MAGNETIC LEVITATION VEHICLE-SUPPORTING … · Maglev (derived from magnetic levitation) is a...

http://www.iaeme.com/IJMET/index.asp 589 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 6, November–December 2016, pp.589–603, Article ID: IJMET_07_06_058 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=6 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication

MAGNETIC LEVITATION VEHICLE-SUPPORTING

GRAVITATIONAL AND ELECTROMAGNETIC

PRINCIPLES, THEORIES FOR DESIGNERS

Manjeet Kumar Tummalapalli, Srujan Roha Kommula, Bhargava Sai Edara, Sai Pradeep Pativada,

Aravind Perabathula

Mechanical Engineering Department, KLEF, K L University, Vaddeswaram-522502, Andhra Pradesh, India

A S R Murty

Distinguished Professor, Chair, Research and Industrial Consultancy

ABSTRACT

Magnetic levitation is attractive alternative for fast commuting. The practice of it is not so much

as one would expect. Administrative and governing bodies look at funding limitations and risks which

are justifiable also. Education, systematic steps in understanding and attempts at modeling, DIY, Toy

models etcetera, are also not as many as needed for this technology to take off. This work attempts

at explaining the gravity aspects, the electromagnetic aspects, especially separating the single

magnet repulsive force, understanding aspects for the practitioners to derive help from a self study.

Some useful references are cited.

Key word: Maglev, forces from gravitational aspects and electromagnetic aspects, Para, Dia and Ferromagnetic roles, fundamental laws to be understood, design criteria, historical and cost related.

Cite this Article: Manjeet Kumar Tummalapalli, Srujan Roha Kommula, Bhargava Sai Edara, Sai Pradeep Pativada, Aravind Perabathula and A S R Murty, Magnetic Levitation Vehicle-Supporting Gravitational And Electromagnetic Principles, Theories For Designers. International Journal of

Mechanical Engineering and Technology, 7(6), 2016, pp. 589–603. http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=6

1. INTRODUCTION

Maglev (derived from magnetic levitation) is a transportation method that uses the energy in magnetic levitation to move vehicles with no contacts between the track and moving vehicle .with maglev, a vehicle travels along a guideway using magnets to create both lift and propulsion. This reduces friction to a great extent and also allowing very high speeds. It is proven technology that is very much feasible technically and rather less so financially. Attempts at cost reduction are due. Naturally administrative heads and governing authorities look at the finance aspects besides the risk and safety aspects.

Manjeet Kumar Tummalapalli, Srujan Roha Kommula, Bhargava Sai Edara, Sai Pradeep Pativada, Aravind Perabathula and A S R Murty


2. MOTIVATION AND OBJECTIVE

The need for more sustainable, eco-friendly and efficient mass transportation of people in commuting, commercial freight, military and shop floor applications has led to a rethinking of rail-based transit. The motivation of the present team started in designing and fabricating a short and straight segment of track capable of levitating and accelerating a scale-model maglev train. Design objectives included understanding the governing laws, theories, practical implementation where measurements are formidable, ease of construction, stability of operation, levitation efficiency all respected as primary constraints. The finalized system should have passive lateral stability, passive magnetic support with minimal friction for levitation, and speed in operators control. All the underlying principles, laws, theorems are taken up to help aspiring designers in a clear manner.

3. LITERATURE REVIEW AND RANGE OF ACTIVITY

The following descriptive and explanatory part implicitly follows a brief historical as well as literature review aspects. The numbers in brackets indicate those of references given at the end. Maglev trains have been the main technology of interest to commuting system planners; decision makers in regional planning and researchers. They were first proposed in the 1960s by two the vision of two physicists at Brookhaven National Laboratory led to large-scale research projects in Japan and Germany [8]. Since then maglev test tracks have been built in nations around the world. The first commercially operating maglev train opened in shanghai in 2004 [8]. Recent innovations in maglev technology such as the Inductrack system promises "fail-proof” operation.

