Oscillatory synchronous linear motor withpermanent-magnet excitation

O. Roubieek, Ph.D., and Z. PejSek, M.Sc.

Indexing terms: Linear motors, Permanent magnets

Abstract: The paper describes the construction and principle of operation of a permanent-magnet-excitedlinear oscillatory motor. As part of an automated frequency adaptive drive, the motor is suitable for drivingsmaller resonance mechanisms.7 It points out the prerequisites for the use of permanent magnets in theconstruction of the motor and shows the advantages of the Alnico types of material. The demagnetisationeffect, which is controlled by shielding the magnets, is estimated. The magnets may be designed for thestandard operating mode. Finally, the components of the magnetic field of the motor are analysed and usedfor the determination of the main parameters of the magnetic circuit of the motor. The basis for the deter-mination and optimisation of the motor characteristics is given in the references to other papers by theauthors.

List of principal symbols

a, A = instantaneous, constant magnetic potentialB = constant magnetic flux density/ = instantaneous tractive forcee = double length of functional airgap/ = instantaneous tractive force

H = constant magnetic field intensity/ — instantaneous current

k = coefficient of magnetic potential drop/ = length

m,M = instantaneous, constant penetration of armatureinto stator

S = cross-sectiont = double thickness of ferromagnetic core

x, X = instantaneous, constant dynamic pathZ — height of pole piece

7?M ~ permanent-magnet surface efficiency (reciprocalof leakage factor)

A = permeanceHo = absolute permeability of vacuumra = 2-dimensional magnetic leakage coefficient

i//,<I> = instantaneous, constant magnetic flux

Subscripts

a = a.c. value, synchronisationb = bottom motor halfc = d.c. value, excitationd = dynamical of motion/ = alternativek = critical

m = amplitudemax = maximum

M — permanent magnetn = operating point0 = vacuum, airq = 1/4 of motoru = upper motor half

1 Introduction

The double-acting oscillatory synchronous linear motor ofsymmetrical design was originally developed in the current-

Paper 482B, first received 15th January and in revised form 8thAugust 1979Dr. Roubieek and Mr. Pejsek are with the Department of ElectricSystems of the Research Institute of Electrical Engineering (VUSE),2 5097 Praha 9-Bechovice, Czechoslovakia

excited version.1 4 For the region of lower tractive forces(up to 3 kN) and lower power ratings (up to 3 kW) thisbasic version may be improved using permanent-magnetexcitation (for the main principles see References 4—7).In comparison with the current-excited version this typeprovides a two or three times higher utilisation factor (upto a tractive force of 33 N per 1 kg of weight), is construc-tionally simpler, has a higher efficiency (by up to 15%),eliminates high-voltage induction in the exciting winding(up to several kV) and saves the exciting source. Alternativeversions can achieve a stroke of up to 5 cm, frequencies of6 to 70 Hz, and efficiency up to 0-9.

2 Principle of construction and operation of the motor

The magnetic circuit of the motor (Fig. 1) consists of astrip-iron column (1), two strip-iron pole pieces (2) and twocross-mounted permanent magnets (3). The armature isformed by strip-iron sections (4) carried by nonmagneticjumpers (5) fixed on a pullrod (6). The guideway of thearmature with respect to the stator is ensured by slidingbearings (7) or by slip springs (6). Sections 4 define longi-tudinal functional airgaps (8) between the column 1 andpole pieces 2, providing for strokes up to 5 cm. Column 1carries on both sides series-connected synchronisation-

time

Fig. 1 Construction scheme of the motor, with indicated positivedirections of the quantities

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winding coils (9) fed by the harmonic voltage va from thesource (10). Channels 11 improve the cooling. Both per-manent magnets (3) are provided with a shield winding(12)(one layer of profiled conductor) which may also beused for their magnetisation (or demagnetisation).

The effective airgap may be either direct or rotationallysymmetrical with respect to the longitudinal axis of themotor. In the first case, the motor will have two pull rods,in the second case only one.

The double-acting tractive effect of the motor1 isachieved by the orientation of the magnetic potential Ac

of the permanent magnets 3 and the magnetic voltage aa

due to the current flow in the synchronisation-windingcoils 9, as shown in Fig. 1:

aa = Naia (1)

where Na is the number of turns of the coil and ia theinstantaneous current. The tractive force is transmitted tothe driven mechanism by the feet (13) and eye (14).

When deriving the tractive effects of the motor, one maystart from the permeance of the air portion of a quarter ofthe magnetic circuit:

m

M' oq (2)

where TOQ is the coefficient of 2-dimensional magneticleakage in the vicinity of the functional airgaps, i.e.:

1Toq ~

e d

1 +10~2

2x 10 - 3

(3)

formulated on the basis of approximation coefficients.8

Allowing for an error of 20%, this coefficient can be usedwithin the interval Z>m>e/2. In eqn. 2, ju0 is the abso-lute permeability of vacuum and m the instantaneouspenetration of the armature into the stator; the remainingquantities are apparent from Fig. 1.

