U.S. patent application number 10/623628 was filed with the patent office on 2004-01-29 for interior permanent magnet synchronous motor.
This patent application is currently assigned to SANYO DENKI CO., LTD.. Invention is credited to Matsushita, Manabu, Miyashita, Toshihito, Onodera, Satoru.
Application Number | 20040017123 10/623628 |
Document ID | / |
Family ID | 18762975 |
Filed Date | 2004-01-29 |
United States Patent
Application |
20040017123 |
Kind Code |
A1 |
Miyashita, Toshihito ; et
al. |
January 29, 2004 |
Interior permanent magnet synchronous motor
Abstract
An interior permanent magnet synchronous motor wherein cogging
torque and torque pulsation during feeding of electricity can be
both restrained. 2p (p: a positive integer of 1 or more) magnetic
salient pole sections consists of two groups of magnetic salient
pole sections, a first group of which consists of p magnetic
salient pole sections arranged so as to be spaced at equal
intervals in the peripheral direction while having one magnetic
salient pole section of a second group interposed between each of
two adjacent magnetic salient pole sections, and the second group
of which consists of p magnetic salient pole sections arranged so
as to be spaced at equal intervals in the peripheral direction
while having one magnetic salient pole section of the first group
interposed between each of two adjacent magnetic salient pole
sections. The open angle .alpha. 1 of the p magnetic salient pole
sections of the first group is smaller than the open angle .alpha.
2 of the p magnetic salient pole sections of the second group. Then
the open angles .alpha. 1 and .alpha. 2 are set to satisfy the
expression .alpha.2-.alpha.1.apprxeq.2.beta.-(2n-1).tau.s. n is a
natural number. .beta. is an angle between virtual center lines CL1
and CL2 of two adjacent magnetic salient pole sections which extend
from the center of the shaft through the center of each salient
magnetic pole sections. .tau. s is the slot pitch of the stator
core.
Inventors: |
Miyashita, Toshihito;
(Tokyo, JP) ; Onodera, Satoru; (Tokyo, JP)
; Matsushita, Manabu; (Tokyo, JP) |
Correspondence
Address: |
RANKIN, HILL, PORTER & CLARK, LLP
700 HUNTINGTON BUILDING
925 EUCLID AVENUE, SUITE 700
CLEVELAND
OH
44115-1405
US
|
Assignee: |
SANYO DENKI CO., LTD.
Tokyo
JP
|
Family ID: |
18762975 |
Appl. No.: |
10/623628 |
Filed: |
July 21, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10623628 |
Jul 21, 2003 |
|
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|
09951282 |
Sep 13, 2001 |
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6597079 |
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Current U.S.
Class: |
310/156.53 ;
310/156.45 |
Current CPC
Class: |
H02K 1/276 20130101;
H02K 21/14 20130101 |
Class at
Publication: |
310/156.53 ;
310/156.45 |
International
Class: |
H02K 021/12; H02K
001/27 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 13, 2000 |
JP |
2000/277693 |
Claims
What is claimed is:
1. An interior permanent magnet synchronous motor comprising: a
stator including a stator core provided with a plurality of
magnetic pole sections having windings of at least one phase wound
thereon; a rotor having p pole pairs (p: a positive integer of 1 or
more); said rotor including a shaft and a rotor core fixed on said
shaft; said rotor core having 2p permanent magnets incorporated
therein in a manner to be spaced from each other at intervals in a
peripheral direction thereof; said 2p permanent magnets
constituting 2p permanent magnet magnetic pole sections formed on
an outer periphery of said rotor core; said rotor being formed with
2p magnetic salient pole sections so as to interpose said permanent
magnet magnetic pole section therebetween; said 2p magnetic salient
pole sections consisting of a first and a second groups of magnetic
salient pole sections, said first group consisting of p magnetic
salient pole sections arranged so as to be spaced at equal
intervals in the peripheral direction while each of the magnetic
salient pole sections of a second group is interposed between two
adjacent magnetic salient pole sections and said second group
consisting of p magnetic salient pole sections arranged so as to be
spaced at equal intervals in the peripheral direction while each of
magnetic salient pole sections of the first group is interposed
between two adjacent magnetic salient pole sections; wherein an
open angle .alpha. 1 of said p magnetic salient pole sections of
said first group is set smaller than an open angle .alpha. 2 of
said p magnetic salient pole sections of said second group; said
open angles .alpha. 1 and .alpha. 2 are determined to satisfy the
following expressions:
.alpha.2-.alpha.1.apprxeq.2.beta.-(2n-1).tau.s wherein n is a
natural number, .beta. is an angle between two salient pole section
virtual center lines CL1, CL2 which extend from the center of said
shaft through the center of said two adjacent magnetic salient pole
sections, and .tau. s is the slot pitch of said stator core.
2. The interior permanent magnet synchronous motor as defined in
claim 1, wherein curvature radius R1 of said p magnetic salient
pole sections of the first group is smaller than curvature radius
R2 of said p magnetic salient pole sections of the second
group.