The major advantage of maglev is speed (up to 580 km/h [8]) which range can contest closely with air travel since the later has access delays. Other advantages include energy efficiency and very attractive acceleration. Since levitation eliminates all friction (normally created by rails) to a great extent and aerodynamic friction due to profile shape. Noise pollution is minimal. Reduced travel time summarizes the overall edge which adds to increased productivity of society at large, if the loss of effective time is valuable in a given scenario. Of course, one and the major disadvantage, which is invariably the primary deterrent in the voting for maglev projects throughout the world is cost. It is because unlike with the conventional high-speed rail, a completely new infrastructure has to be built that repels the project proposals. The cost for this can even reach $100 billion [8].

This work investigates the underlying principles, laws, theorems etc., all related to maglev trains, their design and development. It is not focusing on any current maglev technology nor does it seek to improve on it. Rather the purpose of this work is to help the design process with a clear understanding of the principles behind the gravitation, magnetic levitation and propulsion. The team plans to produce a small scale proof-of-concept linear maglev system. This purportedly prompts planners, decision makers, designers, investors, new transportation infrastructure developers in a positive and pragmatic way.

Initial study of the concepts involved in gravitation, magnetism, magnetic levitation of materials, material properties and electromagnetic mechanics etc., this enabled the team to understand the depth of the problem statement and helped to attempt the design of a linear system of magnetic levitation and propulsion. The linear system (where we mean rectilinear motion only) designed is propelled by an AC drive and is levitated by an array of permanent magnets.

Basic requirements for achieving magnetic levitation for transportation are levitation against gravity followed by propulsion. For better understanding of these two we first take up magnets and their properties.

3.1. Magnets

A magnet is any object that has a magnetic field. It attracts ferrous objects like pieces of iron, steel, nickel and cobalt. The space surrounding a magnet, in which magnetic force is exerted, is called a magnetic field. If a bar magnet is placed in such a field it will experience magnetic forces. Just as an electric field is described by drawing the electric lines of force, the same way, a magnetic field is also described by drawing the magnetic lines of force. The magnetic lines of force are the lines drawn in a magnetic field along which a

Magnetic Levitation Vehicle-Supporting Gravitational And Electromagnetic Principles, Theories For Designers


north magnetic pole would move. The direction of a magnetic line of force at any point gives the direction of the magnetic force on a north pole placed at that point.

Figure 1 Interaction between magnetic poles

Figure 2 Magnetic lines of force

Magnetic materials are classified into three categories: paramagnetic, diamagnetic, and ferromagnetic (see Figure 3) [11].

• • Paramagnetic materials are materials that, when placed in a magnetic field, experience an attractive force toward the source of the field. In a paramagnetic material, the atoms, which are magnetic dipoles, are able to rotate and orient themselves in the direction of the permanent magnet. The result is a net magnetic field produced by the material in the same direction as the permanent field, resulting in an attractive force.

• Diamagnetic materials are essentially opposite to paramagnetic materials. If placed in a permanent magnetic field they will experience a repulsive force. When the material experiences a change in magnetic field, a current is induced in the material. According to Lenz’s law, diamagnetic material is repelled from the source of the magnetic field (explained in iv, 6).

• Ferromagnetic materials are essentially permanent magnets. In these materials, quantum effects cause the “spin” (which is what causes a magnetic moment) of the electrons to always be oriented so that there is a net magnetic dipole [11]. Thus these materials always produce a magnetic field.

Figure 3 Diagrams explaining the different types of magnetism. (Image taken from source [11])



3.2. Levitation

Levitation is the process by which an object is held aloft, without mechanical support. To accomplish levitation an upward force that counteracts the pull of gravity should be provided, [16]. This upward force can be fundamental forces like magnetic or electrostatic forces, or it can be reactive forces like buoyancy, optical, aerodynamic, or hydrodynamic.

This work uses magnetic levitation; a method by which an object or a system is suspended with no support other than magnetic fields.

Forces between the magnets depend on:

• Strength of the magnetic field

• Area of the magnets.

