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BACKGROUND OF THE INVENTION
Variable reluctance motors (VR motors) are typically used as step motors
because they can produce rotation in small, discrete steps. This mode of
operation is inherent in the nature of VR motors. VR motors have a
multi-pole stator and a multi-pole rotor, with the separation between
poles on the stator, the pitch, different from that on the rotor. The
stator poles are electromagnetically excited in separate groups or phases
and the rotor rotates until its poles reach a position of minimum magnetic
reluctance relative to the excited stator poles. Upon energizing
successive stator phases, the rotor turns a distance equal to the rotor
pitch minus the stator pitch.
Other characteristics of variable reluctance motors including their low
cost, small size and high torque to inertia ratio make VR motors
attractive for use as general purpose servomotors. Their brushless
construction makes VR motors particularly suitable for applications
requiring spark-free operation.
However, two drawbacks have limited the use of variable reluctance motors
as servomotors: torque ripple and an nonlinear torque to input current
ratio (T/I). Torque ripple is the variation in maximum available output
torque as the position of the rotor poles varies with respect to the
stator poles. The nonlinear T/I ratio is inherent in the design of typical
VR motors because they have no permanent magnets. Torque is created by the
interaction of two magnetic fields, the rotor field and the stator field,
both a function of current.
Efforts to overcome the torque ripple problem have had only limited
success. One approach produces constant torque by modulating the current
to the motor, limiting the current during the high torque part of the
cycle. This has the consequent disadvantage of also limiting the maximum
torque developed by the motor to a level which can be as much as 70% below
peak torque.
Another, more successful technique is to energize more than one phase
during those portions in the motor's rotation where the torque from the
individual phases is near its minimum. This reduces the torque ripple
significantly, i.e., to about 80% of peak torque, but it also requires a
more complex commutator to control the energization of the stator phases,
and is less effective at high current levels.
In the past, in order to optimize the torque characteristics of VR motors,
the stator has been the determinative element in designing the motor.
Stator design balanced magnetic flux leakage, caused by having too many
teeth too close together, against minimum holding torque at the stable
detent position, caused by having too few teeth. The, stator was designed
with many teeth of uniform cross section, to provide the maximum practical
area at the tips of the teeth for the magnetic flux, while maintaining
sufficient intertooth space for the winding coils. The ratio of the width
of the stator teeth to the width of the gap between the teeth, called the
stator tooth ratio, was typically 1.0 or more. The rotor design was
dependent on the stator design, with the number and width of the rotor
teeth chosen to suit the geometry of the stator. This resulted in a rotor
tooth ratio of about 0.5.
It has been the practice to avoid operating VR motors at current levels
that would cause the stator teeth to become magnetically saturated. With
many uniform poles, the VR motor could run close to the saturation point,
without entering saturation where an increase in current would produce
only a negligible increase in torque.
SUMMARY OF THE INVENTION
The present invention provides a VR motor which has very low torque ripple
while maintaining a high peak torque, and produces a linear T/I ratio well
suited for servomotor applications. This is accomplished by making the
rotor rather than the stator the determinative element in the design and
by incorporating a tapered stator tooth configuration. The rotor tooth
width ratio rather than the stator tooth ratio is the basis for optimizing
torque characteristics, resulting in a larger rotor tooth ratio of about
0.78 and a smaller stator tooth ratio of about 0.5. The stator has fewer
teeth than the rotor, and the teeth are tapered so they are wider at the
base than at the tip. Contrary to the conventional teaching of the VR
motor art, the motor of the invention is designed to be run in saturation.
However, due to the tapered shape of the stator teeth, only the tip
portion of the tooth saturates. These characteristics provide a VR motor
which produces high torque with very low torque ripple, and thus a
relatively high maximum speed. Furthermore, when run in saturation the VR
motor of the invention produces a linear T/I ratio, and torque increases
with current up to the resistance heating limit of the motor windings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic cross-sectional view of a conventional VR motor,
illustrating the configuration of the rotor and the stator.
FIG. 2 is a simplified side view of a variable reluctance motor which
embodies the present invention.
FIG. 3 is a simplified cross-sectional view of the motor depicted in FIG.
2, showing the configuration of the rotor and the stator.
