CA1259653A - Variable speed variable reluctance electrical machines - Google Patents

Abstract

A B S T R A C T

A drive system includes a reluctance motor, driving a load.
The motor has stator and rotor poles and magnetising windings for each stator pole. The airgap is small so that saturation occurs during pole overlap, and the poles are constructed so that there is torque overlap between phases as successive phases are energised during rotor rotation. A sensor provides a rotor position input to a reference waveform generator. The output of the generator is determined by rotor position and is applied to a power converter through a current controller.
Accordingly the waveform generator establishes a relative magnitude for motor phase current for every position of the rotor during the period of energisation of a motor phase. A
further input may be applied to the system to determine the absolute magnitude of the phase current, subject to the waveform pattern established by the generator. The rotor poles may be skewed to modify the static torque versus rotor angle characteristic of the motor, the skew being between one-quarter and one-half of rotor pole arcuate extent.

Description

~259653 -- .

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_TLE nF T~E TN~ENTION.

"Yariable speed varlable reluctance electrical machlnes"

~ACKGROUND OF THE I~JYENTION.

Field of the Invention.

The present inventlon relates to power drive systems for or lncorporating variable reluctance electr~cal machines and to varidble reluctance electric~l machines for such systems. More p~rticul~rly, the invention relates to power drive systems for d~ubly-sallent variable or switched reluctance motors and to reluctance m~tors of this kir,d for such power drive systems. The present ~nvention ~lso relates to a construction of varlable reluctance machine operable as a generator.
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Descrip~ion of the prior art. ..
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Variable reluctance motors are among the oldest of ~lectrodynamlc m~shlnes, but their ~ndustrial appllca~ion was for ~ny years lnhibited by the lack of avallabi.lity of suitable s~itching means for reliable progress1ve sequentlal energisatlon of the stator poles to bring about rotation of the rotor. The lengthy history of relative lack of success In adaptlng variable reluctance electrical machine~
for use for higher power drives is emphaslsed in the discussion to the pdpers p~esented at the Small Machines Conference In 1~76 (IEE Conf.
Publ. 13G, lg76 pp 9~-96), where reference was made to the earl~est such motors, designed in 1842 for railway use and demonstrably ancestors of .today`s machines. Reference was also made to a subsequcnt machine of 1~51. SeYeral contributors com~ended on the curinus circumstances that machines o~ this ~in~ should for so lon~
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~l259~53 have failed to find a commerciLl role, and much of the discussion reYolved around the difficulty of successfully applying reluctance motors to an everyday industrial role.
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It would however appear that even the undoubted advances discussed and described at that Conference did not bring about wide use of variable reluctance motors in substitution for conventional industrial AC and DC units.

While variable reluctance motors have been used commercially in more recent ti~es, ln the form of stepping motors, the stepp~ng motor ls fundamentally a digltal devlce controlled by pulsed inputs which yleld predetermined output steps. The development of microprocessor control systems has enhanced the utllity of stepping motor drives, but nonetheless these motors essentially remain suited to positioning applications and are not generally suitable for del~vering significant power outputs. However the inherently high efficiency of the reluctance motor has caused the increaslng availab~lity of high power semiconductor swltching devices in recent years to lead to increasing interest in the posslbility of applying var~able reluctance motors to higher power drlYes in industr~al applicat~ons, while attention has also been drawn to the advantages of operating var~able reluctance motors in the saturated mode. ~n whlch mode the reluctance motor is especially efficlent in oonYertlng electrical energy ~nto mechanlcal work.

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Torque is generated ~n a reluctance motor when a rotor pole moves relative to a stator pole from a position of max~mum reluctance Into a pole overlap configurat~on ~n whlch the reluctance ls a mlnimum. In a practlcal constructlQn, a varlable reluctance motor typically has a number of paired rotor poles and a greater number of paired stator poles. Thus there is a plurallty of posslble stable m~nlmum reluctance posltlons, ln each of which one pair of rotor poles is aligned wlth one palr of stator poles. Each stator pole palr is provided wlth energlsing windlngs and when a particular pair ls ~ ii96~3 energised, a corresponding pair of rotor poles will move into alignment with those stator polesJ thereby developing torque. If energisation is then switched from that pair of stator windings to an appropr.iate other pair, the rotor ma~ then be rotated further through an angle determined by the relationship between the numbers of rotor and stator poles to a new stable minimum reluctance position, and so on by further sequential energisation. In partlcular when intended for a stepping drive, the machine may incorporate permanent magnets so that a force tending to hold the rotor in a specific displacement relative to the stator exists, even In the absence of energlsing currents. Alternatively the stator poles may be magnetised only when excitlng currents are present. ~n the absence of permanent magnets, currents in the reluctance motor are unipolar, l.e. they only flow through the windlngs in one direction, and the rotatlonal dlrection of the machlne is reversed by changing the order in which the windings are energlsed during each revolution of the rotor, r~ther than by reversing the direction of current flow through th~se windings.
Accordingly for one directlon of rotatlon, the stator pole wlndings - are energised so that the rotor poles move into alignment wlth appropriate stator poles from one circumferential side of the stator poles. For the other directlon of rotatlon, the sequence of stator winding excitation is such that the rotor poles move lnto alignment with sta~or poles from ~he other circumferentlal side of the stator pole.

I.n a machine with a multiplicity of poles therefore, the rotor may rotate to bring a pair of rotor poles into a conflguration of min~mum reluctance with a particular pair of stator poles fro~ either of two directions, so that each pair of rotor poles has two posslble positions of maximum reluctance relative to a particular stator pole pair, one such position being to one circumferentlal side of that pole pair and the other maximum reluctance posit~on lying to the other circumferential side of the stator poles in question. Accordlngly for a particular direction of rotation, the sequence of energisation of the stator pole windings is that which will induce rotation of the rotor in the desired direction to b~ing rotor poles into a minimum 3L259t~i;53 reluctance relationship with stator pole pairs from the appropriate circumferential side of the stator poles. Furthermore since each stator pole winding pair or phase may be energised to bring about either forward or reverse rotation, thereby also developing either forward or reverse torque at the motor drive shaft, when therefore the windings are undergoing sequential energisation to produce rotation in a selected direction, they should not be energised to any significant extent during the periods while rotor poles are moving away from their minlmum reluctance dispositions in alignment with stator poles towards their maximum reluctance disposltions in relation to these stator poles, from whlch their displacement towards these poles begins for rotation in the opposite direction. Energisation at this time will develop an opposing torque, acting against the torque now being developed during the continuing rotation of the rotor by the moYement of a further pair of rotor poles into a minimum reluc~ance configuration with the next pair of stator poles now being energ~sed in due turn for this continuing rotat~on4 Thus each-electrical cycle for each stator pole winding phase, i.e. typically a palr of stator pole windlngs, is distingulshed by a half-cycle during which the phase is energised to produce torque to rotate the rotor in the selected direction, i.e. forward or reverse, and a further half-cycle ~uring which the phase windings remain de-energised so that substantially no torque is developed which would tend to oppose the desired direction of rotor rotation. Reversal of the direction of rotation of the rotor involves therefore interchange of the energised and quiescent periods of ~he electrlcal cycle for each motor phase.

A variable reluctance motor may have typically three or four phases and during the period of excitation of each phase~ one or more pairs of stator pole windings are energised for the appropriate half-cycle.

The torque developed during the movement of a particular pair of rotor poles reldtive to an appropriate pair of stator poles may be plotted experimentally against the rotor angle, while the stator pole windings are energised with a DC current to produce a so-called static torque~

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~Z~;9653 .

rotor angle characteristic. The phase torque output of the machine during operation may then be derived by plotting torque against rotor angle for the specific value of current with which each phase is energised at each angular position of the rotor. When the phases are energised witn constant currents in an on-off manner, as is conventional in stepping motor practice, the phase torque output of the machine will have essentially the same shape as the static torque characteristic for each phase for the half-cycle appropriate to the desired direction of rotation. By suitable design of the machine in terms of rotor and stator dimensions, the start of the torque-producing region or half-cycle of each incoming phase may be arranged to overlap that of the outgoing preceding phase so that there is continuity of torque throughout the rotation of the n~otor by virtue of this phase torque overlap. Net output torque at the shaft is then computed by adding the phase torques. Depending on the preclse shapes and angular extents of the phase torques, thls net torque may exhlbit a sign1ficant ripple during torque transitlon between phases.

In the application of known stepping motor systems ~o variable speed drives, it has been found that torque ripple during phase to phase transitions is significant and may be such as to render the motor unacceptable for such drives. In such systems, the static torque - against rotor angle characteristic for a single phase of a saturable variable reluctance motor during a rotor displacement from a maxlmum reluctance position to a mlnimum reluctance posltlon ~s typically distinguished by a very rapid initlal r1se in torque as pole overlap commences, followed by a period during whlch torque remalns substantially constant while pole overlap progresses towards full overlap, and the characteristic terminates with a roll-off portion during whlch torque drops significantly as full overlap is achieved and the relevant rotor pole moves Into a disposition of minimum reluctance. Further displacement of the rotor relatlve to the stator then leads to the poles moving out of overlap and the static torque characteristic of this displacement is substantidlly an inverse mirror image, about the zero-torque full overlap conditior, of that for the - ~2596~3 displacement into the overlap cond~tlon, the direct~on in which the torque is exerted belng reversed. This negative torque developed by the further relative displacement of the rotor and stator poles from their mini~num reluctance relatfonship terminates with arrival of the rotor in a new position of maximum reluctance, from which a further complete cycle may commence with displacement of the rotor pole into overlap with a further stator pole taking place~ While the maqnitude of thè peak static torque will vary depending on the level of energising current, the ~eneral shape of this characterist~c remains the same for all levels of excitation. Accordingly regardless of the extent of the overlap between successive phase torques and the levels of the exciting currents, each incoming phase torque-generating half-cycle has a region during whlch torque rises very rapidly and typically much more rap~dly than the rate at which torque produced by the torque-generating half-cycle of the outgoing phase decays, so that the net machine torque is not smooth and the phase to phase torque '-transfers are distlngulshed by substantial torque fluctuations or ripple.

Apart from its deleterious effect on torque smoothness during transition between phases, th~s rap~d torque r1se experienced in many known reluctance motors at the start of pole overlap, especially when the windings are energised wlth constant or stepfonm energislng currents, also frequently leads to generation of vibration and noise in operation of the motor. The rapidly rising force at the start of the torque/angle characteristic has the same ef~ect as an Impuls~ve "hammer-type" blow. Structural resonance in the motor m~y be trlggered by the repeated torque impulses, leading to ~nter alia stator bell mode vlbrat~on in which the inward attractlon of diametrically opposite statvr poles produces an electrical deformation of the stator. As this deformation progresses around the stator, a bell-like resonance is produced. Other modes of resonance may ~nclude a rotor radial mode arising from deflection or distortion of the rotor under the electrical forces, bearing rattle which may arise out of any looseness in the fit of the bearings on the rotor sha~t, and a ~ 2~9653 .

torsional mode excited by the rotation-induc;ng torsional forces acting on the rotor. Any or all of these modes of resonance may be present and result in noise and vibration. Wh~le they may be damped by such known methods as the use of heavier bearings and structures than are required by electromagnetic considerations alone, such a solution is not fundamentally a satisfactory answer to the vibration and resonance problems frequently experienced in these machines.