3. The interior permanent magnet synchronous motor as defined in
claim 1, wherein the shapes of said 2p permanent magnet magnetic
pole sections and said 2p magnetic salient pole sections are
determined so that the contour of an outer peripheral surface
section of the rotor core formed with said two adjacent permanent
magnetic pole sections and said magnetic salient pole section
interposed therebetween is configured so as to have symmetrical
shapes about the salient pole section virtual center lines CL1 or
CL2 and so that the contour of the outer peripheral surface
sections corresponding to the angle of 360.degree./p about the
center of the shaft of the rotor each may be formed into an
identical shape, thus resulting in the rotor core having p
identical shapes in the outer periphery thereof.
4. The interior permanent magnet synchronous motor as defined in
claim 2, wherein each of the magnetic pole surfaces of said
permanent magnet magnetic pole sections is formed into arcuate or
elliptic configuration; wherein each of said magnetic pole surfaces
of said permanent magnet magnetic pole sections of rotor core and
each of magnetic pole surfaces of said magnetic pole sections of
said stator core are arranged so as to have a gap defined
therebetween and having a dimension .delta. d which satisfies or
almost satisfies the following expression: .delta.d=.delta.d0/cos
[p(.theta.m-.theta.dm)]wherein .delta. d0 is the minimum value of
the dimension of said gap, .theta. m is an angle defined from a
virtual center line CL3 which extends from the center of the shaft
through a center of the two salient pole section virtual center
lines CL1, CL2 toward the side of the magnetic salient pole section
having the open angle .alpha. 1, and .theta. dm is an angle between
the virtual line PL3 which extends from the center of the shaft and
through a position where the dimension of the gap has the minimum
value and the virtual center line CL3.
5. The interior permanent magnet synchronous motor as defined in
claim 4, wherein the following expressions are satisfied while
.phi. 1 is an angle defined between the virtual center line CL3 and
a virtual line PL1 which is one of the two virtual lines PL1 and
PL2 which extend from the center of the shaft through both ends of
each of the magnetic pole sections, the virtual line PL1 being
positioned on the side of the magnetic salient pole section having
the open angle .alpha. 2, and .phi. 2 is an angle defined between
the virtual center line CL3 and the virtual line PL2 which is the
other of the two virtual lines PL1 and PL2 and which is positioned
on the side of the magnetic salient pole section having the open
angle .alpha. 1: .phi.2>.phi.1
.phi.2-.phi.1.apprxeq.0.5(2m-1).ta- u.s-(180.degree./p)
.phi.2+.phi.1.apprxeq.u.multidot..tau.s
.alpha.1+.alpha.2.ltoreq.(360.degree./p)-2(.phi.2+.phi.1) wherein p
is the number of pole pairs and m and u are arbitrary natural
numbers.
6. The interior permanent magnet synchronous motor as defined in
claim 5, wherein said .alpha. 1, .alpha. 2, .phi. 1 and .phi. 2 are
set at such values as to satisfy the following expressions also:
(180.degree./2p)+(.alpha.1/2)-.phi.2.apprxeq.(1/4)(2v1-1).tau.s
(180.degree./2p)+(.alpha.2/2)-.phi.1.apprxeq.(1/4)(2v2-1).tau.s
wherein v1 and v2 are arbitrary natural numbers.
7. The interior permanent magnet synchronous motor as defined in
claim 1, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
8. An interior permanent magnet synchronous motor comprising: a
stator including a stator core provided with a plurality of
magnetic pole sections having windings of three phases wound
thereon; a rotor having four pole pairs said rotor including a
shaft and a rotor core fixed on said shaft; said rotor core having
eight permanent magnets incorporated therein in a manner to be
spaced from each other at intervals in a peripheral direction
thereof; said eight permanent magnets each constituting eight
permanent magnet magnetic pole sections formed on an outer
periphery of said rotor core; said rotor being formed with eight
magnetic silent pole sections so as to interpose said permanent
magnet magnetic pole section therebetween; said eight permanent
magnet magnetic pole sections consisting of a first and a second
groups of permanent magnet magnetic pole sections; said first group
consisting of four permanent magnet magnetic pole sections arranged
to be spaced at equal intervals in the peripheral direction
interposing one permanent magnet magnetic pole section of said
second group between each adjacent two permanent magnet magnetic
pole sections of the first group; said second group consisting of
four permanent magnet magnetic pole sections arranged to be spaced
at equal intervals in the peripheral direction interposing one
permanent magnet magnetic pole section of said first group between
each adjacent two permanent magnet magnetic pole sections of the
second group; said eight magnetic salient pole sections consisting
of a first and a second groups of the magnetic salient pole
sections; said first group of magnetic salient pole sections
consisting of four magnetic salient pole sections arranged to be
spaced at equal intervals in the peripheral direction interposing
one magnetic salient pole section of said second group between each
adjacent two magnetic salient pole sections of said first group;
said second group of magnetic salient pole sections consisting of
four magnetic salient pole sections arranged to be spaced at equal
intervals in the peripheral direction interposing one magnetic
salient pole section of said first group between each adjacent two
magnetic salient pole sections of said second group; wherein the
open angle .alpha. 1 of the four magnetic salient pole sections of
said first group is smaller than the open angle .alpha. 2 of the
four magnetic salient pole sections of said second group; wherein
said open angle .alpha. 2 is determined within the range of
12.9.degree..ltoreq..alpha.2.- ltoreq.17.1.degree. and said open
angle .alpha. 1 is determined within the range of
5.4.degree..ltoreq..alpha.1.ltoreq.9.6.degree., when the slot pitch
of said stator core is 7.5.degree. and the slot opening is
2.1.degree..
