CA1186361A

CA1186361A - Permanent magnet motors and generators having maximized energy density and efficiency

Info

Publication number: CA1186361A
Application number: CA000422140A
Authority: CA
Inventors: John T. Jackson, Jr.
Original assignee: SYNETRON CORP
Current assignee: SYNETRON CORP
Priority date: 1983-02-19
Filing date: 1983-02-22
Publication date: 1985-04-30
Also published as: AU1145383A; GB2135832A; SE441796B; NL8300681A; FR2541833A1; SE8301002L; AU577514B2; JPS59159655A; DE3306758A1; SE8301002D0; GB8304655D0; GB2135832B; FR2541833B1

Abstract

ABSTRACT OF THE DISCLOSURE

An electrical permanent magnet motor gener-ator designed to operate at or near the point of theo-retical maximum energy/product of the permanent magnet without causing irreversible demagnetization thereof. The operating point is created by enlarging the gap between the permanent magnet and core relative to the length of the permanent magnet, and results in maximizing the energy density of the magnet. Moreover output power and power conversion efficiency are maximized by filling the gap substantially entirely with winding, thereby minimizing ohmic heat generation with respect to power output and also minimizing winding-induced and temperature sensitive demagnetizing effects while promoting linear speed-torque characteristics. In high-speed, high-frequency applica-tions, the invention further renders low loss core mate-rials, such as magnetically soft ferrite, compatible with permanent magnets having remanent flux densities higher than the saturation flux density of the ferrite core material, so as to further maximize output power and power conversion efficiency while minimizing thermal effects.

Description

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PERMANENT MAGNET MOTORS AND GENERATORS HAVING

MAXIMI~ED ENERGY DENSITY AND EFFICIENCY

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The present invention is directed to electric motors or generators, specifically those utilizing a per-manent magnet as the source of magnetic flux, in which the energy density and output power density of the motor or generator are maximized with improved efficiency (i.eO
the ratio of output power to input power) and improved linear speed-torque characteristics over conventional brushless permanent magnet designs at either low or high frequencies of operation.
In the text hereof, the following terms will be used from time-to-time and their respective meanings are set forth below for convenient reference:
(1) Magnetic flux -- a characteristic of an energy field produced by a magnetomotive force. When this state is altered in magnitude, a voltage is induced in an electric conductor linked with ito The flux is thought to be a line or lines (imaginary).

(2) Magnetic 1ux density (B) -- the magnitude of magnetic flux perpendicularly passing through a unit area.

(3) Saturation magnetic flux density (Bs~ --the maximum magnetic flux density that can be induced in amaterial. It is the measured magnetic flux density minus that of vacuum space.

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(4) Remanent magnetic flux density (Br) -- the magnetic flux density of a permanent magnet material re-maining after it has been saturated and the maynetic field intensity has been subsequently reduced to zero (sometimes also called residual flux density).

(5) Magnetomotive force (F) -- the spacial distribution of the time derivative of charge whereby the magnetic field is manifested.

(6) Magnetic field intensity (H) -- a charac-teristic of a magnetic field related to the magnetomotiveforce by a line integral (i.e. magnetomotive force per unit length), sometimes referred to as coercive force. It is generated by current loops or a permanent magnet.

(7) Intrinsic magnetic field intensity (Hc3 --the magnetic field intensity required to reduce the mag-netic flux density in a permanent magnet material to zero after it has been saturated (i.e. equal to maximum coer-cive force.

(8) Demagnetization curve -- that portion of the hysteresi~ loop of a permanent magnet material appear-ing in the second quadrant. It is a curve segment ter-minated by Br and Hc.
t9) Energy product tBH) -- a convenient unit in engineering whereby permanent magnets are compared; the product of the magnetic flux density and the magnetic field intensity at a point on the demagnetization curve of a material; units of energy per volume.
(10) Maximum energy product tBHmaX) -- the product of B and El which is larger than at aty other point on the demagnetization curve.

3 IE;~

(11) Energy density (E/V) -- the energy per unit volume in cgs units found by dividing the energy product by 8 ~ .
(12) Output power density -- the output power per unit volume of a motor or generator.
(13) Power conversion efficiency -- the ratio of output power to input power of a motor or generator.
(14) Operating point -- the point on the demagnetization curve of a permanent magnet at which the magnet is utilized in a magnetic circuit, determined by air gap size or other physical characteristics of the magnetic circuit in which the permanent magnet is util-ized, or by other external influences such as external magnetic fields or temperature~
(15) Cogging -- a characteristic of electrical machines employing toothed components such that torque is required to rotate the rotor a displacement of one tooth to the next tooth -- employed to advantage in Stepper motors.
(16) Reluctance (R) -- the ratio of magnetomo-tive orce to magnetic flux in a magnetic circuit or com-ponent thereof. The reluctance o a particular component of a circuit is proportional to its len~th in the direc-tion of the flux lines and inversely proportional to its magnetic permeability and cross-sectional area.
(17) Linear speed-torque characteristic ~- the characteristic of a motor whereby its output torque decreases substantially linearly in proportion to increases in its rotational speed.

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Traditional design~ of electrical machine , such as motors and generators, employing permanent (magnet-ically "hard") magnets, whether of the Alnico, ferrite, cobalt or other types, tend to operate the magnet at an operating point near the point of remanent magnetic flux density by maintaining a small enough air gap component of the magnetic circuit in which the magnet is employed to minimize the reluctance of the circuit and thereby maxi-mize the flux density. In such rotary electrical machines the permanent magnet, which serves as the source of magne~
tic flux in the magnetic circuit, can be located in either the rotor or stator element, the conductive field winding of the machine which interacts with the magnetic circuit to produce rotation of a motor or output electrical power of a generator being mounted on the opposite element typi-cally affixed to a core of soft magnetic material with which the permanent magnet forms the magnetic circuit.
The aforementioned air gap component of the magnetic cir-cuit normally exists between the permanent magnet and the core and, if minimized, usually minimize~ the reluctance of the magnetic circuit. Such minimization of the reluc-tance of the magnetic circuit in turn creates an operating point of the magnet which maximizes the flux in the cir-cuit according to the following basic circuit equation:maanetomotive force flux = ~ - -reluctance The air gap, due to the low magnetic permeability of air, is normally the most significant reluctance-causing ele-ment in the circuit (the mac3net ancl core usually being oE

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i36~

high magnetic permeability unless adversely affected by temperature or high-frequency operation).
Minimization of the air gap to maximize the flux in permanent magnet machines usually is accomplished by the employment o toothed core structures which provide spaces between the teeth to accommodate the winding and which, by bringing the tips of the teeth into close proxi-mity with the permanent magnet, tend to minimize the effec~
tive air gap. On occasion, in the past, designers have abandoned the toothless core structures in permanent magnet devices for special reasons, such as to prevent cogging, to permit easy and economic installation and removal of the winding, to facilitate fabrication or to eliminate harmonics associated with field distribution through teeth so as to obtain a sinusoidal field. However, even when such teeth are omitted from the permanent magnet device, the designers nevertheless have tried to minimize th~ air gap as much as possible so as to maximize the flux in the magnetic circuit. One example of a previous toothless permanent magnet design is shown in Karube U.S. patent 4,130,769 which employs a toothless core structure to per-mit inexpensive winding installation and removal, but nevertheless stresses minimization of the air gap consis-tent with the smallest winding size w~ich will satisfy the torque requirements of the motor. Also Kamerbeek et al.
U.S. patent 4,135,107 utilizes a toothless core structure to eliminate harmonics in order to obtain a sinusoidal field, but likewise stresses minimization of the air gap by utilizing as large a rotor as possible in the structure.