The achievement of torque smoothness and freedom from noise and vibration in operatlon are both dependent on the complex statlc~torque versus rotor angle characteristic of the var~able reluctance motor but are not necessarlly cured by the same remedies, and ~n partlcular a motor in which the characteristics are such that the torqùe ripple at phase torque transltions is perhaps acceptable for certa~n drive purposes may not necessarily be distinguished by sllent and vibratlon-free operation.
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Var~able reluctance machines for use ~n power drlves have been descr1bed in U.S. Patent Specifications Nos. 3,062,979 and 3,171~049 of Jarret and U.S. Patent Speciflcation No. 3~956,678 of Byrne and Lacy. In U.S. Patent Specifica~lon No. 3,062,979 o~ Jarret, the saturatlon inductlon in the rotor teeth magnetic mater~al of a variable reluctance electric machine is reduced to between 15 and 85X
of the maximal Induction selected for the magnetic circu~t materlal of the machine, with the purpose of aliow~ng magnetic fields of relatlve1y large strength to be developed in the gaps adjacent the polar areas wlthout excessive losses and to promote a high ratfo of output power of the machine to its welght. In order to achieve this ob~ect, the rotor teeth are constltuted by alternate sheets of ~r~
magnetic materia1 interspersed with non-magnetlc materlal such as lamina-shaped airgaps. Jarret's U.S. Patent Speclfication No.
3,171,049 describes a development o~ the machine of the earlier Specification No. 3,062,979 in which the rotor Is divided into two co-axial half-rotors axially spaced apart and secured to each other and to d common rot:table shdft. The stator is slmilarly dlvided and ~.2~ ;53- ~

the windlngs are then connected in the fonm of a four-impedance bridge in order to achieve effective decoupling of the AC and DC circuits of the machine and thereby an improved level of machine efficiency. In another aspect the machine of this patent specification is shown to have a plurality of rotor teeth, each of wh1ch is defined by a num~er of sectoral fanned-out portions, so that the movement of the tooth -past a stator pole is accompanied by a step~ise change in magnetic characteristic and the machine may be operated substantially with sine-waYe current. The purpose of this arrangement 1s to alter the waveform of the induced voltage from the substànt1ally rectangular shape induced by the movement of a rotor tooth past a stator pole 1n those constructions of machine in which the rotor teeth have constant magnetic properties throughout their angular deYeloDment. In the particular constructions shown 1n U.S. Spec1ficat10n No. 3,171,049, each tooth is defined by a plurality of groups of sectoral projections. the groups be1ng spaced apart ~n the axial dlrection by air gaps and each tooth being def1ned by four lam1nations in a fanned array so that each step ~n the stepw~se change of magnPtlc characteristic involves a stepfonm incremental increase or decrease of one fifth, as each tooth lamination comes beneath or moves away from a stator pole. In U.S. Patent Speclfication No. 3,956,678, stepping motor techn~ques are described 1n which simpl1ficat~on of the dr~ve and a gain In speclfic output and efficiency are ach~eved by constructions ensuring max1mum saturation of magnetic ~ ux at the stator pole faces, the a1rgaps between associated stator and rotor pole faces being minlmal. A rotor pole structure is descr~bed in whfch a leading part of each rotor pole surface is undermined by deep trapezoidal slots to reduce the gap flux dens1ty compared wlth the unslotted pole surface port10ns, the objectiYe being to extend the mechanical displacement of the rotor over wh~ch a uniform rate of flux increase occurs to correspond to one stator pole pitch, thereby also providing torque continu~ty with d two-phase configuration.

None of these prior art documents contain any comprehensive consideration of the problems of torque ripple and noise generation 3L2~ 653 discussed above. While the Jarret patent specifications disclose a number of features relating to reluctance motor torque in general, the alleged improvement in torque output ach~eved by reducing the packing factor of the laminated steel in the pole face in the arrangement of U.S. Patent Ho. 3,062,979 appears to be based on a misconception, since the mean torque is in fact always reduced by such measures, although reducing the packing factor in the pole face does in some cases offer the possibility of altering the shape of the static torque against angle diagram at constant current with little if any significant loss of static mean torque. In an arrangement described by Byrne and Lacy in a paper entitled UCharacteristics of Saturable Stepper and Reluctance Motors" delivered to the Small Machines Conference in 1976 (IEE CGnf. Publ. 136, 1976 pp 93-96), an echelon array of rotor stampings of graded arc length is used, by v~rtue of which an improved degree of torque uniformity is achieYed over the step length of 90. By virtue of the echelon array, the constriction cross-section 1n the overlap between stator and rotor increases l~nearly over the gO step lensth arc.
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In the classic stepper motor such as is frequently used in computer peripherals and also to some extent in numerlcally controlled machlne tools for positloning movements, the problems of torque trans~tions - and torque rlpple are not of ma~or consequence, since the motor ~s essentially used only for dfgital positioning purposes in which its incremental operat~on or stepping advance between pos1tions of m~n~mum reluctance of the rotor is employed and it ~s not called upon to de~elop signlficant levels of power. Thus, the exact shape of the static torque versus angle characteristic ls not of ~a~or consequence9 slnce the power levels in quest10n are modest and the ~mpulsive force generated by the inltial sharp ~ncrease ~n torque as overlap commences is sufficiently small in absolute terms as not to be of great significance insofar as noise and vibration generat~on is concerned.
In addition, it has been observed that in for example a 200-step permanent magnet stepping machine, in which the stator and rotor teeth are defined by semicircular cutouts in the stator pole faces and the ~25~653 ., l - 1 o-rotor periphery respectively, these cutouts deflning the gaps between the teeth, the successive torque versus angle characteristics o~ the ; -phases tend to be smoothed and may attaln an approxlmately sinusoidal shape. Since In a stepper motor of this kind~ the number of teeth is large relatiYe to the dlmensions of the rotor and stator, the airgap between the rotor and stator is also relatively large ln terms of the dimensions of the indlvidual teeth, and it is believed that thls may contribute to the smoothed shape of the torque-angle curYe. In a technique known as microstepping, a stepper motor of thls kind may be fed with Indlvldually controlled currents ~n its indiv1dual phases so as to produce null posltions addltlonal to those arlslng from the rotor posltions of mlnlmum reluctance. In one such technlque9 the phase currents are appl~ed in the fonm of slne and cos~ne waYes dependent on the angle of electrlcal phase dlsplacement. The system employed uses a counter which accepts a serles of input signals In the form of pulses and generates dlgltal numbers represent~ng the slne and cosine values, look-up tables In the form of ROMs being usable for . thls converslon. The resulting reference slynals are used to control the current by means of a chopper driYe.

BRIEF SUMMARY OF THE INYENTION.

It Is an object of the present Inventlon to provlde a power drive system for or Incorporating a varlable reluctance motor In which trans~tion between phase torques Is ach~eved without substantlal variatlon In net machlne torque output, It Is a further ob~ect of the invention to provlde a power drive system for a variable reluctance machlne In whlch structural resonance of the machine ~n operation Is llmlted by control of the resonance-exclting forces deYeloped during operation o~ the machlne. Stlll further obJects of the present inventlon Include the deYelopment of a varidble reluctance machine In which the ratio of torque to inertia Is high and the provlslon of a variable speed variable reluctance machine capable of economical manufacture ~259653 ., i i According to a first aspect of the invention, there is provided a drive system comprising a saturable variable reluctance electrlcal motbr, sa~d motor comprising a stationary or driving member having a plurality of salient driving poles, a magnetising winding for each driving pole, and a movable or driven member having a plurality of salient driven poles, the number of driven poles being less than the number of driving poles, the airgap between each dr1ving pole and a driven pole positioned in alignment therewith be~ng small relatiYe to the dimensions of the poles transverse to said airgap and at least the driven poles be~ng formed so that in operation of the motor magnetic saturation occurs substantially in the region of the mechanically variable interface or overlap between the drivin~ and driven poles, and the extents and d~spos~tions of the dr~ven poles being related to those of the driving poles so that in operation of the motor the force-produclng ~ncrement of driven member dlsplacement resulting from the mechanical interface or overlap of each driven pole w~th a driving pole overlaps the force-produc1ng Increment of driven ~ember displacement resulting from the overlap of another driYen pole with a 20 further drivlng pole, and the system also comprising driven memberposition-sensing means for generatlng at least one signal, the instantaneous value of which is dependent on the position of the driven member, and power supply means includ~ng a voltage source or sources connect1ble across the driving pole windings, sa1d windings belng connectible across said source or a sa~d source in a predetermined sequence during driven member displacement and each driving pole w1nd~ng being thus connectible for a predetermined increment of driven member displacement, and the power supply means also including means for regulatlng the instantaneous ma~nitude of the current in a driving pole winding when connected to said source or a said source, sald current-regulating means being responsive to the or a said driven member position-dependent signal of the driven-member position-sensing means to regulate said current magnitude so that the instantaneous value of said current set by said regulating means at any position of the driven member within said increment of driven member displacement during which the winding is connectible to said , source or a said source relat1ve to its value at any other sa1d I
position is substantially determined by the instantane~us poslt~on of - the driven member.
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Wh11e the present inventlon is for the most part described 1n relation to rotat~onal embodlments in the following text, the principles embodied in it may also be applied to a linear geometry o~ motor, as set out in the foregoing def1nit10n of the flrst aspect of the inventlon, 1n which a substantially planar driven member or ~rotorU is displaceable past a f1xed member or Ustatoru unlt of the llnear I0 motor. T~e current control feature may be appl~ed to such a construct10n in prec1sely the same manner as subsequently set out herein for rotat1ng mach1nes, it being understood that the terms ~stator" and ~rotorU as appl1ed to a 11near motor equate ~o or represent a driv1ng member and drlven member respect~vely, and references to the cfrcumferen~lal and axial dlrect~ons in a rotary construction correspond to the d~rect~on of dr~ven member d~splacement and a dlrection transverse to that d1splacement ~n a 11near ~otor.

In a rctary construct~ons accord1ng to the flrst aspect of the invention, there 1s provided a dr1ve system compr~s~ng a saturable var1able reluctance electrlcal motor, sa1d motor compr1s~ng a stator havlng a plural~ty of sal~ent stator poles, a magnet~s1ng wlnd~ng for each stator pole, and a rotor hav~ng a plural1ty of sal~ent rotor -poles, the number of rotor poles belng less than the number of stator poles, the rad~al a1rgap between each stator pole and a rotor pole positioned ~n al~gnment therewith be1ng small relative to the dimens10ns of the poles transverse to sa1d airgap and at least the rotor poles be1ng formed so that ~n operat~on of the motor magnet1c saturat10n occurs substantially ~n the reg~on of the ~echan1cally variable 1nterface or overlap between the stator and rotor poles~ and the arcuate extents and dispos1t1ons of the rotor poles be1ng related to those of the stator poles so that 1n operation o~ the motor the torque-produc1ng angular increment of rotor rotat10n result1ng from the mechanical 1nterface or overlap of.each rotor pole w1th a stator i, pole overlaps the torque-producing angular increment of rotor rotation resulting from the overlap of another rotor pole with a further stator pole, and the system also comprising rotor position-sensing means for generating at least one signal, the instantaneous value of which is dependent on the angular position of the rotor, and power supply means including a voltage source or sources connectible across the stator pole windings, said windings being connectible across said source or a said source in a predetermined sequence during rotor rotation and each stator pole winding beil~g thus connectible for a predetermined angular increment of rotor rotat~on, and the power supply means also ~ncluding means for regulat~ng the Instantaneous magn~tude of the current ~n a stator winding when connected to said source or a said source, said current-regulating means being responsive to the or a said rotor posit~on-dependent signal of the rotor position-sensing means to regulate sa~d current magnitude so that the instantaneous value of said current set by sald regulating means at any angular posltion of the rotor within sa~d angular increment of rotor rotation durlng which the w~nding ~s connectfble to said source or a sald source relative to - its value at any .other said angular position is substantially determined by the instantaneous angular posltion of the rotor.

By thus controll~ng the relative instantaneous magn~tude of the current input to typically, each pair of stator phase windings of mach~ne as they are sequentially energised, in accordance w~th the angular posit~on of the rotor wlthin the approprlate angular segment of rotor rotation, the torque developed by each phase of the machine during ~ts per~od of energisation may be closely controlled so that the detrimental effects of rap~d torque rise at the start of pole overlap and torque rlpple where the torques of successiYe phases overlap may be minimised. For example, during torque overlap, the current in the outgoing phase may be regulated so that the torque of that phase is reduced at a rate such that the torque developed by the outgoing phase taken together with the torque being deYeloped by the incoming phase amounts to a substantially constant net machine torque output. The control of torque achieYable by current regulation may ` ~L~5~;5 3 also significantly reduce or substantially eliminate the "hammer-blow"
described above, which ls typic~lly experienced at the start of pole overlap, and thereby also improve machine performance in terms of noise and vibratlon.

In a second aspect, the invention provides a saturable var~able ,' reluctance electrical machine comprislng a stationary or driving-member having a plural~ty of salient drlving poles, a winding for each driving pole, a movable or driven member having a plurallty of driven poles, the number of driven poles being less than the number of driving poles, the airgap between each dr~ving pole and a driven pole positioned in alignment therewith being small relative to the di~ensions of the poles transverse to said airgap and at least the driYen poles being formed so that in operation of the machine magnetic saturation occurs substantlally in the region of the mechanically variable interface or overlap between the driving and driven poles, the extents and dispos~tions of the driven poles belng related to those of the driving poles so that in operation of the machine the force-producing increment of driven member d~splacement resulting from the mechanical fnterface or overlap of each driven pole with a driYing pole over~aps the force-produclng increment of driven member displacement resulting from the overlap of another dr~ven pole with a further driv1ng pole, each driven pole and each driv~ng pole havlng edge regions spaced apart In the direction of relative d~splacement.of the driven and driving members, said spacing of said edge regions being substantially constant throughout the extent of the pole in a direction transverse to said direction of relative d~splacement and each said edge reglon being def1ned in said transverse direction of the pole by a succession of edge region portions, each said edge region portion being displaced in said direction of relative dlsplacement with respect to the or each ad~iacent edge region portion of said edge region, each said edge region portion being advanced in said directlon of relative displacemen~ wlth respect to the preceding edge region portion or each said edge region portion belng set back in said direction of relative displacement wlth respect to the preceding ~L2S~5i3 edge region portlon so that said edge region is skewed relative to said direction of relative displacement, and the spacing in said direction of relative displacement between the edge region portion at one transverse end of one of said edge regions of the pole and that at the other transverse end of the same edge region being between one quarter of the constant extent of the pole in said direction of relative displacement and a value equa1 to said extent.

