Research on Smart Materials: Application of ER and MR ﬂuid in an Automotive Crash Energy Absorber

R.P. Delivorias Reportno. MT04.18

Supervisors: Prof. Dr. Ir. M.G.D. Geers Prof. Dr. Ir. J.S.H.M. Wismans Coach: Dr. Ir. W.J. Witteman

Eindhoven University of Technology Department of Mechanical Engineering Automotive Engineering - Vehicle Safety

Eindhoven, March 16, 2004 ii Summary

The number of serious and fatal accidents in daily traffic is weakening the last ten years. Airbags, modern belt systems and developments in interior and bodywork have mainly provided this positive tendency. However, one thinks that this tendency will not go on in the near future with the present safety applications. Car safety has become an important concept in automotive industry. The safety of a vehicle in relation to the occupants is one of the research areas of institutes like TNO and the TU/e. These developments are of crucial importance to continue this positive tendency. Research is performed on e.g. more intelligent systems like airbags and belt pre-tensioners with variable ignition time. Also, constructive aspect are of importance in this research. The concept ’compatibility’ plays an essential role. It is mainly related to constructive differences between vehicles which can results in a increased risk of injury of the occupants. Differences in weight of the vehicles and the stiffness of the frontstructure are here the most important.

This internship is related to the use of ’Smart Materials’ in crushable zones. The possibilities with so-called electrorheological and magnetorheological fluids are discussed. These fluids are able to change very fast from a liquid state to a nearly solid state when subjected to an electric or magnetic field. The application of these fluids in an crushable zone would be a move in the right direction of compatible behavior. From earlier research follows that at certain velocities (32, 52 and 64 [km/u]) optimal deceleration curves exist in which the level of injury is minimal. A crushable zone determines the deceleration of the vehicle to a large extend. Through application of ER and MR fluids stiffness variations are possible which can be optimized before or during the collision.

In this report there will be a extensive description of ER and MR fluids. Also, the properties of these fluids are discussed and with that the non-Newtonian behavior. A few theoretical models such as the Bingham model and the Herschel-Bulkley model are considered. In here, the possibilities of an advanced crushable zone are discussed. The achievable force level, the dynamic range and the geometry are important aspects which are determined by use of a list of demands. In the final chapter the designs are tested against a list of demands. The conclusions and discussions which follows from this research determines in considerable measure the feasibility of the systems.

iii iv Samenvatting

Het aantal ernstige en dodelijke ongelukken in het dagelijkse verkeer is in de laatste tien jaren drastisch afgenomen. Airbags, vernieuwde gordelsystemen en ontwikkelingen in interieur en carrosserie hebben grotendeels voor deze positieve trend gezorgd. Echter, men verwacht dat deze trend zich in de toekomst niet zal doorzetten met de huidige veiligheidsvoorzieningen. Voertuigveiligheid is een belangrijk begrip geworden in de automotive industrie. De veiligheid van een voertuig t.b.v. de inzittenden behoort tot een van de onderzoeksgebieden in onder- zoeksinstituten zoals TNO en de TU/e. Deze ontwikkelingen zijn van cruciaal belang om deze positieve trend door te zetten. Onderzoek wordt gedaan naar o.a. intelligentere systemen zoals airbags en gordelspanners met variabel ontstekingstijdstip. Ook constructieve aspecten komen in het onderzoek naar voren. Het begrip compatibiliteit speelt hierin een es- senti¨ele rol. Het heeft met name betrekking op de constructieve verschillen tussen voertuigen wat kan resulteren in een verhoogd risico op letsel voor de inzittenden. Verschillen in het gewicht van de voertuigen en in de stijfheid van de voorstructuur zijn hierin de belangrijkste.

Deze stage heeft betrekking op het gebruik van ’intelligente materialen’ in kreukelzones. De mogelijkheden met zogenaamde electrorheologische en magnetorheologische vloeistoffen worden besproken. Deze vloeistoffen zijn in staat om, onder invloed van een magnetisch/electrisch veld, razendsnel van een olieachtige vloeistof in een vaste substantie te veranderen. De toepassing van dergelijke vloeistoffen in een kreukelzone zou een goede stap kunnen zijn in de richting van compatibel gedrag. Uit onderzoek is naar voren gekomen dat bij bepaalde snelheden (32, 52 en 64 [km/u]) optimale deceleratiecurves bestaan waarbij het letselniveau minimaal is. Een kreukelzone bepaalt in grote mate de deceleratie van een voertuig. Door toepassing van ER/MR vloeistoffen zijn stijfheidsvariaties mogelijk die voor of tijdens een botsing geoptimaliseerd kunnen worden naar een bepaalde snelheid.

In dit verslag wordt uitgebreid ingegaan op ER en MR vloeistoﬀen. Er wordt ingegaan op de eigenschappen van deze vloeistoﬀen waarbij met name het niet-Newtonse gedrag naar voren komt. Enkele theoretische modellen zoals het Bingham model en het Herschel-Bulkley model worden behandeld. Vervolgens worden drie ontwerpen met toepassing van MR vloeistof uitgebreid besproken. Hierin komen de mogelijkheden van een geavanceerde kreukelzone aan de orde. Het haalbare krachtenniveau, het dynamische bereik en de geometrie zijn hierin belangrijke aspecten. Deze aspecten zijn vanuit een eisenpakket vormgegeven. In het laatste hoofdstuk worden de ontwerpen getoetst aan een eisenpakket. De conclusies en discussies die hieruit voortkomen bepalen in grote mate de haalbaarheid van de systemen.

v vi Contents

Summary iii

Samenvatting v

1 General Introduction 1 1.1 Description of the research issue ...... 6 1.2 Project Boundaries ...... 7 1.3 Internship Outline ...... 8

2 Introduction to ER and MR fluids 9 2.1 ER fluids ...... 10 2.1.1 Working principle ...... 11 2.1.2 Modes of use ...... 12 2.1.3 Material Composition ...... 13 2.1.4 Applications ...... 16 2.1.5 Design Constraints, Advantages and Disadvantages ...... 18 2.2 MR fluids ...... 19 2.2.1 Working principle ...... 19 2.2.2 Modes of use ...... 21 2.2.3 Material Composition ...... 22 2.2.4 Applications ...... 24 2.2.5 Design Constraints, Advantages and Disadvantages ...... 26 2.3 Requirements for Safety Systems in Automobiles ...... 29 2.3.1 In general ...... 29 2.3.2 Crash Situation Requirements ...... 30

vii viii Contents

2.3.3 Cost Requirements ...... 32 2.3.4 General Applicability Requirements ...... 33 2.3.5 Testing the requirements against ER and MR ﬂuids ...... 35 2.3.6 ER or MR ﬂuid? ...... 41

3 Theory Modelling 45 3.1 Fluid Models ...... 46 3.1.1 Bingham Model ...... 46 3.1.2 Other Viscoplastic Models ...... 48 3.2 Pressure Control Valve Using MR Fluid ...... 52 3.2.1 Pressure-Flow Characteristics of MR Fluid Relief Valve ...... 53 3.3 Quasi-Static Modelling of MR Dampers ...... 56 3.3.1 Basic Geometry Design Considerations ...... 56 3.4 Damper Based on a Disk Shape MR Valve ...... 61

4 Practical Modeling 65 4.1 The Necessity of An Advanced Crushable Zone ...... 66 4.1.1 Cable-supported frontal car structure ...... 68 4.1.2 Optimal decelerations curves ...... 68 4.1.3 Energy absorption by friction ...... 71 4.1.4 Design of a hydraulically controlled frontal car structure ...... 73 4.2 Design of an Advanced Crushable Zone ...... 75 4.2.1 Advanced Crushable Zone Using Pressure Control Valves ...... 75 4.2.2 Advanced Crushable Zone Using Smart Dampers ...... 82 4.2.3 Advanced Crushable Zone Using Parallel Disk Shaped Valves . . . . . 90

5 Feasibility Study 97 5.1 Testing the designs against the list of demands ...... 98

6 Conclusions and Recommendations 103 6.1 Conclusion ...... 103 6.2 Discussion and recommendations for further research ...... 104

A Properties MR ﬂuids 107 Contents ix

B Derivation of NCE 121

C MR Fluid Flow in Annular Duct 125 C.1 MR Fluid Flow in an Annular Duct ...... 126 C.2 Modeling based on the Herschel-Bulkley model ...... 127 C.3 Modeling based on the Bingham model ...... 134

D MR Fluid Flow in Parallel Duct 137 D.1 Modeling based on the Herschel-Bulkley model ...... 140 D.2 Modeling based on the Bingham model ...... 142

E MR Fluid Flow in an Parallel Disk Shaped Valve 145

Bibliography 149 x Contents Chapter 1

General Introduction

During the last years much research is performed in traﬃc safety. One must not only think of vehicles, also motorbikes, bicycles and pedestrians are under discussion. Still the amount of people having an accident, or in the worst case having a fatal accident, is shocking (see ﬁg. 1.1).

Figure 1.1: Tendency of fatal traﬃc accidents in ﬁve categories [CBS 2003]

1 2 Chapter 1. General Introduction

The last years there is a positive tendency, which is mostly attributed to electronic applications such as airbag systems en belt pre-tensioners (fig.1.2) Also constructive applications for example folding steering column, SIPS (Side Impact Protection System) by Volvo (fig.1.2) and applications of ’Smart Materials’ will entry. The government has realize compulsory crash tests by way of legislation. It is an absolute necessity for manufacturers to satisfy these regulations. Nevertheless there are various opinions about this topic. The regulations have to extend with tests like side-impact crashes and rear crash tests. A big problem in designing crash safety devices is the restricted flexibility in the constructed safety cage and the crushable crash zones. Since the vehicle is only tested on two crash tests, one has only paid attention to constructive applications which satisfy these tests.

Figure 1.2: Constructive and electronic safety applications: SIPS by Volvo [www.ciragan.com] and airbag technology [www.cookecorp.com] 3

About 60 percent of the car collisions are frontal, of which two-third is between two vehicles. The circumstances, in which collisions take place, differ a lot. Crash parameters like velocity, crash angle and the configuration of the vehicle differ strongly. They are totally dependent on the sort of collision and the collisions of the vehicles itself. The concept of compatibility [1] 1 plays an important part. At first sight, it seems to be obviously that collisions between vehicles are mostly ’fair’. Nothing is further from the truth, in the daily traffic there are still accident situations in which the energy distribution is very unfair. A dramatic consequence of this fact is an increased risk of injury (fig.1.3). In short, it means that the amount of absorbed energy totally depends on the sort of collision and the configurations of the collisions of the vehicle itself. A crushable crash zone with a high stiffness results in deceleration levels which are unacceptable, especially in case of low crash velocities. Only a part of the front of the vehicle will crumple and is not able to absorb the total amount of crash energy. On the other hand, a crushable crash zone with a low stiffness will led to intrusion of the passenger cage. The crushable zone is not able to fully absorb the amount of energy, the passenger cage will take a part of the crash energy. This will result in serious risk for the passengers.

Figure 1.3: Left: Distribution of car occupant deaths by crash type. Under: Nonfatal injuries: Distribution of moderate and more severe (MAIS 2+) car occupant injuries by crash type. Right above: Car occupant deaths, all car models [1]

1It refers to vehicle design differences that can adversely affect occupant injury risk in two-vehicle crashes. Weight differences are one example, because in crashes between heavy and light vehicles the people in the light vehicles have higher injury risks than the people riding in heavy vehicles [1]. 4 Chapter 1. General Introduction

An optimal deceleration level and the possibility to keep the passenger cage undamaged can only be achieved with a system which is able to vary the stiffness in coherence with the crash situation and crash parameters. The system will be triggered by a precrash sensing system with sensors which is able to obtain data of the collision. By means of this sensors the crash parameters are written in a map. This map also has the possibility to read data about the passenger and the remaining occupants. One must think of the position of the driver in relation to the steering wheel and also the weight and/or the length of the occupants. The whole map will apply an optimal configuration of the crushable zone which is able to require an optimal stiffness on the hand of the data from the map. Nowadays it is very complicated for engineers to design a flexible (mechanical) crushable zone with a variable stiffness. The current technology offers many possibilities in the field of car safety. Much research has been done into so- called ’smart materials’[9] 2 These materials are multi-functional and dispose of the possibility to adjust to external stimuli. One is also speaking about ’inherence intelligence’.

Figure 1.4: Left: Application of ER ﬂuid in an active damping system (Cadillac Seville STS) [GM Techlink,Vol.1, No. 1 Jan.,2002] Right: Application of MR ﬂuid dampers in buildings like the Kyobashi Seiwa Building (1989)[5].

The major materials within the group are the ferromagnetic shape-memory alloys, piezoelec-

2Smart Materials: Materials that possess adaptive capabilities to external stimuli, such as load or environment, with an inherent ’intelligence’. This ’intelligence’ or the adaptive capability of the material can be ’programmed’ by material composition, processing, defects, microstructure etc.[9] 5

tric materials, electrostrictive and magnetostrictive materials and the field responsive composites. Electrorheological (ER) and Magnetorheological (MR) fluids belong to the class of field responsive composites and they have both the capacity to undergo significant, reversible and controllable transformations with respect to their material characteristics. Thanks to these properties they can be applied in energy transducers, like dampers, to extend adaptive properties. The difference between ER and MR fluids is mainly the type of activation. ER fluids are activated by electric fields, MR fluids by magnetic fields. ER fluids have a few advantages in relation to their magnetic opposites. The use of electrical fields and their marginal response time. On the other hand, the advantages of MR fluids are the higher achievable values of the yield stress, the superior stability with relation to the temperature and the use of permanent magnets will guarantee free of interference operation. The application of ER and MR fluids in energy transducers like in an advanced crushable zone offers a good prospect. Together with a precrash sensing system, a fast and flexibel system is possible in which optimal damping characteristics can be obtained. A few publications can be found about the applications of ER and MR fluids in automotive engineering. The most common publications relate to fluid clutches in which ER and MR fluids are used to regulate the couple transfer. Volvo en Cadillac have applied a new active damping system in their new models which is able to respond super-fast on for example irregularities of the road to prevent instable vehicle behavior (fig.1.4). Hereby, there is use of a new type of shock absorbers with ER fluid. However many publications can be found about the application of ER and MR dampers in structural projects. Much research has been performed in the static and dynamic behavior of such dampers in buildings which are liable to earthquakes (fig.1.4). 6 Chapter 1. General Introduction

1.1 Description of the research issue

This assignment will take place in an internship. Mainly, this internship will consists of research in the applicability of ER and MR fluids in energy transducers such as damper- spring systems and piston-cylinder combinations with or without restrictions. This is of interest when we are looking at the present compatibility problems between mainly vehicles. The improved frontal crashworthiness of cars necessitates totally new design concept, which take into account that the majority of collisions occur with partial frontal overlap and under off-axis load directions. Realistic crash tests with partial overlap have shown that conventional longitudinal structures are not capable of absorbing all the energy in the car front without deforming the passenger compartment. An advanced crushable zone must also be able to pass through an optimal deceleration curve. Research shows that relevant injury criteria (HIC,CHEST-G,CHEST-D,FEMUR-F,NECK-M) are minimized by this optimal deceleration curves (by a typical velocity). This research lays the foundation of further researches which are related to advanced crushable zones which are compatible for different crash situations and which have the possibility to pass through an optimal deceleration curve in accordance with the crash situation. The description of the research issue is as following: ’Performing research on the possibilities of ER and MR fluid applications in crushable zones of vehicles for the benefit of crash safety’ Depending on the result of this internship, the subject of the research will be determined. This research mainly consist of a feasibility study in which an answer is given to the question: ’Do field responsive composites, like ER and MR fluids, have future perspective in the development of advanced crushable zones?’ If the feasibility study offers sufficient potency for further research in the applications of ER and MR fluids than this shall be expressed in the master thesis. The thesis object shall then consist of a complete design of an advanced crushable zone based on energy transducers by means of field responsive composites. 1.2. Project Boundaries 7

1.2 Project Boundaries

Since the internship only consists of a few weeks, there must be a clear formulation about the topics which come up and the topics which not come up in this research. This is of great importance, because the result of the research determines the further course of the thesis object. The internship will consist of the following main topics:

• Plan of Approach

• Literary Study ER and MR ﬂuids:

– Theoretical Modelling – Practical Modelling – Applications: ∗ Automotive Applications ∗ Structural Applications

• Choice ER or MR ﬂuid by means of a literary study

• Brainstorming about the possibilities to apply ER and/or MR ﬂuids in an advanced crushable zone:

– Spring-Damper Systems – Damper Systems with or without restrictions – Etc. etc.

• Design phase:

– Stress Course in Fluid – Global Design Advanced Crushable Zone – (Dynamical Calculation System (Finite Element Methode) – (Statical Construction Calculations)

• Feasibility Study:

– Arguments – Conclusion – Discussion – Recommendations for further research – Presentation 8 Chapter 1. General Introduction

1.3 Internship Outline

The contents of this internship are structured as following. In chapter 2 an introduction about field-dependent fluids is given and in particular about ER and MR fluids. Specifications of these fluids are given, also there’s paid attention on the modes of use. Further there will be a critical view on the possibilities of these fluids, what are the advantages and disadvantages of the fluids and then mainly with regard to the use of these fluids in car safety applications. The fluids do have potency within this sector, when they satisfy a list of demands to a greater extent. To test the possibilities of these fluids, an extensive list of demands is used which is intended for safety applications in the automotive sector. With the help of these results, conclusions are drawn about the potency of ER and MR fluids in safety applications. With this there will be a look at the possibility of ER and MR fluids in an advanced crushable zone. In chapter 3 three theoretical models are discussed which forms the foundation of the final designs. In particular, there will be a description about the behavior of non-Newtonian fluids, which can be used to describe the behavior of these fluids. In chapter 4, these theoretical models are applied in three designs. These designs are calculated with the help of a few basis equations which follows from the theoretical models. Finally there will be a feasibility study in chapter 5. In this chapter the designs are compared against each other. With the help of the list of demands of chapter 2, the most suitable design is chosen for further research. The chapter will be closed with a final conclusion, discussion and recommendations for further research. Chapter 2

Introduction to ER and MR ﬂuids

1Within the class of Smart Materials there is a sub-set of materials as the field responsive (or controllable) composites. The composites are able to respond in a continuous, rapid and reversible manner to an applied electric or magnetic field with a change in their physical properties. In this way it is possible for these materials to react to changes in their environment. In most cases these field responsive fluids consist of particles dispersed in a base/carrier fluid. They have the ability to provide simple, quiet and above all, rapid-response interfaces between electronic controls and mechanical systems. Main differences between these field responsive fluids and the traditional smart materials is the fact that they are soft materials (dispersions or gels) rather than solids, which makes them usable in other types of applications.

1This chapter considers an literature survey about ER and MR ﬂuid, the information mainly comes from the literature survey ’Smart Materials in Automotive Applications’ by S. Rutten[9]. When the information is taken somewhere else, than this shall be indicated by a separate reference.

9 10 Chapter 2. Introduction to ER and MR ﬂuids

2.1 ER ﬂuids

ER fluids experience a significant change in their magnetic, electric, thermal, acoustical and optical properties upon exposure to an electric field. The most important change, however, takes place in their microstructure and with that in their rheological behavior: the resistance to flow increases with increasing electric field. This is caused by an increase of the viscosity of the fluid, because of which the consistency of ER fluids can change from a thick fluid (similar to motor oil) when no field is applied, to a nearly solid substance when subjected to an electric field. This change in the structure and also in the rheological properties of a liquid or another type of dispersed system under the application of an external electric field is called the ER effect. The liquid or the dispersed system is generally called an ER fluid.

Figure 2.1: ER ﬂuids have a response time smaller then a few milliseconds. The change in the structure is called the ER eﬀect[9]/(www.lord.com).

This change can take place within the span of a few milliseconds from the moment the field is applied. Furthermore, it is a fully reversible process. ER fluids that have solidified under subjection to an electric field can start to flow again by removing the electric field or by applying a shear stress that exceeds a certain critical value. This critical shear stress that makes ER fluids flow is also known as the yield stress, which is one of the most important factors in evaluating the performance of the fluid. In table 2.1 typical values for the most important properties of ER fluids are already given.

Still, however, ER ﬂuids are not used on a large scale in commercial devices. Reasons for this are the relative low yield stress, the temperature dependence of this yield stress, the sensitivity 2.1. ER ﬂuids 11

Table 2.1: Typical values for several properties of ER fluids[9] Maximum Yield Stress τ 2-5 [kP a] Maximum Field Strength E 4 [kV/mm] (Limited by breakdown) Viscosity η 0.1-1.0 [P a.s] Operable Temp. Range: +10 [oC] to +90 [oC] (ionic,DC) -25 [oC] to +125 [oC] (non-ionic, AC) Stability Cannot tolerate impurities Response Time < a few milliseconds Density 1-2 [g/cm3] 2 −7 −8 Active Volume Figure of Merit (ηp/τy ) 10 − 10 [s/P a] Maximum Energy Density 101 [J/m3] Power Supply 2-5 [kV ] at 1-10 [mA] (2 − 50[W ]) of ER fluids to impurities (which can alter the polarization mechanisms) and finally the need for relatively expensive high voltage power supplies. Recently it has been predicted that ER fluids are able to achieve yield strengths of around 16 [kP a]. This predicted value is very attractive to academic studies and engineering applications because it is a step closer to the order of the yield stress of MR suspensions, the magnetic counterpart of ER fluids

2.1.1 Working principle

Most ER fluids are dispersions of small dielectric particles, which can be solid or liquid, with sizes in the order of a few microns, suspended in a non-conducting carrier liquid. In the absence of an electric field the ER fluid is in the ’off’ state. The particles are then randomly dispersed throughout the carrier liquid. In this state, the consistency and also the value for the viscosity of ER fluids can be compared to motor oil (0.1 [P a.s] at low shear rates). When subjected to an electric field, the viscosity of ER fluids increases. Winslow first explained the effect in the 1940s using oil dispersions of fine powders. The electrorheological effect, sometimes called the Winslow effect, is thought to arise for the difference in the dielectric constants of the fluid and particles[8]. Physically, the ER effect originates from the polarization of particles in carrier liquid. The field induces dipoles in the dielectric particles and these particles then will start to aggregate. They will start to form fibrous structures (chains or column-like structures) between the electrodes, aligning along the direction of this applied field. They do so to minimize the dipole-dipole interaction energy, because minimization of the potential energy leads to a stable position. These chain-like structures restrict the motion of the fluid, thereby increasing the viscous characteristics of the suspension, changing the rheology of the ER fluid to a near solid state. Fig.2.1 shows this change of the microstructure of an ER fluid between before and after an electric field is applied. The stronger the electric field (E), the higher the yield stress of the ER fluid gets (up to a certain maximum). Reason for this is that the stronger the applied field is, the stronger the bond between the particles is and the harder it will be to break this bond. Electric field strengths up to 4 [kV/mm] (limited by the breakdown of the ER fluid) are required, which makes the strength of ER fluids range from 2 to 5 [kP a], depending on the strength of the electric field and the composition of the fluid. Higher values of around 10 [kP a] are achievable at this moment, but not yet commercially applicable. The fact that the yield stress is field dependent can be useful in 12 Chapter 2. Introduction to ER and MR fluids

energy transducers in several possible manners. These modes of use are discussed in the next subsection.

2.1.2 Modes of use

Energy transducers using field responsive fluids are almost always based on one of the following three principles: flow, shear or squeeze mode. These can occur alone or in combination with each other. The three modes are illustrated in figure 2.2.

Figure 2.2: Basic operating modes for controllable ﬂuid devices[5] 2.1. ER ﬂuids 13

In the flow or valve mode (a), the ER fluid has to flow through a gap in the electric flux guide. The strength of the electric field determines the flow resistance of the ER fluid and by this the pressure drop across such a valve. This use of ER fluid as a working medium can make electromechanical valves and any other moving parts redundant and is therefore very interesting because of low wear and maintenance. Possible applications for flow mode include servo valves, shock absorbers, vibration dampers and other hydraulic systems with ER fluid as hydraulic medium. The direct shear mode (b) can be seen as two plates with ER fluid in between, which move parallel to one another. The transferred force from one plate to the other, via the ER fluid, can be controlled by the strength of the electric field. Possible applications for this shear mode are clutches, brakes and electrically controllable dampers. Finally, the squeeze-film mode (c) is used in low motion, high force applications. In this mode the fluid is subjected to compressive stress, rather than shear stress. It had been reported that field responsive fluids provide a high yield stress under tension and compression, which is an order of magnitude higher that that in shear mode. The ER fluid is located between parallel plates. If the distance between these plates is changed, the ER fluid is squeezed out. The case with which the fluid is squeezed out can be adjusted through the strength of the electric field. In this way relatively high forces can be achieved and this makes it especially suitable for the damping of vibrations with low amplitudes (up to 1 [mm]) and high dynamic forces. The squeeze mode can be used in applications such as machine tools and to control deformation.

