2006:341 CIV MASTER’S THESIS

Simulation and Validation of Tire Deformation under Certain Load Cases

HENRIK ANDERSSON

MASTER OF SCIENCE PROGRAMME Mechanical Engineering

Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Computer Aided Design

2006:341 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 06/341 - - SE Eine einfache Formel genügt nicht mehr, auch wenn sie magisch ist — Michael Gipser Abstract

This master’s thesis deals with computer aided simulations of mechanical systems in the automotive industry. The specific target of simulation is the pneumatic tire and its behaviour. The aim is to establish a method to use computer simulations for shortening the development cycle and reducing the need for testing and physical prototypes. The work has been separated into several steps, starting with a thorough information study, continuing with creative methods and concept creation. Later on, an evaluation of the concepts has been performed, to find the best approach to continue working on. The selected concepts from the evaluation were further developed to result in the final simulation method. The results of the simulations have then been validated against measurements. A proposal for further work in the subject has been made, as well as ideas for other projects.

Keywords

Tire simulation, Vehicle simulation, Product development process.

i Preface

The work presented in this masters thesis is to obtain the Master of Science degree in Mechanical Engineering, with specialization in Computer Aided Engineering. This the- sis has been written at the BMW Group Research and Innovation Center (FIZ) in Munich Germany, during the second half of 2006. The thesis project was initiated and granted by Mr. Robert Hartl, head of the wheel design team at the Wheel and Tire department EF-33 at BMW. I wish to express my appreciation to my supervisor at BMW, Thomas Kellner for all his help and support during my time at BMW in Munich and to my examiner Tobias Larsson at Luleå University of Technology. Many thanks also goes to Erich Rott and Jens Holtschulze, as well as all the other colleagues at the BMW Research and Innovation Center for their help during my thesis. Finally, I would like to thank my family and friends for their support during the entire thesis work.

Munich, November 30th, 2006

—————————————- Henrik Andersson

ii Contents

Contents

List of Figures vi

List of Abbreviations viii

List of Symbols ix

1. Introduction 1 1.1. Tire clearance ...... 1 1.1.1. Purpose ...... 2 1.1.2. Schematic overview ...... 3 1.2. Observations ...... 11 1.3. Problem formulation ...... 11

2. Theory 12 2.1. Product design & Development processes ...... 12 2.1.1. Introduction to product development ...... 12 2.1.2. Design space exploration phase ...... 13 2.1.3. Roadmap phase ...... 13 2.1.4. Concept Design & Prototyping ...... 14 2.1.5. Detail design & Manufacturing ...... 16 2.2. Simulation in Engineering ...... 16 2.2.1. The simulation process ...... 16 2.2.2. Simulation in Automotive Engineering ...... 17 2.3. Product Lifecycle Management ...... 17 2.3.1. Computer Aided Design ...... 18 2.3.2. Computer Aided Engineering ...... 19 2.4. Theory of ground vehicles ...... 23 2.4.1. Vehicle dynamics ...... 24 2.4.2. Tires ...... 28 2.5. Programming languages ...... 49 2.5.1. MATLAB ...... 49 2.5.2. Python ...... 49 2.5.3. C/C++ ...... 49 2.5.4. FORTRAN ...... 49

3. Method 50 3.1. Design space exploration ...... 50 3.1.1. Benchmarking ...... 50 3.1.2. Related technologies ...... 52 3.2. Roadmap ...... 54 3.2.1. Mission statement ...... 54

iii Contents

3.2.2. Product characteristics ...... 54 3.2.3. Thesis delimitation ...... 55 3.3. Concept design ...... 55 3.3.1. Brainstorming ...... 55 3.3.2. Concepts ...... 56 3.3.3. Evaluation of concepts ...... 58 3.4. Detailed design ...... 60 3.4.1. Concept refinement ...... 60 3.4.2. Input data for simulations ...... 62 3.4.3. Output from simulation models ...... 63 3.4.4. Initial model verification and validation ...... 64 3.4.5. Final testing and validation ...... 66

4. Results 69 4.1. Measurements ...... 69 4.2. Concepts ...... 70 4.2.1. FTire concept ...... 70 4.2.2. RMOD-K 7 concept ...... 71 4.2.3. Mathematical/Empirical Concept ...... 71

5. Discussion and conclusion 72 5.1. General conclusions ...... 72 5.1.1. Simulations ...... 73 5.1.2. Physical/MBS tire models ...... 73 5.1.3. Finite element models ...... 74 5.2. Concept results ...... 75 5.2.1. FTire concept ...... 75 5.2.2. RMOD-K 7 concept ...... 76 5.2.3. Mathematical/Empirical concept ...... 77 5.3. Sources of errors ...... 78 5.3.1. Tire simulation models ...... 78 5.3.2. Tire parameterization ...... 78 5.3.3. Pressure variations ...... 79 5.3.4. Contour and deformation measurement ...... 79 5.4. Future work ...... 80 5.4.1. Validation of the tire models and parametrized data ...... 80 5.4.2. Additional test rig measurements ...... 80 5.4.3. Improvement of simulation models ...... 81 5.4.4. MBS full vehicle simulations ...... 81 5.4.5. Universal Tire model ...... 82

6. Summary 83

A. Appendix: Results 84 A.1. Measurement data ...... 85 A.2. Measured tire contour ...... 94 A.3. Tire contour validation ...... 96 A.4. Comparison of deformations ...... 98 A.5. Modification of the RMOD-K model ...... 109

iv Contents

References 113

Index 120

v List of Figures

List of Figures

1.1. Volumetric decomposition of a BMW 3 SERIES Sedan (E90) ...... 3 1.2. Overview of the tire clearance process ...... 4 1.3. ETRTO Standards for generating the static envelope contour ...... 5 1.4. Measurement of deformation on test vehicle ...... 6 1.5. Post-processing in Catia of the measured tire deformation ...... 6 1.6. Sectors for measuring tire deformation ...... 7 1.7. Different types of RHK geometries ...... 7 1.8. Example of SRHK, combination of RHK for different tire dimensions . . . 8 1.9. RGB for front and rear wheels ...... 9 1.10. Foam mounted on inside of wheel well ...... 9 1.11. Definition of tire deformation ...... 10

2.1. Schematic description of a simulation process ...... 17 2.2. Illustration of the axle loads ...... 25 2.3. Theory of cornering ...... 27 2.4. Design of a radial tire ...... 30 2.5. Illustration of the naming conventions for rims and tires ...... 31 2.6. Comparison of SAE and ISO axis systems ...... 32 2.7. Friction circle ...... 33 2.8. Tire/Road friction interaction ...... 34 2.9. Friction dependence on relative velocity ...... 35 2.10. Friction dependence on contact pressure ...... 35 2.11. Description of slip angle phenomenon ...... 36 2.12. Cambering effects ...... 38 2.13. MTS Flat-Trac CT tire test rig ...... 40 2.14. Pacejka’s Magic Formula ...... 42 2.15. Discretization of FTire flexible ring model ...... 44 2.16. Cross-section representation in the flexible ring model ...... 45 2.17. Structure representation in the FETire model ...... 45 2.18. Structure representation in the RMOD-K 7 Flexible belt model ...... 47

3.1. Simple tire model used in Volkswagen study ...... 51 3.2. Statistics of tire deformation ...... 56 3.3. Adams tire model ...... 57 3.4. Mechanical tire model ...... 58 3.5. FTire based tool for tire simulation ...... 61 3.6. RMOD-K tool for tire simulation ...... 61 3.7. ABAQUS FE modelling ...... 62 3.8. Measurement of forces acting on the wheels ...... 63 3.9. Measurement from the handling course at Aschheim ...... 63 3.10. Validation of vertical load ...... 64

vi List of Figures

3.11. Validation of lateral slip ...... 65 3.12. Validation of longitudinal slip ...... 66 3.13. Measurement cycle on the test rig ...... 67 3.14. Mirrored deformations ...... 68 3.15. Post-processing of results in Catia V5 ...... 68

4.1. Comparison of simulations and measurements ...... 70 4.2. Comparison between measurements and Gnadler’s approximation for- mulas ...... 71

5.1. Influence of the rim flange to the deformations at large lateral forces . . . 74 5.2. Different location of the rim node ...... 74

vii List of Abbreviations

List of Abbreviations

Notation Description 4WD Four wheel drive

ABS Antiblockier System, Anti-lock brakes ALK Auslenkkontur, Deformation contour

CAD Computer Aided Design CAE Computer Aided Engineering CATIA Computer Aided Three-dimensional Interactive Ap- plication cg Centre of gravity CTI Cosin Tire Interface

ESP Electronic stability program ETRTO European Tire and Rim Technical Organization

FEA Finite Element Analysis FIZ Forschungs- und Innovationszentrum FORTRAN Formula Translation Language FWD Front wheel drive

ISO International Organization for Standardization

MATLAB Matrix Laboratory MBS Multibody Dynamics Simulations

NVH Noise, vibrations and harshness. Related to comfort and unwanted vibrations in a vehicle

PLM Product Lifecycle Management

rc Roll centre RGB Reifengebirge, Wheel envelope RHK Reifenhüllkurve, Tire envelope RMOD-K Reifenmodell K, Tire model K RWD Rear wheel drive

SRHK Summenreifenhüllkurve, Summary tire envelope SWIFT Short Wavelength Intermediate Frequency Tire

viii List of Symbols

List of Symbols

α Slip angle [deg]

β Sector angle on tire [deg]

∆K Tire deformation (Gnadler Formula) [mm]

γ Camber angle [deg]

µ Coefficient of friction [−]

µ Population mean (Normal distribution) [−]

Ω Actual wheel rotation speed [rad/s]

Ω0 Reference rotation speed at actual velocity, vertical force, slip angle and inclina- tion angle and for longitudinal force Fx = 0 [rad/s]

σ2 Variance (Normal distribution) [−]

θ Hill gradient angle [deg]

A Rim width [mm]

Amax Maximum rim width [mm]

2 ax Longitudinal acceleration [m/s ]

2 ay Lateral acceleration [m/s ]

B Stiffness factor (Magic Formula) [−]

C Reference tread width [mm]

C Shape factor (Magic Formula) [−] cα Cornering tire stiffness [N/deg]

∗ cRp Pressure dependent stiffness in Radial direction [N/mm/bar]

∗ cRv Speed dependent stiffness in Radial direction [N/mm/m/s] cR Vertical tire stiffness (Radial stiffness) [N/mm] cSidewall Sidewall stiffness coefficient [N/mm]

ix List of Symbols

cy Lateral tire stiffness [N/mm]

D Peak value (Magic Formula) [−]

DA Aerodynamic drag [N]

DG Maximum tire overall diameter in service [mm] dr Nominal rim diameter [mm]

E Curvature factor (Magic Formula) [−]

E Young’s modulus of elasticity [N/mm2]

ET Einpresstiefe, wheel inset distance [mm]

fRL Tire load factor, relative to tire load index [−]

Fs Side force [N]

FX Longitudinal force [N]

FY Lateral force [N]

FZ Normal (vertical) force [N]

G Shear modulus [mm] h Center of gravity height [mm] ha Aerodynamic force arbitrary height [mm]

L Length [m]

MX Overturning moment [Nm]

MY Rolling resistance moment [Nm]

MZ Self aligning moment [Nm]

OD Tire outer diameter [mm]

Pi Tire inflation pressure [bar]

R Tire undeflected radius [mm] r Radial distance from wheel center to point on sidewall (Gnadler Formula) [mm]

RI Tire inner radius (Gnadler Formula) [mm]

RX Tire rolling resistance [N]

Sh Horizontal shift (Magic Formula) [−]

x List of Symbols

Sv Vertical shift (Magic Formula) [−]

SG Maximum tire overall width in service on intended rim width Amax [mm]

SR Slip ratio [%] tp Pneumatic trail [mm]

W Tire width [mm]

W Vehicle load (total) [N]

Wf Vehicle load on front wheel pair [N]

Wr Vehicle load on rear wheel pair [N] xm Peak location (Magic Formula) [−] ya Horizontal asymptote (Magic Formula) [−]

xi 1. Introduction

1. Introduction

The recent centuries of product development in the industry have seen a lot of revolu- tionizing changes. Not long ago product development and manufacturing were made by the local blacksmith or other skilled craftsmen. The lifecycle for a product was usu- ally very long and new products could take many years to develop.

Since the beginning of the industrialization and onwards, the globalization has affected how business is done and has led to increased competition between companies on a global market.

Nowadays, the time between idea and final product can be just a few months; this ap- plies especially to the computer and electronics industry where new products appear within months and older products become obsolete in the same short time.

For the vehicle industry the tough competition and demands on high profitability have led to big changes in recent years. Manufacturers merge and cooperate on the develop- ment of new vehicles to reduce the costs and to save time.

These big changes have led to the demands of shorter, more economic development cycles. To be able to achieve this, the companies wish to move the expensive and time- consuming prototyping to a very late step in the development process. By using com- puter aided tools for virtual product development these demands can be fulfilled.

The introduction of virtual product development started in the 60s with the introduction of computer based tools and has since then gained further momentum due to the ever increasing capacity of computers.

1.1. Tire clearance

In the early steps of a vehicle development process, the specifications for chassis, sus- pension, drive train and other important system components are set.

At the tire development department the complete range of approved rims and tires is determined in close cooperation with the tire manufacturers and other internal depart- ments involved in vehicle development.

1 1. Introduction

To ensure fitment and clearance of all these wheel and tire combinations in the wheel housings of the vehicle, tire clearance investigations are performed.

In a simple static analysis, where all components are assumed to be infinitely stiff and to not deform, the clearance between different components is easily verified in the CAD system.

The case, however, is not this simple. During driving, i.e. dynamic conditions the com- ponents do not behave in the same way as for a simple static case. An example of this is the deformation of the tire structure due to the external forces generated by the in- teraction between tire and road. To ensure that the clearance can be guaranteed for all conditions, the deformation of the tire also has to be taken into consideration.

The first step in the clearance process is to create a so called wheel envelope for all possible tire and rim combinations. It contains information on rim size and positioning, tire dimension, worst case of tire deformation and also the snow chain geometry. These different geometries are superpositioned so that they represent the space required for the wheels in the suspension movement.

During the course of the development process, the wheel envelope is used for clearance investigations in different departments, including packaging, suspension, styling, etc. If there is a problem with the wheel envelope and this is discovered in a later step, during prototype testing, it will be very costly to go back in the development process and correct it.

1.1.1. Purpose

The packaging of components in cars today is becoming more and more complex. With increasing safety requirements, demands on weight distribution, more system compo- nents in the engine bay and also to give room for passengers and luggage, optimizing the use of space has a high priority.

When looking deeper into how much space each different subsystem on a car takes, calculations show that the passenger compartment allocates about 4.1m3, a little more than half the total volume of the car. Both wheel housings in the front require more space, (0.8m3) than the two rear wheel housings (0.5m3) due to the steering of the wheels in the front.

The four wheel housings account for about 17% of the total vehicle volume and much of this space is only used during large suspension and steering movements. It is therefore desired to use this space as efficiently as possible.

2 1. Introduction

Vehicle: 1.6m3 4.1m3 2.1m3 Wheels: 0.8m3 0.5m3 50% 25%

Figure 1.1.: Volumetric decomposition of a BMW 3 SERIES Sedan (E90)

Also for styling purposes, there is a strong need for more accurate knowledge of the tire clearance, so that the designers can have as much freedom as possible to design the wheel arches and the body panels around the wheels.

The local deformation of the tire is one of the components in the clearance process that can be further analysed, to improve the tire clearance process.

1.1.2. Schematic overview

The beginning of the development process for a new vehicle with respect to tire clear- ance starts with the concept design of possible tire and rim combinations for series and aftermarket equipment. As soon as the evaluation and selection of the different tire and rim concepts have been done, the creation of wheel envelopes for the upcoming vehicle can begin.

The first step is the creation of the "base tire profile" (RFNP: 1.1.2) and the "new tire limit profile" (NRGK: 1.1.2) for the range of approved tire and rim combinations.

The next step is to take into consideration the use of snow chains and the worst case of tire deformation (ALK: 1.1.2) to create the tire envelope (RHK: 1.1.2).

Combining the surfaces for all the approved tire and rim combinations results in the so called summary tire envelope (SRHK: 1.1.2). A SRHK is composed of several RHK’s.

With the suspension geometry as basis for the kinematics, the SHRK is then superposi- tioned at all the possible positions in the suspension movement, to finally create the end result in the tire clearance process, the wheel envelope (RGB: 1.1.2).

3 1. Introduction

TyreClear Process overview Elast. Driving maneuvers Driving maneuvers Displacements CAD Axle (max. lat force) (Compl. tyre Clearance ) kinematics Calculations Control data F(x) ......

Snow chain TyreClear-Module geometry Administration / Tyre Industry Summary Settings Tire Tire deformation envelope • User-Admin (ALK) (SRHK) • RDM-Admin Tire New • PRISMA/RDM- cross Wheel Use tire Login section Tire limit Wheel • History profile profile envelope envelope • RDM- (RHK) (RFNP) (NRGK) (RGB) • Read Reconnect

Oracle-DB for Tire-Data-Management / Guideline-Management (RDM)

P R I S M A (PDM)

Figure 1.2.: Overview of the tire clearance process

RFNP1 - Base tire profile

The base tire profile (RFNP) is the foundation of the tire clearance process. A problem with tires is that a specific tire dimension is not always exactly the same size depending on manufacturer and when the tire was produced.

To take this into consideration, the tire profile is created based on ETRTO2 standards [1]. These state exactly how to create the tire contour for any tire dimension, based on a design and maximum in service measurement of the base diameter and width for the tire (figure 1.3).

NRGK3 - New tire limit profile

From experience it is known that the tire manufacturers rarely use the maximum al- lowed diameter and width for their tires, for economical and other reasons they try to stay below this limit.

By starting out from the ETRTO standards used to create the RFNP and then reducing the overall contour by a few millimetres, a better corresponding tire geometry is created, the NRGK.

1Reifenprofil - Base tire profile 2European Tire and Rim Technical Organisation 3Neureifengrenzkontur - New tire limit profile

4 1. Introduction

SG

T

Rt Re C

Rf

S S

Rbf G

D P P min G r d A B max max

Figure 1.3.: ETRTO Standards for generating the static envelope contour

ALK4 - Deformed tire contour

The deformed tire contour, ALK is one of the most important parts in the tire clearance process. It contains information on how the tire deforms during driving, as this has a big effect on the required clearance.

The first step to create the ALK, is to drive a test vehicle on a track under varying con- ditions and expose the tire to the maximum lateral forces that can occur. The driving style is more extreme than during normal conditions, but still not misuse. The resulting vertical and lateral forces lead to a deformation of the tire sidewall.

The deformation is measured with a foam plate mounted to the spring strut (figure 1.4). The foam is positioned to sit firmly against the inner sidewall of the tire.