9. The interior permanent magnet synchronous motor as defined in
claim 8, wherein the shapes of said eight permanent magnet magnetic
pole sections and said eight magnetic salient pole sections are
determined so that the contour of an outer peripheral surface
section of the rotor core formed with two said adjacent permanent
magnetic pole sections and said magnetic salient pole section
interposed therebetween is configured so as to have symmetrical
shapes about the salient pole section virtual center line of CL1 or
CL2 and yet so that the contour of the outer peripheral surface
sections of said rotor core corresponding to the angle of
90.degree. about the center of the shaft of the rotor each may be
formed into an identical shape, thus resulting in the rotor core
having four identical shapes in the outer periphery thereof.
10. The interior permanent magnet synchronous motor as defined in
claim 9, wherein .phi. 1 is an angle defined between the virtual
center line CL3 and a virtual line PL1, which is one of the two
virtual lines PL1 and PL2 which extend from the center of the shaft
through both ends of each of the magnetic pole sections, the
virtual line PL1 being positioned on the side of the magnetic
salient pole section having an open angle .alpha. 2, and .phi. 1 is
set within the range of 11.025.degree..ltoreq..phi.1.ltore-
q.15.225.degree., and .phi. 2 is an angle defined between the
virtual center line CL3 and the virtual line PL2, which is the
other of the two virtual lines PL1 and PL2, the virtual line PL2
being positioned on the side of the magnetic salient pole section
having an open angle .alpha. 1, and .phi. 2 is set within the range
of 14.775.degree..ltoreq..phi.2.ltore- q.18.975.degree.said open
angles .phi. 1 and .phi. 2 are determined to satisfy the following
expression: 1.65.degree..ltoreq..phi.2-.phi.1.ltore- q.5.85.degree.
and 27.9.degree..ltoreq..phi.2+.phi.1.ltoreq.32.1.degree.
11. The interior permanent magnet synchronous motor as defined in
claim 10, wherein magnetic pole surface of said permanent magnet
magnetic pole sections are formed into arcuate or elliptic shape,
each of said magnetic pole surfaces of said permanent magnet
magnetic pole sections of rotor core and each of magnetic pole
surfaces of said magnetic pole sections of said stator core being
arranged so as to have a gap defined therebetween and having a
dimension .delta. d which satisfies the following expression:
.delta.d=.delta.d0/cos [p(.theta.m-.theta.dm)] (2) wherein .delta.
d0 is the minimum value of the dimension of the gap, .theta. m is
an angle defined from a virtual center line CL3 which extends from
the center of the shaft through a center of the two salient pole
section virtual center lines CL1 and CL2 toward the side of the
magnetic salient pole section having an open angle .alpha. 1;
wherein .theta. dm is an angle within the range of
1.25.degree..ltoreq..theta.dm.ltoreq.3.75.degre- e..
12. The interior permanent magnet synchronous motor as defined in
claim 2, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
13. The interior permanent magnet synchronous motor as defined in
claim 3, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
14. The interior permanent magnet synchronous motor as defined in
claim 4, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
15. The interior permanent magnet synchronous motor as defined in
claim 5, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
16. The interior permanent magnet synchronous motor as defined in
claim 6, wherein said rotor core having a first and a second
non-magnetic sections at both ends in the peripheral direction of
the magnets, the first and second non-magnetic sections being
formed of recesses; said first non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 1 and said second non-magnetic section being arranged
on the side of the magnetic salient pole section having the open
angle .alpha. 2; wherein the shape of said first and second
non-magnetic sections are determined that an area of the cross
section of the second non-magnetic section is larger than an area
of the cross section of said first non-magnetic section.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] The present application is a divisional of U.S. patent
application Ser. No. 09/951,282, filed Sep. 13, 2001, which issued
as U.S. Pat. No. 6,597,079 on Jul. 22, 2003.
BACKGROUND OF THE INVENTION
[0002] This invention relates to an interior permanent magnet
synchronous motor wherein a rotor core has a plurality of permanent
magnets incorporated or embedded therein and includes magnetic
salient pole sections defined between each two adjacent permanent
magnets, and more particularly to a permanent magnet-equipped
synchronous motor utilizing both reluctance generated due to the
salient pole sections of the rotor core and torque by the permanent
magnets.
[0003] One of conventional synchronous motors wherein a core
between magnetic poles of permanent magnets is provided with
magnetic salient pole sections is disclosed in Japanese Patent
Application Laid-Open Publication No. 205499/1996. The synchronous
motor is constructed in such a manner that rotation of a rotor is
limited to only one direction, to thereby displace the silent pole
sections, resulting in restraining generation of torque
pulsation.
[0004] Also in Japanese Patent Application Laid-Open Publication
No. 256455/1996 a technology in which generation of torque
pulsation is restrained by changing the width of magnetic poles of
magnetic salient pole sections of reluctance synchronous motor or
by displacing a part of pairs of magnetic salient pole sections
thereof in a peripheral direction is disclosed.