2.1.3 Material Composition

Most ER fluids are made up of three components: the dispersed phase, the continuous phase and small amounts of unavoidable additives, such as inorganic salts, water and other (water- free) additives 2. ER fluids can be divided into two main groups, based on the type of dispersed phase they contain. The first is the heterogeneous ER fluid, which consists of solid particles dispersed in an insulating carrier liquid. In the second phase, the homogeneous ER fluid, these solid particles are replaced by another liquid, so they form liquid-in-liquid suspensions. Another way to divide the ER fluids is by looking at whether they contain water or not. Water-based ER fluids have advantages as well as disadvantages compared to water-free ER fluid. In figure 2.3 the classification of the different types of ER fluids is illustrated.

2The reader is referred to [9] for more information about the three components of ER ﬂuids. 14 Chapter 2. Introduction to ER and MR ﬂuids

Figure 2.3: Classiﬁcation of ER ﬂuids[9]

Heterogeneous versus Homogeneous

Heterogeneous ER fluids are dispersions of small dielectric solid particles, with sizes in the order of a few microns, suspended in a non-conducting carrier liquid. The particles can be made of inorganic, organic or polymer materials. Heterogeneous ER fluids have already been studied for a long time and there is a large body of literature on the subject. Still, the main problem for the heterogeneous ER fluid is the sedimentation of particles when the fluid is inactive for a long period. To solve this particle sedimentation problem, recently much effort has been expended in developing homogeneous ER fluids. Benefit of these homogeneous ER fluids is that they do not contain solid particles inside; they consist of a liquid dispersed into an insulating oil (or other type carrier liquid), so a liquid in a liquid. They are believed to be a new and promising type of ER fluid. However, the viscosity under zero electric field, which is several orders in magnitude greater than that of heterogeneous fluids, and liquid-liquid segregation problems are still obstacles for these fluids. Water-based versus Water-free

Before 1985, all existing ER fluids contained small amounts of water. Such water-based ER fluids, called extrinsic ER fluids, have several shortcomings. First, the low boiling point of water will lead to the evaporation of the adsorbed free water at elevated temperatures. This will lead to a decrease of the ER effect, resulting in large temperature instability of water-based ER fluids. Another shortcoming is the high conductivity of water, which can result in a large leaking current density of water-based ER fluids. Finally, the water in the ER fluid can also lead to device erosion. To overcome these shortcomings in 1985 the first water-free, or intrinsic, ER fluid was developed. This was an acenequinone radical polymer ER fluid, developed by Block. This new class was termed anhydrous ER fluids and they were 2.1. ER fluids 15

believed to hold high potential for industrial applications. These anhydrous ER fluids are able to work in a wide temperature range and have superior properties in comparison to most ER fluids. Many other kinds of water-free or intrinsic ER fluids were developed thereafter. In the late 1980’s, however, it was realized that water-free ER fluids had one big problem: particle sedimentation. This can cause the ER fluid to malfunction completely, severely limiting its practical applicability. It was also discovered that conventional, water-based ER fluids have some advantages over water-free ER fluids, such as their higher yield strength and the numerous different types that had already been developed, compared to intrinsic ER fluids. Moreover, it was proved that small amounts of water are especially effective to ER activity. The function of this absorbed water is considered to be that the water forms mobile charge carriers on the surface of the particles, due to the solvency to impurity ions. The charge carriers tend to migrate and this leads to an interfacial polarization, which induces the ER effect under an electric field. Unfortunately, this important effect has been neglected due to the disadvantages that are present in the extrinsic or water-based ER fluids. Most research from that time has been concentrated on improving the properties of water-free ER fluids, instead of trying to work on the shortcoming of water-based ER fluids. ER fluids can be dis- tinguished into three phases: the continuous phase, the dispersed phase and several additives. The primary function of the continuous phase or carrier liquid is to provide a matrix material in which te particles (dispersed phase) can remain suspended. The continuous phase consists of an insulating oil of some type. The dispersed phase consists of particles which typically range in size from 0.1 to 100 [µm]. The particle volume fraction is between 0.05 and 0.50. Additives form the third component of an ER fluid. Water, alkali, salt and surfactants are the most common. They are firstly used to hydrolyze ER fluids. This is necessary because it’s usually not possible to activate an ER system without water. 16 Chapter 2. Introduction to ER and MR fluids

2.1.4 Applications

Because of the rapid and reversible response to the applied external electric field, ER fluids were believed to hold great potential in many applications which require an electric and mechanical interface. Another benefit is that the use of such a field responsive fluid reduces the complexity of devices, for example the fact that controllable valves become unnecessary, because the flow properties of the fluid can be controlled here. ER fluids must be able to perform their task over wide temperature ranges, especially for automotive applications. Therefore future studies will have to continue to emphasize the development of high performance ER fluids with a strong ER effect and no sedimentation trouble. Several commercial applications have been explored, mostly in the automotive industry, such as ER fluid-based engine mounts, clutches and seat dampers[8](figure 2.4).

Figure 2.4: Three operating modes of ER dampers a) ﬂow, b) mixed and c) shear mode[9]

It seems to be that ER fluids are widely used, but several applications in real-life applications and the commercialization of ER fluids has been very limited. There are several reasons for this. Closed-loop control is a difficult problem because of the complexity and nonlinearity of the fluid behavior. In addition, the need for high voltage to control ER fluid-based devices creates safety concerns for human operators, especially devices that will be in contact with humans. Their relatively high cost and the lack of a large variety of commercially available ER-based devices with different properties to satisfy various design specifications have made the commercialization unprofitable. An example of research that may lead to the needed boost is the development of composite particles (conducting particles coated with a thin non- conducting outer layer), which show a very strong ER effect. The metal core, which is still present in many of the particles used nowadays, makes the density of these particles very high, resulting in a high risk of sedimentation. By replacing this typical metal core by a composite particle with a dielectric core of high strength and low mass and a conducting inner layer, a novel doubly coated particle is produced. One totally new technological area is the virtual 2.1. ER fluids 17

reality and telepresence, enhanced with haptic (i.e. tactile and force) feedback systems, and for use in medical applications, for example[8]. A beautiful example of this new technology is MEMICA (remote mechanical mirroring using controlled stiffness and actuators) that was recently conceived by researchers at Rutger University and the Jet Propulsion Laboratory. MEMICA is intended to provide human operators an intuitive feeling of the stiffness and forces in remote or virtual sites in support of space, medical, underwater, virtual reality, military, and field robots performing dexterous manipulation operations (figure 2.5). The key aspects of MEMICA are miniature Electrically Controlled Stiffness (ECS) elements and Electrically Controlled Force and Stiffness (ECFS) actuators that mirror the stiffness and forces at remote/virtual sites. The ECS elements and ECFS actuators are integrated on an instrumented glove. Forces applied at the robot end-effector will be reflected to the user where a change in the system viscosity will occur proportionally to the force to be transmitted.

Figure 2.5: Performing virtual reality medical tasks via the electrorheological ﬂuid based MEMICA haptic interface[8] 18 Chapter 2. Introduction to ER and MR ﬂuids

2.1.5 Design Constraints, Advantages and Disadvantages

The main design constraint that has to be kept in mind when applying ER fluids is the low achievable maximum yield stress. Typical ER fluids are only able to attain shear stresses around 5 [kP a], with 10 [kP a] being the maximum value at this time. The maximum value that ER fluids are predicted to reach, based on theoretical models, is approximately 16 [kP a]. This is still much lower than the attainable values of their magnetically activated cousins, the MR fluids, which are typical in order of magnitude of 50-100 [kP a]. This difference has some consequences for the amount of active fluid required and with that the size and weight of the device. The advantages are:

• ER ﬂuids undergo a reversible and controllable change in their rheological properties when subjected to an electric ﬁeld.

• Electric ﬁelds are fairly easy to supply.

• The response time of ER ﬂuid based devices is estimated to be fewer than 10 [ms]. Therefore ER ﬂuids are very suitable for dynamic applications.

• The particles in ER ﬂuids typically have a density that is close to that of the carrier liquid. This means that the density mismatch is relatively low, leading to a lower tendency of sedimentation of the particles.

• The low density of the particles also helps to keep the density of the entire ER ﬂuid at a moderate level, ranging from 1 to 2 [gr/cm3].

• Finally, the lower density of the particles also results in relatively low base viscosity (below 100 [mP a.s]) of the ER ﬂuid as a whole. This results in low friction or ﬂow losses, which can be important in hydraulic circuits.

• ER ﬂuids show very low abrasiveness. Together with the fact that they can make several moving parts redundant, this can lead to an increase in reliability and a reduction of maintenance requirement.

The disadvantages are:

• The relatively low attainable yield stress τ, which result in the need of a relatively large amount of active ER ﬂuid. This can lead to large device sizes and weights to achieve a certain performance level.

• ER ﬂuids are voltage driven. They require large voltages (some [kV ]) at a low current (few [mA]), which means that they require relatively expensive high voltage power supply.

• ER fluids are very sensitive to impurities or contaminants, as these can negatively affect the polarization mechanism. This can lead to a significant decrease of the ER effect or even a complete malfunctioning of the device. 2.2. MR fluids 19

2.2 MR ﬂuids

MR fluids react to an external stimulus in a similar way as ER fluids, which are discussed in the previous section. They also undergo a dramatic change in their rheological properties when subjected to a specific field. The difference is that MR fluids respond to a magnetic field instead of an electric field. When subjected to a magnetic field, MR fluids undergo a change in their viscosity and can change from a liquid state with a relatively low viscosity, like motor oils, to an almost solid state. The time span in which this change occurs lies within a few milliseconds and the effect is completely reversible. Upon removal of the applied field, the fluid returns to its original configuration. In table 2.2 below, typical values for some of the most important properties of MR fluids are already given. Over the next pages the working principle, composition, modes of use and possible applications are discussed in that order. Finally the design constraints and the advantages and disadvantages are treated.

Table 2.2: Typical values for several properties of MR ﬂuids[9] Maximum Yield Stress τ 10-100 [kP a] Maximum Field Strength H 250 [kA/m] (Limited by saturation) Base Viscosity η 0.3 [P a.s] Operable Temp. Range -40 [oC] to +150 [oC] Stability Unaﬀected by most impurities Response Time < a few milliseconds Density 3-4 [g/cm3] 2 −10 −11 Active Volume Figure of Merit (ηp/τy ) 10 − 10 [s/P a] Maximum Energy Density 103 [J/m3] Power Supply 2-25 [V ] at 1-2 [A] (2 − 50[W ])

2.2.1 Working principle

Recently MR fluids have enjoyed a new surge in their engineering application possibilities, due mainly to their relatively high yield stress and the low voltage required in contrast to ER fluids. The area of vibration control has attracted most of the MR fluid applications. Nowadays the LORD Corporation is one of the key players in the development of MR fluid based devices. They have successfully introduced some MR devices in commercial applications, such as an active suspension system for automobiles, controllable fluid brakes, which are applied in fitness equipment etc. In the absence of an applied field, the controllable fluid exhibit Newtonian-like behavior. When the MR fluid is subjected to a magnetic field, the particles become magnetized (induced dipoles) and they start to behave like tiny magnets. This is the ’on’ or magnetized state of the MR fluid. The magnetic interaction, and with that the total potential energy, between these particles can be minimized if the particles line-up along the direction of the magnetic field lines. With the potential energy minimized, the particles are in a stable position. The interaction between the resulting induced dipoles causes the particles to aggregate and form fibrous structures within the carrier liquid (chains or column-like structures), changing the rheology of the MR fluid to a near solid state (see figure 2.6). These chain-like structures restrict the flow of the fluid, thereby increasing the viscous characteristics of the suspension. 20 Chapter 2. Introduction to ER and MR fluids

The mechanical energy needed to yield these chain-like structures increases non-linearly with increasing applied magnetic field H, resulting in a field dependent yield stress. This nonlinearity is explained by the non-uniform magnetization of different parts of the particles.

Figure 2.6: Illustration of the structural change in an MR ﬂuid [www.lord.com]

Magnetic fields intensities up to 160 [kAm−1] are required, which are easy to obtain using a standard 12 [V ] or 24 [V ] power supplier, such as the battery in a car. Depending on the flux density B and the composition of the fluid, an apparent yield stress ranging form 10 to 100 [kP a] can be achieved. Materials with higher magnetization saturation can be used to increase this even further, but these are often less available and thus more costly. The process is fully variable and also reversible. By controlling the strength of the magnetic field, the shear strength of the MR fluid can be altered and with this the resistance to flow can be varied. The fine tuning of the magnetic current allows for any state between the low forces of ’off’ to the high forces of ’on’ to be achieved. Reversible means that when the magnetic field is removed, the chains are broken and the particles return to their original statistical distribution. Both the activation and the deactivation of the MR fluid are completed within a few milliseconds after the introduction or removal, respectively, of the magnetic field. The response time of a complete system using MR device(s) is estimated to be around between 15- 25 [ms], strongly depending on the nature of the device. The density of the whole suspension ranges from 3 to 4 [gr/cm3]. A final remark about MR fluids is that they, unlike ER fluids, are not highly sensitive to contaminants or impurities, which can be commonly encountered during manufacture and also during usage. 2.2. MR fluids 21

2.2.2 Modes of use

Energy transducers using MR fluids as coupling medium are, like ER fluids, almost always based on the following three principles: flow, shear and squeeze mode (see figure 2.4). These can occur alone or in combination with each other. The only difference between the modes of use of ER and MR fluids is that the MR fluid is located in a gap in the magnetic flux guide. The field lines of the magnetic field H run perpendicular to the shear/flow direction and parallel to the squeeze direction, inducing the formation of column-like structures in this direction. This is illustrated in figure 2.7.

Figure 2.7: Schematic of the prototype 20-ton large-scale MR fluid damper: the field lines of the magnetic field run perpendicular to the flow direction [5] 22 Chapter 2. Introduction to ER and MR fluids

2.2.3 Material Composition

MR ﬂuids are built up of 3 components: the dispersed phase (the magnetizable particles), the continuous phase (the carrier liquid) and small amount of additives and stabilizers. Each of these components is described separately below.

• Dispersed Phase The requirements set on the choice of particle material are that the particles have to be magnetically multi-domain and they exhibit low levels of magnetic coercivity. In addition, maximizing the inter-particle forces and thus maximizing the MR eﬀect can be achieved by choosing the particle material of the saturation magnetization Js[T esla]. The higher Js, the higher the inter-particle forces and the higher the MR eﬀect is. The material most used today is high purity carbonyl iron (F e) powder, made by chemical vapor deposition (CVD) of iron pentacarbonyl (F e(CO)5). The reasons for this are:

– The high chemical purity (>99.9%), which leads to less domain pinning. – The mesoscale dimensions, which have many magnetic domains. – The spherical shape, which minimizes the magnetical shape anisotropy.

– Its high magnetization saturation (Js = 2.4[T esla]). – The particles are magnetically soft and thus non-abrasive.

The best available particles are alloys of iron and cobalt that have saturation magnetization of about 2.4 [T esla]. Unfortunately, such alloys are prohibitively expensive for most practical applications. The best practical particles are simply pure iron, as they have a saturation magnetization of 2.15 [T esla]. Virtually all other metals, alloys and oxides have saturation magnetization signiﬁcantly lower than that of iron, resulting in substantially weaker MR ﬂuids.

• Continuous Phase The primary function of the carrier liquid is to provide a low permeability, non-magnetic base liquid in which the magnetically active phase particles can remain suspended. The liquid has to be low permeable to allow the particles to polarize with the utmost effectiveness, thus enhancing the MR effect. Furthermore, the carrier liquid is chosen based upon its rheological and tribological properties, as well as on its temperature stability. Important aspects to consider are the boiling temperature and the vapor pressure at elevated temperatures and at the freezing point. Also, the carrier liquid has to be largely non-reactive towards the magnetic particles and to the materials used in the device construction. Finally, the ’off’-state viscosity of the MR fluid depends largely on the selection of the base fluid. To avoid large friction losses, the ’off’-state viscosity should be as low as possible. Typical materials used as carrier liquid are water or other polar organic liquids (such as glycol), silicone oils, (semi-)synthetic oils, mineral oils, petroleum based oils and combinations of several types of oil. Also polyesters and polyethers are used. The volume ration of the carrier liquid ranges from 0.5 to 0.9.

• Additives 2.2. MR ﬂuids 23

Additives form the third part of a MR fluid. Because the magnetic polarization mechanism, the working principle of MR fluids, is not affected by the surface chemistry of surfactants, it is relatively straightforward to use additives in MR fluids for all kind of purposes, such as:

– Prevention or minimization of sedimentation. – Prevention or minimization of coagulating of the particles: ∗ To maintain a coating on the particles in order to enhance redispersibility. ∗ To enhance anti-oxidation. ∗ In water-based carrier, liquids additives are used to control the pH-value.

The prevention of sedimentation is one of the most important aspects. If this is not prevented, MR fluids will alter their properties significantly over time. Some examples of additives are given which help to prevent this. Sedimentation is typically controlled by the use of thixotropic agents and surfactants such as xantham gum, silica gel, stearates and carboxylic acids. The thixotropic networks disrupt the flow at ultra low shear rates (the viscosity becomes nearly infinite), but thins as the shear rate is increased. The stearates form a network of swollen strands when used in conjunction with mineral oil and synthetic esters that serve to entrap particles and immobilize them. Fine carbon fibers have also been used for this purpose. The fibers increase the viscosity through physical entanglement but exhibit shear thinning due to shear-induced alignment. In this way they all contribute to keep the particles suspended in the carrier liquid and in this way the MR fluid will not alter its properties much over time. An important conclusion that was derived from the literature is that for each application and for each device, a specially formulated MR fluid should be developed. This because each MR fluid application or device has its own distinct working conditions, such as the environment in which it has to operate and the forces it is subjected to. Four types of MR fluids manufactured by the LORD Corporation are now commercially available. Appendix A presents the main properties of these four types of MR fluid: MRF-132AD (Hydrocarbon-Based), MRF-241ES (Water-Based), MRF-336AG (Silicone-Based) and MRF- 122-2ED (Hydrocarbon-Based). Furthermore, the characteristics of the yield stress versus magnetic induction, shear stress as a function of the shear rate (with no magnetic field applied at 40[oC]) and the magnetic properties are given in the appendix. It can be seen in combination with the B-H curve of the MR fluid that MR fluids have an approximately linear magnetic property when the applied magnetic field is small. As the magnetic field increases, a gradual magnetic saturation is observed; consequently, the MR fluid yield stress saturates due to its direct relationship with the magnetic field[5]. Figure 2.8 gives the relation between viscosity and the shear rate, it is clear that MR fluids exhibit a shear thinning effect because of both the addition of suspension agents and changes in the magnetic particle microstructure during shear[5]. 24 Chapter 2. Introduction to ER and MR fluids

Figure 2.8: Characteristic of the LORD MRF-132LD oil-based MR ﬂuid: relation viscosity - shear rate[5]

2.2.4 Applications

MR fluids are, like other field responsive fluids, able to respond in a rapid and reversible manner to external stimuli. Therefore, MR fluids hold great potential in many applications that require an electromechanical interface, such as clutches, brakes, valves, dampers and robotics. Another benefit is that the application of field responsive fluids can reduce the complexity of devices significantly, by making controllable valves redundant. Unlike the ER fluids discussed in the previous subsection, MR fluids have already been successfully introduced in commercial applications. This is mainly due to the fact that at the moment MR fluids are able to meet industry requirements much better than any other field responsive fluid. Some of their properties are superior to those of other field responsive fluids, such as the much higher yield stress, the fact that they are relatively insensitive to impurities or contaminants and the lower cost. However, recently researchers have come to the conclusion that MR fluid technology may not be the most successful of the field responsive composites. Therefore also more and more research has focused on the improvement and application of other field responsive fluids, like ER fluids. The area vibration control has created most of the MR fluid applications available today. Dampers for vibration control using MR fluid in the flow mode of operation are already employed in washing machines, prosthetic limbs, active suspension systems for cars and very large MR fluid dampers for seismic damage mitigation in civil engineering structures (see figure 2.9). Over the past several decades, much attention has been given to the use of active control in civil engineering structures for earthquake hazard mitigation. These types of control systems are often called protective systems and offer the advantage of being able to dynamically modify the response of a structure in order to increase its safety and reliability. Passive control devices, including base isolation, metallic yield dampers, friction dampers, viscoelastic dampers, viscous fluid dampers, tuned mass dampers and tuned liquid dampers, are well understood and are an accepted means for mitigating the effects of dynamic loadings. How- ever, passive devices have the limitation of not being capable of adapting to varying usage 2.2. MR fluids 25

Figure 2.9: Left: MR fluid damper/Right: MR fluid rotary brake[9] patterns and loading conditions. An alternative approach offering the reliability of passive devices, yet maintaining the versatility and adaptability of fully active systems is found in semi-active control devices3. The MR damper is one of the most promising new devices for structural vibration reduction. Because of its mechanical simplicity, high dynamic range, low power requirements, large force capacity and robustness, this device has been shown to mesh well with application demands and constraints to offer an attractive means of protecting civil infrastructure systems against severe earthquake and wind loading[13]. An example of active vehicle suspension is the MagneRideTM system, developed by Delphi and Lord Corporation. Here the MR fluid is used as a working medium within fluid-based struts and shocks. By controlling the current to an electromagnetic coil inside the piston of the damper, and thus controlling the strength of the magnetic field, the shear stress of the MR fluid can be altered and with that the resistance to flow can be varied. By varying the magnetic current it is possible to allow any state, between the low forces in the ’off’ state to the high forces in the ’on’ state, to be achieved in the damper. The result is continuously variable real-time damping. Another main application area is that of torque transfer, as in clutches and rotary brakes (figure 2.9). Controllable MR fluid-based brakes are already being used since 1995 in various types of fitness equipment and will soon be ready for successful employment in automotive applications. They are also used in haptic force feedback devices, such as steer-by-wire systems.

3Semi-active control device: a semi-active control device is one which cannot input energy into the system being controlled. Examples of such devices include ER and MR fluid dampers, variable orifice dampers, friction controllable isolators and dampers and variable stiffness devices. 26 Chapter 2. Introduction to ER and MR fluids

2.2.5 Design Constraints, Advantages and Disadvantages

The main design constraint of the use of MR fluids is that they require magnetic fields for activation. To provide a magnetic field a coil and a magnetic flux guide is needed, which can have implications for the weight, size and shape of the device. The fact that a magnetic field cannot be shielded off very easily and that this can influence the functioning of other devices in automobiles in a harmful manner also makes it difficult to use. During the development and commercialization phases of several recent MR fluid devices, problems with the MR fluid were discovered that were not apparent in the early research phases of these projects[2]. An example of one such problem is a phenomenon called ”In-Use-Thickening” or IUT. It means that MR fluid will thicken after it is subjected to high stresses and high shear rates over a long period of time. On originally low-viscosity, i.e. becomes an unmanageable paste having the consistency of shoe polish. An example of the IUT problem is illustrated in figure 2.10. In this example, the ’off’-state force of an early version of the MotionMasterTM RD-1005 truck seat damper is shown over the course of a life-cycle test. The IUT phenomenon appears as a progressive increase in the ’off’-state force. By the time the damper had experienced 600.000 ’on’-state cycles, the off-state force has increased from 200 [N] to 500 [N].

Figure 2.10: Example of IUT problem in an early MR ﬂuid formulation[2] 2.2. MR ﬂuids 27

Today the ”in-use-thickening” problem has not only been identified but has been solved (see also figure 2.11). Depending on the conditions of the specific application, all the MR fluids will show some degree of deterioration. The amount of deterioration depends on the shear rate, temperature and duration. An useful measure is the lifetime dissipated energie or LDE for predicting the expected life of a MR fluid:

1 Z LIF E LDE = P dt (2.1) V 0 where P is the instantaneous mechanical power being converted to heat in the MR device. Thus, LDE is simply the total mechanical energy dissipated per unit volume of MR ﬂuid over the life of a device.

