research article low frequency axial flux linear...

Research ArticleLow Frequency Axial Flux Linear Oscillating Electric DriveSuitable for Short Strokes

Govindaraj Thangavel

Department of Electrical amp Electronics Engineering Muthayammal Engineering College Rasipuram 637 408 India

Correspondence should be addressed to Govindaraj Thangavel govindarajthangavelgmailcom

Received 23 September 2013 Accepted 20 October 2013 Published 30 January 2014

Academic Editors M Hopkinson and R Newcomb

Copyright copy 2014 Govindaraj Thangavel This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The design analysis and control methodology of an energy efficient and high force to weight ratio rare earth N42 NdFeB basedpermanent magnet linear oscillating motor has been described For this axial flux machine the mover is consisting of Aluminiumstructure embedded with rare earth permanent magnets of high energy density Microcontroller based drive is developed forfrequency and thrust control of the machine Finite element method using FEMM is employed for analysis of various performanceparameters of machine The same parameters are also compared with the measured ones which yields a good agreement to theproposed design

1 Introduction

Permanent magnet linear oscillating motors (PMLOMs)are finding increased suitability for many applications [1ndash3] These motors require accurate oscillatingreciprocatingcharacteristics for high precision application Also the powerrequirements for these motors play an important role fromefficiency point of view The use of linear reluctance motorsis already studied [2] under alternating current and also withdirect current supply [3 4] The dc motors are having neg-ligible core losses and therefore show higher efficiency thanthe ac ones although the ac motors are employed in manyapplications [3]The ac motors are used in pumps andmanylinear actuators [5] The linear oscillating motors (LOMs)differ in terms and technologies as well as construction [3]from their rotating counterparts The motors with the smalloscillating frequency but high stroke length are used as ashuttle power drive for looms (in the textile industry) oras electric hammers In [1 3] the different applications forlow frequency operation are given In [6 7] magnetic fieldanalysis for tubular motors has been presented for mostly flatinductionmotors In [5 8 9] the field circuitmodels have alsobeen applied for simulation of dynamic characteristics of thetubular motors However the investigations did not includethe permanent magnet axial flux type linear oscillatingmotors (PMLOMs) The short stroke oscillators are mainly

applicable in water pumps These motors work relatively athigher frequenciesTheproposedmotor as given in this paperis suitable for short stroke and low frequency application from0 to 5HzThis machine has applicability for the developmentof heart pump with adjustable stroke frequency and thrustforce

In the present work the field calculations of the PMLOMsand their speed and thrust control techniques are presentedIn formulated motion and electrical circuit equations thecalculated parameters are used A PMLOM is a device whichdirectly uses the forces of attraction and repulsion between apermanentmagnet and an electromagnetThemain structureof the motor is shown in Figure 1 The proposed motorcan easily be powered and controlled by a small portablemicrocontroller based power system It has a high force-density high efficiency and smaller size and weight Itcan satisfy the performance requirements with a variablestroke volume and beat rate control Suitable simulations andexperiments validate the proposed concept

2 Permanent Magnet Linear OscillatingMotor (PMLOM)

21 Principle of Oscillating Motion PM attractionrepulsiontype linear motor is shown in Figure 1 from which it follows

Hindawi Publishing CorporationISRN ElectronicsVolume 2014 Article ID 765161 5 pageshttpdxdoiorg1011552014765161

2 ISRN Electronics

+

+

+

+

Mover

N

L

H

Stator 1 Stator 2

S N S

N SN S

N S N S S

N S

S

S

S

S

S

S SN S

a c

b d

Linearoscillation

FA FR

g

Linearbush

ShaftdD

Lm

a998400

b998400

c998400

d998400

Figure 1 Principle of operation of the PMLOM attraction force andrepulsion force

that the motor is a controlled magnet system and has avariable axial airgap Several topological variations of theelectromagnetic structures are feasible The proposed motorhas a cylindrical structure with two stators each having twoslot-embedded coils (coil 1 in stator 1 consists of coils aa1015840 andbb1015840 and coil 2 in stator 2 consists of coils cc1015840 and dd1015840) and amover with ring type rare earth permanent magnets For therelative polarities of the currents in the various coils it may bereadily verified that there will be an attraction force betweencoil 1 and the permanent magnets and a repulsion forcebetween coil 2 and the permanent magnets Thus the moverwill tend to move to the left At the end of the stroke thepolarities of the currents in coils 1 and 2 are simultaneouslyreversed This reversal changes the directions of the forces Arepulsion force now exists between coil 1 and the permanentmagnets and an attraction force exists between coil 2 andthe permanent magnets Consequently the mover tends tomove to the right At the end of the stroke the polaritiesof the currents in coils 1 and 2 are reversed again andgo on cyclically Hence sustained oscillations are obtainedPMLOMs are based on several phenomenaThe fundamentalis the change in magnetic energy with the mover movementThe energy is maximumwhen the mover is situated nearer toany one of the statorsWhen it is moved away from the statorenergy is lower The energy changing produces the magneticforce which results in the oscillating motion of the mover

