Optimal design of a disk type magneto- rheologic fluid clutch M. Jaindl, A. Ko ¨ stinger, Ch. Magele, W. Renhart To transmit a continuously adjustable torque from the main shaft to the move shaft electromagnetic clutches can be used in cars. In contrast to friction clutches, electromagnetic clutches transmit rotation by a magneto-rheologic fluid consisting of a base fluid mixed with numerous ferro-magnetic micro-sized particles. In the absence of a magnetic field a small basic torque is passed on only. Once the flux density is increased, the micro-sized particles start to form firmly tied chains increasing the transmitted torque. The magnitude of the torque can be regulated by the application of an appropriate magnetic field which is simulated by the Finite-Element- Method. The optimal design of the clutch requires a certain torque being transmitted while keeping the weight as small as possible. This task of multi-objective optimization is performed using a higher order Evolution Strategy, a stochastic optimization method. Keywords: nonlinear magnetostatics; magneto-rheologic fluids; stochastic optimization; multi-objective optimization Optimaler Entwurf einer magneto-rheologischen Flu ¨ ssigkeitskupplung. Zur U ¨ bertragung eines stufenlos regelbaren Moments in einem Getriebe kann man elektromagnetische Kupplungen verwenden. Anders als bei normalen Druckkupplungen wird in diesem Fall das Moment mittels einer magneto-rheologischen Flu ¨ ssigkeit u ¨ bertragen. Diese besteht aus einer Tra ¨ gerflu ¨ ssigkeit, die mit unza ¨ hligen Mikropartikeln versetzt ist. Ist kein Magnetfeld vorhanden, u ¨ bertra ¨ gt die Kupplung lediglich ein geringes Grundmoment. Sobald allerdings die Flussdichte erho ¨ ht wird, beginnen die Mikropartikel, feste Ketten zu bilden. Damit erho ¨ ht sich auch das u ¨ bertragene Moment. Das fu ¨ r die U ¨ bertragung verantwortliche Magentfeld wird mittels der Methode der Finiten Elemente simuliert. Ein optimales Design der Kupplung soll ein gegebens maximales Moment u ¨ bertragen und dabei ein mo ¨ glichst geringes Gewicht aufweisen. Diese Optimierungsaufgabe, einander widersprechende Ziele zu erfu ¨ llen, wird mit einer Evolutionsstrategie, einem stochastischen Optimierungsverfahren, gelo ¨ st. Schlu ¨ sselwo ¨ rter: nichtlineare Magnetfeldprobleme; magneto-rheologische Flu ¨ ssigkeiten; stochastische Optimierungsverfahren; multiple Zielfunktionen Received May 4, 2007, accepted after revision May 29, 2007 ß Springer-Verlag 2007 1. Introduction Electromagnetic clutches for cars have gained more and more interest, recently. Several disks are connected either with the main shaft or the move shaft. The space between the disks is filled with a magneto- rheologic fluid (Lord, 2007). A base fluid (e.g. hydrocarbon) is mixed with micro-sized magnetisable particles. Without a magnetic field, only a small basic torque exists between the disks. But as soon as a magnetic field is applied the viscosity of the fluid drastically changes from an oily state to a semi-solid state. This field can be simulated with excellent accuracy by the Finite Element Method. Due to the axial symmetry of the clutch under investigation, a 2D package can by used (Elefant, 2007). An optimal design of the clutch is very important because of the limited space and the limited amount of power in a car and due to the requirement of low weight while still transmitting a certain amount of torque. In this paper a higher order (=; ) evolu- tion strategy (ES), namely a (4=2,20) ES (Rechenberg, 1994), (Alotto et al., 1998) is applied to design a clutch which transmits a required torque while keeping the weight as light as possible. The objective function formulating these technical requirements in a mathematical way is stated using fuzzy membership functions for normalizing the individual objectives before applying appropriate inference rules to them (Bellman, Zadeh, 1970), (Magele et al., 1997). 1.1 The model of a magneto-rheologic clutch Figure 1 shows an axi-symmetric sectional drawing of the model to be optimized. The coil is responsible for the generation of the magnetic field. The main body and the primary disks are rigidly coupled, while the secondary disks make up the part of the system to be coupled. The geometric constraints as well as the dimensions of the model to be adjusted are introduced later. 1.2 Variable viscosity of magneto-rheologic fluids Magneto-rheologic fluids exhibit a distinct enlargement of their viscosity when being exposed to a magnetic field. The reason for this behaviour can be found in the countless micro particles dis- solved in a base liquid, which are distributed randomly within the base liquid in the absence of a magnetic field (Fig. 2). However, as soon as the fluid is exposed to a magnetic field, the micro-sized magnetic particles tend to form rigid chains and hence enlarge the viscosity of the fluid remarkably. In case of the clutch under consideration it looks as if the two disks connected by a gap of fluid were coupled rigidly (Fig. 3). 1.3 Magnetic and mechanical behaviour of magneto- rheologic fluids The commercially available fluid MRF-132AD (Lord, 2007) displays a classical nonlinear B–H behaviour (Fig. 4). This material behaviour as originalarbeiten Elektrotechnik & Informationstechnik (2007) 124/7/8: 266–272. DOI 10.1007/s00502-007-0453-4 Jaindl, Michael, Dipl.-Ing., Ko ¨ stinger, Alice, Dipl.-Ing., Magele, Christian, Ao. Univ.-Prof. Dipl.-Ing. Dr., Renhart, Werner, Ao. Univ.-Prof. Dipl.-Ing. Dr., Institute for Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Kopernikusgasse 24=4, 8010 Graz, Austria (E-mail: Christian.Magele@TUGraz.at) 266 | heft 7–8.2007 e&i elektrotechnik und informationstechnik