Switched reluctance motor with damping windings

A reluctance machine including one or more damping windings placed within the stator or within the rotor which are used to store and provide energy so as to reduce unwanted machine vibration and noise, improve current commutation, and improve the efficiency and torque output of the machine.

BACKGROUND OF THE INVENTION 
In general, a reluctance machine is an electric machine in which torque is 
produced by the tendency of a movable part to move into a position where 
the inductance of an energized phase winding is maximized. In one type of 
reluctance machine the energization of the phase windings occurs at a 
controlled frequency. These machines are generally referred to as 
synchronous reluctance machines. In another type of reluctance machine, 
circuitry is provided for detecting the position of the movable part 
(generally referred to as a "rotor") and energizing the phase windings as 
a function of the rotor's position. These types of machines are generally 
known as switched reluctance machines. The present invention is applicable 
to both synchronous and switched reluctance machines. 
The general theory of the design and operation of reluctance machines in 
general, and switched reluctance machines in particular, is known in the 
art and is discussed, for example, in Stephenson and Blake, "The 
Characteristics, Design and Applications of Switched Reluctance Motors and 
Drives", Presented at the PCIM '93 Conference and Exhibition at Nuremberg, 
Germany, June 21-24, 1993. 
As explained above, the basic mechanism for torque production in a 
traditional reluctance motor is the tendency of the rotor to move into a 
position to increase the inductance of the energized phase winding. In 
general, the magnitude of the torque produced by this mechanism 
corresponds to the magnitude of the current in the energized phase winding 
such that the motor torque is heavily dependent on the phase current 
waveforms. For an ideal traditional reluctance motor with no magnetic 
saturation, the instantaneous torque T, per phase, is: 
##EQU1## 
Where i is the instantaneous current in the energized phase winding and 
dL/.sub.d.theta. is the derivative of the phase inductance L with respect 
to the rotor position .theta.. While all practical reluctance motors have 
some magnetic saturation, this equation is useful for purposes of the 
present analysis. 
As a switched reluctance motor (or generator) operates, magnetic flux is 
continuously increasing and decreasing in different parts of the machine. 
The changing flux results in fluctuating magnetic forces being applied to 
the ferromagnetic parts of the machine and in rapidly varying and 
pulsating radial forces. These forces can produce unwanted vibration and 
noise. One major mechanism by which these forces can create noise is the 
ovalizing of the stator caused by forces normal to the air-gap. Generally, 
as the magnetic flux increases along a given diameter of the stator, the 
stator is pulled into an oval shape by the magnetic forces. As the 
magnetic flux decreases, the stator springs back to its undistorted shape 
with possible overshoots. This ovalizing and springing back of the stator 
can cause unwanted vibration and consequently produce audible noise. 
In addition to the distortions of the stator by the ovalizing magnetic 
forces, unwanted vibration and acoustic noise may also be produced by 
abrupt changes in the magnetic forces in the motor. These abrupt changes 
in the gradient of the magnetic flux (i.e., the rate of change of the flux 
with time) may be referred to as "hammer blows" because the effect on the 
stator is similar to that of a hammer strike. Just as a hammer strike may 
cause the stator to vibrate at one or more natural frequencies (determined 
by the mass and elasticity of the stator) the abrupt application or 
removal of magnetic force can cause the stator to vibrate at one or more 
of its natural frequencies. In general, the lowest (or fundamental) 
natural frequency dominates the vibration, although higher harmonics may 
be emphasized by repeated excitation at the appropriate frequency. These 
abrupt changes in machine flux often occur at the current commutation 
instant when the energization of an active phase winding is switched off. 
This current commutation contribution to unwanted noise and vibration is a 
difficult problem since such current commutation is an inherent 
characteristic of conventional switched reluctance machines. Moreover, the 
problem of unwanted noise and vibration is particulate significant at low 
rotational speeds where the stator has more time to "spring back" in 
response to changes in the magnetic characteristics of the machine. 
Although the problem of unwanted acoustic noise and vibration has been 
recognized, known solutions often do not adequately solve the problem 
and/or require complex, and potentially expensive, controls for 
controlling the current in the windings of a reluctance machine. 
As explained briefly above, in most switched reluctance machines, current 
in an active phase winding is switched on to produce positive torque when 
the inductance of the phase winding is increasing and switched off to 
avoid negative torque when the inductance of the phase winding is 
decreasing. To produce the appropriate amount of output torque it is 
important that the magnitude of the current be at a sufficient value over 
an appropriate portion of the positive-rising inductance region. The 
inductance of the phase winding, however, limits the rate at which the 
current in the phase winding may change and tends to slow down the current 
rise and fall time. This inductance, thus, tends to limit the current 
available for torque production. Moreover, the back-EMF produced by an 
operating machine also tends to limit the rate of change of the current 
and thus potentially limit the torque output of the machine. The limiting 
effects of the phase winding inductance and the back-EMF become more 
serious as the rotational speed of the machine increases and the back-EMF 
becomes greater and the time allowed for current rise and fall time 
becomes more limited. 
A further limitation of conventional reluctance machines concerns the 
rating of the power converter and DC bus (or DC link) capacitor often 
required with such machines. It is known in the art that during each 
stroke period of an active phase winding (e.g., the period over which the 
phase winding is energized and then de-energized) a significant portion of 
the electrical energy that is applied to the phase winding when the 
winding was energized and that is not converted into output torque or 
motor losses is returned to the power converter. This significant energy 
circulation characteristic often necessitates the use of power converters 
having relatively high volt-amp ratings (to provide all of the required 
power) and in the use of relatively large DC bus (DC link) capacitors (to 
absorb the power returned to the power converter). Such high rated power 
converters and large capacitors may significantly add to the overall cost 
of a reluctance machine system. 