By carefully studying these two factors a force can be calculated and achieved to magnetically levitate objects by simply utilizing two permanent magnets. But the real problem is to stabilize this levitated object.

Stability refers to ensuring that the object or the system does not flip or slide from its levitated position. Earnshaw’s theorem from [15] states that it is impossible for a static system to stably levitate against gravity. (Explained in IV, A). Stability is thus needed to ensure that the levitated object stays in its fixed position, without flipping and sliding. From Earnshaw's theorem at least one stable axis must be present for the system to levitate successfully and other axes can be stabilized using ferromagnetism quite hopefully.

3.3. Techniques to accomplish stable levitation

3.3.1 Mechanical Constraint: Reference [16] shows that with a small amount of mechanical constraint, stability can be achieved. An example is: if two magnets are mechanically constrained along a vertical axis it is possible to achieve a stable levitation system.

Figure 4 Mechanical constraint

Figure 5 Permanent magnets between supports



This physical imperative or the damping can be defined in any of the 6 axis and the body can be stabilized. It is how the magnetically levitated bodies with permanent magnets are stabilized.

3.3.2. Servomechanisms (Electromagnetic suspension): In this case the levitation effect is mostly due to permanent magnets. Electromagnets are only used to stabilize the effect. This stability for the object can be achieved by constantly altering the strength of a magnetic field produced by electromagnets using a feedback. As mentioned in [16] this servomechanism formed by continually changing the electromagnets to correct the object’s motion are extensively used in Electromagnetic Suspension (EMS).

Figure 6 Electromagnetic suspension

In EMS, magnetic attraction is the prime cause for levitation.

3.3.3. Induced currents (Electro dynamic suspension): When the magnets attached on board move forward on the inducing coils or conducting sheets located on the guide way, the induced currents flow through the coils or sheets and generate the magnetic field.

Figure 7 Electro dynamic suspension.

While EMS uses attraction force, EDS uses repulsive force for the levitation. The present work plans to utilize this technique to achieve levitation.

3.3.4 Guidance or Propulsion: The Maglev train is a noncontact framework that requires a controlling power for the counteractive action of sidelong relocation. As in the case of levitation, the guidance is accomplished electromechanically by magnetic repulsive force or magnetic attraction force.

A repulsive force and an attractive force induced between the magnets are used to propel the vehicle. The propulsion coils located on the track are energized by a three-phase alternating current, creating a shifting magnetic field on the guide way. The on-board magnets (superconducting or permanent) are attracted and pushed by the shifting field, propelling the vehicle.

4. PRINCIPLES INVOLVED IN MAGNETISM

Usage of magnetic levitation in transportation has two major challenges: levitation against gravity and propulsion .The following are some of the fundamental principles, theorems, formulae and information that help us to view this concept from a better perspective.



Magnetic levitation is a process or method in which an object is suspended in air against the gravitational acceleration of earth. Here two types of forces which are required; one to counteract the weight of the body and the second to stabilize the lifted body. Earnshaw’s theorem states that a magnetically levitated body isn’t self-stabilized.

4.1. Earnshaw’s Theorem

It states that collection of point charges cannot be maintained in stable equilibrium solely by electrostatic forces. The same applies to magnetic levitation. Hence some other means are to be used to magnetically lift a body. Usage of combination of forces like gravitational, electrostatic and magneto static forces enables static stability.

Dynamic stability can be achieved in various ways such as:

• External mechanical damping (in the support), such as dashpots, air drag etc.

• Eddy current damping (conductive metal influenced by field)

• Tuned mass dampers in the levitated object

• Electromagnets controlled by electronics

4.2. Maxwell’s Equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents and changes of each other.

4.2.1. Gauss’s Law: Gauss's law describes how electric fields emanate from electric charges. It states that the magnetic field B has divergence equal to zero. It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole.

(1)

The equation states that the electric flux leaving a volume is proportional to the charge inside.

4.2.2. Gauss's law for magnetism: Gauss's law for magnetism describes magnetic fields as closed field lines.

(2)

The equation states that there are no magnetic monopoles; the total magnetic flux through a closed surface is zero.

