fatigue analysis of engine brackets subjected to road...

IN THE FIELD OF TECHNOLOGYDEGREE PROJECT VEHICLE ENGINEERINGAND THE MAIN FIELD OF STUDYMECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2016

Fatigue analysis of engine brackets subjected to road induced loads

THERESE EK

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES

www.kth.se

Abstract

In this master thesis, methods for fatigue analysis of front engine brackets subjected to road inducedgravity loads (g-loads) are studied. The objective of the thesis is to investigate the possibility to improvesimulation and test analysis for the components. The powertrain is modeled with varying degrees ofcomplexity and the different models are compared to each other and to Scania’s models for analysis ofthe engine suspension. The analysis begins with g-loads and proceeds with time-dependent loads. It isinvestigated how simulated strains in the cylinder block correspond to measured strains from the testtrack at Scania. Finally, it is investigated how component tests corresponds to actual loads by comparingthe results.

The results from the first part of the thesis indicate that worst load case is loading in the negativez -direction and the model of the powertrain with isolators modelled as spring elements is the best forg-loads lower than -3g and the model is sufficient for loads lower than -8g. The results from the secondpart of the thesis indicate that the simulated strains generally correspond to the measured strains, butwith a slight difference in strain amplitude.

Sammanfattning

I detta examensarbete studeras berakningsmetoder for utmattning av motorfasten som utsatts for vagin-ducerade gravitationslaster (g-laster). Syftet med examensarbetet ar att undersoka forbattringsmoj-ligheter for komponenternas beraknings- och provmetoder. Drivlinan modelleras med olika grader av kom-plexitet och de olika modellerna jamfors med varandra, samt med Scanias modell av motorupphangningen.Berakningsanalysen borjar med g-laster och fortskrider med tidsberoende laster. Undersokning av hur valsimulerade tojningar i cylinderblocket motsvarar uppmatta tojningar fran Scanias provbana genomfors.Slutligen undersoks hur komponentprovning motsvarar verkliga laster genom att jamfora resultat.

Resultaten fran den forsta delen av examensarbetet indikerar att det varsta lastfallet ar for last i dennegativa z -riktningen och att modellen av drivlinan dar isolatorerna har modellerats med fjaderelementar den basta for laster lager an -3g och den ar tillracklig for laster lagre an -8g. Resultaten fran den andradelen av examensarbetet indikerar att de simulerade tojningarna stammer val overrens med de uppmattatojningarna, dock med en liten skillnad i tojningsamplitud.

Acknowledgements

I would like to express my sincere gratitude to my supervisor Jonas Lenander for giving me the opportunityto write this thesis, for the interesting discussions, for his enthusiasm, encouragement and expertise. Icould not have asked for a better supervisor at Scania. I thank everybody at NMBS for welcoming meand giving me insight about how great it is to work at Scania, and alongside such an amazing group.

Besides my supervisor at Scania, I would like to thank my supervisor at KTH, Prof. Soren Ostlund forhis interest in my progress, meticulousness, immense knowledge for being a truly inspiring role model inthe field of solid mechanics.

Last but not least, I give all my love to my wonderful family, for always believing in me, for your incrediblepatience, honesty, wisdom and unconditional love.

Stockholm, August 2016

Therese Ek

Contents

1 Introduction 51.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Catia V5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 FE-Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 MATLAB 2014b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Outline of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Background 82.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Equivalent loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.3 Gravity loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Test methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Acceptance criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.4 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Models 143.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Linear model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Nonlinear model No.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 Nonlinear model No.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6 Time-dependent model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Method 234.1 Linear model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Nonlinear model No.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Nonlinear model No.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Time-dependent model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Results and analysis 265.1 Model analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Time-dependent analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Discussion 38

7 Summary 40

2

Nomenclature

α Material constant

β Material constant

ε Strain

ν Poisson’s ratio

Φ Normal distribution function

ρ Density

Θ Central safety factor

C01 Mooney-Rivlin material constant

C10 Mooney-Rivlin material constant

D Damage

d Pseudo damage

D1 Mooney-Rivlin material constant

Dlife Design life

E Young’s modulus

eabs Absolute error

fs Sample frequency

L Load

M The total mass for each component

m The mass for each component

N One cycle

PR Reliability

R Resistance

Samp Amplitude stress

Se Endurance limit

Smax Maximum stress

Smean Mean stress

Smin Minimum stress

t Time increment

tp Safety index

VL Variance coefficient for the resistance R

VR Variance coefficient for the load L

3

CONTENTS CONTENTS

Nf Fatigue life

M Moment vector

R Distance vector

r Distance vector

g-loads Gravity loads

p Percent of survival

DL6 6 - cylinder engine

DOF Degrees of freedom

FE Finite element

NCG New Cab Generation

ODB Output database

SPC Single point constraint

SPCLB Left back node set

SPCLF Left front node set

SPCRB Right back node set

SPCRF Right front node set

STR Scania Technical Report

TKX71 Name of strain gauge




4

Chapter 1

Introduction

The powertrain is the most vital system of a vehicle. The related components in the system are designedto withstand influencing factors such as combustion pressure, high temperatures, noise and vibrations.Some components are designed for road induced loads due to uneven roads which may cause fatiguedamages. Among the components that are exposed to such loads are the engine brackets, the cylinderblock and the flywheel housing. This study focus on the front engine suspension of a truck and mainlyon the engine brackets.

In year 2010, at a R&D Technology meeting in association with the New Cab Generation (NCG) project,recommendations for new isolators were introduced. The primary function of the isolators is to connectthe powertrain to the chassis. The secondary function is to reduce transmitted vibrations from, forexample, the engine, unbalanced shafts, gear contact and ignition of fuel. The isolators also reducevibrations due to road induced loads. Since the Technology meeting in 2010, the isolators developed byScania have changed significantly. They are made of a different rubber material and the geometry haschanged. Furthermore, the test track has been rebuilt and, thus, the loads that the truck is subjectedto have changed. This report investigates how the new isolator configuration affect the loads that theengine brackets and the cylinder block are subjected to.

Previous analysis of the engine suspension at Scania has been evaluated as well as test methods. Thepowertrain was modeled with varying degrees of complexity and the different models were compared toeach other. The analysis began with g-loads and proceeded with time-dependent loads. Finally, it wasinvestigated how test results corresponded to actual loads from the test track at Scania by comparisonof strains and load levels.

5

1.1. PROBLEM DESCRIPTION CHAPTER 1. INTRODUCTION

1.1 Problem description

Due to the new isolator configuration there is need for evaluation of load changes on the engine suspension,particularly the engine brackets and their connection with the isolators and the cylinder block. The changeof loads might change the fatigue life and in order to evaluate this, models of the powertrain are needed.A finite element model (FE-model) of the powertrain was created and modified with varying degrees ofcomplexity. The modifications were made in order to create a model that possibly better corresponds tothe reality.

The objectives of the thesis are subdived into two analysis parts. In the first part, different models ofthe powertrain are analysed, using g-loads that are applied in different directions. In the second part,time-dependent loads that are applied on the isolators are analysed. The objectives of the first part wereto:

• determine how the constraint point configuration in a linear model influences the results.

• determine if the FE-model needs to be nonlinear or if a linear model is sufficient.

• compare fatigue life using the chosen model to fatigue life from Scania’s previous analysis model.

The objectives of the second part were to:

• evaluate if it is possible to perform analysis of quasi-static time-dependent loads in a time effectivemanner.

• compare simulated and measured strain results, from the test track, in the cylinder block in orderto validate results.

1.2 Software

1.2.1 Catia V5

Component geometries created in Catia V5 R24 [1] were used in the development of the FE-model.

1.2.2 FE-Software

In this section, the software packages used in order to construct models, perform simulations and evaluateresults are presented.

