Method for double-layer winding layout applicable to asymmetrical winding machine
The invention relates to a double-layer winding layout method suitable for asymmetrical winding machine. The method is implemented by three main steps: 1) the design of the initial double-layer winding layout structure for each machine unit, which is based on the principle of the largest number of spokes belonging to phase A; 2) rearranging the number of spokes in positive (e.g., labeled a-phase belt) and negative sectors (e.g., labeled x-phase belt) belonging to phase A for making slot numbers equally divided; 3) solving the serial number of the stator slot in reverse to get the final winding layout schemes which contain multiple layout structures for one slot-pole combination. The method of the present invention improves the conventional star-of-slot theory based on the distribution characteristics of the asymmetrical windings, perfects the general design theory of double-layer asymmetrical winding structure.
1 . A method for double-layer winding layout applicable to an asymmetrical winding machine, wherein the method comprises the following steps:
1) designing an initial double-layer winding layout structure for each machine unit of the asymmetrical winding machine, which is based on a principle of a largest number of spokes belonging to phase A;
2) rearranging a number of spokes in a positive sector labeled as an a-phase belt and a negative sector labeled as an x-phase belt belonging to phase A for making slot numbers equally divided;
3) Solving a serial number of a stator slot in reverse to get final winding layout schemes which contain multiple layout structures for one slot-pole combination,
wherein in the initial double-layer winding layout structure depicted in a star of slots diagram for each machine unit of the asymmetrical winding machine, a direction of a first spoke in the star of slots diagram for each machine unit labeled 1 is set to point to the right horizontally and the other spokes lag behind the first spoke successively by an angle θ N in a clockwise direction, as detailed below:
θ
N
=
(
N
-
1
)
3
6
0
v
Q
N
=
1
,
2
,
L
,
3
Q
/
v
where N is a virtual slot number of each spoke in the star of slots diagram; vis a greatest common divisor between a slot number O and pole pairs p;
wherein the asymmetrical winding machine specifically includes h machine units,
where h=v/3, and there are three-layer slot vectors in the star of slots diagram for each machine unit, where a number of spokes in a one-layer star of slots diagram is q=O/v.
2 . The method for double-layer winding layout of claim 1 , wherein the method further comprises the following steps: the star of slots for machine unit is defined as the basic star plot and each machine unit has the same star of slots, and therefore the winding layouts of the other (h−1) machine units can directly replicate the winding layouts of the basic star plot, wherein based on the pitch of the asymmetrical winding machine and the basic star plot, the double-layer winding layout structure of the entire asymmetrical winding machine can be determined.
3 . The method for double-layer winding layout of claim 1 , wherein the method further comprises the following steps: in step 3, in order to facilitate the winding embedding processing, according to the virtual slot number, the actual slot number can be inversely solved, wherein for each machine unit of the asymmetrical winding machine, the specific details are as follows:
S
l
N
=
⌊
Abs
[
Rem
(
U
1
×
p
/
h
,
I
1
×
p
/
h
)
-
I
1
×
p
/
h
]
⌋
gU
1
×
p
/
h
T
where S IN is the actual slot number corresponding to the virtual slot number N of each spoke in the star of slots diagram of machine unit; p is the pole pairs; h is the number of the machine units; matrix U 1×p/h is the solution to slot number from a pair of poles to p pairs of poles; I 1×p/h is identity matrix.
4 . The method for double-layer winding layout of claim 3 , wherein the method further comprises the following steps: for the solution to slot number from a pair of poles to p pairs of poles matrix U 1×p/h , the specific details are as follows:
U
1
×
p
/
h
=
(
N
-
1
+
p
/
h
)
I
1
×
p
/
h
+
3
Q
/
v
[
0
,
TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
1
,
TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
2
K
,
p
/
h
-
1
]
p
/
h
where N is the virtual slot number of each spoke in the star of slots diagram; v is the greatest common divisor between slot number Q and pole pairs p; h is the number of the machine units; I 1×p/h is identity matrix.
