TVE 14 041 juni Examensarbete 15 hp Juni 2014 Force Measurements on Permanent Magnets and Demagnetization Effects of Assembling Halbach Arrays Andreas Östman Max Ivedal Abstract Force Measurements on Permanent Magnets and Demagnetization Effects of Assembling Halbach Arrays Andreas Östman and Max Ivedal Teknisk- naturvetenskaplig fakultet UTH-enheten This project has studied axial forces for the attractive and repulsive cases between paris of NdFeB permanent Besöksadress: magnets at different distances. Demagnitization when Ångströmlaboratoriet Lägerhyddsvägen 1 assembling Halbach arrays has also been studied. The Hus 4, Plan 0 practical measurements of the magnetic forces corresponded to the performed simulations with some Postadress: exceptions. Those exceptions were due to Box 536 751 21 Uppsala measurement errors. Permanent demagnitization was not noticed when assembling the Halbach arrays nor Telefon: when pushing two repulsive magnets together in the 018 – 471 30 03 force measurements. Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student Handledare: J. José Perez Loya and Stefan Sjökvist Ämnesgranskare: Henrik Olsson Examinator: Martin Sjödin ISSN: 1401-5757, TVE 14 041 juni Contents 1 Introduction 2 1.1 Background . .2 1.2 Motivation . .2 1.3 Aim of the project . .2 2 Theory 3 2.1 Permanent magnets . .3 2.2 Halbach Arrays . .4 2.3 Hysteresis curves . .5 2.4 Calculations . .6 2.4.1 Calculations in MATLAB . .7 3 Simulations 8 3.1 Simulations using FEM . .8 3.2 2D-force simulations between two cylindrical magnets . 10 4 Experiment preparations 10 4.1 Holder design . 11 5 Method 15 5.1 Calibration of load cell . 15 5.2 Force measurements . 16 5.2.1 Setup . 16 5.2.2 Procedure . 17 5.3 Assembly of Halbach Arrays . 18 6 Results 19 6.1 Calibration of load cell . 19 6.2 Force Measurements . 20 6.3 Demagnetization in force measurements (repulsive case) . 23 6.4 Demagnetization when assembling Halbach arrays . 23 6.5 Error calculations . 24 6.5.1 Instrument errors . 24 6.5.2 Calibration errors . 24 6.5.3 Force measurement errors . 24 7 Discussion 25 7.1 Causes of errors . 25 7.2 Improvements . 25 8 Conclusions 25 1 1 Introduction 1.1 Background Permanent magnets have got many application areas in society, ranging from small fridge magnets to smart mobile phones. In order to develop new technologies involving magnets and to improve existing ones, it is necessary to thoroughly understand the physics behind them. 1.2 Motivation This project was performed at the Division of Electricity at Uppsala University and studied how forces between two permanent magnets vary with the distance between the magnets. An additional assessment was to investigate whether demagnetization occurs when two repulsive magnets approach one another. Demagnetization in different permanent magnet applications can cause undesirable effects. Using models for demagnetization can help engineers to predict problems with their design.1 1.3 Aim of the project The goal of this project was to measure the forces that arise when permanent magnets are approaching each other. Since a magnetic field sufficiently strong acting on a magnet will cause it to become partly demagnetized, it is an important aspect to know exactly how close the magnets can be pushed without causing changes to its magnetic abilities. Two types of setups were studied. These included Halbach arrays and pairs of cylin- drical magnets. In the case of the Halbach array setups the main object to assess was whether demagnetization occurs when a Halbach array is assembled. All magnets used were of the type Neodymium Iron Bromide (NdFeB). The dimensions of the cylindrical and cube magnets can be seen in table 1 and 2 respectively Table 1: Dimensions and types of cylindrical magnets studied. Magnet type Diameter [mm] Height [mm] N45 4 3 N45 4 2 N42 20 10 Table 2: Dimensions and the type of cuboidal magnet studied. Magnet type Side length [mm] N45 3 1Ruoho S. \Modeling demagnetization of sintered NdFeB magnet materials in time-discretized finite element analysis". Helsinki: Aalto print. 2011 2 2 Theory 2.1 Permanent magnets Permanent magnets are objects that produces magnetic fields. The magnetic fields are not visible for the human eye but the impact of these fields can be clearly seen in many everyday situations. The source of magnetism is partly a result of unfilled electron shells of atoms as well as due to the rotation of the electrons around the nucleus. Unfilled atomic shells gives rise to a net magnetic field because of the electrons spin. A filled atomic shell would have an equal amount of electrons with spin up and down, resulting in no net magnetic field . An unfilled shell on the other hand, would result in the small magnetic contributions from the orbiting electrons not canceling out and thereby give rise to a net magnetic field of the atom.2 Looking at a