Permanent magnet rotary electric machine including flux barriers shaped along flux lines
According to one embodiment, a first permanent magnet and a second permanent magnet are disposed in each magnetic pole of a rotor core. When angular coordinates of intersections of a flux line in a d-axial direction passing an outer end A 1 of the first permanent magnet, a flux line in the d-axial direction passing through an inner end A 2 of the first permanent magnet, a flux line in the d-axial direction passing an outer end B 1 of the second permanent magnet, a flux line in the d-axial direction passing an inner end B 2 of the second permanent magnet and a circumscribing circle of the rotor core are respectively defined as θ dA1 , θ dA2 , θ dB1 and θ dB2 , the θ dA1 , θ dA2 , θ dB1 and θ dB2 satisfy a formula (−34/p<(θ dB1 -θ dA1 )<22/p, −34/p<(θ dB2 −θ dA2 )<22/p).
1. A rotor of a rotary electric machine comprising: a shaft rotatable around a central axis; a rotor core comprising a plurality of magnetic poles arranged along a circumferential direction and fixed coaxially to the shaft; and a first permanent magnet and a second permanent magnet, disposed in a plurality of layers of flux barriers formed in the plurality of magnetic poles, respectively,
wherein
in a lateral cross section of the rotor core, normal to the central axis,
when an axis extending from the central axis in a diametrical direction between each adjacent pair of the magnetic poles is referred to as a q-axis, and an axis electrically normal to the q-axis is referred to as a d-axis in each of the magnetic poles,
the flux barrier of each of the magnetic poles includes a first flux barrier provided between the d-axis and the q-axis and a second flux barrier provided in an inner circumferential side the rotor core with respect to the first flux barrier between the d-axis and the q-axis,
the first flux barrier is formed between a first outer circumferential-side edge extending from a vicinity of the d-axis to a vicinity of an outer circumference of the rotor core, and a first inner circumferential-side edge extending from a vicinity of the d-axis to a vicinity of the circumference and located an inner circumferential side of the rotor core with respect to the first outer circumferential-side edge with a gap therebetween,
the second flux barrier is formed between a second outer circumferential-side edge located on an inner circumferential side of the rotor core with respect to the first inner circumferential-side edge with a gap therebetween and extending from the vicinity of the d-axis to the vicinity of the outer circumference of the rotor core, and a second inner circumferential-side edge extending from the vicinity of the d-axis to the vicinity of the circumference and located on the inner circumferential side of the rotor core with respect to the second outer circumferential-side edge with a gap therebetween,
the first permanent magnet has a cross-sectional shape comprising a first long side with an inner end and an outer end, a first short side intersecting the inner end of the first long side and a second short side intersecting the outer end of the first long side, the first permanent magnet is disposed in the first flux barrier in a state that the first long side opposes the first outer circumferential-side edge of the first flux barrier, the inner end and the first short side are located on a side of the d-axis, and the outer end of the first long side and the second short side are located in the outer circumferential side of the rotor core, and
the second permanent magnet has a cross-sectional shape comprising a second long side with an inner end and an outer end, a third short side intersecting the inner end of the second long side and a fourth short side intersecting the outer end of the second long side, the second permanent magnet is disposed in the second flux barrier in a state that the second long side opposes the second outer circumferential-side edge of the second flux barrier, the inner end and the third short side are located on a side of the d-axis, and the outer end of the second long side and the fourth short side are located in the outer circumferential side, and where,
R: represents a radius of a circle around the central axis, which circumscribes the circumference of the rotor core;
r: represents radial coordinates of a polar coordinate system interposed between with the d-axis and q-axis with respect to the central axis as a central point;
θ: represents angular coordinates of the polar coordinate system interposed between the d-axis and q-axis with respect to the central axis;
