The present invention relates to electromagnetic devices, that is single- or multi-phase generators and motors of unlimited stroke or of limited stroke (actuators), each device comprising, for each phase, at least two relatively-movable sets of teeth of soft magnetic material, one set of teeth being associated with the stator and the other with the moving part that moves with rotary or linear motion (hereinafter xe2x80x9crotorxe2x80x9d). Each set of teeth can comprise a plurality of teeth and the number of teeth can be different between the stator and the rotor. In the limit, one or even both sets could have only one tooth.
In many devices of this type, the pitch between the teeth is substantially constant and substantially the same for both sets of teeth. The reluctance opposing the passage of the magnetic field between these sets of teeth, and consequently the permeance which is the inverse of reluctance, varies during displacement. When one end of a stator tooth and one end of a rotor tooth face each other, they define between them an air-gap of minimum width E. In the devices to which the invention applies, the unit displacement dx (cf. FIG. 5) of a rotor tooth is parallel to the tangent to the end of a stator tooth, thus distinguishing such devices from electromagnets where displacement takes place in the minimum air-gap direction.
Rotary or linear motion devices having the above-mentioned characteristics can be motors, actuators, or generators with variable reluctance, that is without a permanent magnet, or motors, actuators, or generators that are hybrid or having xe2x80x9cpolarized reluctancexe2x80x9d, that is including at least one permanent magnet in the stator or the rotor.
In its most commonplace rotary versions, the device comprises a rotor that is generally cylindrical in shape, being constituted by at least one coaxial assembly comprising at least one rotor pole piece fixed on a shaft, each pole piece of the rotor presenting a set of teeth formed by radial teeth disposed along its periphery at a uniform pitch. The device also comprises a stator which comprises a magnetic circuit portion of soft magnetic material, which is generally annular in shape being disposed coaxially around the rotor, and constituted by a peripheral portion and a plurality of stator pole pieces. Each stator pole piece is powered by at least one electrical coil and comprises one or more teeth directed radially so as to face the teeth of the rotor. If there are two or more teeth per pole piece, then the teeth of the stator are disposed substantially at the same pitch as the teeth of the rotor, one rotor tooth and one stator tooth placed facing each other defining between them a radial air-gap having a minimum width E. Variants also exist in which the air-gap is axial, or oblique.
Such electromagnetic devices have been known for several tens of years. Hybrid types are in widespread use, particularly in the form of two- or three-phase stepper motors. Descriptions of such devices can be found for example in the book xe2x80x9cStepping motors and their microprocessor controlsxe2x80x9d by Takashi Kenio and Akira Sugavara, Clarendon Press, Oxford, 1994, 2nd edition, pp. 28 to 36 for variable reluctance motors, pp. 37 to 44 for hybrid motors, or in the Treatise on Electricity of xe2x80x9cl""Ecole Polytechnique Fxc3xa9dxc3xa9rale de Lausannexe2x80x9d, Vol. IX, entitled xe2x80x9cElectromxc3xa9caniquexe2x80x9d [Electromechanics], by Marcel Jufer, Presses polytechniques et universitaires romandes, xc2xa7 11.2.5 xe2x80x9cMoteur rxc3xa9luctant à simple circuitxe2x80x9d [Single circuit reluctance motor] and xc2xa7 11.2.11 xe2x80x9cMoteur rxc3xa9luctant polarisxc3xa9xe2x80x9d [Polarized reluctance motor]. Linear motion variants correspond to rolling rotary motors out flat and are described, for example, on page 33 of the above-specified work by T. Kenjo and in xc2xa7 11.13 in the above-cited work by M. Jufer.
Numerous theoretical studies have been done on such devices, cf. in particular the article by Marcel Jufer and Gunter Heine xe2x80x9cHybrid stepper motor torque and inductance characteristics with saturation effectsxe2x80x9d published in xe2x80x9cIncremental Motor Control Systems and Devices (IMCSD) Proceedingsxe2x80x9d, Fifteenth Annual Symposium, 1986, pp. 207-211, and the references cited in that article.
In the traditional design of such devices, it is considered that the width of the air-gap between two facing teeth should be as narrow as possible in the light of the technical constraints that stem from manufacturing tolerances in terms of diameter, concentricity, centering, burring, and other sources of inaccuracy. T. Kenjo states this clearly on page 30 of the above-cited work in its chapter entitled xe2x80x9cAir-gap should be as small as possiblexe2x80x9d. That concept has been supported by the theory. The well-known fundamental expression for calculating force or torque in electromagnetism and derived from the expression for the magnetic energy stored in the air-gap, for two sets of teeth in relative displacement with degree of freedom xcex1 states that the torque C that is generated will be proportional to:             ⅆ              xe2x80x83            ⁢      A              ⅆ      α        ⁢      U    2  
where U is the magnetic potential difference applied between the two sets of teeth, and A is the permeance between them. In a variable reluctance motor, this can be constituted by a magnetic potential difference due solely to the ampere-turns generated by one or more coils carrying electric currents, placed in various possible ways, or in a hybrid motor due to the algebraic sum of the magnetic potential difference Ua polarizing the air-gap under the influence of the permanent magnet plus the magnetic potential difference Uni generated by the above-mentioned coil(s).