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Similar toothless core designs are shown in Volkerling et al. U.S. patent 2,952,788; Faulhaber U.S. patent 3,360,668; Kagami U.S. patent 4,019,075, and Karube U.S.
patent 4,080,540.
There are several reasons why minimization of the air gap and consequent ma~imization of the flux in the magnetic circuit have dictated the design of previous per-manent magnet motors and generators. One reason is the knowledge that the output power developed by such a motor or generator is proportional to the magnetic circuit flux density and, since there is usually a desire to maximize output power, there is a corresponding desire to maximize~
the flux density.
More important, previous teachings have emphat-ically encouraged designers to operate permanent magnets at high flux densities because of the danger of irrevers-ible demagnetization of the permanent magnet. The prob-lem of irreversible demagnetization in any permanent mag-net motor or generator is a serious one because any of several external influences can change the operating point of a permanent magne~ during operation such that the point becomes too near the "knee" of the demagnetization curve.
Thereafter, i the 1ux density is further decreased for any reason, anc~ then increased, the operating point will not recoil along the origin~l demagnetization curve but rather will recoil along a minor loop of the curve to a lower flux density. If the external effects causing such shifting of the operating point continue in a cyclic manner, further demagnetization can occur in subsequent 3~

cyclic changes along sequentially lower minor loops which emerge one after another, until ~ final minor loop appear~
which is reversible. When this stage i9 reached, no further demagnetization occurs but the magnet thereafter operates at a much lower flux density with a corresponding loss in energy. The external influences which can cause such demagnetiæation, if an initial operating point of relatively low flux density is created~ are: (1) tempera-ture changes which change the configuration of the demag-netization curve; (2) changes in the reluctance of themagnetic circuit, due to temperature, frequency or mechan-ical variables, which tend to raise the reluctance, lower the flux density and thus shift the operating point lower on the demagnetization curve; and ~3) changes in external reverse magnetic fields created by the winding of the device. Because of these dangers, previous teachings have uniformly recommended that the designer select an operat-ing point which, considering the temperature levels to be expec-ted, lies substantially above the knee of the demag-netization curve and therefore is at a relatively highflux density close to the remanent flux density point. As mentioned above, this is accomplished by minimizing air gap size.
Most designers have previously been aware of the fact that the above-described, generally accepted practice of minimizing the air gap size and maximizing the flux density, although maximiæing output power of a permanent magnet motor and preventing irreversible demagnetization, does not theoretically produce a permanerlt magnet motor of ~L~ 8~;3~

the highest possible output power density (i.e. does not theoretically provide a permanent magnet motor of the smallest possible volume capable of producing a given power output). This is because, although output power is proportional to output torque which i8 in turn proportional to the flux density, output power density is lnversely proportional to the dimensions of the permanent magnet (i.e. its length between poles and its area normal to the direction of flux). Such dimensions affect the overall volume of the motor. Permanent magnet demagnetization curves are such that increases in flux density produce corresponding decreases in magnetic field intensity, and vice versa. Accordingly, pursuant to the aforem~ntioned basic magnetic circuit equation, a given percent increase in Elux density, because of the corresponding d~crease in magnetic field intensity, requires a more than proportional increase in magnet length to compensate for the reduced magnetic field intensity, so as to thereby provide suffi-cient magnetomotive force (the product of magnet field intensity Hm and magnet length Lm) to support the increa~ed flux density. Likewise, a given percent increase in mag-netic field intensity, due to the corresponding decrease in flux density, requires a more than proportional increase in magnet area to maintain a desired flux. The dispropor-tionality o the enlargement of the relevant magnet dimen-sions increases as flux density or magnetic ield intensity is maximized, as -the case may be, This indicates that the highest output power densi~ will therefore correspond to an operating point on the demagneti~ation curve which is --~3 ~8~36~

somewhere between maxim~lm flux density and maximum field intensity. It has been shown mathematically that the maximum theoretical output power density is achieved by operating the magnet at a point on the demagnetization curve where the product of the flux density and magnetic field intensity (i~e. the energy product of the permanent magnet) is maximized.
However the desire to maximize output power (rather than output power density) or, more commonly, the fear of irreversible demagnetization of the permanent magnet if operated near the operating point of theoretical maximum output power density, has dictated the contrary, and generally accepted, principle of maximizing flux den sity as discusqed abovea Accordingly, even when a design objective is to maximize the output power density of per-manent magnet devices/ the traditional answer, because of fear of irreversible demagnetization, is to select a per-manent magnet material having a relatively high remanent flux density, such as an Alnico magnet, and minimize the air gap to maximize the flux density since this is con-sidered to be the practical way to maximize output power density (i.e. consistent with stability of the permanent magnet). This is the opposite of selecting an operating point on the demagnetization curve at or near the lower flux density corresponding to the point of maximum energy product and theoretical output power density.

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It should be noted that the same design prin-ciples and problems do not necessarily apply to nonper-manent magnet devices, i.e. where the magnetomotive force of the magnetic circuit is induced during operation.
There are several reasons for this. First, there is no danger of irreversible demagnetization of nonpermanent magnet devices. Second, whereas permanent magnets operate along a second-quadrant demagnetization curve where a sub-stantially predetermined relationship exists among mag-netic field intensity, flux density and reluctance o~ the magnetic circuit, nonpermanent induction magnets operate in the first quadrant of their hysteresis curves where magnetic field intensity and flux density need not be dependent upon the reluctance of the magnetic circuit but rather can be dependent primarily upon an induced magnetic field. Accordingly there are a number of example~ of non-permanent magnet machines, such as those shown in Horsley U.S. patent 3,082,337, Watanabe et al. U.S0 patent 3,963,950 and Belova et al~ U.S. patent 4,23~,702, where toothless cores and relatively high-reluctance, wide air gaps have been utilized because of the greater flexibility in the design oE the magnetic circuit permitted by nonper-manen-t magnets. However, such gap widening exacts a price with respect to efficiency because greater input power with higher resultant heat loss is required to induce the same magnetic flux density in a high reluctance magnetic circuit than in a low-reluctance magnetic circuit.
There are also some types of permanent magnet devices, such as that shown in Johnson U.S. patent No. 4,151,431, to which differellt principles and problems apply because they are with~ut cores and/or windings.
Returning to the design of permanent magnet ma-chines of the more normal type having cores and windings, with which the present invention is concerned, the above discussion has pointed out why designers have ollowed the ~186;36~

