Electrical Engineering

International Review of

Electrical Engineering (IREE) Contents On the Study of Modernized Lightning Air Terminal by M. A. B. Sidik, H. Ahmad Dynamic Single-Phase DVR System with Instantaneous Power Factor Estimator by B. Dobrucky, P. Spanik, M. Pokorny Overvoltage Protection Optimization of Medium Voltage Network by M. Marttila, P. Verho, K. Kannus Electrostatic Shaft Voltage at the Crack–Gas Compressor: the Phenomenon Analyses, Testing, Measuring and the Problem Solution by B. I. Jeftenić, L. B. Ristić A New Artificial Neural Network Approach with Selected Inputs for Short Term Electric Load Forecasting by Z. H. Ashour, M. A. Farahat A New Method for Evaluation of Distribution System Losses due to Load Unbalance by R. M. Ciric, H. Nouri Multiobjective Genetic Algorithms for Online Management Problem of Microgrid by F. A. Mohamed, H. N. Koivo Application of Numerical Distance Relays in Dispersed Generation by D. Labed, A. Bouzid, M. Zellagui, M. Bouchahdane A New Control Method of Hybrid Active Filter to Eliminate the 5th and 7th Harmonic Frequency Using SelfTuning-Filter in the Feedforward Loop by M. Abdusalam, P. Poure, S. Saadate Design Aspects of the Series Active Power Filter by J. Turunen, H. Tuusa Modeling and Adaptive Control of Two-Stage Matrix Converters by M. Hamouda, F. Fnaiech, K. AL-Haddad A New Design for Analogue Maximum Power Point Tracking by R. Chenni, L. Zarour, M. Amarouayache, A. Bouzid Step by Step Design of the Power Stage of a Light Electric Vehicle by F. J. Pérez-Pinal, C. Núñez, R. Álvarez, M. Gallegos Analytic Design of a Permanent Magnet Synchronous Motor Dedicated to EV Traction with a Wide Range of Speed Operation by B. Ben Salah, A. Moalla, S. Tounsi, R. Neji, F. Sellami Analysis of a Cylindrical Passive Suspension System Using Finite Element Method by A. Najjar-Khodabakhsh, S. Vaez-Zadeh, A. Hassanpour Isfahani The Soft-Starters Modeling, Simulations and Control Implementation for 2 MW Constant-Speed Wind Turbines by L. Mihet-Popa, O. Prostean, I. Szeidert Dynamic Modeling, Simulation and Control of the Power Conditioning System for a Variable-Speed WindTurbine by J. Castelló, R. García-Gil, J. M. Espí, S. A. González Fractional Order Speed Observer for Sensorless Induction Motor Drives by M. Ben Hamed, L. Sbita Induction Motors Bearing Failures Detection and Diagnosis Using a RBF ANN Park Pattern Based Method by I. Yilmaz Önel, M. E. H. Benbouzid Design of a New Sensorless Controller of Induction Motor Using Backstepping Approach by A. Abbou, H. Mahmoudi The Finite Element Method in Shielding Problems by M. Lascu Combining the Moments Method and the PEEC Method with the Kron’s Transformation for Studying Embedded Systems EMC by J. Ben Hadj Slama, O. Maurice, D. Baudry, A. Louis, B. Mazari A Dual-Function RF Filter for 5 GHz WLAN and UWB with Narrowband Interference Rejection by A. Dinh, L. Chen, D. Teng, B. Pham Methods of Modeling and Identifying the Electrical Characteristics of Super Capacitor Energy Storages by Y. Cheng, J. Van Mierlo, P. Lataire The Contribution of Vehicle Headlights to Visibility of Targets in Road Lighting Environments by A. Ekrias, M. Eloholma, L. Halonen

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Copyright © 2008 Praise Worthy Prize S.r.l. - All rights reserved

International Review of Electrical Engineering (I.R.E.E.), Vol. 3, N. 1 January – February 2008