Pre-processors

Two pre-processors were used when constructing geometries, discretizing the model and managing contactareas. The pre-processors both belong to Altair [2]. SimLab 14.0 [3] was used for discretization of eachcomponent in the powertrain and Hypermesh [4] was used for assembling the components into one model.Hypermesh was also used to create contact areas. The software generates geometry data, which are thencalled from an input data file, created in EditPad Pro 7 [5]. In the input data file, material parameters,contacts, loads and load steps were defined.

Solver

Abaqus 6.14-2 [6], was the software that carried out the FE-analysis of the model defined in the input file.Reaction forces, displacements, stresses and strains are all computed and output is saved to an outputdatabase (ODB)-file which can be further processed and analysed by a post-processor.

6

CHAPTER 1. INTRODUCTION 1.3. OUTLINE OF THESIS

Post-processors

In order to perform a fatigue analysis the software FEMFAT 5.1.1 [7] was used to analyse the results fromthe FE-analysis. FEMFAT estimates the safety factor and stress amplitude of the analysed model byapplying conventional fatigue theory such as the stress-life approach further described in subsection 2.1.1.Abaqus was also used to visualize the results from the FE-analysis and the fatigue analysis.

1.2.3 MATLAB 2014b

In this thesis, Matlab 2014b [8] is used for general numerical calculations, but it is a software that also hascapabilities of for instance, data analysis and visualization, programming and algorithm development.

1.3 Outline of thesis

This thesis starts with a background, which contains information about how loads and fatigue can bedefined and analysed together with the terminology that will be used throughout the report. The chap-ter proceeds with a historical background on how analysis and testing of fatigue previously have beenperformed and evaluated at Scania.

Chapter 3 introduces geometry and materials of the components in the powertrain. Furthermore, theFEM-model and its linear and nonlinear variants are presented. The models described in this chapter arethen used in Chapter 4. In order to meet the objectives of the thesis, Chapter 4 describes the methodsused for development of a final model and how to compare the results from this model with test results.

Results and analysis are presented in Chapter 5. In this chapter the methods described in Chapter 4are used in order to determine the final model. Chapter 6 discusses the evaluation of the models, thesimulation analysis and results. Chapter 7 summarizes results and conclusions. This chapter also containsa recommendation for further development of acceptance criteria, analysis and test methods.

7

Chapter 2

Background

This chapter introduces theory in the area of solid mechanics that are relevant for the thesis and ahistorical background of analysis and test methodology at Scania.

2.1 Theoretical background

2.1.1 Fatigue

In the automotive industry, it is of importance to consider fatigue. Fatigue failure occurs at a lower loadthan the yield limit of the material due to the cyclic nature of the loading. In ASTM E1823 [9] thedefinition of fatigue is:

“The process of progressive localized permanent structural change occurring in a material sub-jected to conditions that produce fluctuating stresses and strains at some point or points andthat may culminate in cracks or complete fracture after a sufficient number of fluctuations.”

This process of structural change is a result of cyclic loading. A cycle, shown in Figure 2.1, is one completesequence of values of force that is repeated under constant amplitude loading.

Time

Str

ess

0

Samp

N

Smax

Smin

Figure 2.1: Constant amplitude loading for two cycles with the amplitude Samp. N = 1 is marked witha horizontal arrow.

The mean stress (Smean) is derived according to Eq. (2.1),

8

CHAPTER 2. BACKGROUND 2.1. THEORETICAL BACKGROUND

Smean =Smax + Smin

2(2.1)

where the maximum and minimum stresses are shown in Figure 2.1.

Fatigue life, denoted Nf, is the number of cycles that the specimen can sustain at a constant amplitudeloading before failure occurs. In the stress life approach, specimens are tested at different load levels untilfailure. The graphical representation of the results is a logarithmic diagram where the stress amplitude(S ) versus number of cycles until failure (Nf) are presented. The construction of this S-N diagram , alsocalled Wohler diagram [10], is a method developed in 1870 to present fatigue data. One test of a specimenloaded at constant amplitude until failure gives one failure point in the S-N diagram. The S-N curve isthe average curve drawn through these failure points, see Figure 2.2 [10].

Figure 2.2: S-N diagram, each test gives one failure point and an average curve is drawnthrough them. The endurance limit (Se), also called fatigue limit, is the stress magnitude foran infinite number of cycles, theoretically speaking.

If nothing else is stated, the S-N curve refers to the fatigue life that 50 % of the specimens can sustain[11]. The specimens are the population in the quote from ASTM E1823:

“Fatigue life for p percent survival - an estimate of the fatigue life that p percent of thepopulation would attain or exceed under a given loading. The observed value of the medianfatigue life estimates the fatigue life for 50 percent survival. Fatigue life for p percent survivalvalues, where p is any number, such as, 95, 90, and so forth, also may be estimated from theindividual fatigue life values.”

Nf can be expressed according to Basquins equation, where the constants α and β are material parameters[12].

Nf = αSamp−β (2.2)

2.1.2 Equivalent loads

The fluctuations mentioned in the first ASTM E1823 quote, caused by different kinds of loading arenot constant. For example, pot holes of varying sizes, curbstones and speed bumps all cause differentkinds of loads that a truck can be subjected to. By deriving a constant amplitude that would give thesame fatigue damage per kilometer as the measured damage, the load amplitude can be simplified to beconstant. This constant load amplitude is the equivalent load (Samp,eq) [13].

The rainflow method developed by professor Tatsuo Endo in the 1960s transforms a complicated loadsequence to damage equivalent cycles (Nf,k) for constant load amplitudes (Samp,k) [14]. The damageaccording to Palmgren-Miner’s damage rule [15] for the measured load over time is expressed as,

D = α−1∑k

Samp,kβ k = 1, 2, 3... (2.3)

9

2.2. HISTORICAL BACKGROUND CHAPTER 2. BACKGROUND

The damage can also be expressed as in Eq. (2.4) where the parameter (Nf,k) comes from Eq. (2.2).

D =∑k

1

Nf,k(2.4)

Failure occurs if D is greater than or equal to 1. The pseudo damage (d) in Eq. (2.5) is the damagewithout the constant α.

d =∑k

Samp,kβ (2.5)

The design life (Dlife) is the damage that the component is designed for. The constant K in Eq. (2.6) isthe number of repetitions that gives the design life.

Dlife = K ·D (2.6)

When the equivalent damage in Eq. (2.7) is damage equivalent to Dlife, the Samp,eq equals to Eq. (2.8).

Deq = Nf · α−1 · Samp,eqβ (2.7)

Samp,eq =

(K · dNf

)1/β

(2.8)

The advantage of using Samp,eq is that it can be used for comparison of measured loads on different kindsof roads or for different vehicles [11].

2.1.3 Gravity loads

There are different kinds of loads that can be applied when analysing a structure. Gravity load is a deadload, which is defined according to the quote:

“Dead loads: refer to loads that typically don’t change over time, such as the weights ofmaterials and components of the structure itself...” [16]

The definition of acceleration of gravity in the Science Dictionary, quoted:

“The acceleration of a body falling freely under the influence of the Earth’s gravitational pullat sea level. It is approximately equal to 9.806 m (32.16 ft) per second per second, thoughits measured value varies slightly with latitude and longitude. Also called acceleration of freefall.” [17]

Thus, gravity (g) is a constant acceleration that is included in the term weight of a structure. The massof a structure is always subjected to a gravity load (g-load) of g. In static finite element analysis, themagnitude of the g-load that the structure is subjected to has to be defined. It can be defined to besmaller or greater than g and the direction of the acceleration has to be defined as well as the densitiesof the components of the structure. It is an advantage to define the load that the structure is subjectedto as a g-load since all elements in the model is subjected to the g-load. This load definition reduce highstress gradients at points, lines or surfaces where a load with a corresponding amplitude could have beendefined since the g-load act on the whole structure.