principle that the practical way to maximize the output power density of a permanent magnet in a motor or genera-tor is to minimize the reluctance and maximize the flux density of the magnetic circuit, primarily to avoid irre-versible demagnetization. This has been the conventionalapproach despite the knowledge that the theoretical maxi-mum output power density does not in fact occur at a high flux density near the remanent point on the demagnetiza-tion curve, but rather occurs at a lower flux density on an intermediate portion of the demagnetization curve where, although the flux density factor of the energy product is somewhat reduced, the magnetic field intensity factor is greatly increased so that the product of the two i5 at its maximum value. (This contrasts with the situation in the first quadrant of a hysteresis curve, applicable to non-permanent magnets, where the point of theoretical maximum energy product would normally correspond to the point of maximum flux density). Al~hough the operating point of theoretical maximum energy product and output power density on the demagnetization curve of a permanent magnet has been avoided by those skilled in the art for the foregoing reasons, it would nevertheless be extremely advantageous with respect to maximizing the output power density and thus the economy of permanent magnet devices .if a practical approach were devised whereby the theoretical operating point of maximum energy product and output power density could in fact be utilized efÇectively.
However, overcoming the irreversible demagne-tization problem in order to operate the permanent magnet 36~

at or near its theoretical point of maximum energy product does not solve all of the problems. There remain the prob-lems of maximizing output power despite reduced flux den-sity, and of doing so in such a way as to minimize the in-put power requirements and promote the linear speed-torque characteristic of brushless permanent magnet devices (the latter helping to simplify the precise control thereof).
These are primarily problems of power conversion effi-ciency dependent on minimizing wasteful heat generation.
Creating an operating point of reduced flux density corresponding to the theoretical maximum energy product and output power density of a permanent magnet could be accomplished in a number of alternative ways.
Since a reduction in flux density in the magnetic circuit to an intermediate point on the demagnetization curve, con~iderably below the remanent point, is needed in order to achieve the operating point of theoretical maximum energy product, and since the flux density is inversely proportional to the reluctance of the magnetic circuit in accordance with the basic magnetic circuit equation set forth above, various different ways of increasing the reluctance of the circuit may be considered to achieve the desired operating point. One possible method is adjust-ment of the air gap between the permanent magnet and core ~5 (i.e. widening it), another possible method is inserting an air gap in another location in the magnetic circuit, such as inside a hollow tubular permanent magnet rotor by filling the inside with air or a nonmagnetic material;
another possibility might be to ~educe the permeability or -~3-~i 3~

cross-~ectional area of the core material to thereby increase i.ts reluctance. Too great an increase in the reluctance of the circuit by any of these means will cause operation of the permanent magne-t at a flux density too far below that corresponding to its maximum energy product, thereby decreasing the output power densi.ty and increasing the likelihood of irreversible dema~netization as in the case of the aforementioned Siemens motor. Moreover, only one of these al~ernative~ will optimize power conversion efficiency by minimizing wasteful heat generation. Reduc-i.ng the permeability or cross-sectional area of the core material will only increase heat generation, while insert-ing an air gap in a location other than between the per-manent magnet and core will do nothing to minimize heat generation.
Another problem which has plagued permanent magnet motors and generators is the high frequency problem of excess.ive core loss, in the form of hysteresis and eddy current heat losses which adversely affect efficiency, create exaggerated nonlinear speea-torque characteristics and limit the maximum operating frequency of -the winding as well as the revolution rate of the motor or generator.
Tamaru et al. U.S. patent No. 3,657,583, Wennerberg U.S.
patent No. 2,885,645 and British paten-t No. 760,269 all teach the advantage of using a magnetically soft ferrite core material to reduce the aforementioned core energy losses in h.igh frequency applications of nonpermanent mag-net devices. However, because most permanent magnets have higher remanent flux densities than the saturation flux density of magnetically soEt ferrite and are conventionally 36~

operated near such remanent f]ux densities for the rea~ons described above, and because conventional design princi-ples of all electrical machines require that the satura-tion flux density of the core be at least as great as the flux density available to the magnetic circuit so that the available flux density can be fully utilized, it has been considered inconsistent to utilize maynetically soft fer-rite or other possibly advantageous core materials in combination with permanent magnets having higher remanent flux densities than the saturation flux density of -the core material. Accordingly, no teachings can be found as to how to take advantage of such potentially advantageous core materials in devices employing permanent magnets having higher remanent flux densities than the saturation flux density of the core material.
Accordingly, what is needed is a design approach for permanent magnet motors and generators by which the permanent magnets can be operated at or near their operat-ing points of theoretical maximum energy product and out-put power density without irreversible demagnetization ofthe permanent magnets. Further, the manner of creating such operating points should be the one best suited to maximize the output power, power conversion efficiency and linear speed-torque characteristics oE -the permanent mag-net device. Finally, the design should make the use ofmagnetically sof-t ferrite, and other advantageous low-loss core materials, compatible with the use o permanent mag-net materials having higher remanent flux densities than the saturatiorl flux density of the core m~terial.

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Summar~ oE the Present Invention _ _ The present invention i~ directed to principles Eor the design and operation of permanent magnet motors and generators, primarily of the brushless rotary type, but also applicable to other types such as those employing rectilinear motion, which satisfy all of th~ above-described competing needs in a compatible manner to maxi-mize output power density, power CQnVersiOn efficiency and linear speed-torque characteristics. The application of the inventive principles yields the smallest and most efficient permanent magnet machine for a given permanent magnet material and power output level or, stated another way, yields the most powerful and efficient permanent magnet machine for a given external volume and given per~
manent magnet material.
The manner chosen to set the operating point of the permanent magnet at or near the point of theoretical maximum energy product on the magnet's demagnetization curve is to ad~ust (i.e. widen) the gap between the per-manent magnet and the core and thereby increase the reluc-tance of the magnetic circuit sufficiently to reduce the flux density of the circuit and permanent magnet to a flux density which is in the vicinity o~ the flux density cor-responding to the operating point of theoretical maximum energy product. The danger of irreversible demagnetiza-tion normally expected from -this choice of operating point is avoided in several ways. One of these is the employ-ment of permanent magnets selected from an e~clusive group whose demagnetization curves are shaped such that changes -~6-3~