Figure 2.11: Progressive development of IUT resistant MR ﬂuid formulations[2] 28 Chapter 2. Introduction to ER and MR ﬂuids

It is very useful to distinguish the advantages and disadvantages of MR ﬂuids, because it is give us the knowledge about the possibilities of designing a device with MR ﬂuid. The advantages are:

• MR ﬂuids show a reversible and controllable change in their rheological properties upon subjection to a magnetic ﬁeld.

• MR fluids are current driven. For the control of the field coil voltages below 10 [V ] and currents below 2 [A] can be sufficient to operate the device properly. These can be obtained using a standard 12 [V ] or 24 [V ] power supplier, such as the battery in a car.

• The response time of MR based devices is estimated to be around 15-25 [ms], which is still very fast, but slower than their electrically activated cousins, the ER ﬂuids.

• MR fluids are able to attain high shear stresses in the order of magnitude of 50-100 [kP a], which results in the fact that only a small amount of active fluid is required to achieve a certain performance level. This can positively affect the size and weight of a MR based device.

• MR ﬂuids are not very sensitive to contaminants and impurities, which can be commonly encountered during manufacture and also during usage.

• This insensitivity of the working principle of MR ﬂuids towards contaminants also holds for the surface chemistry of surfactants and additives. That is why it is relatively straightforward to stabilize MR ﬂuids against particle-liquid separation (sedimentation), in spite of the large density mismatch.

• Fail-safe operation of MR based devices can be achieved through the use of permanent magnets MR ﬂuids. In this way MR ﬂuids can be energized without the need for any steady-state power.

• MR ﬂuids are able to operate over a wide range of temperatures.

The disadvantages are:

• Magnetic ﬁelds are not easy to supply and use.

• The density mismatch between that of the particles and the carrier liquid is typically fairly high, which can lead to a higher risk of sedimentation.

• This high density of the particles also leads to a relatively high density of the entire MR ﬂuid, ranging from 3 to 4 [gr/cm3].

• The typical ’off’-state viscosity of MR fluids is relatively high. This can lead to relatively high friction or flow losses in devices, such as rotary fluid brakes, when no activation of the fluid is required. 2.3. Requirements for Safety Systems in Automobiles 29

2.3 Requirements for Safety Systems in Automobiles

In the previous sections there’s paid attention to the properties of ER and MR fluids, for instance the working principle, general advantages and disadvantages and examples of applications. This section will discuss the requirements for safety systems in the automotive engineering. This requirements will be tested by practical experience and in particular there will be paid attention to ER and MR fluids. Further, conclusions are drawn about the possibilities of applications of ER and MR fluids in advanced crushable crashzones. There will also be a pronouncement upon which of the two fluids is the most suitable. The next chapter gives a description of the theory which is used for describing such fluids. Mainly the theory will describe the Non-Newtonian behavior and with that models like the Bingham and the Herschel-Bulkley model.

2.3.1 In general

Nowadays safety systems, for the promotion of the crashworthiness, are classified into two main groups namely: passive and active safety. Active safety can be defined as being all measures that are aimed at avoiding collisions and passive safety includes all measures that are taken to positively influence the outcome of an accident. Safety measures and devices can also be classified in another way, being with respect to the time period during the crash event (pre-crash, crash and post-crash) and to what type of measure or (risk) factor influences the crash (human, vehicle and environment). This can be illustrated in what is referred to as an alternative Haddon’s Matrix, containing preventive measures for each of the factors and the different time periods (see figure 2.12)[11]. The active safety measures can be found

Figure 2.12: Haddon’s Matrix for classifying preventive safety measures[11]

in the upper row, the pre-crash factors. Passive safety strategies are the ones located in the centre row, the time period crash. This internship is mainly related to the indicated rectangle in ﬁgure 2.12 (passive safety). This category consists of restraint systems (seatbelt systems, airbags), the crashworthiness of the vehicle (crumple zones) and the protection of the occupants in case of contact with the car interior (padding). 30 Chapter 2. Introduction to ER and MR ﬂuids

2.3.2 Crash Situation Requirements

The ﬁrst and probably the most important design constraints to consider are the requirements which vehicle safety devices have to meet from the point of the view of the car crash event. When these requirements cannot be met, it is virtually impossible for the device or material to be applied in adaptive crash safety. There are ﬁve important requirements which are discussed below. These requirements are the following:

• Fast Response Time

• Sensing Properties

• Actuating Properties

• Reliability

• Durability

Fast Response Time

The maximum amount of time for a safety system to sense a disturbance of some kind and react accordingly is set on 20 ms. A typical car crash only lasts for about 90 ms. If the safety device has to be adaptable, i.e. it has to be able to adjust itself multiple times during the entire crash event, then its reaction has to be even quicker. A precrash sensing system can be useful to increase the eﬀectiveness of the safety device. One must think of anticipatory systems like radar, camera or infrared. Such a system can make extra time available for adaptive systems for a quicker and more eﬀective device. Sensing properties

Sensing properties are only important when a safety device is used for its sensory capabilities. Such a device has to be able to deliver reliable and accurate information on the various important parameters that deﬁne a crash event. Furthermore, the device has to be very fast in sensing external inﬂuences and deliver the obtained information to some kind of controller. In the case of this internship the sensing properties of an crushable crashzone are not present. Actuating properties

To improve the crashworthiness of a vehicle the safety device has to be able to generate a significant amount of displacement, force, work or other useful adaptable properties. More- over, for a safety device to be adaptable the device has to be ably to satisfy a wide range of different requirements set out by various crash situations and different occupants. A large range of different speeds, different kinds of collisions with a variety of obstacles, differently sized and weighing occupants and so on have to be dealt with. Therefore, the factor by which the physical properties of an adaptable system, such as the deformation, stiffness, energy absorption etc. can be altered, has to be large enough to cover the desired spectrum of crash situations. 2.3. Requirements for Safety Systems in Automobiles 31

Reliability

Safety devices have to function correctly, if there are required to. So, safety devices have to be extremely reliable. Reliability can be inﬂuenced more and more by the design of the safety design in especially by smart materials. For example, a reduction in the number of parts can already lead to an increase in the reliability of the entire device. Also a predictable behavior is desirable, that means that the materials has to show a relatively stable behavior with respect to time (ageing), temperature and other working conditions. Durability

Vehicle safety devices have to dealt with two aspects: external influences and crash influences. In both situations the safety devices has to work perfectly. In case of external influences the safety devices are exposed to rough conditions like bumpy roads, rough use and so on. In case of a collision or crash event, the durability is of special importance because the entire car is subjected to large decelerations and forces. Not all safety devices (for example: small sensors as part of an airbag system) have a high durability. The designer of such a system has to make sure that these parts are not subjected to large forces or moments. The designer has to work this out in a design in which such parts are protected against the huge influences. 32 Chapter 2. Introduction to ER and MR fluids

2.3.3 Cost Requirements

The second factor that forms major design constraints for automotive applications are the costs. Costs are always important when we dealt with designing and production. The automotive engineering is characterized by mass production and related to this low costs. Although safety is nowadays considered to be an important sales argument, new safety devices still have to meet the same stringent constraints concerning the cost other parts do. The cost of typical product and devices can be split up into three main groups, being the cost for research and development, the cost of material used and the production cost of the entire device (see ﬁgure 2.13).

Figure 2.13: Cost structure of a typical product[9]

Cost of Research and Development (R&D)

In the development stage of safety devices the contribution of the R&D costs to the total is typically a little higher, because they might rely on relatively new and innovative technologies and are ﬁrst applied on a small scale.

Material Costs

The material costs are built up of the costs for the raw materials and the costs for the possible special treatments. These materials have to undergo to enhance their properties. The costs for raw materials depend on both the type and amount of material used and with that on the availability of this material. Materials with special properties, like smart materials, are typically not as widely available as common engineering materials and possibly require special production methods. Therefore they will typically have a higher price tag than conventional, mass-produced materials.

Production Costs

The production costs can be subdivided into labour and overhead costs. The latter are mainly constituted by the costs for the machinery needed to produce the materials and to fabricate the devices. For these production costs the same as above applies, being that materials typically require special production methods and more skilled workers, which will lead to an increase in the costs. 2.3. Requirements for Safety Systems in Automobiles 33

2.3.4 General Applicability Requirements

Finally, another main design consideration is whether or not a safety device and the materials used for it are easy to apply in passenger cars. The applicability is mainly determined by a number of parameters, such as the weight, volume, the sensing and activation properties. Material/Device Weight

The weight of a vehicle is an important issue. A heavier vehicle will lead to deterioration of the energy fuel economy. Also this will lead to a higher performance powertrain and other running gear (brakes, suspensions etc.). This has a negative inﬂuence on the weight of the vehicle. Therefore the additional weight of safety devices should not be too high, as this will limits its applicability. Material/Device Size and Shape

The volume and shape of a device or material also are restricting factors. There’s little room to put new safety devices, because cars are already stuﬀed with all kind of devices. A potential solution would be to integrate the design of the new safety design into the design process of the entire car. In this way the size and shape of the device can be taken into account during the design process. Sensing&Activation: Principles and (Power) Requirements

The sensory capabilities of most smart materials are based upon one of the four principles: a change in the temperature, in the electric field, in the magnetic field or a deformation. Smart materials are thus capable to sense such changes and moreover, to act on them by generating a significant amount of displacement, force, work or show any other useful adaptable property. Thermal sensing in automobiles is not very useful to use for safety purposes. Also the sensing of electric fields doesn’t hold much potential. Magnetostrictive effects can be used to detect transient stress signals. Sensing of deformations is very useful, as by means of this a contact between a car and another object can be sensed directly. Thermal activation is not always easy to apply. The fact that very fast activation is required during a crash event results in the need for a lot of heat to be able to activate the safety device fast enough. Pyrotechnics can be a possible solution, but the problem is that pyrotechnics can not be used openly in cars. Electrical activation holds much potential, because an electric field is easy to provide by use of the car battery. Because the safety device is only used in case of more or less severe car crashes and the car probably is being retired after such a crash anyway, the entire capacity of the battery can be used for the activation of the device. However, these batteries are typically not capable of generating very strong electric fields, so in most cases a special type of power source is needed which has great implications for the cost and other important factors. Magnetic fields, on the contrary, are not so easy to use and apply. Although very high magnetic field strengths can be achieved with a regular 12 or 24 [V ] car battery, there are some huge disadvantages to the use of magnetically activated devices. A magnetic field cannot be shielded off very easy and this can influence the functioning of other devices in a harmful manner. Efficiency 34 Chapter 2. Introduction to ER and MR fluids

Energy eﬃciency is not a big issue for safety devices, because they are typically intended for activation only in the event of an imminent car crash. Therefore the entire capacity of the battery or any other energy source can be used for the activation of the device. Maintenance

The maintenance and service on new technologies in passenger cars has to be able to be done at a local car dealership. Therefore, also the maintenance of new, to be developed safety devices has to be simple enough so that every dealership can instruct their mechanics to be able to ﬁx any problems with them. Temperature stability and Operable temperature range

Nowadays, cars are sold on a worldwide basis and therefore they have to function in all the various climates of the world. Because of this, cars and all of their onboard devices are subjected to a wide range of operable temperatures. Therefore it is necessary that safety devices and the materials used are able to work equally well within a wide range of temperatures, which will be approximately between -40[oC] and 100[oC]. Fatigue

Fatigue is typically not an important factor to consider in safety devices, as they are intended to work only once, or in some cases only a couple of times. Ageing

Ageing, in contrast to fatigue, is important to consider. A car crash may occur within a month after the car has been built, but it may also occur late in the car’s life. Therefore, the safety device has to have a stable working principle and the materials used must have stable properties with regard to the time. The proper functioning of safety devices, however, also needs to be checked continuously by some kind of monitoring device, because ﬂawless performance can never be guaranteed. Such a monitoring device can also be used to keep an eye on the ageing of the materials etc. 2.3. Requirements for Safety Systems in Automobiles 35

2.3.5 Testing the requirements against ER and MR ﬂuids

With the help of the formulated requirements in the previous sections, it is possible to test the properties of ER and MR fluids against these formulated requirements. As already stated, the crash situation requirements are the most important. When the properties and characteristics of the fluids are not consistent with these requirements, than it is basically not possible to apply ER and MR fluids in the car safety.

ER Fluids

Crash Situation Requirements

Fast Response Time

The change in the rheological properties of ER fluids can occur within a few milliseconds of the application when applying an electric field. The response time of a complete system using ER device(s) is estimated to be under 10 [ms], somewhat faster than that of MR fluids. Note that the response time is totally dependent of the application in which the fluid is used. So the response time can be greater than 10[ms], but it can also be somewhat lower. When a safety device have to react very quickly, it is very important for the designer to design the device with as few fluid as possible to obtain a quick response time. Sensing Properties

ER ﬂuids aren’t generally used for their sensory capabilities. The working principle behind the sensing capabilities isn’t explained anywhere. Actuating Properties

ER fluids have to be employed as coupling media in energy transducers, like rotary brakes, clutches and hydraulic systems. The most important controllable property of ER fluids is the field dependent yield stress, for which typical maximum values range from 2 to 5 [kP a]. These maximum values depend both on the strength of the electric field and the composition of the fluid. There are many parameters which have influence on the amount of energy dissipation by changing for example the yield stress. In chapter 4 there will be a detailed description about the parameters which have influence on the energy absorption in the advanced crumple zone. Reliability

A main benefit of the use of ER fluids is that they can significantly reduce the complexity of devices, they can make the use of some moving parts redundant. A main concern is the risk of sedimentation of particles because of the differences in density between the particles and the carrier liquid, especially when the fluid is inactive for a long period. However, in ER fluids this density mismatch is generally lower than in their magnetically activated cousins, the MR fluids. For reliable operation it is very important that ER fluids are protected from sedimentation and contaminants. The fluid has to be operated within its specification limits. 36 Chapter 2. Introduction to ER and MR fluids

Durability

The durability of an ER based device depends largely on the design of the entire system and not so much on the durability of the ER ﬂuid. Cost Factors

The costs for producing ER ﬂuids are fairly high. The fact that ER based devices require large voltages (some [kV ]) at a low current (few [mA]), could mean that they require relatively expensive high voltage supply. In chapter 4 there will be a further description about this section. General Applicability Factors

Material/Device Weight

The density of a typical ER suspension ranges from 1 to 2 [gr/cm3]. However, ER fluids cannot be used as actuators directly, they have to be employed as coupling media in energy transducers. So, adding a safety device based on ER fluid is totally dependent of the design, the volume of the device and the peripheral equipment (for example power supply). When compared to their MR cousins, ER fluids have a lower density. However, this benefit is can- celled out by the fact that in comparison a larger amount of ER fluid is needed and with that a larger device to achieve a certain performance level due to the much lower achievable yield stress. Material/Device size and shape

The shape and size of ER based devices depends on the type of transducer. The size of the device is also strongly related to the working conditions it is subjected to, such as the range of force levels etc. The employment of ER or other field responsive fluids could result in much more compact designs, because of the ER effect is dependent of the dimensions of the transducer. The smaller the dimensions, the stronger the ER effect due to higher achievable field strengths. ER fluid has a maximum yield stress which is a factor ten smaller than that of MR fluids. The consequences are that a much higher volume of active fluid is required for a comparable performance (factor 10). This will lead to much larger devices. An advantage of ER fluid is the fact that electric fields are easy to provide using a couple of electrodes. MR fluids has the disadvantage of relatively heavy parts like a magnetic coil and guide flux to provide in a magnetic field. 2.3. Requirements for Safety Systems in Automobiles 37

Sensing and Activation

ER fluids or devices based on them are not typically used as sensors. They are mainly used for their adaptable actuating properties. For the activation of ER fluids and the control of their properties very strong electric fields are required. This can be achieved with relatively low power consumption, large voltages, up to 4 [kV/mm], at a lower current (few [mA]) have to be provided. This means that relatively expensive high voltage power supplies are needed. Efficiency

As stated above, the activation of ER fluid based devices requires little power. The ’off’- state viscosity of ER fluids as a whole is relatively low (below 100 [mP a.s]), when compared to that of MR fluids. This base viscosity has influence on the viscous forces which are always present in fluid dynamics. The forces in an energy transducer can be classified into two groups: viscous forces and a controllable force as a consequence of the controllable yield stress τ. The lower the base viscosity, the lower the viscous forces. This will result in low friction or flow losses in systems in the ’off’-state. This detail can be very useful when designing an ER device, but it can also be very needless. Viscous forces are always present, so a high base viscosity will lead to a lower dynamic range. The controllable force becomes in proportion to an increasing uncontrollable force (viscous force) lower and lower[5]. Maintenance

Recent developments concerning ER fluids have addressed the important property of non- abrasiveness, so the ER fluid will be gentle the materials and parts used in a device, such as pistons. This will lead to a reduction of wear. Together with the fact that the use of ER fluids can make the use of moving parts redundant this can lead to a reduction in maintenance requirements. Note that ER fluids are very sensitive to contaminants and impurities and they are usually hygroscopic. Another important fact to monitor is the sedimentation of particles. A regular maintenance is necessary to avoid a complete malfunctioning of the device. Temperature Stability and Range

The apparent yield stress of ER fluids depends somewhat on the temperature. Water-free ER fluids have been developed that have an operable temperature range close to that of MR fluids, ranging from -25 [oC] to + 125 [oC]. This range can be sufficient for most automotive applications. Fatigue

In the literature it is mentioned nowhere that ER fluids should suffer from fatigue. On the contrary, as long as ER fluid devices are used regularly, sedimentation, which is one of the main concerns in using field responsive field, will be prevented. Ageing

The prevention of sedimentation is one of the most important aspects to consider with respect to ageing. Research has shown no deterioration in performance will occur during long-term use in closed systems, as long as the fluid is operated within its specification limits (see also 38 Chapter 2. Introduction to ER and MR fluids

section 2.2.5.

MR Fluids

Crash Situation Requirements

Fast Response Time

MR fluids have a response time lower than that of ER fluids. Typical response times for complete system using MR device(s) are estimated to be around 15-20 [ms]. Note that the response time of a field responsive fluid is totally dependent of parameters which are established by the design of the device. Sensing Properties

Devices based on MR ﬂuids cannot be used as sensors. Actuating Properties

The actuating properties of MR fluids are the same as the ER fluids. The only different is the maximum yield stress, which ranges from 10 to 100 [kP a]. This is a factor ten higher than the ER fluids. Device properties, like the maximum amount of energy dissipation, depends of the type device and several device parameters. Reliability

The use of MR fluids as active medium can significantly reduce the complexity of devices by making several moving parts, such as adjustable orifices in conventional controllable valves, redundant. The problem of sedimentation is bigger than that it is for ER fluids, because of the typically larger density mismatch between the carrier liquid and the particles. On the other hand, MR fluids are not very sensitive to impurities or contaminants, as they typically don’t affect the working principle behind the MR effect. This makes it possible to use a variety of additives and therefore MR fluids can be stabilized against sedimentation fairly straightforward. Finally it has to be noted that MR fluids can also be energized without any steady-state power requirement at all through the use of permanent magnets, which can guarantee fail-safe operation. 2.3. Requirements for Safety Systems in Automobiles 39

Durability

The durability of an MR based device depends largely on the design of the entire system and not so much on the durability of the MR ﬂuid. Cost Factors

The costs for producing MR fluids are fairly high. For the control of the magnetic field coil voltages below 10 [V ] and currents below 2 [A] can be sufficient to operate the device properly. This power requirement can be met by using a standard 12 [V ] or 24 [V ] power supplier, such as a regular battery. General Applicability Factors

Material/Device Weight

The density of a typical MR suspension ranges from 3 to 4 [gr/cm3]. MR fluids has a density twice that of ER fluids. Also, MR fluids cannot be used as actuators directly, they have to be employed as coupling media in energy transducers. To achieve similar performance, ER fluids require a significantly larger amount of active fluid, thereby resulting in a potential lower mass of MR devices. The fact that MR fluids have to use a coil and a magnetic flux guide for providing magnetic fields can possibly cancel out this weight advantage. Material/Device size and shape

When compared to conventional controllable transducers with similar capabilities, the use of MR fluids could possibly result in much more compact designs. A comparison with ER fluids shows that the difference in the maximum yield stress makes it possible for MR based devices to be made more compact. Sensing and Activation

MR fluids and devices are mostly used for their excellent actuating purposes. For the activation of MR fluids and the control of their properties very strong magnetic fields intensities, up to 160 [kAm−1], are needed. These field strengths can be provided with low power and low voltages at high currents, such as standard 12 [V ] or 24 [V ] car battery. But there are some disadvantages to the use of magnetically activated devices. As already mentioned, magnetic fields require a coil and a flux guide, which can have implications for the size and the weight of the device. Secondly, magnetic field can negatively influence the functioning of other devices, because they cannot be shielded off very easily. 40 Chapter 2. Introduction to ER and MR fluids

Eﬃciency

Because of the use of permanent magnets, MR fluids can be energized without any steady- state power requirement. The typical ’off’-state viscosity of MR fluids is relatively high, this has a negative influence on the dynamic range. Maintenance

A main advantage of MR fluids is that they are not very sensitive to contaminants and soiling, which can be commonly encountered during manufacture and also during usage. MR fluids typically contain magnetically soft particles, which results in a relatively low overall abrasiveness. However, when compared to ER fluids the abrasiveness is typically higher in MR fluids. Combined with the fact that the use of MR fluids, this can make several moving parts redundant, can lead to a reduction in maintenance requirements. Temperature Stability and Range

MR ﬂuids have a relatively high temperature stability and can therefore be operated over a much wider range of temperatures, from approximately -40 [oC] to +150 [oC]. Fatigue

As long as MR fluid devices are used regularly, sedimentation, which is one of the main concerns in using field responsive fluids, will be prevented. Therefore, fatigue doesn’t have to be taken into consideration. Ageing

The prevention of sedimentation is one of the most important aspect to consider with respect to ageing. As long as the device is used or inspected regularly and within its speciﬁcation limits, ageing can be controlled. 2.3. Requirements for Safety Systems in Automobiles 41

2.3.6 ER or MR ﬂuid?

To make a comparison between ER and MR fluids, it is necessary to test these fluids on the list of demands which is described in the previous sections. Some of these demands are left out here, because they are not related to ER and MR fluids (in this case the sensing properties). In chapter 5 a feasibility study will be described in which three designs, discussed in chapter 4, will be compared to each other. In the table below the demands are estimated. The procedure is as following: each demand is tested to each other, the most important will get the value ’1’, the other will get the value ’0’. The value, classified in the column ’weight factor’, is the total score of the demand in proportion to the other demands.

Figure 2.14: Estimating the diﬀerent demands: ’0’- demand ’x’ is less important than opposite demand ’y’/’1’- demand ’x’ is more important than opposite demand ’y’

After that, the fluids are tested against the demands with the specific weight factor. The value ’0’ means that the fluid is not able to fulfil the demand. A value ’1’ means that the fluid is able to fulfil the demand sufficiently. A ’2’ means that the fluid is able to fulfil the demand very well. 42 Chapter 2. Introduction to ER and MR fluids

Figure 2.15: Testing the ﬂuids against the demands: 0:bad / 1:moderate / 2:good

From the figure 2.15 follows that MR scores much better then ER fluid. In specially the actuating properties and the reliability scores much better in contrast to the opponent. The crash situation requirements are the four most important demands. Together with the demand ’ageing’, they form the critical factors of the design. When a design is not able to satisfy these critical factors, then there is a big chance that the design is not able to fulfil a final solution. Such a design must be rejected. The costs of a design with ER of MR fluid is difficult to estimate. The costs are mainly determined by the peripheral equipment such as activation (electric / magnetic field) and the control of several functions. This is also the reason why costs not belong to the critical factors.