During driving, abrasion of material from the foam occurs, leaving an imprint of the tire deformation behind. The foam plate is then removed from the vehicle and measured with a laser scanner to create a geometry for import in the CAD-system (figure 1.5a).

In the final step of creating the ALK, the contours of the deformations in the foam are extracted from twelve sectors around the tire circumference, according to figure 1.6. These extracted curves constitute the ALK (figure 1.5b).

4Auslenkkontur - German for deformed tire contour

5 1. Introduction

(a) Foam plate mounted on front suspension (b) Front suspension and tire with foam plate upright mounted

Figure 1.4.: Measurement of deformation on test vehicle

(a) Scanned foam plate imported into Catia V5 (b) Extracted deformation curves from foam plate

Figure 1.5.: Post-processing in Catia of the measured tire deformation

RHK5 - Tire envelope

The tire envelope, RHK contains information about tire deformation from the ALK and also snow chain geometry. It is created by sweeping a surface around the tire circumfer- ence using the curves from the ALK.

As tire deformation with respect to clearance is only seen as critical on the inside of the tire, the resulting RHK only contains information about the deformation on the inside (figure 1.7a).

The deformations for a new tire dimension can also be approximated, by using the ALK from one tire dimension to create the corresponding RHK for another dimension. For example; the deformation for a 195/65 R15 tire can be approximated from a 185/65 R15 tire.

5Reifenhüllkurve - German for tire envelope

6 1. Introduction

Direction of travel v0 0/360°

Circumference angle β 45° 315°

Direction of rotation

ω 90° 270°

105° 255°

120° 240°

135° 225°

180°

Figure 1.6.: Sectors for measuring tire deformation

(a) RHK with tire deformation (b) RHK with tire deformation and snow chain geometry

Figure 1.7.: Different types of RHK geometries

SRHK6 - Summary tire envelope

The summary tire envelope, SRHK is created by combining all tire envelopes (RHK) for the range of allowed tire and rim combinations.

6Summenreifenhüllkurven - Summary tire envelope

7 1. Introduction

Figure 1.8.: Example of SRHK, combination of RHK for different tire dimensions

RGB7 - Wheel envelope

The creation of the wheel envelope or the "tire mountain"8, RGB is a two step process where several parameters such as kinematics, elastokinematics, steering of the wheels, etc. are taken into consideration.

In the first step certain vehicle parameters are determined. This takes the following vehicle data into account, such as: drive train (4WD, RWD, FWD), suspension type (Independent, Solid axle), wheel travel and driving conditions (Off-road, etc.).

Based on these parameters, control data is retrieved from a database, which contains all the possible positions of the wheel in the suspension. The second step is then to super- position the SHRK geometry at these positions. The end result is the wheel envelope (RGB), illustrated in figure 1.9.

TyreClear Application

As an aid in the creation of the different geometries used in the tire clearance process, a special software called TyreClear is used by BMW. The application takes care of the creation of all curves and surfaces that make up the different geometries (RFNP, NRGK, ALK, RHK, SHRK and RGB) and the positioning of these in the the suspension travel.

7Reifengebirge - Wheel envelope 8The expression "tire mountain" - Reifengebirge originates from the appearance of the tire geometries looking from above, resembling the altitude-curves of a map.

8 1. Introduction

(a) Front wheel RGB (b) Rear wheel RGB

Figure 1.9.: RGB for front and rear wheels

Validation of tire clearance

The verification of the simulated tire clearance is performed on a prototype of the pro- duction vehicle, this time with pieces of foam attached to the inside of the wheel housing liner (figure 1.10).

Figure 1.10.: Foam mounted on inside of wheel well

In the same way as with the foam plate mounted to the inside of the wheel, material will be worn off from the foam during driving. By scanning the surfaces of the foam and comparing this with the computer analysis, the simulated clearance can be validated.

9 1. Introduction

Definition of tire deformation

The tire deformation is defined as the difference between the undeformed inflated tire profile and the deformed tire contour (figure 1.11). The outermost point on the unde- formed tire profile is used as the reference and a vertical line is created at this point. The tire deformation (∆K) is then the perpendicular distance from the maximum outer point on the deformed tire profile to the reference line. A positive deformation equals a deflection outwards with respect to the tire centre line.

Undeformed sidewall reference line

Deformed tire profile

Undeformed tire profile (inflated)

Tire deformation ∆K

Tire centre line

Figure 1.11.: Definition of tire deformation

10 1. Introduction

1.2. Observations

The following important observations of the current method for measuring the tire de- formation have been made:

• The foam measurements performed on the test vehicle only gives detailed infor- mation about the deformation of the tire sidewall; the tread area cannot be mea- sured using this method. The deformation of the this area has to be extrapolated from the deformation of the sidewall to form the complete tire contour. From ex- perience and theory it is known that the tire not only deforms in lateral direction, but also in radial direction.

• Deformation measurements on a test vehicle cannot be performed for each and every approved tire/rim combination; it would mean too much work. Also, when measuring a specific dimension, tires from different manufacturers have to be tested, to be certain that the most compliant tire is used as the reference.

• There are certain cases, when a completely new tire dimension, that does not yet exist on the market, is developed for a new vehicle. For these unknown dimen- sions, the deformation has to be approximated from another tire.

• Efficient use of resources during the development cycle is important and measure- ments with test vehicles take a lot of time. To be able to perform these tests, a prototype of the car model in question has to exist. Waiting for this prototype is not always possible, so either another car or the measurements from another tire are used to approximate the deformations.

1.3. Problem formulation

The main objective for this thesis is to research and develop a method to simulate the behaviour of the tire and determine the deformation of the tire under different condi- tions. The aim is to replace the current method, which requires full vehicle testing and measurements, with simulations.

Different tools and approaches are to be investigated, to result in a final method for simulation of the tire deformations.

11 2. Theory

2. Theory

This chapter brings the reader deeper into the theory of product development, simula- tion in the automotive industry, vehicle dynamics and the pneumatic tire. It can be seen as a kind of reference manual for the work performed in this thesis.

2.1. Product design & Development processes

Much of the information in this section has been found in the works by Ulrich & Ep- pinger [2] and Pugh [3].

2.1.1. Introduction to product development

What is a product? According to ISO1 and the ISO9000 standards [4] the definition is:

A product is an output that results from a process. Products can be tangible or intangible, a thing or an idea, hardware or software, information or knowledge, a process or procedure, a service or function, or a concept or creation.

A process uses resources to transform inputs into outputs. In every case, inputs are turned into outputs because some kind of work, activity, or function is carried out. Processes can be administrative, industrial, agricultural, governmental, chemi- cal, mechanical, electrical, and so on.

Ulrich & Eppinger [2] sums up all this to describe what product development really is about.

The set of activities beginning with the perception of a market opportunity and ending in the production, sale and delivery of a product

1International Organization for Standardization

12 2. Theory

The different phases in the development of a product are compiled in a "Product devel- opment process", which can be somewhat different depending on which kind of com- pany and what kind of product it concerns. In general, however, most product develop- ment processes are quite similar.

As described by the Participatory Innovation Process [5] used at Luleå University of Technology, the different steps or phases in product development can be described as:

• Design space exploration - Need finding, benchmarking and related technology

• Roadmap - Mission statement, product characteristics

• Concept Design & Prototyping - Concept generation, evaluation and selection.

• Detailed Design & Manufacturing - Virtual and physical prototypes

• Product launch

Using a well defined process ensures that lead times are kept short, development costs are reduced and a high quality of the end product is achieved.

2.1.2. Design space exploration phase

In the beginning of a product development process, it is usual that not much information is known about the product to be created. In the case of a completely new product, everything starts from scratch.

To determine what kind of product to create, a need finding analysis can be applied to research for market opportunity and customer needs. When an opportunity and needs have been found, existing products that fulfil these are benchmarked to see if there is any interesting information that can be of use.

Another step is to research related technologies for other interesting ideas that could be applied to the new product.

This results in the information describing market needs and the potential for creating a new product.

2.1.3. Roadmap phase

When the needs are clearly defined it its time to document the product description and characteristics to have a clear understanding of exactly what kind of product to create during the upcoming design phases.

13 2. Theory

2.1.4. Concept Design & Prototyping

Using the product description, a lot of different product concepts are created, evaluated and finally a selection of the best ideas is made.

Ideas and concepts are generated with different creative methods, to come up with so- lutions to problems or creating complete concepts. Sometimes these creative methods give you a direct solution to the problem, other times you will end up with a list of ideas eventually resulting in a solution.

Creative methods

Random word

The random word method is perhaps the simplest of creative techniques. A person confronted with a problem is given a random word. The idea is that the random word could connect to the problem and make way for new ideas.

A variation of this is to use a random image or some other form of random information to associate to.

Brainstorming

Brainstorming is a creative method to generate ideas for a new product. It is most effi- cient when performed in a small group. The most important thing is not to judge any ideas in advance and let everybody present their thoughts. No ideas should be turned down this early in the process. Brainstorming is really more about quantity than having a single good idea.

Brainwriting

Brainwriting is another creative method, where in contrast to brainstorming ideas are written down on a paper, rather than being discussed openly. The participants can sit down and write down their ideas in peace and quiet, without being distracted by oth- ers.

The benefit of brainwriting is that quiet people, that have difficulties to verbally express their opinions, have the same chances, as more open people.

The first stage of a brainwriting session is to gather as many ideas as possible, without any restrictions. An evaluation of the ideas is later done in the second phase to narrow down to the best ones.

14 2. Theory

Rohrbachs method

Another form of brainwriting was developed by Rohrbach [6].

A brainwriting session with Rohrbach’s method can be described as sitting down with 6 people in a group, handing out a paper to each person. During 5 minutes, each person sketches down 3 ideas on a predefined theme. Each idea is then passed on to the 5 other people to develop the ideas further.

Advantages of this method is that it is easy to use, generates a lot of new ideas and no ideas will be criticized. Some drawbacks are that there is no real feedback on ideas and it can also inhibit creativity, due to the many restrictions.

The Rohrbach method is best suited as a compliment to a brainstorming session, for example to further develop already discovered ideas.

Concept evaluation

To determine which concepts that are most suitable, it is common to perform a concept evaluation. The evaluation is usually based on different criterion, which the concepts are compared against.

Pughs method

Pughs method [3], scores and evaluates the concepts relative to each other.

One concept is selected as a datum, for example the favourite candidate or maybe the current method that is to be improved on. The other concepts are then compared to the datum for each criterion and graded depending on if they are better (+), equal (S) or worse (-). The evaluation is performed using a simple matrix to group the data.

Pugh’s method will give an insight to the best alternatives, but not a conclusive candi- date for selection.

Quantitative method

Another form of evaluation is the quantitative method, where the concepts are scored against each other with weighted criteria.

The quantitative method is however, very sensitive to whom does the scoring and the degree of confidence in the results cannot really be justified. The danger is that you can be convinced to trust the numbers and say that a concept that has 1.32 points really is much better than the concept with 1.26 points.

15 2. Theory

2.1.5. Detail design & Manufacturing

This is the phase of the development process where the selected concept is developed into a real product. The concept is optimized for product launch and manufacturing with high quality, few problems and low cost.

Much of the work is performed with computer aided tools, to aid the design and sim- ulation processes. This ensures that many of the problems can be corrected long before the product goes out to manufacturing and market launch.

A very important step in the development process is the testing. Using virtual and real prototypes, the product can be rigorously tested to comply with the specifications. Even though this step is desired to be entirely performed with computer aided tools, real testing is still today an important part of any development process.

2.2. Simulation in Engineering

As defined by Smith [7],

Simulation is the process of designing a model of a real or imagined system and conducting experiments with that model. The purpose of simulation experiments is to understand the behaviour of the system or evaluate strategies for the operation of the system. Assumptions are made about this system and mathematical algo- rithms and relationships are derived to describe these assumptions - this constitutes a "model" that can reveal how the system works. If the system is simple, the model may be represented and solved analytically.

2.2.1. The simulation process

A simulation process [7] can be described as:

• Define the problem, i.e. the system to be simulated

• Create a simple model representing of the system and collect input data for the model

• Create a computer software for the model

• Verify and validate the model, iterate back to correct errors in software & model.

• Design model experiments & perform simulations

16 2. Theory

• Collect output from the simulations, analyse the data and document the results

• Expand and adapt model for other types of simulations

Real system Analyze system and define model Simulation model

•Collect input data •Create computer model •Verify and validate

Design Experiments

Model optimizations Expand & Adapt

Documented results Evaluate and analyse results Formal results

•Graphical, tabular, animation, written evaluations

Figure 2.1.: Schematic description of a simulation process

2.2.2. Simulation in Automotive Engineering

The use of simulations in the automotive industry is very common today. Charlés [8] describes how the digital revolution started in the 1960s with CAD/CAM and since then been extended to include full simulation of the entire design, manufacturing and assembly processes of vehicles.

The benefits of using simulations will increase further in the future as more advanced models are developed, taking advantage of increased computer performance.

2.3. Product Lifecycle Management

PLM is the term used for the process to manage the complete lifecycle of a product, from concept, design, manufacturing to service and finally end disposal. The term PLM covers several other capabilities such as CAD, CAE and CAM2.

2Computer aided manufacturing

17 2. Theory

2.3.1. Computer Aided Design

CAD is a common term for the use of computer based tools for engineers, architects and designers in their design work. CAD is the tool used to create the 3D geometries within the PLM process.

Thirty years ago, most of the design drawings in the industry were created on paper, resulting in a lot of effort to change a design. Since the introduction of computers as the primary tool to create drawings, the process of designing products has changed drastically.

The first CAD systems were used to create 2D drawings. Later came the transition to 3D, which enabled creation of simple solid geometries and to combine them to form other solids. Today, the CAD technology fulfils all the demands for complete virtual product development.

CAD Software

CATIA

CATIA is a PLM/CAD/CAM/CAE software developed by Dassault Systemés [9]. CA- TIA is widely used in the engineering industry, especially in the aerospace and automo- tive sector. Many German automotive companies such as BMW, Porsche and Daimler- Chrysler use CATIA. Other big users are the aircraft manufacturers Boeing and Air- bus.

The history of CATIA [10] began in 1969 when French aircraft company Avions Mar- cel Dassault needed a software to create drawings. In 1975 they bought the software CADAM3 from Lockheed. CADAM was a 2D software which was combined with in house developed 3D software called CATI. Dassault Systèmes was then founded in 1981. Around this time a deal was made with IBM to market CATIA to other companies.

From 1982 until 1988 version 1 to 3 of CATIA was released. In 1993 came the release of version 4 (V4). The latest version of the software is version 5 (V5), introduced in 1999. V5 was a complete rework from the old V4, with availability for the Microsoft Windows platform.

3Computer-Augmented Drafting and Manufacturing

18 2. Theory

2.3.2. Computer Aided Engineering

CAE is the area within PLM that encompasses the simulation, validation and optimiza- tion of products and manufacturing tools. The use of CAE tools has drastically reduced the effort of testing and validation by using computer software for simulations. Es- pecially in the automotive industry, CAE tools have revolutionized the development process, making products cheaper but in the same time more durable and safer.

A CAE simulation process can be summarized in three steps:

• Pre-processing - creating the simulation model with geometry, loads and bound- ary conditions.

• Analysis - solving the equations behind the model

• Post-processing - analysis of the results using visualization tools

The main uses of CAE are:

• Stress analysis on components using Finite Element Analysis (FEA);

• Thermal and flow simulations with Computational Fluid Dynamics (CFD);

• Simulation of kinematics and dynamics with Multibody Simulation (MBS);

• Manufacturing process simulation such as casting, moulding, and die press form- ing.

Finite element analysis

A finite element analysis (FEA) uses the finite element method, which is a technique for solving complex engineering problems. It can be applied to a wealth of problems, including component strength, heat transfer and vibration, etc.

It is difficult to pinpoint the exact origin, due to different interpretations of what really counts as a finite element method. Oden [11] describes several different works, which all have contributed to the theory of the finite element method.

The ABAQUS documentation [12] gives a good introduction to the theory of the FE method.

19 2. Theory

Finite element theory

The finite element method can be explained as dividing a geometric body into smaller parts, in the form of elements. Each element in the model is a discrete part of the complete structure, which is composed of several elements, connected to each other by nodes. The collection of elements and nodes is referred to as the mesh.

The elements can be of different type, size and shape, and depending on the number of elements the mesh can be a better description of the real physical problem. Increasing the number of elements and nodes in the mesh also means that the computational cost increases, giving longer simulation times.

Depending on the type of problem to solve, different equations that describe the phys- ical properties of these elements are used. An example is Hooke’s law, which describe the relation between stress and strain for a material using Young’s modulus of elasticity, σ = e ∗ E.

The analysis can be performed with mainly two methods, implicit and explicit. In an implicit analysis the solver must iterate to determine the solution to a problem, where in the explicit case the solver determines the solution without iterating, by explicitly advancing the kinematical state from the previous increment.

An implicit method is more efficient for solving smooth nonlinear problems, where the explicit is the choice for a wave propagation analysis, i.e. more dynamic problems.

Hanley [13] explains the difference between these two methods, where the explicit solv- ing does not use the large stiffness matrices, therefore reducing both the number of calculations and required disk space. A drawback of the explicit solving is the need of shorter time steps, to obtain numerical stability and good accuracy.

FE Software

ABAQUS

ABAQUS is a software package for finite element analysis, which is widely used in the automotive, aerospace and industrial product industries. The package is also very popular with academic and research institutions due to the wide material modelling capabilities.

The software package consists of two analysis components: ABAQUS/Standard and ABAQUS/Explicit, for implicit and dynamic problems.

20 2. Theory

Multibody Dynamics

Multibody Dynamics (MBS) is a field of work which involves the kinematics and dy- namics of bodies connected to each other with joints. It can be used to build and sim- ulate mechanical systems and determine the system behaviour without building real prototypes.

Examples of the application for the MBS method are:

• Analysis of complex mechanical systems

• Virtual prototyping of different product concepts

• Determining static/dynamic loads and stresses on structures

• Load cases for Fatigue and FE analysis

• Design experiments to optimize certain product parameters

During the last four decades, the use of MBS in the industry has seen a big increase due to the introduction of virtual product development. The MBS tools enable to build models of complex systems in a fraction of the time it would take to create prototypes.

MBS theory

MBS describes the kinematics and dynamics of rigid bodies and has its foundation in the science of mechanics, which is the oldest and maybe the most important of the physical sciences in engineering today.

Archimedes was the first person to write down his discoveries in mechanics, in the form of the mathematics behind the lever and the principle of buoyancy. Further achieve- ments that led to progress in mechanics was the work of Stevin [14], who formulated much of the theory behind statics and how to combine forces with vector algebra.

The first documented dynamic experiments date back to Galileo (1564-1642) [15]. He performed and documented experiments with falling stones and derived the physics and mathematics behind them.