Neglecting the finite permeance of the passive ferro-magnetic parts, the instantaneous longitudinal tractiveforce of half of the motor will be

fl = ^j = u or b (4)

where a0 is the total instantaneous magnetic voltage acrossthe two effective airgaps (across the length e). For theupper and lower half of the motor, it evidently holds(Fig. 1) that

aou —

aob =

+aOa

—aOa

(5a)

(5 b)

where AOc and aOa are the magnetic voltages across the twoeffective airgaps, respectively, i.e. due to the permanentmagnet (AOc) and the current flow (see eqn. 1) in thesynchronisation-winding coil (aOa). The condition for thecorrect function of a symmetric motor is AOc>\aOa\(Reference 1).

IEEPROC, Vol. 127, Pt. B, No. 1, JANUAR Y1980

The resultant tractive force is equal to the differencebetween the tractive forces of the two halves1

= fu ~fb (6)

determined by eqn. 4 after substitution from eqns. 2 and5. Correcting the result for finite permeance of the passiveferromagnetic parts1 we obtain for the instantaneoustractive force of the complete motor the relation

t I ef = 2/io 7 U --)keckeaAcaa (7)

In this equation kF is a force constant; kec is the drop co-efficient of the permanent-magnet magnetic potential Ac

along the paths of the d.c. flux \pc (Fig. 1) in the passiveferromagnetic parts, and kda is the drop coefficient of themagnetic voltage aa due to the current flow in thesynchronisation-winding coil along the paths of the a.c.flux \pa in the passive ferromagnetic parts:1

AQC

Ac

an

(Sa)

(8b)

The coefficient given by eqn. 8b also takes into account theeffects of eddy currents in the passive ferromagnetic partsat higher frequencies.5'6

With a periodically varying current flow in the synchro-nisation winding,2'3'4 the form of the tractive force willalso be periodically varying with an amplitude proportionalto the current amplitude and with a frequency equal to thesource frequency (see eqn. 7).

3 Choice of permanent-magnet type

The choice is a compromise between three requirements:high motor utilisation factor, resistivity of the magnet todemagnetising effects and low magnet price. Magnets of theAlnico9'10 type of alloys are very satisfactory. TheCzechoslovak alloy Permag—OK 6064 used for thesemagnets gives a maximum energy product of 24—30 kJ/m3,a remanent flux density of 1-2—1-38 T and a coerciveforce of 51— 63kA/m. The disadvantage of the lowerresistance of this material to demagnetising effects iseliminated by the symmetrical design of the motor witha shielding winding on the magnets. Magnetisation mustbe secured with the motor assembled.

4 Motional demagnetising effects

The main magnetic flux of the permanent magnet passingthrough its face (Fig. 1) may be expressed, using eqn. l ,asthe sum of the partial fluxes in both halves of the motor

^c = 4>cb + ^cu (9)

Correcting for finite permeance of the d.c. flux path inthe passive ferromagnetic parts, we obtain

&CJ = A-Ogjk0cAc, j = u or b (10)

Substituting the obvious relations, including the instan-

9

taneous dynamic path x of the armature with respect tothe stator,

mu = M + x (lie)

mb = M-x {Ub)

for m in eqn. 2 we obtain from eqns. 10 and 9

(12)= noj 1 -^}kdcM(l+Toq)Ac = 4>c

Owing to the symmetrical design of the motor, the flux(eqn. 12) is theoretically constant, i.e. independent of theposition of the armature with respect to the stator. Theprerequisite is, however, the invariance of all terms in themiddle part of eqn. 12 with JC. With regard to the way i//cwas expressed in eqn. 9 from eqns. 10 and 11, this con-dition is satisfied by equal geometric parameters of bothhalves of the motor and by independence of Taq and kgc

from x. The coefficient raq may, in good agreement withreality, be assumed to be constant within the intervalZ > w > e / 2 , which usually is not exceeded during therunning of the motor. The only source of uncertainty isthe coefficient kQc, which depends on the permeance and,consequently, on the flux density of the passive ferro-magnetic parts.1 From eqns. 9 to 11 it follows that thisflux density varies with x. However, as long as the maxi-mum flux density in the passive ferromagnetic parts doesnot exceed 1-4T, the variations of kgc will not be sub-stantial because, owing to the d.c. magnetic biasing, themagnetisation characteristic of the above-mentionedferromagnetic parts is partially linearised.1

The positional dependence of the magnetic flux leakagefrom the permanent-magnet sides (Fig. 2) takes practicallyno part in the demagnetisation effect. A more generalformulation of this relationship is not possible. Specificcases may be checked by calculation and on the basis ofexperimental results.