Figure 2.16: Toetsing van de vloeistoﬀen aan de kritische factoren: 0:bad / 1:moderate / 2:good

When only the critical factors are taken into consideration (figure 2.16), than the difference between ER and MR fluid is much smaller. ER fluid scores better on the response time and (in the field of) ageing (this with regard to the smaller chance on sedimentation). MR fluid, on the other hand, scores better on the actuating properties because of the higher yield stress and it also scores better in the field of reliability and durability which follows from the desirable peripheral equipment. When designing a safety system the designer has to pay attention on the strong and weak points of the two fluids. One must be careful to make a choice between ER and MR fluid. A careful conclusion is that MR fluid is better suitable for an application in an advanced crushable zone. In chapter 5 there will be an extensive description about the different possibilities with MR fluid. This shall happen with the help 2.3. Requirements for Safety Systems in Automobiles 43

of a feasibility study in which three (global) designs, with the application of MR ﬂuid, are compared and evaluated. 44 Chapter 2. Introduction to ER and MR ﬂuids Chapter 3

Theory Modelling

Many common ﬂuids, including air, water and liquid metals, are accurately presented by the Newtonian constitutive equation[3]. We can illustrate this by an experiment sketched in ﬁg- ure 3.1.

Figure 3.1: Simple shear flow experiment, used to define fluid viscosity[3]

A fluid is confined between two parallel plates, one of which is translated parallel to the other with a constant velocity. This generates the linear velocity profile shown in the figure, for all Newtonian fluids this stress is proportional to the derivative of the velocity:

∂v τ = µ x (3.1) yx ∂y where vx is the velocity of one of the parallel plates, this will induce a shear stress τxy which is also proportional to µ, the shear viscosity [P a.s]. A general derivation of the Newtonian constitutive equation is given in appendix A. However there also many materials whose behavior is distinctly non-Newtonian: molten poly- mers, molten glass, semisolid metals, grease and foods such as mayonaise. The behavior of ER and MR fluids is also non-Newtonian, so it is important to pay attention on non-Newtonian fluids. The mass and momentum balance equations of Newtonian fluids are the same for

45 46 Chapter 3. Theory Modelling

non-Newtonian fluids, the difference is in the constitutive equations for stress. The study of the deformation and flow of materials, particularly of non-Newtonian fluids, is the subject called rheology. Rheologists create experimental techniques to measure viscosity and other flow properties, they develop constitutive equations that describe non-Newtonian behavior. Newtonian fluid differs from another only by its value of viscosity. However, there are many different types of non-Newtonian behavior. It is possible to group different non-Newtonian behaviors into categories according to how their stress depends on the rate of deformation. If the stress at any time depends only on the rate of deformation at that time, that is, if

τ(t) = f(D(t)) (3.2) then we have a purely viscous material. Newtonian fluids exhibit a linear relationship between τ(t) and D(t), so they belong to the viscous materials. If the relationship is nonlinear then we have one type of non-Newtonian model, called a generalized Newtonian fluid. When we again return to the experiment to measure fluid properties use a simple shear flow. Suppose that we can create a drag flow between parallel plates (shown in figure 3.1) at any desired ∂vx shear rateγ ˙ = ∂y and measure the resulting shear stress τyx. Assume that the fluid is purely viscous, so its obeys (3.2). The non-Newtonian viscosity η is defined as the ratio of shear stress to shear rate in this experiment:

τ η = yx (3.3) γ˙

We can distinguish two different situations, namely shear thinning and shear thickening. If the shear stress versus shear rate curve turns downward as the shear rate is increased, then the fluid is said to be shear thinning (or pseudoplastic). The viscosity η decreases with increasing shear rate. If a fluid has the opposite type of behavior, in which its viscosity increases as the shear rate increases, it is called shear thickening (or dilatant). Some fluids will not flow at all unless the stress exceeds a minimum value. Such fluids are said to possess a yield stress, and this is also a type of non-Newtonian fluid behavior. Even if the stress-strain rate curve is linear after yielding, the viscosity η decreases with increasing strain rate. Thus, having a yield stress is particular type of shear-thinning behavior.

3.1 Fluid Models

3.1.1 Bingham Model

A plastic material is one that shows little or no deformation up to a certain level of stress. Above this yield stress the material flows readily. Plastic is common to widely different materials. Many metals yield at strains less 1%. Concentrated suspensions of solid particles in Newtonian liquids often show a yield stress followed by nearly Newtonian flow. These materials are called viscoplastic or Bingham plastics after E.C.Bingham, who first described paint in this way in 1916. House paint and food substances like margarine, mayonnaise, and ketchup are good examples of viscoplastic materials. A simple model for plastic material is 3.1. Fluid Models 47

Hookean behavior at stresses below yield and Newtonian behavior above. For one-dimensional deformations

τ = Gγ for τ < τ y (3.4) τ = ηγ˙ + τy for τ ≥ τy

The model also can be written as allowing no motion below the yield stress,

γ˙ = 0 for τ < τ y (3.5) τ = ηγ˙ + τy for τ ≥ τy

Figure 3.2: Bingham plastic behavior. a) Shear stress versus strain at constant strain rate according to eq. 3.4 b) Shear stress versus strain rate following eq.3.5 compored to power law and Newtonian models[7]

Figure 3.2 illustrates eqs.3.4 and 3.5 and compares the Bingham model to Newtonian and power law fluids. An important feature of plastic behavior is that if the stress is not constant over a body, parts of it may flow while the rest acts like a solid. Consider flow in a tube: the shear stress goes linearly from zero at the center of the tube to a maximum at the wall. Thus the central portion of the material flows like a solid plug (see also appendix C.1 and figure C.1. Figure 3.3 shows Bingham plots of data for an iron oxide suspension. Data over a wide shear rate range are shown in figure 3.3a, while the lower shear rate change of data is shown in figure 3.3b, both on linear scale. The constants of the Bingham model fitted to these two ranges of data are considerably different. The difference is more obvious when the data are examined on a log-log plot (figure 3.3c), especially in lower shear rate range. Large errors in τy can result by picking the wrong shear rate range to fit the Bingham model. 48 Chapter 3. Theory Modelling

Figure 3.3: Bingham ﬁts for experimental data of 6.0 vol% iron oxide suspension in mineral oil in a) the higher shear rate, b) the lower shear rate range, and c) all data on a log-log scale[7]

3.1.2 Other Viscoplastic Models

Casson (1959) proposed an alternate model to describe the ﬂow of viscoplastic ﬂuids. The one-dimensional form of the Casson model is given by:

γ˙ = 0 for τ < τy 1 1 1 (3.6) 2 τ 2 = τy + (ηγ˙ ) 2 for τ ≥ τy

This model has a more gradual transition from the Newtonian to the yield region. For many materials, such as blood and food products, it provides a better fit. The iron oxide suspension data, including even lower shear rates, are shown in figure 3.4. Curves of the Bingham and Casson models are also shown; Bingham model parameters from figure 3.3b are used instead of a best fit. Note that values of the parameters for the Casson model also depend on the range of shear rates considered. Using a critical shear rate rather than shear stress as a yield criteria makes application to numerical calculations much easier. Papanastasiou (1987) proposed a modification to the viscoplastic fluid models that avoids the discontinuity in the flow curve due to the incorporation of the yield criterion. Papanastasiou’s modification 3.1. Fluid Models 49

Figure 3.4: Comparison of Bingham and Casson fits to the iron oxide suspension data over the entire range of experimental data obtained: parameters for the Bingham model are η=0.25 [P a.s] and τy=1.66 [P a.s], while for the Casson model they are 0.15 [P a.s] and 1.66 [P a], respectively[7] involves the incorporation of an exponential term, thereby permitting the use of one equation for the entire flow curve, before and after yield. The one dimensional form of Papanastasiou’s modification is:

τ [1 − exp(−aγ˙ )] τ = η + y γ˙ (3.7) γ˙

Perhaps the best picture of a viscoplastic fluid is that of a very viscous, even solidlike, material at low stresses. Over a narrow stress range, which can often be modelled as a single yield stress, its viscosity drops dramatically. This is shown clearly in figure 3.3b, where viscosity drops over five decades as shear stress increases from 1 to 3 [P a]. Above this yield stress the fluid flows like a relatively low viscosity, even Newtonian, liquid. Because of the different behaviors exhibited by these fluids, the model (Bingham, Casson, etc.) and the range of shear rates used to calculate the parameters must be chosen carefully. It also important to note that experimental problems like wall slip are particularly prevelant with viscoplastic materials. A simple Bingham visco-plasticity model is effective at describing the essential field-dependent fluid characteristics. In this model, the total shear stress τ is given by:

τ = τ0(H)sgn(γ ˙ ) + ηγ˙ (3.8) where τ0 is the yield stress caused by the applied field, H is the magnitude of the applied magnetic or electric field,γ ˙ is the shear strain rate and η is the field-independent plastic viscosity. η is defined as the slope of the measured post-yield stress versus shear strain rate. 50 Chapter 3. Theory Modelling

Note that the ﬂuid post-yield viscosity is assumed to be a constant in the Bingham model.

Figure 3.5: Visco-plasticity models of MR ﬂuids[5] 3.1. Fluid Models 51

Because MR and ER fluids exhibit shearing thinning effect which is also shown in figure 3.5, the Herschel-Bulkley visco-plasticity model can be employed to accomodate this effect. So, it is very useful to replace the constant post-yield viscosity in the Bingham model with a power law model dependent on shear rate. This will lead to:

1 τ = [τ0(H) + K|γ˙ | m ]sgn(γ ˙ ) (3.9) where m en K are ﬂuid parameters (note: m, K > 0). It is easy to see that the equivalent plastic viscosity of the Herschel-Bulkley model is:

1 −1 ηe = K|γ˙ | m (3.10)

(3.10) indicates that the equivalent plastic viscosity ηe decreases as the shear strain rateγ ˙ increases when m > 1 (shear thinning). Note that the Herschel-Bulkley model reduces to the Bingham model when m = 1, therefore η = K. 52 Chapter 3. Theory Modelling

3.2 Pressure Control Valve Using MR Fluid

The first theory that will be discussed, is a pressure control valve in combination with MR fluid[10]. The principle is very simple, the theoretical background lays the foundation of the what more complicated applications which will discussed in the next sections. A pressure control valve in combination with a cylinder-piston device is able to regulate the pressure drop with a regulable magnetic field. The MR valve consists of a flow channel between a pair of magnetic poles and the differential pressure is controlled by the applied magnetic field intensity. It features simple, compact and reliable structure without moving parts. MR fluid

Figure 3.6: Pressure Control Valve using MR ﬂuid

flows through the passages between core A and core B. When the power of the coil is turned on and the magnetic field is exerted on the MR fluid, then the MR fluid flowing through the relief valve will change its state into semi-liquid or solid. Only when the supply pressure gets high enough to offset the yield stress, the fluid can flow through the valve again. Thus the relief valve can regulate the pressure of a MR fluid system under a certain flow rate. When the power is off, MR fluid valve does not work. The most important performance parameter of the relief valve is the operating pressure and flow rate. And the most important performance of the relief valve is the pressure-flow characteristics. As the flow through the passages of cores is a flow, the regulated pressure of the valve can be written as:

2L 12ηL P = τ (M) + Q (3.11) H y WH3 in which L is the active pole length, H the gapsize and W is the width of the channel. η is the base viscosity, τy is the controllable yield stress and Q the ﬂow through the valve. Only when the sizes of the valve are determined correctly, the new type MR ﬂuid valve can be designed to a relief valve. Assuming that:

2L P = τ (M) (3.12) 1 H y 3.2. Pressure Control Valve Using MR Fluid 53

12ηL ∆P = Q (3.13) WH3

∆P λ = (3.14) P1

The parameter λ has great effect on the characteristics of the valve. It is desirable that λ takes a small value. That means the regulated pressure of the valve changes slightly with that of the fluid flow rate.

3.2.1 Pressure-Flow Characteristics of MR Fluid Relief Valve

The magnetic poles have parallel plates with W =20 [mm] in width, L=30 [mm] in length and G=3 [mm] in gap length. The magnetic material is mild steel and the nonmagnetic material is brass. Diameter and the number of turns of a wire for the electromagnet are 1 [mm] and N=910 [mm], respectively. The measured electric resistance is 3.1 [Ω]. The MR fluid is MRF-126QD developed by Lord Corporation. The density is 2.7*10−3 [kgm−3] and the measured base viscosity is 0.9 [P a.s] at room temperature. The magnetic flux density B0 between the magnetic poles in air is measured by using a gauss meter. The marks in fig. 3.7 show the relation between the magnetic flux density B0 and the electric current I of the electromagnet[14].

Figure 3.7: Measured relation between magnetic ﬂux density B0 in air and electric current I[14] 54 Chapter 3. Theory Modelling

The solid line in ﬁgure 3.7 shows the analyzed results as follows:

1 NI µ0N B0 = µ0H0 = = I (3.15) WL µ0G G WL where, H0 is the magnetic field intensity between the magnetic poles in air and µ0 the permeability in vacuum. Eq. 3.15 is obtained under assumptions that both magnetic leaks and reluctances of the core are negligible small and the magnetic flux density is homogeneous between the magnetic poles. It is found that the magnetic flux density B0 increases linearly with some hystereses for small electric current I, although there is saturation for large electric current I, which is caused by nonlinear characteristics of the magnetic material. There are some differences between the measured and analyzed results because of the magnetic leaks and reluctances of the core. For the same electric current I, the magnetic field intensity in MR fluid is slightly different from the value in air, however, in the experiments for simplification, the magnetic field intensity is estimated as H0 based on the results of figure 3.7 (right) having the hystereses.

Figure 3.8: Experimental apparatus[14]

With an experimental apparatus shown in figure 3.8, the static characteristics of the fabricated MR valve are experimentally investigated. In the experiments, the flowrate Q through the fabricated MR valve is varied by manually adjusting the throttle valves A and B which divide an output flowrate of the gear pump. The upstream and downstream pressures Pu and Pd are measured by semiconductor pressure sensors and the differential pressure ∆P = Pu − Pd is calculated. The electric current of the electromagnet is I=0-0.78 [A](I.N=0-710 [A.turns]) and the magnetic field intensity H0 is estimated based on figure 3.7 (right) having the hystereses. The electric current I is in no saturation range as mentioned above. The flowrate Q is obtained by measuring the outflow mass of the MR fluid in a measuring time. The fluid temperature is 25 ± 1[◦C]. From this experiment, the following results are obtained:

• The MR valve is proposed for ﬂuid control systems. 3.2. Pressure Control Valve Using MR Fluid 55

• Since there is no moving part, new type MR ﬂuid relief valve has a simple construction and long life, compared with the traditional relief valve.

• The static characteristics are experimentally clariﬁed. The proposed MR valve has static characteristics corresponding to a pressure control valve.

• The input electric current and power changes of (710 [A.turns]) and 1.9 [W ] produces the diﬀerential pressure and output power changes of 0.68 [MP a] and 20 [W ]. 56 Chapter 3. Theory Modelling

3.3 Quasi-Static Modelling of MR Dampers

A lot of research has been done on applications of MR dampers. Mainly they are related to applications of such dampers in structural projects. These dampers have their applications in the semi-active control of seismic excitation in high buildings. Most of these dampers are based on the direct shear mode, in which the MR fluid is pressed through a narrow gap by a pressure driven flow. This narrow gap is located between the piston and the cylinder housing. That part of the fluid which is pressed through this gap will be exposed to a magnetic field. The rheological properties of the fluid will be influenced. A schematic of the large- scale MR fluid damper is shown in fig.2.7 The damper uses a particularly simple geometry in which the outer cylindrical housing is part of the magnetic circuit. In such projects the forces (approximately 200000 [N]), caused by earthquakes, are enormous. The design of such dampers is very interesting for research on applications of MR fluids in advanced crushable zones. Designing dampers based on the above principle is not simple, also it is difficult to find good articles about the design of such dampers. The research of Guangqiang Yang, B.S.([5]) is very usable to make a model of a damper in a crushable zone. By means of a few ’design rules’ it is possible to say something about the application in an early stage of the internship. And it must also be possible to give answer to the question: Does the application of ER and/or MR in such dampers offers perspective? In the research of Guangqiang Yang, B.S.([5]) two quasi-static models are used: a parallel-plate model and an axisymmetric model. The Herschel-Bulkley model is employed to describe the MR fluid-dependent characteristics and shear thinning/thickening effect. For quasi-static analysis of MR fluid dampers, the following assumptions are made:

• MR dampers move at a constant velocity.

• MR ﬂuid ﬂow is fully developed.

• the Herschel-Bulkley visco-plasticity model is utilized to describe MR fluid field-dependent characteristics and shear thinning/thickening effect.

In the report of Guangqiang Yang, B.S.([5]) a derivation of the shear stress profile in an annular duct and a parallel duct is given. Proceeding from these derivations, the Herschel- Bulkley and the Bingham model are used to formulate derivations of the velocity profiles of the flow in the gap. Finally a comparison is made between the two models. The conclusion of this comparison is that the parallel plate model is usable for initial design of MR dampers by means of the Bingham model. In this report the entire derivation is given, because some of the design rules are better explained by means of these derivations in Appendix C and D. Note that the design rules are only usable in the initial design phase of MR dampers. A full validated device is only possible when more detailed formulations are taken into account. By means of numerical calculations a more detailed design can be obtained.

3.3.1 Basic Geometry Design Considerations

Based on the parallel-plate Bingham model that is developed in appendix C, simple equations are given which provide insight on the impact of various damper parameters; these 3.3. Quasi-Static Modelling of MR Dampers 57

equations can be used in the initial design phase. Eﬀect of geometry on MR damper performance, controllable force and dynamic range, are also discussed in this section. In the next chapter these design rules will be applied for the design of MR dampers in an advanced crushable zone. By means of the optimal crash pulse by diﬀerent velocities of the research of dr.ir.W.J.Witteman[12], an initial design is made of the MR dampers which can be applied in a crushable zone.

Controllable force and dynamic range

The controllable force and the dynamic range are two of the most important parameters in evaluating the overall performance of the MR damper.

As illustrated in ﬁg. 3.9 the total damper force can be decomposed into a controllable

Figure 3.9: Illustration of force decomposition of MR dampers[5]

force Fτ due to controllable yield stress τ0 and an uncontrollable force Func. 58 Chapter 3. Theory Modelling

The uncontrollable force includes a plastic force Fη and a friction force Ff . The dynamic range is deﬁned as the ratio between the damper controllable force Fτ and the uncontrollable force Func as follows: F F D = τ = τ (3.16) Func Fη + Ff

Based on the parallel-plate Bingham model, Fη and Fτ are deﬁned as:

wHV 12ηQLA F = 1 + 0 p (3.17) η 2Q wH3

τ LA F = c 0 p sgn(V ) (3.18) τ h 0 in which the parameter w is taken to be the mean circumference of the dampers annular ﬂow path which equals to π(R1 + R2), H is taken to be the gapsize which equals to R2 − R1 (R2 is the radius of the cylinder housing and R1 is the radius of the piston), L is the active pole 1 length, Ap the piston area and c ≈ 2.07 + (1+0.4˜τ) bounded to the interval [2.07,3.07]. The controllable force in 3.19 can also be rewritten by using eq. D.14 from appendix D.2 as

12Qη τ0LAp Fτ = 2.07 + 2 sgn(v0) (3.19) 12Qη + 0.4wH τ0 H which indicates that the controllable force is inversely related to the gap size. However, a small gap size decreases the dynamic range. As shown in eq. (3.17) and eq. (3.18), the viscous force increases two orders of magnitude faster than the controllable force with a small gap size if one assumes that the magnetic ﬁeld is saturated; consequently, the dynamic range tends to zero. As the gap size becomes large, both the controllable force and the viscous force decrease. Note that the friction force is a constant, so again the dynamic range tends to zero. It is obvious that an optimal dynamic range must exist. Figure 3.10 provides a typical relationship between gapsize, dynamic range and controllable force. 3.3. Quasi-Static Modelling of MR Dampers 59

Figure 3.10: Relationship between gapsize, dynamic range and controllable force[5]

Geometry constraints

Eq. (3.17) and eq. (3.18) are certainly useful in the design of MR dampers, however they often do not provide the best insight into the significance of various parameters. Therefore, the minimum active fluid volume V is introduced. This is the volume of MR fluids exposed to the magnetic field and thus responsible for providing the desired MR effect. By using eq. (3.17) and eq. (3.18), one obtains:

12k η F wH2 = )( τ Q (3.20) c τ0 Fη

wHv0 where k = 1 + 2Q . Because eq. (3.18) can also be written as:

Fτ cτ0L ∆Pτ = = (3.21) Ap H eq. (3.20) can be further manipulated to give:

12k η Fτ V = 2 2 Q∆Pτ (3.22) c τ0 Fη

where V = LwH which is the minimum active ﬂuid volume, ∆Pτ is the pressure drop due to the yield stress. Note that for most design cases, wHv0 Q and therefore k ≈ 1. For initial geometry design of MR dampers, one can assume that the friction force Ff has the Fτ same order as the plastic viscous force Fη. Thus, , where D is the required dynamic Fη+Ff range. Knowing the damper ﬂow rate Q, required dynamic range D, cylinder size w, yield stress τ0, plastic viscosity η and pressure drop ∆Pτ , the gap size H and active pole length 60 Chapter 3. Theory Modelling

L can be obtained from eq. (3.20) and eq. (3.22). However, this initial design needs to be veriﬁed by a more accurate axisymmetric model. Typically, a detailed design also involves iterations with the magnetic circuit design. 3.4. Damper Based on a Disk Shape MR Valve 61

3.4 Damper Based on a Disk Shape MR Valve

This type of damper is based on the principle of radial flow of a MR fluid between two fixed parallel disks[4]. This damper is examined at the University of Nevada, USA with the aim to design a semi-active suspension system for vehicles. Vibrations exceeding certain limits can cause poor ride quality and stability resulting in rollover or severe damage to vehicle elements and/or passengers. In this section only a few basis equations are given which are essential for the research on dampers in an advanced crushable zone. The reader is referred to Appendix E for the derivation of the equations described in this section. With use of the equations in Appendix E, it is possible to derive a few basic equations which are necessary for designing a damper based on a disk shape MR valve. The total damper force can be expressed as follows:

Fd = (∆Ptotalvis + ∆Pm + ∆Pdiskmr sign(u ˙) + Pa)A1 − PaA2 + Ff sign(u ˙) (3.23) in which A1 is the eﬀective piston area corresponding to volume 2, A2 is the piston area corresponding with to volume 1. In Appendix E the radial pressure gradient (eq. E.7) is integrated to give the following equations:

τ ∆P = 2.85 y (R − R ) (3.24) diskmr H 2 1

6µQ R2 ∆Pdiskvis = 3 ln (3.25) πH R1 where R1 and R2 are the outer and inner radius of the discs. The viscous pressure drop in the circular entrance can be expressed as:

128µQ ∆P = L (3.26) vis1 πD4 where D is the diameter, L the length and Q the flowrate of an orifice, respectively. µ is viscosity of the fluid. For the entrance channels with the rectangular orifices, one has:

12µQ ∆P = L (3.27) vis2 WH3 where W is the width of the channel and H the height of the channel. For the exit channels one has:

2µQ ∆P = L (3.28) vis3 πC where, 62 Chapter 3. Theory Modelling

4 4 r2−r1 c1 2 2 c1 2 2 c2 2 2 C = 4 − 2 (r2 ln r2 − r1 ln r1) + 4 (r2 − r1) + 2 (r2 − r1)

r2−r2 c = 1 2 1 ln r1−ln r2

r2 ln r −r2 ln r c = 1 2 2 1 2 ln r1−ln r2 here, r1 is the radius of the inner cylinder and r2 the radius of the outer cylinder. Therefore, the total viscous drop is:

∆Pvis = ∆Pdiskvis + ∆Pvis1 + ∆Pvis2 + ∆Pvis3 (3.29)

In addition to the pressure drop due to major losses there are minor losses due to elbows, expansions, entrance and exit eﬀect. These are considered to be minor losses in long pipe systems, but in damper applications due to the short oriﬁce length, they may become significant, especially at higher velocities. For the proposed MR damper minor losses should be taken into account. The overall pressure drop associated with minor losses can be expressed by:

K ρV¯ 2 ∆P = L (3.30) m 2 where KL is the overall minor pressure drop coefficient, ρ is the fluid density and V¯ is the average velocity of the fluid. The total force of the MR damper can be written as:

Fd = P1A1 − P2A2 + Ff sign(u ˙) (3.31)

where P1 and P2 are the pressures of the volume 1 and volume 2, respectively and Ff is the seal friction force. Also,

P1 − P2 = ∆Pdiskmr sign(u ˙) + ∆Pvis + ∆Pm (3.32)

In order to determine P2 the gas inside of the accumulator is assumed as an ideal gas. There- fore,

γ γ PoVo = PaVa (3.33)

where Po is the initial pressure of the accumulator, Vo the initial volume of the accumulator, Pa the final pressure of the accumulator, Va the final volume of the accumulator and γ the coefficient of thermal expansion. Additionally, conservation of mass for an incompressible fluid yields:

Va − Vo = Asu (3.34) 3.4. Damper Based on a Disk Shape MR Valve 63

By combining eq. 3.33 and eq. 3.34, one had:

Vo γ Pa = Po (3.35) Vo + Asu 64 Chapter 3. Theory Modelling Chapter 4

Practical Modeling

In the previous chapter three theoretical models are discussed. These three models lay the foundation for this chapter. The theoretical models of chapter 3 are followed from earlier research. This chapter is mainly intended to apply those theoretical models in an advanced crushable zone in which a variable stiffness is the most important property. In this chapter global designs are shown in which the working principle of the systems is explained. Design calculations are done to verify this most important property. This shall be done with use of the optimal deceleration curves from section 4.1.2. These curves are optimized for three velocities namely 32 [km/u], 56 [km/u] and 64 [km/u]. A collision with the decelerations from these optimal curves will result in a minimum risk of injury. With the help of design calculations, finally it’s possible to give a pronounce upon the possible future perspective of field dependent composites. This shall reveal itself in chapter five in which a (short) feasibility study is discussed. It is important to know that every system is calculated with a mean crash velocity of 9.72 m/s. This velocity is estimated with use of a numerical simulation [12]. These crash forces, which follows from the optimal deceleration curve, are calculated in this chapter. These forces serve as a guideline in the next sections.

