DEGREE PROJECT, IN LIGHTWEIGHT STRUCTURES , SECOND LEVEL STOCKHOLM, SWEDEN 2015

Light Weight Suspension System for KTH Research Concept Vehicle

DESIGN AND CONSTRUCTION OF A COMPOSITE SUSPENSION SYSTEM WITH FOCUS ON APPLICATION IN KTH RESEARCH CONCEPT VEHICLE WITH ANALYSIS OF FUTURE SOLUTIONS SUITABLE FOR THE AUTOMOTIVE INDUSTRY.

WILHELM JOHANNISSON

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES, AERONAUTICAL AND VEHICLE ENGINEERING

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 1 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Masterexamensarbete inom lättkonstruktioner SD240X

Hjulupphängningssystem i lättkonstruktion för KTH Research Concept Vehicle

Wilhelm Johannisson

900104-5872

Godkänt Examinator Handledare

2017-09-25 Stefan Hallström Magnus Burman

Sammanfattning I detta projekt undersöks konstruktionen av en transversell bladfjäder för användning i en bil, byggd i kompositmaterial. En transversell bladfjäder är en annan lösning för att implementera det som traditionellt är spiralfjäder i bilen hjulupphängning. Istället används en fjäder som fungerar genom balkböjning. Det finns sedan tidigare flera olika lösningar på hur sen sådan bladfjäder kan fungera, däribland lösningar där bladfjädern sträcker sig från sida till sida på bilden och därmed kallas transversell bladfjäder. Denna lösningen har även den extra egenskapen att bladfjädern fungerar som en krängningshämmare för bilen.

Den transversella bladfjädern konstrueras för en forskningsbil på Kungliga Tekniska Högskolan (KTH). Denna bil är ett konceptfordon konstruerat för att efterlikna en liten stadsbil och väger ca. 600 ��. Hjulupphängningen på denna bil är av typen Double Wishbone med spiralfjädrar och dämpare. Hjulupphängningen är konstruerad modulärt och är exakt densamma för fram och bak hjulupphängning, och ursprungliga fästpunkter på bilen hålls intakta. Konstruktionen av den transversella bladfjädern görs för att efterlikna de egenskaper som det ursprungliga systemet för hjulupphängningen.

Analytisk optimering används primärt för att hitta en första lösning, sedan implementeras denna lösning i FEM-programvara för att vidare undersöka dess egenskaper och konstruktion. Detta leder fram till en slutgiltig lösning som uppfyller kravspecifikationerna, varvid en fullskalig transversell bladfjäder byggs och prövas om den uppfyller kravspecifikationerna.

Wilhelm Johannisson 2 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 3 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Degree Project, in Lightweight Structures, Second Level SD240X

Light Weight Suspension System for KTH Research Concept Vehicle

Wilhelm Johannisson

900104-5872

Approved Examiner Supervisor

2017-09-25 Stefan Hallström Magnus Burman

Abstract In this project, the design of a transverse leaf spring for an automotive vehicle is investigated. A transverse leaf spring is a concept for implementing the traditional coil spring for the vehicle, into a spring operating through beam bending. There are different constructions and layouts of said leaf spring developed previously. One solution is where the spring is spanning from one side to the other of the vehicle, making it a transverse leaf spring. This solution has an extra gain; it is also providing an anti-roll bar action to the ride characteristics of the vehicle.

The design of the transverse leaf spring is made for an automotive research vehicle at Royal Institute of Technology (KTH). This vehicle is designed to represent a small city vehicle, weighing approximately 600 ��. The design of the original suspension system is of the type Double Wishbone with push rod and coil springs with damper. The system is modular and exactly the same for the front and rear of the vehicle. Original mounting positions on the vehicle are to be kept intact. The design of the transverse leaf spring is made in order to mimic the exact characteristics of the original suspension system.

First analytical optimizations are made in order to find an initial solution. This design is then implemented in FEM-software in order to further investigate the characteristics and design. A final design is found that is fulfilling the requirements and a full scale version of the transverse leaf spring is built and examined with regards to its fulfilment of requirements.

Wilhelm Johannisson 4 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 5 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Foreword I first and foremost would like to thank my advisor Dr. Magnus Burman for the opportunity to do this project and all discussions regarding design and construction. It has been very exciting working with this topic that has provided me with many stimulating challenges in a broad variety of fields, including automotive suspension system characteristics, fiber composites and viscoelastic materials.

I would also like to dedicate my gratitude towards Dr. Mikael Nybacka for the assistance on automotive suspension systems, and Dr. Per Wennhage and Prof. Dan Zenkert for thoughts on composites and sandwich constructions.

Additionally, a thank goes to my family with interesting discussions and thoughts on the requirements for a composite suspension system.

Wilhelm Johannisson

October 14th, Royal Institute of Technology, Stockholm, Sweden

Nomenclature Mathematical and Engineering symbols are described in Table 1 and abbreviations are described in Table 2.

Table 1: Notations

Symbol Description � Young’s modulus (��) � Width (��) ℎ!"# Height of end section (��) �!"# Flange thickness of end section (��) �!"# Web thickness of end section (��) ℎ!"##$% Height of middle section (��) �!"##$% Flange thickness of middle section (��) �!"##$% Web thickness of middle section (��) �!"##$! Rubber thickness (��) �!"# Mounting positions outer diameter �!" Mounting positions inner diameter � Moment of inertia � Cross section height �!"# Deflection due to bending of end section �!"##$% Deflection due to bending of middle section � Applied load � Beam length � Spring constant �!"#! !!!!" Two-wheel spring constant �!"# !!!!" One-wheel spring constant � Anti-roll bar addition

Wilhelm Johannisson 6 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Table 2: Abbreviations

Abbreviation Description KTH Royal Institute of Technology, Stockholm Sweden CAD Computer Aided Design FEM Finite Element Method RCV Research Concept Vehicle FEM Finite Element Method TCO Total Cost of Ownership

The expression transverse leaf spring represents the part that is designed and manufactured in this report. Depending on the academic viewpoint, the transverse leaf spring can represent solid mechanics beam sections, a structural mechanics sandwich construction or vehicle dynamics suspension member, spring, damper and anti-roll bar.

The expression original suspension system represents the parts, mounted in KTH- RCV as designed from the start. The original suspension system is mounted in KTH- RCV in order to limit the movement of the wheels in order to travel safely as well as the spring and damper in order to travel comfortably.

Wilhelm Johannisson 7 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

1 Table of Contents Sammanfattning ...... 2 Abstract ...... 4 Foreword ...... 6 Nomenclature ...... 6 1 Table of Contents ...... 8 2 Introduction ...... 12 2.1 Background ...... 12 2.2 Objective ...... 12 2.3 Delimitations ...... 13 2.4 Method ...... 13 2.5 Inspiration ...... 14 3 Frame of Reference ...... 16 3.1 Suspension Systems ...... 16 3.2 Anti-roll bar ...... 16 3.3 Damping ...... 17 3.4 Current Composite Suspension Systems ...... 17 3.4.1 Suspension Components in Composites ...... 17 3.4.2 Corvette Composite Leaf Spring ...... 18 3.4.3 SÅNÄTT Composite Leaf Spring ...... 19 3.4.4 Transverse composite leaf spring – Anti-roll bar characteristics ...... 20 3.5 Viscoelastic Material ...... 20 4 Requirements and Limitations ...... 22 5 Method ...... 28 5.1 Anti-roll bar for KTH-RCV ...... 28 5.2 Damping for KTH-RCV ...... 28 5.2.1 Viscous Damping in KTH-RCV ...... 29 5.2.2 Generalization for Viscoelastic Materials ...... 29 5.3 Testing of Viscoelastic Materials ...... 30 5.3.1 Testing of Tensile Properties ...... 30 5.3.2 Testing of Shear Properties ...... 31 5.4 Design ...... 32 5.4.1 Material Selection ...... 32 5.4.2 Analytical Optimization ...... 32 5.4.3 FEM Compared to Analytical Optimization ...... 34 5.4.4 FEM Optimization ...... 34 5.5 Manufacturing ...... 37 5.6 Laboratory Testing ...... 38 6 Results ...... 40

Wilhelm Johannisson 8 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.1 Testing of Viscoelastic Materials ...... 40 6.1.1 Soft Rubber (Para Rubber) ...... 41 6.1.2 Hard Rubber ...... 41 6.1.3 Viscoelastic Foam ...... 42 6.2 Design ...... 42 6.2.1 Composite Material Selection ...... 42 6.2.2 Analytical Optimization ...... 43 6.2.3 FEM Compared to Analytical Optimization ...... 43 6.2.4 FEM Optimization ...... 44 6.3 Manufacturing ...... 47 6.4 Laboratory Testing ...... 47 6.5 Costs ...... 49 6.5.1 Cost of Transverse Leaf Spring ...... 49 6.5.2 Cost of Current System ...... 50 7 Discussion ...... 52 7.1 Testing of Viscoelastic Materials ...... 52 7.1.1 Soft Rubber (Para Rubber) ...... 52 7.1.2 Hard Rubber ...... 52 7.1.3 Viscoelastic Foam ...... 53 7.2 Viscoelastic Materials Overall ...... 53 7.3 Design ...... 53 7.3.1 Composite Material Selection ...... 53 7.3.2 Analytical Optimization ...... 53 7.3.3 FEM Compared to Analytical Optimization ...... 54 7.3.4 FEM Optimization ...... 54 7.4 Manufacturing ...... 55 7.5 Laboratory Testing ...... 55 7.6 Costs ...... 55 7.6.1 Total Cost of Ownership (TCO) ...... 56 7.6.2 Selling factor ...... 56 8 Analysis of Requirements and Limitations ...... 58 9 Conclusions ...... 60 10 Recommendations and Future Work ...... 62 10.1 Viscoelastic Materials ...... 62 11 Postscript ...... 64 12 Bibliography ...... 66 13 Appendix ...... 70 13.1 Conventional Suspension Systems ...... 70 13.1.1 Live- and Dead Axle ...... 70 13.1.2 Double Wishbones Suspension ...... 71 13.1.3 MacPherson Strut Suspension ...... 71

Wilhelm Johannisson 9 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13.1.4 Torsion Beam Suspension ...... 72 13.2 Analytical study of Anti-roll bar characteristics ...... 73 13.2.1 Beam loaded in one free end – representing one-wheel bump ...... 73 13.2.2 Beam loaded in both free ends – representing two-wheel bump ...... 74 13.2.3 Anti-roll bar characteristics ...... 74 13.3 Material Testing Results ...... 75 13.3.1 Soft Rubber (Para Rubber) ...... 75 13.3.2 Hard Rubber ...... 76 13.3.3 Viscoelastic Foam ...... 76 13.3.4 Shear Relaxation ...... 76

Wilhelm Johannisson 10 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 11 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

2 Introduction The project investigate the possibility of designing a spring, damper and suspension system for the Royal Institute of Technology Research Concept Vehicle (KTH-RCV). The project also study the possibility of future use of the system in vehicles for the general public and automotive industry.

2.1 Background The use of composites in aircrafts has today become a common occurrence in everything from personal helicopters like KC 518 Adventourer (CH, 2012) to massive personal airliners like the Airbus A380 (Marks, 2005). The automotive industry however has not yet seen the transformation of the industry towards composites in spite of anticipation of the change to come, dating back to the late 1970s (Red, 2013).

Nevertheless, the demand has never been higher for automotive composite technology than today with target emission levels for 2025 at about half of what is permitted today (Red [2], 2013). The number one solution to minimizing fuel consumption, thus emissions, for a vehicle is to minimize the weight. Composite technology can be used in virtually any part of a vehicle design, from chassis, suspension, drivetrain, breaks etc. to cosmetic pieces all over car interior and exterior, as well as wheels, as seen on Koenigsegg Agera R (Koenigsegg, 2012). With this in mind in addition to the recently introduced BMW i3 with a body of carbon- fiber reinforced plastic the transformation of the industry is right at the doorstep.

2.2 Objective The objective in this project is to design, construct and build a working composite spring prototype, including damper and suspension system for KTH-RCV, in this report called transverse leaf spring. Another aim of the project is to use knowledge gained from constructing the system for KTH-RCV, to predict future usage of composite suspension systems in mass production for the automotive industry.

KTH-RCV is designed at KTH and is used as a testing and research platform; hence the vehicle is not specifically designed for use in mass production or for the consumer market.

The vehicle is to be seen as a small city car, in the same class as Smart ForTwo, BMW i3 etc. KTH-RCV is powered by four electric motors mounted at the end of each suspension configuration and powers each wheel individually. A photo of the KTH- RCV can be seen in Figure 1.