3 Performance Analysis of PMLOM

31 Attraction Force Using the model and dimensions asgiven in Figure 1 the inductance of the exciting coil can bewritten as

119871 =120595

119868=12058301198732119909120587119889

2119892 (1)

where 120595 is flux linkage 119873 is number of turns 1205830= 4120587 times

10minus7Hm 119889 is diameter of the mover 119868 is current in exciting

coil 119892 is axial airgap length and 119909 is displacement of themover at any point of time

From Amperersquos law neglecting the reluctance drop in theiron the main flux density in the airgap is determined by themagnetic circuit analysis of the permanent magnet and theelectromagnet When the polarities are opposite the MMFsof primary coil and secondary PM assist each other butwhen the polarity is the same the MMfs of primary coil andsecondary PM oppose each other Knowing coil inductance 119871from (1) the force in terms of coil current 119868 and the variationof the inductance 119871 with the position 119909 are given by

119865119860=1

21198682 119889119871 (119909)

119889119909=120583011987321198682120587119889

4119892 (2)

It may also be shown from the basic electromagnetic fieldequations that the energy119882

119898stored in the airgap is given by

119882119898=

1198612

119892

21205830

2119892119909120587119889 (3)

where 119861119892is airgap flux density

The electromagnetic force is obtained from

119865 =120597119882119898

120597119909=

1198612

119892

21205830

2119892120587119889 (4)

In these machines the flux density 119861119892 can be increased

to 1 tesla without saturating the core in which case the forcedensity becomes 4 times 105Nm2

32 Repulsion Force Now considering the repulsion forcewe have the polarities of the currents reversed The fluxesin the airgap are predominately radial Qualitatively it maybe seen from Figure 1 that we now have a force of repulsionbetween the coil and the permanent magnets For a smallairgap and for a uniform flux density in the airgap a simplemagnetic circuit approach yields the magnetic stored energy

From Amperersquos law neglecting the reluctance drop in theiron the flux density of coil is related to the potential (MMF)by

119861119864= 1205830119867119864=1205830119873119868

119867 + 2119892

119867119864=119873119868

119867 + 2119892

(5)

ISRN Electronics 3

(a)

Den

sity

plot

|B| (

Tesla

)

1343e + 000 1418e + 0001269e + 000 1343e + 0001194e + 000 1269e + 0001119e + 000 1194e + 0001045e + 000 1119e + 0009702e minus 001 1045e + 0008956e minus 001 9702e minus 0018210 e minus 001 8956e minus 0017464e minus 001 8210e minus 0016718e minus 001 7464e minus 0015972ee minus 001 6718e minus 0015225e minus 001 5972e minus 0014479e minus 001 5225e minus 0013733e minus 001 4479e minus 0012987e minus 001 3733e minus 0012241e minus 001 2987e minus 0011495e minus 001 2241e minus 0017490e minus 002 1495e minus 001lt2912e minus 004 7490e minus 002

1418e + 000 gt1492e + 000

(b)

Figure 2 (a) Finite element mesh of PMLOMwhile mover is oscillating with in stator 1 (b) Magnetic flux plotting of PMLOMwhile moveris oscillating with in stator 1 at 1 Hz

where 119867119864is magnetic field intensity along radial direction

and 119861119864is flux density along radial direction Referring to

Figure 1 119861119864 120601119864 120595119864 and 119871

119864can be obtained as

120601119864= 119861119864120587119889 (119897119904minus 119909) =1205830119873119868120587119889 (119897

119904minus 119909)

119867 + 2119892

120595119864= 119873120601

119864

119871119864=120595119864

119868= 12058301198732120587119889 (119897119904minus 119909)

119867 + 2119892

(6)

where 120601119864

is magnetic flux along radial direction 120595119864

ismagnetic flux linkage along radial direction 119871

119864is inductance

along radial direction 119897119904is stroke length and 119867 is thickness

of moverThe above expression may be combined to give the

repulsion force 119865119877in terms of 119868 and the variation of 119871

119864with

119909 as

119865119877=1

21198682 120597119871119864

120597119909=1205830

2(119873119868)2 120587119889

119867 + 2119892 (7)