Based on Galileo’s discoveries, Newton (1643-1727) [16] continued with this work and in 1687 the first edition of the book Principia was published. In Principia, Newton formu- lated the universal laws which govern the motion for almost all bodies. These include the law of gravitation and also the so called three laws of Newton[17], which are as fol- lows :

First law

21 2. Theory

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is com- pelled to change that state by forces impressed thereon.

Second law The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Third law To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

These three laws can all be summarized into the well known equation, which states that the force is directly proportional to the acceleration,

F = ma

By using the laws of Newton together with the work of people like Lagrange and Hamil- ton [18] [19], systems of equations describing the motion for bodies in a MBS system can be formulated.

Degrees of freedom

An important conception in three dimensional modelling is degrees of freedom (DOF). As the position of a body in space is described with three coordinates, the total number of natural DOF is six, i.e. both translation and rotation in all three coordinates (x,y,z).

In a multibody system the total DOF can be calculated as follows:

Total DOF = 6 × (Number of parts − 1) − (Number of constraints)

The reason of subtracting one part from the total number of parts has to do with the non moving ground, which is counted as a part in the system.

Joint types in a MBS System

Parts in a multibody system are all connected with joints. Depending on the type of joint, it will constrain and restrict the motion, reducing the number of DOF.

Something that might happen is the subject of over-constraining or redundant con- straints, i.e. when two or more constraints describe the same motion. This occurs when the total number of DOF in the system is less than zero.

22 2. Theory

Solving of the multibody system

The formulation of the equations of motion for the parts in a multibody system often lead to a matrix with the larger part of the elements being zero. Such a matrix is referred to as a sparse matrix. Solving such a matrix is relatively fast, making it possible to analyse complex mechanical systems in relatively short time. Compared to solving finite element or fluid dynamics problems the time for solving a MBS system is much faster.

Depending on if the problem is linear or not, the solver uses different techniques to compute the results. The Newton-Raphson [20] technique is one method that can be used for solving.

MBS Software

The history of computer simulations with MBS started with text based or simple graph- ical methods, based on the kinematics of the components. One of the first applications was KAM [21] developed by Cooper et al., which could solve simple mechanical sys- tems and determine displacements, velocity and acceleration of the components. COM- MEND [22], was another software for solving planar systems.

The Adams package by MSC.Software [23] is possibly the most used MBS software to- day. The origin of Adams can be traced back as far as 1963, to the work initiated by Chace [24] [25] [26] [27] at the University of Michigan.

Adams/Car is a part of the Adams software package. This software enables the use of advanced simulations for predicting and verifying vehicle dynamics and performance. It is used by many vehicle manufacturers as well as their subcontractors.

Adams/Car is also available in a special version, known as Adams/Car-AT [28]. It is the result of a cooperation between MSC.Software and BMW.

2.4. Theory of ground vehicles

The works from Gillespie [29] and Milliken et al. [30] have been used as reference for the theory of ground vehicles.

23 2. Theory

2.4.1. Vehicle dynamics

The mechanics behind ground vehicles can be described using Newton’s laws. A vehi- cle, independent of configuration can be treated as a body moving in space, affected by forces and accelerations. The big difficulties come when you add aerodynamics and tire mechanics to the model.

History of road vehicles

The first motorized vehicles appeared in the end of the 18:th century, invented by people like Cugnot [31], Watt and Trevithick [32]. These vehicles were powered by steam and rather slow. In 1886, the first gasoline powered automobiles were created by Daimler and Benz [33]. Further developments to vehicle technology, including the introduction of the Model T and the moving assembly line, were made by Ford [34] in the beginning of the 20th century.

Due to the advancements in automotive engineering, the speed capability of vehicles soon exceeded what the roads of the time could handle. As a result of these higher speeds, the dynamics of vehicles became more important. Much of the understanding was however hindered by the lack of knowledge in tire mechanics. Then, in 1931, the first equipment to analyse tire behaviour was created [35]. This became the starting point for more research in the area, which led to much of the understanding of vehicle dynamics as we know it today.

Basic theory

To understand tire behaviour it is also important to have a basic knowledge in vehicle dynamics. By studying the forces that the vehicle applies to the tires, the behaviour of the tire can be determined.

Force equilibrium

Using the reasoning of Gillespie [29], a free body diagram for the forces acting on the vehicle can be drawn (figure 2.2).

The loads on the front and rear wheels during acceleration on an inclined road are de- scribed by equation 2.1:

24 2. Theory

D A

ma x W sinθ ha W cos θ W h R xr F W xr f b R c xr Z Fxr L θ W X r

Figure 2.2.: Illustration of the axle loads

Wf = (W · c · cos(θ) − max · h − DA · ha − W · h · sin(θ))/L (2.1) Wr = (W · b · cos(θ) + max · h + DA · ha + W · h · sin(θ))/L

To calculate the static load distribution on level ground, set DA, θ and ax to zero.

The acceleration capability of a vehicle, with a combined tractive force FX on the wheels is described by:

W ma = a = F − R − D − W · sin(θ) (2.2) x g x x x A

Roll centre

The roll centre, rc (figure 2.3), is defined as a virtual point in the suspension geometry which the chassis rotates (rolls) around under influence from lateral forces. The lateral force acts through the centre of gravity (cg) and results in roll moment through the lever between rc and cg. The location of the roll centre depends on the type of suspension.

Roll centre can be defined for both the front and the rear suspension, drawing a line between these points give a roll axis, which the complete car wants to roll around.

Steady state cornering

To enable a vehicle to drive through a corner, the driver has to turn the steering wheel and follow the curvature of the road. The forces that are generated have to be reacted by the tires.

25 2. Theory

Known from basic mechanics [36], the centripetal force is the force required to make a body move in a circular path. This can be any physical force (gravity, electromagnetic, friction, etc.). For ground vehicles this force is generated by the friction between the road and the tires.

The centripetal force, which depends on vehicle mass, speed and cornering radius is defined as:

mv2 F = − (2.3) c r

A fictitious force4 related to the centripetal force is the centrifugal force, which can be observed as the force pushing a passenger in a vehicle outwards in a corner. The cen- trifugal force is equal in magnitude and opposite in direction to the centripetal force.

Following this reasoning, the centrifugal acceleration (lateral acceleration) in the vehicle y-direction can be defined as:

v2 a = (2.4) y r

Due to the lateral acceleration in a corner, the vehicle will be affected by a force acting on the centre of gravity. As the centre of gravity usually lies higher than the ground plane, this will lead to a moment around the point defined as the roll centre.

Consider the following simple example with a BMW 325i 3 Series (E90) from 2006. The vehicle is assumed to have the following specifications, vehicle weight mtotal 1500 kg , cg location hcg 500 mm from the ground plane, track width t 1500 mm, weight distribution 50/50 front/rear. The roll centre location (rc) is assumed to be in the road plane.

To simplify the problem, only the loads on the rear axle are studied. With the given weight distribution (50:50), this gives us half the total vehicle weight on the rear wheels, m=750kg. Each wheel will then have a load of 3679 N. Studying the lateral load transfer for the forces in y and z directions, as well as for the moment around the rc, gives us the equations for the wheel loads:

mg may · hcg FZ1 = + 2 t (2.5) mg may · hcg F = − Z2 2 t

4Physics literature does not consider the centrifugal force as a real force

26 2. Theory

Z

cg may Y

hcg

Fy1 mg Fy2 rc t F z1 Fz2

Figure 2.3.: Theory of cornering

With the given vehicle data, equation 2.5 gives FZ1 =4905 N and FZ2 =2453 N at a lateral acceleration of 1g. Compared to the static weight distribution this gives a 33% increase of the load on the outer wheel.

Vehicle simulation with MBS

Simulation of vehicle dynamics often requires solving multiple equations to get a re- sult. Simple static cases can be calculated by hand, but for more complex situations, a computer simplifies the simulation process drastically. The main types of tools for performing these simulations, according to Crolla [37] are:

1. Purpose designed simulation tools (MSC.Adams/Car)

2. Multibody simulation tools that are numerically based

3. Multibody simulations tools that are symbolic

4. General mathematic software tools (MATLAB)

Many of these tools, such as MSC.Adams/Car [23] [28] use predefined templates of the vehicle subsystems, such as suspension, steering, engine and transmission to create a full vehicle simulation model.

27 2. Theory

2.4.2. Tires

Tire history

The wheel, maybe one of the greatest inventions in the history of man kind, was in- vented around 3500 BC [38]. The first models were simple and often made of a solid piece of wood or stone. Later developments were the spoked wheel and reinforced wheels with a steel ring around it for improved abrasion.

The invention of the modern wheel, consisting of a metal rim and a rubber tire, is rela- tively new. Early types of rubber were difficult to find a useful application for, as they did not retain shape and behaved very different depending on the environment temper- ature. It was not until Goodyear invented the vulcanization process in 1839 [39] that the widespread use and development of the modern tire really took of.

The vulcanization process transforms the sticky raw rubber together with addition of sulphur and other materials to a firm bendable material, perfect to make tires from.

For Goodyear, things did not work out very well, despite this great invention. He died bankrupt at the age of 60. It was not until 1898 when the Seiberling brothers from Ger- many decided to name their company Goodyear [39] that he got some credit for his invention.

This new rubber technology was directly put to use in form of solid rubber tires [40]. These were strong, absorbed shocks and could resist all forms of cuts and abrasions. The disadvantage was that the tires were very heavy and did not give a smooth ride.

Thomson [41] was the original inventor of the air filled tire in 1845, which was a big improvement of the solid rubber tire. Unfortunately his invention came too early and never really took off.

In 1888 Dunlop [42] also claimed to have invented the pneumatic air filled tire. At that time bicycles had started to become popular and the new tire gave a substantially im- proved ride, which gave the new invention good success.

Tire theory

From the beginning of the formulation of the mechanics and mathematics behind vehicle dynamics, the understanding of the tire has been very important.

Except for aerodynamic and gravitational forces, all the primary control and disturbance forces which affect the vehicle are generated in the contact patch of the tire. These forces

28 2. Theory act on an area not much larger than the palm of a hand. A good understanding of the behaviour of the tire is essential to determine the dynamics of the total vehicle.

The main functions of the tire as described by Pacejka[43] are:

• Support the vertical load of the vehicle, while also providing shock absorption.

• Develop longitudinal forces for acceleration and braking.

• Develop lateral forces to enable cornering.

Tire design and construction

Basically, the tire is a simple visco-elastic toroid 5. The structure of the tire, consists of a composite of several materials including different rubber compounds, steel and textile fibres, inflated with air. This gives the tire a very complex non-linear behaviour.

Most modern tires are composed of a flexible carcass of high tensile strength cords fas- tened to steel cable beads that attach the tire to the rim. The carcass is made from a rubberized fabric reinforced by cords of nylon, rayon, polyester or fibreglass. The inter- nal inflation pressure loads the structure and causes every external force deforming the tire to be reacted with a tire reaction force.

There are two main types of tire designs available, radial and bias-ply tires. The first tires used the bias-ply design and they were popular in the early years of the modern tire. The radial tire was invented by Michelin [44] in 1946 and soon became popular in Europe. Around 1960 the benefits of the radial tire was discovered in the USA and has since then gradually become the standard tire for use in passenger cars in all parts of the world.

Radial tire

The radial tire is characterized by parallel plies 6 (the carcass) running at a 90 degree angle to the circumference. This type of design makes the tire sidewall very flexible and gives a soft ride. To provide directional stability, a belt made from fabric or steel wire is placed between the tread and the carcass. Normal orientation of the belt is around ±20 degrees from the tread.

5doughnut-shaped circular object 6layers of reinforcement in tire structure

29 2. Theory

Tread blocks Rib Sipes Cap plies Tire shoulder 2nd Steel belt

Tread side profile 1st Steel belt

2nd Carcass layer (plies)

1st Carcass layer (plies)

Tread groove

Tread- base Sidewall

Rubber liner Bead reinforcement

Bead filler Bead Rim protector

Bead wire

Rim flange profile

Figure 2.4.: Design of a radial tire

Bias-ply tire

In a bias-ply tire design the carcass consists of plies running in alternating angles from the rim bead. The angle of the plies is around 35-40 degrees. Higher angles result in a soft ride, as for a radial tire. To give directional stability, smaller ply angles are used.

Benefits of the radial tire

The differences in tire design give the models both advantages and disadvantages [45] [46]. For passenger cars, the benefits of the radial tire clearly outperforms its drawbacks, hence the radial tire has become the standard. For other applications where it is impor- tant to have good sidewall cut resistance, the bias ply tire can be a better choice.

Tire and rim designation

Tires can be denoted in many different ways, passenger car tires usually follow the met- ric designation, for example 225/45 R17 denotes a tire with 225 mm overall section width, 45% aspect ratio, R for radial tire and 17 for the rim diameter in inches. The aspect ratio describes the side profile height in percent of the overall section width. This information is printed on the tire sidewall.

The ETRTO standards [1] describes the naming conventions for tires and rims..

30 2. Theory

Radial Bias Vehicle Steadiness - + Cut Resistance - Tread + - Cut Resistance - Sidewall - + Reparability - + Self Cleaning - + Traction + - Heat Resistance + - Wear Resistance + - Floatation + - Fuel Economy + -

Table 2.1.: Benefits of radial and bias tires

SG C

B A G D Bead seat Rim flange G Hmin D

Figure 2.5.: Illustration of the naming conventions for rims and tires

Rims are named after width and diameter. An example is a 8Jx18 ET32 rim, which stands for 8 inch wide, J profile, 18 inch nominal diameter and inset (ET) 32 mm. Recommen- dations for suitable rim and tire combinations can be found in the ETRTO Manual [1].

Tire terminology and tire axis systems

There are several very important variables (forces, moments and angles ) that are used to describe tire behaviour. To have a common description of these variables, SAE has created the tire axis system [47], which describes the forces, moments and angles in a predefined coordinate system.

There is also the ISO-tire system, which describes the same physical parameters, but with a different orientation.

31 2. Theory

MZ γ γ

MY ω ω

MX MX MY

FY MZ

FX FX FY α α FZ FZ

(a) SAE tire axis system (b) ISO tire axis system

Figure 2.6.: Comparison of SAE and ISO axis systems

The systems describe forces in all three directions, Fx the longitudinal force (braking, traction), Fy lateral force and Fz the vertical load (Normal force). Important moments are: Mz aligning moment, Mx overturning moment and My traction/brake/rolling re- sistance. The two angles in the tire axis system are camber γ and slip angle α.

The tire footprint and generation of grip

The generation of grip in the footprint, the area of the tread in contact with the road, is one of the most important aspects in tire mechanics. Without grip, there cannot be any transfer of force from the car to the road.

Friction

From the basic mechanics [48], it is known that the friction between solids is dependent on the properties of both contacting surfaces. In general, the frictional force is said to be proportional to the vertical load, but independent of the contact area between the two surfaces. It is also known that the static friction (stiction) is higher than the kinetic (sliding) coefficient of friction.

For tires, the laws of friction can be somewhat limited under certain conditions, as the coefficient of friction for tires depends both on the relative velocity and the ground pres- sure.

When the tire is rolling straight ahead with zero lateral force, the maximum longitudinal force (traction) is limited only by the coefficient of friction times the vertical tire load

Fmax = Fx = µN.

Under combined driving and steering, both longitudinal and lateral forces are generated in the contact patch of the tire. In this case, the total amount of grip (total force) will be

32 2. Theory

q 2 2 the resultant of these forces, according to: Fmax = (Fx) + (Fy) = µN. The maximum grip Fmax is still the same as for the straight ahead case, therefore reducing the grip during combined braking and steering.

This phenomenon can be illustrated with a so called friction circle, where the outer ring can be used to represent the maximum acceleration (g) the tires can sustain. In some cases the circle can also be illustrated with an ellipse, when the tire can take higher forces in lateral direction. The horizontal axis corresponds to steering and the vertical axis is acceleration/braking.

In the simple example illustrated in figure 2.7, combined driving and steering in a corner limits the longitudinal force (braking) to 0.87g at a lateral force of 0.5g. If there is only steering, the lateral force can be higher, up to 1g.

Acceleration

0.87g

Low μ

Left Right 0.5g

High μ

Braking

Figure 2.7.: Friction circle

Mechanisms

Gillespie[29] describes two main mechanisms responsible for generating friction be- tween the tire and the road surface. First there is the molecular adhesion mechanism, which creates molecular bonds between the rubber and the texture of the road surface. This component is predominant on dry roads and is heavily reduced if the road surface is covered with water, resulting in less grip on wet roads.

33 2. Theory

The other mechanism is mechanical stiction7 in form of hysteresis, where energy is lost when the rubber deforms. Hysteresis can be explained as a sort of memory effect in the rubber, where the material does not return to its original state directly after relaxation.

RUBBER V

Aggregate Binder

Hysteresis Adhesion

Figure 2.8.: Tire/Road friction interaction

Sliding friction

Studies by Kummer [49] shows that the coefficient of friction is dependent on a relative sliding velocity between tire and road. Figure 2.9 shows the characteristic curve for this phenomenon.

The conclusion of this is that the generation of grip requires a relative velocity (slip) between the road and the tire. When the sliding velocity becomes to high, the friction decreases.

Tire load sensitivity

According to experiments by Mäckle and Schirle [50], the coefficient of friction is also dependent on the ground pressure between the road and the tire. This is not related to the inflation pressure of the tire. This phenomenon, where the coefficient of friction varies depending with the tire load is called tire load sensitivity.

7Static friction

34 2. Theory

2

1.5 ] - [ µ 1 Friction

0.5

0 0.001 0.01 0.1 1 10 Relative velocity [m/s]

Figure 2.9.: Friction dependence on relative velocity

3

2.5 µ [−]

2

1.5

1

0.5 maximum coefficient of friction

0 0 0.5 1 1.5 2 2.5 3 3.5

ground pressure pB [bar]

Figure 2.10.: Friction dependence on contact pressure

The curve depicted in figure 2.10 shows how the coefficient of friction decreases with higher loads (higher ground pressure). Having a tire with larger surface area gives lower ground pressure, resulting in a higher coefficient of friction and more grip.

Slip angle, aligning moment and pneumatic trail

During cornering, the driver turns the steering wheel and the wheels to keep the vehicle along the curvature of the road. At slow speeds and low lateral accelerations, only a small amount of steering is required.

At higher speeds, the centrifugal force increases (equation 2.4) and exposes the tires to a side force. To follow the curvature of the road, the driver has to increase the steering an-

35 2. Theory gle additionally. This means that there will be a difference between the vehicle heading and the tire rolling direction. This is called the slip angle.

z F s y

F y

x α Direction of heading Direction of Cα travel y F

e c

t or M p f z y eral t La F y

Slip angle α [deg]

(a) Illustration of slip angle (b) Plot of slip angle as function of lateral force

Figure 2.11.: Description of slip angle phenomenon

It is difficult to translate the angle of the steering wheel to a slip angle, as it depends on both speed and corner radius. The Michelin tire handbook [51] states that 20 degrees on the steering wheel easily generates a slip angle of 1 degree.

