Construction and Modelling of Horizontal Shaft Repulsive-Type Magnetic Bearing

Construction and Modelling of Horizontal Shaft Repulsive-Type Magnetic Bearing

Rajeev Kumar

Department of Electrical Engineering Technique Polytechnic Institute Kolkata, India

Shamik Chattaraj

Department of Electrical Engineering Technique Polytechnic Institute Kolkata, India

Permanent magnet which shown in Figure 1. The radial (X and Y-axis) stability can be achieved by proper configuration and design of the permanent magnets. To reduce the effect o radial disturbance, higher radial stiffness is desired which can be achieved by placing a section of permanent magnet on the upper section of the stator. Figure 1 shows the two dimensional view of the permanent-magnet configuration. At the same time placement of the upper stator permanent magnet will reduce the levitation force. So the arc length should be critically selected. With the help of finite-element analysis a trade-off between stiffness & levitation force can be achieved The Z-axis vibration can be controlled by the attraction force between electro magnet and flywheel. A controller will sense the Z-axis vibration or displacement by a sensor and contro the current through the coil of electromagnet.

B. Representation of Forces in the Model

The model of the rotor for such a system is shown below:

f

AbstractThis paper aims in modeling the performance of horizontal shaft repulsive type magnetic bearing. The model of the system is designed by using an industry level modelling software ANSYS Maxwell 16. The nature of the magnetic bearing designed is passive type and the bearing action takes place in accordance with the repulsive technology used in magnetic bearing assemblies. The model consists of two continuous shaped rotating bodies and two discontinuous shaped stator bodies with

a certain amount of air gap clearance between the two distinct –

structures.

Keywords Magnetic Bearing; Horizontal Shaft; Repulsive Type

1. INTRODUCTION

   Horizontal Shaft Repulsive-Type Magnetic Bearing (HRMB) is one of the most promising bearing due its low cost and simple construction. This bearing has low loss, low noise, require low lubrication and no hazards. This paper introduces a Horizontal Shaft HRMB, which consists of permanent magnets for radial stability and electromagnets for levitation & radial stability. Being a bearing HRMB is to serve two basic purposes, supporting of the rotor and minimizing of vibration of the rotor system. The rotor part is fixed with the horizontal axis of rotation known as the shaft and on the center of which a large circular disc is fixed known as Flywheel. In front of one face of the Flywheel, current controlled electromagnets are attached which along with the Flywheel plays an important role in maintaining the axial stability of the setup.

2. ABBREVIATIONS AND ACRONYMS Horizontal Shaft Repulsive-Type Magnetic Bearing (HRMB) Horizontal shaft Passive Magnetic Bearing (HPMB)

A. Horizontal shaft Passive Magnetic Bearing (HPMB)

A single-axis controlled repulsive-type magnetic bearing is a device which supports the rotor system by magnetic levitation and allows it to rotate freely with less vibration and low loss. Here two things are important; number one the rotor system should be levitated and number two the vibration of the rotor system should be less as much as possible at steady running condition as well as in different transient conditions like sudden change in load, on & off of the machine etc. For horizontal shaft magnetic bearing the levitation force can be achieved by the repulsive force between stator and rotor

.

l

1. Lower stator magnet, 2. Upper stator magnet, 3. Rotor magnet, 4. Flywheel, 5. Controlled electromagnet, 6. Gap sensor, 7. Induction motor,

8. Motor shaft, 9. Base of motor, 10. copper plate, 11. Fe plate

C.

Fig. 1. Bearing Construction and configuration of the magnets for horizontal shaft magnetic bearing

Fig. 2. Model of the rotor

The forces acting on the rotor are shown in the above figure. Here f1, f2, f3, f4are the forces acting on the rotor by electromagnet, flx, fly and flz are the forces on the left due to the permanent magnets and frx, fry and frz are the corresponding forces on the right as shown in the figure 2.

1. Forces due to permanent magnets

   The forces flx, fly, flz, frx, fry and frz are a function of the displacements of the rotor along three directions measured from a predefined origin, usually the point of geometrical symmetry of the rotor. The following equation shows the dependence of these forces on rotor displacements.

   surface area of the core of the electromagnet, permeability of free space etc.

   Linearizing the operating characteristics of the electromagnet

   [] =

   [

   ] + []

   around the normal equilibrium operating point, expressing

   them by the deviated quantities from the steady state values,

   [

   ]

   we get:

   = 2 (

   )

   By Finite Element Analysis method, it can be shown that in the above equation, the following terms are negligibly small i.e.

   F, I and W are the generated force, current and gap at a steady state of the electromagnet. e, i and f are the incremental

   =

   = =

   =

   = 0

   values of the impressed voltage, current and generated force

   respectively.