The repulsion force 119865119877will assist the attractive force 119865

119860as

shown in the Figures 2(a) and 2(b) Then combining (2) and(7) the total force 119865

119905becomes

119865119905= 119865119860+ 119865119877=1205830

2(119873119868)2120587119889(1

2 119892+1

119867 + 2119892) (8)

4 Magnetic Field Analysis Simulation

The proposed model was analyzed through FEMM environ-ment which provides the analysis through finite elementmethod The inductance of the stator at different frequencyis calculated from the analysis The magnetic flux density atthe mover exciting winding and airgap region are calculatedwith FEM method The calculation process involves themodeling of the geometry setting boundary conditions and

Table 1 PMLOM parameters

Rated input voltage 70VRated input power 175wattsStroke length 10mmOuter diameter (stator) 93mm

Stator core type Cold rolled grain orientedsilicon steel

Thickness of lamination 027mmStator length 30mmNumber of turns in coils aa1015840 and cc1015840 500Number of turns in coils bb1015840 and dd1015840 250Coil resistance 142 ohmsSlot depth 17mmMagnet type Rare earth N42 NdFeBPermanent magnet length 2mmCoercivity 975000AmRemanence 12 TOuter diameter (mover) 65mmShaft diameter 8mmCoil inductance 018 Henry

domain properties generating the finite element mesh andcalculating the internal parameter at different frequency aswell as at different displacement Thus after including themain dimensions of the machine (Figure 1) the physicalproperties of materials under investigation have been givenThe correspondingmesh andplot of flux lines for themachinewith the mover position are shown in Figures 2(a) and 2(b)respectively

The simulation was done with dimensions and parame-ters of the same machine taken for experiment The parame-ters are given in Table 1

4 ISRN Electronics

Triac

R1

Rg

230V50HzAC Diac

D1

D2

D3

D4

C1

C2

T1

T2

T3

T4

Thrust control

Gate pulse

Gate drive

PIC 16FA877microcontroller

Frequency control

Statorof

PMLOM

Figure 3 Power circuit of PMLOM

Figure 4 Current waveform of PMLOM taken from Tektronixmake Storage oscilloscope

5 Experimental Results

The machine was given a variable voltage as shown inFigure 3 The input to the motor is through an IGBT basedinverter whose gate drive is controlled by a PIC16F877Adigital microcontroller The output of the PIC processor isfed to a gate driver which ultimately supplies the gatingsignals The stroke frequency can be controlled through themicroprocessor whereas the thrust force can be controlledby a phase angle controller through a triac The inputcurrent waveform is taken through a Tektronix make Storageoscilloscope and shown in Figure 4 for 2Amps 50 Voltssupply at 5HzThe forcemeasurement is done through a forcetransducer and then compared with theoretical values Theaxial airgap length versus total force from (8) is shown inFigure 5Themeasured current versus power inwatts voltage

Tota

l for

ce (N

)

Airgap (mm)

30

25

20

15

10

5

00 01 12 23 34 5 6 7 6 5 4

Figure 5 Airgap versus total force resultant of oscillating mover ofPMLOM

160

140

120

100

80

60

40

20

0

16 22 25 27

Power

Voltage

Force

Current (A)

Pow

er (W

) vo

ltage

(V)

forc

e (N

)

Figure 6 Measured coil current versus power (W) Voltage (V) andForce (N) characteristics of PMLOM

in volts and force inNewton at 1Hz frequency characteristicsis plotted and shown in Figure 6

6 Conclusion

Analytical solution to the forces and determination methodof the integral parameters of a PMLOM are presented Finiteelement method with FEMM42 is used for the field analysisof the different values of the exciting current and for variablemover position Computer simulations for the magnetic fielddistribution and forces are given To obtain experimentallythe field distribution and its integral parameters a physicalmodel of the motor together with its electronic controllersystem has been developed and tested The prototype hasbeen operated in the oscillatory mode with small loads atlow frequency up to 5Hz The theoretically calculated resultsare compared with the measured ones and found a goodconformity

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

ISRN Electronics 5

References

[1] I Boldea and S A Nasar Linear Motion ElectromagneticSystems Wiley New York NY USA 1985

[2] E A Mendrela ldquoComparison of the performance of a linearreluctance oscillating motor operating under AC supply withone underDC supplyrdquo IEEETransactions on Energy Conversionvol 14 no 3 pp 328ndash332 1999

[3] S A Nasar and I Boldea Linear Electric Motors Prentice-HallEnglewood Cliffs NJ USA 1987