Analysis of a Cylindrical Passive Suspension System Using Finite Element Method A. Najjar-Khodabakhsh, S. Vaez-Zadeh, A. Hassanpour Isfahani Abstract – The analysis of cylindrical suspension systems has usually been carried out by their approximated flat structures so far. In this paper the lift and drag forces of a passive electrodynamic suspension system, consisting of a permanent magnet block levitated over a rotating cylindrical conducting shell, is fully investigated with no structural approximation. A FEM-base procedure for numerous simulation runs is followed to consider the influences of many system operating conditions and specifications on the system performance. In particular, the effects of rotating speed, shell thickness and conducting resistivity, permanent magnet dimensions and air gap length are analyzed. The concluding remarks presented in the paper can be used in the optimal design of such a suspension system. Copyright © 2008 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Electrodynamic levitation, Passive suspension, Performance, Finite element method

Nomenclature B Bx By E Fx Fy J V σ v µ0

Magnetic field density Magnetic field density in x direction Magnetic field density in y direction Electric field intensity Lift force Drag force Current density Volume of conductor Conductivity of conductor Transaction speed Relative permeability of air

I.

Introduction

Typically, there are three types of levitation technologies: electromagnetic suspension (EMS), electrodynamic suspension (EDS) and hybrid electromagnetic suspension [1]. EDS traditionally has been built by superconducting coils. However, passive electrodynamic suspension (PEDS) in which permanent magnet block replace superconducting coils has recently gained increasing attention due to its simplicity and cost saving merits. It does not need power supplies, power conversion, transmission means, superconducting coils and cooling facilities. A number of researches on PEDS for industrial applications including magnetic bearing have been reported in the literature so far [2]. PEDSs with short circuit sidewall coils as their secondary have been analyzed by circuit equation and their lift and drag forces have been calculated [3],[4].

Manuscript received and revised January 2008, accepted February 2008

123

The rotation of permanent magnets above a conducting non-magnetic surface such as aluminum creates a traveling time varying magnetic field that can inductively produce levitation and propulsion forces simultaneously. The use of Halhach magnets enables a sufficient levitation to weight ratio to be attained [5]. Lift force, thrust and lateral force characteristics of “partial overlap type magnet wheel” are presented in [6], where “magnet wheel” is a proposed electromagnetic device constructed with revolving permanent magnets and conducting plate. The influence of changes in system specifications on the system performances have also been investigated for a PEDS by means of finite element method (FEM) [7]. However, extensive system analyses are still required to fully comprehend the various aspects of PEDS performance and design. In the previous works, the classical configuration of PEDS consisting of a flat conducting sheet has been analyzed. However, in many cases the cylindrical conducting shells are used. This configuration, to be analyzed accurately by FEM, needs heavy computations due to its large and unsymmetrical geometry. Therefore, the shell is usually approximated by a flat sheet and the curvature nature of shell is ignored. However, in certain cases, i.e. where the shell diameter is relatively small, this approximation causes noticeable inaccuracy in the results. So, more realistic analyses are required in such cases which are now feasible due to ongoing progress in computation methods and means. In this paper a system of PEDS with a cylindrical structure is analyzed. The system consists of a permanent magnet block levitated over a rotating cylindrical conducting shell of aluminum (Al) material. Copyright © 2008 Praise Worthy Prize S.r.l. - All rights reserved

A. Najjar-Khodabakhsh, S. Vaez-Zadeh, A.Hassanpour Isfahani

This special structure with its compactness makes it suitable for integrated suspension systems as well as magnetic bearing. Also, it may be regarded as an easily feasible experimental PEDS setup. The production of lift and drag forces in this structure are studied by FEM and the effects of specifications on the system performances are then investigated in detail via extensive simulations. The properties of conducting sheet are also considered in the analysis which did not gain enough attention so far.

II.

System Structure and Specifications

The PEDS system consists of a basic permanent magnet (PM) piece with the nominal dimensions of 10×25×40 mm which is levitated over a rotating cylindrical Al shell with 25 cm inner radius and 2 mm thickness. The nominal air gap between the PM and Al is 5 mm. A schematic view of the system and the force directions are shown in Fig. 1. The system performances with the nominal specifications and also with changes in the rotational speed and the thickness of Al shell are studied. The PM dimensions are also varied to study their effects on the system performance. The volume of PM is always kept constant. Finally, the air gap between the PM and the Al shell is changed.