4.2.3 Maxwell–Faraday equation (Faraday's law of induction): This law shows the relationship between electric circuit and magnetic field.

The law states that when the magnetic flux linking a circuit changes, an electromotive force is induced in the circuit proportional to the rate of change of the flux linkage.

Figure 8 Faraday’s Law of Induction



(3)

This is a homogeneous equation describes how the fields "circulate" around their respective sources. The equation means that the voltage induced in a closed circuit is proportional to the rate of change of the magnetic flux it encloses.

Faraday's law states that the EMF is also given by the rate of change of the magnetic flux:

(4)

The negative sign used in Faraday's law of electromagnetic induction, indicates that the induced emf ( ε ) and the change in magnetic flux ( δΦB ) have opposite signs. The direction of the electromotive force is given by Lenz's law.

4.2.4 Ampère's circuital law (with Maxwell's addition): Ampère's law with Maxwell's addition describes how the magnetic field "circulates" around electric currents and time varying electric fields, while Faraday's law describes how the electric field "circulates" around time varying magnetic fields.

(5)

The equation means that the magnetic field induced around a closed loop is proportional to the electric current plus displacement current (rate of change of electric field) it encloses.

4.2.5. Lenz's Law: Lenz's law is an addition to Faraday’s law and gives the direction of induced current.

It states that when an EMF is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced EMF is such, that it produces an current that's magnetic field opposes the change which produces it.This is very important law appearing as ' for every action there is a countering reaction ' type, similar to Newton's law, but in Electromagnetism.

Figure 9 Lenz’s Law

From the above figure depicting the Lenz law, it can be noted that with the change in magnetic flux direction according to Lenz Law, the polarity of the induced EMF changes.

4.5. Lorentz Force

In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force F.

(6)



5. FORCES BETWEEN MAGNETS

The forces between magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles that make up the material. Since both these are modeled as tiny loops of current called magnetic dipoles, the most elementary force between magnets, therefore, is the magnetic dipole–dipole interaction.

5.1. Gilbert model

The Gilbert model assumes that the magnetic forces between magnets are due to magnetic charges near the poles. While physically incorrect, this model produces good approximations that work even close to the magnet when the magnetic field becomes more complicated.

5.1.1. Force between two magnetic poles: If both poles are small enough to be represented as single points then they can be considered to be point magnetic charges. The force between two magnetic poles is given by

(7)

Where,

F is force (SI unit: newton)

qm1 and qm2 are the magnitudes of magnetic poles (SI unit: ampere-meter)

μ is the permeability of the intervening medium (SI unit: tesla meter per ampere)

r is the separation (SI unit: meter).

5.1.2. Force between two bar magnets: The force between two identical cylindrical bar magnets placed end to end is approximately:

(8)

Where,

B0 is the flux density very close to each pole, in T,

A is the area of each pole, in m2,

L is the length of each magnet, in m,

R is the radius of each magnet, in m, and

x is the separation between the two magnets, in m

relates the flux density at the pole to the magnetization of the magnet.

5.1.3. Force between two cylindrical magnets: For two cylindrical magnets with radius , and height , with their magnetic dipole aligned and the distance between them greater than a certain limit, the force is approximated as

(9)

Where, M is the magnetization between the magnets x is the distance between them



5.2. Ampere’s Model

In Ampere’s model the calculations are done by considering the microscopic or atomic currents in the object, hence this is difficult. The force between two permanent magnets is given by:

(10)

Gilbert’s model has formula relating to magnets being as poles, for two bar magnets and for two cylindrical magnets whereas Ampere’s model has intrinsic calculations, which are difficult. The model designed by the team is based on a bar magnet and disc magnet. So Gilbert’s model isn’t applicable. Since the problem statement is in understanding the principles, the team has decided that such calculations aren’t required. While assembling, one can use trial and error method and vary the weight of the body to achieve the required levitation with the track.

