super magnet brake system

7/24/2019 Super Magnet BrakE SYSTEM

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IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014 8600404

Analytical and Experimental Modeling and Simulation of a

Magnetic Braking System for Pipeline Oil ApplicationsRicardo F. Pinheiro Filho, Andrs O. Salazar, Francisco E. C. Souza, and Paulo L. B. da Silva

Federal University of Rio Grande do Norte, Natal 59072-970, Brazil

This paper presents a study on the braking effect of the electromagnetic forces produced by eddy currents induced in nonmagneticmaterials. The purpose of this paper analyzes the behavior of a moving device within ducts when a constant magnetic field is appliedon its inner surface, causing induction of eddy currents in pipeline walls, and verifies how the interaction effects of these currentswith the field that induced them might be significant on the device movement.

Index Terms Analytical models, eddy currents, electromagnetic devices, pipelines.

I. INTRODUCTION

THE eddy currents induction effect is a problem in electro-magnetic devices. But, the brake effect associated to thiscurrents interaction with magnetic fields through Lorentz force

opens a larger range of applications [1], [2]. Magnetic brakes

are widely used in drive systems powered by electric machines,

bullet trains, and automotive systems. Currently, eddy currents

has been also applied in many systems, metal detectors, andmost varied sensors, as in the case of verifying the integrity

of oil and gas pipelines.

The velocity of the pipeline instrumented gadgets (PIGs)

should to be maintained between 1 and 5 m/s. However,

this movement is only provided by the fluid pressure behind

the device and its velocity control is hampered by obstacles

formed by material deposition along the line. This leads to

interruptions in PIG travel and a later shot caused by pressure

increase when the device is stopped by an obstacle. This shot

becomes a problem for monitoring the integrity of the pipes

because of the speed increment, above acceptable limits for

proper operation of the sensors instruments.

This paper deals with an analysis of a brake system to be

embedded in PIGs with purposes to get control of its velocity

through the pipes.

The braking effect and control of the velocity of a small

vehicle that moves over a nonmagnetic surface will be stud-

ied by development of analytical models, simulations pro-

vided by engineering support software using finite element

method (FEM), and experimental prototype testing. The pro-

posed PIG braking system, formed by an arrangement of

electromagnets is illustrated in Fig. 1, the mechanical structure

of the experimental prototype is shown in Fig. 3, and the

analytical modeling will be performed from its parameters,

which are specified in Table I and illustrated in Fig. 2.

I I . SYSTEMD ESCRIPTION

The system developed for this paper is a small-scale vehicle

that runs over a steel flat bar used as rail, having an embedded

Manuscript received March 5, 2014; accepted May 26, 2014. Date of currentversion November 18, 2014. Corresponding author: R. F. P. Filho (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2014.2328520

Fig. 1. Mechanical structure arrangement proposed to the PIG brake system.

electromagnet with E-shaped core. The vehicle that runs overthe rail and simulation model are implemented to emulate the

interaction of one of the electromagnetic units with the inner

surface of the pipeline in which the proposed system will

shift.

The steel rail is a flat bar with low reluctance that will

be used as a guide shift for the vehicle, carrying the elec-

tromagnet, which will interact with a nonmagnetic (and low

resistivity) copper plate positioned between electromagnet

poles and the guide plate, as shown in Figs. 2 and 3. This steel

flat bar will attract the field generated by the electromagnet,

thereby reducing the system reluctance and leading a greater

amount of flux lines through the conducting plate, increasing

the flux intensity therethrough and the field skin depth, and

reducing the skin effect which minimizes the induced currents.

Thus, the system and its skin effect nonlinear phenomenon can

be approximated by a simpler model.

III. MODELING ANDS IMULATION A NALYSIS

Figs. 3 and 4 show the full system arrangement, which

is driven by gravity load on the braking train (P). The magneticflux moving over the metallic surface induces eddy currents,

0018-9464 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


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8600404 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014

TABLE I

SYMBOLOGY: D IMENSIONS, M AGNITUDES,AN D M ATERIALP ROPERTIES

Fig. 2. Magnetic flux of prototype core through metal surfaces and the

induced eddy currents.

as it is illustrated in Fig. 2. These currents interacting with the

moving flux produce the Lorentz force, given by (1) [3], [4],

which opposes to the system movement, reducing it, and

allowing get control of the lowering speed by the field intensity

of the electromagnet, controlled by the magnitude of the

injected current in coil. The magnetic flux density B, for the

proposed case, is given by

Find=J B (1)

Fig. 3. Experimental prototype mechanical structure.