in thc operating point clue to the external influences men-tioned previously, even -though the operating point i8 in the vicinity of the point of theoretical maximum energy product~ are likely to cause only reversible, rather than irreversible, demagnetization. This exclusive group of magnets includes barium or strontium ferrite permanent magnets, rare earth and other cobalt permanent magnets (such as samarium cobalt and platinum cobalt) and other permanent magnets of a type having ratios betw~en the magnitudes of their remanent magnetic flux densities and their intrinsic magnetic field intensities, respectively, of no more than about 2:1, or mixtures thereof. Not included in the group are ~lnico (aluminum-nickel cobalt) permanent magnets.
The choice of a widened gap between the perma-nent magnet and core as the means for setting the operat ing point of theoretical maximum energy product also aids in -the prevention of irreversible demagnetization by mini-mizing the effect upon the operating point of changes in external reverse magnetic fields created by the winding, and by minimizing temperature variation effects on the demagneti~ation curve and on the reluctance of the mag-netic circuit due to heat generated in the winding, for reasons to be explained hereafter.
The choice of a widened gap is further signifi-cant in maximizing the output power and power conversion efficiency of the permanent magnet machine. Since, according to the present invention, gap size is determined solely by the permanent magnet's desired operating point ~1~63~

trather tllan by other factors such as winding size as in the above-referenced Karube patent), and since the gap i8 an enlarged one to achieve the reduced flux density cor-responding to the desired operating point, a winding of greater cross-sectional area having larger individual turns and~or a greater number of turns filling the en-larged gap can be utilized. The enlarged winding proviaes signîEicant benefits when employed in combination with a permanent magnèt operating point at or near the point of maximum energy product. For example, the ratio between ohmic heat generation in the winding and power output will be reduced by the reduced resistance of larger individual windings due -to their increased cross sections, thereby aiding powar conversion efficiency by minimizing heat loss. Likewise, an increased number of turns in either a parallel or series conEiguration permits a reduction of current in each turn sufficient, when compared to the increased number of turns, to also reduce the ratio be-tween ohmic heat generation and output power. It can be seen from the ohmic equation, P = I2R, that heat dissipa-tion varies by the square of -the current and by the first power of the resistance. Thus, although the amount of resis-tance may be increased by adding turns to the wind-ings, the second power reduction in current which is per-mitted thereby has a greater impact on the total powerdissipated than the single power increase in resistance.
The minimized ohmic heat generation also mini-mizes the temperature fluctuation of the device, thereby minimiæing the temperature-sensitive demagnetizing efeots ~8~36~

discussed above, preventing excessive heating of other nearby temperature-sensitive components, and promoting linear speed-torque characteristics of brushless device~.
Also, the enlarged winding compensates for possible reductions in output power which might otherwise result from the reduced flux density which corresponds to the operating point of theoretical maximum energy product.
Moreover, the enlarged gap aids in the preven-tion of irreversible demagnetization by minimizing the effect upon the operating point o the magnet of changes in external reverse magnetic fields created by the winding. According to the aforementioned basic magnetic circuit equation, the total flux in the magnetic circuit, including not only that created ~y the permanent magnet but also that created by the external reverse magnetic field of the winding, is as follows:

flux = mmf. of magnet (HmLm) - mmf. of wind~ng (NI) reluctance From the equation it can be seen that, even if the mag-~0 netomotive force (mmf.) of the winding (NI) is increased by filling the enlarged gap with winding to increase the current or number of turns in order to compensate for a reduced flux density of the permanent magnet corresponding to the point of maximum energy product, the increased reluctance of the magnetic circuit due to the enlargement of the air gap will normally have a reducing effect upon the level of the demagnetizing magnetic flux induced by the winding in the permanent magnet. For example, if the gap length were to be doubled so as to double the reluc-tance by removal of core teeth or, in the absence of such 3~;~

teeth, by decreasing the size of a permanent magnet rotorsituated inside a surrounding winding, the resultant cross-sectional area of the gap which could be filled with winding would not thereby be doubled. Accordingly, although the reluctance of the circuit would be doubled, the number of turns and thus the magnetomotive force and resultant demagnetizing flux induced in the permanent magnet by the winding coil would be less than doubled.
Therefore the excursions about the permanent magnet's operating point caused by the demagnetizing flux of the winding would actually be reduced, further enabling the operating point to be set close to the "knee" of the demagnetization curve (i.e. in the vicinity of maximum energy product) without the danger of irreversible demagnetization.
The widening of the gap between the permanent magnet and core, and its beneficial utilization as described above, is made possible by the recognition of the fact that if the permanent magnet's operating point is set by widening of the gap, such operating point will be substantially independent of the magnetic flux introduced by thc windings.
It w:ill be recognized that, if it is assumed that virtually all c,f the reluctance of the magnetic cir-cuit is located ]n the enlarged air gap, the energy gener-ated by the permanent magnet, i.e. the product of its flux density and its magnetic field intensity, is virtually exclusively concentra-ted in the gap where it will benei-cially interact with the winding. Thus, if the operating ~L~8~3~L

point of maximum energy product i5 utilized, the energy density of the magnet and the energy density within the gap are both substantially maximized.
With the high-flux-density operating points selected for permanent magnets under previous design theory, core materials capable of handling correspondingly high levels of magnetic flux were required. However, with the lower flux densities obtained when operating near the point of theoretical maximum energy product on the demag-netization curve in accordance with the present invention,core materials having much lower saturation flux densities can be used. This, then, permits the use of magnetically soft ferrite or amorphous metal core materials, with their adv~ntageous high-frequency, low-loss characteristics, in combination with permanent magnets having much higher rem-anent flux densities than the saturation flux density of the core material. Thus the creation of the operating point at or near the point of maximum energy product fur-ther promotes power conversion efficiency and linear speed-torque characteristics in high-frequency applica-tions by minimizing heat loss from the core, which is accomplished by rendering a high-frequency, low-loss core material of low saturation flux density compat.ible with permanent magnets having higher remanent flux densitites.
Moreover, because the reluc~ance of such core material does not incxease with increased operating frequency to the same degree as iron and other core materials previ-ously used Witll such permanent magnets, the stability Qf the reluctance o -the magnetic circuit an~ thus of the 3~

operating point is, in turn, maximized thereby urther reducing the li~elihood of irreversible demagnetization of the permanent magnet.
A general mathematica] Eormula has been devised by the inventor herein by w~ich the magnetic circuit of any permanent magnet motor or generator can be designed to achieve the objective of operating the permanent magnet at or near its operaking point of theoretical maximum energy product. The formula establishes a desired ratio between the total length of all gaps in a magnetic circuit and the total length of all permanent magnets in the same circuit.
According to the formula, the ratio is proportional to the ratio between an imaginary intrinsic magnetic field inten-sity of the particular permanent magnet material employed (determined by projecting that portion of the magnet's demagnetization curve which lies above the "knee" onto the field intensity axis), and the remanent flux density of the particular permanent magnet material. The formula is as follows:
Lgt = uo¦Hcp Lml~ Br wl~ere Lg~ is the total length of all gaps in the magnetic circui~, Lmt is the total length of all permanent magnets in the same circuit, uO is the permeability of free space (I in cgs ~nits), Hcp is the imaginary intrinsic magnetic field in~ensi~y oE the magnets projected rom the portion of thPir demagnetization curve lying above the knee, and Br is the remanent flux density of the permanent magnets.
The ~ormula is a simplified approximation because it makes ~2~-~18~36~

