Theoretical and Experimental Forces for a New Linear Switched Reluctance Traction Motor

8/4/2019 Theoretical and Experimental Forces for a New Linear Switched Reluctance Traction Motor

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Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1145

978-1-4244-1736-0/08/$25.00 2008 IEEE 1

Theoretical and Experimental Forces for a NewLinear Switched Reluctance Traction Motor

D.S.B. Fonseca, C.P. Cabrita, MR.A. CaladoElectromechanical Eng. Dept. and CASE-Unit Research on Electrical Drives and Systems

University of Beira Interior, Edifcio 1 das Engenharias,Calada Fonte do Lameiro, 6201-001 Covilh, Portugal,tel: (+351) 275 329 945; fax: (+351) 275 329 972

e-mail: [email protected]

Abstract- The purpose of this paper consists in thecharacterization of the traction force for a new Linear SwitchedReluctance Machine (LSRM) for low speed light electric tractionapplications. In this work the machine is tested, for each position,at standstill. The experimental methodology allows thedetermination of the magnetization characteristics as well as thestatic mechanical resistant force.

I. INTRODUCTIONOne of the electrical drive applications with greater

contribution for a more sustained and structured development

of modern societies, is the electric traction, namely in the

railway systems, which represents an industry in constant

development.

As well known, the rotating drives are the most effective

solution in the majority of the electric traction applications.

However, there are circumstances where the linear drives can

successfully replace the rotating drives, particularly when, due

to space limitations, such as in underground motor rolling

stock, it is important to reduce the wheel diameters.

Regarding linear drives, they are usually based either oninduction or permanent magnet synchronous motors. However,

the switched reluctance motor represents a good alternative,

especially in urban traction.

Linear Switched Reluctance Machines (LSRMs) have been

explored before in the literature, although none of them with

this topology and designed to light railway electric traction

applications [1,2]. Fig. 1 shows the topology of the machine

used in this work, and Table I presents its dimensions.

Fig. 1. New 4-phase 8/6 Linear Switched Reluctance Machine geometry, andenvelope dimensions defining electromagnetic volume.

TABLE ISOME OF THE LSRMELECTROMECHANICAL DATA.

m 4 bs [mm] 18 Ne 1680

Nr 4 P[mm] 132 lb [mm] 24

Nbr 1 S[mm] 48 hb [mm] 50

N2 6 w [mm] 33 Dcu [mm] 0.5

g[mm] 3 hp [mm] 50 Imax [A] 0.68

bp [mm] 18 hs [mm] 42 R [] 27.6

As can be seen, the LSRM has a cheap secondary and

modular primary construction. In addition, this topology

increases significantly the electric, magnetic, thermal and

physical independency between phases. In fact the mutual

inductances between phases may be neglected with no loss of

accuracy concerning machine analysis [1,2].

The geometric data exposed in Table 1 are related to the

LSRM drawing of Fig. 1, except the following:m phase number,

N number of turns per primary phase,N2 secondary pole number,

Nr number of parallel paths of each primary phase,Nbr number of coils per winding parallel path,Ne number of turns per primary coil,R coil resistance.

II. TEST METHODOLOGYThe experimental electromagnetic characterization was

carried out by positioning and blocking the primary for

different relative positions concerning the secondary.

For each position, a square wave voltage was applied to the

phase terminals. Note that each phase consists of two series

connected coils, in view to ensure that all turns are carried out

by the same current. Once guaranteed the phase fulldemagnetization at the beginning of each transient

phenomenon, based on the analysis of all transient phenomena

it became possible not only to get the magnetization curves,

but also to relate the current values and relative position with

the useful traction force, developed by each phase.

The mechanical adjustment of the primary position was

achieved through a precision screw, connected to the load cell,

as can be seen in Fig.2.


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Fig. 2. Prototype under tests.

Taking into account the electromagnetic symmetry of the

machine, it was decided to test only positions where the

machine develops a compression force on the load cell.

On the other hand, the electromagnetic topology of the

machine, unlike the classic design of concentrated windings,

the four phases are completely independent from the magnetic

point of view, with no end effects that weaken the magnetic

field and consequently the traction force developed by both

end phases. In order to validate this fact two distinct phases

were tested, that is one central phase and one end phase.

Fig.3 shows the electrical scheme used for each phase test.Because all phase turns are series connected it is possible to

increase the input voltage without reaching a dangerous current

rms value.

The electric circuit switches are power IGBTs, being both

controlled by a PWM signal with a duty cycle, , about 20%

and a very low switching frequencyf(1Hz) in order to assure a

complete restart of phase for each cycle, because this setup

allows to increase the input voltage, then the current range is

also increased maintaining its rms value below its rated value.

Thus, the time /fmust be sufficiently high in order to assure

that the phase current reaches a high steady state value.

III. THEORETICAL BASISAs seen, the test methodology is based on the analysis of a

set of transient phenomena.

Thus, As well know, by application of the 2nd Kirchhoffs

law one obtains the following time-dependent equation for an

excited phase circuit:

( ) ( )( )t

ttiRtu

+= (1)

Fig. 3. Electric scheme per phase.