As slip angles are defined as a difference between the rolling direction and the vehicle heading, it also means that slip angles can be generated on the rear wheels, even though these cannot be steered.

By measuring the lateral force on a tire test rig as a function of the slip angle (the slip angle is generated by steering the tire), a characteristic curve for the tire behaviour can be created (figure 2.11b).

The curve is linear in the beginning, but when the tire reaches the maximum coefficient of friction, the lateral force will fall of. The linear part of the curve is called cornering

36 2. Theory

stiffness cα and it is an indication of how fast the tire can generate a lateral force when the slip angle increases.

When subjected to lateral forces, the tread elements of the tire are locally deflected side- ways. Along the contact patch this deformation continues until the lateral force is larger than the friction and slip occurs. At this point, the tread elements will quickly return to their undeformed position.

By integrating the lateral force along the contact patch, the force distribution results in a moment around the tire z-axis. This is known as the aligning moment Mz.

The moment arm that the lateral force acts on the centre point of contact is called pneu- matic trail tp and can be derived as:

Mz tp = Fy

Depending on the suspension design, this aligning moment can have different magni- tude. It is an important design parameter, as it can be used to automatically realign the wheels to a straight ahead direction if the driver lets go of the steering wheel.

Longitudinal slip

Contrary to slip angles, which is related to the build-up of forces in the lateral direction, there is also something called longitudinal slip. This relates to the slip occurring from forces in the longitudinal direction during acceleration and braking.

A useful measure of the longitudinal slip is the so called slip ratio (SR), which is defined as the quotient between the wheel rotation and vehicle speed:

Ω − Ω Ω ∗ R SR = 0 = e − 1 (2.6) Ω0 V ∗ cos(α)

The slip ratio zero corresponds to a free rolling tire, negative values braking.

According to Gillespie [29], the explanation of the longitudinal slip comes from the compliance of the tread elements. To create forces between tire and road, these tread elements have to bend, which can only occur if the tire is rotating faster than the tread circumference.

37 2. Theory

Camber

According to SAE [47], camber is defined as tilting of the tire in the lateral direction relative to the vertical wheel plane. Negative camber is the inclination of the tire inwards to the centre line of the car.

Standing tire Rolling tire

γ −γ

Fy Fz

N

Figure 2.12.: Cambering effects

The effect on cambering is the generation of a lateral force in the same direction as the tire inclination. Running with a cambered tire at zero slip angle, this lateral force is called camber thrust.

Milliken et al. [30] describe how the origin of the camber thrust comes from the dis- tortion of the contact patch into a curvature. When the tire is rolling, the road tries to eliminate this curvature, resulting in a lateral force.

Vertical and lateral stiffness

The properties of the tire in the vertical and lateral directions have a big influence on handling and comfort. Higher vertical stiffness of the tire is directly connected to re- duced ride comfort. This also applies to lateral stiffness, where higher stiffness results in better handling response. Combining both comfort and handling is a matter of com- promise; it is difficult to have both.

38 2. Theory

Many of the studies on how to determine the vertical stiffness have resulted in simple formulas, based on empirical data. Other research came up with more complicated tire models that require experientially determined parameters, which often turn out to be highly dependant on a specific tire. Rhyne [52] describes how the vertical stiffness of the tire could be calculated using simple and easy obtainable tire parameters. His work ends up with a very simple formula where the tire stiffness depends only on tire width, overall diameter and inflation pressure,

q Kz = 0.0274 ∗ Pi ∗ (W(OD) + 33.8 (2.7)

Holtschulze [53] describes how the vertical stiffness depends on three parameters: side- wall structure, inflation pressure and velocity coefficients.

∗ ∗ cR = cSidewall + cRp ∗ pi + cRv ∗ v (2.8)

For the lateral stiffness, similar investigations have been done. Holtschulze [53] de- scribes a method of determining the lateral stiffness using simple parameters. He begins by defining the pressure dependent stiffness of the tire as:

F F · φ Bd c ≈ T = P = ∗ p (2.9) yP y φ · h h i

The total lateral stiffness is composed by the pressure dependent stiffness and the side- wall stiffness:

Bd 2 ∗ E ∗ d ∗ t3 = ∗ + s cy pi 3 , (2.10) h (h ∗ ks)

Tire measurement and testing

An essential part of bringing better understanding to the behaviour of the tire, was the creation of the first tire measurement equipment in 1931 [35]. Today, equipment for performing tire measurements are available at most automotive and tire companies as well as at different universities. These measurements can be performed in a number of different ways, either with a dedicated tire test rig or directly on a vehicle. Vehicle testing is usually carried out with a so called fifth wheel which is operated independent of the other wheels.

39 2. Theory

Flat Track test-rig

A flat track test-rig [54] is composed of two rotating cylinders with a stainless steel belt simulating the rolling road. The surface of the steel belt is coated with different materials to give the right coefficient of friction. The vertical load is taken up by a hydrodynamic water bearing, placed in between the rollers, directly under the tire. This gives a flat and stiff surface for the tire and also prevents the tire load from damaging the expensive steel belt. The hydrodynamic bearing is also cooled to keep the temperature of the steel belt down.

The tire is attached to a movable spindle which is mounted on a A-shaped frame. This frame can be tilted to simulate tire camber, while the spindle is used to steer and put vertical load on the tire. The tire forces are measured using strain gages mounted on the spindle. The inflation pressure of the tire can be controlled and monitored, to ensure constant running conditions.

Figure 2.13.: MTS Flat-Trac CT tire test rig

Figure 2.13 shows the direction of rotation for the tire and belt. The coordinate system for the test rig is defined according to the ISO tire axis system (2.4.2).

Tire simulation

There are different types of tire simulation models. Pacejka [43] and Blundell [55] de- scribe some of the most commonly used models.

The simplest approach is to use measured data to create an empirical model of the tire, where mathematical formulas are used to calculate the tire response in form of lateral

40 2. Theory and longitudinal forces. This approach works well with smooth roads, where the verti- cal properties of the tire do not have a big influence.

To capture the transmission of forces to the chassis on uneven roads, a more refined approach is needed. The simplest way is to add a single spring/damper between rim and tire to represent the vertical stiffness and damping properties. The model can be further refined by adding more springs and dampers around the circumference.

The most complex alternative is to use finite element software and model a detailed material based description of the tire.

Parameterization of tire models

Simulation with many tire models are based on input of a number of parameters which empirically or physically describe the tire behaviour.

The parameterization process [56] is usually performed by independent research insti- tutes, universities or the developers of the tire models.

The tire is measured on a test rig, under varying conditions on both flat roads and rolling over cleats. From the measured data, the important parameters are extracted to create a tire data set.

Mathematical tire models

Fiala tire model

Fiala [57] has developed a simple tire model, which requires only ten input parameters. These parameters are directly related to the physical properties of the tire. The Fiala model is included as one of the standard tires in MSC.Adams/Car.

The simple approach for the Fiala model also gives it some limitations, as it cannot be used in combined cornering and braking/acceleration. The influence of camber is not included in the model.

Magic Formula and the MF-Tyre

Pacejka has created the Magic Formula [58] which can be used to describe tire behaviour with tangent functions. The MF-Tyre model [59] is based on the Magic Formula and is the result of the cooperation between Volvo Car Corporation and the Technical Univer- sity of Delft, Holland [60].

In its simplest form the Magic Formula needs only 4 parameters to empirically describe slip and lateral forces.

41 2. Theory

Y y

Sh

D arctan(BCD) y0

x X Sv xm

Figure 2.14.: Pacejka’s Magic Formula

y = D ∗ sin[C ∗ arctan(Bx) − E(Bx − arctan(Bx))]

Y(X) = y(x) + Sv

x = X + Sh

As concluded by Blundell [55], the main disadvantage with the Magic Formula is that these parameters (C, D, E) have no engineering significance, as they do not correlate to the physical properties of the tire. They are only used to interpolate and empirically recreate measurements.

MBS / Physical tire models

The physical tire models describe the complex tire behaviour on a mechanical basis. They can be seen as kind of simplified FE model, developed for the purpose of full vehicle simulations with MBS software.

These models can be used for both comfort and handling simulations on even and uneven roads with wavelengths down to a few millimetres, depending on model dis- cretization.

The modelling approach of the physical tire models resemble a MBS system, with bodies (mass points) connected to each other with a network of springs, dampers and different types of joints. The tire models benefit from the sparse matrices of a MBS system, giving fast computational times.

42 2. Theory

The basic idea behind these models is to keep the number of DOF as few as possible, only representing the relevant tire properties for the application. This also reduces the computational time.

FTire model family

As the result of work by Gipser, FTire [61] is a family of advanced tire models for vehicle simulations. They can be used with MBS vehicle models for ride comfort and handling simulations on smooth and uneven roads.

The FTire family consists of three models, each with a different modelling approach and recommended usage. First there is the RTire model, which is the simplest of the models, featuring a rigid ring to represent the tire structure. Then, there is the FTire model with a flexible ring, which can be seen as the most important model. It has a good compromise between simulation performance and accuracy. The most detailed model in the family is the FETire model, using some ideas from FE modelling.

FTire consists of separate tools for simulation, tire property file creation (parameteriza- tion) and validation, as well as plug-ins for the most common MBS simulation tools. FTire is included as one of the standard tire models in MSC.Adams/Car.

CTI programming interface

The tire models in the FTire family are built around the COSIN Tire Interface (CTI), a programming interface which is used as the link between FTire and other MBS software. CTI is used in MATLAB/Simulink, MSC.Adams, etc. This interface can also be used with in-house developed programs. The programming languages that can be used with the CTI interface are either C/C++ or FORTRAN.

RTire - Rigid ring tire model

RTire8 is the most basic model in the FTire family. It features a rigid ring representing the belt, which can move in all 6 DOF relative to the rim. The RTire model uses ideas from the BRIT model [62] also developed by Gipser.

The connection between belt and rim is made with translational and rotational stiffness and damping elements in all three directions.

Although the ring is considered to be stiff, a certain part of the belt, near the footprint is allowed to deform. The resulting pressure distribution is then described by a mathe- matical shape function.

8Rigid ring tire model

43 2. Theory

FTire - Flexible ring tire model

The FTire9 [63] model is the most important member of the FTire family. It is a compro- mise between the simpler rigid ring model RTire and the more complex FETire model.

Some important properties of the FTire model are:

• Simple implementation, can be used in multiple instances in MBS-software.

• Fully nonlinear 3D model, valid for frequencies up to 120 Hz

• Simulation time, about 10-20 times real time.

• Accurate for simulating single obstacles like cleats and pot-holes

The model consists of two parts, one describing the mechanical structure and the other the tire to road interaction with pressure distribution and friction.

The mechanical structure is a flexible ring with about 80 to 200 mass nodes (belt seg- ments), representing the steel cord of the tire. The nodes are connected to the rim and each other by different kinds of non-linear elements, which have stiffness, damping and frictional properties. The inflation pressure also affects the properties of these ele- ments.

Tire forces and moments acting on the rim are calculated by numeric integration of the forces in the belt.

cbend

crad cbelt c tang

Figure 2.15.: Discretization of FTire flexible ring model

The modelling of the sidewall is relatively simple, it is assumed to have constant length and that it will deflect according to the radial and lateral displacement of the tread.

9Flexible ring tire model

44 2. Theory

clong

c bend-out-of-plane cbend-in-plane

ctorsion

Figure 2.16.: Cross-section representation in the flexible ring model

FETire

The FETire10 model is the most advanced and detailed of the models in the FTire family. It uses a finite element approach, but is not nearly as complex as a real FE model. The model is based on further development of the DNSTire model [64] [65].

FETire requires about 50 to 100 times more CPU time than FTire, which limits the usage to certain special investigations such as high frequency simulations.

As in the FTire model, FETire is modelled with separate structure and tread parts. The structure is much more detailed compared to FTire and consists of 1000 to 5000 nodes each having 3 DOF. These nodes are connected to each other in a mesh consisting of springs and dampers.

(a) Springs representing the structural proper- (b) Elements describing bending stiffness ties

Figure 2.17.: Structure representation in the FETire model

10Finite Element Tire model

45 2. Theory

This mesh is automatically generated based on the cross-section geometry of the tire. The sidewall is represented by a number of nodes placed on the sides of the carcass at each cross-section.

MF-Swift

SWIFT [66] is a combined physical and mathematical tire model which represents the physical structure of the tire. It can be used with many popular MBS tools.

The model is composed of the following parts:

• Belt modelled as a rigid ring

• Contact patch with flexible tread elements in longitudinal direction. Uses Pacejka’s Magic Formula (2.4.2) to describe the non-linear slip and moment properties

• Stiffness and damping elements between contact patch and rigid ring to imitate tire stiffness in vertical, longitudinal, lateral and yaw direction

• Generic 3D obstacle model for simulation on uneven roads.

RMOD-K

Developed by Oertel and Fandre, RMOD-K [67] is a system of tire models with a detailed description of the tire structure.

The RMOD-K system contains models of varying complexity for different kinds of sim- ulations. In the most recent version (RMOD-K 7) there are two models, one simpler model with a rigid ring representation of the belt and another fully flexible belt model for more advanced simulations.

RFNRB - Rigid belt model

The rigid belt model RFNRB11 has a simple representation of the belt modelled as a rigid ring. It can be used for frequencies up to 100 HZ and ground obstacles down to 100 mm.

The connection between rim and belt can be done in different ways:

• Fixed joint between the rim and the belt, i.e no degrees of freedom. Only the contact between road and footprint will be simulated

• Planar joint and bushing between the rim and the belt, resulting in rotational free- dom of the rim, as well as translation in longitudinal and vertical direction.

11Reifenmodell Rigid Belt

46 2. Theory

• Single bushing between the rim and the belt, which results in complete freedom of movement (6 DOF). The stiffness and damping of this bushing is calculated internally by RMOD-K.

With the belt modelled as a rigid ring, there cannot be any deformation and resulting pressure distribution in the footprint. The deformations are approximated with help of a geometric calculation. The contact forces in the footprint are then calculated based on these deformations and the stiffness of the tread rubber.

RFNFB - Flexible belt model

The flexible belt model RFNFB12 [68] is the most detailed of the two models in the RMOD-K tire system. It can be used in simulations with very short wavelengths, down to a few millimetres.

The model is composed of two different parts, the mechanical structure and the contact part. During simulations the information on position, velocity and forces are exchanged between the parts.

2β

(a) Modelling of flexible belt (b) Modelling of cross-section

Figure 2.18.: Structure representation in the RMOD-K 7 Flexible belt model

The structure is based on a predefined cross-section, defined with nodes along the car- cass. These nodes are influenced by the internal inflation pressure as well as from the external loads in the tread.

The level of detail of the structure mesh (discretization) can be increased by adding addi- tional nodes to the cross-section geometry or by increasing the number of cross-sections on the circumference. When adding extra nodes to the cross-section, the relative bend- ing stiffness in x and y direction may have to be adjusted to ensure numerical stability of the model.

12Reifenmodell Flexible Belt

47 2. Theory

Finite Element Tire modelling

For performing tire simulations in the tire industry, it is very common to use the finite element method for analysis of the tire development and engineering process.

Kabe and Koishi [69] describe the simulation process for tire cornering simulations using the FE method. They conclude that although the explicit method is efficient for dynamic highly transient simulations of a rolling tire, it has the drawback of high CPU cost. For static, steady state simulations, the implicit method is much more efficient, requiring around 30 times less computing time.

In other situations, such as described by Hauke [70] [71], full vehicle misuse simula- tions can be performed with finite element tire models. In this case, the need of high resolution of the short impact time span requires the use of explicit solving.

It should be noted that the computational effort for the implicit method is independent of the rolling speed of the tire, whereas the explicit method, due to its time increment based solving, will result in longer simulation for higher rolling speeds with the same accuracy.

The process of building an accurate tire model using FE codes [72], independent of method, can be described as follows:

• A detailed description of the 2D tire cross-profile is built up in the finite element modeller. This describes the exact geometry of the cross-section, including the structural constituents such as the belt, cords and carcass. With this technique, it is then possible assign different material properties and direction to the structural parts of the tire (sidewall, carcass, belt and tread).

• To reduce computation time, a pre-3D analysis is performed, i.e. that inflation of the tire is simulated for the 2D cross-section.

• The results from the 2D analysis are then symmetrically transferred by revolving the profile 360 degrees to form a 3D model. Discretization of the structure can be selected arbitrary, that is mesh refinement can be done locally in selected areas, for example in the contact patch.

A problem in creating FE models of a tire is to get data on the materials used in the tires. The tire manufactures are very secretive about the material data of the different rubber compounds used in their tires.

48 2. Theory

2.5. Programming languages

2.5.1. MATLAB

MATLAB [73] is a programming language for use in technical computing applications. It can be used to quickly perform calculations involving large amounts of data, including matrices and vectors.

For the simulation of dynamic systems, MATLAB also includes Simulink, in which ad- vanced models can be created by building graphical block-diagrams.

2.5.2. Python

Python [74] is a powerful programming language available for many different plat- forms, including Windows and UNIX. It is relatively easy to use, which makes it ideal for prototype development.

Another benefit of Python is that it can be embedded into an application to provide a scriptable interface, for example in MSC.Adams, MSC.Marc and ABAQUS FE.

2.5.3. C/C++

The C programming language was developed by Ritchie [75] at Bell Laboratories in the beginning of the 70s. The reason was the need for a platform independent programming language for the newly developed UNIX operating system.

The later development of C++ also took place at Bell Laboratories, where Stroustrup [76] saw the need for a simple programming language to enable programmers to create good software. C++ was based on C, but was extended with additional features to simplify the programming.

2.5.4. FORTRAN

FORTRAN is a programming language used for numeric and scientific computation. It was originally developed by Backus [77] at IBM in the 1950s, for scientific and engi- neering applications. Still today, more than 50 years later, FORTRAN is widely used for all sorts of numerical computing, such as tire modelling (RMOD-K, FTire), climate and weather simulations, etc.

49 3. Method

3. Method

This chapter describes the method of work for this thesis. The Participatory Innovation Process [5] used at Luleå University of Technology has been used as an inspiration for how the planning and organization have been structured.

3.1. Design space exploration

In the initial phase of a development process, it is important to conduct a thorough information study. By learning as much as possible about the product and related tech- nologies early in the process, much time can be saved.

The first step was to study the current process for tire clearance used at BMW. A lot was learned about the process, the benefits and what improvements that can be made. Other departments were also visited to study other kinds of related technologies already in use.

Next came the information study in the subject of tire deformation and in other related areas of interest. The studies included both scientific reports, excerpts from conferences and basic vehicle theory. Relevant patents were also investigated.

3.1.1. Benchmarking

By studying how other automotive manufacturers perform their tire clearance, the de- velopment of a new method can make use of already discovered ideas and improve on them.

