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A mathematical model for a superconducting motor What state and other requirements are necessary for a high efficiency superconducting electric motor? Joshua Mickelsen Abstract: High efficiency is becoming prominent in today’s world due to fears of the greenhouse effect. This has caused the efficiency of motors to skyrocket into the high 90’s which is meant to save money on electricity by not wasting it as heat. Despite this, there are still some major losses of heat. One of the most notable of these comes from the mechanical deficiency of friction between the axle and the housing that holds it in place. The aim of this project is to make this effect negligible by suspending the axle without touching the housing. This can be achieved using the assistance of superconductors on either end of axle. Superconductors expel magnetic fields that stabilize levitation of rotor in relation to housing, generating almost no heat from friction. Advantages include parts not wearing out over time. Without parts touching, they can’t wear out and the machine won’t break down because of mechanical problems. The second advantage is that the efficiency of the device would increase because heat is not lost to friction which means more work is produced for less input energy. This is similar to the design for a maglev train whose benefits can easily be seen in both terms of speed and economy which is what is expected from this motor. Ultimately the principles of the design of this motor are solid, but due to some equipment malfunctions, my motor does not currently satisfy a high efficiency motor. Design Goals and Parameters for experiment The object of this project is to create an AC motor in which the axle does not touch the motor housing. This will be accomplished by suspending two superconductors on either end of the induction rotor. The induction rotor itself will have to be a dewar so that the liquid nitrogen coolant does not evaporate quickly. The drive mechanism for the motor is simply a couple of electromagnets with a capacitor. As the electromagnets are turned on, they will repel the diamagnetic induction rotor which will result in a spinning motion free of solid-solid friction. An alternative method of levitation can be achieved by using ac power to induce a current in a conducting surface. This generates a repulsive force that can then levitate and be turned using an extra set of electromagnets. It uses the same principles, but is modified to make up for the losses of resistance in traditional conductors. It is not as efficient and is therefore not the preferred method. Background Research: Superconductors were discovered just a few years after liquid helium was condensed. Oddly enough this was by the same person whose name was Heike Kamerlingh Onnes. Onnes was measuring the resistance of mercury when he was surprised to see a sharp decline in resistance that went to almost zero when it was cooled with liquid helium. This became the first synthetic superconductor. Since then, it was discovered that superconductors completely expel magnetic fields. They are able to do this thanks to Lenz’s law which essentially states that when a conducting material is exposed to a changing magnetic field, a current will run in the opposite direction of the magnetic field and create a magnetic pressure between the tow. This means that superconductors can shield objects from magnetic fields and levitate over magnetic fields. The magnetic field does not even have to be particularly large for this effect to occur as a magnetic field strength of 2 Tesla is what many maglev trains operate on. The amount of weight a superconductor can support is limited by the strength of the magnetic field, distance from magnet, area of superconductor, and critical magnetic field of the superconductor. This is expressed in the equation Fm=(flux)^2/8pi*muon0x^2 where muon0 is the magnetic free space permeability constant of 4pi*10^-7 and x is the distance between the magnetic field and the superconductor. Superconductors are also widely used in MRI’s, supercolliders and a large variety of purposes as none of the electrical energy is lost as heat as occurs in a normal conductor. In fact, it is estimated that there should be no measurable loss in electrical current of a superconductor even after a period of 10,000 years. Superconductors can also be made into supercapacitors which can potentially hold as much energy as a battery, but be charged in seconds. The applications of superconductors are nearly limitless, but most of them have to be operated at very cold temperatures which presents problems. There are two types of superconductors-Type I and Type II as they were so aptly named. Type I superconductors generally need to be cooled with liquid helium and have critical magnetic, electrical, and temperature parameters which dictate when it is superconducting or not. Type II superconductors generally operate at higher temperatures and were discovered in the 1980’s. They differ from conventional superconductors in that they are not completely explained by the theories of superconductivity(BCS) and by the fact that they can have mixed states where part of the material is superconducting while another portion of the material is not. Many of these Type II superconductors are ceramic and are very difficult to form into wires which make them uncommon despite the fact that many of them can be cooled with liquid nitrogen instead of helium. Superconductors are truly unique and their applications limitless. Their unique levitation properties are why they have been chosen for this experiment. AC levitation works off of similar principles and is also very common to the world today. The only major difference is that the conductor that is being induced with electrical current loses its power as heat and heat is therefore needed to be replenished by a continually changing ac current. The maximum amount of pressure that is generated from this is Fp=B^2/2muon0 where B is the strength of the magnetic field and muon0 is the magnetic permeability constant. Magnetic field strengths decrease with an inverse cube relationship whereas gravity decreases with an inverse square relationship. It is because of this relationship that engineers place electromagnets as close to each other as possible to increase efficiency. If one looks at a solenoid, which is just a bunch of wire wound in a circle, then they will discover that the magnetic field is constant within a solenoid, but degrades quickly outside of the magnet and is practically nonexistent on the sides. This is why applications of electromagnets occur near the ends of the magnet and not elsewhere. Ohm law is also very important in my experiment as it has been used in numerous