Fig. 1. Schematic view of the system

The force per unit of volume is as follows:

(

J × B = −σ B × ( v × B ) = σ B 2 v − ( v ⋅ B ) B

)

(7)

The drag force per unit volume is:

(

)

f x = −σ vx By2 + Bx2 = σ vx By2

(8)

Since Bz = 0 , hence the total drag force is:

III. Analytical Theory

∫

Fx = σ vx B y2 dV

The physical arrangement under study consists of a conducting plate moving under a permanent magnet piece. The problem is considered in two-dimensions only, so the z component of the magnetic field and all derivatives with respect to z are zero. Using Maxwell’s equations [8]: ∇⋅B = 0

(1)

∇× B = µ 0 J

(2)

J =σ E

(3)

E = v×B

(4)

∂By ∂Bx =− ∂x ∂y

(5)

with ohm’s law:

and the motional EMF:

gives:

2

∂ By ∂x

2

2

+

∂ By ∂y

2

= µ0σ vx

∂B y ∂x

(6)

(9)

The lift is evaluated the same way and is:

∫

Fy = σ vx Bx B y dV

IV.

(10)

Method of Analysis

In this section, 2-D nonlinear time-stepping FEM is employed to analyze the model. The relative movement is taken into account in the FEM by using time-stepping analysis and Lagrange multiplier method [9]. The forces are then calculated using local virtual work method. A flowchart of the FEM is shown in Fig. 2. The problem domain is divided into 17392 six-node-triangle elements and 34901 nodes. The analysis is carried out by over 2500 simulation runs. The span of each simulation is 30 s. The time required for the analysis by a Pentium D 2.8 GHz (Dual-core) processor and 4GB of memory is about 1250 minutes.

V.

System Analysis

The magnetic flux paths for two different values of angular speed, 50 and 15 round per second (rps), of cylindrical shell are depicted in Fig. 3.


International Review of Electrical Engineering, Vol. 3, N. 1

124


1.4 1.2

Force (N)

1 Lift Force Drag Force

0.8 0.6 0.4 0.2 0 0

20

40

60 Speed (rps)

80

100

120

Fig. 4. Effect of angular speed on system performance Fig. 2. Flowchart of the FEM

Using curve fitting on the numerical results, it is revealed that at low velocities (v), lift force increases as v2 and drag force increases as v. At the drag peak velocity, lift force and drag force are equal and the maximum drag force is about 50% of the maximum lift force. Above the drag peak velocity, the lift force approaches an asymptotic maximum value, and drag force decreases as 1/v. It is desirable to reduce the drag peak velocity as much as possible so that significant lift is generated at low speed values and the PM “lift-off” velocity is minimized.

V.2.

(a)

Effects of Al Shell Thickness

The effects of the Al thickness on the performance of the system are shown in Figs. 5-7. It is seen that the lift force changes significantly when the Al shell thickness increases from 0.25 mm to 2 mm. However, increasing of the Al thickness beyond 2 mm does not affect the lift force especially in higher speeds. With the increasing the Al thickness, the drag force decreases at low speeds. Ratio of the lift to drag increases with the increasing of speed and Al thickness; however, it is constant when the speed is constant and the Al thickness increases. It shows that one can select the best lift to drag ratio for the sake of cost saving by adjusting the Al thickness. According to Figs. 5 it is wise to select the speed of 50 rps and the thickness of 2 mm as a basis for further analysis.

(b) Fig. 3. Magnetic flux paths at (a) 50 rps (b) 15 rps

It is seen that in the higher speed value the flux lines are significantly localized between the magnet and Al shell.

V.1.

Effects of Shell Speed

The lift force and the drag force in terms of angular speed are illustrated in Fig. 4. It is seen that the lift force increases and the drag force first increases and then decreases with increasing speed as anticipated. However, above a certain speed of about 50 rps, the rate of increase in the lift force decreases. Copyright © 2008 Praise Worthy Prize S.r.l. - All rights reserved

V.3.

Effects of PM Height

Dimensions of PM piece also affect the performance of the system as seen in Figs. 8-10. The height of PM is changed here for a constant PM volume and the results are shown for a speed range. It is seen that for the height of 8 to 11 mm, the maximum value of the lift and drag forces are achieved and at this state the lift to drag ratio changes almost solely due to changes in the Al shell speed. It is also seen that the lift to drag ratio rises when the speed increase. It means that at the high speed performance we expect a high lift to drag ratio.