   1. Forces acting on the rotor

      From this we can conclude that force developed on the rotor along any direction is hardly dependent on the displacement of the rotor along the other directions. Hence the simplified force

   2. Torques acting on the rotor

3

4

equations acting on the rotor due to permanent magnets can be expressed as follows: –

Along x-axis: 1 + 2 + +

Along y-axis: +

= (

) ( ) +

Along z-axis:

= ()

Here c represents and , b represents and , a represents

and

Let us Assume:-

Here denotes the total weight of rotor.

Along x-axis: 0

Along y-axis: 01 02 1 + 3

Along z-axis: 01 02 2 + 4

Here denotes the total weight of rotor.

= ( ) is the rotor stiffness along z direction

• is electromagnetic torque of the motor

  = () is the rotor stiffness along x direction

  = ( ) is the rotor stiffness along y direction

• 0is load torque acting on the shaft of the motor

• p is the angular velocity of the motor

• is the coefficient of friction of the rotor.

• 01, 02 are the distance of the centers of the two rotor permanent magnets from the center of the

and is the steady state repulsive force acting on rotor

along z and x direction. =0 (approximately)Azand Axis the

flywheel (usually 1

and 2)

nominal displacement of rotor permanent magnets in steady state.

, , are ctual displacements of rotor permanent magnets.

1. Forces due to electromagnets

   The expression of the force on the rotor due to electromagnets is based on following assumptions:

   1. The force produced by the electromagnet is proportional to the square of the current and inversely proportional to the square of the gap distance.

   2. Deviation around the nominal equilibrium operating point is small.

The equations of the electromagnets will be written as follows:

= +

2

= ( )

L and R are the inductance and resistance of the electromagnet, e is the impressed voltage to the electromagnet and i is the current through the electromagnet, f is the electromagnetic force generated by the electromagnet and k is a constant used in the force expression which depends on the number of turns,

l is the distance of the center of the electromagnet from the center of the shaft.

Assuming L01 = L02 and f1 = f2 = f3 = f4 i.e. same force due to the four electromagnets, the expressions for torque around y and z axes are found to be dependent only upon the difference of force acting upon the two permanent magnets along z and y directions respectively. The smaller this difference, smaller will be the torques along these two directions.

1. Expressions for air gaps

   1 = 1 + 3 = 3

   2 = 2 + 4 = 4

   = =

   = + 01 = + 02

   = + 01 = + 02

   Here:

   • W1 to W4: nominal gaps of the electromagnets

   • g1 to g4: actual gaps of the electromagnets

   • xs, ys and zs: displacements of the rotor along the three axes

   • : angle of pitch

   • : angle of yaw

2. Basic state equations

= 1 + 2 + 3+4

= +

=

ACKNOWLEDGMENT

We take this opportunity to convey our immense gratitude to Dr. Debabrata Roy (Professor of the Department of Electrical Engineering, IIEST, Shibpur) for his invaluable advice,

guidance, active supervision and constant encouragement

= + 01

02

1

+ (

)

without which it would not have been possible for me to give

3 1

this shape to the paper.

= + 01

02

1

+ ( )

REFERENCES

Here:

4 2

1. S.C. Mukhopadhyay, J. Donaldson, G. Sengupta, S. Yamada, C. Chakraborty and D. Kacprzak. Fabrication of a Repulsive-Type

   • Jx: moment of inertia of the rotor along x-direction

   • Jy: moment of inertia of the rotor along y-direction From the above state space equation for the current flowing in the electromagnets can be obtained. It is given as follows:

     Magnetic Bearing Using a Novel Arrangement of Permanent Magnets for Vertical-rotor Suspension, IEEE Trans. on Magn., vol. 39, no. 5, pp. 3220-3222, Sep 2003

2. T. Ojhi, Yoshiyuki Katsuda, Kenji Amei, and Masaaki Sakui, Structure of one-axis controlled repulsive type magnetic

   =

   +

   ( j=1 to 4 )

   bearing system with surface permanent magnets installed and its levitation and rotation tests

3. Qingchang Tan, Wei Li and Bo Liu, Investigations on a

   Gap sensors are used to measure the distance separating the electromagnets from the rotor. When for the jth electromagnet, the actual gap gj deviates from the nominal gap Wj; these gap sensors send a signal to the control circuit such that the disturbance is minimized. These gap sensors are scaled to give an output of 1V/mm.

   permanent magnetic-hydrodynamic hybrid journal bearing,

   Tribology International, 35, pp. 443-448, 200

4. J. P. Yonnet, Passive magnetic bearing with permanent magnets, IEEE Trans. Magn .. 1978,14, (5), pp. 803-805