Wilhelm Johannisson 12 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 1: Picture of KTH-RCV 2.3 Delimitations The project is limited in time by the extent of a Master of Science Thesis (Degree Project) that has the extent of 30 University credits, corresponding to 20 weeks.

Further requirements and limitations to the design of the transverse leaf spring are discussed in the section 4 Requirements and Limitations.

2.4 Method The method consists of constructing, initially multiple, solutions for solving the design and construction of a composite suspension system. The solutions are analysed and evaluated using definitions of the system from section Requirements and Limitations. Analytical and numerical (FEM) calculations are made in order to verify that the solutions comply and practical considerations are made as to what is possible to perform for KTH-RCV. For design data, both tabular material characteristics and tested material characteristics are used in order to build robustness of assumptions. Furthermore, the project is investigating in future possibilities of the found solutions for use in automotive industry, as a substitute or addition to conventional solutions; by literature studies and knowledge gained from KTH-RCV.

Wilhelm Johannisson 13 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

2.5 Inspiration A quote by famous professional racecar driver, engineer, and author Carroll Smith (1932–2003), from his book “Engineer to Win” (Smith, 1985), is chosen to finish off this section and give inspiration for the project.

“If I were involved in the design of a new passenger vehicle, however, I would give serious consideration to the use of a transverse composite single leaf spring of unidirectional glass or carbon filament in an epoxy matrix. This would be the lightest practical spring configuration and, although space constraints would seem to limit its use in racing, it should be perfectly feasible on road-going vehicles, from large trucks to small commuter cars. (Since I wrote this paragraph the new-generation Corvette has come out with just such a spring to control its independent suspension systems-at both end of the car.)” (Smith, 1985)

Wilhelm Johannisson 14 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 15 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

3 Frame of Reference

3.1 Suspension Systems As the focus of this project is on the suspension system of a vehicle it is necessary to familiarize with the different suspension systems present in vehicles today. There are numerous different solutions for making the ride confortable and safe, some of the most common are explained in Appendix section 13.1 Conventional Suspension Systems.

KTH-RCV is currently using a double wishbone suspension system, modified with the use of push-rod spring and damper connection, explained in detail in section 13.1.2 Double Wishbones Suspension.

3.2 Anti-roll bar One important part of a vehicle suspension is the usage of an Anti-roll bar. The Anti- roll bar prohibits the natural roll and swaying of the car as it corners. The Anti-roll bar is traditionally a metal tube mounted across the car connecting the left and right suspension parts, Figure 2. It works so that if one side of the suspension is compressed, the bar transfers the load to the other side of the vehicle essentially making the compressed suspension side stiffer and prohibit roll. If both wheels are compressed at the same time no addition in stiffness will be present from the Anti- roll bar (Longhurst C. J., 2013).

Figure 2: Schematic representation of an Anti-roll bar, reproduced from (Longhurst C. J., 2013)

Wilhelm Johannisson 16 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

3.3 Damping Another part of vehicle suspension is the part of the damping. The damping is used to stop the undamped swinging oscillation of the vehicle by controlling speed and resistance of the suspension movement. The damping can be adjusted by changing the fluid viscosity and damper geometry but also outer characteristics like the spring rate. The mechanical part that is used for the damping is commonly called a Shock Absorber and consists of a damping fluid and plate that move through the fluid, a conceptual layout of a damper is shown in Figure 3.

Figure 3: Conceptual layout of a simple damper, reproduced from (Calver, 2001).

3.4 Current Composite Suspension Systems On the market and in research today are some suspension systems that use composite materials as a replacement or contribution to conventional coils springs.

3.4.1 Suspension Components in Composites Different suspension components can be produced out of composites, mainly in order to reduce the mass of the vehicle. Especially prominent in motorsport such as Formula 1 for weight reduction (Preston, 2010) where most of the suspension system components are made out of composites. As far as the author’s knowledge goes and what sources could be found, no composite components has been used for load carrying suspension components in the public automotive industry. However, different suspension systems incorporating composite spring technologies are in development and use. Some solutions incorporate a composite substitution of the conventional coil spring (Composite World, 2014). Other incorporate different solutions for a composite leaf spring as further presented below.

Wilhelm Johannisson 17 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

3.4.2 Corvette Composite Leaf Spring Starting from 1963 GM’s Chevrolet Corvette has used transverse Composite Leaf Springs for, initially rear, and later both front and rear suspension, a composite transverse leaf spring systems can be found in the Volvo 960 Wagon. Some Triumph models and the Ford Model T instead use transverse leaf springs made from steel. The suspension system consists of a conventional Double Wishbone Suspension stabilizing the wheel movement. In the suspension the conventional coil spring is replaced by a transverse glass fiber composite leaf spring. The spring is mounted such that it connects the left and right suspension systems, separate dampers are still used. A presentation of the Composite Leaf Spring system can be seen in Figure 4.

The setup has some disadvantages; being for instance a somewhat expensive option. The composite is also in contacts with oils and heat from engine and transmission which could weaken and damage the spring. Furthermore, composites have a huge amount of design variables adding to the complexity of designing and adjusting the spring, especially in high performance and racing situations. When wanting to change spring characteristics the spring has to be replaced, leading to further cost. This has led to Chevrolet Corvette racing teams replace the composite spring to a coil-over system. Mostly due to ease of adjustment but also due to previous experience from coil springs, as well as some racing events don’t allow for the use of composite leaf springs.

A Composite Leaf Spring has many advantages, first of all the system is significantly lighter with weight reduction of almost 70 % (Longhurst C. , 2013). The reduction in weight does not only lower the overall weight of the vehicle, but also lower the unsprung mass of the suspension system resulting in a more responsive ride. Furthermore, the composite in itself is highly corrosion resistant and the durability is unprecedented. Meaning that the spring does not wear out like conventional coil springs; laboratory tests have been made that show composite leaf springs to outlive 8 million cycles, from maximum to minimum deflection, whereas the steel coil counterpart only made 75,000 cycles (Car Bibles, 2013). Continuingly, the packaging of the spring allow for a lower center of gravity as well as being space conservative allowing for a smaller and lower cars. Another great benefit of the transverse spring setup is the fact that in cornering, when the outer wheel wants to compress the suspension and the inner wheel wants to expand the suspension. The action from the transverse spring somewhat prohibit the action leading to the same action as an Anti- Roll (Sway) Bar would exhibit. The transverse spring does not necessarily take up all these roll forces but will limit the necessary size of the Anti-Roll Bar for a conventional system, leading to further weight reductions.

Wilhelm Johannisson 18 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 4: Composite Leaf Spring as in Chevrolet Corvette, reproduced from (Longhurst C. , 2013). 3.4.3 SÅNÄTT Composite Leaf Spring The SÅNÄTT Composite Leaf Spring suspension is a result of industry and research collaboration in Sweden. The project set out to design an integration of a multi- functional suspension system for a personal road-going vehicle. The aim was to implement functionalities to the setup while still keeping the overall performance characteristics such as; handing, steering, comfort, noise and vibrations. The safety was also a major design factor. Furthermore the cost of the final part, in terms of materials used, but also the manufacturing and assembly of the system was of great interest.

The resulting design focuses on the front axle of the vehicle and consists of a transverse leaf spring that overcomes the need for coil springs, lower wishbone and anti-roll bar. The saved weight for the spring system is 10 ��, giving a 50 % reduction in weight. The unit has a higher unit cost but add value in handling and safety. The final design can be seen in Figure 5.

Figure 5: SÅNÄTT suspension system, adapted from (FFI, 2013).

Wilhelm Johannisson 19 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

3.4.4 Transverse composite leaf spring – Anti-roll bar characteristics A transverse composite leaf spring setup, such as seen in the Corvette Composite Leaf Spring or the SÅNÄTT Composite Leaf Spring does inherently have characteristics that represent those of a conventional Anti-roll bar as described above. This is due to the construction and mounting of the spring with loading in one edge and mounted on two points in the middle, calculated using solid mechanics, detailed calculations are presented in Appendix 13.2: Analytical study of Anti-roll bar characteristics. It is found that the maximum theoretical anti-roll bar addition is 33 % (and the minimum is zero).

3.5 Viscoelastic Material The viscous damping of a material is governed by many parameters; usually the frequency of loading (where the rate of loading is the governing factor) and the temperature dependence are the most important. Other parameters are the strain rate, static pre-load and long-time effects, including creep, relaxation and aging. Plotting the strain of a viscous material with respect to the applied stress for cyclic motion the resulting shape will be elliptic (Macioce, 2002). The elliptic shape is called a hysteresis loop and looks like in Figure 6. This loop relates to the energy dissipation in the material.

Figure 6: Hysteresis loop for Viscoelastic Material, reproduced from (Macioce, 2002).

Wilhelm Johannisson 20 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 21 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

4 Requirements and Limitations Other than the overall limitations defined in the Introduction, the requirements and limitations for designing a suspension system are investigated individually below, for both the application on KTH-RCV and for use in the automotive industry. The word “shall” is compulsory and the word “may” is optional but requested.

1. Conditions 1.1. Loads 1.1.1. Static loads – The static design loads for the suspension system for KTH-RCV is defined as 2500 � in each of the �, �, �-directions with the forces applied to the wheel. Where � is defined forwards in the car, � is defined out from the vehicle and � straight up. For a system in the automotive industry the static design loading condition might differ from the one used in KTH-RCV, other loading conditions than for KTH- RCV will not be investigated. 1.1.2. Vehicle mass – The dry mass of KTH-RCV is 600kg where the unsprung mass is 25 �� per wheel, resulting in a sprung mass of 500kg. A vehicle for the automotive industry is most likely to have a similar or higher mass, no other vehicle masses will be investigated. 1.1.3. Dynamic loads – The durability due to dynamic loads on the system will not be investigated instead the static loading will be used with safety factors. In the automotive industry the dynamic load conditions are of high interest and should be investigated. 1.2. Suspension characteristics 1.2.1. Geometric similarity – The geometric similarity in the suspension of KTH-RCV is 0.475. 1.2.2. Spring constant – The spring for KTH-RCV gives the vehicle suspension stiffness at the wheel to 20 ! for the front suspension and 35 ! for !! !! the rear suspension. 1.2.3. Damping constants – The damper curve for KTH-RCV is not linear and thus no specific damper constant can be obtained, see 5.2 Damping for KTH-RCV. An approximate value is calculated to 6.67 !" for the !! damper, thus giving with the geometric similarity an approximate suspension damping coefficient of 3.17 !" . Furthermore, with the use !! of the vehicle mass and the undamped natural frequency the damping ratio for KTH-RCV is 0.8. 1.2.4. Anti-roll characteristics – The desired anti-roll bar characteristics for KTH-RCV are defined in section 5.1 Anti-roll bar for KTH-RCV. The desired anti-roll bar addition for the front wheels is determined to be 20 % and for the rear wheel 0 %.

Wilhelm Johannisson 22 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

1.3. Environmental durability, a suspension system for KTH-RCV may comply with these requirements. In this project these requirement are investigated by literature studies. 1.3.1. Temperature – A system for the automotive industry shall carry out its lifetime in temperatures between −55 ℃ and 120 ℃, material testing and literature studies are required for verification. 1.3.2. Humidity – A system for the automotive industry shall carry out its lifetime in relative humidity between 0% and 100%, material testing and literature studies are required for verification. 1.3.3. Water – A system for the automotive industry shall withstand water according to ISO 11997 testing, material testing and literature studies are required for verification. 1.3.4. Salt-water – A system for the automotive industry shall withstand salt water according to ISO 11997 testing, material testing and literature studies are required for verification. 1.3.5. Oils – A system for the automotive industry shall withstand spray of oil for the whole extent of its lifetime, material testing and literature studies are required for verification. 1.3.6. Glycol – A system for the automotive industry shall withstand spray of glycol for the whole extent of its lifetime, material testing and literature studies are required for verification. 1.3.7. Fuels (Gasoline, Diesel, Ethanol) – A system for the automotive industry shall withstand spray of fuels for the whole extent of its lifetime, material testing and literature studies are required for verification. 1.3.8. Durability to hits, sand spray and stone chip – A system for the automotive industry shall withstand hits, sand spray and stone chip for a full inspection cycle and the damages shall be classified as smaller types of damages (see paragraph 3), material testing and literature studies are required for verification. 1.3.9. UV radiation – A system for the automotive industry shall withstand UV radiation according to ISO 4892 for its lifetime, material testing and literature studies are required for verification. 1.3.10. Corrosion – The constituent parts of the suspension system shall not, within itself or with other parts of the vehicle, cause galvanic corrosion leading to lowering of mechanical properties or in other way limit its lifetime.

