Design, analysis and fabrication of linearpermanent magnet synchronous machine

Monojit SealDept. of Electrical Engineering,

IIEST, Shibpur, Howrah - 711103W.B., India.

email: seal.monojit@gmail.com

Mainak SenguptaDept. Electrical Engineering,

IIEST, Shibpur, Howrah - 711103,W.B., India.

email: mainak.sengupta@gmail.com

Abstract—This paper deals with design, analysis andfabrication of 320 W, 5 m/s, 4-pole permanent magnet basedlinear synchronous machine (LPMSM). The design dealswith rigorous hand calculations, analysis using standardFEM packages and fabrication of the machine at the worksof a local small machine manufacturer after procurementof imported PMs. The same will be used in a linear motordrive development research.

Index Terms—Linear permanent magnet synchronousmachine, LPMSM, design optimisation, finite elementmethod.

I. INTRODUCTION

Linear motors have been the subject of research anddevelopment for over 100 years. Though presently onlya few of such companies are known to supply linearmotors across the world ( [1], [2]). However, with theincrease in cost of energy since 1970’s, recent trendsare focusing towards use of energy efficient drives. Theavailability of permanent magnets (PM) with consider-able energy density and the advent of power electronicconverters with digital controllers led to the developmentof energy efficient drive with precision in motion con-trol. Fig.1 shows how the linear AC machines can becategorized [3].

Fig. 1. Hierarchy chart illustrating types of linear machines

The present paper deals with the fabrication of a shortprimary LSM. Compared to linear IM (LIM), where sta-

Fig. 2. Single sided flat PM LSMs with slotted armature core and (a)surface PMs, (b) buried PMs. 1 - PM, 2 - mild steel pole, 3 - yoke.

tor current provides both magnetising and thrust produc-ing component; in LPMSM, the PM produces the fieldflux the causing mainly the thrust producing componentof stator current to be drawn from supply. Since, thereis no copper loss in the rotor circuit (unlike LIM), forthe same output, LPMSM will operate at much higherpower factor and efficiency with consequent reduction insize and weight.

Primarily, two different types of construction are pos-sible for LPMSM. A cross-sectional view of the firsttype having PMs on the surface as shown in Fig.2(a) andthe other with PMs buried inside the mild steel pole asshown in Fig.2(b). In surface mounting arrangement ofLPMSM, the yoke (back iron) is made of ferromagneticmaterial and the direction of magnetisation of the PMsare perpendicular to the active surface. However, forburied LPMSM, the yoke is made of non-ferromagneticmaterial(e.g. aluminium) and the PMs are magnetised inthe direction of travelling magnetic field [4].

II. BASIC PRINCIPLES

In a PMSM the DC-field is obtained from permanentmagnets (PM) instead of DC-exited electromagnets. Inthe present work the DC-field system is kept static whilethe 3-phase armature has been made the ’linor’ (moving

member). A linear synchronous motor (LSM) is a variantof the conventional synchronous motor in which themechanical speed is the same as the speed of the linearlytravelling magnetic field. Hence, the thrust (propulsionforce) can be generated as an action of

• travelling magnetic field produced by a balancedpolyphase winding energised from a balancedpolyphase supply.

• magnetic field produced by electronically switchedd.c. windings

The part producing the travelling magnetic field is calledarmature (or forcer). For PM machines, the difficultyremains in the design of the PM of minimum volumeand at the same time preventing demagnetisation of thePMs. In the following sections, the design of LPMSMhas been presented ( [4]–[8]).

III. DESIGN AND ANALYSIS OF LPMSM

A. Initial specification and selection of main dimensions

The nominal specifications of the machine are givenin Table.I. An efficiency of η = 0.85 and fundamentalp.f. cosΦ = 0.9 have been taken as targeted perfor-mance indices. This gives efficiency-power factor prod-uct (η.cosΦ) as 0.765. The present prototype has beendeveloped using the existing lamination of the alreadymade developed LIM in our laboratory. This has anadvantage of reduction of overall cost since the majorcost involved is the cost of die and tooling of themachine.

