Optimizing Repulsive Lorentz Forces for a Levitating Induction Cooker

Transcription

1 214 IEEE Proceedins of the International Power Electronics Conference - ECCE Asia (IPEC 214), Hiroshima, Japan, May 18-21, 214 Optimizin Repulsive Lorentz Forces for a Levitatin Induction Cooker C. Zinerli, T. Nussbaumer, J. W. Kolar This material is published in order to provide access to research results of the Power Electronic Systems Laboratory / D-ITET / ETH Zurich. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertisin or promotional purposes or for creatin new collective works for resale or redistribution must be obtained from the copyriht holder. By choosin to view this document, you aree to all provisions of the copyriht laws protectin it.

2 The 214 International Power Electronics Conference Optimizin Repulsive Lorentz Forces for a Levitatin Induction Cooker Claudius M. Zinerli, Thomas Nussbaumer, Johann W. Kolar ETH ZUrich, Power Electronic Systems Laboratory Physikstrasse 3, 892 ZUrich, Switzerland zinerli@lem.ee.ethz.ch Abstract-In this paper we study a novel way of induction cookin. Traditionally, an alternatin manetic field is used to induce currents in a ferromanetic pan to heat foods. We use non-ferromanetic materials and optimize the desin for hih repulsive forces in order to levitate the pan while simultaneously heatin it and its contents. Our approach is simulation-based to study the influence of different parameters and to perform multidimensional analyses for hih force versus power or loss oals. Finally, an perimental prototype has been realized and successfully operated. Ind Terms-Manetic levitation, modelin, eddy currents, induction motors, induction cookin, home appliances, education I. MOTIVATION The proliferation of induction cookers is constantly rowin. Compared to traditional electrical stoves, quick reaction time and - dependin on the source - hih enery efficiency speak for them [1]. In a typical induction cooker, a flat induction coil creates an alternatin manetic field. The field induces a current flow in the conductin pan on top of the coil [2]. This leads to losses in the pan caused by its electrical resistance, heatin up the pan and its contents. The currents in the two coupled coils (citation coil and pan) also have a force effect. In this publication, we investiate if these forces can be used to levitate the pan. Further, we study desin variants taretin stable levitation and concentration of the losses in the pan and keep them away from the citation - or bearin - coil(s). A desin variant is shown in Fiure 1. While newer developments [3] override this restriction, in conventional induction stoves the base of the pan must typically contain ferromanetic material. Such materials conduct the manetic field well and concentrate the manetic flux. This primarily leads to a lower skin depth (hiher resistance) as well as to a reduction of the flux path and consequently to an attractin force owin to the reduced reluctance. The current flow in the base of the pan is opposed to the one in the citation coil, why a repulsive force is created (Lorentz force). The minimization of this force is often the oal of optimizations in applications like metal production [4]. In our investiation, we follow a completely different approach: that of maximizin Lorentz forces in order to allow the pan to levitate so that an observer may witness an air ap between the citation/cooktop surface and the pan. Generally, hih citation currents lead to hih repulsive forces. But there are limits on the citation current because the removal of ohmic losses in the citation coil becomes more and more challenin. Thus one criterion for optimization is to maximize the quotient of losses in the pan versus losses in the citation coil. A further criterion is the maximization of the bearin force at a certain loss level. To simplify the construction, solely repulsive manetic fields shall be used. Additionally, no parts shall be added to the pan (permanent manets, coils, back iron). For this reason, active, top or radially actin manetic bearin desins will not be considered. Fiure 1: Desin variant of a levitated induction cooker /14/$ IEEE 3365