Wilhelm Johannisson 23 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

1.4. Design space – The design space is defined only by and for the overall size of KTH-RCV as well as the limitation in the use of current motors, breaks and steering arrangements. 1.5. Suspension mass – The spring and suspension system shall not have a higher mass than the current system mounted in KTH-RCV. The masses are approximately as follows: Lower wishbone 1 ��, Push-rod + rocker 0.5 �� and Spring + damper combination 1 ��, per wheel. The limitation on weight for the automotive industry will be significantly different. Still, connections can be drawn from and to KTH-RCV, but are not explicitly applicable for the automotive industry. 1.6. Lifetime – The lifetime for a suspension system designed for the automotive industry shall be approximately 15 years or 320,000 �� which is corresponding to average lifetime and longevity of a normal production vehicle in 2012, calculated from car longevity of about 320,000 �� (Ford, 2012) and average car travel by 24,000 �� per year (EPA), material testing and literature studies are required for verification. However KTH-RCV, being designed as a concept vehicle, it is not designed for long time service. Thus the lifetime requirements may apply to the suspension system, literature studies are performed in this project for verification. 2. Characteristics 2.1. Function – A suspension system for both KTH-RCV and the automotive industry shall function similar to an original suspension system for KTH-RCV or conventional a suspension system, meaning that it shall restrict as well as enable the movement of the wheels in ways for the vehicle to travel safely and comfortably. 2.2. Mounting – A new design of spring and suspension system shall be possible to mount on KTH-RCV with simple mechanical tools; adhesive bonding is not allowed for final mounting to KTH-RCV. The suspension system mounting points for KTH-RCV, not being originally designed for utilizing the design characteristics of a composite suspension system, may limit the design of such. A suspension system designed for the automotive industry, originally for use of composite materials, may provide design possibilities that are not applicable for KTH-RCV. 2.3. Driving characteristics – The driving characteristics for KTH-RCV and for the automotive industry with an old or a new suspension system shall not be significantly different; a new suspension system shall mimic those of the old. However some differences may be present but shall be limited to either improvements to driving characteristics, as defined in (Jerrelind, 2013), or characteristics that are not changing the overall behavior of what is currently popularly defined as a road vehicle. 2.4. Spring characteristics – The spring-action of a suspension system shall take up proportional forces from bump, roll, breaking and acceleration of the vehicle and may be of non-linear type, for both KTH-RCV and for the automotive industry.

Wilhelm Johannisson 24 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

2.5. Damping characteristics – The damping-action of a suspension system shall be designed to take up kinetic forces from bump, roll, breaking and acceleration of the vehicle and may be of non-linear type, for both KTH-RCV and for the automotive industry. 2.6. Active spring and/or damping – Both, or any, of the spring-action and damping-action of a suspension system may be of active type; the spring and/or damping characteristics may be changed with optional frequency independent of movement or not, both for KTH-RCV and for the automotive industry. 3. Serviceability 3.1. Repair – A suspension system in the automotive industry shall be possible to repair from smaller types of damages by a licensed technician. The system may require factory-repairs and/or exchange of parts for larger damages. However, the use of KTH-RCV will be limited to education and research, thus canceling the explicit need for reparability as if in the automotive industry, but the system may be repairable. 3.2. In service inspection – A system for either KTH-RCV or the automotive industry shall not exceed a frequency of inspections corresponding to common service intervals found in new vehicles, chosen to one year or 15000 km whichever occurs first (Toyota, 2007). The regular inspections shall be performed with visual and/or physical inspection of the part. Furthermore, upon concern for damages, inspection for the automotive industry may require advanced tools (such as X-ray or ultrasonic), this requirement does not apply for KTH-RCV due to economy and time constraints. 4. Safety 4.1. Characteristics upon failure in service – A suspension system for the automotive industry shall not cause dangerous changes in driving characteristics upon catastrophic structural damage. Since KTH-RCV is a research vehicle not designed for the public this requirement is not applicable. 4.2. Composite shattering upon failure – A suspension system for either KTH-RCV or the automotive industry shall not cause parts of the system the break lose upon catastrophic failure.

5. Environmental impact

Wilhelm Johannisson 25 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.1. Direct impact from the product – A suspension system for either KTH-RCV or the automotive industry shall not have any environmental impact, e.g. being poisonous and/or cause damage to its intimate natural surroundings when in service. 5.2. Impact from manufacturing – The manufacturing of a suspension system for KTH-RCV or the automotive industry shall not cause any environmental damages, the manufacturing may cause toxins but those shall be possible to properly take care of at the manufacturing site. 5.3. Recycling and annihilation – For both KTH-RCV and the automotive industry the aim when designing and manufacturing a suspension system shall be to use materials that can be recycled. However with the current inherent difficulties of recycling composite materials (Rush, 2007); constituents of a system may be annihilated upon its end of service. 6. Economy 6.1. Part cost – The material and manufacturing cost of a composite suspension system shall not be more expensive than 150 % of a conventional suspension system, for both KTH-RCV and the automotive industry. 6.2. Total cost of ownership (TCO) – The TCO for a composite suspension system shall be less than that of a conventional suspension system, for both KTH- RCV and the automotive industry. 6.3. Selling factor – Specifically carbon fiber composite traditionally had a very high selling factor being a “future, high class and extreme” material. Initially this labeling stayed as traditional, however with composites introduced further and further to the general public the material is losing its glamour. Selling to the common people the selling factor can no longer be pure “extreme”; instead composites shall be used as a selling factor by minimizing fuel consumption, environmental impact and TCO, for both KTH-RCV and the automotive industry. 7. Production 7.1. Safety – Any human interaction to the manufacturing or assembly of a suspension system shall be possible to perform safely by licensed technicians according to current regulations and with appropriate protection, for both KTH-RCV and the automotive industry. 7.2. Production volume – A suspension system specifically for KTH-RCV shall be designed and manufactured for production of one unit only, however with scalability in mind (see paragraph 7.3). The overall goal for production volume of a carbon fiber composite car is around 40,000 vehicles per year (Red, 2013) and thus the production volume of a composite suspension system for the automotive industry shall be assumed similar.

Wilhelm Johannisson 26 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

7.3. Scalability – A suspension system in its final form for mounting on KTH-RCV may not directly be possible to scale for the thought after production volume. However the system shall be designed with scalability of the final system in mind. A composite suspension system for the automotive industry shall be possible to scale to the desired production volume. 7.4. Automation – A suspension system in its final form for mounting on KTH- RCV may not be designed for automation in production, however the requirement of scalability (paragraph 7.3) may require the possibility for automation. For the automotive industry, with the paragraph 7.3 in mind, a composite suspension system shall be designed for production by automation with limited human interaction. 7.5. Inspection at manufacturing – A suspension system shall be possible to be inspected for manufacturing errors and flaws by means of visual and/or physical inspection. This concerns both the KTH-RCV and any possible industrial process. Furthermore, upon concern for manufacturing errors, the inspection may require advanced tools (such as X-ray or ultrasonic), this requirement does not apply for KTH-RCV due to economic and time constraints.

Wilhelm Johannisson 27 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5 Method

5.1 Anti-roll bar for KTH-RCV KTH-RCV does not incorporate an Anti-roll bar in its suspension, instead the suspension is tweaked slightly stiffer to prohibit roll of the car. The addition of an Anti-roll bar for KTH-RCV is simulated to assist the overall characteristics of the handling of the car. An increase in one-wheel compression stiffness of 16.5 % will have very positive results; with up to 1.5° less in roll on steering (Figure 7) and a much more balanced car. If the Anti-roll bar can have an increased stiffness, >16.5 %, the suspension characteristics will improve even further. For the rear suspension no anti-roll bar is needed (Nybacka, ADAMS study on Anti-roll bar for KTH-RCV, 2014).

Figure 7: Roll angle during steering impulse, solid (red) line represents KTH-RCV with anti-roll bar attached and dotted (blue) line KTH-RCV without Anti-roll bar attached, reproduced from (Nybacka, ADAMS study on Anti-roll bar for KTH-RCV, 2014). The addition of an anti-roll bar would greatly improve the driving characteristics of KTH-RCV. As transverse leaf springs inherently have anti-roll characteristics, as discussed in 3.4.4 Transverse composite leaf spring – Anti-roll bar characteristics, it is natural to incorporate the anti-roll bar behavior in the design. A target of 20 % anti-roll bar addition is chosen for the front suspension and 0 % anti-roll bar addition for the rear.

5.2 Damping for KTH-RCV The new damping characteristics should mimic the damping behavior of the original suspension system as closely as possible. The damper characteristics for the damper originally mounted on KTH-RCV can be seen in Figure 8.

Wilhelm Johannisson 2 8 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 8: Damper curve for the original damper on KTH-RCV, reproduced from (Nybacka, ADAMS study on Anti-roll bar for KTH- RCV, 2014). 5.2.1 Viscous Damping in KTH-RCV The temperature dependence for current automotive dampers is negligable .Therefore the temperature dependence of the viscous damping of materials to be used in this studie will not be investigated. However, the time effects are very important for future designs of dampers with polymeric materials. The creep, relaxation and aging should be investigated but due to time constraints are not included in this project. In this project the frequency of loading (and accompanying strain rate) will be investigated in order to comply with desired damping characteristics for KTH-RCV. Also, the possible pre-load characteristics of the material will be investigated.

5.2.2 Generalization for Viscoelastic Materials The behavior of the original damper on KTH-RCV is linearized for simplicity in the calculations, at:

0 �/� the damper addition is naturally zero and the complete spring and damper system has the spring constant of the spring

0.025 �/� (representing low wheel rate damping) the addition from the damper would be 4.2 �/�� given a spring deflection of 50 ��, providing the system of spring and linearized damper a combined spring constant of 24.2 �/��

0.25 �/� (representing high wheel rate damping) the damping addition would be 73.7 �/�� giving the system a linearized spring constant of 93.7 �/��.

For a more correct representation of viscoelastic materials it would be recommended to use a Prony Series representation as described in (Chen, 2000).

Wilhelm Johannisson 29 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.3 Testing of Viscoelastic Materials Three different viscoelastic materials are tested for tensile and shear viscoelastic characteristics. The main objective of the testing is to find the elastic (tensile and shear) moduli of the materials to be used in FEM-simulations. The strain (and stress) at failure is not of primary interest. The tensile testing machine used is an Instron 5567 with a 5 �� load cell.

The tested materials are:

• Soft rubber with high content of natural rubber (Para rubber) • Hard natural rubber • Viscoelastic (Slow Recovery SR 60) foam, SR 60 characteristics are not available online, instead see (SR 65 Medium).

Measurements are performed at three different strain rates, with machine speeds !! !! !! 3 !"#, 250 !"# and 500 !"#, to find viscous characteristics for the individual materials. !! Higher velocity testing (5000 !"#) is performed in shear for hard rubber in order to further examine its characteristics, these tests where performed on a hydraulic testing machine (Schenck Hydropuls PSA) in order to reach the higher velocity.

The viscoelastic characteristic of the viscoelastic foam originate from air being forced to move through the semi-closed cells of the material and rubber has inherently viscoelastic behavior due to conformal changes in the polymer entanglements and backbone responding to applied force (Roland, 2011).

There are some difficulties associated with testing soft materials, the viscoelastic foam for instance is easily deformed and then stay deformed for a long time. Therefore before measuring the dimensions of the test specimens they are placed to rest prior to any measurement. Geometric measurements are performed using a vernier caliper. Furthermore, the soft rubber is significantly difficult to cut; band saw or knife do not work (foam and hard rubber are cut with high accuracy with a band saw), instead scissors are used providing an acceptable cut but with some roughness.

5.3.1 Testing of Tensile Properties The test consists of the material being cut into test specimen and mounted in gripping-handles. The specimen is then loaded in tensile direction while measuring the load and displacement. Knowing the dimensions of the test specimen, the material elastic (tensile) modulus can be calculated.

The approximate thickness of the test specimen is 8 �� and the width varies between 15 �� and 20 �� depending on tested material, the length of the test specimens is approximately 200 �� and the effective length of the tested specimen is measured to calculate strain. All test specimen are individually measured by a digital vernier caliper to the second decimal [��] for width, thickness and length at three separate

Wilhelm Johannisson 30 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures positions, the average value for each specimen is used to calculate the specimen area. The test specimens are conditioned at 23 ℃ for at least 16 ℎ before being tested.