Synchronous speed vs 5 m/sNumber of primary phases m1 3

Operating line voltage VL 100 VOperating frequency f 50 Hz

Number of poles P 4Rated power Pm 320 W

Air-gap length g 2 mm

TABLE ITARGETED SPECIFICATIONS OF THE LINEAR PMSM

B. Initial calculation steps

Following Table.I, one may find that the• Pole pitch (τ ) = 50 mm• Transverse length of primary (Lτ ) = 200 mmVolt-Ampere (VA) rating of the machine,

V A =Pm

η.cosφ= 418.3V A ' 420V A

No-load induced e.m.f. at rated speed as obtainedwhen excited by PMs (without armature reaction) is, Ef= 45V [4].

Rated primary current I1 is given by (assuming Y -connection),

I1 =V A√3.VL

=420√3.100

= 2.41A

Therefore, VA transferred across air-gap (Selm), is325.86 VA. The pitch factor (kp1) is 1. Distribution factor(kd1) is given by,

kd1 =sin[

∏/2.m1]

qs.sin[∏/2.m1.qs]

sin(∏

/2.wcτ

) = 1

Winding factor (kw1) = kp1 X kd1 = 1 and flux per poleis found to be, Φm = 0.8 mWb.

After repeated iterations and considering appropriatedesign constraints, the following values are obtainedshown in Table II. Designing the effective length ofarmature magnet (Li) is a little involved as it considers:-

1) Designing of high density machine for reducingthe cost of magnet.

2) Prevent demagnetisation of the magnets.3) Cheap availability of magnets of standard size.

After iterations, the value of Li is obtained as 36 mmand it matches well with our requirements.

Design parameter ValueSpecific magnetic loading Bav (T) 0.445

Magnitude of transverseline current, Amy (Ac/m) 25862Bmz.Amy product (TA/m) 18103

Output co-efficient, σp (VAs/m3) 9052

TABLE IIOBTAINED VALUES OF Bmz , Amy , Bmz .Amy AND σp

C. Determination of Magnet size

Determination of PM size is most critical to theentire design exercise. Designing of permanent magnetinvolves considering the effect of demagnetisation ATsand availability of appropriate magnet. An optimumdesign will ensure reduced cost. However, at the sametime for lagging load currents the PMs should not getdemagnetised beyond the allowed limit. The magnethas been designed considering the average air-gap fluxdensity, Bav = 0.445 T. Applying Ampere’s circuitallaw to the closed flux line in Fig.3, we have the totalampere-turns required in the magnetic circuit is nearly1960 AT (considering B-H characteristics of NdFeB, N-35 at temperature 1000C). Leakage and fringing flux areneglected [9].

So, magnet thickness is given by,

lm =TotalAT

Hm= 5.774mm ' 6mm

Fig. 3. LPMSM magnetic circuit

The dimensions of the procured magnetic tablet is12mm X 12mm X 3mm, orientation is along thicknessof 3mm.

D. Selection of turn per phase

The transverse current density, Amy is 25862 A/m.We have,

Amy =2√

2m1I1N1

τP(1)

where, N1 is number of primary turns/phase.Here, total number of slots (z1) and slots per pole per

phase (qs) are 12 and 1 respectively. Solving (1), N1 isnearly 254 which gives number of conductors/phase/slot(Nsl) as 127. Current density of primary conductors (J1)is assumed as 6 A/mm2, which gives diameter of theconductor (d) as 0.813 mm (corresponding to SWG 21).

E. Estimation of Electrical Parameters

TABLE IIICALCULATED VALUES OF ELECTRICAL PARAMETERS OF LPMSM

Electrical parameters (per phase) ValuesLength of mean turn (Lmt) 0.267 m

Primary resistance (r1) 3.52 ΩSlot leakage reactance (X1l) 2.13 Ω

Overhang leakage reactance (X1ov) 1.20 ΩDifferential leakage reactance (X1d) 11.48 Ω

Armature reactance (Xa) 11.47 ΩPrimary leakage reactance (X1)

(= X1l + X1ov + X1d) 14.81 Ω

F. Winding arrangement

Slot per pole per phase =12

4× 3= 1. A double layer

full-pitched winding consideration is used.

Coil span =No.ofslots

No.ofpoles=

12

4= 3.

(a) Double layer winding arrangement

(b) Winding arrangement for the one phase of LPMSM. SA is the startingend and FA is the finishing end.

Fig. 4.

The double layer winding arrangement in the respec-tive slots and the winding chart for one phase is shownin (Fig.4(a)) and (Fig.4(b)) respectively.