[4] B Tomczuk and M Sobol ldquoInfluence of the supply voltageon the dynamics of the one-phase tubular motor with reversalmotionrdquo in Proceedings of the 39th International SymposiumElectrical Machines (SME rsquo2003) pp 417ndash426 GdanskJurataPoland June 2003

[5] N Sadowski R Carlson A M Beckert and J P A BastosldquoDynamic modeling of a newly designed linear actuator using3Dedge elements analysisrdquo IEEETransactions onMagnetics vol32 no 3 pp 1633ndash1636 1996

[6] M Rizzo ldquo3-D finite element analysis of a linear reluctancemotor by using difference scalar potentialrdquo IEEE Transactionson Magnetics vol 32 no 3 pp 1533ndash1536 1996

[7] B Tomczuk andM Sobol ldquoAnalysis of tubular linear reluctancemotor (TLRM) under various voltage supplyingrdquo in Proceedingsof the 16 International Conference on Electrical Machines (ICEMrsquo04) vol 3 pp 1099ndash1100 Cracow Poland September 2004

[8] L Nowak ldquoDynamic FE analysis of quasiaxisymmetrical elec-tromechanical convertersrdquo IEEE Transactions onMagnetics vol30 no 5 pp 3268ndash3271 1994

[9] B Tomczuk ldquoThree-dimensional leakage reactance calculationand magnetic field analysis for unbounded problemsrdquo IEEETransactions on Magnetics vol 28 no 4 pp 1935ndash1940 1992

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation



DistributedSensor Networks


2 ISRN Electronics

+

+

+

+

Mover

N

L

H

Stator 1 Stator 2

S N S

N SN S

N S N S S

N S

S

S

S

S

S

S SN S

a c

b d

Linearoscillation

FA FR

g

Linearbush

ShaftdD

Lm

a998400

b998400

c998400

d998400

Figure 1 Principle of operation of the PMLOM attraction force andrepulsion force

that the motor is a controlled magnet system and has avariable axial airgap Several topological variations of theelectromagnetic structures are feasible The proposed motorhas a cylindrical structure with two stators each having twoslot-embedded coils (coil 1 in stator 1 consists of coils aa1015840 andbb1015840 and coil 2 in stator 2 consists of coils cc1015840 and dd1015840) and amover with ring type rare earth permanent magnets For therelative polarities of the currents in the various coils it may bereadily verified that there will be an attraction force betweencoil 1 and the permanent magnets and a repulsion forcebetween coil 2 and the permanent magnets Thus the moverwill tend to move to the left At the end of the stroke thepolarities of the currents in coils 1 and 2 are simultaneouslyreversed This reversal changes the directions of the forces Arepulsion force now exists between coil 1 and the permanentmagnets and an attraction force exists between coil 2 andthe permanent magnets Consequently the mover tends tomove to the right At the end of the stroke the polaritiesof the currents in coils 1 and 2 are reversed again andgo on cyclically Hence sustained oscillations are obtainedPMLOMs are based on several phenomenaThe fundamentalis the change in magnetic energy with the mover movementThe energy is maximumwhen the mover is situated nearer toany one of the statorsWhen it is moved away from the statorenergy is lower The energy changing produces the magneticforce which results in the oscillating motion of the mover

3 Performance Analysis of PMLOM

31 Attraction Force Using the model and dimensions asgiven in Figure 1 the inductance of the exciting coil can bewritten as

119871 =120595

119868=12058301198732119909120587119889

2119892 (1)

where 120595 is flux linkage 119873 is number of turns 1205830= 4120587 times

10minus7Hm 119889 is diameter of the mover 119868 is current in exciting

coil 119892 is axial airgap length and 119909 is displacement of themover at any point of time

From Amperersquos law neglecting the reluctance drop in theiron the main flux density in the airgap is determined by themagnetic circuit analysis of the permanent magnet and theelectromagnet When the polarities are opposite the MMFsof primary coil and secondary PM assist each other butwhen the polarity is the same the MMfs of primary coil andsecondary PM oppose each other Knowing coil inductance 119871from (1) the force in terms of coil current 119868 and the variationof the inductance 119871 with the position 119909 are given by

119865119860=1

21198682 119889119871 (119909)

119889119909=120583011987321198682120587119889

4119892 (2)

It may also be shown from the basic electromagnetic fieldequations that the energy119882

119898stored in the airgap is given by

119882119898=

1198612

119892

21205830

2119892119909120587119889 (3)

where 119861119892is airgap flux density

The electromagnetic force is obtained from

119865 =120597119882119898

120597119909=

1198612

119892

21205830

2119892120587119889 (4)