125


0.1

20

6

0.3

10

100

5

50

2 Thickness (mm)

0.4

0. 4

0.3

0.2

0.3

0.2 0.2

20

0.1

0.1

0.1

Speed (rps)

0 0

0.2

0.3

0.4

0.1

4

0.2

0.5

0

15

0.5

0.5

Drag Force (N)

0.3

0.1 0.2

1

0.5 0.4 0.3

Height of PM (mm)

Lift Force (N)

1.5

0.1

0. 2

0.2

25

40 60 Speed (rps)

Fig. 5. Variations of lift force in terms of Al thickness and speed

80

Fig. 9. Variations of drag force with PM height and speed

3

Lift to Drag Ratio 5

1

2

4

0.6

20

4

50 Speed (rps)

6

Thickness (mm)

5 1

Lift to Drag Ratio

40 60 Speed (rps)

80

In other words, the PM height has marginal effect on the lift to drag ratio.

6 4 2

V.4.

0 6

100

4

Thickness (mm)

2

50 Speed (rps)

0 0

Fig. 7. Variations of lift to drag ratio in terms of Al thickness and speed 25

0.4

Lift Force (N)

0.2

20

0.6

0.4

0.6

0.2

8 0.

1.2

1 0.

6

1.2

0.2

20

1

0.8 0.4

0.6

0.8

0.2

40 60 Speed (rps)

One of important factors affecting the system performance is the sell material resistivity. Therefore, to have an accurate estimation of system performance this factor must be considered. The influences of changing the resistivity of Al sheet is considered as depicted in Fig. 11. It is seen that the lift to drag ratio reduces when the resistivity of Al increases. This may occur due to a replacement of the type of used alloy or due to a temperature change as result of induction losses.

0.4

V.5.

1

1

10

Effects of Shell Resistivity

0.8

0.8

0.6

15

0.4

Height of PM (mm)

20

Fig. 10. Variations of lift to drag ratio with PM height and speed

8

5

1

Fig. 6. Variations of drag force in terms of Al thickness and speed

2

6

4

3

0

10

5

2

5

0

100

15 2

0

1

0.2

4

Height of PM (mm)

0.4

3

Drag Force (N)

25

1 0.6 0.2

0.8

Effects of Air Gap Length

Finally the influence of changing the air gap length is considered as depicted in Figs. 12-13. It is seen that both the lift and drag forces increase with the decreasing of the air gap length as expected.

80

Fig. 8. Variations of lift force with PM height and speed



126

L ift F o rc e (N )


1.25

L ift to D ra g R a tio D ra g F o rc e (N )

1.2

20

25

30

35

20

25

30

35

0.2

It is seen that the lift force increases significantly with an increasing shell thickness up to a certain thickness. With a constant PM volume, the lift force reaches a maximum for a certain PM dimensions. However, the dimensions of PM piece have marginal effect on the ratio of the lift to drag forces when the PM volume remains constant. The ratio of lift to drag forces reduces when the resistivity of Al increases and the lift and drag forces increase when the air gap length decreases. These results can be used in the optimal design of cylindrical passive electrodynamic suspension systems.

7

Acknowledgements

6 5 20

25 30 Resistivity (nohm.m) −9

Resistivity ( Ωm)

(×10 )

35

The Authors wish to thank Center of Excellence on Applied Electromagnetic Systems at the University of Tehran for its finical support.

Fig. 11. Variations of system performances with shell resistivity

References [1]

Lift Force (N)

4

[2]

3 2

[3]

1

[4] 0 100

0 50 Speed (rps)

0 20

10 Airgap (mm)

[5]

Fig. 12. Variations of lift force with air gap

[6] [7]

Drag Force (N)

1.5

[8]