3 The 214 International Power Electronics Conference II. PREVIOUS WORKS IV. SIMULATION The principle involved in usin eddy currents for heatin and levitation is not new. Previous works include applications on contactlessly melt metals [5] and many educational hibits. We use an eddy current bearin in one of our lectures to demonstrate a very simple manetic bearin where the levitated object ets very hot quickly. In science and technoloy museums one can often find an hibit with a levitatin aluminum rin on top of a coil connected to the mains [6, 7]. What is new about our device is that we want to apply said principle for cookin such as a demonstration of induction or as a show effect. III. ANALYSIS The shape of the pan has a reat influence on the force development. The stronest vertical forces (hih axial stiffness) act on surfaces orthoonal to the coil axis, but these surfaces cause no radial stiffness; therefore, a pan consistin solely of such surfaces (e.. a sheet) would simply slip out and fall down. On the other hand, a spherically shaped pan offers a positive radial stiffness but, despite the tendency to riht itself, it has a zero tiltin stiffness. A flat bowl/plate shaped pan offers a positive axial, radial and tiltin stiffness and is thus researched. For an efficient citation, the citation coil is operated in a (series) resonant circuit. As the pan moves, the inductance chanes and hence, the resonant frequency. Experiments have shown that without any tra means of dampin, the levitated pan would oscillate and eventually touch the coil surface or even fall out. We adaptively control the citation frequency by trackin the coil current. Assumin that the major part of the flux in the citation coil induces a current in the pan and that the pan is thick To verify the feasibility of the concept and to optimize the desin, a simulative approach has been chosen. Due to the rotational symmetry, all simulations were 2D FEMbased in a cylindrical coordinate system in the eddy current domain. All dimensions were parameterized in order to allow variation and tunin runs, since with today's computer power, multidimensional searches could be performed within only hours (for ample frequency versus coil diameter and pan thickness ). Fiure 2 shows the simulation model used for a simple cylindrical pan. The mesh in the levitated object (Pan) was manually adjusted to include multiple elements in the material thickness. The coil below was cited with a fixed amplitude AC current. This constant current citation was used because in the periment the number of turns and maximum amplifier current are fixed while independent of the inductance, the resonant tank can always be tuned to push the voltae amplitude hih enouh to drive that current. d j z Pan & r-.., Coil l:;::.j ---ol r i -rpan Fiure 2: Model of a manetically levitated induction cooker. The vertical (z) axis shows the rotational symmetry. The citation coil is stranded and supplied with a fixed amplitude AC current. enouh to shield the field, an increase of the coil radius leads As pected, the followin proportionalities of the repellin to an increase of the current in the pan and - at a constant air ap field strenth - to a proportional increase of the Lorentz force actin on the pan. At a fixed eometry and air ap, the couplin between citation and pan is constant. A hiher citation current then leads to a proportionally hiher manetic air ap field and current in the pan. The Lorentz force actin on the pan is proportional to the current in the pan and air ap flux density which is aain proportional to the air ap field. Therefore this force should increase with the citation current squared. force F were confinned: F Ii 2 zc cos () l/z Inner coil radius Ii Ampere turns ic of citation Pan wall anle Vertical distance z between citation coil center and pan Fiure 3 shows that the repellin force actin on the pan rises proportionally to the citation coil radius. If the pan is 3366

4 The 214 International Power Electronics Conference , -Aluminium o Copper Iron "" "" ;,, I, Excitation coil radius Ti (mm) Excitation frequency fc (khz) Fiure 3: Simulated force F as a function of the citation Fiure 4: Force F as a function of citation frequency fc at coil radius Tj at different pan radii Tpan (flat aluminum pan, different pan materials = (ic 5 A. turns, hpan = 4 mm, = ic 1 A. turns, hpan = 33 mm, radial citation coil Tj = 5 mm). Aluminum and copper show no sinificant thickness: 2 mm). difference, while iron enerally enerates lower repulsive forces, yet (at low frequencies) produces attractin forces. smaller than the citation coil, the force starts to decrease aain, so matched pan and coil sizes are important. Good conductin materials (AI, Cu) lead to repulsive forces with little dependency on fc (Fiure 4). The forces are similar in both materials, but aluminum bein about three times lihter than copper, the air ap will be wider at the same current. Iron (Fe-l 1 ) reveals a stron dependency on fc in the studied frequency rane, even showin attractin forces when remanence dominates at frequencies below 12 khz. Due to the hih resistivity of iron, the force versus heatin power quotient is also low. In Fiure 5, the dependence of the force on the citation frequency fc and the pan thickness d is shown. The hihest repellin force is enerated with a pan thickness of about 417 of the correspondin skin depth. This findin has been tested aainst different materials (Aluminum, Copper and Manesium) and frequencies = (fc 1 khz... 1 khz). If the pan is thinner, the force decreases rapidly. If the pan is thicker, the decrease is less. At a constant citation current, however, the heatin power rises fast, hence, dependin on the application - heatin power versus levitation - an optimum can be found. Studies on the influence of the citation current ic and levitation heiht z at two different coil radii r; = {5 mm, 1 mm} were performed (Fiure 6 and Fiure 7). While in both desins, the force increases with the current squared, the smaller coil only allows for levitated loads in a low rane, even at hiher currents or small aps. "" , fc = 1. khz (8 = 2.67mm).1 -fc = 2.2kHz (8 = 1.8mm) -'fc = 4.6 khz (8 = 1.25mm) -fc = 1kHz (8 =.27mm) L- -'-- -'-- -'- -' o Pan thickness d (mm) Fiure 5: Force F as a function of the pan thickness d at different citation frequencies = fc (ic 5 A. turns, hpan = 4 mm, r; = 5 mm, aluminum pan). At low frequencies «3 khz) a force maximum can be found near d = 4/7. <5 with the skin depth <5. The decreasin force with increasin ap size z (Fiure 8) can be approximated by a hyperbolic curve l/hpan. The decrease is due to the smaller couplin which eventually leads to less ohmic losses in the levitated pan than in the citation coil at hih distances (Fiure 9). In the rane studied, the loss distribution is solely a function of the eometry, independent of the electrical citation. 3367