certain assu~ptions, including the assumption that the portion of the demagnetizakion curve above the knee is substan~ially a straight line, that there are no signifi-cant temperature variations, and that there is no fringe flux. If any substantial temperature variation is ex-pected (for example due to external conditions) it would be wise to apply the design formula to the demagnetization curve of the magnet at the lowest expected operating tem-perature to minimize the likelihood of thermal demagneti-zation.
Because of the characteristics of the demagneti-zation curves of the ferrite, and rare earth and other cobalt permanent magnets to which the invention is espe-cially applicable as discussed above, the Eormula will usually yield an optimum result wherein Lgt is approxi-mately equal to Lmt, which is a much higher ratio o total gap length to total magnet length than has previously been used in permanent magnet motor and generator designs under previous design principles, which tend to maximize mag-netic flux density. The ratio of Lgt to Lmt, according tothe present invention, should be within the range of 0.5 to 2.0, and preferably within the range of 0.8 to 1.2, clepencling upon the particular permanent magnet material.
Accordingly, it is a principal objective of the present invention to devise a way to operate permanent magnet motors and generators at an operating point of the permanent magnet at or near to the operating point of theoretical maximum energy procluct, without thereby causing irreversible demagnetiz.ation o the permanent -~3-i36~

magnet, so as to maximize the energy density of the per-manent magnet and the energy density within the air gap.
It is a further principal objective of the pres-ent invention to maximize the output power density and power conversion efficiency of the permanent m~gnet motor or generator in a manner compatible with the aforementioned operating point of theoretical maximum energy product.
It is a further principal objective of the pre-sent invention to make the employment of permanent magnets having relatively high remanent flux densities compatible with the employment of core materials having saturation flux densities substantially lower than such remanent flux densities, so as to enable the benefits of such core mate-rials, such as magnetically soft ferrite, to be obtained iE needed for the particular application.
The foregoing and other objectives, features and advantages of the present invention will be more readily understood upon consideration of the following detailed description of the invention taken in conjunction with the accompanying drawings.

Brief Descri~tion of the Drawin~s FIGSo 1-4 are partially sectional, ~implified axial views of the interior configurations of different types of prior art permanerit magnet rotary motors con-structed in accordance with previously accepted design principles.
FIGS. 5-8 are partially sectional, simplified axial views of the interior coniguratiotls of e~emplary -2~-~..:t. !3~;36~

motors eomparable to those of FIGS. 1-4 respectively, but constructed in aecordance with the design prineiples of the present invention for puLposes oE comparison.
FIG~ 9 is a simplified axial view of the inter-ior of a further type of rotary motor constructed inaceordance with the prineiples of the present invention.
FIG. 10 depicts a demagnetization curve for a typical rare earth cobalt permanent magnet~ and a eompara-tive virgin ma~netization curve for a typical magnetic-ally-soft ~errite eore material.
FIG. 11 is a graph showing eomparative demagne-tization eurves for different known permanent magnet materials.

Detailed Deseription of the Invention FI~ 1 is a simplified axial view of the inter-ior of a eonventional rotating brushless permanent magnet motor in which a radially symmetrical four-pole motor 10 eomposed of permanent magnets 12, 14, 16 and 18 bonded to an iron shaft 20 is journaled in bearings (not shown) supporting the shaft 20 so as to rotate inside a eoneen-trieally wound field stator 22. As in all of FIGS. 1-9, alternating current in the winding 24 of the stator 22 is synehronized with the position of the rotor lO by eonven-tional means, sueh as Hall effeet elements and appropriatecireuitry. Cireuitry of this general type is deseribed, for example, in Karube U.S. Patent No. 4,130,769. The magnets 12, 14, 16 and 18 could be composed of any il~8~36~

commercially available permanent magnet material.
However, for purposes of comparison it will be assumed, unless stated otherwise, that all magnets in the figures are rare earth cobalt, such as samarium cobalt, having the demagnetization curve of FIG. 10. The stator 22 is manu-factured by stamping toothed laminations from sheets of electrical steel or other iron alloys which are stacked employing any of a variety of well-known techniques to form a stator core 26. The winding 24 is then inserted into the slots 26a, between the teeth 26b of the core, after which it is common to pot the entire structure with epoxy, or vacuum impregnate it with a varnish.
The flux path through one of four basic radially symmetrical magnetic circuits of the motor of FIG. 1 is inclicated by the dashed line 28. The magnetic circuit comprises that portion of the rotor 10 between the south pole of magnet 14 and the north pole of magnet 12, the core 26 and ~he two air gaps 30 and 32 between the magnets 12 and 14 and the teeth of the core, respectively. The total reluctance of this magnetic circuit is the sum of the individual reluctances of the magnets 12 and 14, the shaft 20, gaps 30 and 32 and the core 28. However, under - normal conditions the only components of any substantial reluctance are the gaps 30 and 32 which have no magnetic material therein and, as seèn in FIG. 1, are quite narrow so as to minimize the total reluctance of the magnetic circuit. This in turn maximizes th~ flux and flux density of the magnetic circuit. Because of the low reluctance and consequent hiyh flux density of the magnetic circuit, -2~

3~

the operating point of the magnets i8 approximately at the point denoted by Xl in FIG. 10. It will be noted that th.is operating point i5 quite near to the remanent flux density Br of the permanent rnagnet, and has a relatively small energy produc~ represented by the area of the rec-tangle 34 determined by multiplying the magnetic flux den-sity and magnetic field intensity at the point Xl. This results in a relatively low energy density magnet.
FIG. 5 shows a machine comparable to that of FIG. 1 except that it is designed in accordance with the principles o the present invention. The construction of the rotor 110 of FIG. 5 is the same as, and has the same demagnetization curve as, the rotor 10 of FIG. 1. ~ow-ever, the stator 122 of FIG. 5 is quite diferent from the stator 22 of FIG. 1. Because there are no teeth present on the stator core 126, the effective lengths Lg of each of the gaps 130 and 132 are substantially larger than the effective lengths of the gaps 30 and 32 of FIG. 1. This increase in total gap length of the magnetic circuit 128 of FIG. 5, relative to that o FIG. 1, renders the reluc-tance of the magnetic circuit of FIGo 5 substantially grea-ter than that of FIG. 1. This means that the flux density in the magnetic circuit of FIG. 5 will be substan~
tially lower than that of FIG. L, creating an operatin~
point on the demagnetization curve of FIG. 10 on an inter-mediate ~ortion of the curve at or near the point X2 of theoretical maximum energy product represented by the area of the rectangle 36, wl~ich is substantial].y larger than that of rectangle 34 thereby provid.ing ~ correspondingly higher energy density.