65 66 Chapter 4. Practical Modeling

4.1 The Necessity of An Advanced Crushable Zone

The necessity of an advanced crushable zone is quite big, when we are looking at the present problematic in the daily traffic. Although collisions between vehicles are not always ’fair’, the construction plays an important part by the occurrence of injury. From research has been found that a present crushable zone in theory never is able to comply the variety in crash configurations. A designed crushable zone is always constructed with the help of mean values that are related to parameters like the mass of the vehicle, number of occupants, length of the drivers etc. Also a vehicle is exposed to two compelled crash tests, namely a frontal crash test against a fixed rigid barrier and an 40 per cent offset crash against a fixed deformable barrier. The first at a velocity of 50 [km/u], the second at a velocity of 56 [km/u]. Similar crash situations are very common in the daily traffic, but these compelled crash tests cannot cover the total variation of crash situations. There are many situations in which the crushable zone is not able to fully absorb the crash energy of the collision. Obviously, one must know the entire spectrum of all possible collision types in order to design a car that will be safe enough in any collision that may occur. From databases (NASS, FARS) important parameters can be obtained, the most important are the collision speed, the obstacle type, the impact location and the impact direction. Also the following observations can be made [12]:

• At least 90 percent of all frontal collisions take place at speeds up to 56 [km/u].

• A major division can be made into three standard obstacle types, i.e. the rigid wall, the deformable barrier (simulating other vehicles) and the pole (simulating trees and pillars).

• The majority of frontal collisions happen with frontal overlap percentages (the part of the bumper that makes contact with an obstacle) varying from 30 to 100 percent.

• Frontal collisions are considered to occur in impact directions having angles of incidence with the longitudinal car axis varying from -30 degrees up to 30 degrees. 4.1. The Necessity of An Advanced Crushable Zone 67

Much research is performed in the field of crushable zones and in particular in the field of compatibility (fig. 4.1). These researches are mainly specialized on the design of flexible crushable zones, which are able to handle with different crash situations. A good example of a similar research is that of Dr.Ir. W.J.Witteman[12]. This research shall be discussed in detail in the next subsections. Further there will be a description about optimal crash pulses which are very desirable in a car collision to minimize the injury level of the occupants.

Figure 4.1: Changing vehicles’ geometric designs can mitigate incompatibility [Insurance Institute For Highway Safety: Status Report Vol.34, No.9 Oct 30,1999] 68 Chapter 4. Practical Modeling

4.1.1 Cable-supported frontal car structure

Figure 4.2 shows a 3D view of a cable-supported frontal car structure which is the design of Witteman,W.J.[12]. Main topic of the research is to find a solution for the problems in compatibility and in particular for three different crash configurations. Under the most favourable circumstances, the crash energy most be equal for this three crash configurations. Also, a stable folding process in the longitudinals is used to obtain a optimum of crash energy. A solution is offered for the asymmetric loading of the vehicle due to an offset or an oblique impact. In that way the ’missed’ longitudinal is forced to crumple as well. Three different crash situations are taken into account, namely a 30 degrees collision, a 40 per cent offset collision and a full overlap collision. The design is simulated with PAM-CRASHTM.

Figure 4.2: Left: 3D view of the cable-supported longitudinal structure Right: Complete frontal vehicle system with cable supported structure

The system consists of two rods, two cables and four cable guides. The stiff rods are placed within the longitudinal members. The rods are longer than the longitudinals and extend beyond the vehicle’s firewall. A cable is connected to the end of each rod. The cable is guided to the front end of the other longitudinal via two cable guides, where it is connected to the cross member. The working principle is simple: if one longitudinal is loaded and start deforming, the corresponding rod moves back to the rear and pulls the cable, which leads the crushing force via the cable guides directly to the other, unloaded longitudinal. This force transmission occurs without loss of energy. Note that if both longitudinals are loaded (full overlap crash), the cable construction has no influence on the crash behavior. In figure A.4 the energy absorption of both longitudinals are presented for a full overlap, a 40 per cent offset and a 30 degrees impact all with 56 [km/u]. As a reference, also the energy absorption of the longitudinal in case of a 40 per cent offset without the cable is shown. The conclusion can be drawn that using an advanced longitudinal design with cable system increases the energy absorption considerably in case of an offset and an oblique impact.

4.1.2 Optimal decelerations curves

The research of Witteman [12] also consists of research on minimalisation of the injury level. In this research a reverse approach is used, in which an answer is given to the question which crash pulses gives the lowest injury levels with an already optimized restraint system, instead of ﬁnding the optimized restraint system for a given crash pulse. 4.1. The Necessity of An Advanced Crushable Zone 69

Figure 4.3: Total energy absorption of the longitudinals in diﬀerent crashes[12]

If an undeformable passenger compartment and no intrusion of vehicle parts like steering wheel, dashboard and pedals are assumed, the injury level is only influenced by means of g forces of the deceleration pulse generated by the vehicle front. To be sure that the injury level is the lowest possible, a numerical model is necessary to calculate the expected injury level by variation of the deceleration pulse. If the optimal deceleration pulse for a specific crash velocity is known, the structure must be designed to generate such a desired crash behavior. Research has been carried out to find a deceleration pulse with a minimum injury risk, based on the lowest value of the overall severity index, at a 56 [km/u] crash during 90 [ms]. This pulse determines the occupant loading and hence the injury risk for a passenger in a vehicle involved in an accident [12]. In figure 4.4 the optimal pulse for 56 [km/u] is given with the corresponding velocity and deformation length curve against time. Since more than 90 per cent of all frontal collisions occurs at a velocity lower than the prescribed crash velocity of 56 [km/u], also an optimal pulse for lower collision velocities is necessary to minimize the occupant injury level at that lower velocity. If the initial crash velocity is decreased to 32 [km/u], this results in a decrease of crash energy of 67 per cent with respect to a crash speed of 56 [km/u], so the vehicle might just too stiff. An increase of the initial crash velocity to 64 [km/u] results in an increase of energy of 31 per cent, so the structure might be too supple. So it is necessary to give three optimal pulses for three different initial velocity. These pulses are plotted together in figure 4.4. Note that the optimal pulse obtained for higher velocities has a higher deceleration level in the first interval and the levels of the middle and the third interval remain unchanged in comparison with an optimized pulse for 56 [km/u]. The obtained optimal pulse for a collision with 32 [km/u] has a constant deceleration level of 9 [g], the same level as the higher velocity pulses have during their middle interval. 70 Chapter 4. Practical Modeling

Figure 4.4: Three optimal decelerations curves in three phases [12]

With the help of the optimal pulses, it is possible to calculate the mean crash forces for the three velocities. The next simple equation is used to calculate these mean forces,

d2x(t) ΣF¯ = m (4.1) d(t)2 in which m is the mass of the vehicle. Three phases can be distinguish from figure 4.4, namely the crash initiation phase, the airbag deployment phase and the occupant contact phase. For each phase and velocity the mean crash forces are calculated (the mass of the vehicle is assumed to be 1100 [kg]), these values are given in table 4.1. These forces and collision phases are also illustrated in figure 4.5. An advanced crushable zone must have the ability to pass through these curves. The nominal force level is of importance here. This level must be absorbed in each phase of the collision, the dynamic range is then defined as in equation 3.16. In this case the dynamical range is defined as:

F D = max (4.2) Fnom

The dynamic range of a full overlap frontal collision follows from table 4.1 and ﬁgure 4.5:

495 D = = 5[−] 99

This nominal force level Fnom and the dynamic range D determines in considerable measure the design of the system. 4.1. The Necessity of An Advanced Crushable Zone 71

Table 4.1: Mean Crashforces Velocity Crash Initiation Phase Airbag Deployment Phase Occupant Contact Phase 32 [km/u] 9 [g] 9 [g] 99 [kN] 99 [kN] 56 [km/u] 32 [g] 9 [g] 23 [g] 352 [kN] 99 [kN] 253 [kN] 64 [km/u] 45 [g] 9 [g] 23 [g] 495 [kN] 99 [kN] 253 [kN]

Dynamic Range Relation Deformation Length − Force Level 500 64 km/u

450

400

350 56 km/u

300

250

Force Level [kN] 200

150

100 32 km/u

Nominal 50

0 0 10 20 30 40 50 60 70 80 Deformation Length[cm]

Figure 4.5: Three optimal force curves in three phases

4.1.3 Energy absorption by friction

From the research of Witteman [12] a solution is offered for the compatibility issue considering different crash configurations (full overlap, 40 per cent offset and 30 degrees impact). An advanced crushable zone consist of a combination of a solution for the different crash configurations and a solution for obtaining the optimal decelerations. There a few different possibilities to apply such a combination in a crushable zone. One design is also from the research of Witteman [12], in which a global design possibility is given for energy absorption by friction blocks (figure 4.6). Changing the pressure force on a friction block regulates the energy absorption. The well functioning idea of hydraulic vehicle brakes can be used on the backwards moving cable rod. The application of friction blocks around the two square rigid rods can generate the desired additional deceleration forces. In case of an offset or an oblique collision where only one longitudinal is directly loaded, it is not allowed to use the additional friction force on the other, not directly loaded, longitudinal. The fracture force of the cable (279 [kN]) is only sufficient to resist the peak load of the folding process (180 [kN]). For this reason, two sensors are required inside the bumper, in front of the longitudinal, which detect a contact with an 72 Chapter 4. Practical Modeling

Figure 4.6: Sketch of the friction pistons against the cable rod[12]

object by means of a pressure force or with radar detection. If only one signal is detected (oﬀset collision), only on the cable rod in the longitudinal at that side the maximal needed additional friction must be generated. In the case of two signals (full overlap collision), both cable rods must be loaded with half of the total needed additional force.

In this research also pronounces have been made about possible future possibilities and then namely with regard to the optimal deceleration curves. A crushable zone in combination with a computer controlled system would be an ideal solution for the compatibility issue. A computer controlled system measure continuously the actual deceleration level and adjust at the same time the pressure to reach the programmed optimal deceleration pulse. In this way, it is also possible to compensate for the stiﬀness, velocity or weight of the colliding obstacle.

If this system is fast enough and very reliable, it is possible to think about a structure which has only two very stiff beams, which can fully slide backwards without deformation. A heavy computer controlled break system regulates the desired deceleration. In this case, a cable system to direct asymmetric forces to a symmetric force distribution is not necessary, because sensors already send signals to increase the friction of one loaded beam to reach the same energy absorption. In addition, the telescope structure is not longer necessary, because the new beams have not to crumple to absorb energy so they can be made very stiff with a high bending resistance. Only problem could be the space behind the firewall or under the vehicle floor. 4.1. The Necessity of An Advanced Crushable Zone 73

4.1.4 Design of a hydraulically controlled frontal car structure

Witteman also discussed a design consisting of a hydraulic system instead of the proposed cable system [12]. To load the missed longitudinal member during a asymmetric collision, it is possible to use a hydraulic system instead of the proposed cable system. In figure 4.7, a principle sketch of the system is shown with besides the longitudinals two cylinder with pistons. The cylinder rods are fixed to the cross member, just like the front ends of the longitudinals. If one of the longitudinal is loaded during an offset crash, it start to deform and because of the connection to the cylinder, the rod slides into the cylinder. The oil inside the cylinder is pressed via a tube or pipe to the rod side of the cylinder of the unloaded longitudinal. Under the influence of this oil pressure, the piston of this cylinder is also pushed backwards. Because this piston is connected to the unloaded longitudinal member, it is forced to collapse in an axial folding mode. The pressure that arises in the cylinder of the unloaded longitudinal is led back to the rod side of the cylinder of the loaded longitudinal, where it helps to further move the piston inside the cylinder. Hence, the hydraulic cylinder form a closed-loop system. Note that in the case of a full overlap collision where both longitudinals are loaded, the system is in equilibrium and does not influence the crash behavior. One

Figure 4.7: A hydraulically controlled frontal car structure[12] problem is however, that the oil volume in the cylinder does not fit in the other cylinder at the rod side, because of the volume of the rod itself. Because the rods move inwards, the total available volume decreases. Solution is s piston with at each side a rod, where the second rod has not a force function but causes identical volume exchanges. For this solution there must be space behind the firewall where the additional rods can move backwards. Advantage is the same area at each piston side, which gives a 1:1 force transmission. A second problem is the available deformation length, because a cylinder with piston can be shortened less as half of the original length. For this reason it is also necessary that there is much horizontal space under the passenger floor, because then the cylinders could be mounted at the rear of the firewall. The hydraulic supported structure generates a constant deceleration force, independent of the overlap percentage. However, to reach the optimal crash pulse, control of the oil flow is necessary. In this case, a valve with a controllable flow restriction or several valves must be 74 Chapter 4. Practical Modeling

used in the outlet of the backside of the cylinders. Reducing the outlet area increases the pressure and therefore the stiffness of the system. After the first deceleration interval, the valve can be fully opened and for the third interval, if necessary the total area can be reduced again. In this research the possibility with pressure control valves is shortly discussed. This discussion serves as a guideline for further research. In this chapter three other designs are discussed. First the design with pressure control valves is further discussed (especially with application of ER and MR fluid). Further, there will be an extended description about smart dampers. The last one concerns the application with two parallel disk shaped plates. All the designs are based on the use with MR fluid (this follows from section 2.3.6. 4.2. Design of an Advanced Crushable Zone 75

4.2 Design of an Advanced Crushable Zone

4.2.1 Advanced Crushable Zone Using Pressure Control Valves

Figure 4.8: Schematic representation of the advanced crushable zone using PCV’s

The first design that will be discussed is the crushable zone with pressure control valves. The pressure control valve is also discussed in section 3.2. In this design the pressure control valves are combined with a cylinder-piston system. The system is illustrated in figure 4.8. The choice of electromagnets is by coincidence. To make use of ER fluid, the magnetic poles have to be replaced by electrical poles. To make sure that the fluid will stay in the device a membrane is used at the end of the pressure control valves (is not illustrated in the figure). Before the crash, the system will be in rest and the coils of the electromagnets will not be powered. During the crash the coils are powered and the pressure control valves will create a specific pressure drop. The pressure drop across the pressure control valve will result in a force at the piston of the cylinder. From equation 3.12 and equation 3.13 the viscous component and the field dependent induced yield stress component respectively, can be calculated by varying a few important parameters. Equation 3.12 is modified by the next equation which satisfies a more general case:

cL P = τ (M) (4.3) 1 H y 76 Chapter 4. Practical Modeling

where L and H are the length and gap of the flow channel between the fixed poles. τy is the yield stress developed in response to an applied field. The parameter c has a value ranging from a minimum value of 2 (for ∆Pτ less than ∼ 1) to a maximum value of 3 (for ∆Pτ greater ∆Pη ∆Pη than ∼ 100). The dynamic range is 5, so c has approximately the value 2.3. The force in the device is totally dependent on the area on which the pressure works. In this case, the piston determines the total force which is the result of the pressure drops in the valves. So, the total force (viscous force and induced force) at the piston can be calculated using equation 4.4:

2.3Lτ (M) 12ηL F = y + Q πr2 (4.4) valve H WH3 p

where rp is the radius of the piston in the device. The force Fvalve is not the total force acting at the system. Also the viscous effects in the cylinder must be taken into account. These forces are the result of the flow of the fluid in the cylinder. This force can be calculated using equation 4.5: 128ηQL F = (4.5) cyl πD4 In the next two figures, the viscous pressure drop and the induced pressure drop are illustrated. These pressure drops are calculated with a few assumed parameters, namely η = 0.67 [P a.s], L=10*10−2[m], W =140*10−2[m] and τ=80*103[kP a] (Nowadays, this value of τ is the highest possible value for a MR fluid). For calculating the force acting at the piston, we assume a

Relation gapsize − Viscous Pressure Drop Relation gapsize − Induced Pressure Drop 5 10

6 10

4 10 5 10

4 10 Pressure [kPa] Pressure [kPa]

3 10

2 10

2 10 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Gapsize H [m] Gapsize H [m]

Figure 4.9: Pressure Characteristics

−3 piston radius rp of 70*10 [m]. The following two ﬁgures illustrate the characteristics of the force (viscous and induced force) acting at the piston against the gapsize. 4.2. Design of an Advanced Crushable Zone 77

Relation Gapsize − Viscous Force Relation Gapsize − Induced Force 4 3 10 10

3 10

2 10

2 99 kN 10 56 kN Force [kN] Force [kN] 1 10

1 10

0 10

−1 0 10 10 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Gapsize H [m] Gapsize H [m]

Figure 4.10: Force Characteristics

Relation Gapsize − Dynamic Range 16

Dynamic Range [−] 6

0.55

0 0 0.005 0.01 0.015 0.02 0.025 0.03 Gapsize H [m]

Figure 4.11: Dynamic Range

When the calculations are performed with ER ﬂuid than this results in a much lower pressure drop and so much lower forces acting at the piston. Since the pressure drop and the forces are linear dependent of the yield stress, the choice of ER ﬂuid will result in a force decline with a factor 8. From the graphs one can see that a gapsize H of 5.1 [mm] will result in a 78 Chapter 4. Practical Modeling

desirable nominal force level of 99 [kN]. However, this choice will result in a controllable level 55 of just 55 kN. The dynamic range D is then just 99 = 0.55. This is much to low to receive the complete controllable level. From the figures also follows that by very low gapsizes, the viscous forces get enormous (with the power of 3) in contrast to the controllable force (with the power of 1). It is necessary to design with gapsizes which are not to small with reference to the decline of the dynamic range (see figure 4.11). To receive the desirable dynamic range, the controllable force has to increase. The controllable force is dependent on a few parameters which are nearly a fixed value. The yield stress τ is assumed to be maximal. There are at the moment no field dependent fluids commercially available which have a higher yield stress. The maximum activation length of the valve (the pole length L), the part of the valve which is actuated by an electric or magnetic field, has both influence on the viscous forces as the controllable forces. On the other hand, the gapsize has a negative influence on the dynamic range at very low values, higher values of the gapsize (H > 1∗10−2) have a positive influence. Variation of the width of the channel W will result in better results. The width of the channel has no influence on the controllable force, but it has influence on the viscous, uncontrollable forces. However, the controllable force must increase with a factor 4, will the crushable zone be fully regulable at a crash speed of 64 [km/u]. Also the flow Q, dependent of the piston speed and piston area, has only influence on the uncontrollable viscous forces. Increasing the dimensions of the channel (width and length) has a positive influence on the dynamic range (see also eq. 4.4). When one makes the recommendations mentioned above, it is possible to realize the optimal dynamic range. However, such dimensions has consequences for the final design. Figure 4.8 shows that there’s a diameter reduction between cylinder and the pressure control valve, this will result in a velocity increase. In the next calculation this velocity increase and the resulting force at the piston is calculated. The flow, Qcyl = VpAp must be pressed through the whole system and so through the pressure control valves. As mentioned before this will result in pressure variations. This pressure variation will result in a force acting at the piston. These forces can be classified by the uncontrollable forces in the system. The fluid velocity in the cylinder caused by the piston is 9.772 m/s and shall increase as a result from a diameter reduction further in the system. In the next calculation a pressure control valve with a width W =400.10−3[m] and a gapsize H=10.10−3[m] is taken. The flow in the cylinder:

−3 2 3 Qcyl = 9.772(π(70.10 ) ) = 0.1504[m /sec] (4.6)

The ﬂow area of the pressure control valve:

−3 −3 −3 2 Av = WH = (400.10 )(10.10 ) = 4.10 [m ] (4.7)

The velocity increase of the ﬂow follows from mass conservation:

Qcyl = Qvalve ⇒ 0.1504 = VvAv ⇒ Vv = 37.6[m/s] (4.8)

The pressure increase involved,

2 2 6 ∆Pstat ∼ 0.5ρv ⇒ ∆P = 0.5(1000)(37.6) = 0.706 ∗ 10 [P a] (4.9) 4.2. Design of an Advanced Crushable Zone 79

This results in an increase of the force,

6 ∆Fstat = ∆PAp = (0.706 ∗ 10 )(0.0153) = 10.8[kN] (4.10)

This force will not play an important part in the design of the pressure valve. But one must pay attention by the determination of the dimensions of the pressure valve. The nominal force level shall be 10.8 [kN] lower than in the ﬁrst situation. The dynamic range D should be higher, because a bigger regulation level is required. This will led to a nominal force level of 87.2 [kN]. A velocity of 32 [km/u] will result in a lower nominal force, this in contrast to 64 [km/u] in which the nominal force shall be a higher. The following table is formulated for the situation of 56 [km/u].