It was described in Section 2.1.1 that in fatigue analysis, the equivalent load is used as a simplification.Gravity loads can also be used as equivalent loads and the fatigue analysis is performed in the samemanner, with the difference that the load amplitude is defined as a g-load.

2.2 Historical background

In this section, the information is mainly from the report Operativa mal avseende utmattning. Langtid-sprov och skakprov [18].

10

CHAPTER 2. BACKGROUND 2.2. HISTORICAL BACKGROUND

2.2.1 Test methods

Scania performs different kinds of test, two examples are full vehicle tests and rig tests for a system ofcomponents or single components. Full vehicle tests are performed at the Scania test track. The testtrack has passages, corresponding to different road conditions. The engine suspension has historicallybeen tested in a verifying shake test where the load sequence is simulated and more recently the frontengine suspension is tested in a Wohler test [19]. The Wohler test performed at Scania is described inDesign guidelines [20]. The purpose of performing tests is to ensure the quality of the products and todevelop component designs, targets, requirements as well as acceptance criteria and reliability.

The two test methods complement each other in a sense how time consuming they are and how wellthey corresponds to reality. Components tested in a full vehicle test have accurate installation, bound-ary conditions and environment, such as temperature and weather conditions. Therefore, this methodcorrespond well to reality. The full vehicle test is very time consuming and expensive, the fatigue testsperformed at Scania are in general destructive. Usually only one specimen of each component in thevehicle is tested at the same time, therefore, it is impossible to estimate the statistical spread for thecomponents from a single test.

A rig test performed on a big system of components, a partly assembled vehicle, is less time consumingthan a full vehicle test, but it is more complicated to recreate the real boundary conditions and envi-ronment. Interaction between between air forces, road conditions, corrosion and rust are examples ofparameters that are not reproduced in rig tests. Rig tests performed on single components are even lesstime consuming and the statistical spread and component characteristics can effectively be analyzed.

2.2.2 Statistical methods

The fatigue life of a component until failure generally has a log-normal distribution. This assumption ofdistribution is consistent with general fatigue analysis for high cycle fatigue found in the literature andwith experiences at Scania. High cycle fatigue is when Nf is greater than 103 cycles [21]. The meaningof a log-normal distribution is that the logarithm of Nf has a normal distribution.

The reliability (PR) is a parameter that describes how strong the component is for a specified load andresistance [11]. The parameter p in Eq. (2.9) is the percent age of survival and the reliability is definedas,

PR = 1 − p

PR = Φ(tp)

(2.9)

tp =Θ − 1√

VL2 + (Θ · VR)

2(2.10)

where Φ is the normal distribution function, Θ is the central safety factor and tp is the safety index. InEq. (2.10) VL and VR are variance coefficients defined as standard deviation divided by expectancy forthe load (index L) and resistance (index R). Solving Eq. (2.10) for Θ with p ≤ 50%, the safety factorcan be expressed as,

Θ =

1 +

√1 −

(1 − (tp · VR)

2)·(

1 − (tp · VL)2)

1 − (tp · VR)2 (2.11)

thus, the safety factor can be estimated when VL and VR are determined from the performed rig tests.

11

2.2. HISTORICAL BACKGROUND CHAPTER 2. BACKGROUND

2.2.3 Acceptance criteria

When designing components, every component have to meet an acceptance criterion. The acceptancecriterion can be targets or requirements. In revision 2 of STR6000001 [18], all acceptance criterion aredenoted as targets, but with different levels of fulfillment of the acceptance criterion. The engine brackethas an old acceptance criteria of a safety factor > 1 with p = 50 % for 105 cycles [22]. The engine bracketis a component with the reliability ”higher”, which means that when failure occurs it is very costly andmay lead to personal injury.

With the assumption that equivalent loads corresponds to real loads and that the fatigue loads havea log-normal distribution, the loads can be described as the product of road conditions, speed, springstiffness among other factors. If the acceptance criterion is not met, the component design need to berevalued. When there is a change of the component design or a change of design in adjacent components,the acceptance criteria may need to be redefined as well. The isolator design has changed and therefore,the acceptance criterion for the front engine bracket is under development.

2.2.4 Models

According to Design guidelines, the Wohler test performed at Scania is simulated. An example of a modelthat has been used in a Wohler test simulation is shown in Figure 2.3 [22] and it is not only the enginebrackets that are of interest when performing the Wohler test simulation. Other components of interestare for instance, the cylinder block, the main bearing caps and the flywheel housing.

Figure 2.3: Model used in the simulated Wohler test performed at Scania. The frontcover is illustrated in blue, the left engine bracket in grey, the ladder frame in purpleand the cylinder block is illustrated in beige.

In order to develop acceptance criteria and to determine the strength of a new component design of thepowertrain, in 2015 different departments at Scania initiated a common analysis model of the powertrain[23]. The model of the powertrain, shown in Figure 2.4 is an example of a reference model used whendeveloping a model of the powertrain for fatigue analysis of the flywheel housing.

12

CHAPTER 2. BACKGROUND 2.2. HISTORICAL BACKGROUND

Figure 2.4: Reference model of the powertrain for development of a powertrain modelfor fatigue analysis of the flywheel housing.

Note that the V-engine cylinder block in Figure 2.4, and other components can be substituted by otherdesigns, therefore, the powertrain has various model variants. Another example of a model used infatigue analysis is where only a part of the cylinder block, a part of the front cover and the enginebracket is modeled [24]. The boundary conditions and load cases depends on the analysis. Wohler testsimulation, general fatigue analysis with a load sequence from measurement data and fatigue analysiswith equivalent loads all have different analysis methods. The constraint point configuration has notalways been consistent at Scania, although the analysis has been the same or similar and this is one ofthe reasons to why the analysis in the first part of this thesis has been performed.

13

Chapter 3

Models

This chapter contains information about the different model geometries, defined contact surfaces and thematerial properties of the components. There are four types of models: one linear model, two nonlinearmodels and one time-dependent model. Linear model has three different configurations for boundaryconditions that will be described. Nonlinear model No.1 contains nonlinear springs and Nonlinear modelNo.2, in addition, contains front isolators meshed with solid elements.

Time-dependent model has four configurations, two of the configurations have different strain gauges ofdifferent lengths, with the same contact surfaces as in all previous models. One configuration of themodel has a decreased contact surface between the engine brackets and the cylinder block and the lastconfiguration has an increased contact surface. This is described further in Section 3.6.

3.1 Geometry

To create a more realistic interface for the engine brackets the chosen components are the outer adjacentcomponents of the powertrain. The components used in the geometry and the global coordinate systemcan be seen in Figure 3.1 and are listed below:

1. front cover

2. engine brackets

3. ladder frame

4. cylinder block

5. transmission plate

6. flywheel housing

7. front gearbox housing

8. back gearbox housing

9. suspension beam

Figure 3.1: Exploded view of the components used in the model of the powertrain.

14

CHAPTER 3. MODELS 3.1. GEOMETRY

Screw joints are not included in any model since sliding between contact surfaces tend to be small enoughthat it can be neglected for the 6 - cylinder (DL6) engine [25]. All components were descretized inSimLab separately and were then imported to Hypermesh, where all contact surfaces were defined. Allcomponents, aside from the cylinder block, were discretized with second order elements. The cylinderblock is discretized with first order elements in order to save computation time. When the powertrain ismounted to chassis, there is a 5◦ angle between the powertrain’s local x -axis and the ground, therefore,the model was rotated 5◦ around the y-axis according to the arrow θy in Figure 3.2.

Figure 3.2: There are six degrees of freedom (DOF). The first DOF is movement along thex -axis. The second DOF is movement along the y-axis and the third DOF is movement alongthe z -axis. The fourth, fifth and sixth DOF is the rotational movement around the x, y andz -axes, respectively. The arrows illustrate the positive direction for each degree of freedom.