larger scale, a material will align its atoms and chunks of atoms (domains) in a different manner, namely the one that requires the lowest energy. Since each atom with an unfilled shell gives rise to a small magnetic field, the atoms themselves could informally be considered as small bar magnets. When the small "magnets" are aligned in an non-ordered fashion the resulting field will be very weak but when they are aligned in an ordered fashion the resulting field will be strong, see figure 1 and 2. Figure 1: Several atoms (left) illustrated as small bar magnets. When all of these \mag- nets" are aligned in the same direction the material will produce a net magnetic field and as indicated by the arrow, behave as a permanent magnet. 2Jindal UC. Material Science and Metallurgy. Pearson Education India; 2013 3 Figure 2: Magnetic domains in a material with their directions of magnetization aligned differently. When the domains are ordered in this fashion, no significant net magnetic field will be observed. There is a way of achieving an alignment of the magnetic domains in certain materials. This is done by placing a sample in an external field, causing its domains to align in the direction of the applied field. When the external field later is removed the magnetic domains might stay in its new directions and if that is the case, the material has become magnetized. A material will have different properties depending on how the magnetic domains will align after the external field have been removed. If the domains revert to their original directions the material is called paramagnetic. If on the other hand the domains will remain in the directions caused by the external field the material is called ferromagnetic. Examples of ferromagnetic materials are iron and nickel. There are also materials which are anti-ferromagnetic and diamagnetic. Anti-ferromagnetic materials align the domains in a pattern with neighboring spin causing no net magnetic field while diamagnetic ma- terials align the domains in the opposite direction of a field when it is present. The magnetization of a magnet is dependent on temperature and a certain material has a critical point where its intrinsic magnetic moment change direction called the Curie temperature. In experiments it is important to consider these effects, especially when using materials with a critical point close to temperatures occurring in the experiment. Two permanent magnets that are placed with their net magnetic fields in opposite direction to one another will exert repulsive forces, pushing the magnets away from one another. This phenomena is used in a few applications for creating low friction bearings. To be able to predict how much weight that can be added to a magnetic bearing one needs to know how close the repulsive magnets will be positioned with an applied weight. 2.2 Halbach Arrays Halbach arrays is an arrangement of permanent magnets that augment the field on one side and nearly cancel the field on the other side, see figure 3. One sided magnetic fluxes were first discovered by Mallinson in 19733 and later independently discovered by Klaus 3Mallinson J.C. \One-Sided Fluxes − A Magnetic Curiosity?" . IEEE Transactions On Magnetics. 1973; 9 (4) : 678-682 4 Halbach 4. At the time Mallinson described what he called \A magnetic curiosity", not many possible applications were considered. When Halbach later made the discovery he saw applications in particle accelerators among other things. The effect of producing a strong one sided magnetic field makes Halbach arrays useful in some applications, for example magnetic levitating trains. Figure 3: An example of a Halbach array with the net magnetic field pointing upwards. The field on the other side of the array nearly cancels out. 2.3 Hysteresis curves To visualize the behavior of permanent magnets when exerted to an external field so called hysteresis curves are used. These curves, often referred to as BH-curves, shows how the flux density B of a magnet varies with the applied external field H. There are two curves that are studied on the hysteresis plots. These are the normal curve and the intrinsic curve. The intrinsic curve shows the same data as the normal curve, plus an additional term of M, the magnetization of the magnet itself. The magnets always operate on the normal line, so this is the line to study for design purposes. The hysteresis curves of the magnets used in the experiments are shown in figure 4 and 5. 4Rennie G. Magnetically levitated train takes flight [Internet]. [Place unknown] : [U.S Department Of Energy Research News]; [Date unknown] [2004; cited 2014-05-23]. Available from: http://www. eurekalert.org/features/doe/2004-11/ddoe-mlt111104.php 5 Figure 4: Hysteresis plot for the N42 magnets showing the normal curve Figure 5: Hysteresis plot for the N45 magnets showing the normal curve.