5.3.2 Testing of Shear Properties The ASTM standard (ASTM:C273-11, 2014) is commonly used for testing sandwich foam cores but is fully applicable for testing shear properties of viscoelastic foam and rubber. The test consists of the tested material were adhesively bonded with Araldite 420 (Huntsman Arladite 420, 2000) between two loading plates, the plates are then loaded in tensile direction resulting in a shear stress in the tested material, see Figure 9. Load and displacement are measured during the testing and the elastic shear modulus is calculated. Due to difficulties with bonding of the specimen to the loading plates, the specimen where only tested at low strains.

Specimens are the same width as the loading plates (25 ��) and have a thickness of approximately 8.6 �� for the soft rubber, 14 �� for the hard rubber and 19 �� for the viscoelastic foam, the length is approximately 100 �� for all materials. All specimens are measured individually at three positions and the average value is used for calculations. All test specimens are conditioned at 23 ℃ for at least 16 ℎ before being tested.

Figure 9: Schematic representation of shear testing rig, reproduced from (ASTM:C273-11, 2014)

Wilhelm Johannisson 31 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.4 Design The design of the transverse leaf spring for KTH-RCV is performed in iterations. The first iteration is a 2-dimesional analytical concept that is optimized numerically. Then the analytical concept is imported into a FEM-software, where calculations are performed in order to verify the analytical results. With analytical results verified, the overall concept is refined to produce a 3-dimesional design for manufacturing and final assembly on KTH-RCV. The front suspension setup is used in this report for calculations and design.

All designs are optimized with respect to minimizing the mass and with constraints given below. Values for spring constants and anti-roll bar are given in requirement 1.2 Suspension characteristics.

• Two-wheel spring constant; found through the deflection at wheel position when the beam is loaded at both ends with a magnitude of 1000 � each. • One-wheel spring constant; found through the deflection at wheel position when the beam is loaded at one end with a magnitude of 1000 �. This is representing the anti-roll bar characteristics of the beam. • Damping as defined in section 5.2.2 Generalization for Viscoelastic Materials. • Stresses in face-sheets for the composite, less than material maximum. • Shear stress in viscoelastic rubber, less than material maximum.

Furthermore, the dimensions of the lower wishbones are kept constant, and so is the distance between the wishbone-mounting positions on the vehicle and the width of the spring is set to 200 ��. Calculations are also performed with the dimensioning static loads as defined in 1.1.1.

5.4.1 Material Selection

5.4.1.1 Composite Material The material used in the analytical concept is fully isotropic. The use of an isotropic material is not necessarily optimal for transverse spring performance but is chosen for simplicity in in initial analytical calculations. In the FEM-design calculations orthotropic material characteristics are chosen for a more thorough simulation.

5.4.1.2 Viscoelastic Material The viscoelastic material chosen for the design of the transverse leaf spring for KTH- RCV is the Hard rubber, see Discussion and Conclusion section 7.1 Testing of Viscoelastic Materials. The material characteristics for the rubber are found from material testing as defined in the results from section 6.1 Testing of Viscoelastic Materials.

5.4.2 Analytical Optimization An analytical solid mechanics concept is set up where the dimensions, i.e. web thicknesses, flange thicknesses, heights and width are used as variables. The generic design is seen in Figure 10.

Wilhelm Johannisson 32 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 10: Schematic representation of the analytical beam construction Using conventional solid mechanics the transverse leaf spring can be simplified as three sections; outer left (red), middle (blue) and outer right (red). The yellow parts represent the hard rubber used for viscoelastic characteristics, with a cover sheet (green) in order to transfer shear load to the rubber. The loads applied from the wheels are represented as orange arrows and the mounting points to the chassis are marked by boundary conditions. The outer sections are symmetrical with respect to the middle plane, leaving the two sections; end- and middle section to be investigated. The loads and boundary conditions are:

End section – Cantilever beam; load on outer edge with fixed boundary condition on the inner.

Middle section – Simply supported beam with applied moment in each end, the moment load is equal to the load on the end section times the end section length.

The analytical concept is optimized using MATLAB with the method fmincon where the above stated dimensions are variables. The rubber thickness is a secondary optimization variable limited by manufacturer’s standard thicknesses, due to the difficulty of processing natural rubber. Furthermore, the minimum face-thickness anywhere on the beam is limited to 1 ��, which is found to be a practical limit for manufacturing of the transverse leaf spring.

Wilhelm Johannisson 33 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.4.3 FEM Compared to Analytical Optimization The deflection results from the analytical optimization are compared to the results from a FEM-analysis of the same geometry. The FE software used is ANSYS Workbench R14.5.

Mimicking the boundary conditions of each beam section proved to be a challenge. A solution was found that would produce an infinitely stiff “boundary section” (marked red in Figure 11) between the end and middle section, the full beam is simply supported at these boundary sections.

Figure 11: CAD model based on analytical optimization, used for comparison between FEM results and analytical results The loading used in all the FEM calculations are, unless other stated, 1000 � applied at each end of the transverse leaf spring. The spring constant of the transverse leaf spring is found from the equation below.

� � = � Where � is the applied load (in each side), � is the deflection in the end of the beam and � is the calculated spring constant.

5.4.4 FEM Optimization The dimensions and behaviors found from the analytical optimization are used to design a final computer model. Using the analytical design as a baseline, iterations are then performed to find the final dimensions. In addition to the optimization constraints defined above, the spring is also to be designed with respect to manufacturability. Furthermore, consideration has to be made for mounting and assembly constraints.

Wilhelm Johannisson 34 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.4.4.1 Manufacturing Challenges The spring design from analytical optimization is very difficult to manufacture, especially the hollow sections. To manufacture a hollow section there are some manufacturing methods (Åström, 1997). However, none will be fast and cost-efficient enough to be applicable for the automotive industry. Instead, the spring could be manufactured with a very weak core material in order to keep the shape during manufacturing and not add too much mass to the spring. On the other hand, the spring will get slightly stiffer from the addition of a core material. In order to minimize this a core material that is as weak as possible is chosen as well as the overall spring dimensions might need to be optimized further. The addition of a core material in the box section does not make it a common sandwich structure; the spring is still designed as a box section in order to take side-loads as defined in Static load condition 1.1.1.

5.4.4.2 Assembly Challenges There are some restrictions for the assembly of the damper in KTH-RCV; first the connection between uprights and lower wishbones. The present system has two arms on the lower wishbones connecting to either side of the uprights, this is to ensure free movement of the uprights in both turning and spring movement, as well as the steering rod. The system may not be optimum for the use together with a transverse leaf spring. Nevertheless, it has been decided not to change other parts on the vehicle (Mounting requirement 2.2). Thus the present system stays the way it is and the leaf spring is designed around it. This leads to that the end of the leaf spring (and simultaneously lower wishbone) is designed with two separate arms in order to mount to the uprights, see Figure 12.

Figure 12: End of lower wishbone and the transverse leaf spring. Showing the design alterations made in order to accommodate the steering uprights and steering rod. Uprights are mounted in the right of the figure.

Wilhelm Johannisson 35 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Secondly, the connection between the lower wishbones to the vehicle chassis has to be designed and manufactured. The present connection is made above the lowest point of the vehicle bottom plate (approximately 75 ��). This will not work with a transverse leaf spring and the mounting positions have to be moved further down in order for the leaf spring to span under the bottom plate. Moving the inner position for the lower wishbone will change some vehicle dynamics characteristics, especially the camber gain on bump will be increased. From analysis (Nybacka, ADAMS study on Anti-roll bar for KTH-RCV, 2014) it is found that the camber gain is not dramatic and will not change the overall characteristics of the vehicle.

5.4.4.3 Design Alterations from the Analytical Design The viscoelastic behavior of the spring was found to be too low (as discussed in Discussion section 7.3.2 Analytical Optimization). An alternative design is made in order to make the viscoelastic characteristics more distinct. This design consists of a face-sheet for the viscoelastic material that is mounted to a secondary mounting position on the vehicle chassis (green in Figure 13). This mounting position is free to rotate and will produce a larger shear deformation in the viscoelastic material, due to the rotation of the main beam around the main mounting position (circle in light blue material).

Figure 13: Figure of the mounting solution for the connection between the transverse leaf spring and the vehicle chassis. Centre of spring is to the left and the wheel is mounted to the right. Figure is zoomed and cropped. Light blue represents the composite material, red is the manufacturing foam, yellow is the viscoelastic material and green is the face-sheet for the viscoelastic material. The change from isotropic material characteristics as in the analytical analysis to orthotropic material characteristics (in the detailed FE analysis) will change the calculated stiffness of the spring especially to the outer section. In addition the box section stiffness increase due to adding of foam core material and then also the stiffness decrease from the two beam ends for mounting (as defined below in section 6.2.4.3 Mounting of the Transverse Leaf Spring). The reduction in stiffness becomes large and thus the spring thickness has to be increased for compensation. All other dimensions are kept the same (face- and web sheet thicknesses kept at 1 �� and spring width of 200 ��).

Wilhelm Johannisson 36 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

The stiffness of the middle section, however, is close to unaffected by the change to orthotropic material characteristics. Also, changing the mounting of the viscoelastic material to a secondary position significantly lowers the anti-roll bar addition for the spring. In order to counter these effects, the section thickness is reduced, with face sheet thicknesses kept at 1 �� and spring width of 200 ��.

5.5 Manufacturing A physical, full-scale model of the transverse leaf spring for KTH-RCV is manufactured. The construction of the transverse leaf spring is made according to the design characteristics as defined in results section 6.2.4 FEM Optimization. An appropriate manufacturing method is chosen for the given design. All manufacturing is performed at KTH (Royal Institute of Technology), in the Lightweight Structures laboratory and the author performs all manufacturing.

In addition a mounting bracket for the transverse leaf spring is manufactured for attaching the spring to existing mounting positions on the KTH-RCV. This is not specifically part of the investigation performed herein, and is thus manufactured in steel. This is due to the fact that the vehicle was manufactured before the introduction of the leaf spring. A picture of the bracket can be seen below in Figure 14.

Figure 14: Mounting bracket for attaching the transverse leaf spring to existing mounts on KTH-RCV.

Wilhelm Johannisson 37 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

5.6 Laboratory Testing The laboratory testing-rig is designed specifically for the transverse leaf spring. The goal is to mimic the spring design loads as used in FEM calculations. However, the testing equipment available at KTH does not fit the size and loading condition for the transverse leaf spring. Instead, a separate testing setup is developed in order to examine the transverse leaf spring, measuring deflection and load in each end of the transverse leaf spring. All laboratory testing is performed at KTH (Royal Institute of Technology), in the Lightweight Structures laboratory and the author performs all testing.

The testing setup consists of a Dyna-Link DL-W3 ERT-05 load gauge (Vetek, 2010) and two Mitutoyo Absolute Digimatic 543-494B extensometers (Mitutoyo, 2009), and the loading is applied with a 1300 �� ratchet hand winch (ClasOhlson, 2013). The transverse leaf spring is attached with the actual mounting bracket manufactured for attaching the leaf spring to the vehicle. All parts are securely mounted to secure fastening points in the floor. A picture of the testing setup can be seen in Figure 15, where the load cell is marked green, the two extensometers are blue and the transverse leaf spring is marked red. The manufactured transverse leaf spring is loaded incrementally and a measurement of the load and the extensions at each increment is noted.

Figure 15: Picture of the testing rig for the finished transverse leaf spring. The load cell is in the top of the picture (marked green), where the load is applied. The two extensometers (blue) are mounted on either side of the transverse leaf spring (red).

Wilhelm Johannisson 38 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 39 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6 Results

6.1 Testing of Viscoelastic Materials The results given from material testing are presented below in Figure 16 and Figure 17. Figure 16 is show the results for the tensile modulus as function of strain rate and Figure 17 is showing the shear modulus.

For viscoelastic comparison, normalized material properties are presented in Figure 29 and Figure 30 in Appendix 13.3: Material Testing Results. Complete testing results are also presented in the Appendix.

9

8

7

6

5 Hard rubber Soft rubber 4 Viscoelastic foam

3 Tensile Modulus [MPa] 2

1

0 0 1 2 3 4 5 6 7 8 9 Strain rate [%/s]

Figure 16: Tensile material characteristics from testing

3

2.5

2

Hard rubber 1.5 Soft rubber Viscoelastic foam

1 Shear Modulus [MPa]

0.5

0 0 100 200 300 400 500 600 Strain rate [%/s]

Figure 17: Shear material characteristics from testing

Wilhelm Johannisson 40 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.1.1 Soft Rubber (Para Rubber)

6.1.1.1 Tensile Characteristics The Soft rubber tested in tension has a initial modulus of approximately 1.58 ��� and as the test progresses the elastic modulus is reduced, ending with a modulus of approximately 0.21 ���. The viscoelastic behavior of soft rubber in tensile loading is very low, with close to no increase in elastic modulus with higher strain rate. Complete results are presented in Figure 31 in Appendix 13.3: Material Testing Results.