The contacts surfaces between the different components in the powertrain model are shown in Figure 3.3.

Figure 3.3: Defined contact surfaces are illustrated in pink.

The geometry in Figure 3.3 is used in Linear model and Nonlinear model No.1. In Nonlinear model No.2the only difference is that the geometry of the isolators are added to the model geometry. A principalsketch of the left isolator is shown in Figure 3.4.

15

3.1. GEOMETRY CHAPTER 3. MODELS

Figure 3.4: The light grey illustrates the rubber of the isolator and the dark greyillustrates the top and bottom metal parts of the isolator. The rubber part ofthe isolator consist of three different rubber components, a compression rubber, arebound rubber and a main rubber.

16

CHAPTER 3. MODELS 3.2. MATERIALS

3.2 Materials

Material properties for each component except the isolators are given in Table 3.1.

Table 3.1: Material properties for components used in the model.

Component Material E [GPa] ρ [kg/m3] ν [-]

Front cover Aluminum 46000 75 2750 0.33

Engine brackets Nodular cast iron 167.5 7200 0.26

Ladder frame Aluminum 46000 75 2750 0.33

Cylinder block Grey cast iron 105 7200 0.26

Transmission plate Steel 208 7800 0.3

Flywheel housing Aluminum 46000 75 2750 0.33

Front gearbox housing Aluminum 46000 75 2750 0.33

Back gearbox housing Grey cast iron 110 7100 0.23

Suspension beam Nodular cast iron 167.5 7200 0.26

The rubber parts of the isolator follow a Mooney - Rivlin material model which is an incompressiblehyper elastic model. The contact surfaces between aluminum and rubber is assumed to have a kinematicfriction coefficient of 0.5 [26]. In FEMFAT, fatigue analysis is performed with the stress life approachdescribed in subsection 2.1.1. The material properties of the engine brackets are defined in FEMFATaccording to Table 3.2 and the parameters are the same for all models.

Table 3.2: Parameters used in fatigue analysis of the engine brackets.

Parameters Value Unit

Endurance limit 170 MPa

Ultimate strength 500 MPa

Yield strength 320 MPa

Surface roughness 200 µm

Cycles 1 · 105 -

Survival probability 50 %

All components of the powertrain are not included in the geometry, and thus the model’s center of gravityand total mass need to be modified in order to correspond to the engines real center of gravity. Thiswas done by modifying the densities of all components except for the engine brackets’ since they are thecomponents of interest in the analysis. First, all component mass centers and volumes were extractedfrom the geometry in Hypermesh and with known material properties the model’s total mass could bedetermined. The model’s total mass and center of gravity in global coordinates were determined by use ofthe Center of Mass for Particles formula [27]. One center of mass coordinate for the system is the sum ofthe components individual mass mi multiplied with their individual center of gravity in that coordinateand then divided by the total mass (M) of the system. Eq. (3.1) show how the center of gravity in theglobal coordinates x, y and z were determined.

17

3.3. LINEAR MODEL CHAPTER 3. MODELS

x =

∑Ni=1mixiM

y =

∑Ni=1miyiM

z =

∑Ni=1miziM

(3.1)

The model’s center of gravity and total mass were then modified to correspond to the powertrain’s centerof gravity and total mass by changing the component densities. Due to lack of components that couldaffect the center of gravity in some coordinates it was assumed that the most important center of gravitycoordinates to get right were x and z.

An object in space rotates around the center of gravity if the extended load vector does not cross thecenter of gravity. It is therefore of importance to modify the model’s center of gravity to make the model’smovement correspond to the real system’s movement. Newton’s first law of motion, also called the lawof inertia, relates to the importance of the system’s total mass. Inertia is the resistance of an object tochange in its state of motion and the inertia increases with the object’s total mass. Therefore, the totalmass of the model also need to correspond to the real system’s total mass.

3.3 Linear model

The geometry used in Linear model can be seen in Figure 3.1 and the materials used in the model arefound in Table 3.1. The isolators are not included in the geometry. The nodes around the engine brackets’screw holes on the bottom surface are connected to a node on each side by a single point constraint (SPC),see Figure 3.5.

Figure 3.5: Nodes around the left engine bracket’s screwholes are connected to aSPC node, the white node in the middle.

The white SPC node in Figure 3.5 is located on the left engine bracket, but the nodes around the screwholes on the right engine bracket and the suspension beam were connected to a node in the same manner.These four SPC nodes are where the boundary conditions were applied. The engine brackets’ SPC nodesare the front SPC nodes and the suspension beam’s SPC nodes are the back SPC nodes and the threemodel configurations of Linear model are shown in Table 3.3.

18

CHAPTER 3. MODELS 3.3. LINEAR MODEL

Table 3.3: Constraint point configurations, the constraint points for the engine brackets (the front SPCnodes) and the suspension beam (the back SPC nodes) are either moved or unmoved.

SPC configurations Front Back

Configuration 1 Unmoved Unmoved

Configuration 2 Moved Unmoved

Configuration 2 Moved Moved

In order to evaluate how much the constraint points influence the results when using this model, thesethree configurations of the model were compared to each other. The unmoved position is when the nodeswere close to the screw holes according to Figure 3.5 and the moved position is when the nodes weremoved a distance from the screw holes. The moved positions corresponds to a calculated load position inthe isolators [23]. The unmoved position for the SPC nodes can be seen in Figure 3.6(a) and Fig. 3.7(a).The moved SPC nodes are shown in Figure 3.6(b) and Figure 3.7(b).

(a) Unmoved position (b) Moved position

Figure 3.6: Unmoved and moved front SPC nodes.

(a) Unmoved position (b) Moved position

Figure 3.7: Unmoved and moved back SPC nodes.

The moved SPC node in Figure 3.6(a) and Fig. 3.7(a) were positioned at the point where the grey linesmeet.

19

3.4. NONLINEAR MODEL NO.1 CHAPTER 3. MODELS

3.4 Nonlinear model No.1

The same geometry and material properties were used in this model as in Linear model, but insteadof having the nodes around the screw holes connected to one node, that node was connected to threenonlinear spring elements for each of the x, y and z -directions. The spring elements for the left enginebracket are illustrated in Figure 3.8.

Figure 3.8: Spring connection, the blue point connecting the springs illustrate themoved position described in section 3.3 and the red points are the constrained nodes.

The node connecting the springs in Figure 3.8 is only a connection and the other red nodes in Figure 3.8are the nodes that were constrained. There are three springs for every SPC node, one spring with stiffnessin the x -direction, one spring with stiffness in the y-direction and one spring in the z -direction. The springstiffness for each spring comes from measurements. The two x -springs have the same stiffness, the twoy-springs have the same stiffness and the two z -springs have the same stiffness. The spring stiffness forthe back springs were defined in the same manner. However, the springs constraining the back SPC nodeshave a lower stiffness compared to the springs constraining the front SPC nodes.


In this model the front spring elements in Nonlinear model No.1 and Figure 3.8 were replaced with thefront isolators modeled with solid elements. The nodes at the isolator’s bottom surface were connectedto a new SPC node by a kinematic coupling. The same springs that were used to connect the suspensionbeam in Nonlinear model No.1 were used in this model.

3.6 Time-dependent model

The time-dependent model is model Configuration 3 of Linear model with four strain gauges added tothe geometry. The strain gauges were modeled with T3D2 elements, which is a three dimensional 2-nodetruss element. In January 2016, load measurements were performed on the powertrain and the straingauges in the model were positioned according to Appendix C in the associated load measurement report[28]. The strain gauges were positioned on the left side of the cylinder block, close to the left enginebracket. The strain gauges are listed and schematically illustrated in Figure 3.9

20

CHAPTER 3. MODELS 3.6. TIME-DEPENDENT MODEL

1. TKX712. TKX733. TKX744. TKX75

Figure 3.9: The strain gauges, positioned on the left side of thecylinder block are illustrated in yellow.

