# The History of Electromagnetic Suspension System

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Published: *Wed, 13 Dec 2017*

As the knees are the important part of the human body because of which he can walk, run, sit and jump properly, the suspension system is a knee of a vehicle, with which the vehicle can give us a comfortable ride.

The automobile frame and body are mounted on the front and rear axle not directly but through some form of springs and shock absorbers. This is done to damp to road shocks transmitted to the frame by the wheels as they roll over the road. All these parts which perform this function are together called as a suspension system. Thus the suspension system includes springs, shock absorber and there mountings. The suspension system of a motor vehicle divided into the rear end suspension front end suspension.

## 1.1 Need of suspension system:

- To avoid the road shocks which are pass on to the vehicle frame.
- To preserve the steadiness of a car in pitching or rolling, when in motion.
- To safeguard the occupant from road shocks.
- To provide good road holding while driving, cornering and braking.
- To maintain proper steering geometry.

## 1.2 Types of suspension systems:

The following are the suspension systems which rare used in the modern vehicles,

- Dry friction or Leaf spring
- Coil spring
- Air bag
- Rubber spring
- Electromagnetic suspension system

## 1.3 History of suspension system:

Rolls Royce (1913) illustrates that how the different situations was in the early years where rear dampers stopped to use.

Dry snubbers were used in between 1910-1925.

However, the period 1925-1980 was very extensive by simple hydraulics, primarily simply constant force blow off, then proportional characteristics, then adjustable, leading to mature product.

In the period of 1980 to 1985, there was an enthusiasm about the possibilities for the different types of active suspension, and they had the ability to get rid of the ordinary dampers.

Then after some period in 1985, the fast auto-adjusting dampers, turn out to be more and more obvious, because they found a good deal profit of active suspension much more cheaply, and from that period the damper unexpectedly became an interesting, developing component again (Dixon & John, 2010).

In 1966 for high-speed transportation Danby and Powell introduced an EDS system using super conducting magnets with a “null flux” suspension. After some period some more designs proposed using continues sheet guide ways. Then some from U.S., Japan, Germany, UK and Canada have developed further innovations (such as ladder type guide way for increased lift efficiency), but there are still a number of technical problems that needed resolution. (T. Thompson, Richard D. Thornton and Anthony Kondoleon, 2010)

## 1.4 Current Details Of Electromagnetic Suspension (Maglev):

There are three primary types of Maglev technologies:

- superconducting magnets ( electrodynamic suspension)
- feedback controlled electromagnets ( electromagnetic suspension)
- A new but very cheaper permanent magnet system Inductrack.

The several approaches and designs have been produced by Japan and Germany. These two countries are very active in maglev research. The design used for trains in which the train levitate by the repulsive force of the same poles of the magnets. A linear motor is used to propel the train or on the locomotive or both. In this system massive electrical induction coils produce the magnetic field and the need of this magnetic field which is placed along the track is to propel the train, leading some to speculate that the cost of constructing such tracks would be enormous. ( Heller & Arnie 2010).

“Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.”

As Earnshaw’s theorem says Magnetic bearings are unstable; the conventional maglev systems stabilized with the help of the electromagnets which have electronic stabilization.

In actual to levitate the train that is to keep the train up in the air with the help of an magnetic field it needs very strong magnetic field which only can generate by a large electromagnet but large electromagnet is also a big issue for the design, so instead of using the large magnets, superconductor for an capable electromagnet.

Inductrack is a cheap in cost compare to other systems. The system relies on the current induced in the passive electromagnetic array generated by permanent magnets, so that it provides the better load carrying capacity related to the speed. In the model, the permanent magnets are placed on both sides of the model; the function of these magnets is to provide horizontal lift and vertical stability. There is collection of wire loops in the track which is also called as array. There is no power supply in magnets and the model, apart from the speed of the model. The basic concept behind this system is to store the power by developing the inductrack as a motor and flywheel bearing. With only slight design changes, the bearings were unrolled into a linear track. William Post is the father of such a great innovation like inductrack. He had done this experiment at Lawrence Livermore National Laboratory. (Heller & Arnie 2010).

## Chapter 2

## LITERATURE REVIEW

## 2.1 Principle of Suspension System:

The suspension system of an automobile has input force and output as shown in above fig.

