pressure could act on the bottom surface in that area of the piston ring, but

5.3. Main conclusions 63

around the opening the twist is unaected and the lower pressure could not surelybe aligned at the bottom surface. But still the objective of using the new design isconrmed, even though it does not work as perfectly as in the case without pressureconditions. Another aspect could be to compare the ratio between axial height andradial thickness of the dierent piston ring dimensions in the dierent cases.

If a piston ring with a new specic temperature eld, which probably could becomparable to a piston ring in a real running engine (see section 4.4.5), is examined,it becomes clear that the new temperature eld induces a distinct piston ring twist,see gure 4.18. In this state, the bottom surface of the piston ring is aected bythe higher pressure which, for best performance, only should be acting on the topand inner surfaces of the piston ring. Section 4.4.5 is performed, to investigate thepossibility of preventing this twist and to force the piston ring to twist less than theslope of piston ring groove, by using the new inner proles introduced earlier. Byusing the new design it becomes possible to manage and control the features of thepiston ring and transform it, but it is impossible to get a suciently strong eectin order to prevent the piston ring twist under high pressure loads.

It is obvious that the increased twist caused by the temperature gradient could bereduced, but it is still dicult because it is mainly the back of the piston ring whichis aected by the new design. When A1=A2=10 approximately only 30 percent ofthe piston ring have condentially small twist. This is not a good working conditionfor a piston ring and it becomes more possible for the piston ring to experience ringuttering and release from the piston ring groove. This is a drastic movement andthe piston ring will become more sensitive to ring collapse when the combustionchamber becomes unsealed.

One possible way to overcome this problem could be to use dierent cross sectionproles along the piston ring, because more draft will clearly be needed around theopening where the eect is less noticeable. This is not totally certain to work either,because parts of the diculties arises with the high pressures acting on the pistonring.

5.3 Main conclusionsThe method appears to be accurate enough to investigate the typical behavior ofa piston ring in a marine two-stroke diesel engine. All processes is executed au-tomatically and several investigations of the piston ring behavior have been done.Totally this satises all three objectives in section 1.4. It appears to give resultswith reliable characteristics, but if more accurate measurements are required, a nermesh could easily be used within the tool.

Experience of two typical piston ring designs has been gained during the workon the thesis. The main content and most valuable results which were simulatedwith the automatic simulation tool, and are of interest in development work, are

Knowledge about piston ring behavior and twist during a complete enginecycle.


The eect on the twist for dierent temperature elds in the piston ring issubstantially established.

Thermal expansion and deformations are considered to correspond to approx-imately 30% of the measured angle of the wear on the outer surface.

The desired twist eect, using dierent cross sections, does not fulll thepurpose under high pressures.

Ring collapse is more common for CPR designed piston rings than for straightcut designed.

5.4 Further workThere are some improvements which need to be carried out, to reach the maximumpotential of the simulation model. Some suggestions on further work to achievebetter and more accurate results are

Improve the mesh generation and perform simulations on a more powerfulcomputer.

Implement dynamic pressure conditions on the piston ring surfaces.

Specify temperature and pressure conditions in greater detail.

Construct a conguration to adjust the inner prole dierently along the pistonring.

Design a dynamic simulation that involves gas ow, thermal capacities, oillm and friction, to leave the simulation of steady states.

Bibliography[Ansys 2007] Ansys. Release 11.0 documentation for ansys. ANSYS Inc. SAS IP

Inc., 2007. 11, 24, 30

[Britannica 1990] Encyclopedia Britannica. The new encyclopedia britannica. En-cyclopedia Britannica, Chicago, 1990. 3

[Corbat 1974] Jean-Pierre Aimé Corbat. Mechanic der kolbenringe mit unsym-metrischem querscnitt. Druckerei Sailer & Cie., Winterthur, 1974. 7, 45

[Daros 2002] Daros. Daros piston rings handbook. Daros Piston Rings AB, Mölnly-cke, 2002. 9

[Grahn 2009] Sebastian Grahn and Henrik Pedersen. Temperature and contact pres-sure of marine piston rings. Chalmers University of Technology, Gothenburg,2009. 8, 21, 42

[Larson 2007] Mats G. Larson and Fredrik Bengzon. A rst course in nite ele-ments lecture notes. Depertment of Mathematics and Mathematical Statis-tics, Umeå University, 2007. 17

[Larson 2009] Mats G. Larson and Fredrik Bengzon. Applied nite elements. De-pertment of Mathematics and Mathematical Statistics, Umeå University,2009. 18, 20

[Marinediesels 2010] Warsash Maritime Academy www.marinediesels.co.ukMarinediesels. 2010. 5

[Tian 2002] T Tian. Dynamic behaviours of piston rings and their practical im-pact. part 1: ring utter and ring collapse and their eects on gas ow andoil transport. IMechE, 2002. Proc Instn Mech Engnrs Vol 216 Part J: JEngineering Tribology. 59

Appendix A

Algorithm description

Initialize.

Set parameters.

Read geometry les.

Calculate additional parameters.

Geometrical construction.

Construct the outer prole. Construct the cross section. Combine the proles and generate the piston ring. Construct the piston ring opening (straight cut or gas lock). Construct the CPR-grooves (only if CPR design).

Mesh the piston ring.

Model the piston ring groove.

Model the cylinder liner.

Model the contact surfaces.

The radial contact between cylinder and piston ring. The contact between the piston ring groove and the piston ring. The contact in the gas lock (only if CPR-design).

Enter solution processor.

Compress piston ring into cylinder. Press down against piston. Apply the specied pressures around the piston ring.

Write results to les.

Appendix B

Input parameters

This appendix contain the used input parameters during chapter 4 (Results).

B.1 GeometryThe geometry parameters for the gas lock and the CPR grooves.

GLH2 47+8 GLH3 68 GH2 12.3GR4 4+0.1 GR5 8 GR6 8GLH1 47 GR1 4-0.1 GR3 5CPR_D 4 CPR_W 3 CPR_A 3CPRA1 30 CPRA2 90 GW2 20.3

Table B.1: The geometry conguration, in millimeter, for the gas lock and the CPRgrooves.

B.2 TemperatureThe default temperature eld in the simulations. This is also the temperature eldused within the lathe curve generator.

TKI 100 TKY 100TKZ 0DTI 100 FITI 100DTY 100 FITY 100DTZ 0 FITZ 0

Table B.2: The default temperature conguration in degrees Celcius.

Ring Piston

Documents

Transcript of Ring Piston