Instead of two node sets for the front and back SPC nodes, the time-dependent model had four node sets,one node set for each constraint point. The node sets are itemized and described below:

1. SPCLF is the Left Front constraint point

2. SPCLB is the Left Back constraint point

3. SPCRF is the Right Front constraint point

4. SPCRB is the Right Back constraint point

Each constraint point was connected to the nodes around the screw holes on the bottom surface on theengine brackets and the suspension beam. Two configurations of the strain gauges in the model wereused according to Table 3.4.

Table 3.4: Length of strain gauges.

Gauge configuration TKX71 TKX73 TKX74 TKX75 Unit

Configuration 1 4.33 2.47 2.74 5.03 mm

Configuration 2 2.5 2.5 2.5 2.5 mm

Three configurations of the contact surfaces between the engine brackets and the cylinder block wereused, while the length of the strain gauges was kept constant. The contact surfaces used for Linearmodel and Nonlinear model No.1 were common for all models. The contact surfaces between the left andright engine bracket and the cylinder block were altered by first decreasing the contact surface and thenincreasing the surface. Therefore, the total number of configurations is four. The three contact surfaceconfigurations for the left engine bracket are shown in Figure 3.10.

(a) Original contact surface (b) Decreased contact surface (c) Increased contact surface

Figure 3.10: The different contact surface configurations used in the time-dependent model.

21

3.6. TIME-DEPENDENT MODEL CHAPTER 3. MODELS

All configurations are summarized in Table 3.5.

Table 3.5: Gauge and contact surface configurations.

Configurations Description

Configuration 1 Model where the length of the strain gauges were in an interval of 2.47mm to 5.03 mm with original contact surfaces

Configuration 2 Model where the length of the strain gauges were 2.5 mm

Configuration 3 Model with decreased contact surfaces for the contact between the enginebrackets and the cylinder block, the length of the strain gauges were keptconstant

Configuration 4 Model with increased contact surface for the contact between the enginebrackets and the cylinder block, the length of the strain gauges were keptconstant

22

Chapter 4

Method

In this chapter, the methods used to attain the results for each model are described as well as the methodsused to compare the results. Stresses, strains, reaction forces and safety factors are the results evaluatedwhen applying loads, constraints, and performing fatigue analysis. Quasi-static analysis was performedon all models.

4.1 Linear model

As described in Section 3.3 the linear model has three configurations for the position of the front andback SPC nodes where the boundary conditions were applied according to Table 3.3. In order to evaluatehow the position of the constraints influences the results, the same load was applied for each one of thethree configurations in the x, y and z -directions, respectively. The applied load was a g-load, describedin Section 2.1.3. The model was subjected to a g-load of +10g in the x and y-direction and -10g in thez -direction. Boundary conditions with constrained degrees of freedom (DOF) for the different load casesare presented in Table 4.1 [23].

Table 4.1: Constrained DOFs for each load case.

Load case Front DOF Back DOF

X 2, 3 1, 2, 3

Y 2, 3 1, 2

Z 2, 3 1, 2, 3

Two node sets were created for each engine bracket. One node set contain 7 nodes in a point close to thefillets where the stress concentration was the highest. There was one node set for the engine bracket’supper surface and one node set for the corresponding point on the lower surface. The arithmetic meanwas derived for the results in each node set according to Eq. (4.1) [29], where xi represents the result ineach node.

x =1

n

n∑i=1

xi (4.1)

The mean 1st Principal stress for the two node sets in the three different configurations were comparedby deriving the absolute error (eabs) [30] according to,

eabs = x0 − x (4.2)

23

4.2. NONLINEAR MODEL NO.1 CHAPTER 4. METHOD

The parameter x0 in Eq. (4.2) is the mean 1st Principal stress in Configuration 2 and x is the mean 1stPrincipal stress in Configuration 1. This absolute error is the first item in the list below, the deriveddifferences between the three configurations:

1. the difference between Configuration 1 and Configuration 2.



Fatigue analysis was performed in FEMFAT for Configuration 3 with the parameters defined in Table 3.2and the extracted fatigue results were:

• the amplitude stress

• the safety factor

In the fatigue analysis, Smean was -g for loading in z and 0g when loading in y. This is discussed furtherin Chapter 6. The absolute mean for the fatigue results were also derived according to Eq. (4.1). Theresults were then compared in order to meet the objectives of the thesis, to determine how the constraintpoint configurations influence the results and how to determine which model is to be preferred.


In Section 3.4, Figure 3.8 show the SPC nodes and the node connecting the springs to the nodes aroundthe isolator’s screw holes. The SPC nodes were constrained in all DOFs for all load cases. The appliedloads are both negative and positive g-loads. There were four load cases, the first load case is zero gravityto -10g in y for one load step and an increment size of 0.1. All load cases had the same step and incrementsize. The second load case is zero gravity to +10g in y. The third load case was zero gravity to -10g in zand the fourth load case was zero gravity to +8g in z. The load cases and boundary conditions are givenin Table 4.2.

Table 4.2: Load cases and constrained DOFs for each SPC node.

Load case Negative load Positive load DOF

Y 0g to -10g 0g to 10g 1, 2, 3

Z 0g to -10g 0g to 8g 1, 2, 3

The same node sets as in Linear model was used in the analysis and the fatigue analysis was performedin the same manner, including calculation of the mean value of the node sets. The extracted results were:

• the 1st Principal stress

• the 3rd Principal stress

• the amplitude stress

• the safety factor


The SPC nodes and loads were applied according to Table 4.2 and the fatigue analysis was performed inthe same manner as in the previous section with the same extracted results.

24

CHAPTER 4. METHOD 4.4. TIME-DEPENDENT MODEL

4.4 Time-dependent model

The two gauge configurations and the three contact surface configurations were used in the quasi-staticanalysis, previously described in Section 3.6. The first strain gauge configuration shared the same modelconfiguration as one of the tie configurations, therefore there are in total four configurations. Eachderived load component in the x, y and z -direction in the time domain from the load measurements[28] were applied to each one of the four node sets: SPCLF, SPCLB, SPCRF and SPCRB. The chosenload sequence come from measurements on the truck over the toughest passage at the test track. It wasassumed that the powertrain was subjected to loads that would cause the most damage at this passage.The greatest load amplitude in the load sequence was chosen to be in the middle of a 4 seconds longsignal. The sequence start before the greatest load amplitude since the load is zero at the beginning ofthe load sequence.

If the loads are applied to the nodes in the node sets, the constraints can not be defined at the samenodes. Thus, in the static stress analysis performed in Abaqus, inertia relief is used [31]:

“Inertia relief: involves balancing externally applied forces on a free or partially constrainedbody with loads derived from constant rigid body accelerations”

Density or mass needs to be specified for computing inertia relief loads and the altered component densitieswere used in the analysis. The step was static and having a static step means that the inertia relief loadingvaries with the applied external loading, the model is in equilibrium in every step. The measurementsample rate, fs [Hz], was used to derive the time increment (t) according to Eq. (4.3), which was used inthe analysis.

t =1

fs(4.3)

The strain results in the four strain gauges were extracted with a code written in Matlab by JonasLenander [32]. The strain results from the measurements and the analysis were compared.

25

Chapter 5

Results and analysis

This chapter contains the results for the first and second part of the thesis, described in Section 1.1.The first part is a comparison of models and the second part include the time-dependent results andanalysis.

5.1 Model analysis

Comparison between the constraint point configurations

The greatest stress in the points on the upper and lower surface on the engine bracket seen in Figure 5.1occurred in the load case where the load was applied in the negative z -direction with a mean accelerationload of -g.