Fig: 2.1 (Dr. Erping Zhou, 2010)

where, M1 is the body mass of the vehicle

M2 is the mass of the suspension system

K1 is the spring constant for suspension system

K is the constant for the tyre (spring).

C is the damper constant

Y is the input force form the road to the suspension system.

Y1 is the input force from suspension system to the body of vehicle.

X is the output displacement.

So the mathematical diagram of the vehicle is given as:

M2

K1(Y1- X)+ C. d(Y1- X)/ dt

K2(Y-Y1)

Therefore now we can have,

K1(Y1- X)+ C. d(Y1- X)/ dt = M1 d2x/dt2……………………………(1)

And

K1(Y1- X)+ C. d(Y1- X)/ dt – K2(Y-Y1) = M2 d2Y1/dt2……………(2)

By lapalce theorem, consider d/ dt = S

K1(Y1- X)+ C. S(Y1- X) = M1 S2X……………………………………..(3)

K1(Y1- X)+ C. S(Y1- X) – K2(Y-Y1) = M2 S2Y1………………………(4)

So by solving equation (3) we get the input,

K1Y1 – K1X + CSY1 – CSX = M1S2X

X/Y1 = K1 + CS/ (M1S2 + CS + K1)

Y1 (INPUT) = X (M1S2 + CS + K1) / K1 + CS (Dr. Erping Zhou, 2010)

## 2.2 Basic Concept:

Take a cylindrical hollow shock absorber frame placing two magnets inside it. In this cylinder the arrangement of the magnets is in such a way, place one magnet at the top of the cylinder with any polarity let us consider south polarity on down side. Then place another magnet at the bottom of the cylinder having south polarity upside so that they can be parallel each other. Then due to the same polarity of both the magnets the repulsive force generates which gives the movement to the shaft to avoid any unwanted shocks and the fixed hydraulic damper absorbs the vibrations and instability.

## 2.3 Theory of Vibration:

“Any motion that repeats itself after an interval of time is called vibration or oscillation.” The best examples for vibration are pendulum and a plucked string. The theory of vibration explains the study of oscillatory motions.

## Free vibration without damping

## To begin with the study of the mass-spring-damper, let’s consider the damping is insignificant and the mass is free from any type of force that is called free vibration.

Where, ‘k’ is the constant of stiffness

‘x’ is the length of stretched spring

‘m’ is the mass of body

So the force is given by,

Fs = – kx

By Newton’s second law of motion the generated force is proportional to the acceleration of the mass

E F = ma = m.d2x / dt2

Then the sum of the forces on the mass is equals to zero:

ma + kx = 0

If the system starts to vibrate by stretching the spring by the distance of A, we get the following equation.

x(t) = A cos(2Ï€ fnt)

The above explanation state that the system oscillates with the simple harmonic motion with an amplitude A , frequency fn. The number fn is called as the undamped frequency which is defined as:

fn =

To simplify the equation the angular frequency Ï‰ (Ï‰ = 2Ï€f) which has a unit radians per second.

If the mass is heavy and inflexibility of the system is known, then the frequency concludes when the force is applied to the system, it will vibrate. When the system once disturbed it vibrates because it has one or more frequencies. The above formula shows the complexity in the real complex designs. (Tustin & Wayne 2010)

## The causes of vibration in the system (conservation of energy)

Conservation of energy explains the vibrational motion. In the above example the value of the spring is ‘x’ and therefore it has stored some potential energy (kx2). Once the spring became free it tries to gain its original shape which has minimum potential energy and in the process accelerates the mass. As the spring reached at its original state that is in unstreched position all the potential energy then converted in to the kinetic energy (mv2). The system then starts to deaccelerate because of the compression of the spring and in this process it transfers kinetic energy into original potential energy. Thus oscillation of the spring transfers the kinetic energy into potential energy.

In the above given simple system the mass remains oscillate at the same magnitude, but this doesn’t happened in the real system because of the damper which disperse the energy and therefore the system finally bringing it to rest. (Tustin & Wayne 2010)

## Free vibration with damping

Now in this system a “viscous” damper is added to the system which generates an opposive force against the motion of the body which is relative to the velocity of the mass. Where c is the proportionality constant and has units of Force over velocity (N s/m).

x

m

k

c

Fig: 2.3 (Tustin & Wayne 2010)

Fd = – cv = -c. dx/dt

By summing the forces on the mass we get the following ordinary differential equation:

ma + cv + kx = 0

The result of the above equation relies on the amount of damping. For the small damping effect the system vibrates but after some time it slows down and finally stops vibrating. This case is called underdamping – this case is of most interest in vibration analysis. If the damping effect increases until the last point of the oscillation of the system, the system then goes in to the critical damping.