5 . The method for double-layer winding layout of claim 1 , wherein the method further comprises the following steps: in step 1, based on the principle of the largest number of spokes belonging to phase A, the initial double-layer winding layout structure depicted in the star of slots diagram for each machine unit of the asymmetrical winding machine is constructed, wherein for each machine unit of the asymmetrical winding machine, the specific details are as follows:
1.1) the spokes in the star of slots diagram for each machine unit have equally displaced along the circumference, and the angle between two spokes is m=360v/Q;
1.2) based on the design principle that the number of spokes belonging to phase A is largest and the resultant MMF vector of the other two-phase windings is symmetrical about the resultant MMF vector of phase A, all of the J=3mod (Q/v, 3) spokes should be assigned to phase A, where J represents a number of additional spokes assigned to phase A and mod represents a modulo operation, and meanwhile the spokes belonging to phase B and phase C of machine unit are symmetrically distributed in space with phase A axis as the central axis;
1.3) the number of spokes in the positive a-phase belt and negative x-phase belt belonging to phase A, the positive b-phase belt and negative y-phase belt belonging to phase B, and the positive c-phase belt and negative z-phase belt belonging to phase C should be divided equally as much as possible, and meanwhile it is necessary to ensure that the number of spokes in the positive sectors is no less than the number of spokes in the negative sectors, in order to complete the design of the initial double-layer asymmetrical winding layout structure.
6 . The method for double-layer winding layout of claim 5 , wherein the method further comprises the following steps: in step 1.3, the number of spokes in the positive and negative sectors of phase A, phase B and phase C is written as
{
Q
a
=
3
⌈
Q
/
(
3
v
)
-
J
/
9
+
mod
(
Q
/
v
,
3
)
2
⌉
Q
x
=
3
⌊
Q
/
(
3
v
)
-
J
/
9
+
mod
(
Q
/
v
,
3
)
2
⌋
Q
b
=
Q
c
=
3
⌈
Q
/
(
3
v
)
-
J
/
9
2
⌉
Q
y
=
Q
z
=
3
⌊
Q
/
(
3
v
)
-
J
/
9
2
⌋
where (Q a , Q x ), (Q b , Q y ) and (Q c , Q z ) are the number of spokes in positive and negative sectors belonging to phase A, phase B and phase C, respectively;
if one or more of the number of spokes of phase A, phase B and phase C in machine unit cannot be evenly divided, the number of spokes in positive sectors should be greater in quantity than the number of spokes in the negative sectors, that is, the number of spokes Q a in positive a-phase belt is greater than or equal to the number of spokes Q x in negative x-phase belt, the number of spokes Q b in positive b-phase belt is greater than or equal to the number of spokes Q y in negative y-phase belt, and the number of spokes Q c in positive c-phase belt is greater than or equal to the number of spokes Q z in negative z-phase belt.
7 . The method for double-layer winding layout of claim 5 , wherein the method further comprises the following steps: in step 2, based on the principle of evenly dividing the number of stator slot number, the number of spokes in the positive sector which is labeled as the a-phase belt and the negative sector which is labeled as the x-phase belt belonging to phase A is rearranged, wherein for each machine unit of the asymmetrical winding machine, the specific details are as follows:
in order to make stator slot number equally divided, only all the 2mod (Q/v, 3) spokes from phase A of machine unit should be assigned equally to phase B and phase C, wherein it is necessary to rearrange the number of spokes in positive and negative sectors belonging to phase A of machine unit, wherein with the purpose of maximizing the back-EMF, the three spokes of a-phase belt and x-phase belt closest to y-phase belt and b-phase belt should be assigned to phase B, and the three spokes of a-phase belt and x-phase belt closest to z-phase belt and c-phase belt should be assigned to phase C; according to the parity of the number of spokes of phase A, the number of spokes in positive and negative sectors belonging to phase A is rearranged in order to complete the initial double-layer winding layout structure for secondary construction.