Table 4.2: Design With Pressure Control Valve: 3 −3 −2 H=11.4*10 [m], Rp=70*10 [m], η=0.67[Pa.s], L=52*10 [m] 3 τmax = 80∗10 [P a.s] Phase one Phase two Phase three 3 3 Yield Stress τ0 = 80∗10 [P a.s] τ0 = 0[P a.s] τ0 = 49.5 ∗ 10 [P a.s] Fτ 129.19 [kN] 0 [kN] 79.94 [kN] Fη 46.8 [kN] 46.8 [kN] 46.8 [kN] Ft 176 [kN] 46.8 [kN] 126.74 [kN] Ft 2 cylinders 352 [kN] 93.6 [kN] 253.48 [kN] Required F¯c = 352[kN] F¯c = 99[kN] F¯c = 253[kN]

The table above shows that it is possible to achieve the desirable force level, when the gapsize is H=11.4[mm], the width of the channel W =140 [mm], the piston diameter Dp=140 [mm] and the effective pole length L = 520 [mm]. The width W is taken equal to the diameter of the cylinder to obtain better built-in possibilities. The viscous part, Fvis, caused by the flow in the cylinder (equation 4.5) is also taken into account. However, this viscous force is small in comparison with the forces in the valve (Fvis=0.128 [kN]). In fact this force can be neglected, so in het next calculations it is not taken into account anymore. The figures below are the viscous forces and controllable forces (fig 4.12) and the dynamic range (fig 4.13). 80 Chapter 4. Practical Modeling

Relation Gapsize − Viscous Force Relation Gapsize − Induced Force 8 5 10 10

7 10

6 4 10 10

5 10

4 3 10 10 Force [kN] Force [kN]

3 10

129.2 kN 2 2 10 10 46.8 kN

1 10

0 1 10 10 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Gapsize H [m] Gapsize H [m]

Figure 4.12: Pressure Characteristics: Width channel=400 [mm], Length channel=520 [mm]

Relation Gapsize − Dynamic Range 20

8 Dynamic Range [−]

4 2.76

0 0 0.005 0.01 0.015 0.02 0.025 0.03 Gapsize H [m]

Figure 4.13: Dynamic Range: Width channel=400 [mm], Length channel=520 [mm] 4.2. Design of an Advanced Crushable Zone 81

It also possible to place a few pressure control valve in parallel. This will have a positive inﬂuence on the static pressure of the system Pstat. The ﬂow Qcyl is divided into n channels with width W . From mass conservation yields,

Qcyl = Qnvalves ⇒ Qcyl = VnAn ⇒ Qcyl = Vn(WH) (4.11)

Q V = cyl (4.12) n WH

The pressure increase involved, 2 ∆Pstat ∼ 0.5ρVn (4.13)

Placing four pressure control valves in parallel yields to the following results:

0.1504 V = 4 = 9.4[m/s] (4.14) n (400.10−3)(10.10−3)

2 ∆Pstat ∼ 0.5ρVn < 0 (4.15)

Equation 4.15 shows that four parallel pressure control valves with the same dimension yields to a ’negative’ static pressure. No static force is needed to press the ﬂuid through the valves. However, this system with four valves is totally over-dimensioned. One valve satisﬁes the demands of the system (see table 4.4). Also, there is no space to built in four of such valves in combination with a cylinder-piston system in the front structure of the vehicle. It is an absolute necessity to recalculate the parallel system to obtain the desirable force level. 82 Chapter 4. Practical Modeling

4.2.2 Advanced Crushable Zone Using Smart Dampers

Figure 4.14: Schematic representation of the advanced crushable zone based on ’Smart Dampers’

The principle of this system is partially discussed in section 3.3. The working of the ER/MR damper is summarized as follows: ER/MR fluid flows under influence of a pressure driven flow through a narrow gap, which is formed by the piston and the cylinder housing. The flow shows a combination of a pressure driven flow and a shear flow due to the moving piston. Important design parameters are of course the diameter and velocity of the piston, which determines the flow of the system, and the gapsize between piston and cylinder, which have great influence on the controllable and uncontrollable forces. In this section, the theory of the previous section is applied to an advanced crushable zone. It is very important that the dynamic range previously is determined and by that the magnitude of the controllable force. These parameters are dimensioned in the previous section. The total force at the piston consists of a viscous part, the uncontrollable forces, and the controllable forces which follows from the shear in the fluid. In the figures below the behavior of the controllable and uncontrollable forces are illustrated. These forces are calculated with equation 3.17 and equation 3.18 with a varying −2 −3 3 gapsize H in which η = 1.5 [Pa.s], L=8.443*10 [m], R2=72.7*10 [m] and τ=64.4*10 [kPa]. 4.2. Design of an Advanced Crushable Zone 83

Relation Gapsize − Viscous force Relation Gapsize − Induced Force 7 4 10 10

6 10

5 3 10 10

4 10

3 2 10 10 Force (kN) Force (kN)

2 10

1 1 10 10

0 10

−1 0 10 10 0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04 Gapsize (H) [m] Gapsize (H) [m]

Figure 4.15: Force Characteristics ’Smart Damper’

From these characteristics results that the uncontrollable force increases exponentially by small gapsizes. It is with that of importance that there is paid attention to the dimension of the gapsize H when designing such a system like this. The gapsize H has to be big enough to obtain a greater dynamic range D. In the figure below, the dynamic range is illustrated of the system with the parameters discussed above. In contrast to the system in the previous section the friction force Ff is taken into account in the calculation of the uncontrollable force. This friction force Ff consists of friction forces of the piston rod with the seals. Because of this friction force Ff , the dynamic range will show a different course. The dynamic range shows an optimum by a specific gapsize. The dynamic range decreases drastic by small gapsizes because of the uncontrollable force which increases exponentially. On the other hand, the dynamic range decreases also by bigger gapsizes, because of the friction force Ff which is not dependent of the gapsize H. To obtain a highest possible dynamic range, it is of necessity to know which parameters have influence on the controllable and uncontrollable force. One of the most important parameters by such dampers is the piston velocity and with that the appearing forces. Such characteristics are essential for the design and they are well used for comparison. The next figure illustrates such a characteristic with the parameters mentioned above. The piston velocity is taken as a variable and the gapsize H is assumed to be a constant, namely H =2.7[mm]. From this figure follows that the controllable forces have only influence at low speeds. At speeds greater than 0.2 [m/s] there is no dependence between the piston velocity and the controllable force. The uncontrollable force, on the other hand, is linear dependent of the velocity, which is also clear from equation 3.17. The viscous forces are of big importance at high speeds of the piston. This is in theory very unfavourable for the dynamic range. 84 Chapter 4. Practical Modeling

Relation Gapsize − Dynamic range 1.035

1.03

1.025

1.02

1.015 Dynamic range D [−]

1.01

1.005

1 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Gapsize (H) [m]

Figure 4.16: Dynamic Range ’Smart Damper’

Force Decomposition of MR Damper 800 Viscous Force Induced Force Friction Force 700 Fc

600

500

400 Force (kN) Func 300

200

100

0 0 5 10 15 Pistonvelocity v0 (m/s)

Figure 4.17: Force Decomposition ’Smart Damper’ 4.2. Design of an Advanced Crushable Zone 85

Parameter variation

In this section a few parameters are varied. In the design phase it is diﬃcult to see in which way the dampers have to be dimensioned. So the next parameters are varied:

• Yield Stress τ0 • Active Pole Length L

• Nominal Cylinder Bore ID D2 • Plastic Viscosity η

The next ﬁgures are obtained by variation of just one parameter. The ﬁgure topleft concerns the variation of the yield stress τ0 with the viscous force and controllable force. The param- −2 −3 eters η, L, R2 and H have respectively the values 1.5 [P a.s], 8.443*10 [m], 72.7*10 [m] and 2.7*10−3[m], which are also mentioned above.

500 500

400 400

300 300

200 200 Force (kN) Force (kN)

100 100

0 0 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 0.1 4 Yield stress T0 (Pa.s) x 10 Active Pole Length L (m)

3500 1400 Induced Force 3000 1200 Viscous Force 2500 1000

2000 800

1500 600 Force (kN) Force (kN) 1000 400

500 200

0 0 0.08 0.1 0.12 0.14 0.16 0 1 2 3 4 5 Nominal Cylinder Bore (ID) R2 (m) Plastic Viscosity (Pa.s)

Figure 4.18: Variation of various parameters of the ’Smart Damper’

The figure illustrates the result what would be expected. The viscous force is independent of the influence of the magnetic field. The controllable force shows dependence and is with that linear dependent of the yield stress. This is also clear from equation 3.18. The figure right above concerns the variation of the active pole length (L), the length of the piston which influences effective the fluid by means of a magnetic or electric field. This pole length has both influence on the uncontrollable force and the controllable force. This relation is in both cases linear. The viscous force is stronger dependent of the pole length than the controllable force. The nominal cylinder bore r2 has a quadratic relation with the viscous force and a linear relation with the controllable force. The cylinder bore r2 has direct relation with the 86 Chapter 4. Practical Modeling

piston diameter rp and so with the flow Q (v0Ap) and the perimeter w defined as π(r2 + rp). The figure left above is clear, the plastic viscosity η has a linear relation with both the forces. It also of importance to know how these variations influences the dynamic range. Also the dynamic range is illustrated in the figure below, the same parameters are varied.

0.7 0.61

0.65 0.61

0.6

0.61 0.55 Dynamic Range (D) [−] Dynamic Range (D) [−]

0.5 0.61 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 0.1 4 Yield stress T0 (Pa.s) x 10 Active Pole Length L (m)

0.61 14

0.6 12 10 0.59 8 0.58 6 0.57 4

Dynamic Range (D) [−] 0.56 Dynamic Range (D) [−] 2

0.55 0 0.08 0.1 0.12 0.14 0.16 0 1 2 3 4 5 Nominal Cylinder Bore (ID) R2 (m) Plastic Viscosity (Pa.s)

Figure 4.19: Inﬂuence on the Dynamic Range by Varying Parameters

The dynamical range generally is deﬁned as equation 3.16. The friction force Ff has an important role and it may absolutely not be neglected. It is possible to estimate the friction force as 2Fη and the dynamic range is than be deﬁned as:

F + F D = c eta (4.16) 2Fη

The ﬁgure below illustrates a 3D-plot in which two parameters are varied.

• Yield Stress τ0 & Pistonvelocity v0

• Gapsize H & Pistonvelocity v0

From these figures a few conclusions can be drawn. The piston velocity v0 has in theory nearly no influence on the controllable force Fτ . Only at very low speeds (v0 < 3 [m/s]) the controllable force is suggestible. The controllable force behaves nearly constant above this limiting value. The viscous force shows a linear relation with the piston velocity. This means that high piston velocities are badly for the dynamic range. The dynamic range decreases as the piston velocity increases. Also, the yield stress of the fluid has only effect on the controllable force, which can also be seen in figure 4.18. The dynamic range has to be greater than 2.6 This means that the controllable force must be a factor 2.6 greater than the viscous 4.2. Design of an Advanced Crushable Zone 87

Figure 4.20: Variation of Two Parameters forces. This is not very easy, because the viscous forces are with H3 dependent. Too small gapsizes will lead to a dynamic range which will be nearly zero. To obtain a suﬃcient amount of controllable force, the gapsize has to be quite narrow. It is with that of importance that a gapsize is assumed which limits the viscous forces in considerable measure. Parameters such as the diameter of the piston, the yield stress of the ﬂuid and the gapsize will play an important role in searching for the right design.

Possibilities

To give the final design the right characteristics, one must vary with the right parameters on the right way. The mass of the vehicle is assumed to be 1100 [kg] and the collision is assumed to be full frontal with a collision speed of 56 [km/u]. This will match up with a mean velocity of 9.772 [m/s]. Nowadays a MR fluid is available with a maximum yield stress of 80*103[P a.s], in the near future this value shall be higher. The table below illustrates the possibilities of an advanced crushable zone, in which two single cylinders are used. The mean crash force is in the first phase 352 [kN], in this case this force has to be absorbed by two single cylinders. This concerns for all three phases. With a gapsize H of 9.9 [mm] and a piston diameter of 31.2*10−3 [m] it is possible to achieve the desirable deceleration level for each phase. The gapsize is quite big, this is explained by 88 Chapter 4. Practical Modeling

Table 4.3: Design With Two Single Cylinders: 3 −3 −2 H = 9.9*10 [m], R2=15.6*10 [m], η=1.0 [P a.s], L=8.443*10 [m] 3 τmax = 80 ∗ 10 P a.s Phase one Phase two Phase three 3 3 Yield Stress τ0 = 80∗10 [P a.s] τ0 = 0[P a.s] τ0 = 38∗10 [P a.s] Fτ 127.8 [kN] 0 [kN] 76.7 [kN] Fη 49.8 [kN] 49.8 [kN] 49.8 [kN] Ft 177.6 [kN] 49.8 [kN] 126.5 [kN] Ft 2 cylinders 355 [kN] 99.6 [kN] 253 [kN] Required F¯c = 352 [kN] F¯c = 99 [kN] F¯c = 253 [kN] means of figure 4.15. The viscous forces are enormous at a small gapsize, when the gapsize is large enough, than the viscous force decreases. The controllable force has still a considerable contribution. That’s why a large piston diameter is required to translate the minimal pressure level to a greater force level. When looking to the pressure level, defined as dP = Fτ +Fη , Ap than this pressure is relative low namely 2.6*106 [P a] or 26 [bar]. However the piston diameter is considerable large, when one thinks of the present (mechanical) crushable zones which have a width of nearly 140*10−3 [m]. De built-in space in vehicles is very limited and the application of such a dimensioned system can deliver some problems. The weight plays also an important role, the amount of fluid is with that of significance. From equation 3.22 the minimum amount of fluid can be calculated. This amount of fluid for this system is 7.7*10−4 [m3] or 0.77 litre MR fluid. The reason for choosing MR fluid is logical. As mentioned before, ER fluid has just a yield stress of 10 [P a.s]. This means that in this case the desirable force level cannot be reached. For example, τ0=10 [P a.s], this results in a viscous force of 49.9 kN and an controllable force of 17.2 kN. It is easy to see that ER fluid is not usable in this system. Also, the required amount of fluid shall be a factor 10 greater to reach the desirable force level. In spite of these disadvantages, one must not forget that ER fluid has a response time which is a factor 2 smaller. This can be very desirable, when looking at the available time for changing the properties of the fluid. It is also possible to set up two cylinders in serial or parallel. On this way it is possible to give each cylinder a certain configuration, which maybe results in a more flexible system. Let’s begin to set up two cylinders in parallel. The dimension of this system may not exceed the present dimensions of a crushable zone. So, the piston diameter is assumed to be 140*10−3 [m]. From the calculations results that an arrangement like this is unprofitable. Looking at one side of the crushable zone than 176 [kN] has to be absorbed in the first phase. This means that the viscous part can only be 49.5 [kN]. Higher forces are not desirable, when looking at the second phase of the collision. The controllable force, on the other hand, has to be high, namely 126.5 [kN]. This ratio between the forces is difficult to achieve. When choosing a piston diameter of 130*10−3 [m], a gapsize H of 6.0*10−3 [m] and an active pole length L of 15.5*10−2 [m] than the desirable force level is reached. In the field of dimensioning there is made profit, because the total diameter of one single cylinder becomes 260.10−3 [m] in contrast to the first system which has a diameter of 31.2*10−3 [m]. However, one must not forget that the active pole length of the parallel system is increased. This will result in disadvantages, the deformation length is getting longer which means that there are problems with regard to the built-in space. However, it is useful to vary the active pole length in the first system in which single cylinders are used. When the active pole length is increased to 4.2. Design of an Advanced Crushable Zone 89

−2 −2 16.2*10 [m] than the eﬀective piston diameter R2 is just 10.2*10 [m]. The gapsize is smaller, namely H=7.9*10−3 [m]. The table below gives all the data of the system.

Table 4.4: Design With Two Single Cylinders: −3 −3 −2 H = 7.9 ∗ 10 [m], R2 = 10.2 ∗ 10 [m], η = 1.0 [P a.s], L = 16 ∗ 10 [m] 3 τmax = 80 ∗ 10 [P a.s] Phase one Phase two Phase three 3 3 Yield Stress τ0 = 80 ∗ 10 [P a.s] τ0 = 0 [P a.s] τ0 = 48.5∗10 [P a.s] Fτ 126 [kN] 0 [kN] 78.8 [kN] Fη 48 [kN] 48.0 [kN] 48.0 kN] Ft 174 [kN] 48.0 [kN] 126.8 [kN] Ft 2 cylinders 348 [kN] 96 [kN] 253.8 [kN] Required F¯c = 352 [kN] F¯c = 99 [kN] F¯c = 253 [kN]

The only disadvantage of this system is the increased active pole length. Since the activation of the magnetic field is situated in the piston, the cylinder length has to be increased to obtain a sufficient length of deformation. The pressure in the system is increased with a factor 3, which correspond to 6.259*106 [P a] or 62.6 [bar]. The minimum amount of fluid remains equal (these is totally dependent of the dynamical range, see also equation 3.22), namely 7.73*10−4 [m3]. Also the base viscosity is of great importance, because of the big influence on the viscous forces. A fluid with a low base viscosity has first refusal. Designing an advanced crushable zone is difficult, because the system must be able to obtain the right deceleration for three different phases. The dimensions of the system are dependent of the dynamic range. The dynamic range of the system described above, is determined by the first phase. So, this will results, in this case, in large systems. The first phase needs a mean force of 352 [kN] to decelerate the vehicle to 32 [g]. For higher velocities, for example 64 [km/u], this value has to be greater namely 45 [g]. Shortly, it is better to optimize each phase locally by a different configuration. So, each phase has a configuration with different gapsizes. This can be applied very easy in the cylinder housing. However, this solution has to be work out in further research. In the next section, a system has been discussed what is nearly the same as the first system of section 4.2, a cylinder-piston system with pressure control valves. Only now two parallel disk shaped disks are used, the fluid flows through the gap between this plates. Between the disks the fluid is activated by means of a electric/magnetic field, so this will result in a variation of the forces. 90 Chapter 4. Practical Modeling

4.2.3 Advanced Crushable Zone Using Parallel Disk Shaped Valves

Figure 4.21: Schematic representation of the Advanced Crushable Zone Using Parallel Disk Shaped Valves

The basis of this system is consistent with the first system with pressure control valves. In principle, the pressure control valve is changed by two disk shaped valves. The fluid within these two parallel disk shaped valves is activated by an electric or magnetic field. Two membranes are used to prevent the fluid from flowing away. The fluid is situated already in the channels before the collision take place. On this way the fluid can directly be activated during the collision. A big advantage of this system is that the fluid flows radial between the plates, so the fluid velocity will decreases as the radius of the plates increases. In general, high fluid velocities cause high viscous forces, which have a bad influence on the dynamic range. Also the gapsizes of the two plates can be varied by means of two actuators, which gives more flexibility to the system. The application of two plates has the disadvantage that it takes much built-in space in the front structure of the vehicle. However, this space is very limited. Equation E.12 from appendix E gives the total pressure drop of the cylinder-piston system in serial with a pressure control valve (disk shaped plates). When this equation is worked out, then this yields for the force:

τy 6ηQ r2 128ηQ ∆Ftotal = 2.85 (r2 − r1) + 3 ln + 4 L Ap (4.17) h πH r1 πD | {z } | {z } controllable uncontrollable in which r2 is the outer radius of the disk shaped plates, r1 is the radius of the piston, Q is the ﬂow of the system, H is the gapsize between the plates, L is the length of the cylinder and Ap is the area of the piston. 4.2. Design of an Advanced Crushable Zone 91

And also here a high dynamic range is desirable. To gain insight into the possibilities with this system, parameter variation is necessary. Eq. 4.17 gives an impression of the uncontrollable and controllable forces. The uncontrollable force is dependent of the flow Q, the gapsize H and the geometry L (the length of the cylinder), D1 and D2 (the diameters of the discs). Also the viscosity η is a variable. The controllable part is dependent of the gapsize H, the yield stress τ and the geometry D1 and D2. The gapsize H is an important parameter and this one shall first be analysed. Hereunder two figures are illustrated, in which the uncontrollable and controllable pressure drop are functions of the gapsize H. The following parameters are assumed: τ = 80*103 −3 −3 [kP a], r1 = 70*10 [m], r2=100*10 [m], η=0.67 [P a.s] en v0=9.772 [m/s]. The force level 2 is then defined as ∆F = ∆P (πr1). 92 Chapter 4. Practical Modeling

Relation gapsize − Viscous Pressure Drop Relation gapsize − Induced Pressure Drop 8 5 10 10

7 10

6 10 4 10

5 10

4 10 Pressure [kPa] Pressure [kPa]

3 10 3 10

2 10

1 2 10 10 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Gapsize H [m] Gapsize H [m]

Figure 4.22: Pressure Characteristics

Relation gapsize − Viscous Drop Relation gapsize − Induced Force 7 4 10 10

6 10

5 3 10 10

4 10

3 2 10 10 Force [kN] Force [kN]

2 10

1 1 10 10

0 10

−1 0 10 10 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Gapsize H [m] Gapsize H [m]

Figure 4.23: Force Characteristics

Also follows from figure 4.24 that at a certain critical gapsize H, the dynamic range becomes optimal. It is of importance that one not choose a small gapsize, this will badly influence the dynamical range. Variation in the geometry is also of importance, the figures below illustrate a variation in the piston radius r1 and the disc radius r2. The influence on the forces and the dynamic range D is illustrated. 4.2. Design of an Advanced Crushable Zone 93

Relation gapsize − Dynamic Range 25

10 Dynamic Range [−]

0 0 0.005 0.01 0.015 0.02 0.025 0.03 Gapsize H [m]

Figure 4.24: Dynamic Range

90 140 Viscous Force Induced Force 80 120

100 60

80 50

Force [kN] 40 Force [kN] 60

30 40

20 10

0 0 0 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.25 Piston Radius [m] Disk Radius [m]

Figure 4.25: Variation of the piston radius r1 and disk radius r2

From these figures can be concluded that the piston radius r1 plays an important role in obtaining a high dynamic range. This is also the case by the previous systems. Because the controllable force is relative low in proportion to the uncontrollable force, the piston radius can offer the solution at a certain configuration. A big gapsize H is of importance here. Figure 94 Chapter 4. Practical Modeling

40 1.4

35 1.35

30 1.3

25 1.25

20 1.2

Dynamic Range [−] 15 Dynamic Range [−] 1.15

10 1.1

5 1.05

0 1 0 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.25 Piston Radius [m] Disk Radius [m]

Figure 4.26: Variation of the piston radius r1 and disk radius r2 - Inﬂuence on Dynamic Range

4.24 illustrates clearly that a high gapsize H will lead to a high dynamic range. Perhaps the controllable force is not big enough, but that can be compensated by the piston radius r1 (∆F = ∆PAp). It is also of importance that a big disc radius is chosen. The proportion r2 is an important r1 factor in the definition of the viscous forces of the disc. This one has a logarithmic relation. This in contrast to the controllable force of the disc, the difference r2 − r1 goes linear. This means that at a large proportion r2 , the dynamic range increases. This is clearly seen in the r1 right figure 4.25, in which the controllable force shows a linear relation and the uncontrollable force saturates (lim C ln r2 C ). The dynamic range D in figure 4.26 becomes bigger, x→∞ 1 r1 ≈ 2 as the radius of the disc r2 increases. The disc radius can be compared with the active pole length L of the previous system.

Possibilities

In this section the possibility of the desirable force level is discussed. Also here table 4.1 has been used in which the desirable force levels are illustrated. Also for this system applies that the nominal force level must be 99 [kN]. A frontal collision with a mean velocity ofv ¯ = 9.772 [m/s] is assumed. It is tried to choose the dimensions of this system in coincidence with the present crushable zones. This means that the width W and the piston diameter is limited to nearly 160*10−3 [m]. The length L is limited to 80*10−2 [m]. As mentioned before (in the previous section), it is of importance that there will be a variation of the gapsize H, the piston radius r1 and the disc radius r2. −3 −3 From table 4.5 follows that at a piston radius r1 of 85*10 [m], a disc radius r2 of 203*10 [m] and a gapsize H of 4.8*10−3 [m], the desirable force level can be achieved. Hereby, the 4.2. Design of an Advanced Crushable Zone 95

Table 4.5: Design With Parallel Disk Shaped Valves: −3 −3 −2 −3 H = 4.8*10 [m], r2=203*10 [m], η=0.67 [P a.s], L=78*10 [m], r1=85*10 [m] 3 τmax = 80 ∗ 10 P a.s Phase one Phase two Phase three 3 3 Yield Stress τ0 = 80 ∗ 10 [P a.s] τ0 = 0 [P a.s] τ0 = 48.5∗10 [P a.s] Fτ 127.2 [kN] 0 [kN] 77.1 [kN] Fη 50.8 [kN] 50.8 [kN] 50.8 [kN] Ft 178 [kN] 50.8 [kN] 127.9 [kN] Ft 2 cylinders 356 [kN] 101.6 [kN] 255.8 [kN] Required F¯c = 352[kN] F¯c = 99 [kN] F¯c = 253 [kN]

fluid parameters becomes τ = 80*103 [P a.s] and η=0.67 [P a.s] As is mentioned in section 4.2, the uncontrollable part shall not only consists of the viscous forces of the fluid in the cylinder and plates. One must also take the pressure variations of the curves, diameter changes and 2 KLρV in -and outlet effects into account. These pressure variations ∆Poverall = 2 have big influence on damper systems. These variations are considered to be minor losses in long pipe systems, but in damper applications due to the short orifice length, they may become significant, especially at higher velocities[4].