Volkswagen

Volkswagen AG and University of Hanover have studied the subject of tire deforma- tion and the feasibility of computer simulations [78]. Already in use by Volkswagen at the time, was the suspension development software MOGESSA [79], which with help

50 3. Method from kinematics and compliance in the suspension could create a wheel envelope and perform tire clearance investigations.

The study was conducted with five tires of three different dimensions mounted on two rim widths. For one tire dimension, tires from two different manufacturers where used. These tires were measured on a test rig and the stiffness of the sidewall was determined with ultrasound detectors. With help of this information, a simple mechanical tire model was created, consisting of 3 parts connected with torsional springs. The tire sidewall was assumed to be flexible and non-elastic, while the belt was considered to be stiff.

Tread

Sidewall Sidewall undeformed deformed

Rim

Figure 3.1.: Simple tire model used in Volkswagen study

The conclusion of this study was that it is possible to calculate the deformation of the sidewall with good accuracy for most sectors on the tire circumference

Some important discoveries from the measurements were:

• A higher lateral force results in larger deformations in both lateral and radial di- rections.

• The largest deformations occur close to the contact patch. Deformations up to 20 mm were observed in this study.

• The stiffness of the tire is reduced by lowering the inflation pressure, giving larger deformations in both radial and lateral directions.

• Under influence from lateral forces, the tire expands radially, especially in the 90/270 degree direction (see figure 1.6). Studying these radial deformations more closely shows that the relation between the deformations on the inner and outer shoulder of the tread is about 4:1, i.e. the tread is slightly twisted. This gives the tire a cone shaped form when viewed from above.

51 3. Method

3.1.2. Related technologies

The search for related technologies included both external and internal studies to look for interesting information. In the automotive industry, tire simulations can be used for different kinds of purposes. Often is the case that the tire is not the main object of interest (i.e. crash and misuse simulations), but the simulations require a detailed tire model to get good results.

Tire development with Finite element analysis

Much of tire development today is based on computer simulations trying to predict tire behaviour before building costly prototypes. There are many patents related to tire development and manufacturing, such as the Sumitomo patent [80], which describes a method for the simulation of rolling tires with the FE method.

Tire modelling for vehicle durability simulations

Hanley [13] describes some different trends in durability simulations. He concludes that due to the non-linear nature of the large deformations during misuse manoeuvres, many of the simple tire models are too limited for these kinds of simulations. Physical tire models, such as FTire (2.4.2) and RMOD-K (2.4.2), have a better description of the tire behaviour. However, as the input parameters for these models often are experimentally determined, they cannot be seen as truly predictive.

The use of the tire as a flexible body1 [81] in MBS vehicle simulations is indeed possible, but due to the linear FE approach, it is limited to deformations with low amplitudes.

Another idea that Hanley further describes is the co-simulation between MBS and FEA, where the strengths and benefits of both methods are used. The MBS simulation would send the spindle position to the FE simulation and get the forces acting on the spindle in return.

Hanley concludes, that due to ever increasing computer capacity, the use of FEA for misuse simulations can be motivated, despite the high computational cost.

1A finite element model used in a MBS simulation. The body is allowed to deform during the simula- tions, in contrast to ordinary bodies, which are assumed to be stiff

52 3. Method

NVH and comfort modelling simulations

In NVH2 and other types of comfort simulations, the use of MBS simulations, together with different tire models is very common. By using advanced tire models, both han- dling and comfort can be simulated.

These tire models, such as FTire (2.4.2) and RMOD-K (2.4.2) are based on real physics of the tire, but have much less complexity and computing requirements than FE models.

Vehicle stability control systems

Both Siemens AG [82] and Continental AG [83] [84] patents describe systems to acquire and measure the sidewall deformation. The idea is that the deformation can be used to calculate the forces acting on the wheels, which then can be used as input for different vehicle stability control systems (ABS, ESP, etc.).

Measurement of tire properties

Gnadler et al. [85] have investigated the lateral force response and resulting sidewall deformation for a representative selection of modern car tires. These tires were tested on an inner drum test rig under different conditions, including extreme load cases (up to 15000 N vertical load and 20 degrees camber).

By studying the deformations for the range of measured tires, it was concluded that these could be approximated with a Gaussian bell curve [86].

1 2 2 P(x) = √ e(−(x−µ) /(2σ )) (3.1) σ 2 ∗ π

Further studies took into consideration the influence of different parameters (vertical load, speed, tire dimension, etc) to end up with a universal formula for calculating the sidewall deformation at different slip angles.

The deformation, denoted ∆K is defined as the difference between the undeformed and the deformed sidewall on a certain distance (radius) from the wheel centre. A positive ∆K indicates that the tire is deflected outwards.

For straight ahead conditions, α = 0 the formula for the deformation is:

2Noise, vibration and harshness, common term used to describe unwanted vibrations in an automobile. It covers both mechanical vibrations and noise (acoustic)

53 3. Method

f r − R   (β − 180)2  ∆K = 1.5 + RL · I · −10.35 · exp − (3.2) 1.66 101.1 748.5

At slip angles α = ±10 degrees, equation 3.2 is extended with a second term:

f r − R   (β − 180)2   (β − 184)2  ∆K = 1.5 + RL · I · −10.35 · exp − ± 38.15 · exp − 1.66 101.1 748.5 3058.1 (3.3)

3.2. Roadmap

The roadmap is used as a guideline to link the theoretical information together with the generated ideas to form refined concepts for a final product.

3.2.1. Mission statement

The description of the product developed in this thesis, is a method for simulation of the deformation of the tire structure, which includes knowledge, procedures and software that based on a given set of input parameters can present the resulting deformed tire geometry.

The initial work is focused on theoretical investigations of vehicle and tire dynamics as well as studies of different tire simulation methods. Work will then continue to com- bine the acquired knowledge together with available simulation tools to create different concepts.

In the evaluation phase, the concepts are compared with each other, to determine which ones that are the most suitable to continue working on. These concepts are then further refined for later validation and testing against real measurements to ensure good quality and correspondence of the method.

The end result is a product which can be used to simulate the tire deformation.

3.2.2. Product characteristics

The method must be able to determine the tire deformation using pre-determined input parameters. These parameters consist of a specific tire (type, size, manufacturer, etc)

54 3. Method with related data (material data or physical parameters) and certain load cases in form of vertical load Fz, steering angle α, lateral force Fy, camber γ and vehicle speed v0 applied to it.

Exactly how should the simulations be performed? The first method that comes to mind is full vehicle simulations, as this would imitate the current method with vehi- cle measurements (section 1.1.2). The problem with this approach is that it adds a lot of complexity, in form of the dynamics of the vehicle. The main object of interest is the deformation on tire and not the behaviour of the complete vehicle.

A better approach is break down the problem and study the deformations on a single wheel, a so called quarter car model. This includes the wheel and a simple damper setup to imitate the vehicle suspension.

Refining the quarter car model further and excluding the damper and spring gives a simple model with a single tire. As the flat track test rig (section 2.4.2) is similar to this model, there is something that can be used to validate the simulations with.

The output from the simulations is a geometry describing the deformed tire, which can be opened in different CAD systems.

3.2.3. Thesis delimitation

Tires are one of the most complex systems on a vehicle to simulate. The idea of building a new tire model specifically for this kind of simulations may be tempting, but would not be possible in the time frames of this thesis.

The delimitation of the work will therefore be to use already available tire models, in form of FE-models and MBS Tire models. It also excludes use of simple tire models (Fiala, Magic Formula), which cannot be used for simulation of the tire deformation.

3.3. Concept design

3.3.1. Brainstorming

To enable creative thinking and emphasizing on creating as many ideas for different simulation approaches as possible brainstorming was used to collect interesting ideas for different concepts.

The following ideas came out from the brainstorming.

55 3. Method

• Mathematical/Empirical approach

• Finite element modelling

• Adams MBS tire model

• Simple mechanical approach

3.3.2. Concepts

Mathematical/Empirical approach

This concept is based on the idea that there might be a correlation between tire defor- mation and different parameters of the tire (such as dimension, lateral stiffness, vertical load etc). Using some of the ideas from Gnadler et al. [85] together with more mea- surements, such as the data described in figure (3.2), it would be possible to create an empirical formula to describe the deformations.

Comparision of tire deformation in % of maximum 100,00%

90,00%

80,00%

70,00% ] [%

60,00% on i t

a 50,00% m r

fo 40,00% e D 30,00%

20,00%

10,00%

0,00% 0° 45° 90° 105° 120° 135° 180° 225° 240° 255° 270° 315° 0° radial angle position

165/80 R 14 + 5,5 x 14 175/65 R 15 + 6,0 x 15 195/60 R 15 + 6,0 x 15 195/65 R 15 + 6,0 x 15 205/50 R 16 + 6,5 x 16 205/55 R 16 + 7,0 x 16 205/60 R 15 + 7,0 x 15 225/40 R 17 + 7,5 x 17 225/45 R 17 + 7,5 x 17 225/50 R 16 + 7,0 x 16 225/55 R 15 + 7,0 x 15 225/60 R 16 + 7,5 x 16 235/50 R 16 + 7,5 x 16 235/65 R 17 + 7,5 x 17 245/45 R 18 + 8,0 x 18 255/55 R 18 + 8,0 x 18 TD 230/55 R 390 + 390 x 180 TD

Figure 3.2.: Statistics of tire deformation

Finite Element Modelling

A FE simulation concept would be carried out with some FE software, in this case ABAQUS is available at BMW and has been found useful for this kind of simulation. The approach by Hauke [70] [71] could be used as a starting point for the modelling.

56 3. Method

MBS model of the tire structure

Another idea that came up was to build a simple 2D Adams model of the tire cross section. By dividing the tire cross section into small links each with their own mass and then connecting these links with rotational spring and dampers, a simple tire model can be created. Spring stiffness and damping could then be derived from testing and approximation.

Rim

tire elements

Torsional springs and dampers

(a) Concept for Adams model of a tire (b) Modelled tire in Adams/View

Figure 3.3.: Adams tire model

The deformations close to the tire footprint could then be predicted with this method, but for the other parts of the tire some other method has to be used.

Mechanical approach

Using the approach in equation 2.9 & 2.10 by Holtschulze [53], the lateral stiffness of the tire can be approximated. Together with a simplified sidewall representation in form of a polynomial equation, the deformations in the contact patch could be calculated.

Physical Tire Models

In the information study, the characteristics of different tire models for MBS simulation are described. The physical tire models are well suited for this type of simulation, as they represent not only the generation of grip in the contact patch, but also the mechanical structure of the tire. There are at least three different models available, SWIFT, RMOD-K and FTire (section 2.4.2).

57 3. Method

pi ϕ

h h

pi

F pi T

ϕ FP y FP

Figure 3.4.: Mechanical tire model

3.3.3. Evaluation of concepts

To determine which concepts to continue working on, a concept evaluation has been performed. Many of the concepts from the brainstorming session are interesting, but they would require too much work to turn into complete concepts. The decision in the thesis delimitation, was to not develop new tire models. However, many of the ideas could still be used to complement and improve the other concepts.

The following concepts were put aside, to concentrate on more promising ones.

• Mathematical/Empirical approach

• Adams model of tire

• Simple mechanical approach

Evaluation matrices

The main concepts for evaluation are:

• MBS tire simulation models.

• Finite Element Analysis.

Both methods show promising possibilities and they are already in use for similar sim- ulations at BMW. The synergy effect of cooperation with other departments will be use- ful.

58 3. Method

The information studies gave more insight in the different MBS and FE simulation meth- ods that are available. The concept evaluation will compare these models to find the most suitable ones:

• FTire, RMOD-K 7, RMOD-K 6, MF-Swift, ABAQUS FEA

For the evaluation, these different criterion are used to compare the concepts:

• A, Good ability to simulate tire deformation3

• B, Needs few customizations of the software for simulation4

• C, Good internal experience of the model/method at BMW

• D, Good external support from developers

• E, Easy to obtain the deformation in a CAD readable format

• F, Good extendibility with 3rd party software (Matlab/Simulink,C/C++,python).

• G, Good availability of tire data for the model/method5

• H, Easy to extend method to full vehicle simulations in MBS software

The evaluation was done with Pugh’s method (2.1.4), which scores the concepts relative to each other. The datum for the evaluation was selected to be FTire.

Concept FTire RMODK7 RMODK6 Swift ABAQUS Criteria A S S - - S B S + - S S C S - S - + D S S - S - E S + - - S F S - - S S G S - + - - H S S S S - (+1p) Total + 0 2 1 0 1 (-1p) Total - 0 3 5 4 3 ( 0p) Total S 8 3 2 4 4 Total 0 -1 -4 -4 -2

Table 3.1.: Pugh’s evaluation matrix

The result of the evaluation is that the highest scoring concept is FTire. The second most suitable alternative is RMOD-K 7, followed by the FE analysis with ABAQUS.

3i.e does not require large amount of work rebuilding the model for deformation simulations 4Concept is already feature complete with functions for simulation of tire deformation 5Material data, parameterized data sets

59 3. Method

3.4. Detailed design

3.4.1. Concept refinement

The concepts are first refined and then tested against initial measurements to ensure that the models are correct. Larger differences discovered during testing have to be corrected before the models can be used. Later validation against deformations measured on the test rig will show if the concepts can perform the desired deformation simulations.

For the test rig measurements, a suitable tire has to be decided upon. The Michelin Pilot Primacy 225/50 R17 was selected because of the good availability of tire data, for both FTire and RMOD-K 7.

FTire concept

The FTire model and its complementary software includes a tool for simulating quarter car models 6. This tool does not have the ability to generate the deformed tire in CAD readable format. The models do, however, support manual acquisition of the node po- sitions in the tire structure.

The function to generate the tire envelope geometry has to be implemented in a separate program, by using the CTI interface (2.4.2) to acquire the node positions. The program also controls all important simulation parameters such as vertical tire load, lateral force, rolling velocity, camber, etc.

The FTire family includes three different tire models. The most detailed model is FETire, but it is not as actively developed and mature as the flexible ring model. The decision is therefore to use the flexible ring model.

RMOD-K 7

The RMOD-K tire model includes both plugins for common MBS tools, as well as a standalone simulation program for single tire simulations. This program can be used to simulate the tire deformation and generate a geometry file for import in the CAD system.

There are two different models in the RMOD-K tire system, the rigid ring and the flexible belt model. The flexible belt model is the most detailed and will therefore be used for the simulations.

6A 1/4 model of a vehicle suspension with a single tire, damper and spring

60 3. Method

Figure 3.5.: FTire based tool for tire simulation

Figure 3.6.: RMOD-K tool for tire simulation

ABAQUS FE model

In a very early stage of the detailed design for the ABAQUS concept, it was concluded that due to absence of material data, it would be difficult to build an accurate model and simulate the tire deformations.

As the concept is interesting, it was decided to perform some testing. The FE software ABAQUS contains examples of tire modelling. Using these examples, a proof of concept

61 3. Method was created and the feasibility of deformation simulations investigated.

Vertical loads, longitudinal and lateral velocities were applied to recreate the condi- tions on the test rig. Both implicit (Static) and explicit (Dynamic) simulations were per- formed.

Figure 3.7.: ABAQUS FE modelling

The results from the ABAQUS simulation are stored in a output database file (ODB). By using the built in Python programming (2.5.2) capabilities in ABAQUS, a script can be used to export the positions for the surface nodes in the deformed mesh, to create a geometry file of the tire deformation.

3.4.2. Input data for simulations

Replacing the current method of vehicle testing with simulations, require that the same conditions can be recreated in the virtual simulation environment.

Tire deformation is measured at the BMW test track in Aschheim, outside Munich, by subjecting the tires to the highest lateral forces that could occur during normal driv- ing.

By studying data measured on the test track, some insight in how large the forces on the tire are can be found. A measurement from a test with a BMW 5-Series 550i Sedan [87] (m=2030.5kg) was analyzed and the the forces from three runs were averaged and

62 3. Method

(a) Full view of test vehicle (b) Close-up on wheel measurement hub

Figure 3.8.: Measurement of forces acting on the wheels

filtered to remove transients. The resulting diagrams of the lateral and vertical loads can be seen in figure 3.9.

The maximum forces were found to be about 9500 N for both lateral and vertical loads at a lateral acceleration of about 1g.

These forces could be used as the input to the simulations, but as the validations is performed against the measurements from the tire test rig, the forces from these tests will be used.

Lateral force during driving on handling course at Aschheim Vertical load during driving on handling course at Aschheim 4 10 Averaged Averaged Lateral force 9 Vertical load 2 8

0 7

6 −2 5 −4 4 Lateral force [kN] Vertical load [kN]

−6 3

2 −8 1

−10 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Time [s] Time [s] (a) Plot of lateral force (b) Plot of vertical load

Figure 3.9.: Measurement from the handling course at Aschheim

3.4.3. Output from simulation models

Common for all simulation models it that they use the cloud geometry format (CGO) to describe the deformed tire geometry. The benefit of this format is that it can be directly imported into Catia V5. It is basically a text file, where each line contains the coordinates for points on the surface of the tire geometry.

63 3. Method

3.4.4. Initial model verification and validation

When working with tire simulation models, it is important to verify that the models correspond well to a real tire. By looking at specific tire characteristics, it is easy to verify that the simulation models are correct.

Vertical stiffness

The vertical stiffness is a measure of the force needed to compress the tire in vertical direction. As previously described in section 2.4.2, this stiffness depends both on the tire structure and inflation pressure.

Simulated and measured vertical stiffness, p =2.0 bar, V=50 km/h i 10000

9000 Measured vertical stiffness c =212 N/mm R FTire vertical stiffness c =285 N/mm 8000 R RMOD-K vertical stiffness) c =259 N/mm 7000 R [N]

Z 6000

5000

4000 Vertical force F 3000

2000

1000

0 0 5 10 15 20 25 30 Vertical displacement d [mm] Z

Figure 3.10.: Validation of vertical load

As can be seen in figure 3.10, the vertical stiffness (inclination of the curves) for both the RMOD-K and the FTire models is higher than the measured valued. The measured radial deformation is about 27-28 mm, whereas the simulated radial deformations are smaller, about 24-25 mm.

Lateral slip

Comparing the slip curves for the simulation models gives a hint about how the lateral force increases with slip angles. It is expected that initial slope (cornering stiffness) and the peak values are about the same.

64 3. Method

Lateral slip at Fz=6000N

6000 Measured FTire RMOD−K 4000

2000

0

Lateral force [N] −2000

−4000

−6000

−10−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 Slip angle [degrees]

Figure 3.11.: Validation of lateral slip

Lateral stiffness

The lateral stiffness is a measurement of how much the tire deforms in lateral direc- tion under influence of lateral forces. The lateral stiffness for both FTire and RMOD-K models can easily be simulated. Unfortunately, there was no measurement of the lateral stiffness performed. It would have been good to compare and study the lateral stiffness of the simulation models to ensure that they are correct.

Longitudinal slip

The longitudinal slip describes how the tire grip is generated in longitudinal directions, as a result of acceleration and braking. Slip ratio is defined by equation (2.6).

