# US 10,122,229 B2 · Motor having rotor of optimized shape

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- Number: US 10,122,229 B2
- Document ID: US10122229B2
- Status: Granted
- Kind: B2
- Application number: 15/351,569
- Filed: 2016-11-15
- Published: 2017-05-18
- Granted: 2018-11-06
- Earliest claimed: 2015-11-17
- Assignees: Fanuc Corporation
- Applicants: Fanuc Corporation
- Inventors: Leo Arai
- Web page: https://patentgrep.com/patent/US10122229B2

## CPC

- H02K 1/274: the rotor consisting of two or more circumferentially positioned magnets
- H02K 1/146: {consisting of a generally annular yoke with salient poles}
- H02K 3/18: Windings for salient poles
- H02K 21/16: having annular armature cores with salient poles (with homopolar co-operation H02K21/20)
- H02K 2213/03: Machines characterised by numerical values, ranges, mathematical expressions or similar information
- H02K: DYNAMO-ELECTRIC MACHINES (dynamo-electric relays H01H53/00; conversion of DC or AC input power into surge output power {H03K3/53})

## Abstract

A motor according to an embodiment of the present invention includes a rotor having a rotor core and a plurality of magnetic poles including permanent magnets provided in the rotor core; and a stator having a stator core in which a plurality of teeth disposed on the side of the outer periphery of the rotor so as to be opposed to the plurality of magnetic poles and slots for containing armature winding wound around the plurality of teeth are formed. The rotor is structured such that the distance r(θ) between the center of the rotor and the outer periphery thereof satisfies the following equations (1) and (2): ∫ - ϕ ϕ ⁢  f ⁡ ( θ ) 2 - r ⁡ ( θ ) 2  ⁢ d ⁢ ⁢ θ ≤ ϕ ⁡ ( R 2 - r 0 2 ) 10 ( 1 ) ∫ - ϕ ϕ ⁢  r 1 ⁡ ( θ ) 2 - r ⁡ ( θ ) 2  ⁢ d ⁢ ⁢ θ > 0 ( 2 )

## Claims

### Claim 1

A motor comprising:
a rotor having a rotor core and a plurality of magnetic poles including permanent magnets provided in the rotor core; and
a stator having a stator core in which a plurality of teeth disposed on the side of the outer periphery of the rotor so as to be opposed to the plurality of magnetic poles and slots for containing armature winding wound around the plurality of teeth are formed, wherein
the rotor has an outer peripheral surface, the outer peripheral surface having a curved shape with shape parameters, α, β, γ, and μ as set forth below, such that a distance r(θ) between the center of the rotor and the outer peripheral surface is related to a first function ƒ(θ) describing a first arcuate shape, and a second function r1(θ) describing a second arcuate shape by the following equations (1) and (2):
∫
-
ϕ
ϕ
⁢

f
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≤
ϕ
⁡
(
R
2
-
r
0
2
)
10
(
1
)
∫
-
ϕ
ϕ
⁢

r
1
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
>
0
(
2
)
wherein,
f
⁡
(
θ
)
=
r
0
-
R
-
r
0
cos
α
⁡
(
β
μ
γ
-
1
⁢

θ

γ
)
(
3
)
r
1
⁡
(
θ
)
=
r
0
-
R
-
r
0
cos
⁡
(
p
2
⁢
θ
)
(
4
)
3
⁢
⁢
π
5
⁢
p
≤
ϕ
≤
π
p
(
5
)
1
3
≤
α
≤
2
(
6
)
p
4
≤
β
≤
p
(
7
)
3
⁢
⁢
π
5
⁢
p
≤
μ
≤
π
p
(
8
)
1
2
≤
γ
≤
4
(
9
)
R: the minimum diameter of the stator core
r0: the maximum diameter of the rotor
p: the number of poles of the rotor
θ: an angle [rad] with respect to a straight line (0 [rad]) that extends from the rotation center of the rotor to the center of the pole of the rotor orthogonally to a rotation axis
ϕ: a specified range [rad] of r(θ)
α, β, γ, and μ: parameters each having a range specified by the equations (6)-(9)
wherein μ0=1.