p: represents the number of pairs of poles pairs (the number of magnetic poles/2)
θ a : represents angular coordinates of an arbitrary point of the circumscribing circle,
a flux line in a d-axial direction passing through coordinates (R, θ a ) is defined by formula (1) below,
( r/R ) P ·cos( p θ)=cos( pθ a ) (1)
a flux line in a q-axial direction passing through coordinates (R, θ a ) is defined by formula (2) below,
( r/R ) P ·sin( p θ)=sin( pθ a ) (2)
and when
angular coordinates of an intersection of the flux line in the d-axial direction passing through an outer end A1 of the first long side of the first permanent magnet and the circumscribing circle are defined as θdA1, and angular coordinates of an intersection of the flux line in the d-axial direction passing through an inner end A2 of the first long side of the first permanent magnet and the circumscribing circle are defined as θdA2, and angular coordinates of an intersection of the flux line in the d-axial direction passing through an outer end B1 of the second long side of the second permanent magnet and the circumscribing circle are defined as θdB1, and angular coordinates of an intersection of the flux line in the d-axial direction passing through an inner end B2 of the second long side of the second permanent magnet and the circumscribing circle are defined as θdB2,
the θdA1, θdA2, θdB 1 and 6dB2 satisfy formula (3) below:
-
34
p
<
θ
d
B
1
-
θ
dA
1
<
22
p
-
34
p
<
θ
d
B
2
-
θ
dA
2
<
22
p
(
3
)
2. The rotor of claim 1 , wherein the θdA1, θdA2, θdB 1 and 6dB2 satisfy formula (4) below:
-
22
p
<
θ
d
B
1
-
θ
dA
1
<
9
p
-
22
p
<
θ
d
B
2
-
θ
dA
2
<
9
p
(
4
)
3. Rotor of claim 1 , wherein
the θdA1, θdA2, θdB 1 and 6dB2 satisfy formula (5) below:
-
15
p
<
θ
d
B
1
-
θ
dA
1
<
5
p
-
15
p
<
θ
d
B
2
-
θ
dA
2
<
5
p
(
5
)
4. The rotor of claim 1 , wherein the θdA1, θdA2, θdB 1 and 6dB2 satisfy formula (6) below:
-
10
p
<
θ
d
B
1
-
θ
dA
1
<
-
1
p
-
10
p
<
θ
d
B
2
-
θ
dA
2
<
-
1
p
(
6
)
5. The rotor of claim 1 , wherein
the outer end A1 of the first permanent magnet is located at an intersection of the flux line in the d-axial direction passing through θdA1 and a first flux line in a q-axial direction, and the inner end A2 of the first permanent magnet is located at an intersection of the first flux line in the q-axial direction and the flux line in the d-axial direction passing through and θdA2.
6. The rotor of claim 5 , wherein
the outer end B1 of the second permanent magnet is located at an intersection of the flux line in the d-axial direction passing through the θdB1 and a second flux line in a q-axial direction, and the inner end B2 of the second permanent magnet is located at an intersection of the second flux line in the q-axial direction and the flux line in the d-axial direction passing through the θdB2.
7. The rotor of claim 1 , wherein
in the respective magnetic poles,
the first flux barriers each comprise an inner end adjacent to the d-axis and an outer end adjacent to the outer circumference of the rotor core, and are arranged such that a distance from the d-axis expands from the inner end towards the outer end, and
the second flux barriers each comprise an inner end adjacent to the d-axis and an outer end adjacent to the outer circumference of the rotor core, and are arranged such that a distance from the d-axis expands from the inner end towards the outer end.
8. The rotor of claim 7 , wherein
the first flux barriers each comprise a magnet loading region where the first permanent magnet is disposed, an inner-side cavity extending from the magnet loading region towards the d-axis, and an outer-side cavity extending from the magnet loading region towards the outer circumference of the rotor core,
the second flux barriers each comprise a magnet loading region where the second permanent magnet is disposed, an inner-side cavity extending from the magnet loading region towards the d-axis, and an outer-side cavity extending from the magnet loading region towards the outer circumference of the rotor core, and
the rotor core comprises a first bridge portion formed between the inner-side cavity of the first flux barrier and the d-axis, first outer circumferential bridge portion formed between the outer-side cavity of the first flux barrier and the outer circumference of the rotor core, a second bridge portion formed between the inner-side cavity of the second flux barrier and the d-axis, and a second outer circumferential bridge portion formed between the outer-side cavity of the second flux barrier and the outer circumference of the rotor core.