The derivative of the permeance dA/dxcex1 can be developed in the form of a Fourier series, as can the permeance itself:
A=a0+a1 sin(Nxcex1)+a2 sin(2Nxcex1) 
dA/dxcex1=Na1 cos(Nxcex1)+2Na2 cos(2Nxcex1) 
where N is the number of teeth around the rotor, or if the rotor is incompletely fitted with teeth, the ratio 2xcfx80/(angular pitch) of the teeth that exist.
The first term of the derivative of this expression relative to xcex1, known as the fundamental term, is Na1cos(Nxcex1). In a motor or an actuator for controlling movement, or in a generator from which an accurately sinusoidal voltage is expected, with the number N of teeth being fixed, it is desirable to increase the amplitude a1 of the fundamental and to reduce as much as possible the amplitudes a2, a3, . . . of the harmonics cos(2Nxcex1), cos(3Nxcex1), . . . . The fundamental term of the torque is then given by expression [1]:                     C        =                                                            ⅆ                A                                            ⅆ                                  xe2x80x83                                ⁢                α                                      ⁢                          U              2                                =                                    Na              1                        ⁢                          U              2                        ⁢                          cos              ⁡                              (                                  N                  ⁢                                      xe2x80x83                                    ⁢                  α                                )                                                                        [        1        ]            
It is well known that the term a1 increases with decreasing air-gap. Since the torque C is proportional to this term, it would appear to be logical to select an air-gap that is as small as possible compatible with the manufacturing method.
For a hybrid motor of ordinary size (known as size xe2x80x9c23xe2x80x9d, giving a diameter ≈51 millimeters (mm), length ≈51 mm), the usual minimum air-gap is about 0.07 mm to 0.08 mm, giving rise to severe constraints on manufacturing tolerances and therefore increasing manufacturing costs. In practice, the air-gap E of conventional motors of this size is always xe2x89xa60.1 mm.
For such a hybrid motor, the maximum potential difference Umax that appears in the above formula for torque is Umax=Uni(max)+Ua. For the above-mentioned size and under steady conditions, the coil provides a maximum potential Uni(max)=85 ampere-turns (At) between teeth, for example. Since the torque due to the current is at a maximum when Ua≈Uni(max), Ua is also set to be about 85 At, so Umax=170 At. Ignoring magnetic potential losses in the soft magnetic materials of the stator and of the rotor, the induction B in the air-gap is given by:
B=xcexc0Umax/E. xe2x80x83xe2x80x83[2]
If it is desired to set a limit of B=2 teslas (T) because of saturation of the material of the magnetic circuit, then E=1.07xc3x9710xe2x88x924 meters (m). Thus, an air-gap of 7xc3x9710xe2x88x924 m to 8xc3x9710xe2x88x924 m leads to the silicon-iron used as the soft magnetic material being slightly saturated. However, when that type of motor is used with a duty ratio of only a small percentage, the ampere-turns could be increased during the short periods of activity, thus making it possible to increase the air-gap so as to remain within the linear region described by equation [2]. However, in conventional devices, this is not done for the reasons mentioned above: it is preferred to maximize the derivative of permeance, and thus to have a small air-gap, and to saturate the magnetic circuit further.
For example, in the above-cited work by M. Jufer at xc2xa7 11.19.1 giving the characteristics of a rotary reluctance stepper motor of the Warner trademark it can be seen that E=0.05 mm and Umax=(14/5)80=224 At, that is three times the number of ampere-turns that suffice for raising B to 2 T in the 5xc3x9710xe2x88x925 m air-gap. That does indeed serve to increase peak torque, but above all it generates major distortion in the function C=f(xcex1) which is far from being a sinewave function. This is well illustrated in the work by M. Jufer at xc2xa7 11.11.7 and FIG. 11.85. In addition, torque is no longer a simple function of current: the term a1 itself becomes a function of Umax. In many applications this gives rise to severe drawbacks, by increasing the instantaneous modulation of speed and torque (xe2x80x9ccoggingxe2x80x9d) due to the current when the motor is supposed to turning at constant speed and delivering constant torque, and by an increase in noise level. This also gives rise to poorer positioning quality in an open loop, particularly when it is necessary to subdivide the steps.