It is an object of the present invention to overcome these and other 
limitations of traditional reluctance machines by, inter alai, providing 
an improved reluctance machine that has one or more auxiliary damping 
windings that tend to reduce unwanted noise and vibration in a 
cost-efficient manner; enhance the current commutation characteristics of 
the machine so as to provide increased output torque and/or motor 
efficiencies; and allow for the use of reluctance systems having lower 
rated power converters and smaller DC link capacitors that would normally 
be required. Other objects and advantages of the present invention will be 
apparent to one of ordinary skill in the art having the benefit of this 
disclosure. 
SUMMARY OF THE INVENTION 
In accordance with an exemplary embodiment of the present invention a 
reluctance machine is provided that includes a stator, the stator defining 
a number of stator poles; a rotor defining a plurality of rotor poles 
where the rotor is positioned to rotate with respect to the stator; a 
plurality of phase windings positioned within the stator and a plurality 
of damping windings positioned within the stator, wherein each damping 
winding forms a closed current loop. The damping windings absorb from and 
provide energy to the phase windings in such a manner that unwanted noise 
and vibrations are reduced, current commutation is improved and the 
efficiency and torque output of the machine are improved. 
In accordance with another exemplary embodiment of the present invention a 
reluctance machine is provided including a stator, the stator defining a 
given number of stator poles, a rotor, position to rotate with respect to 
the stator; a plurality of phase windings positioned about the stator; and 
a plurality of damping coils positioned about the poles of the stator, 
where each damping coil is positioned about one stator pole. The damping 
coils may be coupled together in one of many ways to form a damping 
winding that provides a closed current loop. Such a damping winding may 
operate as described above to reduce unwanted noise and vibration to 
improve current commutation; and to increase the efficiency and torque 
output of the machine. The damping coils may be fully-pitched coils, 
fractional-pitched coils; or short-pitched coils. 
In accordance with yet another exemplary embodiment of the present 
invention a reluctance machine is provided that comprises a stator; a 
rotor positioned to rotate with respect to the stator, the rotor defining 
a plurality of rotor poles; at least one phase winding positioned within 
the stator; and at least one damping circuit positioned to rotate with the 
rotor, the damping circuit comprising a closed-current loop. The damping 
circuit may be a conductive coil or a closed current loop formed by 
conductive bars. The damping circuit may be positioned about one or more 
rotor poles, within the rotor yoke, or in the inter-pole regions of the 
rotor. 
Other exemplary embodiments of the present invention and other features of 
the present invention will be apparent to one of ordinary skill in the art 
having the benefit of this disclosure.

Similar reference characters indicate similar parts throughout the several 
views of the drawings. 
DETAILED DESCRIPTION OF THE INVENTION 
Turning to the drawings and, in particular FIG. 1, a cross sectional view 
of a reluctance machine 10 in accordance with the present invention is 
provided. In general, the machine 10 comprises a stator 12 and a rotor 14 
positioned within the stator in such a way that it is free to rotate 
within the stator. 
The rotor 14 comprises a stack of identical steel laminations that define 
four outwardly projecting stator poles. The rotor may be of conventional 
construction 
The stator 12 may constructed from a stack of identical steel stator 
laminations in accordance with standard reluctance machine techniques. In 
the exemplary embodiment of FIG. 1, the stator defines six inwardly 
projecting discrete stator poles and three main phase windings A, B and C 
are positioned around the stator poles so as to define three stator pole 
pairs 12a, 12b, and 12c. In the example of FIG. 1, each phase winding 
comprises two coils (connected in series or parallel) and each phase 
winding is separately energizable from the other phase windings. The coils 
of the phase windings A, B and C are positioned such that the magnetic 
fields established when unidirectional current flows in the phase 
windings, in the same direction, have an orientation corresponding to the 
arrows A, B and C of FIG. 1. For example, the coils may be positioned such 
that, when current flows in a given direction through all three phase 
windings A, B and C, the tips of the arrows would be the north poles of 
the respective magnetic fields. Conversely the tips could be the south 
poles. 
The construction of a stator 12 and phase windings A, B and C meeting the 
above criteria is well within the ability of one of ordinary skill in the 
art having the benefit of this disclosure and will not be discussed 
further herein. 
In addition to the three separately energizable phase windings A, B, and C, 
machine 10 also includes an auxiliary damping winding 15 comprising six 
coils, 15a1, 15a2, 15b1, 15b2, 15c1 and 15c2. Each of the six coils of the 
damping winding 15 is a "short-pitch" coil in that it surrounds only a 
single stator pole. For example, the coil 15a1 surrounds one of the coils 
of the phase A winding and only one stator pole. 
In the exemplary machine 10 of FIG. 1, the six coils of the short-pitched 
damping winding 15 are all connected together to form a closed current 
loop that is short-circuited internally to the machine 10 and that is not 
connected to any external electronics or power source. In general, the 
short-circuited auxiliary short-pitched damping winding 15 functions as a 
damper for noise and vibration; facilitates rapid current commutation to 
allow the current to rapidly increase and thus allow for the production of 
high output torque at high speeds; and retains energy within the motor 
that would otherwise be returned to the power converter, thus allowing for 
the use of lower rated power converters and smaller DC link capacitors. 
The precise configuration of the short-pitched damping winding 15 will, in 
general, depend on the manner in which the coils of the main phase 
windings are coupled. In general, the coils of the auxiliary short-pitched 
damping winding 15 surrounding the coils of a given phase winding should 
be coupled together in the same manner in which the coils they surround 
are coupled. Thus, if the coils comprising each main phase winding are 
coupled in parallel, the corresponding damping coils should also be 
coupled in parallel. The same would be true if the phase winding coils 
were coupled in series. This is illustrated, generally, in FIGS. 2A and 
2B. 
FIG. 2A illustrates the configuration of short-pitched damping winding 15 
for a reluctance machine 10 where the coils comprising each phase winding 
are coupled in series. As illustrated in FIG. 2A, in this exemplary 
embodiment, the appropriate coils from damping winding 15 are coupled in 
series and the ends of the damping winding are coupled together within the 
motor to provide a short-circuited winding. FIG. 2B illustrates the 
configuration of short-pitched damping winding 15 when the coils of the 
main phase windings are coupled in parallel. Again, the ends of the 
damping winding are coupled together to provide a short circuited winding. 