[0005] Another conventional synchronous motor having permanent
magnets incorporated therein is disclosed in Japanese Patent
Application Laid-Open Publication No. 18328/1999. The conventional
synchronous motor disclosed is so constructed that a width of a
core between magnetic poles of permanent magnets is set so as to
establish relationship represented by the following expression, to
thereby restrain generation of cogging torque:
.theta. min.ltoreq..theta..ltoreq..theta. max
[0006] In the conventional interior permanent magnet synchronous
motor, the open angle .theta. of the rotor core between permanent
magnet poles is defined to be within a range of .theta.
min.ltoreq..theta..ltoreq..the- ta. max determined depending on the
number of teeth, a configuration thereof and a size thereof.
However, a timing at which torque is generated between the magnetic
poles of the permanent magnets is varied depending on "the number
of slots per pole and per phase" q of a stator, so that the
synchronous motor fails to satisfactorily restrain cogging torque
and torque pulsation.
SUMMARY OF THE INVENTION
[0007] The present invention has been made in view of the foregoing
disadvantage of the prior art.
[0008] Accordingly, it is an object of the present invention to
provide a permanent magnet-equipped synchronous motor that is
capable of sufficiently restraining both cogging torque and torque
pulsation during feeding of electricity thereto.
[0009] In accordance with the present invention, a permanent
magnet-equipped synchronous motor is provided. The permanent
magnet-equipped synchronous motor includes a stator including a
stator core provided with a plurality of magnetic pole sections
having windings of at least one phase wound thereon, as well as a
rotor having p pole pairs (p: a positive integer of 1 or more). The
rotor includes a shaft and a rotor core fixed on the shaft. The
rotor core has 2p (a plural number) permanent magnets incorporated
therein in a manner to be spaced from each other at intervals in a
peripheral direction thereof. The 2p permanent magnets each
constitute a permanent magnet magnetic pole section formed on an
outer periphery of the rotor core. The rotor is formed with 2p
magnetic salient pole sections arranged so as to interpose the
permanent magnet magnetic pole section therebetween. It is to be
noted that herein "one permanent magnet" means not only one
permanent magnet in physical sense, but also such "one permanent
magnet" as comprises a plural permanent magnets and yet functions
as one permanent magnet magnetically.
[0010] According to the present invention the 2p permanent magnet
magnetic pole sections comprise two groups (a first and a second
groups) of permanent magnet magnetic pole sections. Each permanent
magnet magnetic pole section of the first group is arranged to be
spaced at equal intervals in the peripheral direction interposing
one permanent magnet magnetic pole section of the second group
between each two adjacent permanent magnet magnetic pole sections.
Similarly, each permanent magnet magnetic pole section of the
second group is also arranged to be spaced at equal intervals in
the peripheral direction interposing one permanent magnet magnetic
pole section of the first group mentioned above between each two
adjacent permanent magnet magnetic pole sections. In other words
each permanent magnet magnetic pole section of the two groups is
arranged to appear alternately in the peripheral direction.
[0011] Also the 2p (p: a positive integer of one or more) magnetic
salient pole sections comprise two groups (a first and a second
groups) of magnetic salient pole sections. Each magnetic salient
pole section of the first group is arranged to be spaced at equal
intervals in the peripheral direction interposing one magnetic
salient section of the second group between each two adjacent
magnetic salient pole sections. Similarly, each magnetic salient
pole section of the second group is also arranged to be spaced at
equal intervals in the peripheral direction interposing one
magnetic salient pole section of the first group mentioned above
between each two adjacent permanent magnet pole sections. In other
words magnetic salient pole sections of the two groups are arranged
to appear alternately in the peripheral direction of the rotor
core. In this instance an open angle of each of the p magnetic
salient pole sections of the first group, .alpha. 1, is set to be
smaller than an open angle of each of the p magnetic salient pole
sections of the second group, .alpha. 2. Further the open angles
.alpha. 1 and .alpha. 2 are set to satisfy the following
expression.
.alpha.2-.alpha.1.apprxeq.2.beta.(2n-1).tau.s
[0012] wherein n is a natural number, .beta. is an angle defined
between two salient pole section virtual center lines, CL1 and CL2.
.tau. s is a slot pitch of the stator core (denominated in rad).
The outer peripheral surface sections of the permanent magnet pole
sections of the rotor core may have a contour formed into an
arcuate or elliptic configuration.
[0013] When the open angle .alpha. 1 of the p magnetic salient pole
sections of the first group and the open angle .alpha. 2 of the p
magnetic salient pole sections of the second group are defined as
mentioned above, torque pulsation can be restrained and torque
ripple can be diminished greatly as compared with the case in which
the open angle of the 2p magnetic salient pole sections (each
magnetic salient pole section of both first and second group) is
set at equal value.
[0014] In this instance the curvature radius R1 of the magnetic
pole surface of the p magnetic salient pole sections of the first
group is set to be smaller than the curvature radius R2 of the
magnetic pole surface of the p magnetic salient pole sections of
the second group. Such arrangement permits torque ripple to be
diminished as compared with the case in which the curvature radii
R1 and R2 are set at the same value. In order to increase torque,
on the other hand, the curvature radii R1 and R2 each are
preferably set at a larger value than the curvature radii of the
end portions of the magnetic pole surfaces of adjacent permanent
magnet magnetic pole sections, and yet to satisfy the condition,
R1<R2. However, in order to diminish torque ripple further, at
the sacrifice of the torque strength, the curvature radii R1 and R2
each may, of course, be set at a smaller value than the curvature
radii of the end portions of the magnetic pole surfaces of adjacent
permanent magnet magnetic pole sections.