36:~

Because of the small gaps 30 and 32 in th~ prior art embodiment of FIG. 1, the ratio of total gap length to total magnet length in the magnetic circuit represented by the dashed line 28 is only about 1:4. In contrast, the ratio of the total gap length (2Lg) to the total magnet length (2Lm) of the magnetic circuit represented by the dashed line 128 in FIG. S is on the order of 1:1. This is in keeping with the general mathematical formula set forth previously for establishing the ratio between total gap length and total magnet length in the circuit. According to the formula, the ratio is proportional to the ratio between an imaginary intrinsic magnetic field intensity of the particular permanent magnet material determined by projecting that portion of the magnet's demagnetization curve which lies above the "Xnee" onto the field intsnsity axis (i.e. Hcp in FIG. 10), and the remanent flux density of the magnet material ~Br in FIG. 10). (A projected ima-ginary intrinsic magnetic field intensity H~p, rather than the actual intrinsic field intensity Hc, is used in the formula because it, in combination with Br~ more accu-rately represents the slope of that portion of the demag-netization curve above the "knee" where an operating point can usefully be established without the li~elihood of de~
magnetization according to the present invention.) Since, according to the particular demagnetization curve of FIG. 10, Hcp is 8,000 oersteds while Br is 8,000 gauss, the ratio of total gap length to total magnet length is 1:1 according to the formula meaning that, for the magne-tic circuit 128 of FIG. 5, 2Lg should equal 2Lm and there-fore Lg should equal Lm.

3~8t~6~

In FIG. 5, the removal of the teeth from the stator core 126 and the resultant widening of the gap relative to magnet length have made room for an enlarged winding 124 which substantially fills the gap for optimum benefit. As mentioned previously, the enlarged winding, because it is placed in the enlarged gap where the great majority of the energy of the permanent magnets is applied, maximizes output power while its demagnetizing flux effects are reduced, and minimi~es the ratio between ohmic heat generation in the winding and power output.
This maximizes power conversion efficiency, minimizes tem-perature fluctuation and thus temperature~sensitive demag-netizing effects, promotes linear speed-torque character-istics of the device and prevents excessive heating of other nearby temperature-sensitive components.
If the motor of FIG. 5 is intended for rela-tively high-speed, high-frequency operation, the stator core 126 may be advantageously constructed of magnetically soft ferrite, amorphous m~tal or other high-frequency, low-loss core material. In particular, the application of any magnetically soft ferrite featuring a spinel crystal structure, conforming in most cases to the formula XFe2O~, where X may be manganese, zinc, cobalt, nickel or other metallic ion, or any mixture thereof, is possible. At high frequency operation, the core loss for such a mate-rial would typically be three to four orders of magnitude less than the best electrical iron, such as that from which the stator core 26 of FIG. l is constructed. As can be seen from FIG. lO, the saturation lux density Bs of 6;3~;~

the magnetically soft ferrite is incompatible with the narrow gap structure of FIG. 1 because the fLux density o the operating point Xl of the magnet is higher than the saturation flux density of the ferrite cor~ material and thus cannot be maintained unless a core material, such a~
iron, of at least an equally high saturation flux density is employed. In contrast, the operating point X2, created in accordance with the principles of the present invention by the employment of a much greater ratio between gap lenyth and magnet length, renders the ferrite core material compatible with the permanent magnet because the operating point X2 is at a reduced flux density lower than the sat-uration flux density oE the core material, and the attain-ment of the operating point X2 will not therefore be hind-ered by the ferrite core material as would be the casewith the operating point Xlo The use of such a core mate-rial enables the attainment of very high rates of revolu-tion and frequency of operation without excessive core losses in the form of heat, which further maximizes power output, power conversion efficiency and linear speed-torque characteristics while minimizing temperature-sensitive demagnetizing efects and adverse high-temperature effects on other nearby temperature-sensitive components.
FIG. 11 shows a number of demagnetization curvas 2S of typical permanent magnet materials available on the market which, except for the Alnico material, would be suitable for use in the present invention. For each curve a dashed line is shown projecting that portion of the curve lying above the knee onto the magnetic field intensity ~3~

~8~

axis to show how the value of ~lcp would be arrived at in each case for application of the formula Eor determining -the ratio of total gap length to total magnet length according to the present invention. Such ratio will usually be in the area of unity, and should be within the range of 0.5 to 2.0, and preferably within the range of 0.8 to 1.2, depending upon the particular permanent magnet material.
FIGo 11 also shows why an Alnico magnet is unsuited for the application of the present invention, due to the extremely high ratio (approximately 20:1) between the magnitudes of its rernanent flux density Br and its intrinsic field intensity Hc~ respectively, creating such a steep demagnetization curve as to tolerate very little variation in flux density without demagnetization if the initial operating point is not close to the remanent point.
In general, the permanent magnet materials suitable for application of the present invention will have much lower ratios between the magnitud~s of their remanent flux den-sities Br and their intrinsic field intensities Hc, re-spectively, such ratios being no higher than about 2:1 a FIG. 2 illustrates the permanent magnet motor shown in Karube U.S. patent 4,130,769. This motor feat~res a four-pole rotor 38 upon which the magnets are not seg-mented but rather magnetized into an isotropic magnet. Themotor features a toothless stator core 40 separated by a gap 42 of length Lg from the rotor 38, with a winding 44 interposed in the gap 42. One of the four radially symmet-rical magnetic circuits o the motor o FIG. ~ is indicated ~31-~

3t~L

by the dashed line 46 and comprises a magnet of lenyth Lm~
two gaps of length Lg and a portion of the core 40. As pointed out earlier, this motor employs a toothless core structure to permit inexpensive winding installation and removal, but stresses minimization of the gap consistent with the smallest winding size which will satisfy the torque requirements of the motor. Accordingly, although the ratio between the total gap length 2Lg of the magnetic circuit 46 and the magnet length Lm is illustrated as ap-proximately 1:3, it is in reality much less in accordancewith the teachings of the patent~ Therefore, the operat-ing point of the permanent magnet is not much further from the remanent point than the operating point of the motor of FIG. 1.
In contrast, a motor comparable to the motor of FIG. 2, but designed in accordance with the principles of the present invention, is shown in EIG. 6. The motor of FIG. 6 has the same outside dimensions as that of FIG. 2, but has a substantially greater energy density due to the creation of an operating point X2 (FIG. 10) which is in the vicinity of the theoretical maximum energy product of its permanent magnet rotor 138. The operating point of theoretical maximum energy product is created by increas-ing the ratio between the total gap length 2Lg and the magnet length Lm of the magnetic circuit 146 such that they are approximately equal. This requires enlargement of the gap 142 between the rotor 138 and the core 140, a corresponding reduction in the diameter of the permanent magnet rotor 138, and filling o:~ the enlarc3ect gap 1~2 with an enlarged winding l44 in accordance with the prlnciples of the present invent.ion.
-~2-:i 636~