(a) (b)

Figure 5.1: The critical stress points on the left engine bracket. (a) is the stress point locatedon the upper surface and (b) is the stress point located on the lower surface.

This load case resulted in the highest stress concentration in the point shown in Figure 5.1(b). Therefore,only the 1st Principal stress is presented for this point on the left engine bracket and the correspondingpoint on the right engine bracket. The results for the three configurations in Table 3.3 are described inSection 3.3 and the results are presented in Figure 5.2 with the same axis limits and scaling.

26

CHAPTER 5. RESULTS AND ANALYSIS 5.1. MODEL ANALYSIS

0 2 4 6 8 10Gravity load

1st

Principalstress

Left engine bracket loaded in negative Z

Configuration 1Configuration 2Configuration 3

(a)


1st

Principalstress

Right engine bracket loaded in negative Z

Configuration 1Configuration 2Configuration 3

(b)

Figure 5.2: Trends in 1st Principal stress for different g-loads with applied load in the negativez -direction. (a) is the results for the left engine bracket. (b) is the results for the right engingebracket.

When comparing Figure 5.2(a) and Figure 5.2(b) it can be seen that the stress in the left engine bracketwas greater than the stress in the right engine bracket for all configurations. In Figure 5.2 there is nodifference between the results in Configuration 2 and Configuration 3 for each engine bracket. However,Configuration 1 results in a greater stress. It is therefore concluded that moving the back SPC nodes willnot influence the result in the points where the stress concentration is the highest in the left and rightengine bracket.

In order to get a better understanding of why the stress was higher in Configuration 1, the moment (M)around the stress point in Figure 5.3 was derived for Configuration 1 and Configuration 3. Note thatConfiguration 3 has the same front SPC node configuration as Configuration 2.

Figure 5.3: R and r are the distance in three dimensions from the stress point Aillustrated in red and the SPC nodes for the left engine bracket. B represent theSPC node in Configuration 1 and C represent the SPC node in Configuration 3.

The moment is derived by taking the cross product of the direction vector (r or R) and the reaction force(F) in point B or C. In Eq. (5.1) the moment is derived to show the how the moment varies with thedirection vector. The positive moment directions is illustrated by the rotation arrows in Figure 3.2.

27

5.1. MODEL ANALYSIS CHAPTER 5. RESULTS AND ANALYSIS

R = [Rx, Ry, Rz]>

F = [Fx, Fy, Fz]>

M = R × F

(5.1)

The expression in Eq. (5.1) in matrix form is,

M =

(Ry · Fz) − (Rz · Fy)

(Rz · Fx) − (Rx · Fz)

(Rx · Fy) − (Ry · Fx)

(5.2)

According to Table 4.1 the SPC nodes were not constrained in the x -direction and thus, there were noreaction forces in the x -direction and Eq. (5.2) becomes;

M =

(Ry · Fz) − (Rz · Fy)

−(Rx · Fz)

(Rx · Fy)

(5.3)

The components rx and Rx were very small and they were almost the same in Configuration 1 andConfiguration 3. Therefore, changing the configuration from rx to Rx, will not influence the results. Thereaction force component Fz was almost the same in Configuration 1 and Configuration 3, however, themagnitude of the component Fy increased in Configuration 3. The resultant of the reaction forces on theleft and right engine bracket are schematically illustrated in Figure 5.4.

Figure 5.4: The cylinder block, seen from the front of the truck. The left engine bracket isillustrated in green and the right engine bracket in blue. The reaction forces starting at point Bare the results from Configuration 1 and the reaction forces starting at point C are the resultsfrom Configuration 3.

The greatest moment component in point A, shown in Figure 5.3, was Mx for both Configuration 1(Mx,AB) and Configuration 3 (Mx,AC). The difference between Mx for the left and the right enginebracket, and the difference between the configurations are presented in Table 5.1.

28


Table 5.1: Difference between the absolute value of Mx in point A for the left and right engine bracket,and between Configuration 1 and Configuration 3.

Description Left [%] Right [%]

Difference betweenMx,AB and Mx,AC

10.3 16

Mx,AB [%] Mx,AC [%]

Difference betweenLeft and Right

4.37 10.4

29


Comparison between the models

The greatest stress in the points on the upper and lower surface on the engine bracket seen in Figure 5.1occurered in the load case where the load was applied in the negative z -direction. The presented resultsare the 1st Principal stress and the safety factor for different g-loads in the negative z -direction. Theresults for the right and left engine bracket are presented in the same figure where the results for theright engine bracket is the dashed line. The 1st Principal stress is shown in Figure 5.5.


1st

Principalstress

Loaded in negative Z

Right solidLeft solidRight springLeft springRight linearLeft linear

Figure 5.5: Trends in 1st Principal stress for the left and the right engine bracket. Nonlinearmodel No. 1 is illustrated in blue and Nonlinear model No. 2 is illustrated in red and Linearmodel with Configuration 3 in black.

Linear model with Configuration 3 was used for comparison since the SPC nodes had the same placementas Nonlinear model No. 1. This SPC node configuration corresponds to when the reaction forces acts inthe isolator in Nonlinear model No. 2. The results for Nonlinear model No. 1 and Nonlinear model No.2 were almost the same until -3g, but then the results were diverging. The stress in Linear model is justabove 30 % of the stress in Nonlinear model No. 1 and 50 % of the stress in Nonlinear model No. 2.

The reaction forces in point C, seen in Figure 5.4, were compared for Linear model with Configuration3 and Nonlinear model No. 1. The reaction forces were linear for both models. According to Table 4.2,Nonlinear model No. 1 was constrained in the x -direction. In comparison to Linear model, Fx is notequal to zero in Nonlinear model No. 1, but Fx was small in comparison to Fy and Fz. Mx,AC in theengine bracket is dependent on Fy and Fz according to Eq. (5.3). Fz was the same for both models, butFy was considerably higher in Linear model. Fy reduces the Fz contribution to Mx,AC . Therefore, Linearmodel has a lower moment in point A (the stress point) than Nonlinear model No. 1, thus, the differencein stress. The reason to why Fy was lower in Nonlinear model No. 1 may be due to the definition ofthe spring stiffness in the y-direction. The model is allowed to move in the y-direction, but in Linearmodel, the constraints in the y-direction may cause Linear model to be too rigid. Thus, creating a greaterreaction force in the y-direction.

The stress results were higher for the left engine bracket for all models. The center of gravity is 4 mmcloser to the left engine bracket (4 mm in the negative y-direction) in the model compared to reality andthis may influence the results. The difference between the left engine bracket and right engine bracketis around 14 % for Linear model, 10 % for Nonlinear model No. 2 and 5 % for Nonlinear model No.1. The difference between the center of gravity in the model compared to reality is very small to drawthe conclusion that this is the only factor that influence the stress differences between the left and theright engine bracket. Design difference between the left and right engine brackets may also influence theresults.

30


When the isolator is compressed at -3g, the compression rubber came in contact with the top aluminumpart of the isolator. This means that the reaction force point changes from being in the middle of the mainrubber to the compression rubber. As described in Section 5.1, this results in a change of the reactionforce components and thus, the bending moment in the stress point, shown in Figure 5.3, decreases. Thestress decreases with a decreased moment.

The safety factors are shown in Figure 5.6 and it is a very big difference between Linear model and theother two models. The safety factors for Nonlinear model No. 1 and Nonlinear model No. 2 are similar,but in Linear model the safety factor is very high for lower loads.

31


5 6 7 8 9 100

2

4

6

8

Gravity load

Safety

factor

Loaded in negative Z

Right solidLeft solidRight springLeft springRight linearLeft linear

Figure 5.6: Safety factors for the left and the right engine bracket. Nonlinear model No. 1is illustrated in blue and Nonlinear model No. 2 is illustrated in red and Linear model withConfiguration 3 in black.