6. DESIGNER UNDERSTANDING

Demand is growing for unconventional methods of power generation in industrial, transportation and in daily household needs. A swift shift has been witnessed from base thermal engines to electric driven vehicles. Electric transportation and industrial power generation are in use. These methods not only incorporate environmental benefits but also are comparatively more efficient. A developing salient stream in electric power is electromagnetism. The immense inherent energy possessed by magnets has a strong motivation to its extensive use and it is also being widely preferred. Bullet trains using the technology of magnetic levitation have proved the strong nature of electromagnetic fields. Magnetic levitation is a sub-stream of electromagnetism wherein zero or minimal physical contact between bodies is achieved along with high speeds. Due to absence of friction - energy savings, clean ecology and no thermal related problems make it worth exploring more.

Present work motivated in understanding the complexity in magnetic levitation and also to show that design of such systems is practically possible and achievable. Fabrication attempts are underway with promising outcome.

Forces produced from electromagnetism can be used to power space shuttle launches, revolutionizing the technology. The applications of magnetic levitation and electromagnetism are far and wide and it lies in



our grasp to utilize its potential to the fullest. By this project we would like to show that magnetic levitation is technology more for the future. With its versatility it will play a dominant role in transportation sector.

Magnetic levitation models are found in toys and educational models. These are shown in [3], [6] and [14] posses simple principles of magnetic levitation, but produce very interesting results. For example in [14] a pencil holder was designed which is both convenient and eye-catching. The team is aimed at bringing magnetic levitation models to the next level.

7. MECHANICS

To design the linear propulsion system, two things are to be achieved; levitation and propulsion. A body made of wood and magnets has to be levitated. Propulsion requires the body to move across a 50 cm linear track. So to meet these requirements the design is taken up in such a way that propulsion is achieved in the centre and levitation on either sides of the propulsion track. (Figure 11)

Levitation is designed and achieved through alnico bar magnets which are arranged in an array, parallel and on either side to the line of propulsion.

Propulsion is achieved using the electro magnetism. A three phase lap winding along the length of the central track with 18 gauge insulated copper wire is selected. When the winding is connected to ac power source, it produces an alternating magnetic field. The center of the body with three neodymium magnets is synchronously locked with the travelling magnetic flux and is thus propelled

Table 1 Specifications for levitation

Table II Specifications for propulsion

8. MECHANICS

The usage of magnetic forces to move or lift a body allows minimum frictional losses when compared to mechanical forces. Incorporating this application, the repulsion between two permanent magnets with same poles has been used for levitation. The linear system has two guide ways on the either sides of the propulsion track. These guide ways consist of an array of alnico bar magnets.

The body has strong neodymium disk magnets placed symmetrically at the corners of the body to attain a stable lift. This body when placed on the track, fits into the guide ways and also levitates over the bar magnets. A stable levitation for the body can be achieved owing to its weight and symmetric design. (Figure 10)

Placing the alnico magnets on the track can be done without gaps between adjacent magnets. This is because the faces facing each other of adjacent magnets will have opposite poles. This will cause the body; with magnets of a particular pole facing track to be attracted and repelled by the continuous opposing poles. The application causes the motion of the body over the tracks to be disturbed; the body oscillates vertically. To overcome this, though opposing poles are present, adjacent magnets are forcibly placed together. The result observed thereafter will be smooth. However this is overcome by using a magnetic strip available in market.

Object Type of magnets Dimensions

(cm)

No of

magnets

On track Alnico 4x2.5x1 16

On body Neodymium(Nd2Fe14B tetragonal crystalline structure) 2.5 dia x 0.2cm 4

Object Type of magnets Dimensions No of

magnets

Track Copper winded electromagnet 18 gauge 1

Body Neodymium (Nd2Fe14B tetragonal crystalline structure) 2.5cm dia, .2cm thick

3 3



The propulsion track is an electromagnet. A three phase lap winding has been selected for the primary rotor windings. A 4 slots one pole machine has been selected. The 50 cm linear track could accompany 36 slots with 3cm as pitch. Therefore a 6 pole linear synchronous system was achieved. [5]

The strength of magnetic field depends upon number of turns per coil which is also called as active slot, calculated as follows:

Area of active slot = 8mm*10mm

= 80mm2(1 mm2=0.00155 inch2)

= 0.124

Maximum current turns / active slot = 1000 at / inch2

An active area of 0.124 can have maximum current turns of 124 at

Taking nearest active turns as 150 at,

A maximum coil current is 6 a.