In a rotary construction, a saturable variable reluctance electrical machine according to this second aspect of the invention comprises a stator having a plurality o, salient stator poles, a wind~n~ for each stator pole~ a rotor having a plurality of rotor poles, the number of rotor poles being less than the number of stator poles, the radial airgap between each stator pole and a rotor pole pos~tioned in alignment therewith being small relative to the dimensions of the poles transverse to said a~rgap and at least the rotor poles being formed so that in operation of the machine magnetic saturat~on occurs substantially in the region of the mechanically var~able Interface or overlap between the stator and rotor poles, the arcuate extents and dispositlons of the rotor poles being related to those of the stator poles so that in operatlon of the machine the torque-produc~ng angular increment of rotor rotatlon resultlng from the mechanical interface or overlap of each rotor pole with a stator pole overlaps the torque-produclng angular increment Qf rotor rotat~on resultlng from the overlap of another rotor pole with a further stator pole, each ro~or pole and each s~ator pole having respective circumferentfally spaced apart edge regions, the circumferential spacing of said edge regions being substantially constant throughout the axial extent of the pole and each said edge region being defined in the axial direction of the pole by a succession of edge reg~on portions, each said edge region portion being circumferentially displaced relatiYe to the or each adiacent edge region portlon of said edge region, the circumferential dlsplacement of each said edge region portion being In the same circumferential direction relative to the preceding edge region so that said edge region is ske~ed relative to the axis of lZ59653 rotation of the machine, and the circumferent~al displacement of the edge region portion at one dXidl end of one of said edge regions of the pole relative to that at the other axial end of the same edge region being between one quarter of the constant arcuate extent of the pole and a value equal to said arcuate extent.

In variable reluctance machines according to the present invention, the form or structure of at 1east the driven poles is of importance, in addition to minimisation of the airgap, In ensuring that in operation of the machine, magnetic saturatlon occurs substantially in ;;
the region of the overlap between driven and drlving , poles. The po1e shaping which is a partlcular feature of the invention in its second aspect may be arranged to cause the reluctance of the machine to vary in a predetermined and controlled manner during the initial overlap of a pair of rotor poles w~th a pair of stator poles and thereby modify the shape of the static torque/rotor angle characteristic so as to reduce in particular the rapid r~te of r~se of :
torque normally experienced at the commencement of pole overlap. The ~
rates of change of p.hase torque thus achievable facilitate the ~-extension of the torque-generating portion of each phase while still providing relatively smooth transitions between the phases. Pole ;~
shap~ng also facilitates phase winding current control, in that the phase currents may follow a more regular pattern of change between successive rotor positions, thus enabllng the required current waveshapes to be more read~ly provided, especially at high rotatlonal speeds.
,., The present lnvention relates particularly to variable reluctance machine structures in which the polefaces of at least the drlv~ng poles are substantially smooth or continuous, i.e. they are undivided. In this, polefaces of machines according to the invention differ from the multi-toothed arrangements used in particular for stepping or micro-stepping motors. This, in constructions of machine according to either of the foregoing aspects of the invention, the poleface of at least each driving or stator pole may suitably define d substantially continuous surface facing said airgap.

.

~ 259~53 ln drive systems according to the invention, said current-regulating means is preferably responsive to said rotor-position dependent signal - to regulate said current magnitude so that successive instantaneous values of said current during an initial portion of said angular increment of rotor rotation during which the winding is connectible to said source or a said source increase progressively with progressive rotation of the rotor and successlve instantaneous values of said current during d terminal portion of sald angular increment decrease progressively with said progressive rotation. In this way, the rate of increase of the torque developed by each incoming phase may be m~tched to the rate o~ decrease of the torque produced by each outgolng phase so that a substantially smooth torque transition may be achieved for substantially any shape of static torque/rotor angle characteristic~

Said current-regulating means may be responsive to said rotor~position i dependent s~gnal to regulate said current m~gnitude so that the rate at whlch successive Instantaneous values of said current decrease during said termlnal port~on of said angular increment of rotor rotation Is substantially the same as the rate of increase of successive instantaneous current values during sa~d in~tial portion .
and the succession of ~nstantaneous current values oYer said angular increment of rotor rotation substantially deffnes a substantially symmetrical current waveshape extending over said angular increment.
This feature can be especlally advantageous for bi-directional operation of a reluctance motor in that the current-regulating means may apply s~m~lar current waveshapes to the windings lrrespective of the direction of rotation, thus fac~litating a particularly advantageous reallsatlon of the power supply means.

Said current-regulating means may also be responslve to said rotor-positlon dependent signal to regulate said current magnitude so that successive Instantaneous values of said current during said initial portion of said angular increment of rotor rotation substantially define the rising current region of a substantially sinusoidal current halfwave and successive instantaneous values of ~L25~653 said current during said terminal portion of sald angular increment substantia11y define the falling current region of a substantially sinusoidal current halfwave. The particular advantage of this feature resides in the relative ease with which sinewaves or parts of sinewaYes may be produced or synthesised, especially at high rotational speeds, compared with other waveshapes~ In the application of the system of the invention to a three-phase motor, waveshapes having initial and terminal portions, each of which is part of a sinewave, may be used, with the waveshapes having a constant current portion extending between the peak value of the initial rising current region of the waveshape and the peak value with ~hich the terminal falllng current region commences.

An intermediate portion of said angular increment of rotor rotation may be interposed between said inltial and term~nal por~ions. The angular increment of rotor rotation may thus be considered as beln~ ;
made up of three portions, an initial portion, an Intermediate portion and a terminal portion, and said current magnitude may remain substantially constant dur~ng said intermedlate portion of angular rotation. Alternatively, the lnitial port~on may lead directly into the terminal portion without the interposit~on of an intermediatè
portion. In a part~cularly favoured embodiment of drive system according to the ~nvention, said current-regulating means may be responsfve to said rotor-position dependent siynal to regulate sa~d current magnitude so that said instantaneous curr~nt values dur~ng said angular increment of rotor rotation substantially define a s~bstantially sinusoidal halfwave. The sinusoidal halfwave thus extends in operatlon of the system over the angular increment of rotor rotation during which the winding is energised. This angular increment is determined by the number of po1es and their relative angular extents and in a preferred arrangement is substantially one-half of the angular rotational displacement of the rotor corresponding to one electrical cycle. One electrical cycle of the machine eauates to an increment of mechanical rotation determined by the number of poles and phases, and the frequency of the sinewave during operation ~Z59~i3 of the machine is thus established by machine rotational speed in association with these constructional characteristics of the machine~
This arrangement in which sinewaves are fed into the machine windings is especially favoured for a four-phase machine, in which the wave-shapes for successive phases will be displaced by 90, i.e. theelectrical phase angle.

In a particular embodiment of the current-regulating means, the or each position-dependent signal of the rotor-position sensing means may be a waveshape of appropriate configuration, such as a sinewave, and its instantaneous magnitude at each rotor position is used to establish an appropriate relative value for the winding current. In a further adaptation of this analogue realisation of the current~
regulating means, the position-dependent signal or signals of the rotor pos~tion sensing means mqy be modified to provide-one or more waveshapes of the desired configuration or said waveshapes may be derived from said signal or signals by suitable ana~ogue circuit means.
, The drive system according to the invention nay also comprise means for producing a signal, the value of which is indicative of a desired parameter of motor operation, said current-regulating means also being responsive to said parameter-indicative slgnal to regulate said stator winding current so that the absolute magnitude of said current at every angular po-sition of the rotor within said angular ~ncrement of rotor rotation during which the winding is connectible to sa~d voltage source or a said voltage source is substantially determlned by the value of said parameter-indicative signal. This slgnal may sultably ;
be a set speed signal, the releYant parameter thus being machine speed, and it may applied to the current-regulatlng means in the for~
of a reference voltage, variable between a predetermined positive Yalue and a corresponding negative value to determine both direction and speed of rotation of the machine. The regulating means accordingly establishes in response to the reference signal the appropriate absolute current magnitude required to develop the machine or motor torque necessary to bring the machine speed of rotation to the desired value called for by the level of the reference voltage, while its relative magnitude at each angular rotor position during the period of winding energisation is established by the rotor position sensor signal. Thus net machine torque is controlled to achieve a desired speed, while the phase torques during each revolution of the rotor are controlled to give substantially ripple-free phase-to-phase transitions by the relative current magnitude during each period of winding energisation being constrained to follow an appropriate waveshape. In an alternatlve arrangement~ the reference signal may be directly-indicative of a desired level of torque.

According to a further aspect of the invention directed in particular to generating constructions of systems according to the invention, there is provided a drive system compris~ng a saturable variable reluctance electrical machine, said ele~trical machine comprisi~g a stator having a plurality of sallent stator poles,-a winding for each stator pole, and a rotor having a plurality of salient rotor poles, the number of ro~or poles being less than the number of stator poles, the radial airgap between each stator pole and a rotor pole positioned in alignment therewith being small re1ative to the dimens~ons of the poles transverse to said airgap and at least the rotor poles being formed so that in operation of the machine magnetic saturation occurs substantially ~n the region of the mechanically variable Interface or overlap between the stator and rotor poles, and the arcuate extents and dispositions of the rotor poles being related to those of the stator poles so that in operation of the machine the torque-producing angular increment of rotor rotation resulting from the mechanical interface or overlap of each rotor pole with a stator pole overlaps the torque-producing angular increment of rotor rotation resulting 3~ from the overlap of another rotor pole with a further stator pole, and the system also comprising rotor position-sensing means and a voltage source or sources connectible across the stator pole windings, said windings being connectible across said voltage source(s) ln a predetermined sequence during rotor rotation and each stator pole ~596~i3 winding being thus connectible for a predetermined angular increment of rotor rotatlon, and said windings also being connectible across an electrical load during rotor rotation, also in a predetermined sequence, and each stator pole winding being thus connectible for a predetermined further angular increment of rotor rotation.

In operation of a variable reluctance machine as a motor, the windings, whlch u,ndergo sequential energisation to produce rotation ln a selected direction, should not be energised to any slgnificant extent during the periods whi1e the rotor poles are moving away from their minimum reluctance posftions in alignment with stator poles towards their maximum reluctance positions in relation to these stator poles. In order to operate a machine according to the ~nvention as a generator however, excltation of the windings may be delayed so that torques opposing the direction of rotation are deliberately produced>
and conservation of ener~y then demands that nett currents are returned to the supply. Accordingly In this case voltage ls only applied to the wlndings when substantial overlap of the rotor and stator poles has already taken place, ~.e. after the greater part of the potentlal for produclng forward torque is alreaqy past~ -Energisation of the windings takes place over a relat~vely br~efangular increment of rotor rotation and terminates as the poles start to move Into a relationshlp tending ~o produce negatlve or rotation-opposing torque. The energlsing voltage should be as high as possible and should only be applled over this re7atively br~ef ~ncrement o~
rotor rotatlon. Accordingly little current ~s then drawn from the supply but substantlal fluxes are built up, whlch serve to energise the m~chine after the w~nding voltage is shut off near the m~nimum reluctance positlon. The energy stored in the flux must be returned durlng the further rotat~on of the machine, and thus, as the machlne shaft is driven through the torque-opposing angular increment of rotor rotation by a prime mover, current is generated and returned to the supply, which may be fed from the machine through free-wheeling diodes.

~Z~9653 Each rotor pole and each stator pole of a machine in accordance with the invention may have circumferentially spaced apart edge regions and said rotor and/or stator pole edge regions may be shaped so that the radial dimension of the airgap and/or its axial extent will vary at S least during the commencement of pole overlap. Pole shaping of this kind may be arranged to Gause the reluctance of the machine to vary in a predetermined and controlled manner during the initial overlap of a pair of rotor poles with a pair of stator poles and thereby modify the shape of the static torque/rotor angle characteristic 50 as to reduce in particular the rapid rate of rise of torque normally experienced at the com~encement of pole overlap. The less drastic rates of change of phase torque thus achieved enable the torque-generating portion of each phase to be extended into the initial and terminal pole overlap regions of the statlc torque characteristic while st~ll achieving reiatively smooth torque transitions between phases, in that such transitions may be achieved with less drastic rates of change in the winding currents in the initial and terminal regions of the energising waveshapes than would be requ~red were the static torque/angle characteristics unmod~fied. The establishment of an appropriate magnitude for the winding current at each successlve rotor position during the angular increment for which the winding ls energised is also facilltated, in that the changes in current required between succssive rotor positions follow a ~ore regular pattern compared with those needed for unshaped poles, and it is thus easier for the current-regulatlng means to provide the required current waveshapes, especially at high rotatlonal speeds.