It may be noted that the self-inductance of the short-pitched damping 
winding 15 does not significantly change with rotor position. As such, the 
presence of current in the damping winding 15 does not produce negative 
torque. 
Referring back to FIG. 1, it may be noted from the + and - markings that 
the coils of the short-pitched damping winding 15 are wound (or placed) 
around each stator pole to provide magneto-motive forces ("MMFs") that are 
in the same reference direction as the MMF produced by the main phase 
winding coils they surround. Alternate embodiments are envisioned wherein 
the coils of the short-pitched damping winding 15 are wound (or placed) 
such that the reference directions of the MMFs from the coils of the 
damping winding are opposite those produced by the main phase winding 
coils they surround. Still further embodiments are envisioned where the 
MMF relationship alters between adjacent stator poles (e.g., same, 
reversed, same, reversed) or alters for each phase windings. These 
alternate embodiments of the present invention are believed to be 
potentially applicable to reluctance machines having an even number of 
phase windings. 
The use of the short-pitched damping winding 15 can significantly reduce 
the amount of unwanted noise and vibration produced by a reluctance 
machine. This is generally reflected by FIGS. 3A and 3B. 
As those of ordinary skill in the art will appreciate, at standstill and at 
low speeds, the torque of a switched reluctance machine is typically 
controlled by varying the current in the energized phases over an angular 
period defined by the turn-on and turn-off angles. When current chopping 
is used such current control can be achieved by chopping the current using 
a current reference with phase current feedback. Such current control is 
referred to as "chopping mode" current control. The problems associated 
with the production of unwanted noise and vibration are particularly 
significant at low speed when chopping mode current control is used. 
FIG. 3A generally illustrates a dynamic simulation of the phase currents 
I.sub.A, I.sub.B and I.sub.C and torque output Te of a conventional 
three-phase, twelve-stator pole, eight-rotor pole reluctance machine that 
does not include a short-pitched damping winding in accordance with the 
present teachings. The illustration simulation was performed over a rotor 
rotational interval of 90 degrees and at a rotational speed of 500 rpm. 
Chopping mode current control is reflected by the "chopped" nature of the 
phase currents. In the example of FIG. 3A, the phase A winding is 
energized at the 7.5 degree rotor position and de-energized at the 30 
degree rotor position and again energized at the 52.5 degree rotor 
position and de-energized at the 75 degree rotor position. The 7.5 degree 
and 52.5 degree rotor positions are the unaligned positions of the rotor 
with respect to the phase A stator poles, and the 30 degree and 75 degree 
rotor positions are the aligned positions of the rotor with respect to the 
phase A stator poles. The energization of the other phase windings is over 
intervals similar to that of the phase A winding, but displaced from that 
of the phase A winding by 15 degrees (for phase B) or 30 degrees (for 
phase C). 
The self-inductances L.sub.A, L.sub.B and L.sub.C of the three phase 
windings as well as the flux-linkages .lambda..sub.A, .lambda..sub.B and 
.lambda..sub.C are also provided in FIG. 3A. The values of these 
quantities have been scaled up for illustration purposes. 
As reflected in the torque output Te for FIG. 3A, the intervals at which 
current commutation occurs are associated with abrupt downturns in the 
output torque. In the machine of FIG. 3A, these abrupt downturns in the 
output torque are not counterbalanced or damped in any significant way 
and, accordingly, tend to cause the stator of the reluctance machine to 
begin to vibrate, resulting in unwanted noise and vibration. This is 
reflected in FIG. 3B which illustrates the radial force imposed on the 
phase A stator poles Fr, the displacement of the stator from its rest 
position, d, the velocity of the stator movement v and the acceleration of 
the stator a resulting from the energization and de-energization of the 
phase A winding for the machine reflected in FIG. 3A. It is known that the 
closer the rotor is near alignment positions with the stator poles, the 
larger the radial force on the stator poles if the excitation current is 
the same, as reflected in FIG. 3B. The radial forces on the stator poles 
are subsequently transmitted to the stator back iron to cause mechanical 
responses. 
As reflected in FIG. 3B, at the commutation points for the phase A winding, 
corresponding to rotor positions of 30 degrees and 60 degrees, the forces 
imposed on the stator abruptly change and cause dramatic oscillations of 
the stator in terms of displacement, velocity and acceleration. Before the 
commutation points, vibrations also exist due to the energization of the 
phase A winding and the bang-bang choppings of the current. The choppings 
of the current cause larger variations in the radial forces, hence larger 
vibrations, when the rotor is nearer the alignment positions where the 
radial force is largest. The forces and oscillations resulting from the 
energization and de-energization of the phase B and phase C windings of 
the machine simulated in FIGS. 3A and 3B are similar to those reflected in 
FIG. 3B. 
FIG. 4A illustrates a dynamic simulation of the phase currents I.sub.A, 
I.sub.B and I.sub.C of the three phase windings of a twelve-stator pole, 
eight rotor pole reluctance machine having a short-pitched damping winding 
like that discussed above in connection with FIG. 1. For the machine 
simulated in FIG. 4A, the damping winding would include twelve individual 
coils, one for each stator pole. Like FIG. 3A, FIG. 4A also illustrates, 
with scaling, the self-inductances L.sub.A, L.sub.B and L.sub.C and the 
flux-linkages for the three main phase windings .lambda..sub.A, 
.lambda..sub.B, and .lambda..sub.C. 
In addition to illustrating the currents, self-inductances and 
flux-linkages for the three phase windings, FIG. 4A also illustrates the 
current I.sub.D and the flux-linkages .lambda..sub.D for the short-pitched 
damping winding used according to the teachings of the present invention. 
The phase energization intervals for the phase windings of the machine 
simulated in FIG. 4A are the same as those for FIG. 3A (e.g., for phase A, 
energize over 7.5 degrees to 30 degrees and for phase B, energize over 
22.5 degrees to 45 degrees). Moreover, the assumed rotor speed is the same 
for the simulation of FIG. 4A as it was for FIG. 3A (500 RPMs). 