Therefore, required turns is 150 at / 6a = 25 turns.

For optimal results, eliminating loses and an unseen error 40 turns/coil has been decided.

Table III Magnetic levitation heights

Criteria Design Specifications

Height over LSM 3mm

Height over track 2cm

Table IV Variation in magnetic levitation heights to be achieved

Criteria Desirable displacements

Vertical Stability Operating Elevation Height +/- 5mm

Horizontal Stability Lateral Variation +/- 0mm

Table VI Parameters for magnetic array (propulsion)


Material On track Linear Synchronous Motor (Three phase winding)

On body NdFeB Grade N52

Max B Value For track 1.48 Telsa

For body 14,800 Gauss; 1.48 Telsa

Dimensions of magnets

On track Down the length of track, 50cm

On body 4.0” x 1.0” x 0.1” [3 Thick Disc Magnet Array]

Table VII Parameters for performance of linear synchronous motor


Topology Interacting primary (LSM) & Secondary (Train Body)

Wire Material Copper

Parameter Field Strength B=1.2T

Lorentz Force F=I*(B*L)



9. ELECTRICS

The electrical component in the system is the propulsion system consisting of linear synchronous motor. This is decided after careful study [2], which has similar problem statement to the present work. Linear motors do not use mechanical coupling for rectilinear movement. Therefore, its structure is simple and robust as compared to rotary motor.

A travelling flux will move along the length of the primary rotor. The magnets on the secondary will be synchronously locked with the travelling wave and move at a velocity Vs

Vs=2*pole pitch*frequency of the track. The pole pitch of a single magnet is equal to its diameter; 0.025m. Therefore for 0.025m pole pitch and 50 Hz, (output frequency of a lab volt) the magnet array attempted to accelerate from 0-2.5m/s instantaneously. This rapid acceleration caused vibrations in the body, restricting its forward motion.

A slower acceleration was needed and this is achieved by ramping up the frequency and smoothening the sinusoidal electric signal. Optimal results are achieved at 100v-2.5Hz. To reduce the input signal to the required range, initially an ac generator was used, which can reduce the voltage and modify frequency corresponding to it. But this does not allow regulating both the voltage and frequency as desired. Therefore the signal was smoothened by the use of a pulse width modulator.

10. DESIGN OF LINEAR SYSTEM

The proposed designs for the body, track and the assembly have been done in SolidWorks 2013.

Figure 10 The body made of balsa wood with neodynamiun magents array for levitation and a central array for propulsion.



Figure 11 The track.

Central track with 6 pole lap winding linear synchronous motor. Two guidways on either side of the central track to house the array of alnico magents for levitation

Figure 12. Assembly

The body has it’s legs correctly fitting into the slot for levitation and the central array of magents on the body are locked with the electromagentic wave from the linear motor.



Figure 13 Levitation over the track

11. SUMMARY

After going through three body designs it is clear that any approach to this technology must be taken with much attention paid to the underlying theory, mathematical justification, and all the specifications of the materials used. This work dealt with a design using an effective linear synchronous motor and has mechanics and geometry which allow this construction to a full-length track if it is needed. If magnetic strips were used as rails more robust results would have been achieved against vertical stability. They can continue to be incorporated in the design for stability and levitation.

It is possible to improve the circuit, possibly using sensors and a microcontroller, to regulate energy use. The microcontroller could tell the electromagnets to turn off once a certain velocity is reached and turn back on again only when needed to maintain the velocity. This has wide future scope.

12. CONCLUSION

This work is a modest effort in understanding the principles of magnetic levitation, the magnetic materials and their properties.