10mm

to100°/«

ferromagnetic part

j7-525

75 permanent magnet 12 5

Fig. 2 Calculated permanent-magnet equipotential lines of themotor shown in Fig. 3a

*1M ~ 083 is in good agreement with measurement

5 Demagnetising effects of a.c. feeding

In consideration of the orientation of the synchronisationwinding coils (Fig. 1), and with regard to the low reversiblepermeability of the permanent magnet at the operatingpoint of its magnetisation curve (for Permag—OK 6064material this permeability amounts to about 3-5), theinteractions between the a.c. magnetic circuit and themagnets are negligible. This fact was verified experimentally.

6 Choice of the permanent-magnet operating mode

The total demagnetising effect on shield-protected per-manent magnets was investigated using several researchprototypes of the motor (Fig. 3). The results have shownthat, during operation, the amplitude of magnetic fluxfluctuation does not exceed 4—5% of the flux at rest (form=M, see Fig. 1) in any of the magnet cross-sectionstested. Under these circumstances, the permanent magnetmay be operated in the standard mode, using the par-ameters recommended by the manufacturer for the leastfavourable alternative of production deviations of themagnetisation curves9'10 (for Permag-OK 6064 these par-ameters are: flux density B^ — 1-05T and magnetic fieldintensity Hcn = 46 kA/m). Experience has shown that thecircuit parameter stability of the permanent magnets issatisfactory (Fig. 4).

Fig. 3 Research prototypes of the motor

a Power rating 0-1 kW, efficiency 0-83, stroke up to 1-4 cm, fre-quency 20 Hz, tractive force amplitude 400 N (Covers removed)

6 Power rating 1 kW, efficiency 0-72, stroke up to 1-6 cm, fre-quency 22 Hz, tractive force amplitude 2140 N (Absolute resonanceexciter of the mechanical oscillation)

10 IEEPROC, Vol. 127, Pt. B, No. 1, JANUARY 1980

7 Determination of main magnetic circuit parameters

For the required main magnetic flux <&cn the cross-sectionof the permanent magnet will be

03)

may be constructed:

where r}M is the surface efficiency (i.e. reciprocal of leakagefactor) of the magnet. The magnet length is

BOcl

Hcnket(14)

where BOc is the desired flux density in the effective airgapof the motor.

The value of r\M is checked by calculation and, if necess-ary, is iterated until agreement of assumptions with theresult is reached.

The cross-section of the passive ferromagnetic parts isdetermined with regard to maximum flux density in thecritical cross-sections, which should not exceed the optimumvalue of 14T (Reference 1). Fig. 1 shows, for simplicity,only the critical cross-section Skb of the bottom half of themotor.

In the critical cross-sections Sk, the d.c. magneticflux \pc (as given by eqn. 10) and the instantaneous a.c.magnetic flux \pa are present (Fig. 1). Along the path of theflux i//a, the parallel-connected permeance (2) of the upperand bottom half of the motor is coupled in series. Estab-lishing the relevant expressions, substituting for mu and mb

in the corresponding equations of the upper and bottommotor half, respectively, and rewriting and correcting forfinite permeance of the a.c. magnetic flux path in thepassive ferromagnetic parts, we obtain

(15)

The magnetic flux components in the critical cross-sectionswhen the motor is running must now be determined.

The motor, as part of a frequency-adaptive linear oscil-latory drive,3'4'5'11 is intended for driving resonancemechanisms.3'11 It operates automatically in electro-mechanical resonance11'12 with the practically harmonictime behaviour of the dynamic path x. If eqn. 10 isexpressed (e.g. for j = b) by means of eqn. l ie , where aharmonic function of time with the amplitude Xm hasbeen substituted for x, the following equations for thed.c. component <£cfe and the amplitude 4>cdmfe of the a.c.component of the flux \pc in the critical cross-sections

t 105

o 1OO<

? 95

x 90

oO o

O.nO OO00OO0OOOuu o

1 2 3 5 10 20 30 50 100 200time , days

Fig. 4 Measured stability of the flux density at rest, Boc, in thefunctional airgap of the motor shown in Fig. 3a, depending on thetime of its operation

= 2<$>cdmk = 2aq

(16)

(17)

The magnetic flux i//a of eqn. 15 has a harmonic wave-form whereas the waveform of aa is nonharmonic (inpractical cases, the harmonic distortion is usually small2lS).In the state of mechanical resonance11'12 the waveform ofthe dynamic path x will be phase-delayed by the angleTT/2 with respect to i//a, so that \pa will reach the amplitude<f>amft when x = 0 and aa = Aam.n From eqn. 15 we thenhave

and the maximum flux in the critical cross-sections willbe

<T> = 9cb , 4- -v/f4cl)2j L + cE>2 tS\ fl9^RttldX Cfe » V CCtTTlK QTntZs V '