FIG. 3 illustrates the motor shown in Ka~erbeek et al. U.S. patent ~1,135,107 featuring a two-pole permanent magnet rotor 48, with a steel shaft 49 through its center, separated by a gap 50 from a stator core 52 about which is wound a relatively flat winding 54. One of the motor's two diametrically opposed magnetic circuits is shown by the dashed line 56 and includes a total gap length of 2Lg and a total magnet length of 2Lm. Like the motor of FIG. 2, the ratio between the total gap length of the magnetic circuit and the total magnet length is in reality much less than illustrated. Li~e the motor of FIG. 2, a toothless gap was used in the motor of FIG7 3 for purposes other than maximizing the energy product of the permanent magnet rotor ~8, in that the toothless core was utilized to eliminate harmonics to obtain a sinusoidal field.
However, minimization of the air gap was stressed by utilizing as large a rotor as possible in the structure.
FIG. 7 shows a motor comparable to that of FIG. 3 designed in accordance with the principles of the present invention. As in the motor of FIG. 6, the diameter of the permanent magnet rotor 148 is reduced considerably to en-able a much larger gap 150 between the rotor 148 and the stator core 152. The external windings of the motor of FIG. 3 are dispensed with in FIG. 7 because they are out-side of the magnetic circuit and therefore do not con-tribute to output power. In accordance with the princi-ples of the present invention, the two gap lengths Lg of FIG. 7 are approximately equal to the two magnet lengths Lm~ and the enlarged gap 150 is substantially filled with an enlarged winding 15~.

~ ~ .

~L8~361 FIG. 4 depicts in simplified form the major ele-ments of a hypothetical type of permanent magnet motor not constructed in accordance with the present invention.
This motor has a toothless stator core 58 surrounding a cylindrical two-pole tubular permanent magnet rotor 60 with a nonmagnetic zinc core 62 inside the tubular perma-nent magnet and a steel shaft 63 at its center. A winding 64 is affixed to the stator core 58 within the gap 66 separating the rotor 60 from the stator core 58. In one of the motor's two diametrically opposed magnetic cir-cuits, indicated by the dashed line 68, there are not only two gaps Lg between the rotor 60 and the stator core 58 but also, since the zinc 62 is nonmagnetic, two very large effective gaps Lgz inside the tubular permanent magnet 60 itself, increasing the reluctance of the circuit greatly.
The total length of magnets in the magnetic circuit are the two distances Lm as shown in FIG. 4O Here there exists a ra~io, between total gap length 2Lg+~Lgz to total magnet length 2Lm of the magnetic circuit 68, which is substan-tially the reverse of the relationship of the motors ofFIGS. 1, 2 and 3 in that, in FIG. 4, the total gap length is approximately three times the total magnet length.
This causes an operating point at a flux density far below that of the operating point of theoretical maximum energy product and, in fact, can lead to extensive demagnetiza-tion.
If a motor comparable to that of FIG. 4 were to be designed with a magnetic circuit more in accordance with the principles of the present invention, it would -3~-:~L8636~

look substantially like that shown in FIG. 8 where the tubular permanent magnet rotor 160 is substantially thicker than that of FIG. 4, yielding a larger total magnet length 2Lm. The zinc core 62 would be subs~antially smaller pro-ducing substantially smaller gap lengths Lgz, with the gap166 between the rotor 160 and ~he stator core 158 being approximately the same length Lg as in FIG. 4 such that 2Lg+2Lgæ would approximately equal 2Lm in the magnetic circuit 168. Also, a suitable ferrite or rare earth cobalt permanent magnet would be used. However, more preferably, the motor according to the present invention would not be designed with a zinc core such as 162 at all. Rather, it would be designed more like the motor of FIG. 7 with the entire gap of the magnetic circuit filled substantially with winding 50 that none of the gap is wasted, as in the case of the zinc core~
FIG. 9 shows a still further type of motor designed in accordance with the present invention. In this case a permanent magnet rotor 170, comprising a magnetic steel outer casing 172 upon which are mounted a pair of arcuate permanent magnets 174, rotate~ about an inner stator 176 having a core ring 178 enclo~ed by a winding 180. One of the two diametrically opposed magnetic circuits of the motor is indicated by the dashed line 182.
The magnetic circuit bypasses the center portion 183 of the core ring 178 and winding 180, and it is therefore unnecessary that this center portion contain magnetic material. The two magnet lengths of the circuit are indi-cated as Lm and the two gap lengths are indicated as Lg.

3~

In accordance with the general design formula of the present invention, 2Lm is approximately equal to 2Lg to produce the desired opera-ting point at or near the point of theoretical maximum energy procduct.
In all of the foregoing machines, the wincding i3 fixedly mounted on, and insulated from, the stator core and may advantageously be potted in a suitable material such a5 epoxy to hold its shape and maintain the necessary mechanical clearance between the winding and the rotor.
It will be understood that in any of these machines the role o the rotor and stator can be reversed and that either -the rotor or stator can act as the rotating ele-ment. L,ikewise, the permanent magnets can be placed either on the internal or external member, and likewise with respect to the winding and core. Typical variations of these electrical machines include permanent magnet DC
motors, tachometers, alternators, generators and stepper motors.
The terms and expressions which have been employecl in the foregoing specification are used therein as terms of description and not of limitation, and there is no inten-tion, in the use of such terms and expressions, o~ excluding equivalents of the features shown and descri~ed or portions thereof, it ~eing recogni~ed that the scope of the invention is defined and limited only by the clailrs which follow.

-3~-

Claims

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

1. A method of making an electrical machine comprising the steps of mounting a permanent magnet and a core in predetermined relationship to each other separated from each other by a gap of predetermined size, inter-posing an electrically conductive winding within said gap between said magnet and said core and permitting relative motion between said magnet and said winding, said magnet, said core and said gap forming a magnetic circuit in which said magnet is operated at a predetermined magnetic flux density and a predetermined magnetic field intensity determined by said size of said gap, and further wherein the product of said predetermined flux density and said predetermined field intensity corresponds to an energy product, said magnet having a predetermined remanent flux density and having a predetermined maximum energy product which occurs at a flux density lower than said remanent flux density, characterized by selecting said size of said gap to obtain a corresponding predetermined flux density and field intensity which substantially maximizes said energy product, so that said magnet is maintained in the vicinity of said maximum energy product during said rela-tive motion, selecting the material of said permanent magnet such that the ratio between the magnitude of the remanent magnetic flux density and the magnitude of the intrinsic magnetic field intensity thereof is no more than about 2:1, and filling said gap substantially completely with said winding.