6.1.1.2 Shear Characteristics The shear characteristics for soft rubber closely mimic those for tensile, with very low % viscoelastic behavior. The shear modulus for the higher shear strain rate, 92 ! was % found to be 1.053 ��� with the exact same for the medium rate 46 ! . At the low % shear strain rate 0.6 ! the shear modulus was found to 0.936 ���. Worth noticing in Figure 32 in Appendix 13.3: Material Testing Results is the “bump” is the stress- strain curve for the low pull rate case.

6.1.2 Hard Rubber

6.1.2.1 Tensile Characteristics Hard rubber has higher tensile viscoelastic behavior than soft rubber with elastic modulus ranging from about 5 ��� at low strain rates to about 8.5 ��� at a pull rate !! % of 500 !"# meaning a strain rate of approximately 12 ! (average 70 �� length of specimen), the modulus is calculated at low strain. Complete results are presented in Figure 33 in Appendix 13.3: Material Testing Results.

6.1.2.2 Shear Characteristics The shear characteristics for hard rubber also show higher viscoelastic properties, % % however with stagnating shear modulus between 30 ! to 60 ! and then increasing % % % again for 600 ! . The shear modulus for 30 ! (and 60 ! ) is approximately 2 ���, % whereas the shear modulus for 0.4 ! is approximately 1.4 ���. The shear modulus for % a shear rate of 600 !"# is found to be 2.6 ���. The average width of the specimens is approximately 14 ��. One noticeable behavior for the hard rubber (same as for soft rubber) is the “bump” in the beginning of the stress-strain curve (up to 3 % strain) for % % the 30 ! and 60 ! cases. Complete results are presented in Figure 34 in Appendix 13.3: Material Testing Results.

Wilhelm Johannisson 41 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.1.3 Viscoelastic Foam

6.1.3.1 Tensile Characteristics Viscoelastic foam has the largest viscoelastic characteristics, the tensile modulus for % % the strain rate of 12 ! is 0.149 ��� and for 6 ! it is 0.079 ���. The foam material is very linear elastic up to failure, in contrast to the other materials. Complete results are presented in Figure 35 in Appendix 13.3: Material Testing Results.

6.1.3.2 Shear Characteristics The shear characteristics for viscoelastic foam has a very unique behavior, especially for higher strain rate. Where the stress first goes up until a value of about 0.014 ���, and there has a shelf for about 3 % strain and then goes up again until failure at about % 0.19 ��� (for 22 ! ). This behavior is not present in the tensile case. Complete results are presented in Figure 36 in Appendix 13.3: Material Testing Results.

6.2 Design

6.2.1 Composite Material Selection The modulus of the isotropic composite material is assumed to be 80 ��� with a Poisson’s ratio of 0.3; representing a possible plausible layup of 80% of fibers in the beam direction and 10% in each of the relative ±45° directions. The strength of the material is assumed to be 3 ���.

The chosen material characteristics for the FEM designed spring are kept the same as for the analytical case, however with the addition of using an orthotropic material definition for the carbon fiber composite. Analytical lamination theory is used for calculation of composite properties. A layup is chosen according to; 70 % of fibers in longitudinal direction and 15 % in the ±45° directions respectively. The volume fraction of fibers is set to 50 %, which is a possible volume fraction for manufacturing for KTH-RCV. The fibers are Torayca T800H (Torayca T800H) with a matrix of Reichhold Dion 9102 vinyl ester (Reichhold Dion 9102, 2007), leading to composite material characteristics as follows in Table 3. The longitudinal characteristics are with respect to the length-wise direction of the leaf spring (lengthwise beam) and transverse characteristics are with respect to the two cross-wise direction of the leaf spring.

Table 3: Orthotropic composite material characteristics used for FEM design Property Value Longitudinal tensile modulus 83.84 ��� Transverse tensile modulus 6.84 ��� Shear modulus 2.98 ��� Longitudinal tensile strength 3.04 ��� Transverse tensile strength 0.72 ��� Shear strength 1.34 ���

Wilhelm Johannisson 42 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.2.2 Analytical Optimization The optimum values for the front transverse leaf spring according to the analytical optimization are preseted in Table 4 and the calculated values for the spring are shown in Table 5.

Table 4: Analytical optimization dimensions for the front transverse leaf spring

Dimension Value [��] Spring width (B) 200 End section height (ℎ!"#) 10.4 End section flange thickness (�!"#) 1 End section web thickness (�!"#) 1 Middle section height (ℎ!"##$%) 14.2 Middle section flange thickness (�!"##$%) 1 Middle section web thickness (�!"##$%) 1 Rubber thickness (�!"##$!) 10

Table 5: Analytical optimization results for the front transverse leaf spring Description Value Weight 3.01 �� Two-wheel spring constant 20.5 �/�� One-wheel spring constant 25 �/�� Anti-roll bar addition 18 % Damping 0.6 �/�� addition at 0.025 �/� wheel rate and 1.2 �/�� at 0.25 �/�

The one-wheel spring constant is found from the case when loading the transverse leaf spring in one end only. The limiting constraints for the leaf spring are the two- wheel and one-wheel spring constants (stiffness criterion). The strength criterions for the materials carbon and rubber are safe within one order of magnitude. Investigating the maximum deflection of the middle section it is found to be 9.6 �� and the outer section’s own deflection is 21.1 ��.

6.2.3 FEM Compared to Analytical Optimization The optimal dimensions found from the analytical calculations are used as input to the FEM-software and the material characteristics are kept the same, keeping in mind that the boundary conditions of the analytical optimization is a simplification on the analytical solid mechanics assumptions made for the analytical case. An image of the deflection from two-wheel loading is shown in Figure 18 and summarized results from the calculations are shown in Table 6.

Wilhelm Johannisson 43 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 18: FEM results for two-wheel loading of the front transverse leaf spring

Table 6: FEM results for the front transverse leaf spring

Description Value Two-wheel spring constant 18.3 �/�� One-wheel spring constant 23.1 �/�� Anti-roll bar addition 21 % Damping 0.5 �/�� addition at 0.025 �/� wheel rate and 0.95 �/�� at 0.25 �/�

The damping characteristics are found from exchanging the linearized material characteristics for the rubber for constant wheel rates (velocities). The maximum deflection of the middle section is found to be 10.1 �� and the outer section’s own deflection is 24.7 ��.

The calculated stresses in the materials are one order of magnitude lower than the strength of the materials, both for the carbon fiber composite and the rubber.

When studying the static loads as defined in condition 1.1.1 it is found that the transverse leaf spring will withstand these conditions with a safety factor of 4.

6.2.4 FEM Optimization

6.2.4.1 Secondary Mounting for Viscoelastic Material Extensive analysis was made for the behavior of the secondary mounting position for the viscoelastic material, as described in section 5.4.4.3 Design Alterations from the Analytical Design. The Results show that the material dimensions are too small for the middle spring section resulting in large deflections. The deflections caused are not applicable for KTH-RCV. Further discussion of the secondary mounting position is made in Discussion section 7.3.4.1 Secondary Mounting Position for Viscoelastic Material. When analyzing the characteristics of the secondary mounting position, it was found that the behavior is very promising for use with the rear suspension, according to requirements defined in requirement 1.2 Suspension characteristics.

6.2.4.2 Final Design The final design is a proceeded iteration from the analytical spring. The widths of the spring sections are altered from the analytical case in order to comply with the

Wilhelm Johannisson 44 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures addition in stiffness from foam parts inside the sections and adjustment in shape in the end of the spring. The design is show in Figure 19 where blue represents the composite material and yellow represents the viscoelastic material, foam inner parts are not visible. The design is complete with mounting positions of ∅ 16 �� steel tubes for mounting the spring to KTH-RCV. Complete material dimensions are show in Table 7.

Figure 19: Final design of the front transverse leaf spring for KTH-RCV with complete mounting positions. Blue represents the composite material and yellow represents the viscoelastic material.

Table 7: Final dimensions for the front transverse leaf spring

Dimension Value [��] Spring width (B) 200 End section height (ℎ!"#) 16 End section flange thickness (�!"#) 1 End section web thickness (�!"#) 1 Middle section height (ℎ!"##$%) 12 Middle section flange thickness (�!"##$%) 1 Middle section web thickness (�!"##$%) 1 Rubber thickness (�!"##$!) 10 Mounting positions outer diameter (�!"#) 16 Mounting positions inner diameter (�!") 12

Continuingly, the spring characteristics of the spring are show in Table 9. Where the spring constants are calculated with a design load of 1000 � in both or one of the spring ends for the two- and one-wheel cases.

Table 8: Spring characteristics for the final transverse leaf spring Description Value Two-wheel spring constant 20.1 �/�� One-wheel spring constant 24.1 �/�� Anti-roll bar addition 16.6 % Damping 0.78 �/�� addition at 0.025 �/� wheel rate and 2.83 �/�� at 0.25 �/�

6.2.4.3 Mounting of the Transverse Leaf Spring The design of the mounting positions where chosen in order to simplify manufacturing and handling of the spring. Also, the transverse leaf spring was required to be mounted to existing mounting positions on the KTH-RCV which somewhat limited possible solutions.

Wilhelm Johannisson 45 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

The mounting of the transverse leaf spring to the uprights is made with a cutout from the designed box section in order to give room for movement of the upright in steering and bump. Also, the spring is made thicker to account for screw-mounts in the ends of the beam arms. The spring is also tapered in width in order to make room for the steering-rod. The viscoelastic material is removed on the beam arms in order to simplify manufacturing.

The transverse leaf spring is mounted under the bottom plate of the vehicle with a custom bracket connected to existing position on the vehicle chassis, see section 5.5 Manufacturing. The transverse leaf spring is manufactured with two main rods for mounting to the custom bracket.

6.2.4.4 Maximum Stresses in the Final Design The stresses found in FE-calculations in the final design are shown in Table 9. The stresses are calculated from the static load requirement as described in Loads 1.1.1. The x-direction represents the longitudinal (beam wise) direction, y-direction represents the transverse (in spring plane) direction and z-direction represents the latitudinal transverse (up direction) of the spring.

Table 9: Maximum stresses from FEM calculations

Part Type Maximum/minimum Safety factor value Composite Tensile stress X- 0.421/−0.421 GPa 7.2 direction Shear stress XZ- 0.09/−0.06 GPa 14.9 direction Shear stress XY- 0.03/−0.03 GPa 45 direction Foam Tensile stress X- 1.79/−1.26 MPa 1 direction Shear stress XZ- 0.80/−0.73 MPa 1 direction

Wilhelm Johannisson 46 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.3 Manufacturing The transverse leaf spring is manufactured using vacuum infusion. A bottom mold is used for securing the overall shape of the spring, where the mold is manufactured from MDF-board. The outside shape of the spring is withheld from the shape of the internal core material. Fastening positions for the spring to chassis and suspension are manufactured from steel. The layup is made according to material layup selection Method section 5.4.1.1 Composite Material and secured with a spray adhesive that is compliant with the resin. All dimensions are according to blueprints from the final design. Infusion is made along the long edges with 1 ��� negative pressure and cured at 0.5 ��� negative pressure, according to KTH Test Standard (Norrby, Beckman, & Burman, Composite Laminate and Sandwich Panel - Manufacturing and Vacuum Infusion, 2010). The resin is Reichhold Dion 9102, mixed according to curing system D (Reichhold Dion 9102, 2007). The resin was left for post curing for 12 ℎ. Viscoelastic rubber was bought in the wanted thickness and cut to size and separate composite pieces for the cover for the rubber was manufactured. Rubber and rubber cover where adhesively bonded to the transverse leaf spring with Araldite 420 (Huntsman Arladite 420, 2000). Due to the rubber not withstanding uncured vinyl ester. The transverse leaf spring is clear coated with International Perfection Plus varnish (International Perfection Plus, 2010) for finishing and protection. The final mass of the transverse leaf spring is 4 ��, leading to a 20 % decrease in suspension mass. A picture of the finished transverse leaf spring can be seen in Figure 20.

Figure 20: Finished manufacturing of transverse leaf spring 6.4 Laboratory Testing When loading the transverse leaf spring incrementally, the resulting deflection vs. load plot can be seen below in Figure 21, showing the deflections for the right and left side of the spring when loaded simultaneously. The resulting spring constants, calculated with least square method, are found to be 26.2 �/�� and 31.0 �/�� for the right and left sides respectively. For the one-sided case, where the spring is only loaded in one end, the results can be seen in Figure 22, providing the one-sided spring constant of 32.3 �/��.