### Claim 2 (depends on 1)

The motor according to claim 1, wherein in a cogging torque per rotation of the rotor, the amplitude of the cogging torque of a frequency component at a frequency of the least common multiple of a rotor pole number and a stator teeth number is 0.2% or less of a rated torque.

### Claim 3 (depends on 1)

The motor according to claim 1, wherein in a cogging torque per rotation of the rotor, the amplitude of the cogging torque of a frequency component at a frequency of the least common multiple of a rotor pole number and a stator teeth number is 0.125% or less of a rated torque.

### Claim 4 (depends on 1)

The motor according to claim 1, wherein the shape of the rotor, the shape of the teeth of the stator, and the phase relationship between the rotor and the teeth are invariant in an axial direction, and the plurality of magnetic poles of the rotor have the same shape.

### Claim 5 (depends on 1)

The motor according to claim 1, wherein the parameter ϕ is determined so as to satisfy the following equation (5′), instead of the equation (5)
4
⁢
⁢
π
5
⁢
p
≤
ϕ
≤
π
p
.
(
5
′
)

### Claim 6 (depends on 1)

The motor according to claim 1, wherein the parameter α is determined so as to satisfy the following equation (6′), instead of the equation (6)
1
2
≤
α
≤
3
2
.
(
6
′
)

### Claim 7 (depends on 1)

The motor according to claim 1, wherein the parameter γ is determined so as to satisfy the following equation (9′), instead of the equation (9)
1
2
≤
γ
≤
2.
(
9
′
)

### Claim 8 (depends on 1)

The motor according to claim 1, wherein the parameter β is determined so as to satisfy the following equation (7′), instead of the equation (7)
p
4
≤
β
≤
p
2
.
(
7
′
)

### Claim 9 (depends on 1)

The motor according to claim 1, wherein the parameter ϕ, is determined so as to satisfy the following equation (5″), instead of the equation (5)
9
⁢
⁢
π
10
⁢
⁢
p
≤
ϕ
≤
π
p
.
(
5
″
)

### Claim 10 (depends on 1)

The motor according to claim 1, wherein the parameter α is determined so as to satisfy the following equation (6″), instead of the equation (6)
α=1 (6′).

### Claim 11 (depends on 1)

The motor according to claim 1, wherein the parameter γ is determined so as to satisfy the following equation (9″), instead of the equation (9)
γ=1 (9″).

### Claim 12 (depends on 1)

The motor according to claim 1, wherein the distance r(θ) is determined so as to satisfy the following equation (1′), instead of the equation (1)
∫
-
ϕ
ϕ
⁢

f
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≤
ϕ
⁡
(
R
2
-
r
0
2
)
20
.
(
1
′
)

### Claim 13 (depends on 1)

The motor according to claim 1, wherein the distance r(θ) is determined so as to satisfy the following equation (2′), instead of the equation (2)
∫
-
ϕ
ϕ
⁢

r
1
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≥
ϕ
⁡
(
R
2
-
r
0
2
)
50
.
(
2
′
)

### Claim 14 (depends on 1)

The motor according to claim 1, wherein the distance r(θ) is determined so as to satisfy the following equation (2″), instead of the equation (2)
∫
-
ϕ
ϕ
⁢

r
1
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≥
ϕ
⁡
(
R
2
-
r
0
2
)
20
.
(
2
″
)

### Claim 15 (depends on 1)

The motor according to claim 1, wherein the distance r(θ) is determined so as to satisfy the following equations (10) and (20), instead of the equations (1) and (2)
∫
-
ϕ
ϕ
⁢

f
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≤
ϕ
⁡
(
R
2
-
r
0
2
)
20
(
10
)
∫
-
ϕ
ϕ
⁢

r
1
⁡
(
θ
)
2
-
r
⁡
(
θ
)
2

⁢
d
⁢
⁢
θ
≥
ϕ
⁡
(
R
2
-
r
0
2
)
20
.
(
20
)