Referring to the waveform for the short-pitched damping winding current 
I.sub.D, it may be noted that the current generally remains at a negative 
level except for a limited period following the commutation of an 
energized phase winding. For example, during the interval corresponding to 
7.5 degrees and 30 degrees, the phase A winding is energized and, over 
that interval, no active phase winding is commutated. Accordingly, the 
current I.sub.D in the short-pitched damping winding remains at a negative 
level although it fluctuates in response to the chopping of the current in 
the phase A winding and the energization and choppings in the phase B 
winding. At the rotor position of 30 degrees, however, the phase A winding 
is commutated off. At that point much of the energy that was stored in the 
phase A winding is transferred from the phase A winding to the 
short-pitched damping winding. Accordingly, shortly after the phase A 
winding is commutated off, there is a rapid increase in the current in the 
short-pitch damping winding I.sub.D and the current I.sub.D goes positive 
as the damping winding absorbs some of the energy stored in the energized 
phase windings. Similar transfers of power to the short-pitched 
winding--and similar positive current pulses of I.sub.D --occur at the 
other points where a phase winding is commutated. In the exemplary 
embodiment of FIG. 4A, these points occur at the 45 degree position (as 
phase B is commutated); the 60 degree position (as phase C is commutated); 
and the 75 degree position (as phase A is commutated again). 
The periodic modulation of the current in the short-pitched damping winding 
and the intervals of positive current in the short-pitched damping 
winding, tend to affect the output torque of the machine. This is 
illustrated in the Te output of the machine simulated in FIG. 4A. As 
illustrated, at the points where the current I.sub.D in the short-pitched 
damping winding goes positive, there is a temporary increase in the output 
torque of the machine. This may be observed in FIG. 4A at the points 
corresponding generally to rotor positions 30 degrees, 45 degrees, 60 
degrees and 75 degrees where the output torque Te temporarily exceeds the 
average torque output. 
The temporary increases in the output torque caused by the positive current 
in the short-pitched damping winding of the machine simulated in FIG. 4A, 
and the negative current in the damping winding during non-commutation 
intervals, establish forces in the reluctance machine that tend to dampen 
the mechanical oscillations that would otherwise be produced, thus 
reducing the amount of unwanted noise and vibration. This aspect of the 
present invention is reflected in FIG. 4B which illustrates the simulated 
vibration characteristics for the twelve stator pole, eight-rotor pole 
machine with short-pitched damping winding according to the teachings of 
the present invention with respect to the energization and de-energization 
of the phase A winding. 
Referring to FIG. 4B, the vibrational characteristics for the twelve-stator 
pole, eight-rotor pole machine having short-pitched damping winding are 
illustrated. Comparing the vibration characteristics of the machine of the 
present invention in FIG. 4B with those of a conventional machine as 
reflected in FIG. 3B, it may be noted that the use of short-pitched 
damping winding in accordance with the teachings of the present invention 
can significantly and dramatically reduce unwanted stator vibration and, 
thus, unwanted machine noise. 
In the machine reflected in the waveforms of FIG. 4A and 4B, the ratio of 
the number of turns in one of the coils of the damping winding to the 
number of turns in one of the coils of a main phase winding is 0.2 and the 
total resistance of the damping winding is approximately 5 ohms. In 
general, the ratio of the turns of each coil in the short-pitched damping 
winding to those in a coil of a main phase winding should be relatively 
low (e.g., approximately 0.2). The precise ratio may be calculated 
empirically or through testings or simulations by adjusting the ratio 
until the desired vibrational performance of the machine is achieved. 
In addition to keeping the ratio of the turns in the damping coils to the 
turns in the main coils relatively low, it is also beneficial to keep the 
total resistance of the short-pitched damping winding low (e.g., on the 
order of 5 ohms). Such low resistance tend to reduce the ohmic losses 
associated with the flow of current in the damping winding. While there 
are some ohmic losses associated with the use of a damping winding in 
accordance with the teachings of the present invention, these losses are 
more than offset by the increases in torque and efficiency provided by the 
present invention and the advantages that may be obtained in terms of 
lower converter rating, lower DC link capacitor ratings, and lower 
vibration and noise. 
In addition to selecting the turns of the coils in the damping winding and 
the total resistance of the damping winding (hence transient reactance and 
time constant of the damping winding) to meet the above-described 
parameters the turns in the damping winding coils and the resistance of 
the damping winding should also be selected to meet at least one other 
criteria. Referring to FIG. 4A it may be noted that, while the current 
I.sub.D goes positive after each active phase is commutated, I.sub.D 
returns to negative prior to the energization of the next energized phase 
winding. For example, following the commutation of the phase A winding at 
the 30 degree rotor position the current I.sub.D goes positive. The 
I.sub.D current returns to zero however, prior to the 37.5 degree rotor 
position where the next energized phase winding (the phase C winding) is 
energized. By allowing the current in the short-pitched damping winding to 
drop to zero before the next energized phase winding is energized the 
average value of the flux-linkage remains relatively constant. This is 
important because, if the I.sub.D current was not allowed to drop to zero 
between successive phase energizations, there is a possibility that the 
current in and the flux-linkage of the short-pitched damping winding would 
increase or accumulate to a point that the machine would be damaged. 
In certain embodiments of the present invention, the time constant of the 
damping winding, e.g., the rate at which the damping winding current 
changes from negative or zero to positive and then back to zero or 
negative, may be controlled to ensure that the previously described 
optimum operating conditions are met. In such embodiments, energy 
absorbing or storage devices may be coupled in series with the damping 
winding to provide for a proper time constant (e.g., the rate of current 
rise and fall) and to facilitate energy transfer to and from the winding. 