According to the previously given principle, the followinginequality should hold:

kmax~ 1-4 '

j = u or b (20)

8 Motor characteristics and optimisation of parameters

The stationary characteristics (the load vector diagrams, thevector control characteristics and the internal controlcharacteristic), the dynamic equations and the blockdiagram can be derived from the relations valid for theversion excited by the current13'14'15 if the excitationcurrent flow 6C is substituted by the constant magneticvoltage Ac of the permanent magnet.

The optimisation method16 leading to the design ofthe motor with the minimum mass or minimum price canbe used in the same way.

500

400

300

200

•2 100

•t 005 10 15 20

synchronisation current amplitude lQm,A

Fig. 5 Tractive force characteristic of the motor shown in Fig. 3a

Fam = tractive-force amplitudeIam = synchronisation-current amplitudemeasured curve

calculated curve

IEE PROC, Vol. 127, Pt. B, No. 1, JANUAR Y1980 11

9 Prototypes of the motor

Several research prototypes have been constructed andtested (see, for example, Fig. 3). Test results have showna good agreement between the theoretical basis introducedin this paper and in other papers13"16 and the reality (see,for example, Fig. 4 and Fig. 5).

10 References

1 ROUBICEK, O.: 'Das elektromagnetische und Stromfeld desNiederfrequenz-Synchronmotors mit Translationsbewegung mitgrosser Bahnamplitude', Acta Tech. CSA V, 1970, 15, pp. 425-460

2 ROUBICEK, O.: 'Controlled low-frequency linear oscillatorydrives', Electr. Rev., 1972, 190, pp. 727-729

3 ROUBICEK,O.: 'Elektrisches regelbares Neiderfrequenz-Antriebs-system mit Synchron-Linearmotor', VDI Z., 1971, 113, pp.1082-1088

4 ROUBICEK, O.: 'Contribution of the Czechoslovak research tothe development of linear electrical controlled drives'. IEE Conf.Publ. 120, 1974, pp. 31-38.

5 PEJ§EK, Z.: 'Prumyslovy autooscila^ni linearni pohon (Auto-oscillatory linear drive for industrial applications)', Elektrotech.Obz., 1975, 64, pp. 673-678

6 ROUBiCEK, O., HAJEK, M., and PEJSEK, Z.: 'Novye sposobysoobshcheniya energii processam peremeshcheniya materialovi obrabotki gornykh porod i ikh perspektivy (New methods of

energy transfer in material transport and rock processing andtheir prospects)'. Paper 4B45, presented at the World Electro-technical Congress (WELC), Moscow, June 1977

7 ROUBICEK, O.: 'Linearantriebe fiir Industriezwecke', Electro-tech. Z. ETZB, 1977, 29, pp. 518-521

8 RICHTER, R.: 'Elektrische Maschinen I' (Springer, Berlin, 1924)9 REINBOTH, H.: 'Technologie und Anwendung magnetischer

Werkstoffe' (Technik, Berlin, 1970)10 PARKER, R.: 'Permanent magnets and their applications' (Wiley,

New York, 1962)11 ROUBICEK, O., HOLAN, J. and JOHN, J.: 'Progress in the field

of less common electrical controlled linear drives'. Proceedingsof the first IF AC Symposium on control in power electronicsand electrical drives, 1974, 2, pp. 175-198

12 ROUBICEK, O.: 'Basic equations for the steady state operationof a low-frequency synchronous linear motor with a greatamplitude of path', Acta Tech. CSAV, 1972, 17, pp. 350-360

13 ROUBICEK, O.: 'Die quasistationaren Charakteristiken desNiederfrequenz-Synchronlinearmotors mit grosser Bahnampli-tude', Elektrotech. Z. ETZ-A, 1971, 92, pp. 90-94

14 ROUBICEK, O.: 'Die dynamischen Grundgleichungen desNiederfrequenz-Synchronlinearmotors mit grosser Bahnampli-tude\Acta Tech. CSAV, 1971, 16, pp. 758-769

15 ROUBICEK, O.: 'Die Ubertragungseigenschaften des Nieder-frequenz-synchronlinearmotors', Elektrotech. und Maschinenbau,1973,90, pp. 23-29

16 ROUBICEK, O.: 'Ein optimierter Entwurf des schwingendenSynchronlinearmotors', Elektrotech. & Maschinenbau, 1978,95, pp. 404-412

12 IEEPROC, Vol. 127, Pt. B, No. 1, JANUARY 1980