The surface portlons of the poleface of each rotor pole and/or each stator pole in said edge regions may be radially displaced relatiYe to the central surface portion of the poleface so that the the airgap between an edge region surface port~on of the poleface and the poleface of an aligned pole is greater than the airgap between the central surface portion of the poleface and the poleface of an aligned po1e. Accordingly in this arrangement, the pole shaping is achieved by curving the axially extending edge surfaces of the polefaces ~25~36~;3 radially away from the airgap region to define a larger airgap in these edge surface regions than prevails over the major extent of the - poleface surface. I

Each said edge region may be defined in the axial direction of the ~
pole by a successlon of edge region portions, each said edge region portion being circumferentially displaced relative to the or each adjacent edge region portion of said edge region, and th:e circumferential dlsplacement of each said edge region portion being in the same circumferential direction relative to the precedlng edge region portion so that said edge region is skewed relat~ve to the axis of rotation of the rotor. In this case therefore, pole shap~ng is achieved by skewlng the pole so that its edges have a twist about the axis of the rotor along their axial extent.

The clrcumferential spacing of said edge regions of each po~e may be substantially constant throughout the axial extent of the pole and the circumferential dlsplacement of an edge region portion of one of sa~d edge regions at one axlal end of the pole relative to a said port~on of the same edge region at the other axial end of the pole is between one quarter of the constant circumferentlal spacing of the edge regions of the pole and a value equal to said spacing. This particular constructlon of skewed pole is found to be advantageous in variable reluctance machines in general, apart from lts partk ular advantages in the drive system according to the first aspect of the present invention. Thus both in systems in accordance wlth said first aspect and also in mach~nes In accordance with the second aspect of the invent~on, said circumferent~al displacement between said edge region portions at the axial ends of the pole may be approx~mately one-half of said arcuate extent and may subtend an angle at the rotor axis of not less than 5. A preferred value of said subtended angle is 10.

In a reluctance machine in accordance with this construction of the invention, the magnetic permeance of each phase varies with rotor ~2596i53 position in a controlled manner and abrupt changes of permeance with rotor posltion are avoided. The magnetic permeance may vary with rotor position in a substantia11y symmetrical manner, e.g.
sinusoidally. Such characteristics may be achieved e~ther by skewing the rotor poles or the stator poles or both, or by shaping the poles, e.g~ at their tips, so that there a controlled variation in airgap with rotor position. A symmetrical static torque versus rotor angle ,~
characteristic is especially adYantageous for reversibly operating machines such as motors and is particularly beneficial when used wlth control systems by virtue of which the phase windings are fed with currents appropriately tailored cr selected to give substantially smooth transfer of torque between the phases.

The rotor ln all constructlons of the invention is most suitably built up from a stack of laminations having substantially identical peripheries, each lamination be~ng slightly skewed relat~ve to ~ts - neighbour or neighbours. Pole shap~ng by skewlng ~s constructionally simple and economical and ~s thus preferable to the more complex pole structures of the prior art, such as those embodying fanned teeth or undercut recesses. Surprisingly it has been found by both theoretical studies and by experimentation that the extent of the pole skewing is signif~cant ~n modifylng in particular the rate at which torque rises at the start of the static torque aga~nst rotor angle characterist~c and that moderate skewing (for example, where the circumferentia1 displacement between sald edge region portions at the axial ends of t~e rotor ls approximately one quarter of the pole span between ~ts tips, i.e. depending on the number of poles, it typlcally subtends an angle at the rotor axis of 5 or less) ~s relatively lneffectlve in modifying this initial torque rise. In a preferred embodiment, the circumferential displacement between said axlally outermost edge region portions is approximately one-half of the constant arcuate extent of the pole. ~here this displacement Yaries between one quarter of the pole span between its tips and one-half of sa~d span, the angle subtended at the rotor axis is then typically not less than 5 and a pa ticularly favourable value of the subtended angle ~

~5~653 approximately 10 in d typical construction of rotor, for example~
with eight stator poles and six rotor poles.

Suitably skewed poles may perm~t a substantially symmetrical static torquefrotor angle characteristic to be achieved. Such a characteristic is of particular advantage in a construction of the drive system according to the invent~on ~n which the machine is required to be reversible, in that the current shaping required to bring about smooth transitlons between the phase torques in operation ls then substantially the same for each direction of rotation. Hence the stator wfndings may be energised wlth symmetr~cal current waveforms usable ln both directions of rotat~on.

In partlcular, ln a system according to the invention incorporat~ng a four-phase machine according to the second aspect of the ~nvent~on, ~n which the poles are suitable shaped, substant~ally sinuso~dal static torque/,rotor angle characterlst~cs may be achieved, and energisation of the stator wlnd~ngs w~th sinuso~dal halfwaves, each of wh~ch extends over an angular ~ncrement of rotor rotatlon corresponding to that portion of the static torque/angle characteristic whlch will-produce a phase torque ln operatlon of the mach~ne in the requ~red direct~on of rotatlon, results in the phase torques ~n operat~on of the machine hav~ng substantially the fonm of sine squared waves, since the magnltudes of the phase torques developed when the mach~ne is energised are substant~ally linearly proportlonal to the exc~t~ng currents at least ~n the normal operating range of such a m~chine and the stat1c torque for each phase at each level of energis~ng current itself follows a slnewave. In the four-phase machlne, each succeeding phase is electrlcally dlsplaced by 90, and Its energislng half-sinewave may therefore be described by a cosine wa~e. The phase torques are similarly displaced in operation of the mach~ne and the phase torque sequentlally succeeding a sine squared phase torque wave has therefore the form of a cosine squared wave. Accordlngly in the torque transitlons, the outgoing sine squared torque and the ~ncom~ng cosine squared torque ideally sum to a substantially constant value, giving an exceptiondlly smooth transfer of torque betueen the phases.

~L2!9~;S3 In drive systems according to the invention, sinusoidal-form currents are found to give particularly favourable operating results from the point of view of torque smoothness and reduced noise and vibration.
The controlled transfer of torque from phase to phase is especially S effective in reducing the excitation of vibration modes and resonances in the physical structure of the reluctance machine due to the elimination of abruptly rising torque characteristics. When sinusoidal halfwave currents are associated with substantially sinusoidal static torque versus rotor angle characteristics, such as are achieved by the skewed rotor construction referred to previously, these sinusoidal-form currents also represent a substantial optlmum so far as minlmisation of losses in the windings is concerned, in that the windings are substantially not energisèd except when useful torque can be developed. The absence of rotor windings in the machine of the invention results in the desired high ratio of torque to inertia while economical construction may be achieved in that the machine and system of the invention do not require the poles of the machine to be provided w1th permanent magnets.

In a generator configurat~on of the machine of the invent~on, the winding of each pole may be associated with that of at least one other pole to define a phase of the machine and said associated windings may be connect~ble In parallel across a voltage source or voltage sources. In an alternat1ve generator configuration of the machine of the invention, a field winding is provided, which sets up a constant flux divided between the phases of the machine In relatlon to their relative reluctances. These relative reluctances change as the rotor rotates and accordingly the phase winding flux linkages also change, giving phase voltages.

The variable reluctance machines forming the subject of the present invention are suitable for operation in applications requiring the highest levels of performance, such dS, for example, servomotors in machine tools and robots. However their simplicity of construction, in terms of moving parts and numbers of components, also renders them ~L2~ 3 f suitable for a wide range of general Industrial applications also,lncluding for example, drives for pumps, compressors and hoists etc.

The reiatlve mechanical simplicity of the machines also ~ives then an inherent reliability, so that they are also suited to applications in ,-whlch trouble-free operation is vital. Such applications include transfer lines, nuclear reactors, continuous industrial processes and space vehicles or satellites.

BRIEF DESCRIPT~ON OF THE DRAWINGS

The pr~nclples of operation of variable reluctance machines and stepping motors are now described having regard to Figures 1 to 11 and 14 of the accompanying drawings and embodiments of the present invention are then described havlng regard to F~gures ~2 and 13 and 15 ~o 26.

F~gure 1 is a schematlc plctorlal view of a s~mple reluctance motor having two poles on both the rotor and the stator, .
Flgure 2 is a diagram showing a trajectory in the flux-current plane for a linear magnetic system in the simple motor of Figure 1, Figure 3 ls a diagram showing a trajectory in the flux-current plane for a saturated magnetlc system in a ~ariable reluctance motor, .
Flgure 4 ls a schemat~c end Yiew of a four-phase var~able reluctance motor having eight stator poles and six motor poles, . Flgure 5 ~s a diagram showing ~dealised phase current waYeforms for clockwise rotation of the motor of Figure 4 over one electr~cal cycle, Figure 6 is an outline end view of stator and rotor lamlnatlons for a practical construction of variable reluctance motor having eight stator poles and six rotor poles, showing the rotor in the position of maximum reluctance for phase 1, Figure 7 is a diagram showing ideallsed stat~c torques against rotor angle at constant current for each phase in an idealised motor in accordance with the construction of Figure 6, with torque overlap between phases, 3L2~6S3 Figure 8 is a diagram showing curves for static torque against rotor angle at constant current with torque overlap between phases for .
a three-phase variable reluctance motor having six stator poles and four rotor poles, Figure 9 is a diagram showing static torque against rotor angle for one phase of a three-phase variable reluctance machine at varying .
levels of stator current, ¦ .
Figure 10 is a diagram showing static torque against curren~ for one phase of a four-phase machine with the rotor in the minimum reluctance position, ;
Figure 11 is a cross-section through the rotor and stator of a two-hundred step per revolution permanent magnet stepping motor, Figure 12 is a block diagrdm of a variable reluctance motor drive :
system embodying the principles of the present invention, Figure 13 is i diagram showing static torques against rotor angle :
for two phases of a four-phase YRM (Yarlable re1uctance motorJ uslng .
ramped or trapezoidal current waveforms for producing smooth æ
transitlons between Individual phase torques, together wlth the .
resulting motor phase torques in operation, ~
Figure 14 shows the static torque versus rotor angle l ~;
characteristic achleved by a particular pole arrangement in a known !
construction of reluctance motor, Flgure 15 shows in side (b) and end (a) views, a rotor -construction having skewed poles9 Fi~ure 16 shows in end view practlcal constructions of rotor and stator laminations for a motor havlng a skewed pole rotor in accordance with Figure 15, Figure 17 shows statlc torque agalnst rotor angle curves for two adjacent phases of a varlable reluctance motor having a skewed rotor according to Figure 15, for different levels of exciting current, Figure 18 Is a diagram similar to Figure 13 showing s~nusoidal static torque versus rotor angle characteristics for two phases of a variable reluctance motor, halfwave sinusoidal current waveforms for . ~.
energising these phases and the resultant phase torque outputs from the motor in ope ation for these ph~ses when thus energ1sed, 3L ~ ~6~3 Figure 19 is an end view (a) of a practical construction of a . .
skewed rotor and its associated stator showing an especially advantageous inter-relationship between rotor and stator for the YRM
of a drive system according to Figure 12 together with (b) an enlarged developed side view of some of the rotor and stator poles, showing the dimensional relationships between them, Figure 20 shows curves plotting static torque against rotor angle `for one phase of the motor construction of Figure 19, at varylng levels of energlsing current, Figure 21 is a partial end view of a stator lamination in which the edge regions of the polefaces are shaped to proYide a modified static torque against rotor angle characteristic, Figure 22 is a schemat~c diagram of an analogue realisation of a drive system according to the invention, 15 Figure 23 is a circuit diagram of current regulators or controllers for the drive system of Figure 22, Figure 24 is a circuit diagram of a speed regulator or controller for the drive system of Flgure 2~, Figure 25 is ~ circu~t diagram of multipliers for the dr~e system of Figure 2~, .
Figure 26 is a circuit diagram of a signal conditioner for the speed signals in the drive system of Figure 22, Figure 27 shows a laminatlon of a stator construction for a generator in accordance with the inv.ention, and Figure 28 ~s a schematic diagram of a system incorporat~ng a generator accordinq to the ~nvention.

DETAILED DESCRIPTION OF THE DRA~IHGS.
1 .
As shown in Figure 1, a simple reluctance motor having a stator 1 and I:
a rotor 2 has two stator poles 3 and 4 and two rotor poles 5 and 6.
The motor is excited by the application of an energ~sing current i to .
a field winding N, the driving voltage being e. A flux ~ is thereby produced and a torque is exerted on the rotor so as to minimise the reluctance of the system. In the motor shown, this corresponds to I

~2~i~653 , maximising the overlap in the airgap region g, so that the rotor will turn from the position illustrated through the angle of rotation ~
until its poles 5 and 6 are exactly aligned with the stator poles 3 and 4. The rotor is now stable in this position and cannot be moYed further until the winding N is de-energised. In the simple motor illustrated, continuous rotation is not therefore possible and further phases must be added in order to provide a machine capable of continuous operation.