Wilhelm Johannisson 47 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

800 Right wheel [26.2035 N/mm] Left wheel [31.0272 N/mm] 700

600

500

400

300 Load applied to wheel [N]

200

100

0 0 5 10 15 20 25 30 Deflection [mm]

Figure 21: Showing the trend when incrementally loading the transverse leaf spring simultaneously at both ends. The circles (blue) represent the right hand side and the dots (green) represent the left. The spring constants are found to 26.2 �/�� and 31.0 �/�� respectively.

1200 Right wheel [32.3381 N/mm]

1000

800

600

Load applied to wheel [N] 400

200

0 0 5 10 15 20 25 30 35 40 Deflection [mm]

Figure 22: Showing the trend when incrementally loading the transverse leaf spring in one end (right hand side). The spring constant is found to 32.3 �/��. When the transverse leaf spring was tested, fractures where found in the spring. The fractures appeared before the design load (1000 �) and thus the testing was stopped, the fracture is shown in Figure 23. The fracture is a delamination between the lower face sheet and the foam core, at the mounting position of the spring to the bracket.

Wilhelm Johannisson 48 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 23: Fracture occurring in the transverse leaf spring after testing. A delamination between the lower face sheet and the foam core is found. 6.5 Costs

6.5.1 Cost of Transverse Leaf Spring The manufacturing and material costs for the transverse leaf spring are calculated, based on the dimensions as defined in Results section 6.2.4 FEM Optimization. The costs are applicable to what a manufacturer (first-party or subcontractor) would have. Summary of the different costs applicable can be seen below in Table 10.

Table 10: Summary of costs applicable for manufacturing the transverse leaf spring for KTH-RCV

Material Cost per mass Mass [kg] Cost [SEK] Source [SEK/kg] Raw carbon fiber 280 1 280 (Composites World, 2013) Vinyl ester 200 1 200 (Norrby, Cost of Vinyl Ester, 2014) Rubber 50 2 100 (Kuntze, 2014) Foam 5 0.01 0 (Erlandsons Brygga, 2014) Metal fittings - - 200 Approximation Composite 200 2 400 Approximation manufacturing cost Total cost ����

Wilhelm Johannisson 49 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

6.5.2 Cost of Current System The cost current system is defined from the costs of manufacturing the specific parts for KTH-RCV originally used in the suspension system. A subcontractor performs all manufacturing for the lower wishbones, rocker and pushrod. As well as the spring and damper are bought as off-the-shelf components (Nybacka, Costs for Original Suspension System for KTH-RCV, 2014).

Table 11: Summary of costs applicable for manufacturing the original suspension system for KTH-RCV

Part Cost per No of Cost in KTH- part [SEK] parts [#] RCV [SEK] Lower 400 2 800 wishbones Pushrod and 400 2 200 Rocker Spring 1000 2 2000 Damper 1000 2 2000 Total cost ����

Wilhelm Johannisson 50 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 51 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

7 Discussion

7.1 Testing of Viscoelastic Materials The testing of the viscoelastic materials worked smoothly with some difficulties where found when handling the materials. The soft viscoelastic foam, collapsed under the weight of the shear loading plates. Therefore unique manufacturing stands where developed for the cutting, handling and storing the viscoelastic foam specimen.

In tensile testing there where some difficulties as well, especially with the soft rubber, as it was very difficult to fasten in the testing clamps. The rubber kept creeping out of the testing clamps at large deformations; the rubber shrinks in transverse area upon loading and thus gets smaller than the clamping itself. As an attempt to minimize this behavior, clamps that close themselves upon loading where used as well as tightening the clamp extremely hard. No attempt was made to use pneumatic clamps since the material was found to have material characteristics that didn’t fit requirements, see discussion about soft rubber below.

7.1.1 Soft Rubber (Para Rubber) Soft rubber has material characteristics that are quite low, (tensile properties around 1.5 ��� and shear properties around 1 ���). This might make it challenging for use in a structural part. Additionally, the viscoelastic material characteristics of soft rubber are extremely low and thus will not be useful for viscoelastic damping material in the transverse leaf spring. The “bump” in the shear curves as noted in section 6.1.1.2 Shear Characteristics might be present due to error in measurement, however the cause will not be investigated further since the material is irrelevant for use in the transverse leaf spring.

7.1.2 Hard Rubber Hard rubber has material characteristics that are slightly higher than soft rubber; tensile properties between 5 to 8.5 ��� and shear properties between 1.4 to 2.5 ��� (depending on strain rates). This dependence on strain rate is called viscoelastic behavior and is desired for the transverse leaf spring. Combined with material properties that are satisfactory for a structural part it is found that the hard rubber is the best material for use in further calculations and design for the transverse leaf spring.

The “bump” in the shear curves as noted in section 6.1.2.2 Shear Characteristics is % noteworthy, however the bump is not present in the 600 ! -case. The measurements % for the 600 ! testing was performed in a different machine capable of reaching higher strain rates. The fact that the bump is not present in that case makes the bump likely to be caused by the slower testing machine and possibly cased by the acceleration of the machine head.

Wilhelm Johannisson 52 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

7.1.3 Viscoelastic Foam The viscoelastic foam has material characteristics that are extremely low (about 0.1 ��� in both tensile and shear). This makes the material extremely challenging to use for structural applications. The viscoelastic properties, however, are clearly visible and could be used for other applications. Viscoelastic foam is chosen not to be used as viscoelastic material for the transverse leaf spring due to it’s extremely low material characteristics. The “bump” in the shear curves as noted in section 6.1.3.2 Shear Characteristics is interesting as to the viscoelastic behavior of the material. It could come from machine acceleration behavior as discussed for the hard rubber. No further attempt to find the cause of the deviation was made as the material was found irrelevant for further studies.

7.2 Viscoelastic Materials Overall The viscoelastic materials tested in this thesis are not complete, there are numerous other viscoelastic materials available on the market and all could not be investigated within the timespan available. A selection of the most common, commercially available, viscoelastic materials where chosen for testing in order to find some that could be used for damping of a transverse leaf spring. No attempt of producing a custom viscoelastic material has been made.

The generalization to linearize the damper behavior is not correct. In order to properly investigate the behavior of the transverse leaf spring with damper dynamic models has to be used. No analytical determination of the behavior can be made for the dynamic case and a full vibrational determination of the viscoelastic material has to be performed. Moreover, the FEM calculations have to be performed with a dynamic model and include material properties from testing. Within the scope of this thesis it is not possible to perform such testing and calculations. In order to be able to investigate the possibility of using viscoelastic materials for damping in a transverse leaf spring the linearized generalization is developed and used.

7.3 Design

7.3.1 Composite Material Selection The composite material selection chosen for this project is very limited, a lot more calculations and design work can be put into the design of the composite layup. The layup can be highly optimized with respect to mass as well as internal lamina stresses. There are numerical tools for calculating individual lamina characteristics, e.g. Abaqus Composite Modeler and shell methods for ANSYS Workbench. In this project, focus was on the viscoelastic characterization and behavior of the core material rather than optimizing the composite characteristics further.

7.3.2 Analytical Optimization The results from the analytical optimization are reasonable, it can be found that it is plausible to design and manufacture a transverse leaf spring with the desired spring constant. The material will withstand the loading with a high safety factor, mostly due

Wilhelm Johannisson 53 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures to the fact that the spring is optimized with the spring constant (stiffness) as the limiting constraint. Also, the limit in face-sheet thickness for manufacturing is helping.

The mass of the transverse leaf spring is satisfactory (approximately 3 ��), compared to the mass of the original system of approximately 5 ��. The anti-roll bar addition is good. However the damping addition from the viscoelastic material is not enough and further thought has to go in to how to make the damping larger, at least for the low wheel rate damping.

7.3.3 FEM Compared to Analytical Optimization The FEM calculations showed a slightly weaker behavior than the analytical calculations, e.g. 20.5 �/�� for the analytical calculations and 18.3 �/�� for the FEM calculations. The same behavior was found in all cases of deformations for the complete spring as well as single section deformations. Thus, it can be assumed that the difference in deformation is systematic and not due to any specific error in calculations of the single sections. The error might be related to the fact that the analytical calculations only take into account 2-dimensional deformation. The 3D- case however will exhibit deformations with a curvature in the transverse direction, as well as the main longitudinal curvature and compressions in the latitudinal direction. These 3D-deformations are not part of the analytical calculations. Upon performing FEM-calculations, it was found that the flange thicknesses used in the transverse leaf spring are very sensitive for the stiffness of the spring.

7.3.4 FEM Optimization The solution for the transverse leaf spring found with FEM analysis is found to comply well with the requirements. The damping characteristics of the transverse leaf spring are too low compared to the original system for KTH-RCV, however this was neglected in order to fulfill the anti-roll bar requirement. It is found thorough FEM- calculations that the final design, as defined in Results section 6.2.4 FEM Optimization, is assumed to working as a final design suitable for production and use on KTH-RCV.

7.3.4.1 Secondary Mounting Position for Viscoelastic Material The design for a secondary viscoelastic material mounting position, as suggested in Method section 5.4.4.3 Design Alterations from the Analytical Design, was found to not be compliant with the wanted characteristics for KTH-RCV. Specifically the Anti- Roll bar characteristics wanted for the front suspension setup limited the use of the secondary mounting position. This is due to the addition in effective stiffness for the middle section, generated by mounting method for the viscoelastic material. The design is chosen not to be used for the front suspension on KTH-RCV. However, the design was found to be very promising for the rear suspension. Since for the rear suspension, the wanted Anti-Roll bar characteristics are very low (0 %). The stresses calculated from FEM-simulations show that the transverse leaf spring should withstand the static loads.

Wilhelm Johannisson 54 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

7.4 Manufacturing The manufacturing of the transverse leaf spring progressed smoothly and without any difficulties. The manufactured part complies with blueprints and CAD-model and can upon measurements be assumed to represent the FEM-optimized design sufficiently.

7.5 Laboratory Testing The laboratory testing showed that the transverse leaf spring is stiffer compared to the FE-analysis. This is possibly due to thickness uncertainties and the amount of fibers in the flanges of the spring. In the FE-investigating it was noted that stiffness of the spring was extremely sensitive.the flange-thicknesses. Other dimensions of the spring are not as sensitive and significantly easier to manufacture with the right dimensions. Also, there was a difference in the stiffness of the transverse leaf spring on the different sides, there are two possible reasons for this; the transverse leaf spring is built incorrectly with slightly different stiffness on the different sides, or the mounting of the testing rig was not perfectly symmetrical. To investigate this, one would need to measure the sides individually.

The one-wheel spring rate was found to have accurate addition to the anti-roll bar characteristics of the transverse leaf spring. Only one side could be measured for the anti-roll bar characteristics due to fracture in the other side of the spring.

Furthermore, the strength of the spring was found to not be sufficient, since the spring fractured before the design load. The fracture occurred at the mounting position of the transverse leaf spring to the chassis, which naturally is a very sensitive spot in the design. Different setups were considered, and it is possible that another solution for the mounting would provide a different result. Nevertheless, the final design was chosen due to constraints on the existing mounting positions on the KTH- RCV.

7.6 Costs The manufacturing costs for the transverse leaf spring are a rough estimation based on average costs of the industry. The costs do not specifically reflect the actual costs applying for full-scale production of the transverse leaf spring for the automotive industry. For example, set up costs, explicit man-hours and tool costs are somewhat neglected in the analysis. On the other hand, with the transverse leaf spring combining up to 8 parts from the original suspension system into one, both the assembly time and man-hours are decreased leading to further cost savings.

The manufacturing costs for the original suspension system (lower wishbones, rocker and pushrod) are possibly somewhat over-estimated due to being manufactured by subcontractors, as well as the spring and damper being off-the-shelf components. These costs can likely be reduced significantly with in-house manufacturing, but set up costs and tool costs would follow. The assembly time and man-hours for assembly are significantly higher for the original suspension system.

Wilhelm Johannisson 55 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

7.6.1 Total Cost of Ownership (TCO) With the overall reductions in manufacturing cost for the transverse leaf spring compared to the original suspension system, the TCO of the transverse leaf spring is very promising. The suspension system of a conventional vehicle suspension system require some service, for instance in bushings. Some bushings still exist for the transverse leaf spring. Overall the service costs can be assumed to equal for the transverse leaf spring and the original suspension system. Furthermore, within reparations, the original suspension system, especially the spring exhibit some fatigue during its lifetime. The transverse leaf spring, should inherently, exhibit much less fatigue and have a longer lifetime (Car Bibles, 2013). As well as, the transverse leaf spring being a cheaper in production could lead to some improvements in average repair costs. Furthermore, with the transverse leaf spring having a lower mass leads to on average lower fuel consumption and thus lower cost. It can be assumed that the TCO of the transverse leaf spring is lower than that of the conventional suspension system.