[0015] In this instance the shapes of the 2p permanent magnet
magnetic pole sections and the 2p magnetic salient pole sections
may preferably be determined so that the contour of the outer
peripheral surface sections of the rotor core formed with two
adjacent permanent magnet magnetic pole sections and a magnetic
salient pole section interposed therebetween may have symmetrical
shapes about the salient pole section virtual center lines (CL1,
CL2) and yet so that the contour of the outer peripheral surface
sections corresponding to the angle of 360.degree./p about the
center of the shaft of the rotor each may be formed into an
identical shape, thus resulting in the rotor core having p
identical shapes in the outer periphery thereof. Such arrangement
prevents electrical voltage unbalance or eccentric force against
rotor from being generated because magnetic balance is obtained in
the peripheral direction, even if open angles of magnetic salient
pole sections are set at different values.
[0016] When magnetic pole surfaces of permanent magnet magnetic
pole sections are formed into arcuate or elliptic shape, each of
magnetic pole surfaces of permanent magnet magnetic pole sections
of the rotor and each of magnetic pole surfaces of a plurality of
magnetic poles of the stator core may preferably be arranged so as
to have a gap defined therebetween and having a dimension .delta. d
which satisfies the following expression:
.delta.d=.delta.d0/cos [p(.theta.m-.theta.dm)]
[0017] wherein .delta. d0 is the minimum value of the dimension of
the gap, .theta. m is an angle defined from the virtual center line
CL3 which extends in the center of the two salient pole section
virtual center lines CL1 and CL2 toward the side of the magnetic
salient pole section having the open angle .alpha. 1. .theta. dm is
an angle between the virtual line PL3 which extends from the center
of the shaft through a position where the dimension of the gap has
the minimum value and the virtual center line CL3.
[0018] In the above expression, when the value of .theta. dm is set
at 0 (.theta. dm=0.degree.), the gap formed will constitute a
general gap called "cosec gap". Such a gap configuration permits,
irrespective of the direction of the rotation of the motor, a
distribution of density of a magnetic flux from the permanent
magnets in the gap to approach a sine wave, to thereby restrain
cogging torque.
[0019] In this instance, the value of .theta. dm which permits the
value of cogging torque to be minimum is determined by the
expression, .theta. dm.apprxeq.(.phi.2-.phi.1)/2. Angles .phi.1 and
.phi.2 will be described in the following. However, when the
distribution of density of a magnetic flux from the permanent
magnets in the gap deviates greatly from the sine wave, the minimum
value of the cogging torque exists within a range of
(1/6).times.X.times..tau.s.ltoreq..theta.dm.ltoreq.(1/2).times.X.times..t-
au.s
[0020] wherein X is a natural number which makes .theta. dm most
approach the value of (.phi.2-.phi.1)/2 when the following
expression is almost satisfied:
.theta.dm.apprxeq.(.phi.2-.phi.1)/2.apprxeq.(1/4).times.X.times..tau.s
[0021] In addition to satisfying the above condition, the following
expressions should be satisfied also while .phi. 1 is an angle
defined between the virtual center line CL3 and the virtual line
PL1, which is one of the two virtual lines PL1 and PL2 which extend
from the center of the shaft through both ends of each of the
magnetic pole sections and yet the virtual line on the side of the
magnetic salient pole sections having an open angle .alpha. 2, and
.phi. 2 is an angle defined between the virtual center line CL3 and
the virtual line PL2, which is the other of the two virtual lines
PL1 and PL2 and yet the virtual line on the side of the magnetic
salient pole sections having an open angle .alpha. 1:
.phi.2>.phi.1
.phi.2-.phi.1.apprxeq.0.5(2m-1).tau.s-(180.degree./p)
.phi.2+.phi.1.apprxeq.u.multidot..tau.s
.alpha.1+.alpha.2.ltoreq.(360.degree./p)-2(.phi.2+.phi.1)
[0022] wherein m and u are arbitrary natural numbers. When such
arrangement as above is satisfied, not only cogging torque can be
diminished to the minimum value but also torque ripple can be
restrained.
[0023] Moreover in a motor whose size of the gap .delta. d as
mentioned above does not constitute a so-called cosec gap, it is
also possible to diminish cogging torque and torque ripple when the
relations between the angles .phi. 2 and .phi. 1 and open angles
.alpha. 1 and .alpha. 2 are established as mentioned above.
[0024] Furthermore when .alpha. 1, .alpha. 2, .phi. 2 and .phi. 1
are set at such values as to satisfy the following expressions,
both cogging torque and torque ripple can be arranged to approach
the minimum values.
(180.degree./2p)+(.alpha.1/2)-.phi.2.apprxeq.(1/4)(2v1-1).tau.s
(180.degree./2p)+(.alpha.2/2)-.phi.1.apprxeq.(1/4)(2v2-1).tau.s
[0025] wherein v1 and v2 are arbitrary natural numbers.