FIG. 4 shows a more detailed view of one of the teeth of the stator
depicted in FIG. 3.
FIGS. 5A, 5B, 5C and 5D illustrate the magnetic flux patterns in tapered
and nontapered teeth, when the teeth are aligned and when the teeth are
out of alignment.
FIG. 6 is a graph illustrating the magnetic flux versus winding current
function at various rotor positions for a motor constructed in accordance
with the invention.
FIG. 7A is a graph illustrating the torque versus rotor position function
for a typical conventional VR motor.
FIG. 7B is a graph illustrating the torque versus rotor position function
for a VR motor constructed according to the present invention, such as the
one depicted in FIGS. 2, 3 and 4.
FIG. 8 is a graph comparing the torque to current (T/I) function for a
conventional VR motor and the T/I function for a VR motor constructed
according to the present invention.
DETAILED DESCRIPTION
Description of the Prior Art.
In order to understand the present invention, it is helpful to explain the
design and operation of a conventional VR motor, illustrated in FIG. 1.
The motor depicted has 12 stator teeth and 8 rotor teeth, a typical design
for producing 24 steps per revolution, with a fifteen degree change in
rotor position upon each successive phase energization. The stator teeth
are wound in three phases of four teeth each. For clarity and simplicity,
the winding for only one phase is depicted.
Motor housing 11 encloses stator 12 which has an annular outer portion 3
and inwardly projecting teeth 14. Inside stator 12 is rotor 16, which is
mounted concentrically with stator 12 on shaft 18. Rotor 16 has a central
disc-shaped hub and outwardly projecting teeth 17. The three phases are
labelled A, B and C around the periphery of stator 12, but only the
windings 15 for the A phase are schematically depicted. In an actual
motor, the windings 15 take up most of the space between adjacent stator
teeth 14. Rotor 16 is shown in the stable position it takes when phase A
is energized, with rotor teeth aligned with each of the four excited
stator teeth, thus providing a minimum reluctance path for the magnetic
flux produced in the excited stator teeth. Rotor 16 can be moved 15
degrees clockwise from the position shown by turning phase A off and
turning phase B on. With phase B energized, the magnetic field produces a
torque on the rotor, turning the rotor until its teeth are aligned with
the four phase B stator teeth. Rotor 16 can be moved 15 degrees
counterclockwise by turning phase A off and turning phase C on from the
position shown. Continuous clockwise rotor motion can be produced by
sequentially energizing the phases in the order A-B-C-A-B-C; and
counterclockwise rotor motion can be produced by sequentially energizing
the phases in the order A-C-B-A-C-B.
The stator teeth 14 have substantially uniform cross section, so that the
base 14a is about the same width as the tip 14b. This provides a uniform
flux density through the tooth so that magnetic saturation occurs
throughout the tooth at about the same excitation current and magnetic
field flux.
Magnetic flux considerations must be taken into account in designing other
parameters of the rotor as well. The torque produced by the motor is a
function of the total magnetic flux through the energized stator teeth.
Thus, torque can be increased by using many stator teeth with several
teeth energized for each phase. Torque can also be increased by using
wider teeth which will carry a higher magnetic flux before reaching
saturation. However, if the teeth become too wide and too close together,
the magnetic flux leakage from the sides of the teeth begins to limit
torque and to decrease efficiency. Traditionally, the balance is reached
with a tooth configuration in which the stator tooth ratio is 1.0 or
higher.
As described above, the rotor tooth configuration is determined from the
stator tooth configuration. The tip 17b of the rotor tooth 16 is the same
width as the tip 14b of the stator tooth 14. There are fewer rotor teeth
than stator teeth to produce the required difference in tooth pitch for
creating motive torque. Consequently the rotor tooth ratio is smaller than
the stator tooth ratio. In the motor shown in FIG. 1, the rotor tooth
ratio is about 0.5, again typical for conventional VR motors.
Description of the Preferred Embodiment
A variable reluctance motor which embodies the present invention is
illustrated in FIGS. 2 and 3. FIG. 2 is a side view of the motor and FIG.