The conversion of energy from the electrical ~nput to work or a mechanica; output is illustrated in Figure 2 for a linear magnetic system in which the reluctance of the airgap dominates total reluctance of the system. In this case the flux l~nkage fs directly proportional to the exciting current at all levels of current and the work done durlng a displacement of the rotor through an angle d9 is represented by the area of the tr~angle OabO. It can be shown from theoretical considerations that the torque output of the rotor is proportion~l to the square of the exciting current and that the idealised mechanical work output of the system at constant current (ignoring losses) corresponds to only one-half of the electrical energy input. The remainder of the input energy ~s absorbed as stored energy in the system dur~ng the displacement.

In a practicdl magnetic system, saturation of magnetic ~ater~al ~eans that the relationship between ~lux linkage and current varies w~th the exciting current and a maxlmum substantially constant level of flux linkage prevails once a certain level of excitlng current has been reached. As fn the case of the llnear system, the relatlonshlp between flux linkage and excitlng current var1es for different rotor orientations and Figure 3 shows a typlcal family of flux l~nkage versus exciting current curves for (l) an angle correspondlng to the position of minimum reluctance of the rotor (Omin~, (2) a maxlmum reluctance rotor position (Omax) and (3) a rotor angle (~s) corresponding to the posltion of the rotor when the windlng current is suppressed. The trajectory OaSO thus traversed corresponds to 1~2S9653 excitation of the winding ~ith a constant positive voltage between a rotor position shortly after its position of maximum reluctance and the rotor angular position (Os) at switch-off, and excitation with an equal negative voltage from the switch-off angle to the position of minimum reluctance. The output of mechanical energy during this displacement of the rotor between its positions of maximum and minimum reluctance is represented by the area enclosed within the trajectory and it can be shown that in this case the torque produced is now directly proportional to the exciting current for incremental current changes in the saturated region only, i.e. it is a linear function of that current rather than being proportional to its square, while the torque is also considerably increased (ignoring losses) compared wlth the linear magnetic system. However, it should be noted that this linear relationship does not hold true below the knee of the flux linkage vs. current curve. While losses reduce the overall gain in torque output, a substantial net improvement still prevalls over the linear magnetic system. The stored energy in the saturated case is substantially reduced ln relatlon to the energy converted to ~echanical work, as can be seen from Figure 3. It will however also be apparent from Figure 3 that the behaviour of a reluctance machine in a saturated mode is highly non-linear and is not susceptible to simple analysis.

In the practical construction of variable reluctance motor shown schematically in Figure 4, the doubly salient motor 7 has a stator 8 and a rotor 9. Saturation is achieved by a suitably small value o~
airgap and by the series-connected windings having ~sufficient ampere-turns to establish saturated conditions in the reg10n of the airgap. Thus saturation in the region of pole overlap is brought about not only by selecting a suitable structure and suitable dimensions for the poles and but by also keeping the radlal a~rgap between overlapping aligned poles to a minimum. The stator has eight inwardly projecting poles 10 and the rotor has six outwardly directed poles numbered 1I to 16 in Figure 4. The motor has 4 phases, A,B,C,D, each consisting of a pair of windings, e.g. A, A', on diametr~cally i ,L , opposed stato poles. Only one pair of rotpr poles can be al~gned wlth a pafr of stator poles at any one time. The stator pole spacing fs 45 wh~le the rotor pole spaclng fs 60, and the difference between these two ~alues, ~.e. 15, deffnes the step angle of the machfne, i.e. the angular dfstance through which the rotor will travel between the mfnimum reluctance posft~on when a partlcular phase Is energised and the minlmum reluctance posftion for the a~ acent phase.
~hen phase A ~s energfsed, the rotor rotates so that poles 11 and 14 move Into allgnment with the stator poles of phase A. Further rotat~on through the next 15 incremental StQp is then brought about by energislng efther phase B, for clockwfse rotatfon, or phase D, for counter-clockw~se rotatfon. Thfs constructfon of reluctance motor is both self-startlng and reversfble but the d~rectfon of rotatfon ~s not dependent on the dlrectton of current flow through the phase wlnd~ngs and Is brought about exclus~vely by approprfate sequential unfpolar energ~satlon of the phase wfnd~ngs.

One electrfcal cycle of the mach~ne corresponds to that ~ncrement of mechanlcal rotatfon of the rotor requ~red for each phase ~o be energlsed once and thus advance the rotor through a respect~ve step angle before the sequence of phase excftatfon recommences. ln the four-phase motor the electr~cal cycle ~s equfvalent to 60 mechan~cal, wh~le ~n a slx sta~or pole~ four rotor pole three-phase machfne, the step ang1e wfll be 30 and the electr~cal cycle w~ll extend over 90. The durat~on of stator pole wfnd~ng energ~satfon necessary to ach~eYe stepp~ng advance of the rotor must at least equate to the step angle. Flgure 5 shows ~dealised phase current waveforms over one electr~cal cycle for the motor of Flgure 4, th~s correspond~ng to 60 of rotor mechanfcal rotatfon. The type of waveform 111ustrated is referred ~o as a step current waveform. Each phase fs energlsed fn sequence wfth a constant level of current throughout the fnterval correspondlng to one step angle. Thfs type of excltatfon Is suftable for applicat~ons where ~ncremental motion is requ~red but results in a pulsatfng torque, an effect which is augmented dt low speeds, resulting fn a stepping or cogging motion.

, ~Z5~53 , -33-The abrLptness of th1s stepping transit~on of torque from phase to phase may be partly allevtated by arranging the torque produclng - region of each outgo1ng phase to overlap w1th that of the ~ncom1ngphase. Torque overlap between adJacent phases of a variable reluctance mach1ne (YRM) may be achieved by su1table design of the machine wtth an appropriate inter-relat10nship between the`àrcuate extents of the rotor and stator poles respect1vely and the per~od of excitat10n ls then extended to glve the requ1red torque overlap.
Depending on the relat1ve ansular extents of the rotor and stator and I0 the resultant durat10n of physical rotor and stator pole o~erlap durlng each electr~cal cycle of the rotat10n of the rotor, the per10d of wtndtng energ1satlon may be prolonged up to an angular ~ncrement of rotor rotat~on correspond1ng to substantially one-half of the electr1cal cycle, 1.e. 30 1n the four phase mach1ne already ment10ned. In th1s latter event, each torque generating port~on of a phase w111 overlap with that of a preceding outgo1ng phase for the f~rst half of an electrlcal cycle and with the torque-gen~rat~ng portion of an ~ncom~ng phase for the second half of the cycle, so that there w~ll be substant1ally cont1nuous torque overlap throughout each revolutlon of the rotor, w1th two phases always be~ng act~Ye at any one tlme. However wh11e slmultaneous excttat10n of two phases ls essentlal durtng overlap, 1t ts not necessary for such s~multaneous energtsat10n to t~ke place at all t~mes, although It may do so where the pertod of excitat10n ls prolonged as already noted. In many construct~ons, two phases may be energ1sed only during torque oYerlap, and at other ttmes, only one phase ts energtsed.

A pract1cal constructton of rotor and stator laminat~ons for ach~eving such torque overlap ~s shown 1n F1gure 6. The four-phase machlne illustrated ts agaln doubly sal1ent, the stator lam1nat1cn 17 hav~ng inwardly pro~ecttng stator poles 18 and the rotor lamlnatlon 19 having complementary outwardly pro~ecting rotor poles 20. The stator poles carry phase w1nd1ngs for unlpolar sequenttal energisat~on to develop reluctance torque by the tendency of each rotor pole pa1r to move into alignment wtth an exc~ted stator phase. Rotor lamination 19 is shown 59E;53 1n th~ max1mum reluctance posltlon for phase 1 with adjacent rotor poles 20 positloned so that the gap between them Is symmetr~cally located relat1ve to the diametrai axis of the mach~ne through the stator poles 18 of phase 1. Thls maxlmum reluctance position for this phase may be used to give a rotor angle datum for controll1ng motor rotation and p~ctoriallslng motor behavlour by means of torque versus rotor angle and current versus rotor angle curves.

Flgure 7 shows stat1c torque versus rotor posit1On curves at constant current derlved by energls1ng each phase of a mach~ne In accordance wlth Flgure 6 wlth a d~rect current and displac1ng the rotor through an appropr~ate angular dlstance, the torque value at each of a selected serles of 1ncremental rotor angles dur~ng th~s dlsplacement beln~ recorded. For each phase9 pos~tlve and negat~Ye statlc torque curves w111 be plotted durlng th~s d.c. excltatlon, but by Yirtue of the sequentlal energlsat1On of the stator phase wlnd~ngs for appropriate angular lncrements of rotor rotat~on In operatlon of the motor, only pos~t~ve or negat~ve torques respect~vely are developed In each phase durlng such operat~on dependlng on the selected d~rectlon of rotat~on of ~he rotor. Flgure 7 represents ldeal~sed stat~c phase torques for a mach~ne hav~ng lamlnat~ons such as those of F~gure 6 and the relatlve dlmens~ons of the stator pole 21 to the rotor pole 22 are as lnd1cated schemat~cally at the top of Figure 7, the arcuate extent of the rotor pole therefore somewhat exceed1ng that of the stator pole 1n relat~Ye terms, whlle the absolute arcuate extents of the poles are such that torque ~s de~eloped ~n each phase before the productlon of torque by the preced~ng ph~se ceases. It can be shown from theory, assumlng no frlng~ng ~ ux, that the tangent~al force between overlapplng poles or attacted slabs commences wlth the start of pole overlap, whlch for the Ideal~sed curves of Flgure 7 beg1ns a short angular d1stance after the max~mum reluctance da~um posit~on of F1gure 6. Torque contlnues to be generated as overlap between ~he poles proceeds but the level of the torque 1s, In the 1deal case, 1ndependent of the degree of overlap between the poles. The development of torque ceases when fuI1 overlap is ach~eved be~ween the 96~i3 rotor and stator poles. The effect of the greater arcuate extent of the ro~or pole relatlve to that of the stator pole and the non-development of torque during relatlve pole movement while there ls complete overlap between the rotor and stator poles may be seen In F~gure 7 in the angularly short zero torque region or deadband between the poslt~Ye and negative portlons of the statlc torque curve for each phase.
.~ , The phase torques of a pract~cal motor in fact depart substant~ally from the ideal curves of F~gure 7. Examples of the phase torques to be expected ~n pract~ce are shown in F~gure 8 for the three phases of a three-phase six stator pole four rotor pole machlne, wh~ch ~s a further example of a self-starting and reverslble conf~gurat~on of YRM. At least part of the d~vergence of the curves of F~ure 8 from the ~deallsed character~st~cs of Figure 7 may be accounted for by lS frlnging fluxes and non-linearlties. Consider~ng the character~st~c for phase 1 shown ln F1gure 8 ~nit~ally around the max~mum reluctance pos~tlon ~0), the rotor poles and ~he stator poles for phase 1 are, ~n the particular construct~on for wh~ch the curves ~re plotted, a long way from overlapplng. At about 10, the rotor and stator poles come into close prox~mity and a reg~on of rapldly r~s~ng torque commences. By approximately 12, actual overlap of the poles has commenced and the torque has r~sen to a value wh~ch rema~ns largely constant for further advance ln angle, w~th some roll-off due to bulk saturation effects in the flux paths. From approx~ma~e1y 379 full overlap of the poles ~s approached and torque then rolls off Yery rapidly wl~h further lncrease In angle, due to extenslve and undesirable bulk saturatlon ~n the flux paths. In th~s partlcular construct10n, the torque at the points of intersection between successlve phases ~s approxlmately 54~ of peak torque, so that switching between phases at these points still results in considerable torque ripple. An additional serious problem however in th~s construction, especially at low speeds, ls the exceed~ngly rap~d rise of torque at the commencement of pole overlap. Torque bu~lds up to more or less its full value in the space of approximately 2 of ~259653 rotor mechanlcdl rotation, so that its effect ls simllar to that of an impulsive blow to the poles of the machine, setting up noise and vibration.

Figure 9 shows a family of stat~c torque versus rotor angle curves for phase 1 of Figure 8 for different values of phase current. The period during wh~ch the torque is substantlally constant ~s relatively greater for low values of excitlng current, and the roll-off at the end of the character~stic ~s relat~vely less significant. However the rapld initlal rlse in torque can be seen to be a proble~ at all current levels and is not allevlated by a reduction in exc~tation current.