[0026] In order to form a first and a second non-magnetic sections
with recesses at both ends in the peripheral direction of the
permanent magnets of the rotor core, while the first non-magnetic
section is arranged on the side of the magnetic salient pole
section having an open angle .alpha. 1 and the second non-magnetic
section is arranged on the side of the magnetic salient pole
section having an open angle .alpha. 2, the shape of the
non-magnetic sections may preferably be arranged in such a manner
that the area of the cross section of the first and the second
non-magnetic sections are the same or the area of the cross section
of the second non-magnetic section is larger than the area of the
cross section of the first non-magnetic section. Such arrangement
permits leakage of magnetic flux from permanent magnets (short
circuit of magnetic flux) to be restrained as well as
demagnetization to be prevented. However, according to the present
invention, the open angle .alpha. 1 and the open angle .alpha. 2
have different values, thus the propensity for leakage of magnetic
flux from permanent magnets and propensity for demagnetization are
different at both ends in the peripheral direction of the permanent
magnets. Namely, in case of .alpha.1<.alpha.2, amount of leakage
of the magnetic flux from permanent magnets is larger at the end in
the peripheral direction on the side of the magnetic salient pole
section having the open angle .alpha. 2 than at the end in the
peripheral direction on the side of the magnetic salient pole
section having the open angle .alpha. 1. This leads to more
demagnetization of the permanent magnets at the end in the
peripheral direction on the side of the magnetic salient pole
section having an open angle of .alpha. 2 than at the end in the
peripheral direction on the side of the magnetic salient pole
section having an open angle of .alpha. 1. From the above view
points, the area of the cross section of the second non-magnetic
section is arranged to be larger than that of the first
non-magnetic section in order to positively restrain the leakage of
magnetic flux from permanent magnets from the end portion on the
side of the magnetic salient pole section having an open angle of
.alpha. 2 and the demagnetization of the permanent magnets at the
end portion thereof.
BRIEF DESCRIPTION OF THE DRAWINGS
[0027] These and other objects and many of the attendant advantages
of the present invention will be readily appreciated as the same
becomes better understood by reference to the following detailed
description when considered in connection with the accompanying
drawings, in which like reference numerals designate like or
corresponding parts throughout; wherein:
[0028] FIG. 1 is a schematic view conceptually showing a first
embodiment of an interior permanent magnet synchronous motor or a
permanent magnet-equipped synchronous motor according to the
present invention;
[0029] FIG. 2 is a schematic view conceptually showing a rotor
incorporated in a second embodiment of an interior permanent magnet
synchronous motor or a permanent magnet-equipped synchronous motor
according to the present invention;
[0030] FIG. 3 is a schematic view conceptually showing a rotor
incorporated in a third embodiment of an interior permanent magnet
synchronous motor or a permanent magnet-equipped synchronous motor
according to the present invention;
[0031] FIG. 4 is a graphical representation showing torque ripple
in the embodiments shown in the FIGS. 1-3;
[0032] FIG. 5 is a schematic view conceptually showing a fourth
embodiment of an interior permanent magnet synchronous motor or a
permanent magnet-equipped synchronous motor according to the
present invention;
[0033] FIG. 6 is a graphical representation showing decrease of
torque ripple wherein R1 and R2 are varied;
[0034] FIG. 7 is an enlarged schematic view of FIG. 5;
[0035] FIG. 8 is a graphical representation showing relationship
between .phi. 2 and .phi. 1 which makes the value of cogging torque
the minimum in a synchronous motor with eight pole pairs (P=8), 48
slots and distributed windings; and
[0036] FIG. 9 is a graphical representation showing relationship
between .alpha. 1 and .alpha. 2 that makes the value of torque
ripple obtained by the expressions (1), (8) and (9) the
minimum.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0037] Now, an interior permanent magnet synchronous motor or a
permanent magnet-equipped synchronous motor according to the
present invention will be described with reference to the
accompanying drawings.
[0038] Referring first to FIG. 1, a stator/rotor structure
incorporated in an embodiment of a synchronous motor with built-in
permanent magnets or an interior permanent magnet synchronous motor
according to the present invention is illustrated. An interior
permanent magnet synchronous motor of the illustrated embodiment,
as shown in FIG. 1, includes a stator 1, which includes an annular
yoke 2 constructed by laminating a plurality of silicon steel
plates on each other. The annular yoke 2 has a plurality of teeth 3
formed on an inner periphery thereof in a manner to be spaced from
each other at predetermined intervals in a peripheral direction
thereof. The teeth 3 each constitute a magnetic pole section. The
teeth 3 are so arranged that each of two adjacent teeth thereof
have a slot 4 defined therebetween. The teeth 3 have three-phase
windings wound thereon in order, resulting in forming winding
sections (not shown). The yoke 2 and teeth 3 cooperate with each
other to constitute a stator core.
[0039] In the illustrated embodiment, the stator 1 is so configured
that the number of slots Ns is set to be forty-eight (48), the
number of pole pairs is four (4), and the number of phases is three
(3). Thus, "the number of slots per pole and per phase" q is
determined to be q=48/(2.times.4.times.3)=2, and the slot pitch
.tau. s is 7.5.degree..
[0040] The permanent magnet-equipped synchronous motor of the
illustrated embodiment also includes a rotor 5. The rotor 5
includes a shaft 6, as well as a rotor core 7 fixed on the shaft 6
and having eight permanent magnets 8 incorporated therein in a
manner to be spaced from each other at an interval in a peripheral
direction thereof. The rotor 5 includes magnetic silent pole
sections 9 and 10 defined between two adjacent permanent magnets 8.