Cross-section geometry

Important for good results of the simulations is that the simulated tire profile corre- sponds well to the real tire. This applies especially if the deformations are to be com- pared graphically against each other.

The undeformed tire contour is measured with a testing equipment, TriScan-Tyre [88] and this measurement is then used to adjust the contour of the simulation models. The simulation models used in this thesis have been successfully adjusted and a good corre- spondence has been reached.

65 3. Method

Longitudinal slip at Fz=6000N 8000 Measured 6000 FTire RMOD−K 4000

2000

0

−2000 Longitudinal force [N]

−4000

−6000

−8000 −100 −80 −60 −40 −20 0 20 40 60 80 100 Longitudinal slip [%]

Figure 3.12.: Validation of longitudinal slip

3.4.5. Final testing and validation

Test rig measurements

For the tire measurements on the test rig the rolling velocity is set to 50 km/h with zero camber. The tire has a cold inflation pressure of 2.0 bar, which increases slightly when the tire warms up. It is assumed that this difference in inflation pressure will be small and that it will not influence the results.

In the start-up phase, the vertical load is increased stepwise from zero until the specified vertical load FZ= 6000 N is reached, it is then kept constant.

The lateral forces are generated by turning the tire with different angles against the rolling direction of the flat track belt. This corresponds to a slip angle α, which is in- creased in steps of one degree up to +10 degrees and then to -10 degrees and finally returned to zero.

A slip angle of 10 degrees, means a difference of 10 degrees between the rolling direction of the tire and the heading of the vehicle. A real world example of this is driving through a corner and to follow the curvature of the road the driver has to increase the steering wheel angle so much, that the tire points in a direction with a 10 degree difference from the heading of the vehicle.

The measured lateral force at each of the different slip angles is then used as input the simulations.

66 3. Method

Measurement cycle on Flat track test rig 8000 10

6000 5

4000 0 Vertical load [N] Steering angle [deg]

2000 −5

0 −10 0 20 40 60 80 100 120 140 Time [s]

Figure 3.13.: Measurement cycle on the test rig

Measurement of the deformations

During the test rig runs, the deformations of the tire sidewall are measured with a contact-less optical system, ARAMIS [89] from GOM7. The results of the measurements are saved as STL8 geometry surfaces describing the tire deformation for each different load case.

The measurement method uses a paint pattern on the tire and the rim to be able to measure the deformations. As the pattern in the tread area of the tire wears off after a short time, it is not possible to measure the deformations in the belt region.

As the deformations can only be measured on the outside of the wheel, the measure- ments were performed with both positive and negative slip angles. By assuming that the tire is symmetric and the deformations are independent of which side they are mea- sured on, i.e. that the outside sidewall for positive slip angles is the same as the in- side sidewall for negative slip angles, the surfaces can be mirrored to form a complete overview of the tire deformations.

The STL surfaces are oriented and positioned so that the hub of the flat track test rig is zero in radial direction (xz) and a point on one of the spokes on the rim is zero in lateral direction (y).

7Gesellschaft für Optische Messtechnik, Mittelweg 7-8, 38106 Braunschweig, Germany. 8Stereolithographic Language - Common format for 3D geometries and surfaces

67 3. Method

Rim centreline Rim outside

Mirrored deformation Deformation at slip angle -5 deg at slip angle 5 deg

Figure 3.14.: Mirrored deformations

Analysis of results

The post-processing of the deformations is performed both graphically with 2D draw- ings in Catia V5 at each of the sections described in figure 1.6 and with diagrams show- ing the magnitude of the deformations. The diagrams give a quick overview of the deformations, whereas the drawings give more detailed information.

Figure 3.15.: Post-processing of results in Catia V5

68 4. Results

4. Results

This chapter describes the comparisons of the simulations against the measured defor- mations. The sectors and corresponding angles are defined according to figure 1.6. The tire deformation is described in figure 1.11.

4.1. Measurements

The results from the deformation measurements (Appendix A.1) on the test rig show that:

• For pure vertical loads, the largest deformations occur in the sectors close to the contact patch. On the top half of the tire, the deformations are negative, about -1.6 mm in lateral direction. The radial deformation at a vertical load of 6000 N is about 27-28 mm.

• When exposed to lateral forces, the tire deforms sideways in the same direction as the lateral force. The deformations are largest in sectors close to the contact patch, where a maximum deformation of about 30 mm has been observed at a lateral force of 6100N. The deformations on the upper half of the tire (0 ± 45 degrees) are very small (<±2 mm) independent of lateral force.

• The largest increase in deformation occur for slip angles between 0-5 degrees. For higher slip angles (6-10 degrees), there is little or no change compared to the de- formations at a slip angle of 5 degrees. The reason for this is that the maximum lateral force, about 6100 N, is generated at a slip angle of about 5-7 degrees. At higher slip angles, the tire starts to vibrate and the lateral force oscillates strongly.

• The measured deformations at opposite sector pairs (90-270, 105-255, 120-240 and 135-225 degrees) are constantly larger in the sectors at 180-360 degrees. The differ- ence between two opposite sectors is about 1-2 mm.

69 4. Results

4.2. Concepts

A comparison of the deformations for the two tire models at different sectors is depicted in figure 4.1. The comparison is for a slip angle of +5 degrees and a lateral force of -6091 N. The reference geometry used to calculate the deformations, was the undeformed tire profile from the simulations and the measurements respectively.

Comparision of deformations for slip angle 5 deg Fz=6000N Fy=6091N P=2.0 bar Comparision of simulation errors for slip angle 5 deg Fz=6000N Fy=6091N P=2.0 bar 30 Measured 10 FTire FTire RMOD−K 25 RMOD−K 8

20 6

15 4

10 2 Simulation error [mm] 5 Maximum deformation [mm] 0

0 −2

−5 −4 0 30 60 90 120 150 180 210 240 270 300 330 360 0 30 60 90 120 150 180 210 240 270 300 330 360 Section angle [deg] Section angle [deg] (a) Plot of measured and simulated deforma- (b) Plot of simulation error tion

Figure 4.1.: Comparison of simulations and measurements

The simulation error is the difference between measured and simulated deformation. A negative simulation error means that the simulated deformation is larger than the measured and vice versa.

4.2.1. FTire concept

At a slip angle of +5 degrees (Fy=-6091 N), the simulated deformations with FTire show a fairly good correspondence on the upper half of the tire (between 0-105 degrees and 255-360 degrees), even if the simulated deformations in some sectors are slightly larger than the measured. The simulation error in these sectors is about -2 to +4 mm and the contour of the simulation matches the measured quite well.

Closer to the contact patch 180 ± 60 degrees, the simulated deformations are smaller compared to the measurements and the appearance of the curves differs quite noticeably from the measurements. The maximum error (10 mm) can be found in the 135 and 225 degree sectors. The difference in the contact patch (180 deg) is actually less (about 5 mm) compared to the maximum error.

In general, for smaller slip angles, the simulations give good results and the contour matches the measurments quite well.

70 4. Results

4.2.2. RMOD-K 7 concept

The results of the simulations with the modified RMOD-K model1 shows that at a slip angle of +5 degrees (Fy=-6091 N), the simulation error is about +2 mm in the sectors between 0-120 degrees and 240-360 degrees. Closer to the contact patch in the sectors at 120-240 degrees, the difference to the measurements is about 4-7 mm. The appearance of the deformations close to the contact patch is also for RMOD-K quite different from the measured contour.

At smaller slip angles, the difference between simulation and measurement is much smaller, about ±3 mm.

4.2.3. Mathematical/Empirical Concept

The approximation formula (equation 3.3) by Gnadler et al. [85] described in section 3.3.2 has been compared to the deformations at +10 degrees. The appearance of the curves in figure 4.2 is about the same, but the calculated deformations are smaller at all the sectors on the circumference (constant offset of the curves).

Calculated and measured deformations for slip angle +10 deg at radius 272 mm Calculated and measured deformations for slip angle +10 deg at radius 272 mm 12 30 Measured Calculated 10 25

20 8

15 6

10 Error [mm]

Deformation [mm] 4 5

2 0 Approximation error

−5 0 0 30 60 90 120 150 180 210 240 270 300 330 360 0 30 60 90 120 150 180 210 240 270 300 330 360 Section angle [deg] Section angle [deg] (a) Deformations at slip angle +10 degrees (b) Approximation formula error (compared to measurement)

Figure 4.2.: Comparison between measurements and Gnadler’s approximation formulas

1The rim node was moved closer to the rim flange

71 5. Discussion and conclusion

5. Discussion and conclusion

This chapter contains the author’s personal thoughts and reflections on the work in this thesis. The planning, method and results are discussed and analysed. Sources of error are also determined. In the end, a suggestion for future work is proposed.

5.1. General conclusions

Tires and the modelling of their behaviour is considered somewhat of a black magic. Even when much of the theory behind tire dynamics is understood, there is no single model that can accurately describe all tire characteristics.

The simulation of the tire deformation does not only require the models to recreate the generation of grip, with related forces and moments, but also the how the tire structure deforms under influence by external forces. These requirements put high demands on the tire simulation models. Still, the work in this thesis shows that there are tire models that can fulfil both of these requirements.

The different tire models show that it is possible to simulate and determine the deforma- tion of the tire under different conditions. The maximum difference between simulation and measurement has been found to be about 7 mm in the sectors between 0-120 degrees and 240-360 degrees, which are the most critical sectors with respect to tire clearance.

There are some areas where the differences between simulation and measurement are larger (around 10 mm). These occur close to the contact patch, where the tire clearance is not so critical.

A general observation is that for small slip angles the simulations correlate very well to the measurements. When the slip angle and lateral force increases, the difference becomes slightly larger.

A trend found in both FTire and RMOD-K simulations is a radial expansion (increasing tire radius) of the belt and tread on the outer shoulder of the tire. In the regions where this phenomenon occurs, the belt is slightly twisted compared to the undeformed state.

72 5. Discussion and conclusion

This radial expansion is something that also has been discovered in the foam measure- ments (section 1.1.2). Unfortunately, as the deformations of the belt region of the tire could not be measured, this phenomenon cannot be confirmed.

Comparing the results from the different concepts, RMOD-K gives the best correspon- dence to the measurements. FTire seems to have some problems of describing the de- formations especially in the 90-135 and 225-270 degree sectors.

The initial validation of the simulation models shows a clear difference in vertical stiff- ness for both RMOD-K and FTire. This can have a big effect on the results and should be investigated further.

5.1.1. Simulations

The simulations use the same loads as input as those measured on the tire test rig. When the results of the measurements were studied, it was discovered that for slip angles larger than ±5 degrees the lateral force did not increase. At higher slip angles, the tire structure starts to vibrate. Due to this, it was decided that the simulation and compar- isons with the measurements should only be made for slip angles up to 5 degrees.

5.1.2. Physical/MBS tire models

The physical/MBS tire models have the advantage of being relatively fast in comparison with true FEM models.

Much of the explanation to the fast simulation times for the MBS tire models, lies in the simple representation of the tire structure. By focusing on the most important properties of the tire, the complexity can be reduced.

A clear example of this is in the areas close to the rim. A real tire is kept in place in lateral direction by the rim flange (figure 2.5). As the rim is not included in the simu- lation model, the contour of the simulated tire cannot take any effects of the rim into consideration.

This phenomenon is illustrated in figure 5.1, where the green curve represents the mea- sured deformation and the red curve the simulated (RMOD-K). The simulated contour bulges outwards from the point of attachment at the bead wire, which makes the defor- mations seem less realistic.

A solution to this issue is to position the rim node of the tire model closer to the edge of the rim flange, as depicted in figure 5.2.

73 5. Discussion and conclusion

Figure 5.1.: Influence of the rim flange to the deformations at large lateral forces

Figure 5.2.: Different location of the rim node

Another fact is the variation in stiffness along the sidewall of a real tire. Close to the bead wire, the bead filler makes this region very stiff in bending. Further down the sidewall, it is suddenly very flexible and compliant. This has also shown to be an area where the tire models have some problems of describing the deformations accurately.

5.1.3. Finite element models

As there were no FE simulations performed on the Michelin tire, the quality of such simulations cannot be determined. From the literature studies and the simulation ex- periments performed, there are still some conclusions around FE modelling that have been drawn.

The use of FE modelling means that the simulation model can be almost as detailed as a real tire, but at the cost of increased computational time. The cross section with different layers and material compounds can be accurately described. As the rim can be included in the simulation model, the effects of rim contact can also be handled.

It is important that also the grip generating properties of the FE model are paid attention

74 5. Discussion and conclusion to. No matter how detailed the tire structure is described, the accuracy of the model still depend on the ability to describe the lateral and longitudinal slip characteristics of the tire. If these requirements can be fulfilled, it is therefore realistic to assume good results.

When detailed tire simulations for certain special investigations are needed, where long simulation times and availability of material data is no problem, the finite element method is the right choice. If short computational times are important, there are bet- ter choices than the finite element method available.

Nevertheless, with today’s rapid development of computer technology, the use of de- tailed finite element models can become more widespread as the computational capacity of the computers increase.

5.2. Concept results

5.2.1. FTire concept

The FTire flexible ring model has shown to be a simple and fast tire model giving rela- tively good results.

In the initial simulations with FTire, the simulated cross section was slightly narrower (225 mm) compared to the measured tire section width (240 mm). The reason for this is that FTire uses the denoted dimension 225/50 R17 for generating the tire geometry. As the tire actually is 240 mm wide, this explains the difference.

After discussions with Gipser [90], the developer of FTire, it became clear that the tire and rim width could be adjusted in the tire data set without changing the tire be- haviour. After these modifications, the simulated tire profile corresponded well to the measured.

Conclusions of the simulations with the FTire concept, are that the maximum deforma- tions shows relatively good correspondence with measurements for small slip angles (0-1 degrees), but when the slip angle increases, there are larger differences. The biggest variations are found in sectors close to the contact patch (180 ± 60 degrees), as the de- formations are largest here. For the other sections, on the upper half of the tire, the simulations show better correspondence.

An explanation to these differences lies in the simple representation of the sidewall in the FTire model (see section 2.4.2). A more detailed description of the sidewall would be of benefit for these simulations.

75 5. Discussion and conclusion

A consequence of the simple sidewall representation is that the deformations seem to return to a state with small deformations not far from the contact patch. As the sidewall on a real tire is very stiff close to the bead, it is not realistic that the deformations could decreases so quickly. This can be seen in figure 4.1 where the width of the peak in the FTire curve is much narrower compared to the measurements.

Another problem with the FTire model was that the simulated vertical stiffness is higher compared to the measurements. This does not automatically mean a problem with the tire model, it can also mean that the parametrized data set is not good enough. With a poor quality of the parametrization, the results from the simulations cannot be expected to be very good.

A small test was made by modifying the vertical stiffness of the FTire data set to see of this would improve the results. This showed that the radial deflection in the 180 degree sector became slightly larger, but any differences in the other sectors or for the sidewall deformation could not be found. Further tests could be to modify the lateral stiffness, but without any measurements of this stiffness, it was difficult to know which value of the stiffness to use. It would be a good idea to revalidate the tire data set and see if this gives better results.

A big benefit of the FTire concept is the flexibility of being able to use different simula- tion tools. If the FTire simulation program cannot satisfy the needs, both Matlab and the separate programming interface CTI, can be used to create tire simulations.

5.2.2. RMOD-K 7 concept

The RMOD-7 flexible belt model has a very detailed modelling approach, with a struc- ture consisting of several nodes and elements. As many of the structural properties can be changed, the model is very flexible when it comes to customizations.

The tire cross-section is described by specifying the positions of the nodes and the thick- ness of the rubber material. This means that it is relatively easy to adjust the model so that it corresponds well to the undeformed tire profile.

Additional nodes can be added to the cross section to increase the level of refinement, anywhere from 7 to 18 nodes can be used. The total number of cross sections on the circumference can also be varied, from 3 to 80. This means up to 1440 nodes in the structure. It should, however, be noted that the increased level of detail also means longer simulation times. Compared to FTire, the simulation time with RMOD-K was about 5 times longer.

76 5. Discussion and conclusion

The relative high complexity of the RMOD-K model means that larger changes to the tire structure and node positions can lead to instability. This requires experience and detailed knowledge of the parameters used to defined the properties of the tire model.

In the first version of the tire data set for the RMOD-K simulation model, the rim node1 was positioned close to the rim inner surface, far from the rim flange. This led to un- realistic deformations and excessive bulging of the sidewall close to the rim flange. To improve on this, the position for the rim node was moved slightly closer to the edge of the rim flange, which led to more realistic deformations close to the rim.

Compared to before the modifications, the adjustment of the rim node led to slightly smaller deformations, which is due to an increase in the structural stiffness. If this mod- ification really can be seen as realistic is difficult to say, judging from a single measure- ment. The fact is, that the vertical stiffness of the tire model corresponds better to the measurements when the rim node is placed close the rim inner surface. As the deforma- tions also are larger compared to the measurements with a lower stiffness, gives a cer- tain safety margin. Future investigations have to be made to determine which position of the rim node that gives the best results. A detailed comparison of the deformations for different rim node placements and the difference in vertical stiffness can be found in appendix A.5.

The results of the deformation simulations with RMOD-K can be seen as fairly good. The largest differences between simulation and measurements are found at high slip angles close to the contact patch. This is because the model cannot take the rim and the resulting bending of the tire around the rim flange into account.

Some disadvantages with the RMOD-K 7 tire model is that it does not have any external interfaces to other software (Matlab, C/C++), which limits the usability somewhat.

5.2.3. Mathematical/Empirical concept

With only one set of measured tires, it is not enough data to create a new approximation formula for the tire deformations from.

By using the formula derived by Gnadler et al. [85], the deformations can be approxi- mated. The calculated deformations gives a difference of 3-11 mm. The approximated deformations are smaller than the measured at all the sectors on the tire circumference.

The disadvantage of these empirical formulas is that they can only approximate the de- formations using measured data from other tires, they cannot predict the deformations.

1The first node in the cross section structure. It is placed close to where the tire is attached to the rim (bead wire)

77 5. Discussion and conclusion

For a well known tire, these formulas can give good results, but for other unknown tires, the results might not be that good.

The conclusion is that even if it is possible to approximate the deformations with a sim- ple formula, the calculations does not give the required accuracy. The deformation of the tire structure for different tires is far to complex that a single formula could accurately describe every aspect of the deformations.

5.3. Sources of errors

As the results show, there are some differences between simulation and measurements. To improve the simulations it is important to identify the sources of these errors and study if they can be minimized.

5.3.1. Tire simulation models

The biggest source of error probably lies the simulation models. Studying the FTire parametrization report for the Michelin tire data set [91] shows that the tire models cannot accurately represent all characteristics of a real tire.

The representation of the sidewall in the simulation models has a big effect on the de- formations. As the simulation models do not take the effects of the rim flange into consideration, the largest differences occur in this region.