Cc = 2

Is the final critical damping point calue for the mass spring damper model.

A damping ration is used to differentiate the amount of damping in a system. The differentiation of the damping is defined as to get a critical point the actual damping divided by the amount of damping. The damping ratio (Î¶) given as:

Î¶ = c /

The values of damping factors for airplane fuselage, engine crankshaft are less than 0.05 and for an automotive suspensions the range of 0.2-0.3. The key for the underdamped system for the mass spring damper model is :

x(t) = Xe-Î¶Ï‰t cos ( Ï‰ = 2Ï€f

The value of X, the initial magnitude, and Ï†, the phase shift, are determined by the amount the spring is stretched. (Tustin & Wayne 2010)

## Analyzation of Damped and undamped natural frequencies

The exponential term and the cosine function are the two main points which are noted from the solution. The meaning of exponential term is how quickly the system “damps” down. The damping effect is low when the damping ration is more. The cosine function explains the oscillations in the system, but the frequency of the oscillations is different from the undamped case.

For this case the frequency is called “damped natural frequency”, fd, and there is a relation between the damped frequency and undamped frequency as follows:

Fd = fn

Generally, the undamped natural frequency is more than the damped natural frequency, but in realistic the difference between the damped and undamped frequencies is irrelevant because of the damping ratio which is moderately small. Therefore at the starting phase of natural frequency the damped and undamped description are frequently dropped.for example- when the damping ratio is 0.1, the damped natural frequency is only 1% less than the undamped.

The two damping ratios 0.1 and 0.3 for the design of side shows how they affect the system and also they show how the system takes time to be stable. Also they show, most frequently what happened practically, is to calculate the free vibrations by doing some experiments after an impact on the system and then the system oscillates so by measuring the rate of oscillations conclude the natural frequency of the system as well as the ratio of damping with the help of rate of decay.

Natural frequency and the damping ratio are the important factors in free vibrations but to understand and differentiate the behaviour of the system in different vibrations generated by force is also important. (Tustin & Wayne 2010)

## 2.4 Principle of EMSS:

The basic principle is to build up a contact less spring; the electromagnetic actuators can absorb the instability. The basics in electromagnetic suspension are the opposite polarity of the magnets facing each other absorbs all the bumps. The major difficulty is making the magnets physically powerful when running off a cars electrical system.

## 2.5 Halbach Arrays:

Halbach cylinders are well-suited to magnetic levitation of gyroscope, motor and generator spindles. In these cylinders only permanent magnets and unpowered conductors are used to provide levitation. Rotational motion provides the energy of suspension entirely, efficiency is good, and there is no need of extremely low temperature suspension magnets or electronics. But there is a limit for the linear speed at the bearing race which must be above a meter per second to levitate.

The inductrack maglev train system uses this principle as well, which avoids the problems inherent in actively supported systems.

## Halbach Cylinder:

K = 1

K = 2

K = 3

K = 4A magnetized cylinder which is made up of a ferromagnetic material producing a magnetic field restricted completely inside the cylinder and doesn’t produce any fields outside is called Halbach Cylinder. The Halbach Cylinders can also generate the magnetic field completely outside of the cylinder and then again it doesn’t produce any fields inside the cylinder. Some magnetization distributions are shown below:

Fig: 2.4 magnetization distributions( K. Halbach, J.C. Mallinson, Raich, H., Blümler 2010)

The direction of magnetization within the ferromagnetic material is given by

M = Mr { sin (kÏ•)ð† – cos (kÏ•) Ï•}

Where,

Mr is the magnetic remanance (T/m).

+k is an internal magnetic field and -k is an external magnetic field.