2. The method of claim 1 wherein said magnet, said core and said gap form a magnetic circuit in which a predetermined magnetic flux density and a predetermined magnetic field intensity are induced within said gap, the predetermined flux density and predetermined field inten-sity within said gap being determined by said size of said gap and corresponding to an energy density within said gap, further including selecting said size of said gap so that the value of the predetermined flux density within said gap is substantially less than said remanent flux density, and so that during said relative motion said energy density within said gap is substantially maximized.

3. The method of claim 1 wherein said magnetic circuit has one or more gaps operatively interposed therein and one or more mutually cooperating permanent magnets operatively interposed therein, said magnetic circuit having a total gap length composed of the total length of said gap or gaps and a total magnet length composed of the total length of said magnet or magnets.

4. The method of claim 3, further including selecting the size of said gap so that the ratio of said total gap length to said total magnet length is within the range of 0.5 to 2

5. The method of claim 3, further including selecting the size of said gap so that the ratio of said total gap length to said total magnet length is within the range of 0.8 to 1.2.

6. The method of claim 3, further including selecting the size of said gap so that the ratio of said total gap length to said total magnet length is substan-tially unity.

7. The method of claim l or 2 wherein said magnetic circuit has one or more gaps operatively inter-posed therein and one or more mutually cooperating per-manent magnets operatively interposed therein, said magne-tic circuit having a total gap length composed of the total length of said gap or gaps and a total magnet length composed of the total length of said magnet or magnets, said magnet having a demagnetization curve characterized by a remanent magnetic flux density, by an intrinsic mag-netic field intensity, and by a knee which is positioned between the remanent flux density and the intrinsic field intensity, further including the step of selecting the size of said gap and said magnet according to the formula = wherein Lgt = Total Gap Length;
Lmt = Total Magnet Length;
uo = Permeability Of Free Space;
Br = Remanent Flux Density; and Hcp = Imaginary Intrinsic Magnetic Field Intensity and further wherein Hcp is determined by extending the portion of the demagnetization curve which lies between the knee and Br onto the magnetic field intensity axis of the demagnetization curve.

8. The method of any one of claims 3-5, further including filling each gap, the length of which is included in said total gap length, substantially completely with said winding.

9. The method of claim 1 wherein said core is composed of a magnetically soft material having a prede-termined saturation magnetic flux density less than said remanent magnetic flux density of said permanent magnet, further including selecting the size of said gap to limit the magnetic flux density of said permanent magnet to a flux density less than said saturation magnetic flux density of said magnetically soft material.

10. The method of claim 9 wherein said magneti-cally soft material is magnetically soft ferrite.

11. The method of claim 9 wherein said magnet-ically soft material is amorphous metal.

12. The method of any one of claims 1, 2 or 4 further including the step of substantially preventing irreversible demagnetization of said permanent magnet during said relative motion.

13. The method of any one of claims 1, 2 or 4, further including mounting said permanent magnet and said winding for rotation relative to each other.

14. An electrical machine comprising a perma-nent magnet having a predetermined remanent flux density, a core separated from said permanent magnet by a gap of predetermined size, an electrically conductive winding interposed within said gap between said permanent magnet and said core and means for permitting relative motion be-tween said permanent magnet and said winding, said magnet, said core and said gap forming a magnetic circuit in which said magnet is operated at a predetermined magnetic flux density and a predetermined magnetic field intensity determined by said size of said gap, and further wherein the product of said predetermined flux density and said predetermined field intensity corresponds to an energy product, said magnet having a predetermined maximum energy product which occurs at a flux density lower than said remanent flux density, characterized in that the size of said gap is sufficient to obtain a corresponding predeter-mined flux density and field intensity which substantially maximizes said energy product, so that said magnet is maintained in the vicinity of said maximum energy product during said relative motion, said permanent magnet having a ratio between the magnitude of the remanent magnetic flux density and the magnitude of the intrinsic magnetic field intensity thereof of no more than about 2:1, said gap being filled substantially completely with said winding.

15. The electrical machine of claim 14 wherein said magnet, said core and said gap form a magnetic cir-cuit in which a predetermined magnetic flux density and a predetermined magnetic field intensity are induced within said gap, the predetermined flux density and predetermined field intensity within said gap being determined by said size of said gap and corresponding to an energy density.
within said gap, the size of said gap being sufficient so that the value of the predetermined flux density within said gap is substantially less than said remanent flux density, and so that during said relative motion said energy density within said gap is substantially maximized.

16. The electrical machine of claim 14 wherein said magnetic circuit has one or more gaps operatively interposed therein and one or more mutually cooperating permanent magnets operatively interposed therein, said magnetic circuit having a total gap length composed of the total length of said gap or gaps and a total magnet length composed of the total length of said magnet or magnets.

17. The electrical machine of claim 16 wherein the ratio of said total gap length to said total magnet length is within the range of 0.5 to 2.

18. The electrical machine of claim 16 wherein the ratio of said total gap length to said total magnet length is within the range of 0.8 to 1.2.

19. The electrical machine of claim 16 wherein the ratio of said total gap length to said total magnet length is substantially unity.

20. The electrical machine of claim 14 or 15 wherein said magnetic circuit has one or more gaps oper-atively interposed therein and one or more mutually coop-crating permanent magnets operatively interposed therein, said magnetic circuit having a total gap length composed of the total length of said gap or gaps and a total magnet length composed of the total length of said magnet or magnets, said magnet having a demagnetization curve characterized by a remanent magnetic flux density, by an intrinsic magnetic field intensity, and by a knee which is positioned between the remanent flux density and the intrinsic field intensity, the size of said gap and said magnet being selected according to the formula wherein Lgt = Total Gap Length;
Lmt = Total Magnet Length:
uo = Permeability of Free Space;
Br = Remanent Flux Density; and Hcp = Imaginary Intrinsic Magnetic Field Intensity and further wherein Hcp is determined by extending the portion of the demagnetization curve which lies between the knee and Br onto the magnetic field intensity axis of the demagnetization curve.

21. The electrical machine of any one of claims 16-18 wherein each gap, the length of which is included in said total gap length, is filled substantially completely with said winding.

22. The electrical machine of claim 14 wherein said core is composed of a magnetically soft material having a predetermined saturation magnetic flux density less than said remanent magnetic flux density of said permanent magnet and wherein the size of said gap is suf-ficient to limit the magnetic flux density of said per-manent magnet to a flux density less than said saturation magnetic flux density of said magnetically soft material.

23. The electrical machine of claim 22 wherein said magnetically soft material is magnetically soft ferrite.

24. The electrical machine of claim 22 wherein said magnetically soft material is amorphous metal.

25. The electrical machine of any one of claims 14, 15 or 17, further including means for substantially preventing irreversible demagnetization of said permanent magnet during said relative motion.

26. The electrical machine of any one of claims 14, 15 or 17 wherein said permanent magnet and said winding are mounted for rotation relative to each other.