One example is provided in FIG. 5A which shows the use of an additional 
resistor R coupled in series with the damping winding to absorb any 
excessive energy. For purposes of FIGS. 5A-5D the damping winding is 
schematically illustrated as a single inductive coil although the damping 
winding will actually comprise one or more coupled coils positioned within 
the stator. The use of such a resistor can decrease the time constant of 
the damping winding while maintaining the turn ratio high enough to 
provide adequate mutual coupling between the coils of the damping winding 
and the coils of the main phase winding. FIG. 5B illustrates an alternate 
embodiment where a capacitor C is coupled in series with the phase winding 
to provide a temporary energy storage device in the damping winding. The 
capacitor is charged and discharged with alternating current flowing in 
the damping winding and can be used to adjust the time constant of the 
damping winding. FIG. 5C illustrates a third embodiment where a resistor R 
and a capacitor C are both coupled in series with the damping winding to 
control the time constant of the winding. FIG. 5D illustrates a fourth 
embodiment where a resistor R and a capacitor C are coupled in parallel 
and the parallel connection of R and C is coupled in series with the 
damping winding to control the time constant of the winding. 
It should be noted that the waveforms for FIGS. 3A, 3B, 4A and 4B represent 
optimized waveforms of the appropriate reluctance machines. Also, the 
values provided for the self-inductances and flux-linkages have been 
scaled to fit on the same plot as the current and the values provided 
refer to the current of the various phase windings in amps. Those of 
ordinary skill in the art will appreciate that the current, 
self-inductance, and flux-linkage waveforms, as well as the vibration 
characteristics of an actual machine may differ from those provided in the 
discussed Figures. 
As a comparison of the waveforms for the conventional machine (FIGS. 3A and 
3B) with those of a machine constructed according to the teachings of the 
present invention (FIGS. 4A and 4B) illustrate, the machine of the present 
invention provides for significantly improved vibration characteristics. 
Both before and after the current commutation points, the variations in 
the flux densities on the stator poles due to the current choppings and 
commutation have been softened, since the flux linkage of the damping 
winding, which is reluctant to change without external voltage forcing, 
tends to counter any rapid changes in the flux densities. As a result, the 
variations in the radial forces, which are generally proportional to the 
square of the flux densities, have been reduced. Moreover, the peak radial 
forces applied to the stator poles of a machine constructed according to 
the teaching of the present invention are generally lower than those 
applied to the stator poles of a conventional machine of the same size, 
operating with the same control and the same speed. Even though the rate 
of change in the main winding flux linkage of the machine of the present 
invention is similar to that of a similarly sized and operated 
conventional machine of the same external voltages the magnitude and 
duration of the force excursions are reduced. 
Still further, although it is not particularly pronounced at the relatively 
low rotational speed corresponding to FIGS. 3A-4B, it may be noted that 
the rates of the rise and fall of the currents in the phase windings are 
greater in the machine of the present invention (FIGS. 4A and 4B) than in 
the conventional machine (FIGS. 3A and 3B). Thus, with a machine 
constructed in accordance with the teachings of the present invention, the 
phase currents can be designed and controlled to have a shape closer to 
the ideal square waveforms than that was previously possible. Such 
"squarer" waveforms make fuller use of available torque capacity normally 
wasted in conventional machines. This aspect of the present invention, 
although existent at low rotational speeds, becomes more pronounced at 
high rotational speeds when the current commutation problem becomes more 
restricting. 
As those of ordinary skill in the art will appreciate and as mentioned 
before, as the angular speed of the motor increases, a point is reached 
where there is insufficient time and too much back-EMF for more than a 
single pulse of current to occur or a certain desirable current magnitude 
to be reached during each phase period. Accordingly, at these speeds, the 
type of current chopping strategies used at low speeds are generally 
ineffective. Accordingly, at these relatively high speeds, the torque of 
the motor is commonly controlled by controlling the position and duration 
of the voltage pulse applied to the winding during the phase period. 
Because a single pulse of voltage is applied during each phase period, 
this form of control is referred to as "single pulse control." Just as the 
use of a short-pitched damping winding in accordance with the present 
teachings improves overall performance at low speeds where chopping mode 
current control is used it improves machine performance at higher speeds 
where single pulse current control is used. This is especially true 
because the use of a short-circuited damping winding as disclosed herein 
permits faster phase current rise and fall times, which are important in 
single-pulse mode control. 
FIG. 6A illustrates the phase currents I.sub.A, I.sub.B and I.sub.C ; the 
self-inductances L.sub.A, L.sub.B and L.sub.C ; and the flux-linkages 
.lambda..sub.A, .lambda..sub.B, and .lambda..sub.C for the same 
conventional twelve-stator pole, eight-rotor pole machine whose operating 
characteristics are reflected in FIGS. 3A and 3B. In FIG. 6A, however, the 
conventional machine is operated in the single pulse mode (for phase A on 
at 15 degrees, off at 24 degrees, on at 60 degrees and off at 69 degrees, 
other phases displaced from phase A) at a rotational speed of 1500 rpm. 
Referring to FIG. 6A it may be noted that the current pulses applied to the 
machine do not approach the ideal square pulse, but instead have 
slowly-rising front portions and gradually falling tail portions. For 
example, the current pulse applied to the phase A winding generally 
between rotor positions 60 degrees and 69 degrees has a slowly rising 
front-end 50 and a gradually falling tail portion 51. The same slow-rising 
front end and gradually falling tail are associated with the other current 
pulses applied to the other phase windings. 
The slow-rising and slow-falling current pulses associated with the machine 
of FIG. 6A limit the output torque production of the machine. This 
limitation occurs, in large part, because the torque output of the machine 
corresponds to the magnitude of the phase current and the phase current in 
the machine FIG. 6A does not quickly reach and maintain a desired peak 
current value. It may be noted that the average torque output Te of the 
machine of FIG. 6A is 13.4 Nm. 
FIG. 6B illustrates the phase currents, I.sub.A, I.sub.B and I.sub.C ; the 
self-inductances L.sub.A, L.sub.B and L.sub.C ; the flux-linkages 
.lambda..sub.A, .lambda..sub.B and .lambda..sub.C ; and the torque output 
Te of the twelve-stator pole, eight rotor pole reluctance machine 
reflected in FIGS. 4A and 4B utilizing short-pitched damping winding in 
accordance with the teachings of the present invention. The operating 
speed of the motor is 1500 rpm and the same control angles as were used 
for the conventional machine of FIG. 6A are used for the machine having 
short-pitched damping winding of FIG. 6B. The resistance of the damping 
winding (5 ohms) and the ratio of the turns in a damping winding coil to 
the turns in a main phase coil (0.2) are the same as for the machine of 
FIGS. 4A and 4B. 