Fig. 4. Representation of the forces that act on the experimental prototype.

|Find| = B Iind sin BIB= r0

gapncoilIDC (2)

where r, typically unitary on copper, receives an empirical

correction factor (r 1.175), which emulates the effectof high permeability of the steel rail that increases the flux

through the conducting plate.The induced density current (Jind)behavior is obtained from

(3) [1], [5], which describes the current decrease caused by

skin depth reduction in the field with frequency increase.

The current magnitude is obtained by solving (4), whose

integration variables refer to the Cartesian axes of Fig. 2. The

current attenuation by the field frequency increase is inserted

in the model by (5) that defines skin depth (1)as a functionwith respect of the velocity [6]

Jind(y,z, t)= Jm ey cost2

z y

(3)

Iind

= s

0

0.4s

0.4sJind(y,z, t)

dzdy (4)

=

fr0

S=

vr0

S= v (5)

where is the length of the electromagnet, as illustrated

in Fig. 2. It is equivalent to the wavelength seen by the

conducting plate due to the field movement over it.

The first steady-state model obtained for the braking force

produced by electromagnet neglects the skin depth effect. This

model, in vector form, is given by (6), and its graphical

representation is shown in Fig. 5. Where p is the number

of electromagnet pairs of poles and the other parameters are


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FILHO et al.: ANALYTI CAL AND E XP ER IM ENTAL M ODEL ING AND SI MULAT ION OF A M AGNE TIC BRAKING S YS TE M 8 60 04 04

Fig. 5. Behavior of braking force in function of the speed variations and theapplied current in the coil.

obtained from Fig. 2 and Table I

Find

= 2p

s

s0 ls

lgap

ngapIDC2

V. (6)

The braking force due to eddy currents rises with increasing

velocity, whereas it is reduced due to the skin effect. In order

to better describe this behavior, we must improve the accuracy

of the model. Thus, the geometric system model was built on

a computational platform and simulated using FEM. Fig. 6,

given as simulation result, presents how the induced current

density is distributed in the copper when a relative displace-

ment speed (v = 2 m/s) between the conducting plate and theelectromagnet (supplied by 5 A dc current) is applied. Fig. 6(a)

shows how the steel plate modifies the induced current density

distribution on the nearest copper surface, whose magnitude

increases up to 17.7% compared with the case where the

conductive surface is not above the rail [Fig. 6(b)]. This

difference reaches up to 39.4% in the middle of the copper

plate thickness.

Analysis of braking force got by simulations, with variations

of the coil current magnitude and the conductive plate shifting

speed over the poles, is performed by comparing them with

a more complete theoretical model, given by (7), got for

t= 0 (steady-state), by replacing (2) and (4) in (1)Find= kgeo (ncoilIDC)2

v e

vsin

v+ /4 (7)

where

kgeo= krp S

gap2

S

S03

= S

0

4SS.

The constantkr= 1.458kd(in kgeo)replaces all constantspresent in entire equationing process and joins the effect of

leakage flux in air gap (kf in:kd= kf sin BI) as an empiricalconstant that also represents the Lorentz force decrease due to

the angle (BI) between B and Iind, presented in (1), which

cannot be measured.

The comparison between the developed models and

results obtained by simulation is shown in Figs. 7 and 8.

Fig. 6. Current densities in copper surface (a) with the steel plate presenceand (b) without it, obtained by FEM simulations.

Fig. 7. Effect of velocity variation on the braking force for three differentmagnitudes of injected current Idc.

Significant differences between the curves are due to the model

inaccuracy related to the leakage flux. It is not a properly mod-

eled phenomenon, and may be minimized by reducing the gap.Fig. 7 shows both developed models and compares them

with the results of braking force obtained by simulation when

three different current values are applied to the electromagnet

coil. For velocities where the skin effect becomes evident, the

system behaves according to the developed improved model.