5.3.2. Tire parameterization

The process of parameterization (2.4.2) is important for accurate simulations with the tire models. The measurements that are used to create the tire data sets, can be per- formed in many different ways and on various tire test rigs. As shown by Oosten et al. [92] in the TIME project, there can be variations of between 21-46% depending on which type of tire test rig that was used to measure the same tire.

In the initial validation of the tire models (section 3.4.4), it was discovered that the verti- cal stiffness in the simulations, especially for FTire was higher (about 285 N/mm) com- pared to the measured tire ( 212 N/mm) (see figure 3.10). A higher vertical stiffness leads to smaller radial displacement of the tire and less bulging of the sidewall in the lateral direction.

78 5. Discussion and conclusion

The reason for this difference probably lies in the parameterization of the tire data used for FTire. As concluded in the discussions with Holtschulze [93], the vertical stiffness for a tire varies with rolling velocity. For a standing tire, the stiffness is higher compared to a rolling tire at slow speed. If the vertical stiffness for the FTire data set was measured for a standing tire, it is possible that this is the explanation.

The higher vertical stiffness of the simulation models makes the simulated deformations smaller than they would be and should be seen as a big source of error in the results. It is likely that the deformations would have been slightly better with a lower stiffness.

5.3.3. Pressure variations

The measurements of the deformations were performed with a cold inflation pressure of 2.0 bar. When the temperature of the tire increases during the runs on the test rig, the inflation pressure also increases. It was assumed that this change in inflation pressure would be very small, therefore all simulations were performed at 2.0 bar. The pressure was measured after the testing and was found to have increased about 0.1-0.2 bar.

The contour of the undeformed tire was measured at 2.5 bar inflation pressure and was then used to validate and adjust the tire contour of the simulations. As the inflation pressure on the test rig was 2.0 bar, the simulation models have be able to accurately reproduce any change of the tire contour at this lower inflation pressure. If not, there can be some smaller variations.

5.3.4. Contour and deformation measurement

Large errors originating from tolerances of the equipment used to measure the tire con- tour and deformations are not very likely. According to the specifications [88] [89] of the measurement equipment, the measurement error is less than 0.1 mm.

The most likely source of error is that the measurement conditions and method were not exactly the same. An example of this is the measurement of the tire sidewall. Printed on the sidewalls are text and symbols denoting dimension and manufacturer, with a thickness of about 1-1.5 mm. If the tire contour is measured at a position with text or symbols, it is possible that the overall width can be about 1-2 mm larger.

Another source of error is due to the manufacturing tolerances of the rim. The measured deformations on the test rig used a point on one of the spoke as the reference coordinate. As the tolerance of the spoke surface is ±0.5 mm, this can lead to a small error in the positioning of the deformation geometry in the CAD system.

79 5. Discussion and conclusion

A successive error because of this is the positioning of the deformation surfaces on the rim inside. As the deformations could only be measured on one side of the tire, the surfaces had to be mirrored to give a complete view of the deformations opposing side of the tire. Any errors in the positioning of the original geometry would also propagate onto the mirrored surface.

Summing up these errors gives a measurement uncertainty of about ±1-2 mm due to tolerances, measurement errors and different measurement methods.

5.4. Future work

5.4.1. Validation of the tire models and parametrized data

As it has been discovered during the initial validation of the tire models, the quality of the tire data sets used for the simulation models can be very varying. This can lead to inaccurate results. To ensure accurate simulations of the tire deformation it is essential that the tire models can reproduce the properties of a real tire.

The recommendation is to perform a thorough validation of the tire models and the data sets and compare the vertical and lateral stiffness with measurements, before any deformation simulations are performed.

5.4.2. Additional test rig measurements

Drawing conclusions from a single set of measurements does not give the required con- fidence needed to decide if the results from the simulations are representative for other tires.

Future work would include performing several measurements with different tires to validate the simulations against. Important parameters, such as camber, vertical load, should be varied to have a wide range of data to validate the simulations against.

The following points are recommendations for future measurements

• Study the effects of camber and how it affects the deformation.

• Varying vertical forces, from moderate to more extreme loads (6000, 8000, 10000 N).

• Different running speeds.

80 5. Discussion and conclusion

• Variation of the inflation pressure (2, 2.4, 3.0 bar)

• Measure both vertical and lateral stiffness of the same tire used for deformation measurements to validate the simulation models (both for standing and rolling tires)

• Measurements of both the sidewall and the tread areas of the tire.

• Measure the tire contour at various inflation pressures and compare with the sim- ulation models at the same pressures.

5.4.3. Improvement of simulation models

Tires are still one of the most difficult components on the vehicle to simulate. The tech- nology has come a long way since the first simple tire models, but still there is no com- plete model that can accurately describe all aspects of tire behaviour.

Further development and improvement of tire models together with increasing com- puter capacity would enable the use of more detailed tire models.

5.4.4. MBS full vehicle simulations

When further investigations and measurements show that one or several of the MBS tire models give good results for the deformation simulations, it would be logical to extend the method to full vehicle simulations of the tire clearance.

A first step would be to use the approach described by Späth [94] to obtain the load cases for the different situations that could be critical with respect to tire clearance. These could then be used as input for the single tire simulations.

The next step would be to integrate the deformation simulation directly in the MBS simulation software, such as Adams/Car. As both the FTire and RMOD-K models can be used in Adams/Car, the deformations could theoretically be co-simulated during the vehicle simulations.

According to Gipser [90], developer of the FTire model, integration of the simulation of tire deformation in Adams/Car is possible. As FTire is included as one of the standard tire models in Adams/Car since version 11, it is possible to replace the FTire solver program in Adams with a modified version. This way the deformations could be co- simulated during the Adams/Car simulations.

81 5. Discussion and conclusion

5.4.5. Universal Tire model

The simulation of the deformations for all the different tire dimensions in use at BMW, would require a tire data set for each tire. It is not possible to have tire data sets so many tires without a lot of work and large costs. For new tire dimensions not found on the market, there does not even exist tires to measure and create data sets from.

A solution to this is the suggestion by Gipser, to use of a so called universal tire data file. This means starting out with a good tire data set that validates well to a real tire and use this as a reference to approximate new tire data from. Preferably is to use data from a closely sized tire of the same type. The FTire software features tools for performing these approximations.

Having measurements of the vertical and lateral stiffness for the tire in question, means that corrections could be made to improve the quality of the approximated data set.

Of course, this does not give the same accuracy as a real parametrized tire data set, but could still be useful for this kind of simulations. This way, the amount of tires to be measured and parametrized would be substantially reduced.

82 6. Summary

6. Summary

The following important key aspects concerning tire deformation and the simulation of these have been discovered during this thesis:

• Tire deformation is the result of vertical and lateral forces acting on the tire struc- ture. The largest deformations occur in the contact patch where these forces are applied.

• The magnitude of the deformations increases with higher lateral forces.

• The deformations can be simulated using different kinds of tire models. In this thesis, both Finite Element and Physical/MBS tire models have been used.

• To be able to compare the deformations graphically, it is important that the mea- sured tire profile (undeformed) matches the profile used by the simulation models.

• FE models offer the best ability to exactly recreate the tire structure, but at the cost of longer simulation times and the difficulty of finding material data.

• MBS/Physical tire models are much simpler in their modelling, but can also be used to simulate the deformations. The use of these models also enables the future possibility of tire clearance simulations with a full vehicle simulation model.

• The effect of the rim can have a influence on the deformations in regions close to the contact patch. MBS tire models do not take the effects of the rim into consider- ation, whereas the FE models can do this.

• The results show that it is possible to simulate the deformations and reach within 7 mm accuracy of the measurements in the regions relevant for tire clearance. The best results are delivered by the RMOD-K 7 model, with FTire giving slightly higher differences.

• Variations between the measured and simulated vertical stiffness of the models have been discovered.

• There is a big potential for further improvements of the tire models, to give an even more detailed description of the tire behaviour.

83 A. Appendix: Results

A. Appendix: Results

This appendix contains detailed data from both simulations and measurements for the the Michelin Pilot Primacy 225/50 R17 tire. It is divided into several sub appendices, each containing specific data.

84 A. Appendix: Results

A.1. Measurement data

This sub appendix contains detailed information on all the measured tire properties from the tire test rig and also drawings of the measured deformations. Comparisons of the deformations at different sectors is presented in a diagram.

85 Lateral force as function of slip angle

Measured data from test rig 6000 α [deg] FY [N] -9 5721 -8 5751 4000 -7 5983 -6 6047 -5 5958 -4 5685 -3 4978 2000 -2 3614 [N]

-1 1858 Y

F 0 -308

1 -2215 0 2 -3874 force 3 -5153 4 -5829 5 -6091 Lateral 6 -6136 -2000 7 -6050 8 -5775 9 -5519 10 -5263 -4000

-6000

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Slip angle α [degrees] Vertical stiffness for three different runs on the test rig, v=50km/h p =2 bar (cold) i 7000

6000

Measurement 1 c =222 N/mm r Measurement 2 c =212 N/mm r 5000 Measurement 3 c =210 N/mm r [N] 4000 force

3000 Vertical

2000

1000

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Vertical displacement [mm] Measured deformations at 000 deg

Undeformed tire

Fz=6000N Fy=-6091N alpha=5deg 0.2 mm Fz=6000N Fy=-5829N alpha=4deg -0.02 mm Fz=6000N Fy=-5153N alpha=3deg -0.07 mm

Fz=6000N Fy=-3874N alpha=2deg -0.32 mm

Fz=6000N Fy=-2215N alpha=1deg -0.77 mm

Fz=6000N Fy=- 308N alpha=0deg -1.54 mm

Measured deformations at 045 deg

Undeformed tire

Fz=6000N Fy=-6091N alpha=5deg 0.57 mm

Fz=6000N Fy=-5829N alpha=4deg 0.41 mm

Fz=6000N Fy=-5153N alpha=3deg 0.11 mm

Fz=6000N Fy=-3874N alpha=2deg -0.23 mm

Fz=6000N Fy=-2215N alpha=1deg -0.76 mm

Fz=6000N Fy=- 308N alpha=0deg -1.65 mm

Scale 1:1 Measured deformations at 090 deg

Fz=6000N Fy= -380N alpha=0deg -1.46 mm Fz=6000N Fy=-2215N alpha=1deg 0.09 mm Fz=6000N Fy=-3874N alpha=2deg 1.56 mm Undeformed tire Fz=6000N Fy=-5153N alpha=3deg 3.14 mm

Fz=6000N Fy=-5829N alpha=4deg 4.23 mm

Fz=6000N Fy=-6091N alpha=5deg 4.71 mm

Measured deformations at 105 deg

Undeformed tire Fz=6000N Fy=-6091N alpha=5deg 7.94 mm Fz=6000N Fy=-5829N alpha=4deg 7.11 mm Fz=6000N Fy=-5153N alpha=3deg 5.19 mm Fz=6000N Fy=-3874N alpha=2deg 2.79 mm Fz=6000N Fy=-2215N alpha=1deg 0.55 mm Fz=6000N Fy=- 308N alpha=0deg -1.54 mm

Scale 1:1 Measured deformations at 120 deg

Fz=6000N Fy=-6091N alpha=5deg 12.39 mm

Fz=6000N Fy=-5829N alpha=4deg 11.13 mm

Fz=6000N Fy=-5153N alpha=3deg 8.69 mm

Fz=6000N Fy=-3874N alpha=2deg 5.08 mm

Fz=6000N Fy=-2215N alpha=1deg 1.54 mm

Fz=6000N Fy=- 308N alpha=0deg -1.41 mm

Undeformed tire

Measured deformations at 135 deg

Undeformed tire

Fz=6000N Fy= -380N alpha=0deg -0.52 mm Fz=6000N Fy=-2215N alpha=1deg 3.86 mm Fz=6000N Fy=-3874N alpha=2deg 8.73 mm Fz=6000N Fy=-5153N alpha=3deg 13.75 mm

Fz=6000N Fy=-5829N alpha=4deg 16.86 mm

Fz=6000N Fy=-6091N alpha=5deg 18.49 mm

Scale 1:1 Measured deformations at 180 deg

Undeformed tire

Fz=6000N Fy= -380N alpha=0deg 7.07 mm Fz=6000N Fy=-2215N alpha=1deg 14.11 mm Fz=6000N Fy=-3874N alpha=2deg 20.64 mm Fz=6000N Fy=-5153N alpha=3deg 25.86 mm Fz=6000N Fy=-5829N alpha=4deg 28.67 mm Fz=6000N Fy=-6091N alpha=5deg 29.69 mm

Measured deformations at 225 deg

Undeformed tire

Fz=6000N Fy=-6091N alpha=5deg 21.75 mm

Fz=6000N Fy=-5829N alpha=4deg 20.93 mm

Fz=6000N Fy=-5153N alpha=3deg 18.2 mm

Fz=6000N Fy=-3874N alpha=2deg 13.18 mm

Fz=6000N Fy=-2215N alpha=1deg 6.28 mm

Fz=6000N Fy= -380N alpha=0deg 0.14 mm

Scale 1:1 Measured deformations at 240 deg

Fz=6000N Fy=-6091N alpha=5deg 15.76 mm Undeformed tire Fz=6000N Fy=-5829N alpha=4deg 14.97 mm Fz=6000N Fy=-5153N alpha=3deg 12.85 mm

Fz=6000N Fy=-3874N alpha=2deg 8.8 mm

Fz=6000N Fy=-2215N alpha=1deg 3.83 mm

Fz=6000N Fy= -380N alpha=0deg -0.88 mm

Measured deformations at 255 deg

Fz=6000N Fy=-6091N alpha=5deg 10.19 mm Undeformed tire Fz=6000N Fy=-5829N alpha=4deg 9.62 mm

Fz=6000N Fy=-5153N alpha=3deg 8.33 mm

Fz=6000N Fy=-3874N alpha=2deg 5.44 mm

Fz=6000N Fy=-2215N alpha=1deg 2.16 mm

Fz=6000N Fy= -308N alpha=0deg 1.32 mm

Scale 1:1 Measured deformations at 270 deg

Undeformed tire

Fz=6000N Fy=-6091N alpha=5deg 6.42 mm Fz=6000N Fy=-5829N alpha=4deg 6.09 mm Fz=6000N Fy=-5153N alpha=3deg 5.24 mm Fz=6000N Fy=-3874N alpha=2deg 3.57 mm Fz=6000N Fy=-2215N alpha=1deg 1.2 mm

Fz=6000N Fy= -380N alpha=0deg -1.69 mm

Measured deformations at 315 deg

Undeformed tire

Fz=6000N Fy=-6091N alpha=5deg 1.66 mm

Fz=6000N Fy=-5829N alpha=4deg 1.48 mm Fz=6000N Fy=-5153N alpha=3deg 1.19 mm Fz=6000N Fy=-3874N alpha=2deg 0.72 mm Fz=6000N Fy=-2215N alpha=1deg -0.26 mm Fz=6000N Fy= -380N alpha=0deg -1.51 mm

Scale 1:1 A. Appendix: Results

A.2. Measured tire contour

This sub appendix contains a drawing of the tire contour for the undeformed and in- flated tire, measured on the TriScan-Tyre measurement equipment [88].

94 24.10.2006 Y[mm] 150

DOT 135

120

105

90

75

60

45

30

15

X[mm] 225-50 R17 7,5J Mi So Pilot Primacy, Reifenverf., Dot 0406 -135 -120 -105 -90 -75 -60 -45 -30 -15 15 30 45 60 75 90 105 120 135

Versuchs-Nr. Reifenverf. Reifengröße 225/50 R17 94W Daten-Nr. 225-50 R17 7,5J Mi So Pilot Primacy, Reifenverf.,Dot 0406

Felge 7.5J x 17 Reifen/DOT-Nr.0406 Profil Pilot Primacy*

Dr. Noll GmbH , GermanyFabrikat Michelin Luftdruck 2,5 Umfang 2069.05 Ø 658.6

Ausführung So konv. Datum 25.07.2006 Breite 241.2 Meßsystementwicklung Bemerkungen Kontur zur Reifenverformungsmessung, Rott Maßstab 1:1 A. Appendix: Results

A.3. Tire contour validation

This sub appendix contains a drawing of the tire contour validation. The geometries of the simulation models were compared and adjusted to correspond to the measured undeformed tire profile.

96 Michelin Pilot Primacy 225/50 R17 94W DOT 0406 Measured 2.5 bar

Comparison of the unloaded inflated tire profile between simulationFTire and 2.5 measurement bar Measurement and simulation conditions were: Fz=0 N Fy=0 N V=0 m/s. P=2.5 bar RMOD-K 2.5 bar 242.15 mm

Scale 1:1 A. Appendix: Results

A.4. Comparison of deformations

The sub appendix contains detailed drawings with comparisons of the deformations for different slip angles and tire sections between measurements and simulations. The comparisons were performed for slip angles 0, 1, and 5 degrees respectively. The sector angles depicted in the drawings refers to the angles described in figure 1.6.

98 Slip angle 0 degrees, Fz=6000N Fy=-308N

000 deg

315 deg

270 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 0 degrees, Fz=6000N Fy=-308N

240 deg

225 deg

180 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 1 degree, Fz=6000N Fy=-2215N

000 deg

045 deg

090 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 1 degree, Fz=6000N Fy=-2215N

105 deg

120 deg

135 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 1 degree, Fz=6000N Fy=-2215N

180 deg

225 deg

240 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 1 degree, Fz=6000N Fy=-2215 N

255 deg

270 deg

315 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 5 degrees, Fz=6000N Fy=-6091N

000 deg

045 deg

090 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 5 degrees, Fz=6000N Fy=-6091N

105 deg

120 deg

135 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 5 degrees, Fz=6000N Fy=-6091N

180 deg

225 deg

240 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm Slip angle 5 degrees, Fz=6000N Fy=-6091N

255 deg

270 deg

315 deg

Undeformed 2.5 bar Measured 2.0 bar Scale 1:2 FTire 2.0 bar RMOD-K 2.0 bar 0 10 20 30 40 50 mm A. Appendix: Results

A.5. Modification of the RMOD-K model

This sub appendix contains information about the modification of the RMOD-K data set for the Michelin tire. As described in the discussion chapter, section 5.2.2, the data set was modified to improve the appearance of the deformations close to the rim flange. A comparison of the vertical stiffness before and after the modification is included as well as detailed drawings of the deformations.

109 Vertical stiffness for the RMOD-K model for different rim node placement 10000

9000

8000

Measured vertical stiffness c =212 N/mm R 7000 RMOD-K (Node close to rim bead) c =220 N/mm R RMOD-K (Node on rim flange) c =259 N/mm R [N]

6000 Z F

5000 force

4000 Vertical

3000

2000

1000

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Vertical displacement d [mm] Z Slip angle 5 degrees, Fz=6000N Fy=-6091N Comparision of different placement for the rim node (RMOD-K).