3 is a simplified cross-sectional view showing the configuration of the
rotor and the stator. Referring to FIG. 2, motor 20 has an outer housing
21 and an end bell 22 which enclose the motor and support journals 23 and
which hold bearings 25 and 26 at each end thereof. Stator 30 is mounted
inside housing 21. Rotor 32 is attached to shaft 33 which is mounted
through bearings 25 and 26 for rotation concentric to stator 30. Stator 30
has a plurality of teeth 31 and each of the teeth is wrapped with windings
34. Winding keepers 35 are located at each end of each of the stator teeth
31 beneath the windings. The tapered body of winding keepers 35
compensates for the tapered cross-section of stator teeth 31, making it
easier to wind the windings onto the stator teeth and preventing the
windings from slipping off the tapered stator teeth. Winding keepers 35
are made from nonmagnetic material so that they do not affect the
electromagnetic response of stator teeth 31.
The configuration of the rotor and stator teeth and the cross-sectional
shape of the stator teeth are more easily understood by referring to FIG.
3, which is a schematic view of rotor 32 and stator 30 along the axis of
motor shaft 33. FIG. 3 also shows windings 34 schematically, for clarity.
An important aspect of the invention is that the geometry of the rotor is
the determinative element of the design, and the stator must be designed
within the constraints imposed by the rotor geometry. Also, the rotor
tooth ratio is in the range of 0.75 to 0.90, higher than that customary in
the past.
Rotor 32 has a disc shaped hub attached to shaft 18 and eight teeth 39
which project outwardly from the hub. Rotor teeth 39 are equally spaced
around the circumference of the rotor. The width of rotor teeth 39 is such
that the ratio of the width of the rotor teeth to the width of the space
between the teeth is about 0.78. Rotor 32 is constructed of laminated
layers of transformer iron, instead of low carbon steel used in
conventional motors. The laminated structure minimizes eddy current
losses, thus the motor produces higher torque at higher speeds.
Stator 30 has an annular outer portion 36 and six teeth 31 which project
inwardly from annular portion 36. Each tooth 31 is tapered from a
relatively wide base 37 where it meets the annular portion 36 to a
narrower tip 38 nearer the center of the motor and in close proximity to
rotor 32. The width of the tip 38 is made the same as the width of rotor
teeth 39. This can be done without overcrowding the stator teeth, even
though the rotor teeth are wider than usual, because the number of stator
teeth is greatly reduced. Thus, although the stator teeth are also wider
than usual, because there are 6 teeth rather than 12, the stator tooth
ratio is about 0.5, well below the value at which flux leakage becomes a
problem.
The tapered cross section of the stator teeth also contributes to the
improved performance of the motor. The tip 38 of the tooth becomes
magnetically saturated at a lower magnetic flux than the rest of the tooth
because the tip has a smaller cross sectional area.
FIG. 4 shows a more detailed view of one of the stator teeth. Tip 38
includes a small untapered portion. This portion establishes a limit for
the region in which saturation occurs, which is important in linearizing
the dependence of torque on current. The untapered portion is also
advantageous if the inside diameter of the stator is to be machined to
match the outside diameter of the rotor, providing a small section of
uniform width so that the tip width remains the same after a small amount
is removed. Both sides of the tooth are tapered out below the tip section.
The taper angle 41 is such that the base of the tooth is about twice as
wide as the tip. With such a configuration, when the tip is saturated the
flux density at the base is about half the saturation value, a level that
provides low reluctance. The taper angle in the illustrated embodiment is
15 degrees, which has been found to provide good results for the motor
configuration shown.
FIG. 5 illustrates the magnetic flux patterns in tapered and untapered
stator teeth. FIGS. 5A and 5B show untapered conventional teeth, while
FIGS. 5C and 5D show the tapered teeth of the present invention. When
untapered teeth are in alignment, as in FIG. 5A, the teeth become
magnetically saturated along their entire length, and the large regions of
saturation give rise to a large magnetic reluctance in the tooth. When the
teeth are out of alignment, as in FIG. 5B, the regions of saturation are
limited to the areas near the aligned corners and the magnetic reluctance
in the tooth is smaller. Thus saturation occurs at a low current value
when the teeth are aligned and at a high current value when the teeth are
out of alignment.