Turning to FIG. 6B, it may be noted that, after energy is stored in the 
damping winding and current I.sub.D is established in the damping winding, 
the current commutation occurs much more rapidly than in conventional 
machines and the rise and fall times for the current pulses in the machine 
in accordance with the present invention are much less than those 
associated with conventional machines. For example, the current pulse 
applied to the phase A winding between the 60 degree and 69 degree rotor 
positions has a very steep rise portion 60 and a quickly falling tail 
portion 61. Comparing this current pulse with the corresponding current 
pulse in the conventional machine of FIG. 6A, it may be noted that the 
current pulse defined by rise 60 and fall 61 has a waveshape that is much 
closer to the ideal square waveshape than that associated with the 
conventional machine reflected in FIG. 6A. 
The improved current waveshapes associated with the machine of the present 
invention using short-pitched damping winding result in greater output 
torque since torque production capability wasted in conventional machines 
is used in the machine of the present invention. This is reflected by a 
comparison of the output torque waveforms Te of FIGS. 6A and 6B. The 
average torque output of the machine constructed in accordance with 
teachings of the present invention in FIG. 6B has an average torque output 
of 23.1 Nm, which is 72% greater than the 13.4 Nm average output of the 
conventional machine reflected in FIG. 6A. 
As reflected above, the machine of the present invention provides greater 
output torque than conventional machines under similar operating 
conditions. Alternately, a machine of the present invention could be used 
to produce the same amount of torque as a conventional machine but the 
efficiency of the machine constructed according to the teaching of the 
present invention would be greater. 
A further attribute of the present invention is reflected by the current 
waveform I.sub.D for the damping winding in FIG. 6B. As reflected in FIG. 
6B, the current I.sub.D in the damping winding cycles during operation of 
the machine between positive and negative values. The presence of this 
positive and negative current I.sub.D in the damping winding reflects the 
storage of energy in the damping winding over the entire operating cycle 
of the machine. This retained energy is used to assist the commutation of 
the next active phase (hence the faster current rise times) and is not 
circulated back to the power converter. This storage of energy in the 
damping winding, thus, can reduce the volt-amp rating of the power 
converter and the size of the required DC bus (DC link) capacitor. 
The increase in the torque output of the reluctance machine resulting in 
the use of short-pitched damping winding in accordance with the present 
invention is further reflected by FIG. 7. FIG. 7 illustrates the peak (or 
short duration) torque output of a conventional reluctance machine as a 
function of rotor speed 70, the continuous (or thermal) torque output of a 
conventional machine as a function of speed 71; the peak torque output of 
a reluctance machine using damping windings in accordance with the present 
invention as a function of rotor speed 72; and the continuous torque 
output of a machine using damping windings in accordance with the present 
invention as a function of speed 73. 
As reflected in FIG. 7, the peak and continuous torque outputs for the 
machine using damping windings in accordance with the present invention 
are greater than those for the similarly sized conventional machine at all 
rotor speeds. Moreover, the differences in torque outputs between the 
machine of the present invention and the conventional machine are greater 
at high speeds where current commutation becomes more important and the 
rise and fall times of the current pulses begins to limit torque 
production. 
While the above description was in the context of a machine constructed 
like machine 10 of FIG. 1, alternate constructions are envisioned. FIG. 8 
illustrates one such exemplary embodiment 80. Machine 80 is a reluctance 
machine similar to that of machine 10 of FIG. 1, with the exception being 
that the coils of the short-pitched damping winding 82 are placed "on top" 
of the corresponding coils of the main phase windings. This alternate 
winding configuration for the damping winding 82 provides the same 
benefits as does that illustrated in FIG. 1, but may be better suited to 
particular winding processes. 
FIGS. 2A and 2B illustrate certain configurations of the short-pitched 
damping winding for a machine having six stator poles. Alternate 
configurations are envisioned. For example, FIG. 9A illustrates a 
configuration where the short-pitched damping coils are all serially 
connected and shorted together (as in FIG. 2A) but where an additional 
conductor 90 is provided such that the electrical junction of the damping 
coils corresponding to phase A (the a damping coils) is electrically 
connected to the junction of the damping coils corresponding to phase C 
(the c damping coils). FIG. 9B illustrates a configuration where one of 
the two damping coils of each phase are serially connected and shorted, as 
are the rest of the coils for the other phases, and the two sets are 
separately shorted. 
FIG. 10 illustrates yet another alternate configuration for the damping 
coils. In this configuration, a diode 100 is inserted in the 
series-connected short-pitched damping winding. The use of diode 100 will 
inhibit the flow of current in the damping winding in one direction, but 
may be desirable in certain applications. 
In the embodiments discussed above except the configuration in FIG. 9B, all 
of the short-pitched damping coils were connected together to form a 
single damping winding. The configuration in FIG. 9B is also functionally 
equivalent to a single damping winding. Alternate embodiments are 
envisioned wherein each of the damping coils is short circuited within 
itself, or with only one other damping coil to form modified damping 
windings. Such alternate embodiments are illustrated in FIGS. 11A and 11B. 
Assuming the same motor structure and damping coils as in the machine 10 
of FIG. 1, FIG. 11A illustrates how the individual short-pitched damping 
coils may be short circuited within themselves to create, six single coil 
damping windings. The use of such short-pitched damping windings provided 
advantages similar to those discussed above in connection with the 
six-coil damping winding. 
FIG. 11B illustrates an alternate connection of the six damping coils where 
the damping coils corresponding to a particular phase are connected 
together in series. For example, the two coils associated with phase A 
(the 15a1 and 15a2) coils are connected in series, as are the coils 
associated with the phase B and phase C windings to form three two-coil 
short-pitched damping windings aD, bD and cD. While the two damping coils 
associated with each phase are connected in series in the example of FIG. 