Considering the time t=0s for which both voltage and current

are null, and the iron is fully demagnetized, one can calculate

the phase linkage flux, at time t1, by using the following

expression [3,4]:

( ) ( ) ( )( ) =1

01

t

ttiRtut (2)

In stead of measure the phase resistance by means an

ohmmeter, and in order to take into account the resistance

variation with the winding temperature, it was considered for

the phase resistance the only value able to ensure the null value

of the linkage flux after demagnetization. Thus, considering the

same conditions fort=0s one obtains:

( ) ( )( ) =T

ttiRtu0

0 (3)

where T is the PWM signal period. Consequently one can

calculate the phase resistance by means of the following

relationship:

( )

( )

=T

T

tti

ttu

R

0

0 (4)

IV. EXPERIMENTAL RESULTSFirstly it should be reminded that only the positions between

X=0mm (non-alignment) and X=24mm (alignment) were

tested. The useful force was measured through a load cell, the

effort being applied at compression.

Fig. 4 to Fig. 9 shows some experimental results obtained.

Note that the useful force measured by means the load cell

corresponds to the electromagnetic force generated by the

machine minus the inertia and friction opposite force.

Fig. 4. End phase waveforms for X=6mm.


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It should be also noted that, in Fig. 5 to Fig. 9, the

waveforms correspond always to the same quantities,

expressed in the squared meaning legend of Fig. 4.



Fig. 7. Central phase waveforms for X=6mm.



Fig. 10 to Fig. 12 show the obtained results concerning

linkage flux namely its dependence on the position and phase

current. The linkage flux of both phases can be also compared

by means of Fig. 12.

Fig. 13 to Fig. 15 show the obtained results concerning the

useful force. Note that the inertia and friction opposite force

was experimentally evaluated, being approximately 40N.

Fig. 10. End phase linkage flux [Wb] versus relative position and current.

Fig. 11. Central phase linkage flux [Wb] versus relative position and current.


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Fig. 12. Linkage flux difference between phases [Wb] versus relative position

and current.

Fig. 13. End phase useful force [N] versus relative position and current.

Fig. 14. Central phase useful force [N] versus relative position and current.

Fig. 15. Useful force difference between phases [N] versus relative positionand current.

By analysing the experimental results, one can conclude the

following: The voltage, current, useful traction force and linkageflux waveforms for both tested phases present the

expected theoretical shapes, as can be concluded from

Fig. 4 to Fig. 9. It should be noted that the control mode

used for both rotating and linear switched reluctance

machines is similar, the difference being the position

coordinate, i.e. respectively the angular and the linear

displacement.

As can be seen in Fig. 10 and Fig. 11, the linkage flux for both tested phases present also the expected theoretical

tendency.

Based on the abacus of Fig.12, one can conclude that thedifference between the fluxes linked to both phases isminimum when compared with the respective obtained

absolute values. Moreover, this difference shows positive

and negative values leading to the conclusion that this

small difference has random causes.

The difference between developed forces associated to both phases is also minimum, taking as reference the

measured absolute values, as can be observed in Fig. 13

to Fig. 15. As for the flux, that difference shows

randomly positive and negative values, that is, in the

practice the forces developed by both phases are similar.

Based on the comparison between phases, concerning both the linkage flux and traction force, shown

respectively in Fig. 12 and Fig. 16, one can observe thatthe machine performance is the same for all phases, then

there are not magnetic longitudinal end effects.

V. CONCLUSIONSConcerning the proposed methodology used in the LSRM

experimental characterization, by combining the use of a low

value for the supply voltage, a low switching frequency, and a


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low value for the duty cycle, one can achieve the following

objectives:

To obtain a high value for the peak current. To reduce the rms value of the phase current. To increase sufficiently the powering period in order to

allows that the current can reach its steady state.

To obtain a higher number of points for a better definitionof the magnetization curve.

By considering the power supply circuit topology, takinginto account that both switches are turned off at the time T, by

applying a reverse supply voltage to the phase a complete

demagnetization is performed between T and the current

extinction.

This work corroborates the design methodology proposed by

the authors in previous works [2,5].

Finally, according to the authors opinion, the linear

switched reluctance machines will represent, in a near future,

an enormous success in the field of electromechanical drives

for railway electric traction applications, because of their

excellent performance characteristics allied to low production

costs, and high reliability and robustness.

ACKNOWLEDGMENT

The authors gratefully acknowledge the University of Beira

Interior and the Centro de Accionamentos e Sistemas

Elctricos da Fundao para a Cincia e a Tecnologia of

Portugal.

REFERENCES

[1] D. S. B. Fonseca, C. P. Cabrita, M. R. A. Calado, Linear SwitchedReluctance Motor. A New Topology for Fault Tolerant TractionApplications, Proceedings of the 2005 IEEE International ElectricMachines and Drives Conference IEMDC2005, pp. 823-827, May 15-18, 2005, San Antonio, Texas, USA.

[2] D. S. B. Fonseca, C. P. Cabrita, M. R. A. Calado, A New and FastDesign Methodology for a New Linear Switched Reluctance Motortaking Performance Evaluation and Path Arrangements into account,

Proceedings of the ICEM 2006 XVII International Conference onElectrical Machines , Paper No. 208, September 2-5, 2006, Chania, CreteIsland, Greece.

[3] T.J.E. Miller, Switched Reluctance Motors and their Control OxfordUniversity Press, Oxford, United Kingdom, 1993.

[4] C. Cossar and T.J.E. Miller, Electromagnetic Testing of SwitchedReluctance Motors, Proceedings of the International Conference on

Electrical Machines ICEM92, pp. 470-474, September 14-17, 1992,Manchester, UK.

[5] D. S. B. Fonseca, C. P. Cabrita, M. R. A. Calado, A Prototype of aLinear Switched Reluctance Motor with a New Design Methodology, WSEAS Transaction on Power Systems, Vol. 3, No. 3, pp. 95-102, March2008.

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Theoretical and Experimental Forces for a New Linear Switched Reluctance Traction Motor