Preferably, the structures of these types of cylinders would be formed by an unlimited length cylinder of magnetic material which has the direction of magnetization constantly changing. These types of ideal designed cylinder produce the magnetic flux which is perfectly uniform and entirely confined to the bore of the cylinder. But in real case the infinite length of the cylinders cannot be used and in practice the limited length of the cylinders creates end effects which show the non-uniformities in the field within the bore. The complexity of developed a cylinder with a constantly changing magnetization also frequently directs to the design being broken into sections. ( K. Halbach, J.C. Mallinson, Raich, H., Blümler 2010)

## 2.6 Magnetic Material:

Magnets have the basic property of attraction towards, or repulsion by other materials. A material with high permeability attracted strongly towards a magnet. There are two main examples of materials with very high permeability those are Iron and steel which powerfully attracted to magnets. Liquefied O2 is in fact slightly repelled by magnetic fields because it has very low permeability. People, gases and the vacuum of outer space has quantifiable permeability.

The SI unit of magnetic field strength is the tesla,

SI unit of total magnetic flux is the Weber.

1 Weber = 1 tesla

following through 1 square meter, and is a very large amount of magnetic flux.

## Neodymium magnet:

A neodymium magnet or NIB magnet which is also called as a rare earth magnet which is a good strength of attraction and repulsion, made of a combination of neodymium, iron and boron -Nd2Fe14B.

Neodymium magnet on a bracket from a hard drive

(PengCheng magnets Ltd., 2010)

NIB magnets are comparatively very strong to their mass, they are mechanically brittle and the most powerful results to lose their magnetism at temperatures above 176 degrees fahrenheit or 80 degrees Celsius. In some cases they there strength is slightly more than samarium-cobalt like high-temperature grades will operate at up to 200 and even 230 Â°C. The neodymium magnet industry is constantly working to push the maximum energy product (strength) closer to the theoretical maximum of 64MGOe……………………………………………………………………………………………………….

A neodymium magnet has a capability to lift 1300 times more than its own mass.

The small magnet have some remarkable properties – it exhibits magnetic braking when moved near a non-magnetic metal due to induced eddy currents.

(http://www.statemaster.com/encyclopedia/Neodymium-magnet, 2010)

## 2.7 Summery:

The system mainly based on the repulsion of the two similar polarities of the two different magnets. The two damped and undamped systems gives the different vibration frequencies. The analyzation shows a major difference between damped and undamped system.

The Halbach array stabilize the repulsive effect is to use field that move in space rather than just time. This effect can demonstrate with a rotating conductive disc and a permanent magnet, which will repel each other.

A neodymium magnet or NIB is a powerfull magnet made up of a combination of neodymium, iron and boron- Nd2Fe14B is used in EMSS.

## Chapter 3

## MAGLEV DESIGN

## 3.1 Electromagnetic Suspension System: – (Concept)

The design of the electromagnetic suspension system can be done with two types: 1) By using a Hydraulic Damper or

2) By using Linear Motor as a Damper.

The concept is to design the magnetic suspension system on the front shock absorber of the motor bike to have a better performance with ease of handling and comfort ride. There are two cylinders installed on two separate arms of the front shock absorbing rods. The cylinder contains the pair of the cylindrical magnets having same pole facing each other to create the required repulsive force to have required levitation effect. The two cylindrical magnets having “S” (South Pole) on the outer surface concentric with the inner circle having “N” (North Pole) as shown in following figure:-

## 1) Working for the Hydraulic Damper:

The two magnets are in a cylinder on a shaft, as seen in above figure comprise our required magnet for a motor bike front suspension system. In the fig. it shows the magnets are placed such as they are facing each other but with the same polarity, hence they repel each other according to the properties of magnets & generate an air gap between them. The repulsive force restores displacement towards each other, and displacement away is restored by gravity. A hydraulic damper is fixed on the top of the cylinder and connected with the upper magnet with a shaft. The set of shocks used with magnets inside them that are used as the fork setup. In this cylinder the arrangement of the magnets is in such a way, place one magnet at the top of the cylinder with any polarity let us consider south polarity on down side. Then place another magnet at the bottom of the cylinder having south polarity upside so that they can be parallel each other. Then due to the same polarity of both the magnets the repulsive force generates which gives the movement to the shaft to avoid any unwanted shocks and the fixed hydraulic damper absorbs the vibrations and instability.

