Electrical generator or motor structure – Dynamoelectric – Rotary
Reexamination Certificate
2001-03-29
2003-04-15
Ramirez, Nestor (Department: 2834)
Electrical generator or motor structure
Dynamoelectric
Rotary
C310S06700R, C310S252000, C310S261100
Reexamination Certificate
active
06548923
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a two-phase hybrid type stepping motor, and more particularly to a two-phase hybrid type stepping motor having a structure capable of reducing cogging torque and improving a torque waveform.
2. Description of the Prior Art
As shown in
FIGS. 1A
,
1
B and
1
C, a conventionally implemented two-phase hybrid type stepping motor is composed of a stator
5
having eight magnetic poles
2
arranged on the inner periphery of an annular yoke
1
at equal intervals, windings
3
wound around the respective magnetic poles
2
to form two-phase windings and multiple small teeth
4
provided at the tip end of each magnetic pole
2
, and a rotor
9
having two splitted rotor elements
7
, a permanent magnet
8
held therebetween and magnetized to two polarities of N and S in an axial direction, and multiple small teeth
6
formed on an outer periphery of each of the rotor element
7
at an regular pitch, said rotor elements
7
being shifted from each other in angular position by a ½ pitch of the teeth
6
. The two-phase hybrid type stepping motor rotatably supports the rotor
9
, the rotor
9
being opposed to the stator
5
with a gap therebetween.
The windings
2
are wound on the both sides of N and S polarities and connected so as to constitute two phases A and B with odd numbers and even numbers. As to magnetic flux of a magnet, in case of the phase A, for example, magnetic flux of the rotor magnetic pole on the N polarity side flows from the winding poles of N1 and N5 toward the S polarity through the stator
5
and enters the stator
5
from the winding poles of S3 and S7 and the rotor magnetic pole on the S polarity side to return to the magnetic pole
8
. Since this magnetic flux does not flow through the magnetic pole of the phase B, the phase A and the phase B are magnetically independent from each other without mutual interference.
Taking an equivalent circuit of a magnetic circuit of the hybrid type stepping motor shown in
FIGS. 1A
to
1
C into consideration, the equivalent circuit is as shown in
FIG. 2
when the magnetic resistance in a magnet core is ignored for the sake of simplicity. In
FIG. 2
, reference character F
i
(here, i is 1 to 8) denotes magnetomotive force of an i-th winding pole; P
i
(here i is 1 to 4), a permeance of the i-th winding pole on the N or S polarity side; and F
m
and P
m
, magnetomotive force and an internal permeance of the magnet. It should be noted that the permeances of the winding poles provided at axisymmetric positions are equal to each other and the same reference character is therefore used. Further, in regard to the winding of the phase A, since the N1 and N5 poles are connected in series in the forward direction while the N3 and N7 poles are connected in series in the backward direction, the magnetomotive force to these poles has the same intensity F
A
, but only the polarities vary. As a result, as shown in
FIG. 2
, two circuit groups (sub circuits) having four branches (P
1
and F
A
, P
2
and F
B
, P
3
and −F
A
, and P
4
and −F
B
) are aligned in parallel, and two such circuit groups are aligned in series, thereby equivalently replacing with one sub circuit by the circuit logic. This is shown in FIG.
3
.
Here, the total permeance of the winding poles of the stator will be first examined, and the cogging torque having the structure that the small teeth provided at the end of each winding pole have a pitch and a tooth width different from those of small teeth of the magnetic pole of the rotor will be then examined.
Since the torque &tgr; is given by the angle differentiation of magnetic energy in the equivalent circuit shown in
FIG. 3
, a general expression of the torque is as indicated by Formula 1.
τ
=
N
R
2
∑
i
=
1
M
(
F
i
-
F
0
)
2
ⅆ
P
i
ⅆ
θ
e
(
1
)
Here, F
O
denotes reduction in the magnetomotive force of a gap including excitation; N
R
, a number of teeth of the rotor; 2S, a number of winding poles (in the drawing, S=4); and &thgr;
e
, an electrical angle.
It is to be noted that F
O
can be calculated in accordance with Norton's theorem as expressed by Formula 2.