The absolute difference in safety factor at -5g is 0.56 between Nonlinear model No. 1 and Nonlinearmodel No. 2 which is small compared to difference in safety factor for Linear model at the same load.According to acceptance criteria, the safety factor should be greater than 1 [22] and this is fullfilled fora load lower than -8g for all models. However, Nonlinear model No. 1 is very close to 1 at -8g since thestress is higher for this model compared to Nonlinear model No. 2 for loads greater than -3g.

It is assumed that Nonlinear model No. 2 is closer to reality due to the changes of the reaction forcepoints. This model captures the real movements of the powertrain and the isolator when the isolator iscompressed when loaded in the negative z -direction and extended when loaded in the positive z -direction.This model is used as a reference for the comparisons. However, Nonlinear model No. 1 should correspondwell to reality too since the nonlinear spring deformation comes from measurements, but the springs donot capture the moment in the isolator when loaded. Nonlinear model No. 1 is however recommendedto use for loads lower than -3g in the negative z -direction, which is the most critical load case, since thestress results were the same for Nonlinear model No. 2. Nonlinear model No. 1 can be used for loadslower than -8g in the negative z -direction, but the stress is possible to be higher in the model than inreality which should be taken into account.

The reason to why Nonlinear model No. 1 is preferred to Nonlinear model No. 2 is due to the reductionof computation time when using this model. The isolator in Nonlinear model No. 2 is complicatedcompared to the springs in Nonlinear model No. 1. The isolator in Nonlinear model No. 2 has a rubbermaterial which is nonlinear, contact surfaces, friction and this may result in convergence problems sincethe model would be more complicated for the software to solve.

If the Linear model is used, Configuration 1 would be the configuration that best correlate with theresults for Nonlinear model No. 1 and Nonlinear model No. 2. This configuration resulted in the higheststresses and would reduce the difference in results more than using Configuration 3 that was used in themodel comparison.

32

CHAPTER 5. RESULTS AND ANALYSIS 5.2. TIME-DEPENDENT ANALYSIS

5.2 Time-dependent analysis

The results are presented for each strain gauge in Figure 3.9 and the model configurations are describedin Table 3.5. An interval around one of the highest load amplitudes with the corresponding strainresults in the measured time signal was used in the analysis. The simulated strain results (ε) in time (t)were compared to measured strain results and the results for each strain gauge are presented with thesame axis limits and scaling, note that the measured result is the same for each strain gauge, for all itsconfigurations. Configuration 1 can be seen as the original model result for each strain gauge which theother configurations can be compared to. The strain results for the strain gauge TKX71 are presented inFigure 5.7.

t

0

TKX71

MeasurementSimulation

(a)

t

0

TKX71


(b)

t

0

TKX71


(c)

t

0

TKX71


(d)

Figure 5.7: Results for TKX71, (a) is the configuration where the length of the strain gaugeswas different. (b) is the configuration where the length of the strain gauges was the same.(c) is the configuration with a decreased contact surface and (d) is the configuration with anincreased contact surface.

The whole signal is not shown in Figure 5.7(a) in any of the figures containing Configuration 1 becausethe simulation was not completed. There was no apparent reason to why the simulation did not gothrough since the solution was converging and this is discussed further in Chapter 6. However, thepart of the solution that was completed is still included in order to compare the different configurations.The simulated results were very similar to the measured results, aside from magnitudes at the greatestpeaks which is smaller for all configurations. When comparing Configuration 1 and Configuration 2 inFigure 5.7(b) it can be seen that the there is no difference at all between the results when changinglengths of the strain gauges. Therefore, Configuration 2 which contains the full solution was preferredwhen comparing with the remaining configurations. There is barely any difference between Configuration

33

5.2. TIME-DEPENDENT ANALYSIS CHAPTER 5. RESULTS AND ANALYSIS

2 and Configuration 3 in Figure 5.7(c), but there is a slight decrease in magnitude between Configuration4 in Figure 5.7(d) and Configuration 2.

The strain results for the strain gauge TKX73 are presented in Figure 5.8.

t

0

TKX73


(a)

t

0

TKX73


(b)

t

0

TKX73


(c)

t

0

TKX73


(d)


When comparing the results for strain gauge TKX73, there is no difference between Configuration 1 inFigure 5.8(a) and Configuration 2 in Figure 5.8(b) when changing lengths of the strain gauges. However,there is a difference between Configuration 2 and Configuration 3 in Figure 5.8(c), the magnitude inConfiguration 3 has increased. There is also a difference in magnitude in Configuration 4 in Figure 5.8(d),but in this case the magnitude decreased. Furthermore, the simulated strain results were very similar tothe measured strain results.

34



t

0

TKX74


(a)

t

0

TKX74


(b)

t

0

TKX74


(c)

t

0TKX74


(d)


For strain gauge TKX74, there is no difference between Configuration 1 in Figure 5.9(a) and Configuration2 in Figure 5.9(b). There is a slight increase in magnitude in Configuration 3 in Figure 5.9(c) and thereis a decrease in Configuration 4 in Figure 5.9(d). Furthermore, the magnitude for all configurations havea magnitude lower than the measured strain amplitudes.

35

5.2. TIME-DEPENDENT ANALYSIS CHAPTER 5. RESULTS AND ANALYSIS


t

0

TKX75


(a)

t

0

TKX75


(b)

t

0

TKX75


(c)

t

0TKX75


(d)


The simulated results for strain gauge TKX75 were similar to the measured results in shape, but lessin magnitude for any of the other strain gauges. There is no difference between Configuration 1 inFigure 5.10(a) and Configuration 2 in Figure 5.10(b) and it can be seen that the magnitudes were muchgreater than the measured strains. It can be seen that Configuration 3 in Figure 5.10(c) decrease, which isdifferent from Configuration 3 for the other strain gauges. The simulated strain increase in Configuration4 in Figure 5.10(d) which is also different from results in Configuration 4 for the other strain gauges.

Comparison between the simulated and measured results

The simulated strain results were similar to the measured results in shape, but there is a difference inmagnitudes. The strain gauge TKX73 had simulated results most similar to measured results for all ofthe four configurations. The strain gauge TKX75 had simulated results that were furthest away fromthe measured results in magnitude. There were no difference between the results in Configuration 1 andConfiguration 2, the models with different lengths of the strain gauges. Therefore, it concluded that thelength of the strain gauges in the interval 2.5 mm to 5 mm does not influence the results.

A decreased contact surface generally result in an increased strain magnitude and an increased contactsurface result in a decreased strain magnitude. It was described in Section 5.1 that Linear model with

36


Configuration 1, the configuration with unmoved SPC nodes, should have been used. However, the appliedloads in the time dependent analysis, the second part of this thesis, were calculated for Configuration 3which was the configuration with moved SPC nodes. Therefore, it would be incorrect to apply the loadsas in Configuration 1. In spite of this, the simulated and measured results correlate very well.

37

Chapter 6

Discussion

It was described in Section 3.1 how the densities of the components were modified in order to make themodel center of gravity correspond to the center of gravity in reality. The center of gravity was correct inthe x and z -direction but it was described in Chapter 5 that there was an offset of 4 mm in the negativey-direction compared to the real center of gravity. This may have influenced the difference in resultsbetween the left and the right engine bracket, but in order to disregard the difference as a difference dueto the center of gravity, it is recommended to try a model with the correct center of gravity and mass.The surface roughness was chosen to be the roughest surface possible since the true surface roughnesswas not at hand, therefore, the performed analysis had an extra factor that created a tougher conditioncompared to reality.