8 . The method for double-layer winding layout of claim 5 , wherein the method further comprises the following steps: according to the parity of the number of spokes of phase A, the number of spokes in positive and negative sectors belonging to phase A is rearranged, wherein when the k=(Q a /3+Q x /3) is even, the slot vectors belonging to a-phase belt and x-phase belt are collinear and their included angle is 180 degrees, wherein the allocation procedures are as follows:
a) when Q a /3=1 and J/3=1, the virtual slot number N ax_L1 of the spokes in the positive a-phase belt closest to negative y, z-phase belts and in the negative x-phase belt closest to positive b, c-phase belts can be deduced as
N
ax
_
L
1
=
{
1
+
(
λ
-
1
)
Q
v
(
The
positive
a
-
phase
belt
closest
to
negative
y
,
z
-
phase
belts
)
Q
a
3
+
Q
z
3
+
Q
b
3
+
1
+
(
λ
-
1
)
Q
v
(
The
negative
x
-
phase
belt
closest
to
positive
b
,
TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
c
-
phase
belts
)
wherein N ax_L1 is a virtual slot number of the spokes, and λ (λ=1, 2, 3) is a layer number of the star of slots for each machine unit;
in order to make stator slot number equally divided, it is necessary to take two spokes from the stator vectors whose the virtual slot number is N ax_L1 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
a1) assign any one spoke from phase A which the virtual slot number is N ax_L1 to b-phase belt or y-phase belt;
a2) based on a1), assign any one spoke from the remaining spokes of phase A which the virtual slot number is N ax_L1 to c-phase belt or z-phase belt;
b) when Q a /3=1 and J/3≠1, the virtual slot number of the spokes in the positive a-phase belt closest to negative y, z-phase belts and in the negative x-phase belt closest to positive b, c-phase belts is same as a), wherein in order to make stator slot number equally divided, it is necessary to take four spokes from the stator vectors whose the virtual slot number is N ax_L1 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
b1) assign any two spokes from phase A which the virtual slot number is N ax_L1 to b-phase belt or y-phase belt;
b2) based on b1), assign any two spokes from the remaining spokes of phase A which the virtual slot number is N ax_L1 to c-phase belt or z-phase belt;
c) when Q a /3≠1 and J/3=1, the virtual slot number N ax_L2 of the spokes in the positive a-phase belt closest to negative y, z-phase belts, and the virtual slot number N ax_R2 of the spokes in the negative x-phase belt closest to positive b, c-phase belts can be deduced as
{
N
ax
_
L
2
=
{
λ
Q
v
(
The
positive
a
-
phase
belt
closest
to
negative
y
-
phase
belts
)
Q
a
3
+
Q
z
3
+
Q
b
3
+
(
λ
-
1
)
Q
v
(
The
negative
x
-
phase
belt
closest
to
positive
b
-
phase
belts
)
N
ax
_
R
2
=
{
Q
a
3
+
(
λ
-
1
)
Q
v
-
1
(
The
positive
a
-
phase
belt
closest
to
negative
z
-
phase
belts
)
Q
a
3
+
Q
z
3
+
Q
b
3
+
Q
x
3
+
(
λ
-
1
)
Q
v
-
1
(
The
negative
x
-
phase
belt
closest
to
positive
c
-
phase
belts
)
wherein N ax_L2 and N ax_R2 are virtual slot numbers of the spokes, and λ (λ=1, 2, 3) is a layer number of the star of slots for each machine unit;
in order to make stator slot number equally divided, it is necessary to take one spoke respectively from the stator vectors whose the virtual slot number is N ax_L2 and N ax_R2 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
c1) assign any one spoke from phase A which the virtual slot number is N ax_L2 to b-phase belt or y-phase belt;
c2) based on c1), assign any one spoke from phase A which the virtual slot number is N ax_R2 to z-phase belt or c-phase belt;
d) when Q a /3≠1 and J/3≠1, the virtual slot number of the spokes in the positive a-phase belt closest to negative y, z-phase belts and in the negative x-phase belt closest to positive b, c-phase belts is same as c);
in order to make stator slot number equally divided, it is necessary to take two spokes respectively from the stator vectors whose the virtual slot number is N ax_L2 and N ax_R2 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
d1) assign any two spokes from phase A which the virtual slot number is N ax_L2 to b-phase belt or y-phase belt;
d2) based on d1), assign any one spoke from phase A which the virtual slot number is N ax_R2 to z-phase belt or c-phase belt.