11B, for machines having a greater number of stator poles, the damping 
coils associated with a given phase may be coupled together in series, 
parallel, or a combination of series and parallel. Again the use of 
damping windings as reflected in FIG. 11B provided advantages similar to 
those discussed above in connection with the single six-coil short-pitched 
damping winding. 
Operating at 500 rpm and with the same control as explained in FIG. 3A, 
FIG. 12 illustrates the currents I, self-inductances L, and flux linkages 
.lambda. of the three phase windings A, B and C and for the twelve 
individually shorted short-pitched damping windings (referred to as local 
damping windings) of a twelve-stator pole, eight rotor-pole machine having 
damping windings in accordance with FIG. 11A but with twice as many coils. 
As may be noted from a review of the currents in the three short-pitched 
damping windings 15a1, 15ba and 15c1, the current in each damping winding 
is generally slightly negative during the interval when positive current 
is flowing through its associated phase winding and the phase winding is 
energized (e.g., the periods 7.5 degrees to 30 degrees for phase A) and 
then jumps to a positive value when the associated phase winding is 
commutated off. (e.g., the period around 30 degrees for 15a1). The damping 
winding current remains at this positive value for some time and then 
returns to zero. The current characteristics for all the three phase 
damping windings are substantially identical. 
FIG. 13 illustrates the vibration characteristics of the machine modeled in 
FIG. 12 including the damping windings. As a comparison of FIG. 13 with 
the vibration characteristics of the conventional machine as reflected in 
FIG. 3B indicates, the machine with the damping windings has significantly 
better vibration characteristics and, thus, less unwanted noise and 
vibration. 
While the above discussion focused on the use of a short-pitched damping 
winding, the teachings of the present invention may also be allowed to 
machines including fractional-pitched and fully-pitched damping windings. 
FIG. 14A illustrates twelve-stator pole, eight-rotor pole reluctance 
machine 140 including damping coils 141, 142, 143, 144, 145, and 146 in 
accordance with the teachings of the present invention. For purposes of 
clarity, only the damping windings are illustrated. As FIG. 14A indicates, 
the damping coils in this embodiment are not "short-pitched" coils in that 
they do not surround a single stator pole. To the contrary, each damping 
coil encircles (or spans) two stator poles. For example, damping coil 141 
encircles stator teeth 147 and 148. In the particular embodiment of FIG. 
14A, the reluctance machine is a three phase machine. Because the number 
of stator poles encircled by each damping coil is less than the total 
number of phases for the machine, each damping coil may be referred to as 
a "fractional-pitched" coil. 
In accordance with the teachings of the present invention, the six 
fractional-pitched coils may be short-circuited together to form one or 
more damping windings. FIG. 14B illustrates one exemplary connection where 
the six coils are coupled together to form two three-coil fractional 
pitched damping windings. FIG. 14C illustrates another exemplary 
configuration where each of the fractional pitched damping coils is short 
circuited with itself to form six fractional-pitched damping coils. FIG. 
14D illustrates yet a further embodiment where the six fractional-pitched 
damping coils are coupled together in series to form a single damping 
winding. Those of ordinary skill in the art having the benefit of this 
disclosure will understand that fractional-pitched damping coils can be 
coupled together in other configurations without departing form the scope 
and spirit of the present invention. 
The fractional-pitched damping coils of FIGS. 14A-14D provide the same 
general benefits as the short-pitched damping coils previously discussed. 
Fully pitched damping coils may also be used to implement the teachings of 
the present invention. FIG. 15A illustrates a six-stator pole, four-rotor 
pole reluctance machine 150 having three full-pitched damping coils 151, 
152, and 153. Each of the damping coils is "fully-pitched" in that there 
are three phases for the machine 150 and each damping coil encircles three 
stator poles (i.e., the number of stator poles encircled by each damping 
coil is equal to the total number of phases). Again, for purposes of 
clarity, the main phase windings are not illustrated. 
The three fully-pitched damping coils 151, 152 and 153 of FIG. 15A may be 
coupled together in various ways to form one or more damping windings. 
FIG. 15B illustrates an embodiment where each damping coil is short 
circuited with itself to form three single-coil fully-pitched damping 
windings. FIG. 15C illustrates an alternate embodiment where a single, 
three-coil, fully-pitched damping winding is formed by coupling the three 
damping coils in series. And FIG. 15D illustrates yet another embodiment 
where a single, three-coil, damping winding is formed by coupling the 
three damping windings in parallel. Those of ordinary skill in the art 
having the benefit of this disclosure will recognize that other couplings 
of multiple fully-pitched damping coils are possible and would not depart 
from the scope or spirit of the present invention. 
It is possible to construct a reluctance machine utilizing only a single 
fully-pitched damping coil and obtain the benefits of the present 
invention. The single fully-pitched damping coil, however, must be 
configured such that positive and negative current can flow through the 
single fully-pitched damping coil during normal operation. One such 
embodiment is generally illustrated in FIG. 16A and 16B. 
FIG. 16A illustrates a three-phase reluctance machine 160 having six stator 
poles and four rotor poles. Positioned about the stator poles are three 
phase windings A, B and C. Also positioned within the stator is a single, 
short-circuited, fully pitched damping coil 161. The configuration of the 
damping coil is reflected in FIG. 16B. As reflected in FIG. 16B, the ends 
of the damping coil 161 are short-circuited together such that there is no 
impediment to the establishment of both positive and negative current in 
phase winding. Thus use of such a single fully-pitched damping coil can 
provide improved machine performance in terms of reduced noise and 
increased torque and efficiency as described above. 
The provision of a single fully-pitched damping winding that is capable of 
carrying both positive and negative current provides for a reduced noise 
machine. This is because the establishment of negative current in the 
fully-pitched damping winding during intervals of active phase 
energization (e.g., during the flux-linkage rising period before current 
commutation) both: (i) provides a "damping" to reduce unwanted machine 
noise and vibration; and (ii) stores energy in the damping winding during 
these intervals that would otherwise be returned to the power converter. 