This does not occur at velocities below 1 m/s. With low

influence of this phenomenon, the system has a behavior more

close to the model presented in (6), as shown in linear curves

in Fig. 7.

This same behavior is shown in Fig. 8, in which the

braking force is a function with respect to Idc, got for three


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8600404 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014

Fig. 8. Effect of injected current variation on the braking force for differentvelocities.

Fig. 9. Theoretical and experimental dynamic behavior of the proposedsystem.

different constant velocities. At the lowest one (0.5 m/s), the

curve obtained by simulation moves away from the behavior

described by the model (7) that considers the skin effect and

approaches of model (6) behavior.

IV. SYSTEMDYNAMICA NALYSIS

The system dynamic model is reached by isolating the

variable v(t) in (6), converted into scalar form. Thus, thedynamic model is given by (8), which represents its behavior

curves according to parameters in (9), where the obtained

value to kdwas 0.782.

Curves of the synthesized model are confronted with exper-

imental results from tests with the prototype of Fig. 3, which

runs over a steel rail length 2 m. Results are presented in Fig. 9

v(t)= mtgsingKv

1 ekvt (8)

kv= kdp SS 0

S

gapncoilIDC

2

. (9)

The experimental results point to the validity of the qualitative

behavior of the proposed model and as expected, the prototype

keeps constant velocity in steady state [7].

V. CONCLUSION

The dynamic model proved quite representative of the

studied system when compared with the experimental results,

and can be used to design a control to the system.

Although there are inaccuracies caused by the presence

of friction, mild deformities in the rail, interrupting the

acceleration of electromagnet, inaccuracy in measuring the

air gap and not modeled phenomena, such as leakage flux,

the experiments show a good approximation of the proposedmodel to real operation conditions of the braking system by

induced currents.

The approach of the skin effect on induced currents caused

by magnetic field skin depth in metal surfaces provides a better

approximation of the analytical model at higher velocities.

However, the results obtained by simulation and experimental

tests demonstrate that, at low velocities, linear model that

neglects this phenomenon has a better accuracy of the system

behavior observed by different methodologies.

REFERENCES

[1] A. B. Dietrich, I. E. Chabu, and J. R. Cardoso, Eddy-current brake

analysis using analytic and FEM calculations. I. Theory, in Proc.IEEE Int. Electr. Motor Drive Conf. (IEMDC), Cambridge, MA, USA,Jun. 2001, pp. 454457.

[2] I. Mayergoyz, C. Serpico, and P. McAvoy, Analysis of eddy currentsin magnetically nonlinear conductors, J. Appl. Phys., vol. 109, no. 7,pp. 07E703-107E703-3, Apr. 2011.

[3] M. O. Gulbahce, D. A. Kocabas, and A. K. Atalay, Determination ofthe effect of conductive disk thickness on braking torque for a low powereddy current brake, in Proc. 4th Int. Conf. Power Eng., Energy Electr.

Drives, Istanbul, Turkey, May 2013, pp. 12721276.[4] K. J. W. Pluk, T. A. van Beek, J. W. Jansen, and E. A. Lomonova,

Modeling and measurements on a finite rectangular conducting platein an eddy current damper, IEEE Trans. Ind. Electron., vol. 61, no. 8,pp. 40614072, Aug. 2014.

[5] E. J. Davies, General theory of eddy-current couplings and brakes,Proc. Inst. Electr. Eng., vol. 113, no. 5, pp. 825837, May 1966.

[6] S. Zhou, H. Yu, M. Hu, and L. Huang, Design of permanent magnet

eddy current brake for a small scaled electromagnetic launch model,J. Appl. Phys., vol. 111, no. 7, pp. 07A738-107A738-3, 2012.

[7] F. L. da Silveira, Y. Levin, and F. B. Rizzato, A frenagemeletromagntica de um ma que cai, Caderno Brasileiro Ensino Fsica,vol. 24, no. 3, pp. 295318, 2007.

super magnet brake system

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