7.6.2 Selling factor The decrease in weight of the part is leading to lower fuel consumption, which is a major selling factor. Furthermore, the initial cost of production is less than that of the original system for KTH-RCV, and the fuel consumption is lowered (inherently also fuel cost). Thus it can be assumed that the economic selling factor is well fulfilled. The environmental impact of the transverse leaf spring is not investigated in this project, however with a lower fuel consumption the environmental impact is definitely going in the right direction. Still, the transverse leaf spring is manufactured from carbon fiber, considered a “future, high class and extreme” material that is in itself another selling factor.

Wilhelm Johannisson 56 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 57 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

8 Analysis of Requirements and Limitations Herein an analysis is performed of the Requirements and Limitations as defined in section 4. The analysis is a combination of results from FEM calculations and testing as well as assessments from the Discussion. When applicable, analyses are made for the automotive industry.

1. Conditions 1.1. Loads – The loads for KTH-RCV are fulfilled according to FE calculations. Testing of the spring-direction strength was performed, which provided that the transverse leaf spring did not withstand the provided design loads with a local fracture as a result. 1.2. Suspension characteristics – According to FE calculations, the overall suspension spring characteristics of the transverse leaf spring are fulfilled. Testing of the final transverse leaf spring show that the spring stiffness was too high. Damping characteristics of the transverse leaf spring was not tested. On the other hand, the damping characteristics of the transverse beam spring are not fully fulfilled. Due to a design choice that had to be made between damping and Anti-Roll characteristics, see Discussion section 7.3.4.1 Secondary Mounting Position for Viscoelastic Material. 1.3. Environmental durability – Previous analysis of the environmental durability of composites has been performed (Bachelor Degree Project, 2012). For the viscoelastic material however, no analysis has been made on its environmental durability. 1.4. Design space – The Design space for KTH-RCV is used as reference for all iterations of the design, the design is compliant with the space within KTH- RCV. Furthermore, for the automotive industry the overall design of the transverse leaf spring is expected to be adaptable for use on other types of vehicles. 1.5. Suspension mass – The final mass of the transverse leaf spring is 20 % less than the original. All reduction in mass is defined as unsprung mass. These results are very promising for the automotive industry. 1.6. Lifetime – No explicit analysis of the expected lifetime of the transverse leaf spring is performed. With previous experience of the topic assumptions can be drawn that the transverse leaf spring for KTH-RCV will sufficiently clear its expected lifetime. However, for the automotive industry extensive analysis and testing has to be performed for the lifetime of a transverse leaf spring. 2. Characteristics 2.1. Function – The design of the transverse leaf spring is designed to fulfill the function as a suspension system. 2.2. Mounting – The mounting of the transverse leaf spring to KTH-RCV is performed with simple mechanical tools. The transverse leaf spring is mounted to existing mounting points on KTH-RCV with the addition of a mounting bracket.

Wilhelm Johannisson 58 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

2.3. Driving characteristics – The driving characteristics of the transverse leaf spring could not be tested. 2.4. Spring characteristics – The spring characteristics of the transverse leaf spring are sufficiently satisfied. 2.5. Damping characteristics – The damping characteristics of the transverse leaf spring has been reduced compared to the original characteristics. The reason is a design choice that was to be made between damping and anti-roll characteristics, see Discussion section 7.3.4.1 Secondary Mounting Position for Viscoelastic Material. 2.6. Active spring and/or damping – No analysis of active spring and/or damping characteristics has been performed. 3. Serviceability 3.1. Reparation – No analysis has been performed on the topic of reparability of the transverse leaf spring. The transverse leaf spring being a composite sandwich structure makes it inherently possible to repair. However, since the spring characteristics of the structure is directly connected to the stiffness of the beam, any repairs might alter the spring characteristics of the transverse beam spring. 3.2. Inspection in service – No attempt has been made for KTH-RCV to specifically inspect is while in service, other than optical inspection. 4. Safety 4.1. Characteristics upon failure in service – No analysis of the driving characteristics upon failure of the transverse leaf spring has been performed. 4.2. Composite shattering upon failure – No analysis of catastrophic fracture characteristics has been made. 5. Environmental impact – No analysis of the environmental impact of the suspension system for KTH-RCV has been performed. 6. Economy – The overall economic characteristics for the transverse leaf spring are very promising, with a reduction in cost of almost 70% compared to the original suspension system. However extremely promising, it can be discussed what the actual costs for the automotive industry would end on. The TCO of the transverse leaf spring is improved. The overall selling factor for the transverse leaf spring is extremely promising. For more discussion see Discussion section 7.6 Costs. 7. Production – The production characteristics of the transverse leaf spring has been kept in mind throughout the design process. The transverse leaf spring is possible to further increase the production volume, due to scalability of design and the design being possible for automation in production. The production safety for KTH-RCV has been keep through rules and restrictions according to KTH Lightweight Structures testing rules. No analysis of the production safety has been made for the automotive industry.

Wilhelm Johannisson 59 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

9 Conclusions It can be concluded that it is possible to manufacture a transverse leaf spring for a road vehicle. Sufficient spring-, damping- and anti-roll bar characteristics can be implemented in the transverse spring construction. It is also possible to implement the lower wishbones, providing dimensional stability to the movement of the wheel. All these traditionally different parts and functions are implemented in one single part, which not only lowers weight but possibly also both the cost and TCO of the spring.

One attempt to manufacture a full-scale version of the transverse leaf spring was made, with promising characteristics. However, due to challenges in controlling flange thicknesses and mounting of the transverse leaf spring; the spring was too stiff and did not withstand the design loads required. The transverse leaf spring can likely be repaired to continue further testing.

Wilhelm Johannisson 60 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 61 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

10 Recommendations and Future Work For future work it is recommended to further analyze the composite material and fiber layup. With an optimized fiber layup, further weight reductions can be achieved and hopefully the strength of the final transverse leaf spring can be improved. Especially the strength of the mounting positions of the beam to the chassis of the vehicle has to be improved. Possibly, other solutions for mounting the transverse leaf spring would be necessary in further investigations of the system.

A solution for improving the damping characteristics for the transverse leaf spring was found, however diminishing the anti-roll bar characteristics (discussed in Secondary Mounting for Viscoelastic Material). This solution was found not to work for the front suspension but would be possible for the rear. Thus additional analysis for the rear suspension would be interesting.

For further analysis of the usage of transverse leaf springs in automotive vehicles, a lot more testing would be necessary in order to verify that the system comply with all the parts defined in Requirements and Limitations.

10.1 Viscoelastic Materials Viscoelastic materials need to be explored further for use in automotive transverse leaf springs. A custom viscoelastic material might be possible to manufacture, possibly a stiffer derivative of the viscoelastic foam used in this thesis, or a rubber mixture with even higher stiffness and viscoelastic behavior. Since the viscoelastic behavior of the viscoelastic foam is cased by air being forced to move through the semi-closed cells of the foam material, it might be possible to exchange the air in the material with a liquid in order to make the viscoelastic properties even larger. For future work it would be appropriate to use a Prony Series representation as described in (Chen, 2000).

Wilhelm Johannisson 62 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 63 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

11 Postscript During the extent of this degree project, new solutions for a transverse leaf spring has been designed (LeGault, 2015), with high interest in the automotive industry to the usage of transverse leaf springs. However, no attempts at implementing the damping to the construction have been found. Which show a level of originality to the construction provided in this project. An attempt at filing a patent for the damping solution was made, which was denied due to a too low inventive step.

Wilhelm Johannisson 64 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 65 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

12 Bibliography Åström, B. (1997). Manufacturing of Polymer Composites. Stockholm, Sweden: Nelson Thornes Ltd.

ASTM:C273-11. (2014, March 28). Standard Test Method for Shear Properties of Sandwich Core Materials. ASTM International.

Bachelor Degree Project. (2012). Lastbärande kompositbalk i buss. Royal Institute of Technology. Stockholm: Lightweigth Constructions.

Calver, K. (2001, February 14). SUSPENSION - Shock absorbers (dampers), basic knowledge. Retrieved January 31, 2014 from Mini Mania: http://www.minimania.com/SUSPENSION___Shock_absorbers__dampers___bas ic_knowledge

Car Bibles. (2013). (Car Bibles) From www.carbibles.com/images/fiberglass_spring.gif

CH. (2012, July 22). Retrieved December 28, 2013 from Composite Helicopters International: http://www.compositehelicopter.com/images/specs.pdf

Chen, T. (2000). Determining a Prony Series for a Vicoelastic Material From Time Varying Strain Data. U.S. Army Research Laboratory, Vehicle Technology Directorate. Hampton: NASA.

Composite World. (2014, July 7). Sogefi composite coil spring to be launched by Audi for 2015. Retrieved July 9, 2014 from http://www.compositesworld.com/news/audi- announces-new-rd-in-automotive-composites-applications

Composites World. (2013, December 17). Carbon Fiber 2013: Conference highlights. Retrieved August 11, 2014 from Composites World: http://www.compositesworld.com/news/carbon-fiber-2013-conference-highlights

EPA. (n.d.). United States Environmental Protection Agency. Retrieved December 28, 2013 from http://www.epa.gov/students/pdf/fueleconomymiddleschool.pdf

Erlandsons Brygga. (2014, August 12). Erlandsons Brygga. Retrieved August 12, 2014 from Divinycell: http://www.bryggan.nu/Hemsida/Farg_Batvard/Polyester_Reparation/Distansmat erial/DIVINYCELL_10mm_1220X813?id=09250

FFI. (2013). SÅNÄTT - Heavyweight Ideas, Lightweight Solutions. Fordonsstrategisk Forskning och Innovation (Stategic Vehicle Research and Innovation).

Ford, D. (2012, March 16). The New York Times. Retrieved December 28, 2013 from http://www.nytimes.com/2012/03/18/automobiles/as-cars-are-kept-longer- 200000-is-new-100000.html?_r=3&ref=business&pagewanted=all&

Wilhelm Johannisson 66 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Honda. (2012). 2012 Honda CR-Z, Honda Press Release. (Caricos) Retrieved December 28, 2013 from http://www.caricos.com/cars/h/honda/2012_honda_cr- z/1024x768/163.html

Huntsman Arladite 420. (2000). Aerospace Adhesives Araldite 420 Two component epoxy adhesive. Cambridge: Vantico Limited.

International Perfection Plus. (2010). Perfection Plus Varnish. Akzo Nobel.

Jerrelind, J. (2013). Vehicle Stability. In Course compendium for SD2225 Ground Vehicle Dynamics. KTH.

Koenigsegg. (2012, March 2). Koenigsegg reinvents the wheel. (Koenigsegg Automotive AB) Retrieved December 28, 2013 from http://www.koenigsegg.com/latest-news/koenigsegg-reinvents-the-wheel/

Kuntze. (2014, July 17). Material Purchases. Stockholm.

Longhurst, C. (2013, December 15). (Carbibles) Retrieved December 28, 2013 from The Suspension Bible: http://www.carbibles.com/suspension_bible.html

Longhurst, C. J. (2013, December 15). The Suspension Bible. Retrieved March 17, 2014 from The Car Bibles: http://www.carbibles.com/suspension_bible_pg4.html

Macioce, P. (2002). Viscoelastic Damping 101. Roush Industries, Inc.

Marks, P. (2005, June 29). Aviation – The shape of wings to come. (NewScientist) Retrieved December 28, 2013 from http://www.newscientist.com/article/dn7552- aviation--the-shape-of-wings-to-come.html?full=true#.Ur63O9LuKSo

Norrby, M. (2014, August 12). Cost of Vinyl Ester. Stockholm.

Norrby, M., Beckman, A., & Burman, M. (2010). Composite Laminate and Sandwich Panel - Manufacturing and Vacuum Infusion. Lightweigh Structures. Stockholm: KTH.

Nybacka, M. (2014, March 13). ADAMS study on Anti-roll bar for KTH-RCV.

Nybacka, M. (2014, August 12). Costs for Original Suspension System for KTH-RCV. Stockholm.

Preston, M. (2010). Composite Material Substitution in Formula 1 – Implications for Industry. Oxfordshire: Formtech Composites.