5 .... The 214 International Power Electronics Conference Llz =lomm k. +Llz =2mm -Llz =33mm & 1 +Llz =4mm rj = 5mm k ,-----, ic = 77 A... +ic = 1414A -ic = 2121 A +ic = 2828 A - '<x 1/Llz Excitation current ic (A turns) 1 2 Air ap Llz (mm) 3 4 Fiure 6: Simulated force F as a function of the citation Fiure 8: Simulated force F as a function of the air ap z at current ic at different aps z (T'j = 5 mm). different citation currents ic (T'j = 5 mm, = fc 1 khz) k. & i:l.. 3 :::l ' u at co 15 p... p >< Excitation current ic (A turns) Fiure 7: Simulated force F as a function of the citation current ic at different aps z (T'j = 1 mm). 2 3 Air ap (mm) Fiure 9: Simulated ohmic losses in the pan at = ic 1 A. turns. The loss ratio pan/citation oes below one at wider air aps hpan (rj = 5 mm, = fc 1 khz). To ive an ample, levitatin a load of m = 3 k (Typical caquelon pan and fondue contents for a party of four), usin a coil with an inner radius of rj = 1 mm, at a level of z = 1 mm, needs a current of = ic 2 ka. turns. This current produces ohmic losses on the pan of P = 1. 5 kw which is sufficient for cookin applications. V. EXPERIMENT A small-scale prototype was built and successfully operated. Levitation and heatin have been demonstrated but at a much smaller scale than conventional induction cookers. Table I shows some key data of the first prototype. In Fiure 1, the perimental setup is shown: on the left side, the trapezoidal shaped coil with an aluminium test pan on top. On the riht side are series resonance capacitors, voltae and current probes. The setup was powered from a commercial square wave voltae source (48 V, 1 Arms, DC khz, PWM). Fiure 11 shows the electrical characteristics of the citation coil modelled as a series connected R-L circuit. The bearin coil bein made of liz wire, there is little chane in the series resistance Rs up to an citation frequency = fc 5 khz). Startin at about = fc 1 khz, the manetic field of the citation coil is completely shielded by the pan makin the inductance and resistance stay constant relative to the unloaded coil. Since the quality factor of the coil Q _ L- 2 1f. fc. Ls is very hih (at = fc 18 khz: Q L = 35 without load, Rs 3368

6 The 214 International Power Electronics Conference QL = 15 with a plate and QL = 9 with a pan at z = 33 mm), owin to the low dampin of the lare air ap, a hih voltae ain in the resonant circuit results, shown in Fiure 12. Table I: Key parameters of the perimental setup Parameter Confiuration Coil radius Number of turns Unloaded coil inductance Operatin frequency Value series resonance rj = 5mm n = 99 La = mh fc= 16.7kHz o - 25 J Time (Its) Fiure 12: Measured voltae, apparent power and currents in the setup. Due to the bi air ap, the quality factor of the resonant circuit is hih, resultin in a hih voltae Vc. 6-2 $ I u 1.5 Fiure 1: Prototype setup of a manetically levitated induction cooker. Q) mm mm ---4.mm mm 44.5mm mm (sim) i Q) () B (). -"" O L o Excitation current ic (A turns) Fiure 13: Force F as a function of the citation current ic normalized to one turn at different aps (z) comparin measured and simulated values. The simulated forces in Fiure 6 predict the measured values very ood (Fiure 13, the prototype has a lower limitation on z of 33rmn). VI. DISCUSSION Frequency (Hz) Fiure 11: Series inductance Ls and resistance Rs of the coil as a function of the citation frequency, operatin in free space, loaded with a flat pan "Plate" and round pan ( 21 mm deep, 92 mm radius of the depression). To achieve a bi air ap (a hih levitation level), hih citation currents are needed (F i;xc/ z for aps z «diameter), which inherently lead to an elevated heatin power. If this power is not needed the current has to be reduced and the ap will become smaller with the levitation effect bein less apparent. 3369