G. Calculation and design validation using standardFEM packages

The LPMSM is analysed using standard FEM pack-age. The no-load induced e.m.f. at rated speed obtainedwhen excited by PMs (without armature reaction) of thethree respective phases is shown in Fig.5(a). The inducede.m.f. reads 50 V which is with corelation with thehand-calculated value of 46 V. The flux linkages of thethree phases are shown in Fig.5(b). The relation betweeninduced e.m.f. and flux linkage and of the same phaseis shown in Fig.5(c). It is clearly seen that the inducede.m.f. is leading the flux linkage by 90o. The magneticfield density and the flux lines at 1ms at a distanceof 5mm from initial position is shown in Fig.6(a) andFig.6(b) respectively. The magnetic field in the air gaphas a maximum value of 0.8T which is in excellentcorelation with the calculated value. The overall designdata sheet of the above 320 W, 4 pole, 3-φ, rated speedof 5 m/s LPMSM is shown in Table.IV.

H. Fabrication of LPMSM

The designed LPMSM at the works of a local smallmachine manufacturer after procurement of importedPMs. Fig.7(a) and fig.7(b) shows armature stampings andSS-short primary of the LPMSM after winding arrange-ment. The procured magnet dimensions are shown infig.7(c). The dimensions of the procured magnetic tabletis 12mm X 12mm X 3mm, orientation is along thicknessof 3mm.

(a) Three phase no-load induced e.m.f. in the air-gap at rated speed of 5 m/s whenexcited by PMs

(b) Three phase flux linkage of the LPMSM at rated speed of 5 m/s

(c) Variation of flux linkage and induced voltage of Phase A

Fig. 5.

Fig.8(a) shows the diagram of the yoke. Here, alldimensions are measured in ’mm’. A provision hasbeen made for starting the motor as LIM first and thenswitching to LPMSM. Fig.8(b) shows the wooden baseover which the back-iron, magnet and aluminium willbe placed.

IV. CONCLUSIONS

In this paper design and fabrication of a 3-Φ, 4 pole,320 W, 5 m/s surface mounted LPMSM has been done.For ease of fabrication and for cost reduction the designstarts with the available stampings used previously for

(a) Magnetic field density in air-gap, core, back-iron along with magnet at Position= 5 mm, Time = 0.001 sec from initial position

(b) Flux lines in air-gap, core, back-iron along with magnet at Position = 5 mm,Time = 0.001 sec from initial position

Fig. 6.

TABLE IVDESIGN DATA OF THE FABRICATED LPMSM

Design Data ValueNumber of coils 12

Number of turns per coil 65Wire diameter 0.813 mmTooth width 6.66 mmSlot width 10 mm

Length of armature (or linor/forcer) 200 mmMaterial of armature laminated steel

M-45 0.5 mm thickAir-gap 2 mm

PM material NdFeB, Br = 1.21 TPM height 3 mm

PM face area 144 mm2

fabrication of LIM which prototype exists in the labo-ratory ( [6], [10]). The design has been optimised andverified with the help of standard FEM packages. Thelinor has been fabricated and winding has been com-pleted. The yoke (track) is fabricated with NdFeB N-35grade permanent magnets. The fabricated LPMSM may

(a) Armature stamping of the LPMSM

(b) SS short primary of the LPMSM

(c) Dimension of unit NdFeB N-35 grade procured PMs

Fig. 7.

be used various advanced control speed drive for fastdynamic response and maximum reliability. Predictedvalues obtained from conventional analytical calculationsare validated through FEM packages at different condi-tions. The predicted values and the experimented valuesare found to be in excellent correlation with each other.

V. ACKNOWLEDGMENTS

The authors wish to thank COE (MDAMD), IIEST,Shibpur and TEQIP-II for their support. The authorsacknowledge Mr.Kaushik Pyne and the entire staff ofG.E. Motors for their technical support in fabricatingthe motor. The authors also acknowledge the supportreceived from the colleagues in the Advanced PowerElectronics Lab and particularly Mr. N. Dutta, Project

(a) Design of track (yoke) of the LPMSM. All dimensionsare in ’mm’.

(b) Wooden base for the yoke with PMs, Al sheet and back iron

Fig. 8.

Technical Assistant, APE Lab, Dept. of EE and theauthorities of IIEST, Shibpur towards this work.

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