The velocity V is here the local velocity in for example a diameter change, the factor KL is a factor which is dependent of the geometry of the diameter change and the curves. This pressure drop ∆Poverall has inﬂuence on all the systems discussed in chapter 4. The nominal force level of 99 kN decreases, because of the uncontrollable force level. This means that the uncontrollable, viscous part has to be smaller and the dynamical range has to be bigger. In general, equation E.12 from appendix E will result in:

∆Ptotal2 = ∆Pdiskmr + ∆Pdiskvis + ∆Pcylvis + ∆Poverall (4.18) in which V is the local velocity in the diameter change or curve. The velocity v0 in the uncontrollable part of the equation, namely Q = v0Ap is the velocity of the piston in the cylinder. So, the piston has the mean velocity of the mean crash velocity of the vehicle. 96 Chapter 4. Practical Modeling Chapter 5

Feasibility Study

In this chapter, the feasibility of the three designs from chapter 4 is discussed. This shall happen with the help of a list of demands which is previously determined. The method of verification is also used in chapter 2 for the choice between ER and MR fluid. The list of demands consists of the same demands as the demands used for the choice between ER and MR fluid. After all, the choice between ER and MR fluid is close connected with the design. Only the verification of the designs is more specific now. Also, it is of importance that the design has enough future perspective to solve certain problems (such as the response time).

97 98 Chapter 5. Feasibility Study

5.1 Testing the designs against the list of demands

The following demands with weight factors follows from chapter 2:

Table 5.1: List of demands including weight factors Crash Situation Requirements Actuating Properties 11 Reliability 10 Durability 9 Fast Response Time 8 Cost Factors Material and Production Costs 6 General Applicability Factors Ageing 7 Material and Production Weight 5 Temperature Stability and Range 4 Material and Device Size 3 Maintenance 2 Fatigue 1 Eﬃciency 1

Then, the designs are tested against the demands with the specific weight factor. The value ’0’ for a specific demand means that the design is not able to fulfil the demand. A value ’1’ means that the design is able to fulfil the demand sufficiently. A ’2’ means that the design is able to fulfil the demand very well. Design A is the advanced crushable zone with PCV’s (section 4.2.1), design B is the advanced crushable zone using smart dampers (section 4.2.2) and design C is the advanced crushable zone using parallel disc shaped valves (section 4.2.3).

Figure 5.1: Testing the designs against the list of demands 5.1. Testing the designs against the list of demands 99

The actuating properties of design B, the design with the smart dampers, are by far the best. The dynamic range D of design B can easily by increased. This delivers the designer much freedom in designing the crushable zone. The flow only passes one restriction in contrast to the other designs. Also, the combination of a pressure driven flow with a shear mechanism (the piston) results in better design possibilities. By each of the three designs, the fluid has to be pressed through restrictions. By design A a restriction takes place in the flow area which gives the fluid a local flow velocity of 37.6 [m/s]. The uncontrollable force, Func, is increased with 10.8 [kN]. The dynamic range will decrease. By design C there is also a matter of a reduction in flow area, this one is nevertheless smaller than design A, because the disc shaped flow area is bigger. However, in system C there is a matter of two squared curves. Also such a geometry is coupled with a rise of the uncontrollable force. These curves in the geometry of the system will also come up for discussion in design A, when searching for a compact design in which the dimensions of the parallel plates are incorporated. Design B also deals with a velocity rise of the fluid in the gap between piston and cylinder housing. In the field of reliability all three the designs scores well. Reliability of the system is mainly related to the peripheral equipment. Since the systems are activated with magnetic fields, the reliability is quite big. Permanent magnetic fields can be used to insure that there is always activation of the MR fluid. A big problem is sedimentation of the fluid in the cylinder and the pipes. This can cause total malfunctioning of the system, because the fluid is not responding to the magnetic field. Sedimentation can be prevented by additives in the MR fluid (see also section 2.2.3). However, a MR fluid is insensitive for additives (to reduce sedimentation and ageing) and impurities (dirt, wear) in contrast to ER fluid. Also the use of permanent magnets can offer a solution here. By making use of permanent magnets, the fluid can be (lightly) activated for years to prevent sedimentation. This prevents total malfunctioning of the system. If the systems are reliable, with regard to the desirable force levels, is still the question. It is difficult to determine in this phase of the design, if the theory is achievable in practice. Experiments with one of the designs can clarify some things. The durability of the system is very important. The system has to be able to show the desirable characteristics after ten years. The durability indicates if the system is able to work trouble-free for years. When a design has to have maintenance a few times in a year or several parts has to be replaced, then one is speaking of a non-durable system. System A is quite durable, because of the pressure control valves. Also the system is restricted to a few number of parts. For system B the same applies. Only system C scores a little bit worse, because of the difficult manufacture and positioning of the parallel plates. The production and assembly of this system is much more complicated then the other systems. Application of MR fluid has the disadvantage that the response time is somewhat slower than that of ER fluid. Thereby one must pay attention to the amount of fluid that has to be activated for the desirable force level. The higher the dynamic range, the more fluid has to be activated. So, the response time is also dependent of the minimum amount of fluid that has to be activated. The cooperation with a precrash sensing system should be able to solve the problem of the faster response. The parameters of the system are determined before the collision. The system adjusts itself and no further regulation during the collision is necessary. The reliability of the system is also increased. This solution is easy to realize with design A by simply (de)activate a few pressure control valves. It is possible to estimate the cost of the designs when looking at the complexity and the 100 Chapter 5. Feasibility Study

number of parts of the systems. Thereby, it has to be noticed that design A is far out the most simple. This will result in somewhat lower material and manufacture costs. Design B and C are more complex and they require also more production capacity. So, the score of these systems is somewhat lower. Ageing is basically only related to the fluid. MR fluid is more sensitive for ageing, because of the bigger risk of sedimentation. But there are nowadays additives which makes it possible to solve sedimentation and so the problem of ageing. Also the use of permanent magnets can clarify this problem. However, it is possible that the design has influence on the state of the fluid at a certain moment. Design C is somewhat unfavourable with regard to the geometry. The fluid between the plates has more the risk of sedimentation than the systems A and B. If the fluid once is precipitated then it is, without the use of permanent magnets, very difficult to get the fluid in the right state. The weight plays an important role in designing crushable zones. The weight determines to a certain extent the consumption of the vehicle and with that the environmental impact. Design B is very compact and it has nearly any peripheral equipment. The magnetic coils and cores are located in the piston. The activation length L is in this system much smaller then in the other two systems. The piston moves in the fluid and activates the fluid locally in the gap between piston and cylinder housing. This in contrast to the other two systems, in which the piston has only the function of pressing the fluid through the restrictions which are arranged in serial. The weight of design B shall be lower then the other designs. The fluid properties are strongly dependent of the temperature. The specifications of the different MR fluids are illustrated in appendix A. From this appendix follows that a nearly constant fluid behavior is guaranteed within a certain temperature range. However, outside this range nothing is guaranteed. Not many experiments are done with regard to this temperature dependency. The most applications are applied within this range. However, applications of ER and MR fluids in a crushable zone are quite a different case. Within a small period of time, high forces take place which are caused by the restrictions. The heat, which is created by the restrictions, shall influence the properties of the fluid. The question is how far this heat production influences the system. This has to be investigated in further research. However, design B scores lower on this topic, because there is talk of a closed system and so the heat has more influence on the properties of the fluid. The other two systems can be conceived as open systems, after activation the fluid shall disappear in a reservoir. Design A uses pressure control valves which have an arrangement in serial or parallel. Design C consist of a cylinder-piston in combination with two parallel disc shaped discs. Both design A and C takes up a lot of room in the front structure of the vehicle. Design B is a system which is very compact, the magnetic coils and cores are located in the piston. The fluid is pumped from the right room to the left room during the movement of the piston. A problem is the available deformation length, because a cylinder with piston can be shortened less as half of the original length. For this reason it is also necessary that there is much horizontal space under the passenger floor, because then the cylinders could be mounted at the rear of the firewall. The maintenance of the three systems is quite minimal. When the problem of sedimentation is solved, only preventive check is necessary. Also maintenance is not very important. In principle, a vehicle has a yearly service. The working of the system and the state of the fluid 5.1. Testing the designs against the list of demands 101

can easily be note down in the checklist of the vehicle. Only the question is how the system can be checked on proper operation. Fatigue is less important than maintenance. A crushable zone has to work one time properly. Very often the vehicle is ’total loss’ after a collision and the vehicle end up at a scrapyard. The definition ’fatigue’ is not really applicable here. All three the designs are not liable to fatigue and that’s why they scores maximal on this topic. Also efficiency is of minor importance. It is of minor importance that the system demands a lot of power during a collision. As is mentioned before, a crushable zone has to do his job one time. The electric capacity, on the other hand, shall not be too high. The system has to be feeded by a voltage source of 12 [V ] to a maximum of 24 [V ]. Powerful magnetic fields are easily activated by such a voltage source. But efficiency is of importance if the system is combined with a precrash sensing system. Parameters of the collision are previously recorded by the system, when this is asking too much power, then it is possible that other components fall out. So, there has to be paid attention on the available electrical power in the vehicle. From table 5.1 follows that design B is the most suitable. The actuating properties of this design are the best. With a relative compact system it is possible to achieve a high force level. Such dampers are also used in buildings to compensate the excitation of earthquakes. Large-scale MR dampers are used which have a nominal force level of 200000 [N]. The fact that these dampers are applied successfully in buildings and bridges offers much future perspective for an advanced crushable zone. The designs A and C are able to reach the desirable force level very well, but this is coupled with large dimensions of the system. Since the dimensions and the weight are of importance in designing crushable zones, these designs are not totally suitable. One must not forget that the designs discussed in chapter 4 are based on calculations which follows from theory which is meant only for global design of dampers and pressure control valves. 102 Chapter 5. Feasibility Study Chapter 6

Conclusions and Recommendations

6.1 Conclusion

The conclusion of this internship is that the design with the smart dampers in combination with MR ﬂuid is the most suitable for further research on the possibilities of an advanced crushable zone. With regard to the MR ﬂuid, the following conclusions are drawn:

• MR ﬂuid has very good actuating properties which are of great importance for the energy absorption in the crushable zone.

• MR fluid has a response time which is sufficient in combination with a precrash sensing system. The response time of the fluid depends strongly of the amount of the fluid that has to be activated for the force levels and the desirable dynamic range. The dimensioning of the design plays an important role in obtaining a design which is fully regulable during the collision.

• MR ﬂuid is insensitive for contaminants and impurities and by that it is possible to prevent sedimentation by use of additives. This shall increase the reliability and durability of the system.

• By using permanent magnets it is possible to prevent failures of the system. The ﬂuid can be activated without the use of electrical power. Activation by permanent magnets also holds that the system is less sensitive for sedimentation. The magnetic ﬁelds are easily activated by the current energy source in the vehicle (12 [V ]/24[V ]).

• The application of MR ﬂuid will lead to more compact systems because of the fact that the required amount of ﬂuid is relative small. The achievable yield stress plays an important role here. Compactness of the system also means in this case a lower weight which is very desirable with regard to the energy consumption and the environmental impact.

The design with smart dampers in combination with MR ﬂuid is found to be suitable for the application in an advanced crushable zone. This conclusion is based on the following points:

103 104 Chapter 6. Conclusions and Recommendations

• The use of MR ﬂuid in the design with the smart dampers provides suﬃcient high force levels to obtain the desirable decelerations curves of 56 [km/u] (table 4.4). The dimensioning of the system is kept within the bounds of the current crushable zones. But one must still pay attention on the deformation length of the system.

• The minimum amount of ﬂuid is just 0.77 [liter]. Through the fact that the coils and cores of the magnetic circuit are located in the piston, the system is very compact. Fur- ther, the system doesn’t make use of external pressure control valves and/or restrictions in contrast to the other systems. The application of MR ﬂuid and the construction of the system makes the system compact and light.

• The active pole length L is by this design located in the piston. The magnetic ﬁeld in the piston has the function to activate the ﬂuid locally, the active pole length is limited to just 160 [mm]. The other two systems consist of a cylinder-piston in combination with a restriction. The active pole length of design A is a factor 10 greater, the active pole length of design C is a factor 3 greater. The in-built space of vehicles is very limited, so this design with the smart dampers is the most suitable.

6.2 Discussion and recommendations for further research

This section describes a few discussion points which serves as a guideline for further research. In this phase of the research a few cases are strongly simplified or are totally neglected in the analyse. The theories mentioned in the previous chapters have to be evaluated. Also, the (in)completeness has to be determined. It is with that necessary to specify how far the theoretical models provide for indistinctness in the design. The design with the smart dampers is till now suitable to apply it in an advanced crushable zone. The discussion points mentioned under here are converted in further research and any possible solutions for certain bottlenecks are again converted in the design. The other two designs are still of importance, because a combination of designs can also offer solutions. The following discussion points, with regard to MR fluid and with that the design in combination with the smart dampers are drawn:

• The response time of the fluid is dependent of the amount of fluid which has to be activated for the desirable force level. A fast response time is of big importance to create stiffness variations during the collision. When one takes care of this in the construction of the design, then it is maybe possible to obtain a minimal response time which satisfies the list of demands. It is important to perform research on the relation of the response time and the total amount of fluid.

• With regard to the actuating properties, it is very useful to keep an eye on the developments in the ﬁeld of ﬁeld responsive composites. The maximal yield stress τ is very limited and it is a bottleneck in each design. A higher yield stress is always very desirable.

• The problem of sedimentation by MR ﬂuids can be solved by additives. In the literature nothing can be found about the degree of sedimentation during a certain period. It is 6.2. Discussion and recommendations for further research 105

very important to obtain information about this topic, because sedimentation has a great inﬂuence on the reliability and durability of the system.

• LORD Corporation is market leader in the field of MR fluids. The price of MR fluids is known and LORD Corporation is also supplier of great scale dampers which are used in the design of section 4.2.2. To get an indication of the costs, it is useful to contact LORD Corporation.

• In this internship there isn’t paid attention on the activation by electric or magnetic fields. In the research of Guangqiang Yang, B.S.[5] a few design rules are described which can serve as a guideline for designing an electric circuit of the design. In further design this has to come up for discussion, because better conclusions can be drawn about the efficiency of the system. The electric system determines mainly the weight of the system. At the moment, it is very difficult to make pronounces about the weight of the system.

• In the beginning of this chapter it is noticed that the temperature range of MR fluid is limited till 150 [oC] (MRF-336AG App.A.4). There is until now nothing found about the fluid properties outside this temperature range. Because there is a matter of high force levels, there will be a lot of heat production which shall partly provide for a temperature increase of the fluid. Since the fluid properties are for a great deal dependent of the temperature, it is important that there is performed research on the influence of the temperature with regard to the fluid properties such as the viscosity and the maximum yield stress.

• The same holds for the flow velocity of the fluid. In the theoretical part of Guangqiang Yang, B.S.[5] there is no restriction of the velocity. This means that the flow velocity of the medium has no influence on the controllable and uncontrollable forces, this is very improbable. One can imagine that at a certain flow velocity, the magnetic field has no influence on the MR fluid. The particles in the fluid have such a high velocity that under influence of a magnetic field a stable position is impossible. Further research on this topic has to be performed. The limit of the flow velocity has to be indicated and this could have influence on the final design. To test the dependency of the fluid properties with regard to the temperature and flow velocity, an experimental apparatus discussed in section 3.2.1 can be used. Also the change in speed and direction of the medium has influence on the uncontrollable part of the system. In section 4.2 there is paid some attention on this topic. It plays also an important role by the other two designs. So, this phenomenon has to come up for discussion in further research.

• In the internship the effect of the compressibility of the fluid is neglected. One must pay attention on this, because the compressibility has a great influence on the dynamic behavior of the system. However, in the literature nothing is found about the compression modulus K. Also the influence of the temperature on the compression modulus is of importance. It is of importance to perform research on the effect of the compression modulus on the dynamic behavior of the crushable zone.

• In the practical modelling, a mean velocity of 9.72 [m/s] has been assumed which is related to a full frontal collision of 56 [km/u]. The model has to be extended to a velocity distribution which shall be more realistic. Also, the velocity of 64 [km/u] has 106 Chapter 6. Conclusions and Recommendations

to be taken into account. Calculations have to be made with regard to oﬀset and oblique impacts. The achievable force levels are of course here of importance, but also the loads of the systems such as bent and buckle loads. Maybe that a FEM model is usable here. Appendix A

Properties MR ﬂuids

107 108 Appendix A. Properties MR ﬂuids

LORD RheoneticTM Magnetically Responsive Technology

Hydrocarbon-Based MR Fluid MRF-132AD Product Bulletin[6]

Benefits LORD MRF-132AD is a hydrocarbon-based fluid that offers the following beneficial characteristics:

• Fast Response Time • High Dynamic Yield Stress • Low Oﬀ-State • Broad Operational Temperature Range • High Resistance to Hard Settling • Easy Remixing • Non Abrasive

Application LORD MRF-132AD fluid has been formulated for general use in controllable energy-dissipating applications. Usage Under common flow conditions, no separation is observed between particles and the carrier liquid. A degree of separation may eventually occur under static conditions, but lower-shear agitation (shaking or remixing) prior to use will easily re-disperse the particles into a homogeneous state. A paint shaker can mix the fluid adequately. Keep the container tightly closed when not in use. 109

Table A.1: Properties of MR fluid MRF-132AD Properties Value/Limits Base Fluid Hydrocarbon Operating Temperature -40 [oC] to 130 [oC] Density 3.09 [g/cc] Color Dark Gray Weight Percent Solids 81.64 % Coefficient of Thermal Expansion Unit Volume per oC (calculated values) 0 to 50 [oC] 0.55 x 10−3 50 to 100 [oC] 0.66 x 10−3 100 to 150 [oC] 0.67 x 10−3 Specific heat @ 25 [oC] 0.80 [J/goC] Thermal Conductivity @ 25 [oC] 0.25-1.06 [w/moC] Flash Point >150 [oC] Viscosity: Calculated for slope between 800 [1/s] 0.09 (±0.02) [P a.s] and 500 [1/s] at 40 [oC] 110 Appendix A. Properties MR fluids

Figure A.1: Typical magnetic properties MRF-132AD[6] 111

LORD RheoneticTM Magnetically Responsive Technology

Water-Based MR Fluid MRF-241ES Product Bulletin[6]

Benefits LORD MRF-241ES is a water-based fluid that offers the following beneficial characteristics:

• Fast Response Time • High Dynamic Yield Stress • Low Oﬀ-State Viscosity • High Resistance to Hard Settling • Easy Remixing • Non Abrasive

Application LORD MRF-241ES fluid has been formulated for general use in sealed systems for controllable energy-dissipating applications Usage Under common flow conditions, no separation is observed between particles and the carrier liquid. A degree of separation may eventually occur under static conditions, but lower-shear agitation (shaking or remixing) prior to use will easily re-disperse the particles into a homogeneous state. A paint shaker can mix the fluid adequately. Keep the container tightly closed when not in use. 112 Appendix A. Properties MR fluids

Table A.2: Properties of MR fluid MRF-241ES Properties Value/Limits Base Fluid Water Operating Temperature -10 [oC] to 70 [oC] Density 3.86 [g/cc] Color Dark Gray Weight Percent Solids 85 % Coefficient of Thermal Expansion Unit Volume per oC (calculated values) 0 to 70 [oC] 0.223 x 10−3 Specific heat @ 25 [oC] 0.90 [J/goC] Thermal Conductivity @ 25 [oC] 0.85 - 3.77 [w/moC] Flash Point > 93 [oC] Viscosity: 10 [s−1] Shear Rate 10.8 ±1.5 [P a.s] 50 [s−1] Shear Rate 2.2 ±0.4 [P a.s] 113

Figure A.2: Typical magnetic properties MRF-241ES[6] 114 Appendix A. Properties MR ﬂuids

LORD RheoneticTM Magnetically Responsive Technology

Silicone-Based MR Fluid MRF-336AG Product Bulletin[6]

Benefits LORD MRF-336AG is a silicone-based fluid that offers the following beneficial characteristics:

• Fast Response Time • High Dynamic Yield Stress • Low Oﬀ-State Viscosity • Broad Operating Temperature Range • High Resistance to Hard Settling • Easy Remixing • Non Abrasive

Application LORD MRF-336AG fluid has been formulated for use where temperature extremes or compatibility with a large variety of elastomers is important in controllable energy dissipating applications. Usage Under common flow conditions, no separation is observed between particles and the carrier liquid. A degree of separation may eventually occur under static conditions, but lower-shear agitation (shaking or remixing) prior to use will easily re-disperse the particles into a homogeneous state. A paint shaker can mix the fluid adequately. Keep the container tightly closed when not in use. 115

Table A.3: Properties of MR fluid MRF-336AG Properties Value/Limits Base Fluid Silicone Operating Temperature -40 [oC] to 150 [oC] Density 3.45 [g/cc] Color Dark Gray Weight Percent Solids 82.02 % Coefficient of Thermal Expansion Unit Volume per oC (calculated values) 0 to 70 [oC] 0.58 x 10−3 Specific heat @ 25 [oC] 0.65 [J/goC] Thermal Conductivity @ 25 [oC] 0.20 - 1.88 [w/moC] Flash Point > 150 [oC] Viscosity: 10 [s−1] Shear Rate 8.5 [P a.s] 116 Appendix A. Properties MR fluids

Figure A.3: Viscosity as a function of shear rate with no magnetic ﬁeld applied[6] 117

LORD RheoneticTM Magnetically Responsive Technology

Hydrocarbon-Based MR Fluid MRF-122-2ED Product Bulletin[6]

Benefits LORD MRF-122-2ED is a hydrocarbon-based fluid that offers the following beneficial characteristics:

• Fast Response Time • High Dynamic Yield Stress • Low Oﬀ-State Viscosity • Broad Operating Temperature Range • High Resistance to Hard Settling • Easy Remixing • Non Abrasive

Application LORD MRF-122-2ED fluid has been formulated for use where temperature extremes or compatibility with a large variety of elastomers is important in controllable energy dissipating applications. Usage Under common flow conditions, no separation is observed between particles and the carrier liquid. A degree of separation may eventually occur under static conditions, but lower-shear agitation (shaking or remixing) prior to use will easily re-disperse the particles into a homogeneous state. A paint shaker can mix the fluid adequately. Keep the container tightly closed when not in use. 118 Appendix A. Properties MR fluids

Table A.4: Properties of MR fluid MRF-122-2ED Properties Value/Limits Base Fluid Hydrocarbon Operating Temperature -40 [oC] to 130 [oC] Density 2.38 [g/cc] Color Dark Gray Weight Percent Solids 72 % Coefficient of Thermal Expansion Unit Volume per [oC] (calculated values): 0 to 50 [oC] 0.65 x 10−3 50 to 100 [oC] 0.71 x 10−3 100 to 150 [oC] 0.79 x 10−3 Specific heat @ 25 [oC] 0.94 [J/goC] Thermal Conductivity @ 25 [oC] 0.21 - 0.81 [w/moC] Flash Point > 150 [oC] Viscosity Calculated for slope between 800 [1/s] 0.07 (±0.02) [P a.s] and 500 [1/s] at 40 [oC] 119

Figure A.4: Typical magnetic properties MRF-122-2ED[6] 120 Appendix A. Properties MR ﬂuids Appendix B

Derivation of NCE

121 122 Appendix B. Derivation of NCE

A general derivation of the Newtonian Constitutive Equation (NCE) can be given in Cartesian components [3]. The complete set of velocity derivatives is given by the velocity gradient tensor Ov. The Cartesian components are ( v) = ∂vj . The velocity gradient tensor L is given by: O ∂xi

 ∂v1 ∂v1 ∂v1  ∂x1 ∂x2 ∂x3  ∂v2 ∂v2 ∂v2  L =  ∂x ∂x ∂x  (B.1)  1 2 3  ∂v3 ∂v3 ∂v3 ∂x1 ∂x2 ∂x3

The relation between the velocity gradient tensor L and the velocity gradient tensor Ov is easy to see:

T L = (Ov) (B.2) We can separate L into a symmetric part D, the rate-of-deformation tensor, and an antisymmetric part W, the vorticity tensor.