In the light of those drawbacks, an object of the invention is to provide an electromagnetic device which is arranged in such a manner as to enable the manufacturing costs to be reduced significantly and/or to improve the torque characteristics C=f(a) of the device.
In an application to controlling movement whether in an open loop or a closed loop, it is advantageous to provide an electromagnetic device which is such that for each phase it delivers a relationship for torque that remains substantially sinusoisal up to a magnetic potential value that is only slightly below the maximum design potential.
The objects of the invention are achieved by the device of claim 1.
The electromagnetic device of the invention which is of a size that enables a maximum magnetic potential Umax to be generated of about 1.7xc3x9710xe2x88x924 J/xcexc0, that is about 270 At if J=2 T, or even more, is characterized in particular in that the width of the minimum air-gap measured perpendicularly to the degree of freedom is selected in such a manner that:
E is approximately equal to or greater than the value of:
0.7[1xe2x88x925xc3x9710xe2x88x924(Umaxxe2x88x921.7xc3x9710xe2x88x924J/xcexc0)]xcexc0Umax/J 
when
[1xe2x88x925xc3x9710xe2x88x924(Umaxxe2x88x921.7xc3x9710xe2x88x924J/xcexc0)]xe2x89xa70.5 
or E is approximately equal to or greater than: 0.35 xcexc0Umax/J
when
[1xe2x88x925xc3x9710xe2x88x924(Umaxxe2x88x921.7xc3x9710xe2x88x924J/xcexc0)] less than 0.5 
or E is greater than 2xc3x9710xe2x88x923 m
where:
xcexc0 is the permeability of a vacuum;
Umax is the maximum magnetic potential difference generated to cause the magnetic field to cross the air-gap E, said potential difference being due:
either to the ampere-turns alone of the coil(s) feeding the air-gap E;
or else to the sum of said ampere-turns plus the magnetic potential difference between the two sets of teeth in the absence of current, due to a permanent magnet (xe2x80x9cpolarizationxe2x80x9d potential); and
J is the maximum polarization of the soft magnetic material used for making the teeth; J is defined by the usual relationship B=xcexc0H+J where H is large enough to reach about 99% of the limit value for J, or indeed, when taking consideration of relative permeability xcexcr, by the relationship J=xcexc0(xcexcrxe2x88x921)H (where H is large enough to generate about 99% of the limit value of J).
For the laminated silicon-iron commonly used as the soft magnetic material, J≈2 T.
An in-depth study of the operating conditions of a motor or generator has shown, surprisingly and against the general tendency seeking to reduce air-gap size, that in order to optimize a motor or a generator when sufficient ampere-turns are available, it is on the contrary advantageous to increase air-gap size, particularly for motors or generators in which the maximum magnetic potential is greater than about 1.7xc3x9710xe2x88x924 J/xcexc0.
In the present invention, it is the product a1U2 that appears in the expression [1] that is optimized, contrary to all conventional devices where only the fundamental term a1 of variationin the permeance of the teeth is optimized.
In an electricity generator, e.g. of the polarized variable reluctance type, the voltage is proportional to dxcfx86/dt or to dxcfx86/dxcex1xe2x88x92dxcex1/dt. The term dxcex1 is the angular velocity. The flux is the product of a permeance multiplied by a potential difference; flux variation is proportional to a1Ua. When the generator is delivering current, the current it delivers increases the potential difference between certain sets of teeth, and the relationship again includes a term in a1U2, as for a motor, thus leading to the same conclusions on the topic of the minimum air-gap E.
When the soft magnetic material works with induction that is only 2% greater than its polarization J, then variation in maximum induction B as a function of U as given above by relationship [2] lies in a domain that is substantially linear. It is then possible to replace U in the expression for torque by the value BE/xcexc0, which gives:                     C        =                                                            Na                1                            ⁢                              B                2                            ⁢                              E                2                                                    μ              0              2                                ⁢                      cos            ⁡                          (                              N                ⁢                                  xe2x80x83                                ⁢                α                            )                                                          [        3        ]            
It is clear that it is preferable to increase B, which is a squared term, as far as allowed by the soft magnetic material, while remaining within the specified condition whereby B preferably exceeds J by only 2% or less so as to lose only a small portion of Umax in the soft magnetic material. The criteria for selecting this material includes, for example, ease of manufacture, cost, and the operating frequency of the device.
In the present invention, it is necessary to determine how the product a1E2 varies and not only how a1 varies. The factor a1 is a function of the pitch/air-gap ratio (P/E) of the teeth. This function has been correlated empirically with a power function over a wide domain of variation in P/E. It turns out that for constant pitch P of the rotor teeth (measured along the arc), a1 is substantially proportional to Exe2x88x921.42 and that this applies as far as ratios of P/E that are less than 10. As a result, the product a1E2, and thus C, most surprisingly, turns out to be proportional to E0.58 which is an increasing function. For example, when E is doubled, the term E0.58 increases by about 50%. The power 0.58 can vary slightly as a function of the shape of the teeth, but the conclusion remains that the product a1E2 is an increasing function of E.