calculations. It relates power, volts, amps, and resistance into a single system. They are all interconnected in a system and allows us to increase some if we decrease others. If one increase amps then one will increase the magnetic field strength in a solenoid according to the equation B=muon0nI where B is the magnetic field strength, muon0 is the vacuum permeability constant, n is the number of turns per meter length, and I is the number of amps. Therefore, if we add more turns and increase the amps, then the strength of the magnetic field will increase. Materials 1.Air insulated Dewar 2.2 disk superconductors that can fit inside the Dewar on opposite ends 3.4 powerful magnets on either side of a box 4.Liquid nitrogen 5.Wire for an electromagnet 6.Ac 12 volt transformer 7.Small capacitor 8.Aluminum Soda Can 9.Ac electromagnet Procedure a) Using an insulated glass container, insert two superconductors on either end of the container and place aluminum foil around the outside of the container. b) Secure a lid to the container that liquid nitrogen can be poured into. c) Construct an ac motor with the transformer, wire, and capacitor (the rotor for the motor will be the Dewar.) d) Construct a box with magnets for the superconductors to be suspended from. Pour liquid nitrogen into container until full and wait for superconductor rise. e) Place electromagnets close to aluminum and turn on the circuit. f) Leave until nitrogen boils off. Then turn off. Ac Procedure a) Construct an one large ac electromagnet and 10 electromagnets to support a levitating structure. b) Construct a levitating can out of a soda can. c) Place levitation can in the middle of the apparatus and turn on. d) Watch as the device levitates for ten seconds then turn off. Data/Analysis The dewar did not rise when subjected to liquid nitrogen which gives to reason that the superconductors were faulty. When tested more strenuously, this was proved to be correct and the faulty superconductors made it so that the prototype did not work. When this project is to be retried, superconductors that actually work will need to be used. This will allow the dewar to levitate which will provide a non-contact axle for the electric motor. The second motor also proved unsuccessful at there were not enough amps to create a powerful enough magnetic field to levitate objects. Making a high amp transformer will fix this problem and allow for levitation. However, while this solution is effective, it will waste so much power that it will not be a good solution to the problem stated. The Superconductor listed in the first part will therefore be much better. Conclusion The project to build a motor with a levitating axle has thus far been unsuccessful. The reason for this is due to faulty superconductors which made it so that the main portion of the project was a total failure and thus made the entire project faulty. If this error is corrected, then the motor should operate as expected. It will operate at much higher efficiency than the ac motor and work better as it does not use a continuous strain of energy to achieve levitation. Sources: http://www.open.edu/openlearn/science-maths-technology/engineering-and-technology/engineering/su perconductivity/content-section-2.4 http://www.cdc.gov/niosh/mining/content/electricalandmachinesafety/proximity/hasard.html http://www.engineeringtoolbox.com/air-properties-d_156.html http://web.mit.edu/6.763/www/FT03/Lectures/Lecture8.pdf https://en.wikipedia.org/wiki/High-temperature_superconductivity http://www.physicsclassroom.com/class/thermalP/Lesson-1/Rates-of-Heat-Transfer http://web.mit.edu/6.763/www/FT03/Lectures/Lecture8.pdf https://www.youtube.com/watch?v=BFdq6IecUJc http://chemistry.pixel-online.org/EP_home01d4.html?id=03&tp=03 http://www.scielo.br/scielo.php?pid=s0103-97332001000300027&script=sci_arttext https://www.google.com/search?q=critical+magnetic+field+density+YBCO&source=lnms&tbm=isch &sa=X&ved=0ahUKEwi3qI2htN_KAhVDwGMKHfVXAM0Q_AUIBygB&biw=1252&bih=604#im grc=7MMxNfuDjQWqcM%3A http://www.futurescience.com/scintro.html http://www.futurescience.com/scpart1.html http://www.futurescience.com/kilns.html https://en.wikipedia.org/wiki/Magnetic_levitation http://www.electricneutron.com/electric-motor/single-phase-ac-motor/ http://www.electricneutron.com/electric-motor/single-phase-capacitor-sizing/ http://www.explainthatstuff.com/induction-motors.html http://machinedesign.com/motorsdrives/single-phase-electric-motors-characteristics-applications Research Plan and Post Project Summary B. My project deals with superconductivity and its potential applications to increase efficiency and life of electrical motors. Superconductivity is a solid principle that has proven applications in things like maglev trains in Japan. The idea behind this motor is to put the track into a continuous circle which reduces friction on the housing and axle which means more work is put into mechanical movement and less is put into heat. In addition to this, there is almost no wear and tear on the parts which means that the already long life motor will last much much longer. Superconductors are perfect to tackle this problem because they can completely expel magnetic fields and hold enormous amounts of weight which means it would fit this problem very nicely. C. My Engineering goal is to produce a motor that increases efficiency and decreases mechanical wear and tear. D. Procedure a) Using an insulated glass container, insert two superconductors on either end of the container and place aluminum foil around the outside of the container. b) Construct an ac electromagnet with an attached capacitor. c) Construct a box with magnets for the superconductors to be suspended from. Pour liquid nitrogen into container until full and wait for superconductor rise. d) Place electromagnets close to aluminum and turn on the circuit. e) Leave until nitrogen boils off. Then turn off. Risk and Safety This project does involve liquid nitrogen which is not a hazardous chemical because it is the substance that makes up most of the atmosphere. It is however very cold and skin should be kept away whenever possible, but gloves should not be worn because they could freeze and increase contact time with skin. Data Analysis The success of this project will be based on whether or not the motor is held in place by the superconductors and spins due to the magnet. Bibliography: http://www.open.edu/openlearn/science-maths-technology/engineering-and-technology/engineering/su perconductivity/content-section-2.4 http://www.cdc.gov/niosh/mining/content/electricalandmachinesafety/proximity/hasard.html http://www.engineeringtoolbox.com/air-properties-d_156.html http://web.mit.edu/6.763/www/FT03/Lectures/Lecture8.pdf https://en.wikipedia.org/wiki/High-temperature_superconductivity