F
0
=
∑
i
=
1
M
P
i
F
i
+
P
m
F
m
∑
i
=
1
M
P
i
+
P
m
(
2
)
Furthermore, it is determined that each permeance has a phase difference of 90 degrees and is expressed by Fourier series of Formula 3 and Formula 4.
P
i
=
p
0
+
∑
n
=
1
∞
p
n
cos
n
ς
i
(
3
)
ς
i
=
θ
e
-
(
i
-
1
)
π
2
(
4
)
For example, P
1
can be expressed by Formula 5.
P
1
=&rgr;
0
+&rgr;
1
cos &thgr;
e
+&rgr;
2
cos 2&thgr;
e
+&rgr;
3
cos 3&thgr;
e
+&rgr;
4
cos 4&thgr;
e
+&rgr;
5
cos 5&thgr;
e
(5)
In the above-described two-phase hybrid type stepping motor, torque is generated between the rotor and the stator when the rotor is rotated without energizing the windings, and this torque is referred to as cogging torque.
When a plurality of windings in the two-phase hybrid type stepping motor are sequentially energized to rotate the motor, there is generated synthetic torque obtained from torque generated by energizing the windings and the cogging torque as the torque generated in the rotor. Plenty of pulsation is included in the synthetic torque, which leads to; a problem such as large vibration or noise.
Further, although the vernier method for unequalizing a pitch of the small teeth of the stator and that of the small teeth of the rotor was examined in order to reduce the cogging torque of the two-phase hybrid type stepping motor in the prior art, examination is still insufficient and the satisfactory effect is not obtained. Therefore, it is another object of the present invention to elucidate the theory of the vernier method and obtain the effective vernier method having a high degree of freedom.
In order to solve the problems, a state of occurrence of the cogging torque will be first examined. The cogging torque &tgr;
c
corresponds to the case where the magnetomotive force of the windings is zero (F
A
=F
B
=0) and can be expressed by Formula 6 and Formula 7.
τ
C
=
N
R
2
(
P
m
F
m
P
T
)
2
ⅆ
ⅆ
θ
e
∑
i
=
1
M
P
i
(
6
)
P
T
=
∑
i
=
1
M
P
i
+
P
m
(
7
)
Thus, in order to remove the cogging torque, a sum of respective orders of P
i
in Formula 6 should be zero.
Table 1 shows the primary to quaternary harmonic contents of the respective Fourier series and a sum of these harmonic contents with i=1 to 4.
TABLE 1
PRIMARY
SECONDARY
TERTIARY
QUATERNARY
P
1
cos(&thgr;
e
)
cos(2&thgr;
e
)
cos(3&thgr;
e
)
cos(4&thgr;
e
)
P
2
sin &thgr;
e
-cos 2&thgr;
e
-sin 3&thgr;
e
cos(4&thgr;
e
)
P
3
-cos &thgr;
e
cos 2&thgr;
e
-cos 3&thgr;
e
cos(4&thgr;
e
)
P
4
-sin &thgr;
e
-cos 2&thgr;
e
sin 3&thgr;
e
cos(4&thgr;
e
)
&Sgr;P
1
0
0
0
4cos(4&thgr;
e
)
It is to be noted that the coefficient &rgr;
i
is equal with respect to each polarity, thereby omitting this coefficient.
According to Table 1, in the structure with the eight winding poles, a sum total of P
i
which is the contribution of the cogging torque is zero in the tertiary or lower harmonic contents. In general, since the sum total becomes smaller as the order becomes higher, the quaternary harmonic content remains as the maximum affector. That is why the quaternary harmonic content appears in the cogging torque of the two-phase motor.
In order to remove this torque, the quaternary harmonic content of each magnetic pole permeance P
i
must be set to zero in each winding pole.
Thus, the permeance of each small tooth provided at the end of the winding pole will be examined, and conditions for setting a sum of the quaternary harmonic contents of the respective permeances to be zero will be then examined in accordance with each small tooth.
A flow of the magnetic flux differs depending on the relationship of the relative position of the respective small teeth of the stator and the ro
Isozaki Koki
Ohnishi Kazuo
Sakamoto Masafumi
Japan Servo Co. Ltd.
Mohandesi Iraj A
Patterson, Thuente, Skaar & Christensen LLC
Ramirez Nestor
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