9 . The method for double-layer winding layout of claim 5 , wherein the method further comprises the following steps: according to the parity of the number of spokes of phase A, the number of spokes in positive and negative sectors belonging to phase A is rearranged, wherein when the k=(Q a /3+Q x /3) is odd, the slot vectors belonging to a-phase belt and x-phase belt are arranged alternately, and the spokes in the positive a-phase belt are closest to negative y, z-phase belts, wherein the allocation procedures are as follows:
e) when Q a /3=1 and J/3=1, the virtual slot number N ax_L3 of the spokes in the positive a-phase belt closest to negative y, z-phase belts can be deduced as
N
ax
_
L
3
=
1
+
(
λ
-
1
)
Q
v
where the symbol wherein N ax_L3 is a virtual slot number of the spokes, and λ (λ=1, 2, 3) is a layer number of the star of slots for each machine unit;
in order to make stator slot number equally divided, it is necessary to take two spokes from the stator vectors whose the virtual slot number is N ax_L3 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
e1) assign any one spoke from phase A which the virtual slot number is N ax_L3 to b-phase belt or y-phase belt;
e2) based on e1), assign any one spoke from the remaining spokes of phase A which the virtual slot number is N ax_L3 to c-phase belt or z-phase belt;
f) when Q a /3≠1 and J/3=1, the virtual slot number N ax_L4 of the spokes in the positive a-phase belt closest to negative y-phase belts, and the virtual slot number N ax_R4 of the spokes in the positive a-phase belt closest to negative z-phase belts can be deduced as
{
N
ax
_
L
4
=
λ
Q
v
(
The
positive
a
-
phase
belt
closest
to
negative
y
-
phase
belts
)
N
ax
_
R
4
=
Q
a
3
+
(
λ
-
1
)
Q
v
-
1
(
The
positive
a
-
phase
belt
closest
to
negative
z
-
phase
belts
)
wherein N ax_L4 and N ax_R4 are virtual slot numbers of the spokes, and λ (λ=1, 2, 3) is a layer number of the star of slots for each machine unit;
in order to make stator slot number equally divided, it is necessary to take one spoke respectively from the stator vectors whose the virtual slot number is N ax_L4 and N ax_R4 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
f1) assign any one spoke from phase A which the virtual slot number is N ax_L4 to y-phase belt;
f2) based on f1), assign any one spoke from phase A which the virtual slot number is N ax_R4 to z-phase belt;
g) when Q a /3≠1 and J/3≠1, the virtual slot number of the spokes in the positive a-phase belt closest to negative y, z-phase belts is same as f);
in order to make stator slot number equally divided, it is necessary to take two spokes respectively from the stator vectors whose the virtual slot number is N ax_L4 and N ax_R4 to assign equally to phase B and phase C, wherein the allocation procedures are as follows:
g1) assign any two spokes from phase A which the virtual slot number is N ax_L4 to y-phase belt;
g2) based on g1), assign any two spokes from phase A which the virtual slot number is N ax_R4 to z-phase belt; Through rearranging the number of spokes in positive a-phase belt and negative x-phase belt belonging to phase A of machine unit, the stator slot number equally divided is realized.