This work has lead the team to understand the magnitude of the problem and its wide scope applications.

A good grasp and close study of • Electromagnetics

• Embedded design

• Systems & controls (feedback systems)

• Mechanics

is mandatory before one gets into the activity.

ACKNOWLEDMENT

The team would like to thank Vijay V. for their help in our improving our concept-grasp of fundamentals. We would also like to thank the laboratory staff of Power Electronics division of EEE department whose help came in hand in practically realizing our model.



REFERENCES

[1] A-2.James, Ben. "YouTube - Future Project for Electrodynamics Suspension for a Maglev Train." YouTube - Broadcast Yourself. 23 Apr. 2009 <http://www.youtube.com/watch? v=mumrEE82qAw>.

[2] A-3.Black, Nathan, Ben James, Greg Koo, Vivek Kumar, and Preston Rhea. "The Georgia Tech Maglev Train Project." School of Electrical and Computer Engineering at the Georgia Institute of Technology. 23 Apr. 2009 http://www.ece.gatech.edu/academic /courses/ece4007/09 spring/ece4007l01/sk4/

[3] Amazon, Magnetic Levitation Sets, http://www.amazon.in/Magnetic-Levitation-Floating-Material-Decoration/dp/B00WM40ZFC/ref=sr_1_32?s=toys&ie=UTF8&qid=1481549207&sr=1-32&keywords=Magnetic+Levitation+Toy

[4] electrical4u, Figure 8, http://www.electrical4u.com/faraday-law-of-electromagnetic-induction/

[5] electrical4u, http://www.electrical4u.com/armature-winding-of-alternator/

[6] Everafterguide, Magnetic Levitating Educational Models, https://www.everafterguide.com/solar-mendocino-motor-magnetic-levitating-educational-model-disk-97c82cd991317a9d.html

[7] Geoffrey Pleiss, Maglev Model Train, Menlo School, 2009 http://roundtable.menloschool.org/Issue3/Geoff/Pleiss_MS_Roundtable3_Spring_2009.pdf

[8] Japanese Maglev, 581km/h, online video, (2006), Youtube, http://www.youtube.com/watch? v=VuSrLvCVoVk&feature=related (accessed 30 January 2009).

[9] Hyper physics, Maxwell Equations, http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ maxeq.html.

[10] Maglev Train Technologies, Figure 6,7, https://sites.google.com/site/km4774/ maglevtrain technologies

[11] Mathpages, http://www.mathpages.com/home/kmath240/kmath240.htm

[12] Shark Physics, Figure 9, http://sharkphysics.weebly.com/electromagnetic-induction.html

[13] Tomáš Hron, Model of the Electromagnetic Levitation Device, CZECH Technical University in PRAGUE.

[14] Dr. Srinivasa Baba, V. S. S. N., Giri Raju, B. and Mrs. Srivalli Gundala. Electromagnetic Interference (EMI) Analysis for Oblique Incidence of EM Waves in Double Shields. International Journal of Electronics and Communication Engineering & Technology, 6(11), 2015, pp. 01-09

[15] Aditya Patankar, Rohit Kulkarni, Sanket Kothawade and Sameer Ingale, Design and Development of a Transmission System for an AllTerrain Vehicle. International Journal of Mechanical Engineering and Technology, 7(3), 2016, pp. 351–359.

[16] Trademe, Magnetic Levitation Education Models, http://www.trademe.co.nz/toys-models/educational-toys/science/auction-1217297785.htm

[17] Wikipedia, Earnshaw’s Theorem, https://en.wikipedia.org/wiki/Earnshaw%27s_theorem .

[18] Wikipedia, Magnetic Levitation, https://en.wikipedia.org/wiki/Magnetic_levitation

MAGNETIC LEVITATION VEHICLE-SUPPORTING … · Maglev (derived from magnetic levitation) is a...

Documents

Transcript of MAGNETIC LEVITATION VEHICLE-SUPPORTING … · Maglev (derived from magnetic levitation) is a...