In additlon to the torque versus rotor angle curves of F~gures 8 and 9, curves for torque versus phase current may be plotted for each phase for each rotor angle. An example of a torque versus current characteristic for one phase of a four-phase machine wlth the rotor in a minimum reluctance poslt~on ~s showo in Figure 10. As prev~ously explained in relat~on to the tra~ectory of Flgure 3~ for a saturated magnetic system the relatlonship between torque and excitin~ current is in theory l~near. In practice, at low currents before saturatlon is established, the torque Initially increases In proportlon to the square of the current, and only when magnetic saturation ~s established, does the torque then cont~nue to ~ncrease in linear relationship wlth the current. This change from magnetically 11near conditions to ~agnet~cally saturated condlt~ons is represented by a gradual transitlon zone corresponding to the roll-off in the curve relatlng flux l~nkage to current for the saturated case, as exempllfied by the curve for the mlnimum reluctance pos~tion of the rotor ~n F~gure 3. Above the knee of the 8-H curve, torque ~s substant~ally llnearly related to current. For ~he curve of Fiqure 10, the relationship is generally linear above about 7A. The in~t~al non-linear~ty of the relat~onshlp between torque and current at relatively low current values is also reflected in curves such as those of Flgure 9, where the incremental increase ~n torque for a 1 2~;9653 , specified increase ln current will d~ffer for success~ve sim11ar I
;ncremental increases in current. In the system to which Figure 9 ~ relates, the incremental increase in torque for an ~ncrease in current . from 5 to 10A will be seen to be different from that for an increase from 10A to 15A, the increase in torque for the 5A current ~ncrease from lOA to 15A being substantially greater than that ~or the change in current from 5A to lOA. However it will also be seen that for increases in current once the current exceeds about 20A, successive incremental ~ncreases in current will achieve substantially the same incremental change ~n torque over quite a w~de range of current regardless of the actual current values del~miting the change. At very high levels of current, in excess of the ~aximum 60A value shown in Figure 9, non-llnearity again comes lnto play w~th the onset of bulk saturation, which {s undesirable~ Bulk saturat~on is also reflected in curves such as that of Figure 10 by a roll-off ~n the relat~onship between torque and current ~t very high levels of - current. For ease of control therefore, a variable reluctance motor is preferably rated to operate ln the region ~n wh~ch torque ~s substantially l~nçarly related to current, and whlle the e~fects of torque linearl.ty at low currents and torque roll-off at high currents : are then of llttle practical sign~flcance for stepp~ng motor exempliflcations of varlable reluctance mach~nes, ~t further complicates appl1cation of the YRM to ~ariable speed dri~es, in which in part~cular low current operat$on 1n the non-llnear reg1On of curves such as that of.F~gure 10 may be unavoidable at low shaft speeds and under standstill conditions.

An example of a 200 step permanent magnet stepping motor us~ng bipolar exciting currents is shown ~n F~gure 11, in wh~ch it will be seen that the teeth on the rotor and stator are constituted by respective substantially semi-circular cutouts in the external and internal peripheries of the rotor and stator respectively. It can be seen that .
the dimensions of the teeth are accord~ngly relatively small ln r`elation to other dimenslons of the rotor and stator and ln particular, the airgap is then relatlvely large compared with the ~259653 dimensions of the teeth, whlch it is belieyed results ~n the smoothed static torque versus angle characterlstics of su~h motors, prev~ously referred to in this speciflcation.

A variable reluctance motor drive system under torque control and embodying the pr~nciples of the present invention is shown ~n F1gure 12. As deplcted in thls Figure, the system has only an inner torque control loop, which is relevant to the present discussion, but ~n a typical practical construction, an outer speed control loop ~s also provlded, the torque then belng adjusted or controlled to meet a set speed signal ln operatlon of the system. As shown therefore a ~our-phase reluctance motor 23 drives a load 24 and has a rotor pos~tlon sensor 25 associated with lts shaft 30. The sensor may be for example an encoder generating one or more streams of pulses which are electronlcally processed to provide shaft posltlon informat~on at a succession of angular ~ntervals. Appropr~ate log~c 1s employed to permlt determlnat~on of the dlrectlon of rotatlon and a zero marker i5 also provlded. A reference waveform generator 27 uses position information from the sensor 25, modified as required by sensor interface 26, to provide as an output, a slgnal ~ndicative of the value of current requlred ~n each phase for each angular poslt~on of the shaft to achleve a desired shape of phase torque. The generator 27 has a further "set levelU input ad~ustable by a controller or monitorlng means, for determlning the actual Yalue of the torque to be generated, sub~ect to the shape constralnts also oalled for by th~
generator. The ou~put s~gnal from the generator 27, of a value determined by the comb~natlon of rotor pos~tion slgnal and set level input, is appl~ed to a current controller 2~, wh~ch proYldes an output signal for each of the four phases of the motor in the form of a reference current waveshape. These reference waveshapes then provlde gatlng slgnals or lnputs to a power converter 29 in which the actual phase currents of the ~otor are forced to track the reference current waYeforms. For thls purpose a signal Indlcatlve of the actual current in each phase is fed back to the current controller, so that the sating signal forwarded to the converter from the controller 28 serves to produce the required phase current.

i259~53 I ;
The waveform generator 27 and the current contrpller 28 together form current magnitude regulating means by whlch the relat~e Instantaneous value of the excitlng current in each stator winding at every rotor posltlbn can be controlled so that the energislng current will have a waveshape suitable for achievlng the phase torques des~red during operation of the ~otor for smooth torque trans~t~ons between phases and min~misation of ~hammer-blowB. Accord~ng to varlous constructlons of the system of the lnvention, specific waveshapes may ~e produced by appropr~ate analogue means. In one such embodlment, the output of the sensor may be modifled to provide a sinewave, the lnstantaneous magnitude of ~hich at each rotor posltion ls used d~rectly to establlsh the approprlate relatlve value for the w~nding current. The current regulatlng means formed by generator 27 and controller 28 is further responslve to the "set level~ slgnal to establish an absolute 15 magn1tude for the current at each rotor posit~on, whlle the relative value of the current at that position compared with ~ts value at any and every other positlon ~s determlned by the rotor poslt~on as slgnalled by the sensor 25. A dlgital control strategy ls descrlbed in our co-pending Patent Applicat~on ent~tled UControl Systems for Yarlable Reluctance Motors".

A partlcular strategy uslng ramped current magnltudes to overcome the problem of the ~n~tlal rapid torque r~se at the commencement of overlap and the ~orque ripple aris~ng from swltchlng between the roll-off portlbn of a phase com~ng to an end and the rls~ng torque portlon of a phase beglnnlng pole overlap ls Illustrated ln Figure 13. The drawlng is schematic only and ~s not intended to represent any partlcular mach~ne character~stlc. Static phase torques (t~ are shown agalnst rotor angle for phases A and B, together w1th current waveforms (~) to be applled to these phases to y~eld a relatlvely smooth motor torqueO The strategy lnvolYes swltch~ng current Into a phase (as shown for phase A) at a controlled rate rising l~nearly but com~encing only after the inltial sharp static torque r~se so that the torque (T) produced by this phase In operat~on of the mvtor r~ses at a controlled rate corresponding to the rate of current r~se to a steady ~2~i~653 ;

level of torque correspondlng to the substantially constant torque portion of the static torque curve which preva~ls during the progression of pole overlap followlng the initlal rise in the static torque curve at the commencement of pole overlap. Current in phase A
Is then similarly ramped down towards the end of this constant torque region, commencing at the point where current for phase B begins its controlled rise. Thus the current magnitude remains substantlally constant during an Intermediate portlon of the angular ~ncrement of rotor rotation dur~ng which each windlng ~s energised. The ~nitial and termlnal portlons of the increment of energ~sation ha~e .r.
respectively~ rlsing current magnitudes and fallfng current magnitudes, and, as shown In the Flgure, the rate of ~ncrease of current durfng the ~nlt~al port~on of the angular ~ncrement of rotor rotat~on Is the same as the rate of decllne of current during the terminal port~on. Approprlate selec~ion of the intersections between these current curYes will yield substantlally rlpple-free overall motor torque without the impulslve forces caused by the sharply r~sing inltial parts of the stat~c torque characterlst~cs. The phase torques in operatlon of the motor ~hen cons~st of a succession of those portlons of the Indivldual static torque characteristlcs resulting from energlsat~on of the Individual phase wind~ngs at approprlate stages. The net motor torque during each transitlon between phases is computed by addlng the individual phase torques dur~ng the translt10n. The waveforms required for the strategy of F~gure 13 may be deriYed by computat~on or experlment and constructed ~n operat~on b~ a system in accordance with F~gure 12, for example by an approprlate analogue constructlon of the generator 27.

However such ramped currents are not necessarily easily syntheslsed In an economlca1 construct~on by current-regulating means, such as an analogue embod~ment of the generator, especially at high rotational speeds, and In additlon, phase to phase torque transit~ons may not necessarlly be smoothed for each successlYe transition by s~mllar ramps, in that the preclse shapes of the static ~orques in the trans~tion reglons are to an extent affected by the polarities of the 6~;3 po1es between which the transitlons t~ke place and are not necessari1y identical for each such transition. Accordingly indlv~dual analogue - ramp generators may require to be speclfically tailored for each phase to phase transition~ In addition, it will be evident from Figure 13 that since a proportion of the potential torque-generating capacity of each phase is not fully utilised or is not utillsed at all, there is an effective derating of the machine, which while not unacceptable in many applicat~ons, is preferably avoided. In an alternative strategy, therefore, the shape of the static torque against rot~r angle characterist~c is modif~ed to ease the rate of torque rise at the beginning of pole overlap, thus allowing phase currents ~o be sw~tched during the init~al commencement of pole overlap but without the current regulating means having tc take account of the abrupt changes in torque exper~enced at th~s stage of oYerlap w~th characterist~cs such as those shown in F~gure 13.
.,~, Modification of the shape of the static torque curve may be ach~e~ed by shap~ng either rotor or stator poles or both. In one known construct~on, thç modified statlc torque versus rotor angle character~stic shown In Figure 14 was achieved. This substant~ally trapezoidal character~st~c has a smsothly r~sfng ramp ~n substitut~on for the rapidly r1slng Initial port~on of the curves o~ Flgure 13 and a sim~larly fall~ng ramp, albe~t at a slightly different rate fro~ the rising ramp, takes the place of the roll-off por~on of the curves of Figure 13.

Alconstruct~on of rotor accordlng to the presen~ invent~on for achieving a sultably mod~f~ed static torque aga~nst rotor angle character~stic ~s shown ~n Figure 15. The rotor 48 conslsts of a large number of laminations 49, each of whlch is identlcal w~th its neighbours but is sllghtly displaced rotationally about the axls of the rotor, so that for laminations lntermediate the ends of the rotor, the leading faces of the pole port10ns defined by each laminat~on are slightly in advance of those of the lamination to one axlal side of ~t and slightly tr the rear of the front oole edge defining faces rf rhe ~5~ii3 lamination to lts other axial side, this relative advance being ln a circumferential direction about the ax~s of the rotor. Thus in this arrangement, the poles of the laminated rotor are skewed along the axial length of the rotor relative to its axis of rotation. In order to achieve this, each rotor lamination is slightly displaced relative to its axial neighbours in the laminated rotor assembly. The circumferential direction of this displacement is consistent throughout the length of the rotor, so that each laminatlon is either advanced or set back relat~ve to ~ts predecessor. Accord~ngly each rotor pole ts skewed from one axial end of the rotor to the other~ and the angle of skew as shown ln F~gure 15 ls 15 aboùt the axls of the rotor. Thts angle of skew is deftned about the rotor axls between a rotor radtus passtng through the leading edge of the la~ination at one pole at one end of the stack and that passtng throu~h the leading edge of the lamlnation at the other end of the stack at the same pole.

Figure 16 shows a practical construction of ro~or ~aminatlon 49 suttable for the rotor of F~gure 15 together with an assoctated stator lam~nation 50. Figure 17 shows the torque/rotor angle curves for the machine construction of Ftgures 15 and 16 at a var~ety of levels of phase current, the rotor be~ng skewed ~n accordance with Figure 15.
It n1ll be seen that at a low Yalue of phase current, a somewhat trapezoidal stat~c torque wavefonm is produced, although the ln~t~al rts~ng port~on tends to roll off towards the constant torque port~on rather than to r~se towards It ~n a wholly llnear manner. At higher va~ues of phase current, the flat-topped portion of the curve becomes less signlficant and the curved nature of the rtsing and fall~ng porttons of the curve becomes even more apparent. At a large value of phase current, the simllarlty of the statlc torque curves to a sinewave becomes particularly marked. The curves of Figure 17 relate to a constructton of machine wh~ch ~s less than ideal in terms of spec~flc output but the shapes of the statlc torque curves for all machlnes havlng slmllarly skewed rotor poles reflect the same features dS those shown, trrespectlve of the performance of the motor.

6~i3 i The similarity of the stalic torque characteristics to sinewaves leads to a further strategy for producing smooth operatîon of a variable speed reluctance motor and one which yields a preferred system accordTng to the present invention. This strategy is illustrated for a four-phase machine in Figure 18. The static torques (t) for phases A and B are slnusoidal and each phase is then driven with a complementary sinusoidal exciting current (i). Accordingly the motor phase torques (T) under operating conditions are then sine squared curves, which may be shown graphically by plotting static torque curves for different levels of phase current and transferring the appropriate torque values corresponding to the current in each phase at successive angular positions of the rotor onto the motor torque diagram to define the phase torques in operation. Considered in ~-mathematlcal terms the static torques tA, tB etc. may be described by tA = Kt I Sin~) and tB = Kt.I.Sin(~ +90) = Kt.I.Cost~) ;
etc.
where Kt is a motor constant, so that for phase currents iA and ig, where iA = Ip-Sin(~) and ig = Ip.Cos(~), etc.