In order to be able to benefit from this advantage, it is clear that it must be possible to increase Umax with E, as shown in FIG. 7 where the range 25 plots E=0.7 xcexc0Umax/J for two values of J corresponding respectively to a silicon-iron (line 23) of ordinary type, and to one of the best-available materials, namely cobalt iron (line 23xe2x80x2). This value for E thus goes beyond the value which, with small air-gaps, serves to generate induction close to saturation for the soft material used. At low potentials, that is when Umax is less than about 114 At for silicon-iron, and as shown in range 24 of FIG. 7, air-gap values of less than 5xc3x9710xe2x88x925 m apply, corresponding to the practical limits for mechanical embodiment. The air-gap is then determined by considerations other than the above formula, even though the values overlap.
As a result, the invention applies to devices of size greater than about 40 mm to 50 mm in rotary versions. For such devices, Umax is greater than 1.2xc3x9710xe2x88x924 J/0.7 xcexc0 approximately, as shown by the range 25 in FIG. 7.
In practice, if very high operating quality in terms of controlling movement is not required, it is possible for example to accept B at the tips of the teeth becoming greater than J by 5%. E is then defined by the formula xcexc0Umax/1.05J if potential drop in the soft material can be tolerated. However, in reality, the potential loss in the soft material is no longer negligible, particularly at the teeth, so the potential difference which remains between the two sets of teeth is only about 84% of Umax, for example. It is thus possible to define the limit value for E by 0.84 xcexc0Umax/1.05J, that is Exe2x89xa60.8 xcexc0Umax/J. Nevertheless, with certain soft magnetic materials, more ampere-turns are lost at B=1.05J, and it is reasonable to accept a loss of 30% of the potential generated in said soft material without excessively influencing the linearity of torque as a function of applied or generated electrical power (depending on whether the device is a motor or a generator), such that only 70% of Umax remains between the teeth, that is 0.7 Umax.
The preferred value for E in accordance with the invention thus obeys the following relationship:
Exe2x89xa70.7xcexc0Umax/J xe2x80x83xe2x80x83[4]
It should be observed that the progress of air-gaps in conventional devices also increases with Umax since the increasing size of such devices gives rise to an increase in the tolerances required for manufacture, centering, and the clearance necessary to accommodate thermal expansion. Nevertheless, in conventional devices, attempts are always made to keep the air-gap as small as possible, which means that in conventional machines, air-gaps increase as a function of Umax less steeply than in above relationship [4]. It is thus possible to improve existing devices by increasing their air-gaps without thereby reaching the preferred value of Exe2x89xa70.7 xcexc0Umax/J.
In this respect, for devices of increasing size, capable of generating high values for Umax, the length of the soft material magnetic circuit can give rise to losses that increase but that remain acceptable in certain applications (e.g. traction motors), so that it is possible to accept a reduction in the value of the coefficient of xcexc0Umax/J. This attenuation coefficient can be defined by the following expression:
Exe2x89xa70.7xcexc0Umax/J 
where
k=1xe2x88x925xc3x9710xe2x88x924(Umaxxe2x88x921.7xc3x9710xe2x88x924J/xcexc0) 
with the condition that kxe2x89xa70.5.
Since air-gaps E in conventional devices do not exceed 1 mm to 2 mm, it is possible to improve the performance of large devices by increasing the air-gap beyond 1 mm to 2 mm, even while remaining below the value given above by relationship [4] as being the optimum value for the air-gap.
It is remarkable that with increasing air-gap and at constant induction in the air-gap, the loss of magnetic potential in the soft materials of the stator and the rotor remains substantially constant. Thus, compared with the total magnetic potential difference Umax, this loss is reduced, thereby linearizing the characteristic of the device giving torque as a function of applied electrical power. Like the torque, the applied electrical power has a term in U2. Conversely, in prior art devices of the kind cited above (M. Jufer xc2xa7 11.19.1) potential loss in the soft material can be several times the potential difference that exists between the tips of the teeth. No linearity can be expected between torque and the applied power in conventional devices.
By way of example, in an embodiment concerning a hybrid motor, that is a motor that has a permanent magnet, if the soft magnetic material is a silicon-iron characterized by J=2 T and for which each pole piece of the stator generates 160 At under the effect of the current, Ua must be selected to have a value that is likewise about 160 At, giving Umax≈320 At. The dimensioning rules applied to such a motor leads to a value for E of 1.6xc3x9710xe2x88x924 m or 0.16 mm, which value is considerably greater than that corresponding to the prior art for movement control devices.