The rotor core 7 is formed, on the outer periphery thereof, with a
plurality of grooves 11 which extend in both radial direction and
axial direction in order to clearly form magnetic salient pole
sections 9 and 10. The outer peripheral surface sections of the
rotor core 7 defined outside in the radial direction corresponding
to the eight permanent magnets constitute eight permanent magnet
magnetic pole sections 12.
[0041] The rotor core 7 is likewise constructed by laminating
silicon steel plates on each other. Also, the rotor core 7 has
through-holes formed at portions thereof at which the permanent
magnets 8 are incorporated in the rotor core 7, so that the
permanent magnets 8 may be inserted via the through-holes into the
rotor core 7. The permanent magnets in this embodiment are so
configured to have a cross section of a rectangular shape
respectively.
[0042] In this embodiment the shapes of eight (8) permanent magnet
magnetic pole sections 12 and eight (8) magnetic salient pole
sections 9 and 10 may preferably be determined so that the contour
of the outer peripheral surface sections of the rotor core formed
with two adjacent permanent magnet magnetic pole sections and a
magnetic salient pole section interposed therebetween may have
symmetrical shapes about the salient pole section virtual center
lines (CL1, CL2) and yet so that the contour of each of the outer
peripheral surface sections corresponding to the angle of
90.degree. about the center of the shaft of the rotor may be formed
into an identical shape, thus resulting in the rotor core having
four (4) identical shapes in the outer periphery thereof.
[0043] The eight magnetic salient pole sections comprise two groups
(a first and a second groups) of magnetic salient pole sections.
Each of the four magnetic salient pole sections 9 of the first
group is arranged to be spaced at equal intervals in the peripheral
direction interposing one magnetic salient pole section of a second
group between each two adjacent magnetic salient pole sections 9.
Similarly, each of the four magnetic salient pole sections 10 of
the second group is also arranged to be spaced at equal intervals
in the peripheral direction interposing one magnetic salient pole
section of the first group mentioned above between each two
adjacent magnetic salient pole sections 10. The open angle .alpha.
1 of the four (4) magnetic salient pole sections 9 of the first
group is smaller than the open angle .alpha. 2 of the four magnetic
salient pole sections 10 of the second group. In this embodiment
the slot pitch of the stator core is 7.5.degree. and the slot
opening is 2.1.degree., therefore the open angle .alpha. 2 is
15.degree. and the open angle .alpha. 1 is 7.5.degree.. In this
instance the preferable range of the open angle .alpha. 2 is
12.9.degree..ltoreq..alpha.2.ltoreq.- 17.1.degree. and the
preferable range of the open angle .alpha. 1 is
5.4.degree..ltoreq..alpha.2.ltoreq.9.6.degree..
[0044] The relation between the open angles .alpha. 1 and .alpha. 2
is represented in a general expression as follows and the values of
.alpha. 1 and .alpha. 2 are determined to satisfy the
expression.
.alpha.2-.alpha.1.apprxeq.(2.beta.)-(2n-1).tau.s (1)
[0045] wherein n is a natural number and .beta. is an angle between
the two virtual center lines (CL1, CL2) extending from the center
of the shaft through the center of two adjacent magnetic salient
pole sections. .tau. s is the slot pitch of the above mentioned
stator core. In this embodiment n is six (n=6). When the above
expression is satisfied, the torque ripple can be greatly reduced
as compared with conventional synchronous motors.
[0046] FIG. 2 shows the structure of a rotor incorporated in a
second embodiment of the interior permanent magnet synchronous
motor according to the present invention. This embodiment differs
from the first embodiment on the point that the rotor core is
provided with a pair of non-magnetic sections 13 at both sides in
the peripheral direction of each of the permanent magnets 8. The
open angles .alpha. 1 and .alpha. 2 of the respective four magnetic
salient pole sections 9 and 10 are determined similarly as in the
case of the embodiment shown in FIG. 1.
[0047] The open angle of the grooves 11 can be obtained as the
angle (.beta.d-.alpha.1). In this instance the open angle of the
grooves 11 is 1.875.degree.. The angle .beta. d is determined in
the following expression:
.beta.d.apprxeq.(1/2)(2n-1).tau.s
[0048] wherein n is a natural number.
[0049] FIG. 3 shows the structure of a rotor incorporated in a
third embodiment of the interior permanent magnet synchronous motor
according to the present invention. This embodiment differs from
the second embodiment on the point that the open angle of the
grooves 11 (the dimension of the width of the grooves in the
peripheral direction) is larger than the open angle of the grooves
11 in the second embodiment, and the dimension of the length of the
permanent magnets 12 in the peripheral direction is shorter than
the length of the permanent magnets 12 in the second embodiment.
The structure of the rest of the rotor is the same as that of the
rotor in the second embodiment. In this embodiment the open angle
of the grooves 11 (.beta.f-.alpha.1) is set at 3.75.degree.. .beta.
f is determined in the expression,
.beta.f.apprxeq.(1/4)(2n-1).tau.s, wherein n is a natural number
also.