The constraints in the first part of the thesis were taken from other calculation reports at Scania in orderto be able to compare the created models in this thesis with past models. The constraints for all modelsseem to be valid. The engine bracket was not constrained in the x -direction since road induced loadstypically acts in the z -direction and in the y-direction. Imagine a truck on a bumpy country road, it isnot until a high acceleration occurs (negative or positive) in the direction of the moving truck that therewill be a need for constraints in the x -direction. However, the suspension beam was constrained in thex -direction since the design of the front and back isolator differs. The only load case that did not haveconstraints in the x -direction at all was when load was applied in the y-direction. This constraint wasnecessary in order to allow the model to move correctly and without an increased stiffness when loadedin the y-direction.

In Section 4.1, it was described that the mean of the results in a point was derived. This method reducethe source of error when evaluating results in the case when there is a stress singularity in a single node.However, if such a node is included in the mean, that will affect the result in the whole point which mayinfluence the results regardless. There were two node who had a higher stress when taking the mean inthe point on the left engine bracket, this may have increased the difference in results between the left andthe right engine bracket.

The assumption that Nonlinear model No. 2 best correspond to reality was described in Chapter 5. Thedisadvantage when using the recommended model, Nonlinear model No. 1 is that it will not capture thereal movement for loads greater than -3g in the z -direction and it may be due to the change of reactionforce points. The spring stiffness was defined by force and displacement and if the spring stiffness isdefined incorrectly the movement will not correspond to reality. If the springs in Nonlinear model No. 1is overloaded the spring will become fully stretched and if loaded even more, there will be no isolation,the model will only be constrained. This behavior could also occur when using Nonlinear model No. 2,but the isolator design in this model would capture the movement in a more realistic way. However,Nonlinear model No. 1 can be used for loads lower than -8g, but the difference between the two nonlinearmodels should be taken into consideration.

Nonlinear model No. 1 could be further developed by adding spring elements at the location of thecompression rubber and the rebound rubber. This may enhance the model of the isolator when theisolator is subjected to compression and tension, and this may capture the change of reaction forcepoints. Moment spring elements would give a further improvement, though presently no moment springdata exist. It was described in Chapter 4 that the mean load was -g when loading in the z -direction, but

38

CHAPTER 6. DISCUSSION

0g when loading in the y-direction. The reason for this was that in FEMFAT, only the upper stress andthe lower stress was defined for one load case, therefore when performing fatigue analysis for loads in y,only the stress results from the load case in y were defined. It was assumed that this would not greatlyaffect the results since the normal gravity of -g in the z -direction is a small load, based on the stressresults at -g in the z -direction. Regardless, the worst load case showed to be loading in the negativez -direction.

It would be interesting to perform a Wohler-test simulation with the models in this thesis and comparethem to older models at Scania, as well as compare the results to real Wohler-tests. The main differencebetween the old model and these models is that the old model has screw joints. If the simulated Wohler-test results using the models in this thesis was similar to simulated Wohler-test results with older models,it is recommended to use one of these models to save computation time. It is also recommended to useone of these models if the results were closer to the performed Wohler-test results. Compared to theWohler-test performed in May 2015 on similar engine brackets, the crack initiations correspond well tothe chosen points of stress concentration in the models [33]. In the test report, the right engine brackethad a lower fatigue limit than left engine bracket.

In the second part of the thesis, the time-dependent analysis, the results correspond well to reality. Thewhole analysis was quasi-static, meaning that the loads were applied so slowly that the structure deformsin a static manner. The time increment used in the analysis was derived from the sampling frequency andthe used load sequence were from measurements that captures the whole movement of the powertrainover the toughest passage at the test track. It was motivated to choose this passage since this passagewill cause the highest road induced loads and therefore, the worst load case. For a passage with lessprofound obstacles, the results may have been different since the strain gauges may not give as accurateresults due to measurement errors, therefore, this would be of interest to further analyse. As described inChapter 4, Inertia relief was used in the quasi-static analysis. The method also allows dynamic analysis,which would be of interest to perform since the analysis in this thesis does not include dynamic effects.Until a dynamic analysis is performed, it is not possible to say anything about how the dynamic effectsmay influence the results. The analysis in the second part of the thesis could be developed to be asimulation of the verifying test described in Section 2.2 and with a better basis of which loads that needto be evaluated, the Wohler test simulations could be enhanced.

The load signal was 4 seconds long and it would be interesting to increase the length and see if theresults still corresponds to reality for a longer time interval. As a suggestion, the time increment couldbe increased to save computation time for an increased time interval, though this may lead to a decreasein resolution and peaks could be lost. The computation time was quite fast and therefore increasingthe time increment may be unnecessary. It would also be interesting to have more strain gauges inthe model, tentatively further away from the brackets in order to see that the whole movement in themodel of the powertrain correspond to the real movement of the powertrain. In the second part of thethesis, the loads were calculated for Configuration 3 (moved SPC nodes), but it may be an advantageto use loads calculated for Configuration 1 (unmoved SPC nodes) since this configuration would be lessdependent on the isolator design. It will be easier to compare the engine brackets if the same constrainpoint configuration is used. In addition, the stresses in Configuration 1 better corresponds to the stressesin the nonlinear models. The test track measurement had a different engine bracket design compared tothe engine brackets used in the simulations. It was similar, but more topology optimized and this mayhave influenced the difference in the results but how can not be said until a simulation with this enginebracket design is compared to measurement results.

The simulated results did correlate very well to measured results and if this method was further developedit could reduce the over all analysis time, though it is the post processing, the fatigue analysis thatwould take the longest time to perform. It could be possible to only analyse the highest loads andperform a smaller rainflow analysis in order to acquire equivalent loads that will be used in the fatigueanalysis. If the time-dependent analysis is to be developed, in addition, the acceptance criteria need tobe further developed. Regarding the results for the time-dependent analysis with Configuration 1 (thestrain gauges had different lengths among themselves), the simulation was not completed. There was noseemingly obvious reason to why the simulation was not completed, though at the time the simulationswere performed the software Abaqus was updated to version 2016 and Scania’s computing cluster wasupdated.

39

Chapter 7

Summary

Part 1

The objectives of the first part of the thesis were to:

• determine how the constraint point configuration in the Linear model influence the results.

• determine if the FE-model needs to be nonlinear or if a linear model is sufficient.

• compare fatigue life using the chosen model to fatigue life from Scania’s previous analysis model.

The constraint point configuration on the back SPC nodes did not influence the results, but moved frontSPC nodes did influence the results. Configuration 1 (all SPC nodes were unmoved) resulted in anincrease of the 1st Principal stress and the safety factors in the fatigue analysis decreased.

The worst load case was loading in the negative z -direction and it is recommended to use Nonlinear modelNo. 1, the model of the powertrain where the isolator was modeled with spring elements for loads lowerthan -3 g in the negative z -direction. Nonlinear model No. 1 can be used for loads lower than -8g in thenegative z -direction but it should be taken into consideration that loads between -5g and -8g results inhigher stresses than in reality. Nonlinear model No. 1 could be further developed by adding springs atthe location of the compression rubber and the rebound rubber in order to capture the change of reactionforce point.

If Linear model is used, SPC Configuration 1 in Table 3.3 is recommended since the stresses using thisconfiguration are higher and better corresponds to reality. Configuration 1 is better to use for comparisonof future engine bracket designs and models since it is independent of the isolator design.

Part 2

The objectives of the second part were to:

• evaluate if it is possible to perform analysis of time-dependent loads in a time effective manner.

• compare simulated and measured strain results, from the test track, in the cylinder block in orderto validate results.

It is possible to perform a time-dependent quasi-static analysis, the computation time is short, but thepost process (the fatigue analysis) would take the longest time to perform. It may be possible to onlyanalyse the highest loads and perform a smaller rainflow analysis in order to acquire equivalent loadsthat will be used in the fatigue analysis. If the time-dependent analysis is to be developed according toChapter 6, in addition, the acceptance criteria need to be further developed.

Simulated and measured strain results correlate very well and it is concluded that the model is sufficient,but it is recommended to perform more comparisons and add more strain gauges to the model in orderto further validate the results.

40

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