1

[9] 0.5

H. W. Lee, K. Kim, and J. Lee, “Review of Maglev Train Technologies,” IEEE Trans. on. Magn. vol. 42, no. 7, July 2006, pp. 1917-1925. D. M. Rote and Y. Cai, "Review of dynamic stability of repulsive-force maglev suspension systems," IEEE Trans. Magn., vol. 38, no. 2, Feb. 2002, pp. 1383-1390. J. L. He, D. M. Rote, and H. T. Coffey “Applications of the Dynamic Circuit Theory to Maglev Suspension Systems," IEEE Trans. Magn., vol. 29, no. 6, Nov. 1993, pp. 3315-3317. P. L. Ribani, N. Urbano "Study on figure-eight-shaped coil electrodynamic suspension magnetic levitation system without cross-connection," IEEE Trans. Magn., vol. 36, no. 1, Jan 2000, pp. 358-365. Bird, J.; Lipo, T.A. “An electrodynamic wheel: an integrated propulsion and levitation machine,” Electric Machines and Drives Conference ~. IEMDC03~ 1-4 June 2003. Fujii, N.; Ogawa, K.; Chida, M., “Three Dimensional Force Of Magnet Wheel With Revolving Permanent Magnets,” IEEE Trans. Magn., vol. 33, no. 5, Sept 1997. S. Vaez-Zadeh, S. Ramtin “Performance analysis of passive electrodynamic suspension systems,” in Proc. LDIA Conf., ~LDIA 2005~ pp. 430-432, 2005, Kobe-Awaji, Japan. R. J. Hill, “Teaching electrodynamic levitation theory,“ IEEE Trans. Educ., vol. 33, no. 4, Nov. 1990, pp. 346–354. D. Rodger, H. C. Lai, and P. J. Leonard, “Coupled element for problems involving movement,” IEEE Trans. Magn., vol. 26, no. 2, Mar. 1990, pp. 548–550.

0

0 100 50 Speed (rps)

0 20

10 Airgap (mm)

School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.

Fig. 13. Variations of drag force with air gap

VI.

Authors’ information

E-mails:

Conclusion

A cylindrical structure for passive electrodynamic suspension has been presented and analyzed by finite element method. A systematic procedure including numerous simulation runs is followed to achieve the results using a dual core personal computer. The lift and drag forces in this structure have been studied under various system specifications and operating conditions. Copyright © 2008 Praise Worthy Prize S.r.l. - All rights reserved

[email protected] [email protected] [email protected]


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Abbas Najjar-Khodabakhsh was born in Isfahan, Iran, in 1981. He received a B.Sc. degree in electrical engineering from Islamic Azad University of Najaf Abad, Isfahan, Iran in 2004. He is now an M.Sc. student in electric power engineering at the University of Tehran, Tehran, Iran. His research interests include design, modeling and control of levitation systems and high performance motors.

Arash Hassanpour Isfahani was born in Isfahan, Iran, in 1980. He received a B.Sc. degree in electrical engineering from Isfahan University of Technology, Isfahan, Iran in 2002 and an M.Sc. degree in electric power engineering from the University of Tehran, Tehran, Iran in 2005 where he is a PhD student now. His research interests include design, modeling and control of electrical machines.

Sadegh Vaez-Zadeh (S'95–A'03–SM’05) received the B.Sc. degree from Iran University of Science and Technology, Tehran, Iran in 1985 and the M.Sc. and Ph.D. degrees from Queen’s University, Kingston, ON, Canada, in 1993 and 1997 respectively, all in Electrical Engineering. He has been with several research and educational institutions in different positions before joining the University of Tehran as an assistant professor in 1997 where he became an associate professor in 2001 and a full professor in 2005. He served the university as the Head of Power Division from 1998 to 2000 and currently is the Director of Advanced Motion Systems Research Laboratory which he founded in 1998 and the Director of Electrical Engineering Laboratory since 1998. His research interests include advanced rotary and linear electric machines and drives, magnetic levitation, electric vehicles and power system analysis and control. He has published about 150 research papers in these areas. He is an Editor of IEEE Transactions on Energy Conversion, a Co-Editor of Journal of Asian Electric Vehicles and a co-founder and a member of the editorial board of Iranian Journal of Electrical and Computer Engineering. He is also a member of editorial board of the Journal of Faculty of Engineering as the oldest engineering journal in the Middle East. He has served many IEEE sponsored conferences as a member of technical and steering committees, session chair, etc. Prof. Vaez-Zadeh is a member of IEEE PES Motor Sub-Committee and Power System Stability Control SubCommittee.



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