Ip being the peak current, the phase torques (TA, Tg, e~c.) in operation of the motor w~ll be TA = Kt.Ip.Sin2(0) and TB = Kt.Ip.Cos2(0), etc.

Thus the 90 phase disp1acement between phase A and phase B as shown in Figure 18 means that if the phase torque ~n operation of the motor for phase A ls proportional to sine squared, then that for phase B Is proportional to coslne squared. Assuming operation In the saturated region and similar magnetic circuit conditlons for each phase, the torque exerted by the motor durlng transitlon between phases will then remain constant, since the sum of the squares of the sine and cosine ~2~;96~3~
.

of the same angle equates to unity. This strate~y is favoured oYer the supply of trapezoidal waveforms in that sinusoidal waveshapes have slower rates of change than do step or trape~oidal waveforms at their abrupt transition points~ and sharp changes of torque may therefore be avoided. In addit;on to this a machine having a skewed rotor and fed with corresponding sinusoidal energising currents is significantly quieter than known machines of traditional construction, wh~le since current is applied to the windings only when it is capable of doing useful work by developing torque, and also at all times when it so capable, there is better copper utillsation than in a mach~ne with conventl~nal poles, as well as reduced copper losses.

Flgure 19 shows a particularly advantageous arrangement of skewed rotor and its relationshlp with a stator~ in a system embodylng the principles of the invention, together with a development in transverse view of some of the poles of the rotor and stator to lllustrate preferred circumferential dimensional relationships. It will also be apparent from this Figure that the poleface surfaces of the drivlng or stator poles define substantlally continuous surfaces facing the airgap, as compared with the toothed poleface structure of ~le permanent magnet stepplng motor shown in Figure 11. The stator 51 has elght poles 52 to 59, each of which extends over an arcuate ex~ent of 30 and is spaced from its nelghbours by a gap of 15. The rotor 60 has slx poles 61 to 66 and ls formed of a stack of lamlnations, the arcua~e extent of each outer per1pheral portion of each pole being 20, and each such outer peripheral portion being separated from that o~ the next pole by a gap of 40. The rotor has a ske~ of 10. Accordingly the total arcuate extent of the envelope occupied in space by each rotor pole between its most leading edge portlon and its most trailing edge portion is 30, i.e. the same arcuate dimension as each stator pole. Simllarly the arcuate extent of the gap between the rearmost part of the rearmost lamination of each rotor pole and the foremost part of the leading lamination of the following pole is also 30. Accordingly, when one pa~r of rotor poles, 61 and 64, is al~gned with stator poles 52 and 56 as shown in Flgure l9, the '. :

iron of ~he rotor poles is positioned exactly beneath the iron of the stator poles, with no part of the rotor pole lying outboard of the stator pole or vice versa.

Similar1y the gaps between poles 62 and 63 and 65 and 66 respectlvely are precisely aligned with poles ~4 and 58, with no rotor iron whatever underlying these stator poles. This inter-relat~onship between rotor and stator gives especially efficient transition between phases, and the static phase torque characteristics do not exhibit the zero torque deadband portions shown on the characteristics of, for example, F~gure 7. A further advantageous feature of the rotor lamination of Figure 19 ~s the taper~ng of the rotor poles in an outward direct~on from their bases where they merge into the central c~rcularly apertured part of the lamination by which the lam1nation is received on the motor shaft.
.
Pole taper is an especially advantageous feature of particular embod~ments of the motor of the Inventlon descr~bed herein, namely radially outward taper on the rotor poles, so that these poles narrow towards the~r tlps, and a widening of the stator poles towards their radially ~nner tips, so that the po1e faces of the rotor and stator may be in subs~an~ial overly~ng alignment, in a pre~erred constructlon and a g~ven angular relationsh~p.
.
Referr1ng to the development of these poles, Rx1, the lamination span, pl.us Rx2, the skew, together sum to the rotor po1e span at the pole tip, and Rxl + Rx2 = Sxl where Sxl is the stator pole span at the pole tip. Rx3, the rotor ~nterpole gap between rotor pole tips~ also equates to Sxl. Because of the rotor pole skew, the stator pole tip does not entirely cover or overlie rotor iron when the rotor and stator poles are aligned.
Accord1ngly the stator pole tlp ls of greater slze than the magnetlc 125i9653 ckrcuit strictly requires and it tapers inwardly to a reduced cross-section or waist, Sx2, located between the pole tip and the base of the pole, Sx2 being less than Sx1. This waisting of the stator poles gives increased copper area or space.

The skew is defined by the ratio of Rx2 to Rx1. In a preferred construction, Rx2 = ~ , Rx1 i `
In a fo~r-phase machine, this skew ratio has the surprising result of giving good s~nusoidal static torque characteristics without significantly affecting or reducing the net torque output of the machine. In a three-phase machine, where flat-topped sinusoids are required, this skew ratio is typically less than ~. --While this aspect of the invention has been descr~bed with particular relevance to an eight stator pole, six rotor pole arrangement, It is in no way limited to such a construction and greater or lesser numbers of poles may also be used. Also in addition to the one tooth per pole constructions of rotor and stator already described and illustrated~
each pole face may ~e divided to provide two or m~re teeth9 and this may be advdntageous in certain circumstances.

Figure 20 shows stat1c torque characteristics at a variety of current levels for a rotor having lamlnations in accordance with Figure 19.
~he sinusoldal nature of these characteristics will be especlally apparent in this construction which has a favoured relationship between the rotor and stator pole arcuate extents.

The skewed rotor construction described in relation to inter alia the preceding Figures 15, 16 and 19 is espec~ally applicable to a drive system accordlng to the invention in which sinusoidal current waveshapes are input to the stator windings. It is however also lZ59~;~;;3 usabll wlth other waveforms of stator current and is not neccessarily limited to sinusoids. It will be part~cularly apparent from the static torque against rotor angle characteristics shown in Figure 20 that the characteristics achieved by rotor skewing are also substantially symmetrical, which is especially advantageous in a bidirectional motor, whether in conjunction with current shaping or not. The angle of skew has been found to be significant and a favoured degree of skew is shown in the preferred construction of Figure 19.

However the drive system of the invention as described in relation to Figure 12 may also advantageously be associated with the alternat~ve form of pole shap~ng shown in Figure 21. T~o adJacent stator poies 67 and 68 each have respective polefaces 69 and 7~. The central regions of these polefaces are disposed at a constant alrgap from the path traversed by rotor polefaces passing beneath them but ~n their edge regions, the polefaces ha~e respective profiled surface port~ons 71 and 72 where the alrgap Increases circumferentlally outwardly of the pole by virtue of the poleface surfaces in these edge regions beinq progress~vely set back from a notional circumferential cont~nuatlon of the central regions of the polefaces of the respective poles. Thus each poleface has proFiled surface portions in its edge regions, so that the airgap between the stator pole and an al~gned rotor pole ~s greater along the edges of the stator pole, as compared with ~ts A:
central reglon. At the circumferent~ally outward ends of these edge regions, the polefaces end at tlps 73 and 74, ~here the po7eface surfaces merge with radlal surfaces extend~ng into the ~nterpole spaces where the windlngs are rece~ved. Pole shaplng of this k~nd also achieves a reductlon in the rate of torque change, especlally on ~n~tial overlap, and ~n particular in conjunction with current shaping, enables the torque transitions to be smoothed and noise and vlbration in operation of the machine to be substantially minimised.
In addition, each stator poleface can be seen to have a substantially continuous surface without abrupt changes of profile in the arrangement shown ~n Figure 2l.

A particular and surprising feature of the invention is the reduction in noise production when the phase windings are connected ln parallel rather than in series. In a series connection, the magnetomotive forces in the air gaps are equated, and the fluxes are determined by the air gaps themselves, so that any differences between the air gaps will lead to unbalanced fluxes. By connecting the phases in parallel, equal fluxes are forced on opposite poles and the displacement forces generated are substantially equal. A motor according to the invention may also incorporate a field coil, which excites all phases equally and may be used to modify the non-linear torque-current !~`
characteristics of the phases so that they become substantially linear over the normal operating range of the motor.

Figure 22 shows in schematic diagrammatic form, an analogue clrcuit arrangement espec~ally suitable for but not lim~ted to a six rotor pole, elght stator pole motor having skewed poles and a substantially sinusoidal static torque against rotor angle characteristlc. The same reference numerals as those of Figure 12 are used for s~milar ~tems.
The sensor 25 is arr~nged to have an output which is in the fonm of two triangular wave-forms in quadrature and cyclic in 60 -mechanical. These signals are converted to sinusoida~ wave~orms by i converters 75, giving sine and cos~ne waves. These slne and cosine waves serve to form correc~ reference current waveshapes ~or achievlng smooth torque output in this embodlment.
.
Since ~ositive and negat~ve torque is created in ~he reluctance motor depending on the rotor pos~tion when each phase winding is energised, if a positive half-sinewave is associated with phase 1 for positive torque, then the inverted negative half cosine wave must be associated wlth phase 2, the lnverted negative sine half-wave with phase 3 dnd the positive cosine half-wave with phase 4. For negative torque, the phase sequence is inverted negative half-sinewave, positive cosine half-wave, positive sine half-wave and inverted negative cosine half-wave. Since only unidirectional currents are required in each -, phase, the two-quadrant power controller is arranged to respond to ~59~
!

current ~n one direction only, so that its output is one half-cycle for each of the full waveforms applied to it, and each phase is energised in turn by half waves cf the same polarity.

In Figure 22, a further output from the sensor interface 26 provides a speed output signal which is associated with a speed demand signal to provide an input to a speed controller 76, the output of which is a torque demand signal. This torque demand signal is applied alon~ with one of the slne or cosine waves generated by the con~erters 75 to respective analogue multipliers 77 and 78. The output of multiplier 77 is then a sine wave and that of multiplier 78 a cosine wave, the relative instantaneous magnitudes of these output signals following the sine and cosine waves determined by the conYerters 75 while their absolute magnltudes are set by the torque demand signal. In the case of regular sinewaves used in the present construction of control systems, this torque demand signal may be the peak value of the wave, which then determines the current level at all other points along the waves, but this is not necessarily the case for other waveforms.
Following the analogue multipliers, the sine wave and coslne wave are each paralleled by an inverted sine and cosine wave respectively and these four signals are applied to current controllers 79, in which current feedback signals from the phase windings are associated with the sine and cosine slgnals to provide actual current demand signals for the power converter 29. The final output signals from the current controllers 79 are applied to comparators 80, which also have high fre~uency inputs for pulse wid~h modulation In known manner. The PWM
inpu~ is modulated in each case by the set level signal from the current controller 79 and the resulting outputs proYide said current 'J~
demand slgnals for the two-quadrant power converter 29.

Figures 23 to 26 are circuit diagrams of exemplifications of certain of the components or units of the drive system of Figure 22. Figure 23 shows the current regulators or controllers 79, while Figure 24 shows the speed controller or regulator 76. The multipliers 77 and 78 are illustrated In Flgure 25, and the sensor signal interface or ~:~S~316S3 ll .
triangle-sine converters 75 are dep;cted in Figure 26~ The detailed operation of these circuits will be apparent from the Figures and is accordingly not the subject of detailed description herein.

In Figure 27, a generator configuration of stator lamination for a ~
machine according to the invention is shown. Lamination 101 has si~
stator poles for operation with a four-pole rotor. Two of the interpole spaces which receive the stator windings are enlarged to accommodate a field winding, indicated by reference 102. When energlsed, this field winding sets up a constant flux, indicated by 0 ~n the Figure? which diYides between the three phases of the machlne l!.
on the basis of thelr relatiYe reluctances. As the rotor rotates, the relatiYe permeance of the phases changes, so that flux linkages of the phase windings also change and accordingly phase voltages are produced. The structural features, viz. skewlng etc., applicable to variable reluctance motors accord~ng to the ~nvent10n ln order to shape their torque outputs so that the phase torques become substantlally sinusoidal functlons of rotor angle, may also be applied .
to shape the voltag~ output of a generator accordlng to this embodiment of the Invention.
.,. ,., Figure 28 shows a schemat~c diagram of a three-phase ~enerator according to this aspect of the invention, in which the field windtng 102 is energ~sed by a DC source and the three phase windings 103 are connected in star to the three phases of a load 104.
,- . .