In these machines the flux density 119861119892 can be increased

to 1 tesla without saturating the core in which case the forcedensity becomes 4 times 105Nm2

32 Repulsion Force Now considering the repulsion forcewe have the polarities of the currents reversed The fluxesin the airgap are predominately radial Qualitatively it maybe seen from Figure 1 that we now have a force of repulsionbetween the coil and the permanent magnets For a smallairgap and for a uniform flux density in the airgap a simplemagnetic circuit approach yields the magnetic stored energy

From Amperersquos law neglecting the reluctance drop in theiron the flux density of coil is related to the potential (MMF)by

119861119864= 1205830119867119864=1205830119873119868

119867 + 2119892

119867119864=119873119868

119867 + 2119892

(5)

ISRN Electronics 3

(a)

Den

sity

plot

|B| (

Tesla

)


1418e + 000 gt1492e + 000

(b)




Figure 1 119861119864 120601119864 120595119864 and 119871


120601119864= 119861119864120587119889 (119897119904minus 119909) =1205830119873119868120587119889 (119897

119904minus 119909)

119867 + 2119892

120595119864= 119873120601

119864

119871119864=120595119864

119868= 12058301198732120587119889 (119897119904minus 119909)

119867 + 2119892

(6)

where 120601119864



119864is inductance




119864with

119909 as

119865119877=1

21198682 120597119871119864

120597119909=1205830

2(119873119868)2 120587119889

119867 + 2119892 (7)


119860as


119905becomes

119865119905= 119865119860+ 119865119877=1205830

2(119873119868)2120587119889(1

2 119892+1

119867 + 2119892) (8)









4 ISRN Electronics

Triac

R1

Rg

230V50HzAC Diac

D1

D2

D3

D4

C1

C2

T1

T2

T3

T4

Thrust control

Gate pulse

Gate drive


Frequency control

Statorof

PMLOM





Tota

l for

ce (N

)

Airgap (mm)

30

25

20

15

10

5

00 01 12 23 34 5 6 7 6 5 4


160

140

120

100

80

60

40

20

0

16 22 25 27

Power

Voltage

Force

Current (A)

Pow

er (W

) vo

ltage

(V)

forc

e (N

)



6 Conclusion




ISRN Electronics 5

References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Electronics 3

(a)

Den

sity

plot

|B| (

Tesla

)


1418e + 000 gt1492e + 000

(b)




Figure 1 119861119864 120601119864 120595119864 and 119871


120601119864= 119861119864120587119889 (119897119904minus 119909) =1205830119873119868120587119889 (119897

119904minus 119909)

119867 + 2119892

120595119864= 119873120601

119864

119871119864=120595119864

119868= 12058301198732120587119889 (119897119904minus 119909)

119867 + 2119892

(6)

where 120601119864



119864is inductance




119864with

119909 as

119865119877=1

21198682 120597119871119864

120597119909=1205830

2(119873119868)2 120587119889

119867 + 2119892 (7)


119860as


119905becomes

119865119905= 119865119860+ 119865119877=1205830

2(119873119868)2120587119889(1

2 119892+1

119867 + 2119892) (8)









4 ISRN Electronics

Triac

R1

Rg

230V50HzAC Diac

D1

D2

D3

D4

C1

C2

T1

T2

T3

T4

Thrust control

Gate pulse

Gate drive


Frequency control

Statorof

PMLOM





Tota

l for

ce (N

)

Airgap (mm)

30

25

20

15

10

5

00 01 12 23 34 5 6 7 6 5 4


160

140

120

100

80

60

40

20

0

16 22 25 27

Power

Voltage

Force

Current (A)

Pow

er (W

) vo

ltage

(V)

forc

e (N

)



6 Conclusion




ISRN Electronics 5

References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









4 ISRN Electronics

Triac

R1

Rg

230V50HzAC Diac

D1

D2

D3

D4

C1

C2

T1

T2

T3

T4

Thrust control

Gate pulse

Gate drive


Frequency control

Statorof

PMLOM





Tota

l for

ce (N

)

Airgap (mm)

30

25

20

15

10

5

00 01 12 23 34 5 6 7 6 5 4


160

140

120

100

80

60

40

20

0

16 22 25 27

Power

Voltage

Force

Current (A)

Pow

er (W

) vo

ltage

(V)

forc

e (N

)



6 Conclusion




ISRN Electronics 5

References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Electronics 5

References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article low frequency axial flux linear...

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