1 D = (L + LT ) (B.3) 2

1 W = (L − LT ) (B.4) 2 The symmetric part D will be nonzero if the material is deforming, this will result in some stress. The antisymmetric part W is nonzero when the material undergoes solid body rotation. In a Newtonian ﬂuid we expect the stress to be a function of D. Basic theory shows that the most general way the extra stress τ can depend linearly on the rate of deformation (provided the material is isotropic) is:

τ = 2µD + λ(D)I (B.5)

The general form introduces a second material constant λ, known as the dilatational viscosity. When the ﬂuid has a constant density, then the quantity trD = O.v multiplied with λ will be zero. Substituting (B.5) into the modiﬁed momentum balance equation: 123

Dv ρ = − p + .τ + ρb (B.6) Dt O O this will result in the general form of the momentum balance for a New- tonian ﬂuid:

Dv ρ = − p + .(2µD + λ(trD)I) + ρb (B.7) Dt O O Mostly we assume that the ﬂuid density is constant, so λ is no longer required. This will ﬁnally results in the Newtonian constitutive equation:

τ = 2µD (B.8)

Substituting (B.8) into (B.6) will result in the Navier-Stokes equation:

Dv ρ = − p + .(2µD) + ρb (B.9) Dt O O 124 Appendix B. Derivation of NCE Appendix C

MR Fluid Flow in Annular Duct

125 126 Appendix C. MR Fluid Flow in Annular Duct

In the following section, an axisymmetric model is developed based on the Navier-Stokes equation for the MR flow through an annular duct. To accomodate MR fluid shear thinning/thickening effects, the Herschel- Bulkley visco-plasticity model is utilized. The pressure gradient can be solved numerically from the resulting equations, and the damping force can then be calculated. When the post-yield shear thinning or thickening effect is neglected, the resulting equations of the Herschel- Bulkley model can be reduced to those of the Bingham model by letting the fluid parameter m =1.

C.1 MR Fluid Flow in an Annular Duct

The pressure gradient along the ﬂow is resisted by the ﬂuid shear stress which is governed by the Navier-Stokes equation:

∂ ∂ τ (r) ∂p ρ u (r) + τ (r) + xr = (C.1) ∂t x ∂r xr r ∂x where ux(r) is the flow velocity, τxr(r) the shear stress, r the radial co- ∂p ordinate, x the longitudinal coordinate, ρ the fluid density and ∂x the pressure gradient. Quasi-static motion of the flow means that the fluid inertial can be neglected. In this case, eq.(C.1) can be reduced to:

d τ (r) ∂p τ (r) + xr = (C.2) dr xr r ∂x When solving eq.(C.2) this will lead to: 1 dp(x) D τ (r) = r + 1 (C.3) xr 2 dx r where D1 is a constant which can be evaluated with boundary conditions.

A typical shear stress diagram, along with velocity profile, for MR fluid flow through the annular gap is shown in figure C.1. In regions I and II, the shear stress has exceeded the yield stress and the fluid flows. In region C, because the shear stress is less than the yield stress, there is no shear flow, this is often referred to as the plug flow region. C.2. Modeling based on the Herschel-Bulkley model 127

Figure C.1: Stress and velocity proﬁles of MR ﬂuids through an annular duct

C.2 Modeling based on the Herschel-Bulkley model

To account for the ﬂuid shear thinning and thickening eﬀect, the Herschel- Bulkley visco-plasticity model is employed. In region I, the shear strain dux rateγ ˙ = dr ≥ 0. Therefore, the shear stress τrx(r) given by equation (3.9: section 1.1.2) becomes:

1 du (r) m τ (r) = τ (r) + K x (C.4) xr 0 dr This is substituted into eq.(C.3) and integrated once with respect to r. One obtains

Z r m h 1 1 dp(x) D1 i ux(r) = r + − τ0(r) dr − v0 (R1 ≤ r ≤ r1) R1 K 2 dx r (C.5)

by imposing the boundary condition that the ﬂow velocity at r = R1 is dux ux(R1) = −v0. In region II, the shear strain rateγ ˙ = dr ≤ 0. The shear stress is given by

1 du (r) m τ (r) = −τ (r) − K − x (C.6) xr 0 dr 128 Appendix C. MR Fluid Flow in Annular Duct

Similarly, proceeding in region II with the boundary condition ux(R2) = 0 at r = R2 gives

Z R2 m h 1 1 dp(x) D1 i ux(r) = − r+ +τ0(r) dr (r2 ≤ r ≤ R2) (C.7) r K 2 dx r

Note that the flow velocity is a constant in the plug flow region because the shear stress is less than the yield stress. Thus, the flow velocity at boundaries of the plug flow region satisfies ux(r1) = ux(r2). C.2. Modeling based on the Herschel-Bulkley model 129

Combining eq.(C.5) and eq.(C.7) yields

Z R1 m Z R2 m h 1 1 dp(x) D1 i h 1 1 dp(x) D1 i r+ −τ0(r) dr− − r+ +τ0(r) dr = v0 r1 K 2 dx r r2 K 2 dx r (C.8)

Also the shear stresses τrx satisfy τr1 = τ0(r1) and τrx = −τ0(r2), therefore, D1 can be determined by using eq.(C.3) as

r1r2(τ0(r2)r1 + τ0(r1)r2) D1 = 2 2 (C.9) r2 − r1

The expression for the volume ﬂow rate Q is given by

Z R2 Q = 2π rux(r)dr (C.10) R1

dux(r) Because the shear strain rate dr is zero in the plug ﬂow region r1 < r < r2, eq.(C.10) can also be written as

Z r1 2 2h 1 1 dp(x) D1 m Q = v0Ap = πR1v0 − π r r + − τ0(r) ] dr+ R1 K 2 dx r

Z R2 m 2h 1 1 dp(x) D1 i π r − r + + τ0(r) dr (C.11) r2 K 2 dx r 130 Appendix C. MR Fluid Flow in Annular Duct

Fig. C.2 shows the free body diagram of MR ﬂuids through an annular duct. The equation of motion of ﬂuid materials enclosed by r = r1 and r = r2 is

dp π(r2 − r2)dx + 2πr τ (r )dx + 2πr τ (r )dx = 0 (C.12) dx 2 1 2 0 2 1 0 1 which yields

dp (r2 − r2) + 2[τ (r )r + τ (r )r ] = 0 (C.13) dx 2 1 0 2 2 0 1 1

Figure C.2: Free body diagram of MR ﬂuids through an annular duct

In summary, the resulting equations that can be solved numerically to dp determine r1, r2, and the pressure gradient dx between the two ends of the cylinder using the Herschel-Bulkley model are given by

Z R1 m Z R2 m h 1 1 dp(x) D1 i h 1 1 dp(x) D1 i r+ −τ0(r) dr− − r+ +τ0(r) dr = v0 r1 K 2 dx r r2 K 2 dx r (C.14) C.2. Modeling based on the Herschel-Bulkley model 131

Z r1 2 2h 1 1 dp(x) D1 m Q = v0Ap = πR1v0 − π r r + − τ0(r) ] dr+ R1 K 2 dx r

Z R2 m 2h 1 1 dp(x) D1 i π r − r + + τ0(r) dr (C.15) r2 K 2 dx r

dp (r2 − r2) + 2[τ (r )r + τ (r )r ] = 0 (C.16) dx 2 1 0 2 2 0 1 1 where

r1r2[τ0(r2)r1 + τ0(r1)r2] D1 = 2 2 (C.17) r2 − r1

To solve the resulting algebraic equations numerically, a method based on the constrained nonlinear least-square algorithm is utilized in conjunction with the cubic polynomial interpolation and extrapolation method. The integrals in eq.(C.14) and eq.(C.15) are evaluated using the adaptive Newton-Cotes approach. From eq.(C.16), the thickness of the plug ﬂow region can be obtained by

2[τ (r )r + τ(r )(r )] r − r = − 0 1 1 2 2 (C.18) 2 1 dp(x) dx (r1 + r2) which varies with the fluid yield stress τ0. Note that flow can only be established when r2 − r1 < R2 − R1, which implies that the plug flow needs to be within the gap. Otherwise, there is no flow. The damper force is then computed as

F = ∆pAp (C.19) 132 Appendix C. MR Fluid Flow in Annular Duct

dp(x) where ∆p = PL − P0 = −L( dx ) and L is the eﬀective axial pole length. The velocity proﬁle can be determined from eq.(C.5) and eq.(C.7) as follows:

h im  R r 1 1 dp(x) D1 r + − τ0(r) − v0 R1 ≤ r ≤ r1  R1 K 2 dx r   h im R R2 1 1 dp(x) D1 ux(r) = − r + + τ0(r) r1 < r < r2 r2 K 2 dx r   h im  R R2 1 1 dp(x) D1  r −K 2 dx r + r + τ0(r) r2 < r < R2 (C.20)

Further, the shear stress diagram can be obtained from eq.(C.3). Note that when the yield stress τ0 = 0, there is no plug ﬂow region which implies that r1 = r2. Therefore, eq. (C.16) and eq.(C.17) are no longer valid due to the singularity. However, in this case, the velocity achieves its maximum at r = r1 where the shear stress is zero. By using eq.(C.3), the following equations can be employed to obtain pressure gradient when yield stress τ0 = 0:

Z r1 m Z R2 m h 1 1 dp(x) D1 i h 1 1 dp(x) D1 i r + dr − − r + dr = v0 R1 K 2 dx r r1 K 2 x r (C.21)

Z r1 m Z R2 m 2 2h 1 1 dp(x) D1 i 2h 1 1 dp(x) D1 i Q = v0Ap = πR1v0−π r r+ dr+π r − r+ dr R1 K 2 dx r r1 K 2 dx r (C.22)

Z R2 h 1 1 dp(x) D im π r2 − r + 1 dr (C.23) r1 K 2 dx r C.2. Modeling based on the Herschel-Bulkley model 133

1 dp D = r2 (C.24) 1 2 dx 1 Note that the solution of the MR flow in an annular duct does not reduce to that of the pipe flow as r1 → 0. This is because the annular duct model has a boundary condition at r1, however, there’s no boundary condition at r = 0 for the pipe flow. 134 Appendix C. MR Fluid Flow in Annular Duct

C.3 Modeling based on the Bingham model

The Herschel-Bulkley model reduces tho the Bingham model when the MR ﬂuid parameter m = 1. Using eq.(C.14) - eq.(C.16), the resulting equations for the Bingham model are:

2 2 2 2 dp(x) (R2 − r2 − R1 + r1) R2r1 + D1 ln + D2 − ηv0 = 0 (C.25) dx 4 r2R1

π hdp(x) i Q = v A = πR2v − (R4−R4−r4+r4)+4D (R2−R2−r2+r2)+8D 0 p 1 0 8η dx 2 1 2 1 1 1 1 2 1 3 (C.26)

dp(x) (r2 − r2) + 2[τ (r )r + τ (r )r ] = 0 (C.27) dx 2 1 0 2 2 0 1 1 where

r1r2[τ0(r2)r1 + τ0(r1)r2] D1 = 2 2 (C.28) r2 − r1

Z R2 Z R1 D2 = τ0(r)dr + τ0(r)dr (C.29) r2 r1

Z R2 Z R1 2 2 D3 = τ0(r)r dr + τ0(r)r dr (C.30) r2 r1 and the velocity proﬁle is given by: C.3. Modeling based on the Bingham model 135

 1 dp 2 2 D1 r 1 R R1 − (R − r ) + ln − τ0(r)dr − v0 R1 ≤ r ≤ r1  4η dx 1 η R1 η r   1 dp 2 2 D1 R2 1 R R2 ux(r) = − (R − r ) − ln − τ0(r)dr r1 < r < r2 4η dx 2 2 η r2 η r2   R  1 dp 2 2 D1 R2 1 R 2 −4η dx(R2 − r ) − η ln r − η r τ0(r)dr r2 < r < R2 (C.31) 136 Appendix C. MR Fluid Flow in Annular Duct

In the absence of the magnetic ﬁeld, the yield stress τ0 = 0. The pressure gradient can be obtained directly from

2 2 π 2 R2−R1 2R − R − Ap dp 8ηv 2 1 ln( 2 ) = 0 R1 (C.32) (R2−R2)2 dx π R4 − R4 − 2 1 2 1 ln( R2 ) R1

In general, the yield stress τ0 in the axisymmetric model will be a function of r. But when R2 − R1 R1, variation of the yield stress in the gap can be ignored and eq.(C.28) - eq.(C.30) can be further simpliﬁed substantially as follows:

r1r2τ0 D1 = (C.33) r2 − r1

D2 = τ0(R2 + R1 − r1 − r2) (C.34)

1 D = τ (R3 + R3 − r3 − r3) (C.35) 3 3 0 1 2 1 2

Note that in this case, the thickness of the plug ﬂow region can be calculated using eq.(C.18):

2τ r − r = − 0 (C.36) 2 1 dp(x) ( dx ) which is a constant, and only depends on the yield stress and pressure gradient of the ﬂow. Appendix D

MR Fluid Flow in Parallel Duct

137 138 Appendix D. MR Fluid Flow in Parallel Duct

Because of the small ratio between the flow gap (between the piston and the cylinder housing) and the diameter of the damper piston, one might conjecture that the axisymmetric flow found in the damper can be approximated as the flow through a parallel duct as shown in fig. D.1. Relating the parallel-plate model to the axisymmetric model, the parameter w is taken to be the mean circumference of the damper’s annular flow path which equals to π(R1 + R2) and h is taken to be the gap width equal to R2 − R1.

Figure D.1: MR ﬂuid ﬂow through a parallel duct

Fig. D.2 provides the free body diagram and stress and velocity proﬁles of MR ﬂuids through a parallel duct.

Figure D.2: Free body diagram and stress and velocity proﬁles of MR ﬂuids through a parallel duct

The governing equation for the ﬂow of the parallel-plate model is: dτ dp = (D.1) dz dx

Therefore, 139

dp τ(z) = z + D (D.2) dx in which D is a constant which can be determined with boundary conditions. 140 Appendix D. MR Fluid Flow in Parallel Duct

D.1 Modeling based on the Herschel-Bulkley model

Similar to the axisymmetric model, the shear stress τ in region I is given by:

1 du m τ(z) = τ + K x (D.3) 0 dz Substitution of eq.(D.3) into eq.(D.2) and using the boundary condition ux(0) = 0 gives:

1 1 dpm u (z) = − [hm+1 − (h − z)m+1] (0 ≤ z ≤ h ) (D.4) x m + 1 K dx 1 1 1

In region II, the shear stress is given by

1 du m τ = −τ − K − x (D.5) 0 dz

Using the same procedure as in Region I, with boundary condition ux(h) = −v0 gives:

1 1 dp u (z) = − [(h−h )m+1 −(z −h )m+1]−v (h ≤ z ≤ h) x m + 1 K dx 2 2 0 2 (D.6)

The flow velocity at the boundary of the plug flow region satisfies ux(h1) = ux(h2). Combining eq. (D.4) and eq.(D.7) yields,

1 1 dp 1 1 dpm − hm+1 = − (h − h )m+1 − v (D.7) m + 1 K dx 1 m + 1 K dx 2 0 D.1. Modeling based on the Herschel-Bulkley model 141

The volume rate Q is

Z h Q = Apv0 = w ux(z)dz = 0

w 1 dpm h 1 i w − hm+1 h − (h + h − h ) − v (h − h )(D.8) m + 1 K dx 1 m + 2 1 2 m + 2 0 2 where Ap is the cross area of the piston head and v0 the piston head velocity. Referring to ﬁgure ..., the equation of motion for ﬂuid materials enclosed by h = h1 and h = h2 is

dp (h − h )δx + 2τ δx = 0 (D.9) dx 2 1 0 which yields

2τ0 h2 − h1 = − dp (D.10) (dx)

Therefore, the resulting equations for the parallel-plate model using the Herschel-Bulkley model include eq.(D.7), eq.(D.8) and eq.(D.10). The dp pressure gradient dx can be solved numerically and the damper resisting force is then computed with eq.(C.19). Note that h1 = h2 when the yield stress τ0 = 0. The velocity proﬁle, which satisfy the boundary conditions ux(0) = 0 and ux(h) = −v0, is then given by:

 m 1 − 1 dp [hm+1 − (h − z)m+1] (0 ≤ z ≤ h )  m+1 K dx 1 1 1   m  1 1 dp m+1 ux(r) = m+1 −K dx h1 (h1 < z < h2)    1 1 dp m+1 m+1  m+1 −K dx [(h − h2) − (z − h2) ] − v0 (h2 < z < h) (D.11) 142 Appendix D. MR Fluid Flow in Parallel Duct

D.2 Modeling based on the Bingham model

Again for the Bingham model, the ﬂuid parameter is m = 1. Substitu- tion of eq.(D.7) and eq.(D.10) into eq.(D.8) and deﬁning nondimensional variables,

whv wh V = − 0 = − (D.12) 2Q 2Ap

wh3 dp wh3 dp P = − = − (D.13) 12ηQ dx 12ηApv0 dx

wh2τ wh2τ T = 0 = 0 (D.14) 12ηQ 12ηApv0

results in the nondimensional quintic equation:

3(P − 2T)2 3(P−2T)2(P 3−(1+3T−V )P 2+4T 3)+TV 2P 2 = 0 |V | < P (D.15) Note that V < 0 if the piston motion is in the opposite direction of the ﬂuid ﬂow. The force produced by the damper is then given by

2 dp 12ηA Lv0 F = − A L = p P (D.16) dx p wh3

When |V | >, the ﬂow is governed by the following dimensionless equations which are independent of the dimensionless yield stress T: D.2. Modeling based on the Bingham model 143

3 4V 2 P = 3(P−2T) ≤ V ≤ 3P (D.17) 27(2V − 1)2 P

3 4V 2 P = − −3P ≤ V ≤ −3(P−2T) (D.18) 27 P

P + V = 1 |V | > 3P (D.19) 144 Appendix D. MR Fluid Flow in Parallel Duct

Eq.(D.17) - eq.(2.19) indicate that the pressure gradient depends only on the geometry of the device and that a controllable yield stress has no inﬂuence on the force of the damper. If the piston head velocity v0 = 0, then V = 0 and eq.(D.15) becomes a cubic equation for T. This cubic equation has the realizable root at

2 h 1 T 3 1i P(T) = (1 + 3T) cos arccos 1 − 54 + (D.20) 3 3 1 + 3T 2

Generally, there is no analytical solution for eq.(D.15), but it can be easily solved numerically. An approximate solution can be used to estimate the desired root for 0 < T < 1000 and −0.5 < V < 0 which encompasses most practical designs in which the ﬂow is in the opposite direction of the piston velocity:

T P(T, V ) = 1 + 2.07T − V + (D.21) 1 + 0.4T Appendix E

MR Fluid Flow in an Parallel Disk Shaped Valve

145 146 Appendix E. MR Fluid Flow in an Parallel Disk Shaped Valve

Fig. E.1 illustrates the schematic of the MR damper based on a disk shaped MR valve. The proposed damper is not a through shaft damper, thus an accumulator is connected to ’volume 2’ to compensate for the volume change due to the movement of the shaft. In the following, the analysis to determine the damping force is presented[4].

Figure E.1: Cross-section of a MR damper based on a disk shaped MR valve

The mass ﬂow rate for a control volume containing incompressible ﬂuid can be written as:

d d (m) = (ρV ) = ρ Q − ρ Q = ρ(Q − Q ) (E.1) dt dt i i o o i o where m is the mass of the fluid inside the control volume, ρ is the fluid density (taken as constant for inlet and outlet conditions), V is the volume, Q is volume flow rate and subscripts i and o represent inlet and outlet, respectively. The same flow rate formulation can be derived for rebound and compression states of the damper as presented below.

Eq.(E.1) is applied to the ’volume 1’, V1, of the damper, as shown in ﬁg. E.1. For the rebound state, Qi, therefore, eq.(E.1) reduces to

dV i = −Q (E.2) dt o 147

The geometric dimensions of the damper yield,

V1 = (L1 − u).(Ap − As) dV i = −u˙(A − A ) (E.3) dt p s where u is the piston displacement,u ˙ the piston velocity, Ap the cross sectional area of the piston and As is the cross sectional area of the shaft. Therefore, the ﬂow equation for the rebound case can be derived using eq.(E.2) and eq.(E.3),

Q = (Ap − As)u ˙ (E.4)

A similar equation to eq.(E.4) can be derived for the compression state. Pressure drop due to the fluid’s viscosity is the viscous pressure drop and is determined assuming an incompressible Newtonian flow through the orifices entering and exiting the disk shape MR valve. In the present design, a gap between two parallel fixed disks with radial flow constitutes the MR valve. In the following, an analysis is presented that provides a relation for an MR valve between two fixed rectangular parallel plates. Then, this formulation will be converted the flow rate equation between two parallel fixed disks.

The following equation has been established for the ﬂow between the ﬁxed rectangular parallel plates considering the Bingham Plastic model,

dp3 h12Qµ τ idp2 τ 3 − + 3 y + 4 y = 0 (E.5) dx BH3 H dx H

dp where dx is the pressure drop per unit length of plates, b is the width of the plates, h is the gap between the plates and τy is the controllable yield stress of a MR ﬂuid. dp The solution of eq.(E.5) for dx can be obtained as, 148 Appendix E. MR Fluid Flow in an Parallel Disk Shaped Valve

dp τ 12µQ = 2.85 y + (E.6) dx H BH3 To convert from two parallel plates to two parallel ﬁxed disks, the following transformation are made: b → 2πr dp dp → dx dr Therefore, the radial pressure gradient is obtained as,

dp τ 6µQ = 2.85 y + (E.7) dr H πrH3

Integration of eq.(E.7) yields:

τ ∆P = 2.85 y (R − R ) (E.8) diskmr h 2 1

6µQ R2 ∆Pdiskvis = 3 ln (E.9) πh R1 where R1 and R2 are the outer and inner radius of the disks. The viscous pressure drop in the circular entrance can be expressed as:

128µQ ∆P = L (E.10) cylvis πD4 where D is the diameter, L the length and Q is the ﬂow rate of an oriﬁce, respectively.

The total viscous drop is:

∆Ptotalvis = ∆Pdiskvis + ∆Pcylvis (E.11) The total pressure drop is:

∆Ptotal = ∆Pdiskmr + ∆Pdiskvis + ∆Pcylvis (E.12) Bibliography

[1] Special Issue: Vehicle Compatibility In Crashes. Status Report Vol.34, No.9, Insurance Institute For Highway Safety, October 1999. [2] Carlson, J.D. What Makes A Good MR Fluid? Report, LORD Corporation, July 2001. [3] Dantzig, J.A., TuckerIII, C.L. Modeling in Materials Processing. Cambridge University Press, Cambridge, 2001. [4] Faramarz Gordaninejad, U.D. A New Magneto-Rheological Fluid Damper for High-Mobility Multi-Purpose Wheeled Vehicle. Report, Mechanical Engineering Department, University of Nevada. [5] Guangqiang Yang, B.S. Larg-Scale Magnetorheological Fluid Damper for Vibration Mitigation: Modeling, Testing and Control. Masters thesis, University of Notre Dame, Department of Civil En- gineering and Geological Sciences, Notre Dame, Indiana, December 2001. [6] LORD RheoneticTM. Magnetically Responsive Technology. Product Bulletin, LORD RheoneticTM, January 2003. [7] Macosko, C.W. Rheology: Principles, Measurements, and Applica- tions. VCH Publishers, Inc., University of Minnesota, Department of Chemical Engineering and Materials Science, 1994. [8] Mavroidis, C., Bar-Cohen, Y., Bouzit, M. Haptic interfaces using electrorheological ﬂuids. Report (Chapter 9), Rutgers University, Jet Propulsion Laboratory. [9] Rutten, S.H.L.A. Smart Materials in Automotive Applications - How To Improve Vehicle Crashworthiness By Incorporating Smart

149 150 Bibliography

Materials. Report, Eindhoven University of Technology, Department of Mechanical Engineering, June 2003. [10] Songjing, L., Guanghuai, W., Dong, C., Songying, L. New Type Relief Valve Using Magneto-Rheological Fluid. Report, Harbin In- stitute of Technology. [11] Wismans, J. et al. Course Notes to Injury Biomechanics (4J610). Eindhoven University of Technology, 1993. [12] Witteman,W.J. Improved Vehicle Crashworthiness Design by Con- trol of the Energy Absorption for Diﬀerent Collision Situations. PhD thesis, Eindhoven University of Technology, Eindhoven, 1999. [13] Yang, G., Spencer Jr., B.F., Carlson J.D., and Sain, M.K. Large- Scale MR Dampers: Modeling and Dynamic Performance Consider- ations. Report, University of Notre Dame, Department of Electrical Engineering, November 2001. [14] Yokota, S., Yoshide, K. and Kondoh, Y. A Pressure Control Valve Using MR Fluid. Report, Tokyo Institute of Technology, Precision and Intelligence Laboratory.