7 The 214 International Power Electronics Conference Hih citation currents also lead to hih losses in the citation coil that have to be dealt with. While, in a conventional induction cooker, the cess heat from the citation coil can be dumped into the pan to limit the coil's temperature to the pan's, this cannot easily be done here because of the weak thermal couplin between pan and citation coil durin levitation. We presume that an active (fan based) coolin of the citation coil can hardly be avoided. The repulsive force between citation coil and prototype pan is quite small for cookin applications: as a result, heavier or bier pans cannot be levitated without increasin citation current and heatin power to very hih levels. Simulations of a bier model were performed (Fiure 7, Ij = 1 mm). At bier radii and citation currents or smaller air aps, sinificantly hiher forces can be reached, but there are at least two downsides: First, the force only increases linearly with the radius, while the weiht of the pan enerally scales by volume, radius at the power of three. Second, simple air coolin of the citation coil can only be performed at the coil surface which scales with the radius squared, so coolin of bier coils or hiher currents will become challenin. The simple construction has the further disadvantae of low stiffness compared to actively controlled, PM-based or attractin manetic bearins, which could be disadvantaeous in relation to ternal disturbance forces (stirrin, addin or removin material from the pan). VII. CONCLUSIONS AND OUTLOOK It has been shown that levitatin a pan on an induction cooker is not only feasible, but can also be realized, be it as a small prototype or a typically sized pan includin contents. The heatin power is coupled to the repulsive force and is enerally quite hih. To increase the force-to-power quotient, the application of permanent manet or reluctance based passive and active manetic bearins should be studied. Currently, the desin is rotationally symmetric. Similar to an induction motor, further coils could be added to create a rotatin manetic field in order to spin the levitated pan. The liftin and drivin fields could further be superimposed on the control circuit to allow for a simpler construction with fewer coils. By usin position sensors or applyin one of the several published approaches for sensor-less control, an active control circuit could be realized to enhance the stiffness of the bearin includin axial, tiltin and radial movement. While the first do not need any additional coils, control of the later axes asks for independent control by e.. the coils of the drive. The current desin has the advantae of boostin the heatin power the closer the pan ets to the citation coil. If there is less material in the pan (for ample due to evaporation, boilin or removal), the ap is widened: this results in a lower heatin power provin a passively safe behavior. Given that power is not reduced to zero with an empty pan, however, additional means of supervision are necessary, which may be implemented usin a contactless IR-detector as proposed in [2]. As it is, state of the art levitatin induction cookers open up new and citin possibilities in Fondue event caterin or culinary periences which will not fail to amaze your uests. REFERENCES [1] H. Koertzen, J. Van Wyk, and J. Ferreira, "Desin of the half-bride, series resonant converter for induction cookin," in Power Electronics Specialists Conference, PESC '95 Record., 26th Annual1EEE, vol. 2, 1995, pp vol.2. [2] P. H. Peters, "A portable cool-surface induction cookin appliance," Industry Applications, IEEE Transactions on, vol. IA-lO, no. 6, pp , [3] A. Fujita, H. Sadakata, I. Hirota, H. Omori, and M. Nakaoka, "Latest developments of hih-frequency series load resonant inverter type built-in cooktops for induction heated all metallic appliances," in Power Electronics and Motion Control Conference, 29. IPEMC '9. IEEE 6th International, 29, pp [4] S. Hosseini, A. Kashtiban, and G. Alizadeh, "Particle swarm optimization and finite-element based approach for induction heatin cooker desin," in SICE-ICASE, 26. International Joint Conference, 26, pp [5] E. C. Okress, D. M. Wrouhton, C. Comenetz, P. N. Brace, and J. C. K. Kelly, "Electromanetic levitation of solid and molten metals," Journal of Applied Physics, vol. 23, p. 545, [6] University of Illinois, Urbana-Campain Enineerin Open House, "Floatin fryin pan," March 27. [Online]. Available: LJzCy8hhnZY [7] Crealev Manetic Levitation Technoloy, TSC Group, "Hoverin cookin pan," January 212. [Online]. Available: 337