The importance of allowing both positive and negative current to flow in a 
single fully-pitched damping winding in accordance with certain aspects of 
the present invention (as well as short-pitched and fractional-pitched 
damping winding) may be appreciated by understanding that the presence of 
such negative current tends to slow down the rise in the total flux 
passing through an active stator pole. This "damping" of the total flux 
rise tends to slow down the rise in amplitude of the radial force pulling 
on the active stator poles and also tends to reduce the maximum amplitude 
of such radial forces. Moreover, in the current chopping mode (where there 
are current choppings that cause minor rises and falls of the radial 
forces as the current is chopped) this "damping" of flux changes softens 
and reduces the changes in the flux passing through the active stator 
poles, thus resulting in reduced mechanical vibrations, even before 
current commutation occurs. This aspect of the present invention is 
generally illustrated in FIGS. 17 and 18A-18B. 
FIG. 17 generally illustrates the radial forces that would be generated for 
a stator pole of a conventional reluctance machine that does not include a 
single, fully-pitched damping winding in accordance with the present 
invention that allows for the flow of both positive and negative current. 
The forces illustrated in FIG. 17 are, for illustrative purposes, limited 
to those generated by the current in only one phase winding. In general, 
it may be noted that the changes in the radial forces have relatively 
steep rises and falls during the active periods of the associated phase 
winding (e.g., between 7.5 and 30 degrees and between 52.5 and 75 degrees) 
and that the radial force reaches a relatively high peak value at the 
commutation points (e.g., the 30 and 75 degree points). These abrupt 
changes in the radial forces produce significant mechanical vibration of 
the stator as reflected in the vibration characteristic data of FIG. 17, 
thus producing unwanted noise and vibration. 
FIG. 18A illustrates the phase and damping winding currents, output torque, 
self-inductances and flux linkages for a reluctance machine having a 
single fully-pitched damping winding in accordance with the present 
invention. In the illustrated example, the single fully-pitched damping 
winding has eight turns and a total resistance of approximately 2 ohms. As 
reflected in the waveform corresponding to the current in the damping 
winding ID, the damping winding current is generally negative but rises to 
a positive value during the intervals when a phase winding is being 
commutated off. 
FIG. 18B illustrates the radial forces produced by the energization of one 
phase winding of the machine reflected in FIG. 18A. It also illustrates 
the resulting vibration characteristics. As may be noted from a comparison 
of the force waveforms between FIGS. 17 and 18A, the changes in the radial 
forces over the active chopping periods are less abrupt and have slow rise 
and fall times in the inventive machine of FIG. 18A than they do for the 
conventional machine of FIG. 17. Moreover, the peak force (which occurs 
just prior to commutation) is less for the machine of the present 
invention than it is for the conventional machine reflected in FIG. 17. 
Still further, after the current commutation points, the rate of the 
decrease of the radial forces is softened due to the slower rate of 
decrease of the flux through the de-energized stator poles thanks to the 
induced damping current which is now in the reverse direction. This 
reduction in abrupt force changes during active chopping, the reduction in 
the peak radial force, and reduction in force changes after current 
commutation significantly reduces the overall vibration of the machine as 
may be noted by comparing the vibration characteristics of the machine of 
FIG. 17 with that of FIG. 18A. 
While the above discussion focused on the use of fractional and 
fully-pitched damping windings, the short-pitched damping winding is 
believed to be best suited for many applications because: (i) the use of 
short-pitched windings provides better mutual coupling between the coils 
of the damping winding and the coils of the phase winding than do 
fractional and fully-pitched windings; and (ii) the use of short-pitched 
windings provides better and more distributed contact between the coils of 
the damping winding and the stator iron thus providing for better and more 
distributed heat dissipation than occurs with fractional or fully-pitched 
damping windings. Moreover the end-turns of the short-pitched coils are 
shorter than those of fractional or fully-pitched coils, resulting in less 
required copper and less ohmic loss. 
The damping effect resulting from the use of short-pitched, 
fractional-pitched or short-circuited full-pitched (without a diode) 
damping windings may also be partially produced through the use of damping 
circuits placed about or within the rotor of a switched reluctance 
machine. This aspect of the present invention is illustrated in FIGS. 19 
and 20A-20B. 
FIG. 19 illustrates a three-phase reluctance machine 190 including a 
six-pole stator 191 and a four-pole rotor 192 positioned within the 
stator. Three phase windings A, B and C are positioned within the stator 
in a conventional fashion. Positioned about each pole of the four pole 
rotor are damping windings 193, 194, 195 and 196. Each of the damping 
windings comprises a single coil wound about the rotor pole. In operation 
the damping windings about the rotor poles tend to absorb energy in a 
manner similar to that previously described above in connection with the 
damping windings positioned within the stator. 
It will be apparent to those of ordinary skill in the art that rotor pole 
damping windings as illustrated in FIG. 19 may be positioned around fewer 
than all of the rotor poles and that the damping windings may be 
interconnected to form one or more main damping windings. Further, 
electrically conductive bars (e.g., of copper or aluminum) may be formed 
or placed into the rotor poles and then shorted at the ends to produce the 
rotor damping windings. 
It is not essential to the present invention that the rotor damping 
windings be placed around the rotor poles. One or more damping windings 
may be formed within the rotor yoke or in the inter-pole gaps between the 
rotor poles. Exemplary figures reflecting these embodiments are provided 
in FIG. 20A (which reflects the embodiment with the rotor damping winding 
formed within the rotor yoke) and FIG. 20B (which reflects the embodiment 
with the rotor damping winding formed within the inter-pole regions of the 
rotor). The embodiments of FIGS. 19, 20A and 20B are particularly suited 
to the use of shorted conductive bars to form the rotor damping windings. 
The above description of several exemplary embodiments is made by way of 
example and not for purposes of limitation. Many variations may be made to 
the embodiments and methods disclosed herein without departing from the 
scope and spirit of the present invention. The present invention is 
intended to be limited only by the scope and spirit of the following 
claims.