The shaft controlled the radial instability, the repelling force and the gravity force. The spring has a property to contract and extend but it cannot be stable, so the shaft is use to stabilize the spring. If the magnets are placed in two orthogonal axes, they repel each other but not in any one direction, so they are also instable. A thrust bearing can use to avoid the instability in which the magnets can be placed, and even if the instability take place the movable magnet will not fly has the advantage in that if instability does occur, the unstable magnet will not fly unpredictably away from the fixed magnet. The vibrations and the instability will be absorbed by the hydraulic damper.

“It is stated for completeness that the magnet has two poles North & South”. They will be attract each other if they are facing each other with different polarity, but they will repel each other if they are facing each other with same polarity.That these forces occur is very well known, but the mechanisms that create these forces are beyond the scope of this document. There are several materials of which permanent magnets may be made.

## 2) Working of Linear Motor as a Damper:

A linear electromagnetic motor works in the straight line instead of work in rotary motion. The movement effect of this motor is very quick. L.E.M. can be used at each wheel in a vehicle which has a conventional shock and spring setup. The L.E.M. can extend as it faces any distraction like pothole and retract as it faces any bump just in milliseconds which is much greater speed than a hydraulic damper. These type of quicker retract and extract movement provides the steering stability by controlling the wheels with respect to the body of the vehicle.

The L.E.M. made up of magnets and coils of wires. When current is passed through the coils, the motor retracts and extends so fastly, control unwanted movements. The speed is the major key benefit of the electromagnet. (Bose Elecromagnetic Suspension System, 2010)

Fig: 3.2 (Bose Elecromagnetic Suspension System, 2010)

The L.E.M. is designed in such a way so that it can give the quick respond to absorb the effects of bumps and pothols and also provides a relaxed ride. Moreover, the motor is designed such as it can supply the maximum power in a small package, which allows it to supply sufficient force to avoid the car from rolling and pitching during bad driving.

At the time of acceleration, braking and cornering the L.E.M. neutralize the body motion of a car, which gives the driver a kind of driving idea and passengers comfort ride. For the smooth ride purpose, the wheel dampers are place in each wheel hub to smooth out small road imperfectionst. To generate more power an amplifier is provided which supplies the a great power to the L.E.M.s. The amplifier is a regenerative design that uses the compression force to send power back through the amplifier. (Bose Elecromagnetic Suspension System, 2010)

## 3.2 Goals of the magnetic design

The design of the magnetic spring has the following requirements:

## 1. Freedom instability by one degree:

In freedom instability by on degree generally the stability performance which is forecast by the non linear study is according to the formly build up linearized study. The study of freedom instability by on degree shows the relation between magnitude and velocity. As the velocity increases the magnitude increases which is increased by the stable limit cycle amplitude of vibration.

Actuators are essential for stability control of every unbalanced axis. Hence the amount of unstable degrees of freedom needs to reduce. In addition to it for well organized passive vertical load bearing the direction of the unstable direction must be horizontal.

## 2. Ability to support large loads:

Permanent magnets must be maintained on the entire weight of table plus equipment. This weight which is hold up by the electromagnets utilizes considerable amount of power which is unwanted for cost and heat reasons.

## 3. Effective electromagnet actuator placing:

The forces which are applied asymmetrically by the actuators who apply a moment on the levitating table which would be unwanted. For rejecting vertical disturbances the electromagnet actuators must be used for the stabilizing of unstable axis.

(S. J. Price and N. R. Valerio)

## Chapter 4

## TECHNOLOGY

There are three primary types of MAGLEV Technologies:

One that relies on feedback controlled electromagnets (Electromagnetic Suspension or EMS). Ex.: Transrapid

The another one relies on the superconducting magnets (Electrodynamic Suspension or EDS) Ex.: JR-Maglev

And the last one and newer , potentially more economical system that uses premagnets i.e. Inductrack

## 4.1 Inductrack:

A newer, perhaps less expensive system is called “Inductrack”. The technique used in inductrack has a load carrying capacity which is related to the speed of the vehicle, because the permanent magnets induce current in the passive electromagnetic array In the model, the permanent magnets are placed on both sides of the model; the function of these magnets is to provide horizontal lift and vertical stability. There is collection of wire loops in the track which is also called as array. There is no power supply in magnets and the model, apart from the speed of the model. The basic concept behind this system is to store the power by developing the inductrack as a motor and flywheel bearing. With only slight design changes, the bearings were unrolled into a linear track. William Post is the father of such a great innovation like inductrack. He had done this experiment at Lawrence Livermore National Laboratory. Inductrack uses Halbach arrays for stabilization. Halbach arrays are the system in which there are some arrangements of permanent magnets which stabilize moving loops of wires without electronic stabilization. Halbach arrays were initially developed for beam guidance of particle accelerators. They also have a magnetic field on the track side only, thus reducing any potential effects on the passengers.