In contrast, for the tapered tooth geometry of the present invention, the
length of the saturated region and thus the magnetic reluctance in the
tooth is nearly constant and is independent of tooth alignment. The region
of saturation is confined to the small untapered tip portion both when the
teeth are aligned, as in FIG. 5C, and when they are out of alignment, as
in FIG. 5D. Thus, the contribution of the reluctance in the teeth to the
reluctance of the magnetic circuit is a constant, rather than a complex
function of position as in conventional VR motors. The torque is
proportional to the derivative of reluctance with respect to rotor
position. Since the reluctance of the teeth is constant, in the VR motor
of the invention, that factor does not contribute to nonlinearities in the
torque function.
The relationship between the winding current and the magnetic flux for a VR
motor constructed according to the invention is illustrated in FIG. 6. The
flux to current function is represented by the family of curves 61a, b, c,
d, e and f, for the range of rotor positions from the unstable detent
position, curve 61a, to the stable detent position, curve 61f. The
saturation point for all of the curves is at the same current value,
I.sub.s, because the reluctance of the rotor/stator magnetic circuit is
independent of rotor position. At current values larger than I.sub.s,
magnetic flux continues to increase as current increases. The area of
shaded regions 63 and 65 is proportional to the torque the motor produces
with a small increase in current. During saturation, the incremental
magnetic inductance, which is the slope of curves 61a to f, is constant,
and thus torque is a linear function of current.
The performance of the motor depicted in FIGS. 2, 3 and 4, is further
illustrated in FIGS. 7A, 7B and 8.
FIG. 7A shows the torque versus rotor position function for a typical
conventional VR motor. Each of the three phases has a characteristic
sinusoidally shaped curve for torque versus rotor position and the
overlapping set of three curves gives the torque relationship for the
motor as a whole. The torque curves for each phase show high torque peaks
42a, 43a and 44a, separated by low torque valleys 45a, 46a and 47a where
the torque curves cross. The torque ripple is the difference between the
torque at the peaks and the torque in the valleys. As shown in FIG. 7A,
torque ripple can be significant in conventional VR motors. This can
severly degrade the motor's performance when driving a heavy load at low
speed.
FIG. 7B shows the corresponding torque versus rotor position function for a
motor constructed according to the present invention, such as the one
depicted in FIGS. 2, 3 and 4. Note that the high torque peaks 42b, 43b and
44b for each phase are broader than those for the conventional VR motor.
The low torque valleys 42b, 43b and 44b are not nearly as low because of
the increased overlap of the torque curves for the individual phases. This
results in significantly reduced torque ripple and improved performance.
FIG. 8 shows a comparison between the torque to current (T/I) function 51
for a conventional VR motor and the T/I function 52 for a VR motor
constructed according to the present invention. In the conventional VR
motor, the torque increases until the current reaches the value I.sub.sl
at which the stator teeth become magnetically saturated, at point 53. At
higher current levels, the torque remains nearly constant. Below the
saturation level, the torque to current relationship is nonlinear. For the
motor of the present invention, the torque continues to increase as the
current increases past the value I.sub.s2 at which the tips of the stator
teeth become magnetically saturated, at point 54. Above the saturation
point, torque becomes a linear function of current and continues to rise
with increasing current up to the resistance heating limit of the motor's
windings, I.sub.CL.
In contrast to conventional VR motors which are generally limited to
operation at current levels below the saturation point, the motor of the
present invention can be advantageously operated above the saturation
point. In fact, in this region, the motor has a linear torque to current
function which is ideally suited for servo-controlled operation. The motor
is designed to operate primarily above the saturation point. Here again,
the configuration of the stator is helpful. The increased space between
the stator teeth permits an increased number of turns to be wound on the
stator teeth. This causes saturation to occur at a relatively low current
value, as shown in FIG. 8. As a result, the linear part of the T/I curve
begins at a low current level and relatively high torque can be achieved
to produce higher speeds than those which can be achieved in conventional
VR motors.
It will be understood by those of skill in the art of VR motor design that
the number of stator teeth and rotor teeth can be chosen according to the
desired application. The present invention can be practiced with a wide
range of combinations of rotor teeth and stator teeth so long as the
stator tooth ratio and rotor tooth ratio are maintained within the limits
outlined above, and the number of rotor teeth is greater than the number
of stator teeth.
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