Claims (23)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A drive system comprising a saturable variable reluctance electrical motor, said motor comprising a stationary or driving member having a plurality of salient driving poles, a magnitizing winding for each driving pole, and a movable or driven member having a plurality of salient driven poles, the number of driven poles being less than the number of driving poles, and a plurality of airgaps, the airgap between each driving pole and a driven pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the driven poles being formed so that in operation of the motor magnetic saturation occurs substantially in a region of the mechanically variable interface or overlap between the driving and driven poles, and the extents and dispositions of the driven poles being related to those of the driving poles so that in operation of the motor, a force-producing increment of driven member displacement resulting from the mechanical interface or overlap of each driven pole with a driving pole overlaps a force-producing increment of driven member displacement resulting from the overlap of another driven pole with a further driving pole, and the system also comprising power supply means including voltage source means for connection across the driving pole windings, said windings being connectible across said voltage source means in a predetermined sequence during driven member displacement and each driving pole winding being thus connectible for a predetermined increment of driven member displacement, so that the driving poles may be sequentially energized for displacement of the driven member between successive minimum reluctance positions, and driven member position-sensing means for generating at least one signal, the instantaneous value of which is dependent on the position of the driven member for providing driven member position information at a succession of intervals within each said predetermined increment of driven member displacement during which a driving pole winding is connectible to said voltage source means, and the power supply means also including means for regulating the instantaneous magnitude of the current in a driving pole winding when connected to said voltage source means, said current-regulating means being responsive to said at least one driven member position-dependent signal of the driven-member position-sensing means to regulate said current magnitude so that the instantaneous value of said current set by said regulating means at any position of the driven member within said increment of driven member displacement during which the winding is connectible to said voltage source means relative to its value at any other said position is substantially determined by the instantaneous position of the driven member within said increment.

2. A drive system according to claim 1, wherein the poleface of at least each driving pole defines a substantially continuous surface facing said airgap.

3. A drive system comprising a saturable variable reluctance electrical motor, said motor comprising a stator having a plurality of salient stator poles, a magnetizing winding for each stator pole, and a rotor having a plurality of salient rotor poles, the number of rotor poles being less than the number of stator poles, a radial airgap between each stator pole and a rotor pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the rotor poles being formed so that in operation of the motor, magnetic saturation occurs substantially in a region of the mechanically variable interface or overlap between the stator and rotor poles, and the arcuate extents and dispositions of the rotor poles being related to those of the stator poles so that in operation of the motor, a torque-producing angular increment of rotor rotation resulting from the mechanical interface or overlap of each rotor pole with a stator pole overlaps a torque-producing angular increment of rotor rotation resulting from the overlap of another rotor pole with a further stator pole, and the system also comprising power supply means including voltage source means for connection across the stator pole windings, said windings being connectible across said voltage source means in a predetermined sequence during rotor rotation and each stator pole winding being thus connectible for a predetermined angular increment of rotor rotation, so that the stator poles may be sequentially energized for rotation of the rotor between successive minimum reluctance positions, and rotor position-sensing means for generating at least one signal, the instantaneous value of which is dependent on the position of the rotor for providing rotor position information at a succession of intervals within each said predetermined angular increment of rotor rotation during which a stator pole winding is connectible to said voltage source means, and the power supply means also including means for regulating the instantaneous magnitude of the current in the stator winding when connected to said voltage source means, said current-regulating means being responsive to said at least one rotor position-dependent signal of the rotor position-sensing means to regulate said current magnitude so that the instantaneous value of said current set by said regulating means at any angular position of the rotor within said angular increment of rotor rotation during which the winding is connectible to said voltage source means relative to its value at any other said angular position is substantially determined by the instantaneous angular position of the rotor within said angular increment.

4. A drive system according to claim 3, wherein the poleface of at least each stator pole defines a substantially continuous surface facing said airgap.

5. A drive system according to claim 3, wherein said current-regulating means is responsive to said rotor-position dependent signal to regulate said current magnitude so that successive instantaneous values of said current during said initial portion of said angular increment of rotor rotation during which the winding is connectible to said voltage source means increase progressively with progressive rotation of the rotor and successive instantaneous values of said current during a terminal portion of said angular increment decrease progressively with said progressive rotation.

6. A drive system according to claim 5, wherein said current-regulating means is responsive to said rotor-position dependent signal to regulate said current magnitude so that the rate at which successive instantaneous values of said current decrease during said terminal portion of said angular increment of rotor rotation is substantially the same as the rate of increase of successive instantaneous current values during said initial portion and the succession of instantaneous current values over said angular increment of rotor rotation substantially defines a substantially symmetrical current waveshape extending over said angular increment.

7. A drive system according to claim 6, wherein said current magnitude remains substantially constant during a portion of said angular increment of rotor rotation following said initial portion, said portion ending with the commencement of said terminal portion.

8. A drive system according to claim 6, wherein said current-regulating means is responsive to said rotor-position dependent signal to regulate said current magnitude so that said instantaneous current values during said angular increment of rotor rotation substantially define a substantially sinusoidal halfwave.

9. A drive system according to claim 3, further comprising means for producing a demand signal, the value of which is indicative of a desired level of a parameter of motor performance, said current-regulating means also being responsive to said parameter-level-indicative signal to regulate said stator winding current so that the absolute magnitude of said current at every angular position of the rotor within said angular increment of rotor rotation during which the winding is connectible to said voltage source means is substantially determined by the value of said parameter-level-indicative signal.

10. A drive system according to claim 3, wherein each rotor pole and each stator pole has circumferentially spaced apart edge regions and at least said rotor pole edge regions are shaped so that at least the axial extent of the airgap between overlapping rotor and stator poles will vary at least during the commencement of pole overlap.

11. A drive system according to claim 10, wherein the rotor comprises a plurality of laminations and each said edge region is defined in the axial direction of the pole by a succession of edge region portions, and each lamination is circumferentially displaced relative to an adjacent lamination so that said edge region is skewed relative to the axis of rotation of the rotor.

12. A drive system according to claim 3, wherein each rotor pole and each stator pole has circumferentially spaced apart edge regions and at least said rotor pole edge regions are shaped so that at least the radial dimension of the airgap will vary at least during the commencement of pole overlap.

13. A drive system according to claim 12, wherein surface portions of the poleface of at least each rotor pole in said edge regions are radially displaced relative to the central surface portion of the poleface so that the airgap between an edge region surface portion of the poleface and the poleface of an aligned pole is greater than the airgap between the central surface portion of the poleface and the poleface of an aligned pole.

14. A drive system comprising a saturable variable reluctance electrical motor, said motor comprising a stator having a plurality of salient stator poles, a magnetizing winding for each stator pole, and a rotor having a plurality of salient rotor poles, the number of rotor poles being less than the number of stator poles, a radial airgap between each stator pole and a rotor pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the rotor poles being formed so that in operation of the motor magnetic saturation occurs substantially in a region of the mechanically variable interface or overlap between the stator and rotor poles, and the arcuate extents and dispositions of the rotor poles being related to those of the stator poles so that in operation of the motor, a torque-producing angular increment of rotor rotation resulting from the mechanical interface or overlap of each rotor pole with a stator pole overlaps a torque-producing angular increment of rotor rotation resulting from the overlap of another rotor pole with a further stator pole, and the system also comprising rotor position-sensing means for generating at least one signal, the instantaneous value of which is dependent on the angular position of the rotor, and power supply means including voltage source means for connection across the stator pole windings, said windings being connectible across said voltage source means in a predetermined sequence during rotor rotation and each stator pole winding being thus connectible for a predetermined angular increment of rotor rotation, and the power supply means also including means for regulating the instantaneous magnitude of the current in a stator winding when connected to said voltage source means, said current-regulating means being responsive to said at least one rotor position-dependent signal of the rotor position-sensing means to regulate said current magnitude so that the instantaneous value of said current set by said regulating means at any angular position of the rotor within said angular increment of rotor rotation during which the winding is connectible to said voltage source means relative to its value at any other said angular position is substantially determined by the instantaneous angular position of the rotor, each rotor pole and each stator pole having circumferentially spaced apart edge regions, the circumferential spacing of said edge regions of each pole being substantially constant throughout the axial extent of the pole and one axial end of each of said edge regions of at least each rotor pole having a circumferential displacement relative to the other axial end of the same edge region of the pole of between one quarter of the constant circumferential spacing of the edge regions of the pole and a value equal to said spacing, so that said edge region is skewed relative to the axis of rotation of the rotor.

15. A drive system comprising a saturable variable reluctance electrical machine, said electrical machine comprising a stator having a plurality of salient stator poles, a winding for each stator pole, and a rotor having a plurality of salient rotor poles, the number of rotor poles being less than the number of stator poles, a radial airgap between each stator pole and a rotor pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the rotor poles being formed so that in operation of the machine, magnetic saturation occurs substantially in, a region of the mechanically variable interface or overlap between the stator and rotor poles, and the arcuate extents and dispositions of the rotor poles being related to those of the stator poles so that in operation of the machine, a torque-producing angular increment of rotor rotation resulting from the mechanical interface or overlap of each rotor pole with a stator pole overlaps a torque-producing angular increment of rotor rotation resulting from the overlap of another rotor pole with a further stator pole, and the system also comprising voltage source means connectible across stator pole windings, said windings being connectible across said voltage source means in a predetermined sequence during rotor rotation and each stator pole winding being thus connectible for a predetermined angular increment of rotor rotation, and rotor position-sensing means for generating at least one signal, the instantaneous value of which is dependent on the position of the rotor for providing rotor position information at a succession of intervals within each said predetermined angular increment of rotor rotation during which a stator pole winding is connectible to said voltage source means, and said windings also being connectible across an electrical load during rotor rotation, also in a predetermined sequence, and each stator pole winding being thus connectible for a predetermined further angular increment of rotor rotation.

16. A saturable variable reluctance machine according to claim 15, wherein the stator pole windings are accommodated in interpole spaces defined between the stator poles and at least one of said spaces also accommodates a field winding.

17. A saturable variable reluctance electrical machine comprising a stationary or driving member having a plurality of salient driving poles, a winding for each driving pole, a movable or driven member having a plurality of driven poles, the number of driven poles being less than the number of driving poles, and a plurality of airgaps, the airgap between each driving pole and a driven pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the driven poles being formed so that in operation of the machine, magnetic saturation occurs substantially in a region of the mechanically variable interface or overlap between the driving and driven poles, the extents and dispositions of the driven poles being related to those of the driving poles so that in operation of the machine, a force-producing increment of driven member displacement resulting from the mechanical interface or overlap of each driven pole with a driving pole overlaps a force-producing increment of driven member displacement resulting from the overlap of another driven pole with a further driving pole, each driven pole and each driving pole having edge regions spaced apart in the direction of relative displacement of the driven and driving members, said spacing of said edge regions being substantially constant throughout the extent of the pole in a direction transverse to said direction of relative displacement and one transverse end of each said edge region of at least each driven pole being displaced in said direction of relative displacement with respect to the other transverse end of said edge region by between one quarter of the constant extent of the pole in said direction of relative displacement and a value equal to said extent so that said edge region is skewed relative to said direction of relative displacement.

18. A saturable variable reluctance electrical machine comprising a stator having a plurality of salient stator poles, a winding for each stator pole, a rotor having a plurality of rotor poles, the number of rotor poles being less than the number of stator poles, a radial airgap between each stator pole and a rotor pole positioned in alignment therewith being small relative to the dimensions of the poles transverse to said airgap and at least the rotor poles being formed so that in operation of the machine, magnetic saturation occurs substantially in a region of the mechanically variable interface or overlap between the stator and rotor poles, the arcuate extents and dispositions of the rotor poles being related to those of the stator poles so that in operation of the machine, a torque-producing angular increment of rotor rotation resulting from the mechanical interface or overlap of each rotor pole with a stator pole overlaps a torque-producing angular increment of rotor rotation resulting from the overlap of another rotor pole with a further stator pole, each rotor pole and each stator pole having respective circumferentially spaced apart edge regions, the circumferential spacings of said edge regions being substantially constant throughout the axial extent of the pole and one axial end of each said edge region of at least each rotor pole being circumferentially displaced relative to the other axial end of said edge region by between one quarter of the constant arcuate extent of the pole and a value equal to said arcuate extent so that said edge region is skewed relative to the axis of rotation of the machine.

19. A saturable variable reluctance electrical machine according to claim 18, wherein said circumferential displacement between said axial ends of said edge region is approximately one-half of said arcuate extent.

20. A saturable variable reluctance electrical machine according to claim 18, wherein said circumferential displacement between said axial ends of said edge region subtends an angle at the rotor axis of not less than 5°.

21. A saturable variable reluctance electrical machine according to claim 18, wherein the winding of one stator pole is connected in parallel with the winding of at least one other stator pole, said windings together defining a phase of the machine.

22. A saturable variable reluctance machine according to claim 18, wherein the circumferential extent of each stator pole tip is greater than the circumferential extent of a waist portion of the stator pole located between the pole tip and the base of the pole.

23. A saturable variable reluctance machine according to claim 22, wherein the sum of the span of each rotor pole tip and said circumferential displacement between said axial ends of the edge region of each rotor pole is approximately equal to the stator pole tip span.