## 4.2 Lift and Propulsion:

In the whole world Japan and Germany are the most active in Maglev research; they have produced several difference approaches and designs. The technique used such as the train can be levitated by the repulsive of like poles or the attractive force of opposite poles of magnets. A linear motor propelled the train which is on the track or on the train, or both. In order togenerate the magnetic field which is necessary to propel the train there are massive electrical induction coils are placed along the track.(C.A. Guderjahn & S.L. Wipf,2010)

## 4.3 Stability:

Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.

In the system the static magnetic bearing which uses only electromagnets and premagnets are unstable because of Earnshaw’s theorem; but the diamagnetic and superconducting magnets can support a Maglev steadily. Some conventional Maglev systems the electromagnets having electronic stability are used for stabilization. This works by constantly measuring the bearing distance and adjusting the electromagnets accordingly.

## 4.4 Magnet Weight

The weight of large electromagnet is a major design issue. A very strong magnetic field is required to levitate the massive train, so conventional Maglev research is using superconductor research for an efficient electromagnet.

## Chapter 5

## ANALYSIS

## 5.1 Dynamics of the magnetic suspension system:

The basic principle of a simple electromagnetic suspension system is shown in Fig.1. the current I which is passes through the electromagnet generates the magnetic force Fm which acts opposite to the gravity and cause a steel ball to levitated position. The force relies on the current I, electromagnet properties and the air gap between the steel ball and the electromagnet.The motion of the steel ball in the magnetic field is expressed as

G – Fm = m d2X / dt2…………………..(1)

Where,

m = the mass of the suspended steel ball,

G = mg, the gravity force,

X = the air gap between the steel ball and the electromagnet.

The magnetic force Fm is a nonlinear function of the current I and the air gap X. The linearization of the static characteristic near the set point (F0 , X0 ,I0) is given as

F = F0 + [I0 (X – X0) + ]X0 (I – I0)…………….(2)

The voltage equation of the electromagnetic coil is expressed as

U = RI + L dI / dt………….(3)

Where,

U = the voltage,

R = the coil resistance, and

L = the inductance.

Inductance L=f (X, t) is a function of the air gap, the coil, the core, and the steel ball. The magnetic force which is generated by the electromagnet maintained the steady state air gap between the ball and the electromagnet is manipulated to balance the gravitational force of the ball. The small differences from the operating point are normalized over operating spaces (G, D, Imax , Umax) and they are defined as follows:

f = , x= , i = , u = ……(4)

Where,

f i= the normalized resultant force,

x = the normalized air gap,

i = the ormalized current, and

u = the normalized voltage.

X^ , I^ , and U^ = the steady-state values.

Substituting Eq. 4 into Eqs. 1, 2, and 3 the dynamics of the system

can be presented as follows:

f = -m d2x / dt2 = -m d2x / dt2 = – d2x / dt2……………..(5)

f = ]I0 x + ]X0 i , ……………(6)

u = i + ………………………………(7)

Let the set gains and time constants be

Ke = ]X0 , Km = – ]I0 , Te = , Tm = ……….(8)

Therefore Eqs. 5, 6, and 7 can be rewritten as

f = – T2m d2x / dt2 …………………..(9)

f = – Kmx + Kei ………………………(10)

u = i + Te ……………………………….. (11)

(M. Golob & Boris Tovornik, 2010)

The block diagram of the linearized model of the electromagnetic suspension system is shown in Fig. 5.2. The linear system described in the block diagram in Fig. 5.2 is unstable and controllable.

As per the theory of vibration, there are two types of analysis,

1) The analysis of the Instability and the Vibration without damper and

2) The analysis of the Instability and Vibration with damper.

These analyses were made in the electronic lab with help of the METLAB Software. For these two setups the two types of simulations were made in METLAB Software. The data used for the analysis is as follows:

## Table 3:Nominal System Parameters:

Mass of the steel ball (m)

0.147 kg

Maximum air gap (D)

0.025 m

Number of coils (n)

1200

Coil re

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