Red [2], C. (2013, November 30). Automotive weight reduction is increasingly about avoiding extra costs. (Composites Technology) Retrieved December 28, 2013 from http://www.compositesworld.com/articles/automotive-weight-reduction-is- increasingly-about-avoiding-extra-costs

Wilhelm Johannisson 67 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Red, C. (2013). Automotive CFRP: The Shape of Things to Come. Composite Technology , 18.

Reichhold Dion 9102. (2007). Dion 9102 Epoxy Based Vinyl Ester Resin. Sandefjord: Reichhold.

Roland, M. C. (2011, September). Viscoelastic Behavior of Rubbery Materials. Oxford: Oxford University Press.

Rush, S. (2007, May 1). Carbon fiber: Life Beyond the Landfill. (High-Performance Composites) Retrieved December 28, 2013 from http://www.compositesworld.com/articles/carbon-fiber-life-beyond-the-landfill

Smith, C. (1985). Engineer to Win. Osceola, USA: MBI Publishing Company.

SR 65 Medium. (n.d.). Retrieved March 27, 2014 from Special-Plas AB: http://www.special-plast.se/produkter/item/81-sr-65-soft

Torayca T800H. Torayca T800H Data Sheet. Santa Ana: Toray Carbon Fibers Aamerica, Inc.

Toyota. (2007, June 15). Toyota Sverige. (Toyota Motor Corporation) Retrieved December 27, 2013, from http://www.toyota.se/Images/111011_serviceintervaller.pdf

Wan, M. (2000). Suspension Geometry. (AutoZine) Retrieved December 28, 2013 from http://www.autozine.org/technical_school/suspension/tech_suspension1.htm

Wilhelm Johannisson 68 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Wilhelm Johannisson 69 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13 Appendix

13.1 Conventional Suspension Systems Herein some of the most common suspension system types are presented and compared (Wan, 2000).

13.1.1 Live- and Dead Axle The Live- and Dead Axle suspension system is based on stiff axles that stretch the width of the vehicle and connect the wheels on either side. The terms live and dead refer to whether or not the axle is driving the wheels or not. The system has a lot of unsprung mass resulting in higher wheel momentum, to be handled by the spring and damper or transferred to the chassis resulting in a bumpier ride. Another drawback is the fact that body roll is not suppressed, however the system is cheap. An example with two Live Axle suspension systems can be seen in Figure 24.

An evolution of the Live Axle is the DeDion Suspension system where the final differential for the wheels is not part of the unsprung mass resulting slightly better handling. However the wheels are still linked from side to side and the body roll is not suppressed, but the system is still cheap.

Figure 24: Live Axle suspension system, reproduced from (Longhurst C. , 2013).

Wilhelm Johannisson 70 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13.1.2 Double Wishbones Suspension The Double Wishbone Suspension system (also called Double A-arm Suspension) is, from the handling point of view, the most ideal suspension system. It can be used on both driving and non-driving wheels as well as front and rear. The system has a very good camber control and the suspension system maintains the wheels perpendicular to the road surface. The upper and lower wishbones are of different lengths and angle to minimize tire scrubbing and ensure an anti-dive function, an example of Double Wishbone Suspension can be seen in Figure 25. An evolution of the double wishbone suspension is the Multi-Link Suspension where essentially the wishbones are exchanged for multiple separate links. This ensures greater control of the wheel movement but is more expensive.

Figure 25: Double Wishbone Suspension, reproduced from (Longhurst C. , 2013). 13.1.3 MacPherson Strut Suspension The MacPherson Strut Suspension system is the most common suspension system today in commercial vehicles due to its compactness and low cost. The system is rigid and the spring and damper acts as a control link to position the wheel. The system suffers a bit from body roll and variation in camber due to vertical movement of the wheel, which lead to a poor handling, but not as bad as the Live Axle. Another drawback of the suspension system is that the system takes up a lot of space upwards, resulting in high hood and fenders, which is not desired in sports cars. An example of a MacPherson Strut Suspension can be seen in Figure 26.

Wilhelm Johannisson 71 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 26: MacPherson Strut Suspension, reproduced from (Longhurst C. , 2013). 13.1.4 Torsion Beam Suspension The last of the conventional suspension systems is the Torsion Beam Suspension where the spring is partly consisting of a beam spreading the vehicle width-wise. The beam is connected off-center to the wheels and non-equal forces form the wheel are taken up by twisting (torsion) movement of the beam. It is a very compact suspension system, making room for bigger trunk and a larger rear seat and it is cheaper. The system has an inferior handling compared to a Double Wishbone Suspension, but it is a competitor to the MacPherson Strut Suspension. An example of the Torsion beam Suspension can be seen in Figure 27.

Figure 27: Torsion Beam Suspension, reproduced from (Honda, 2012).

Wilhelm Johannisson 72 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13.2 Analytical study of Anti-roll bar characteristics An analytical study is performed on a transverse leaf spring for KTH-RCV, the leaf spring is modeled with isotropic material with Tensile modulus of 70 ���. This tensile modulus represents a quasi-isotropic, non-optimized, carbon fiber composite with medium material characteristics. The beam has the total length of 1370 �� where the outer parts (loaded edges) of 405 �� represent the lower wishbones in the suspension. The beam is mounted on two points that are centered and with 560 �� between them. See Figure 28 for reference. The beam is assumed to have a constant rectangular cross section with width � and height �, the load applied is �.

Figure 28: Schematic representation for a transverse leaf spring for KTH-RCV. The moment of inertia for the beam is then given by:

� ∙ �! � = 12 13.2.1 Beam loaded in one free end – representing one-wheel bump By using elementary cases for the bending of the free edge, the deflection at the point of loading is given by:

��! � = !"# 3�� where � is the length of the free edge (405 ��).

Furthermore, the bending of the middle part produces a deflection at the loaded end, which is calculated using elementary cases by:

�� ∙ � � = ���� !"##$% !"##$% 3�� where �!"##$% is the length between the mounting points (560 ��). The total deflection at the loaded edge is then:

� = �!"# + �!"##$% The system is applied for a spring system where the global spring constant is given as:

� � = �

Wilhelm Johannisson 73 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

For KTH-RCV the wanted spring constant is 20000 ! and thus, using the equations ! above the width and height of the beam that will produce this spring constant can be calculated. Note, the width and height of the beam is not explicitly calculated but only their relationship, finding the optimum width and height based on weight is not done for the analytical study. The sizes of the beam are calculated as to get an overall impression of the beam. One possible width and height is calculated to:

� = 15 ��, � = 70 ��

This is resulting in the suspension stiffness to be �!"#! !!!!"# = 20.3 �/��, sufficient for primary analytical studies.

13.2.2 Beam loaded in both free ends – representing two-wheel bump Looking at the case with the beam loaded at both edges, the deflections of the beam- ends are as before:

��! � = !"# 3�� The deflection due to bending of the middle part is instead given as:

�� ∙ � � = ���� !"##$% !"##$% 2�� Thus, the total deflection is calculated and following the suspension stiffness

�!"# !!!!" = 26.1 �/��.

13.2.3 Anti-roll bar characteristics The difference between the beam loaded at one edge compared to both edge will result in the beam to have characteristic like and anti-roll bar. The anti-roll bar characteristics are defined by the addition in stiffness that comes through loading at one end compared to both ends. The percentage is given by:

� � = 1 − !"#! !!!!"# = 22% �!"# !!!!" The anti-roll bar addition to stiffness for an isotropic beam is thus 22%.

13.2.3.1 Theoretical minimum in anti-roll bar characteristics The theoretical minimum of the anti-roll bar characteristics is found when the beam is infinitely stiff in the middle part, e.g. elastic modulus goes to infinity. The deflection due to bending of the center of the beam is �!"##$% = 0 and the bending of ! the ends are given by � = !! . The dimensions of the beam would then be !"# !!" � = 15 ��, � = 23 �� to achieve a beam stiffness of 20.4 ��/��. With the same stiffness for both one-wheel bump and two-wheel bump the anti-roll bar percentage of added stiffness would then be 0 (zero), meaning no anti-roll bar characteristics at all.

Wilhelm Johannisson 74 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13.2.3.2 Theoretical maximum in anti-roll bar characteristics The maximum amount of anti-roll bar characteristics would be achieved if the free ends would be infinitely stiff. The deflection due to bending of the ends is then

�!"# = 0 and the deflection due to bending of the middle piece is given by: �� ∙ � �� ∙ � � = ���� !"##$% + !"##$% !"##$% 3�� 6�� With the beam dimensions � = 15 ��, � = 48 �� the two-wheel bump stiffness is

�!"#! !!!!"# = 20.2 �/��, and the one-wheel bump stiffness is �!"# !!!!" = 30.3 ��/ ��. The anti-roll bar percentage addition is then about 33 %, which is the theoretical maximum is anti-roll bar stiffness addition.

13.3 Material Testing Results Complete results from material testing are presented below in Figure 31 to Figure 36, see Results section 6.1 Testing of Viscoelastic Materials and Discussion section 7.1 Testing of Viscoelastic Materials for further description of results.

For viscoelastic comparison, normalized properties for the different viscoelastic materials are given in Figure 29 and Figure 30.

1.9 2.8 Hard rubber [5.09 MPa] 1.8 Soft rubber [1.5 MPa] 2.6 Viscoelastic foam [0.079 MPa] 1.7 2.4

1.6 2.2

1.5 2

1.4 1.8

1.3 1.6 Normalized shear modulus [-] Normalized tensile modulus [-] 1.2 1.4 Hard rubber [1.4 MPa] 1.1 1.2 Soft rubber [0.93 MPa] Viscoelastic foam [0.04 MPa] 1 1 0 2 4 6 8 10 12 0 100 200 300 400 500 600 Strain rate [%/s] Strain rate [%/s]

Figure 29: Normalized tensile moduli for the Figure 30: Normalized shear moduli for the different viscoelastic materials. Normalization different viscoelastic materials. Normalization values as shown in figure legend values as shown in figure legend

13.3.1 Soft Rubber (Para Rubber)

0.16

1.2 0.14

0.12 1

0.1 0.8 0.08 0.6

Stress [MPa] Stress 0.06 Shear stress [MPa] stress Shear 0.4 0.04

10 %/s 92 %/s, G = 1.053 MPa 0.2 0.02 5 %/s 46 %/s, G = 1.053 MPa 0.2 %/s 0.6 %/s, G = 0.936 MPa 0 0 0 50 100 150 200 250 300 0 2 4 6 8 10 12 14 16 18 Strain [%] Shear strain [%]

Figure 31: Tensile testing results for soft rubber Figure 32: Shear testing results for soft rubber

Wilhelm Johannisson 75 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

13.3.2 Hard Rubber

2 0.6

0.5 1.5

0.4

1 0.3 Stress [MPa] Stress Shear stress [MPa] stress Shear 0.2 0.5 12 %/s, E = 8.57 MPa 600 %/s, G = 2.58 MPa 6 %/s, E = 7.85 MPa 0.1 60 %/s, G = 2.02 MPa 0.2 %/s, E = 5.56 MPa 30 %/s, G = 1.94 MPa 0.1 %/s, E = 5.09 MPa 0.4 %/s, G = 1.359 MPa 0 0 0 20 40 60 80 100 120 140 160 0 5 10 15 20 25 Strain [%] Shear strain [%]

Figure 33: Tensile testing results for hard rubber Figure 34: Shear testing results for hard rubber

13.3.3 Viscoelastic Foam

0.03 44 %/s, G = 0.106 MPa 0.25 22 %/s, G = 0.086 MPa 0.025 0.3 %/s, G = 0.04 MPa

0.2 0.02

0.15 0.015

Stress [MPa] Stress 0.1

Shear stress [MPa] stress Shear 0.01

12 %/s, E = 0.149 MPa 0.05 6 %/s, E = 0.133 MPa 0.005 0.2 %/s, E = 0.094 MPa 0.1 %/s, E = 0.079 MPa 0 0 0 50 100 150 200 0 5 10 15 20 25 30 35 40 45 50 55 Strain [%] Shear strain [%]

Figure 35: Tensile testing results for viscoelastic Figure 36: Shear testing results for viscoelastic foam foam 13.3.4 Shear Relaxation

0.3

0.25

0.2

0.15 Stress [MPa] Stress

0.1

0.05

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [h]

Wilhelm Johannisson 76 Stockholm, Sweden 2015

Royal Institute of Technology Degree Project in Lightweight Structures

Figure 37: Shear relaxation behavior for hard rubber, the specimen is loaded to 27.9 % of strain and then kept at fixed strain setting measuring the drop in stress for approximately 4 hours.

www.kth.se Wilhelm Johannisson 77 Stockholm, Sweden 2015