180 deg

225 deg

240 deg

Undeformed 2.5 bar Scale 1:2 Measured 2.0 bar RMOD-K (node on rim flange) 2.0 bar RMOD-K (node close to bead) 2.0 bar 0 10 20 30 40 50 mm Slip angle 5 degrees, Fz=6000N Fy=-6091N Comparision of different placement of the rim node (RMOD-K).

270 deg

315 deg

360 deg

Undeformed 2.5 bar Scale 1:2 Measured 2.0 bar RMOD-K (node on rim flange) 2.0 bar RMOD-K (node close to bead) 2.0 bar 0 10 20 30 40 50 mm References

References

References are in cited order

[1] The European Tyre and Rim Technical Organisation (2003), ETRTO Standards man- ual. http://www.etrto.org, retrieved on 2006-09-12.

[2] Ulrich, K. T. and Eppinger, S. D. (2004) Product Design and Development. McGraw- Hill, 3rd edition.

[3] Pugh, S. (1991) Total design. Addison-Wesley Publishing Company.

[4] International Organization for Standardization, ISO 9000 Standards. http:// praxiom.com/iso-definition.htm, retrieved on 2006-08-20.

[5] Luleå University of Technology (2006), P2I - Participatory Innovation Process. http: //www.ltu.se/polopoly_fs/1.2143!be82ee7c.pdf, retrieved on 2006-08-24.

[6] Rohrbach, B. (1969) Kreativ nach Regeln - Methode 635, eine neue Technik zum Lösen von Problemen. Absatzwirtschaft, 12, 73–76.

[7] Reilly, E. D., Ralston, A., and Hemmendinger, D. (2000) Encyclopedia of computer science. Nature Pub. Group, London, 4th edition., ISBN 0333778790.

[8] Charlès, B. (2004) The age of the digital vehicle experience. Automotive Engineer- ing International, http://www.sae.org/automag/features/futurelook/12-2004/ 1-112-12-56.pdf, retrieved on 2006-10-15.

[9] Dassault Systemes, CATIA. (http://www.3ds.com), retrieved on 2006-07-10.

[10] Dassault Systemes, History of CATIA. http://www.3ds.com/corporate/ about-us/group-profile/history/, retrieved on 2006-07-10.

[11] Oden, T. (1987) Some historic comments on finite elements. Proceedings of the ACM conference on History of scientific and numeric computation, New York, NY, USA, pp. 125–130, ACM Press, ISBN 0-89791-229-2, http://doi.acm.org/10.1145/41579. 41592.

[12] ABAQUS, Inc (2006) Getting started with ABAQUS. ABAQUS Version 6.6 PDF Doc- umentation.

113 References

[13] Hanley, R. (2000) Impact model. Tire Technology International, http://www. mech-eng.leeds.ac.uk/menrh/publications/tiretech.pdf, retrieved on 2006-08-20.

[14] Dijksterhuis, E.J. et. al. (1955-1966) The Principal Works of Simon Stevin. Swets & Zeitlinger, Amsterdam.

[15] Helden, A. V. and Burr, E., The Galileo Project. http://galileo.rice.edu/index.html, retrieved on 2006-08-06.

[16] Weisstein, E. W. (2006), "Newton, Isaac" Eric Weisstein’s World of Physics. http: //scienceworld.wolfram.com/biography/Newton.html, retrieved on 2006-08-06.

[17] Andrew Motte (1729), The Principia. Translation of Newton’s original version of Principia, online version (http://members.tripod.com/~gravitee/), retrieved on 2006-07-10.

[18] Abraham, R. and Marsden, J. E. (1978) Foundations of Mechanics. Benjamin- Cummins, London, ISBN 0-8053-0102-X.

[19] Moon, F. C. (1998) Applied Dynamics With Applications to Multibody and Mecatronic Systems. Wiley.

[20] Weisstein, E. W., "newton’s method." from mathworld–a wolfram web resource. http://mathworld.wolfram.com/NewtonsMethod.html, retrieved on 2006-09-21.

[21] Bitonti, F., Cooper, D. W., Frayne, D. N., and Hansen, H. H. (1965) A computer- aided linkage analysis system. DAC ’65: Proceedings of the SHARE design automation project, New York, NY, USA, pp. 16.1–16.16, ACM Press, http://doi.acm.org/10. 1145/800266.810769, retrieved on 2006-08-20.

[22] Knappe, L. F. (1965) A computer oriented mechanical design system. DAC ’65: Pro- ceedings of the SHARE design automation project, New York, NY, USA, pp. 18.1–18.13, ACM Press, http://doi.acm.org/10.1145/800266.810771, retrieved on 2006-08-20.

[23] MSC.Software, MSC.Adams. (http://www.mscsoftware.com), retrieved on 2006- 07-10.

[24] Chace, M. A. (1963) Vector analysis of linkages. Journal of Engineering for Industry, 1, 289–297.

[25] Chace, M. A. (1964) Development and Application of Vector Mathematics for kinematic analysis of Three Dimensional Mechanisms. Ph.D. thesis, University of Michigan.

[26] Chace, M. A. (1967) Analysis of time-dependence of multi-freedom mechanical sys- tems in relative coordinates. Journal of Engineering for Industry, 1, 119–125.

114 References

[27] Chace, M. A. (1969) A network-variational basis for generalized computer repre- sentation of multifreedom, constrained, mechanical systems. DAC ’69: Proceedings of the 6th annual conference on Design Automation, New York, NY, USA, pp. 169–178, ACM Press.

[28] Fischer, E. (2001) Adams/Car-AT in the Chassis Development at BMW. Pre- sented at the 16th European Mechanical Dynamics User Conference in Berechtes- gaden, http://www.mscsoftware.com/support/library/conf/adams/euro/2001/ proceedings/papers_pdf/paper_4.pdf, retrieved on 2006-07-10.

[29] Gillespie, T. D. (1992) Fundamentals of vehicle dynamics. Society of Automotive Engi- neers.

[30] Milliken, W. F. and Milliken, D. L. (1995) Race Car Vehicle Dynamics, R-146. SAE International.

[31] Rauck, M. J. B. (1969) Cugnot, 1769 - 1969: der Urahn unseres Autos fuhr vor 200 Jahren. Münchener Zeitungsverlag 1969.

[32] Davis, F. A. and Kirby, R. S. (2000) Engineering in History. Dover Publications, ISBN 0-486-26412-2.

[33] DaimlerChrysler Corporation (2004), History of DaimlerBenz. http://www. daimlerchrysler.co.jp/history/index_e.html, retrieved on 2006-07-10.

[34] Ford Motor Company, History of Ford. http://www.ford.com/en/heritage/ history/default.htm, retrieved on 2006-10-02.

[35] Becker, G., Fromm, H., and Maruhn, H. (1931) Schwingungen in Automobillenkungen. M. Krayn, Technischer Verlag, Berlin.

[36] Meriam, J. L. and Kraige, L. G. (1998) Engineering mechanics, volume 2: DYNAMICS. John Wiley & Sons, Inc, fourth edition.

[37] Crolla, D. (1996) Vehicle dynamics - theory into practice. IMechE, Part D, Journal of Automobile Engineering, volume. 210, pp. 83–94.

[38] Encyclopædia Britannica (2006), The wheel. From Encyclopædia Britannica Online: http://www.britannica.com/eb/article-9076749, retrieved on 2006-07-25.

[39] The Goodyear Tire & Rubber Company, Goodyear historic overview. (http://www. goodyear.com/corporate/history/history_overview.html), retreieved on 2006-07- 10.

[40] General Tire (2004), History of the passenger tire. http://www.generaltire.com/ generator/www/us/en/generaltire/automobile/themes/generaluniversity/ history/tire_history_en.html, retrieved on 2006-07-10.

115 References

[41] Cameron, G. R. (1973), The Indispensable Pneumatic Tyre and its Scottish inventor Robert William Thomson 1822-1873. Published to accompany the Commemorative Exhibition marking the 100th anniversary of Thomson’s death, held in Stonehaven Town Hall.

[42] Dunlop tyres, The history of Dunlop. http://www.dunloptyres.co.uk/dunlop/ history/, retrieved on 2006-08-20.

[43] Pacejka, H. B. (2006) Tyre and vehicle dynamics. Elsevier Butterworth-Heinemann, ISBN 0-7506-5141-5.

[44] Michelin Group (2004), The history of Michelin. http://www.michelin.com, re- trieved on 2006-07-14.

[45] Continental AG (2006), Radial vs bias tire construction. (http://www.conti-online. com/generator/www/us/en/continental/otr/themes/tech_dnloads/hidden/ otr_constr_pdf_en.pdf), retrieved on 2006-07-12.

[46] Michelin Tires (2006), Advantages bias vs radial. (http://www.michelinag.com/ agx/en-US/products/advantages/bias_radial/bias_radial.jsp), retrieved on 2006- 07-12.

[47] SAE J670e (1976) Vehicle Dynamics Terminology . Society of Automotive Engineers, Inc., 400 Commonwealth Drive, Warrendale, PA 15096.

[48] Meriam, J. L. and Kraige, L. G. (1998) Engineering mechanics, volume 1: STATICS. John Wiley & Sons, Inc, fourth edition.

[49] Kummer, H. (1966) Unified theory of rubber and tyre friction. Engineering Research Bulletin B-94, The Pennsylvania State University.

[50] Mäckle, G. and Schirle, T. (2002) Active Tyre Tilt Control: Ein Reifen- Fahrwerksystem zur verbesserten Kraftübertragung zwischen Reifen und Straße. 4. Darmstädter Reifenkolloquium, VDI Fortschritt-Bericht Reihe 12 Nr. 511 VDI Verlag GmbH, Düsselldorf, 2002, 12.

[51] Dirk Vincken (2005) Der Reifen - Haftung. Société de Technologie Michelin, F- Clermont-Ferrand, ISBN 2-06-711659-2.

[52] Rhyne, T. B. (2005) Development of a vertical stiffness relationship for belted radial tires. Tire Science and Technology, 33, 136–155, http://link.aip.org/link/?TIR/33/ 136/1.

[53] Holtschulze, J. (2006) Analyse der Reifenverformungen für eine Identifikation des Reib- werts und weiterer Betriebsgrößen zur Unterstützung von Fahrdynamikregelsystemen. Ph.D. thesis, Institut für Kraftfahrwesen, RWTH Aachen.

116 References

[54] MTS Systems Corporation, Flat-Trac R Tire Test Systems. http://www.mts.com/ stellent/groups/public/documents/library/dev_002227.pdf.

[55] Harty, D. and Blundell, M. (1999) The Multibody Systems Approach to Vehicle Dynam- ics. Elsevier Butterworth-Heinemann, 2nd edition.

[56] Institut für Kraftfahrwesen Aachen, Vom Reifen zum Tyre-Property-File. http:// www.ika.rwth-aachen.de/pdf_eb/gb1-06reifensimulation.pdf, retrieved on 2006- 08-17.

[57] Fiala, E. (1954) Seitenkräfte am rollenden Luftreifen. VDI-Zeitschrift 96, 973.

[58] H. B. Pacejka and I. J. M. Besselink (1997) Magic Formula Tyre model with Transient Properties. Supplement to Vehicle System Dynamics, 27, 234–249.

[59] TNO Automotive (2004), Tyre model for simulation of steady state and transient tyre behaviour. http://www.delft-tyre.com/documents/MF-Tyre.pdf, retrieved on 2006-07-10.

[60] Bakker, E., Pacejka, H. B., and Lidner, L. (1989) A new tire model with an applica- tion in vehicle dynamics studies. Autotechnologies Conference and Exposition, January 1989, Monte-Carlo, Monaco. SAE Paper No. 960120.

[61] Gipser, M. (2001-2006), FTire website. http://www.ftire.com/, retrieved on 2006- 08-15.

[62] Gipser, M. (1998) Reifenmodelle für Komfort- und Schlechtwegsimulationen. 7. Aachener Kolloquium.

[63] Gipser, M. (2006), FTire Flexible Ring Tire Model documentation. http://www.ftire. com/docu/ftire_ft.pdf, retrieved on 2006-09-13.

[64] Gipser, M. (1987) DNS-Tire, ein dynamisches, räumliches nichtlineares Reifenmod- ell. In: Reifen, Fahrwerk, Fahrbahn. VDI Berichte, 650, 115–135.

[65] Gipser, M. (1996) DNS-Tire 3.0 - die Weiterentwicklung eines bewährten struk- turmechanischen Reifenmodells. Darmstädter Reifenkolloquium, VDI-Berichte, 512, p. 52–62.

[66] TNO Automotive (2004), Tyre model for simulation of tyre dynamic behaviour. http://www.delft-tyre.com/documents/MF-Swift.pdf, 2006-07-10.

[67] Oertel, C. and Fandre, A. (1999) Ride Comfort Simulations and Steps Toward Life Time Calculations RMOD-K Tyre Model and ADAMS. International Adams Users Conference - Berlin.

[68] Oertel, C. and Fandre, A. (2006), RMOD-K 7.08 Documentation.

117 References

[69] Kabe, K. and Koishi, M. (2000) Tire cornering simulation using finite element anal- ysis. Journal of Applied Polymer Science, 78, 1566–1572.

[70] Hauke, M. (2001) Tire modeling for misuse situations. Tech. Rep. 1234, Society of Automotive Engineers, SAE Paper 2001-01-0748.

[71] Hauke, M. (2004) Simulation of full vehicle misuse behavior. Tech. Rep. 1234, Soci- ety of Automotive Engineers, SAE Paper 2004-01-0192.

[72] ABAQUS, Inc (2004), An integrated approach for transient rolling of tires. http: //www.abaqus.com/solutions/tb_pdf/TB-03-TRT-1.pdf, retrieved on 2006-07-10.

[73] Mathworks, Inc, MATLAB - The Language of Technical Computing. http://www. matlab.com.

[74] Python Software Foundation, The Python Programming Language. http://www. python.org/, retrieved on 2006-08-07.

[75] Ritchie, D. M., The development of the C Language. http://cm.bell-labs.com/cm/ cs/who/dmr/chist.html, retrieved on 2006-08-23.

[76] Stroustrup, B. (1991) The C++ Programming Language. Addison-Wesley: Reading, Mass, second edition.

[77] IBM (1979), John Backus. Think, the IBM employee magazine, http: //www-03.ibm.com/ibm/history/exhibits/builders/builders_backus.html, retrieved on 2006-09-01.

[78] Boekesch, A. M., Dieckmann, T., and Frey, C. (1991) Measurement and calculation of the tire contour of a rolling wheel. Tech. Rep. 123, VDI, ISBN 3-18-090916-1.

[79] Kieltsch, M. (2000) Full Vehicle Models at VW. North American ADAMS User Confer- ence, pp. 1–10, http://www.mscsoftware.com/support/library/conf/adams/na/ 2000/05_VW_full_veh_models.pdf.

[80] Shiraishi, M. and Miyori, A. (2001), Method of and apparatus for simulating rolling tire. United states patent. Patent No.: US 6,199,026 B1.

[81] Mathers, M., Hibbitt, Karlsson and Sorensen, Inc, and Pirelli Pneumatici Spa (2002) Modeling Tire-Vehicle Interactions using ABAQUS and ADAMS. Tech. Rep. 1234, MSC Software, paper presented at the MSC.ADAMS 2002 North Amer- ican Users Conference. (http://support.mscsoftware.com/kb/results_kb.cfm?S_ ID=1-KB10014), retrieved on 2006-07-11.

[82] Fischer, M. and Kuchler, G. (2005), Vorrichtung und Verfahren zur Ermittlung der Seitenposition von Rädern. German Patent. DE 10 2004 001 250 A1.

118 References

[83] Goslar, M. (2004), Verfahren zur bestimmung von auf einen luftreifen wirkenden kräften. German Patent. DE 103 07 191 A1.

[84] Becherer, T., Oehler, R., and Raste, T. (2000) Der Seitenwandstorsions-Sensor SWT. ATZ Automobiltechnische Zeitschrift 102 (2000) 11.

[85] Gnadler, R., Frey, M., and Unrau, H.-J. (2005) Grundsatzuntersuchung zum quan- titativen Einfluss von Reifenbauform und -ausführung auf die Fahrstabilität von Kraftfahrzeugen . FAT-Schriftenreihe, 192.

[86] Weisstein, E. W., "Normal Distribution." From MathWorld–A Wolfram Web Re- source. http://mathworld.wolfram.com/NormalDistribution.html, retrieved on 2006-10-20.

[87] BMW AG, MessDB measurement no. M-04-150837, E60 550i.

[88] Dr Noll GmbH, TriScan-Tyre Reifenmesssystem. http://www.drnoll.de, retrieved on 2006-10-20.

[89] GOM mbH, ARAMIS measuring system. http://www.gom.com/EN/measuring. systems/aramis/system/system.html, retrieved on 2006-09-03.

[90] Gipser, M. Fachhochschule Esslingen, Fakultät Fahrzeugtechnik, 2006-10-06.

[91] BMW (2006), FTire Parameterization Report. Michelin Pilot Primacy 225/50 R17.

[92] van Oosten, J. J. M., Unrau, H.-J., Riedel, A., and Bakker, E. (1999) Standardization in Tire Modeling and Tire Testing — TYDEX Workgroup, TIME Project. Tire Science and Technology, 27, 188–202.

[93] Holtschulze J., EF-331, BMW Forschungs- und Innovationszentrum, 2006-11-07.

[94] Späth, F. (2006) Entwicklung und Validierung einer ADAMS- Simulationsmethode für den Reifenfreigang. Master’s thesis, Munich University of Applied Sciences.

119 Index

Index

ABAQUS, 20, 61 RFNP, 4 ALK, 5 RGB, 8 RHK, 6 Bias-ply tire, 30 Rohrbach method, 15 Brainstorming, 14 Roll centre, 25 Brainwriting, 14 Simulation in Engineering, 16 CAD, 18 SRHK, 7 CAE, 19 Steady state cornering, 25 Camber, 38 CATIA, 18 Tire and rim designation, 30 CTI Interface, 43 Tire design and construction, 29 Tire envelope, 6 Definition of tire deformation, 10 Tire measurement and testing, 39 Degrees of freedom, 22 Tire models Finite element analysis, 19 Fiala tire model, 41 Flat track test rig, 40 FTire, 43 FETire, 45 Mathematical tire models, 41 Flexible ring tire model, 44 MATLAB, 49 Rigid ring model, 43 Multibody dynamics, 21 Magic Formula, 41 NRGK, 4 MF-Swift, 46 MF-Tyre, 41 PLM, 17 Physical tire models, 42 Product design and development, 12 RMOD-K, 46 Programming languages Flexible belt model, 47 C/C++, 49 Rigid belt model, 46 FORTRAN, 49 Tire parametrization, 41 Python, 49 Tire simulation, 40 Pughs evaluation method, 15 Tire vertical and lateral stiffness, 38 Quantitative method, 15 Validation of tire clearance, 9 Radial tire, 29

120