[0050] FIG. 4 shows data of the content of torque ripple in the
embodiments shown in FIGS. 1-3. In the FIG. 4, "A" indicates the
value of torque ripple of a conventional interior permanent magnet
synchronous motor, wherein each of the open angle of eight magnetic
salient pole potions is set at the same value (8.75.degree.). "B",
"C" and "D" indicate the content of torque ripple of the interior
permanent magnet synchronous motors shown in FIGS. 1-3. It is
understood in FIG. 4 that with the embodiments of the interior
permanent magnet synchronous motor according to the present
invention, torque ripple can be reduced greatly.
[0051] FIG. 5 shows the structure of a rotor incorporated in a
fourth embodiment of the interior permanent magnet synchronous
motor according to the present invention. The structure of the
stator core is the same as in the first embodiment of the interior
permanent magnet synchronous motor. In FIG. 5, the same reference
numerals as in FIG. 1 are used for the similar parts as shown in
FIG. 1. In this embodiment eight (2p) permanent magnets 12a, 12b
consist of two groups (a first and a second groups) of permanent
magnets, a first group of which consists of four (p) permanent
magnets 12a arranged so as to be spaced at equal intervals in the
peripheral direction while having one permanent magnet of a second
group interposed between each of two adjacent permanent magnets 12a
and a second group of which consists of four (p) permanent magnets
12b arranged so as to be spaced at equal intervals in the
peripheral direction while having one permanent magnet of the first
group interposed between each of two adjacent permanent magnets
12b, Also eight (2p) magnetic salient pole sections 9, 10 consists
of two groups (a first and a second groups) of magnetic salient
pole sections, a first group of which consists of four (p) magnetic
salient pole sections 9 arranged so as to be spaced at equal
intervals in the peripheral direction while having one magnetic
salient pole section of a second group interposed between each of
two adjacent magnetic salient pole sections 9 and a second group of
which consists of four (p) magnetic salient pole sections 10
arranged so as to be spaced at equal intervals in the peripheral
direction while having one magnetic salient pole section of the
first group interposed between each of two adjacent magnetic
salient pole sections 10. In this instance the open angle .alpha. 1
of the four magnetic salient pole sections 9 of the first group is
smaller than the open angle .alpha. 2 of the four magnetic salient
pole sections 10 of the second group. In this embodiment also, the
open angles .alpha. 1 and .alpha. 2 are set to satisfy the above
expression (1).
[0052] More specifically, the slot pitch of the stator core is
7.5.degree.; the slot opening is 2.1.degree.. Then the open angle
.alpha. 2 may preferably be set within the range of
12.9.degree..ltoreq..alpha.2.- ltoreq.17.1.degree. and the open
angles .alpha. 1 may preferably set in the range of
5.4.degree..ltoreq..alpha.1.ltoreq.9.6.degree.. In this instance
.alpha. 2 and .alpha. 1 are set at 16.degree. and 6.5.degree.,
respectively.
[0053] In this instance the shapes of eight (8) permanent magnet
magnetic pole sections 12a, 12b and eight (8) magnetic salient pole
sections 9, 10 may preferably be determined so that the contour of
the outer peripheral surface sections of the rotor core 7 formed
with two adjacent permanent magnet magnetic pole sections 12a, 12b
and a magnetic salient pole section interposed therebetween 9 or 10
is configured so as to have symmetrical shapes about the salient
pole section virtual center lines CL1 or CL2 and yet so that the
contour of the outer peripheral surface sections corresponding to
the angle of 90.degree. (360.degree./p) about the center of the
shaft of the rotor each may be formed into an identical shape, thus
resulting in the rotor core having four (p) identical shapes in the
outer periphery thereof. Such arrangement prevents electrical
voltage unbalance at each phase or eccentric force against rotor
from being generated because magnetic balance is obtained in the
peripheral direction, even if open angles .alpha. 1 and .alpha. 2
of magnetic salient pole sections 9, 10 are set at different
values.
[0054] In this instance each of magnetic pole surfaces of permanent
magnet magnetic pole sections 12a, 12b of the rotor core and each
of magnetic pole surfaces of a plurality of magnetic poles of the
stator core are arranged so as to have a gap defined therebetween
and having a size or dimension .delta. d which satisfies the
following expression to constitute a so-called "cosec gap":
.delta.d=.delta.d0/cos [p(.theta.m-.theta.dm)] (2)
[0055] wherein .delta. d0 is the minimum value of the dimension of
the gap, .theta. m is an angle defined from the virtual center line
CL3 which extends in the center of the two salient pole section
virtual center lines CL1 and CL2 toward the side of the magnetic
salient pole section having an open angle .alpha. 1. .theta. dm is
an angle between the virtual center line CL3 and the virtual line
PL3 which extends from the center of the shaft through a position
where the dimension of the gap has the minimum value.
[0056] In this instance, the value of .theta. dm which permits the
value of cogging torque to be the minimum is determined by the
expression, .theta. dm.apprxeq.(.phi.2-.phi.1)/2. Angles .phi. 1
and .phi. 2 will be described in the following. However, when the
distribution of density of a magnetic flux from the permanent
magnets in the gap deviates greatly from the sine wave, the minimum
value of the cogging torque exists within a range of
(1/6).times.X.times..tau.s.ltoreq..theta.dm.ltoreq.(1/2).times.X.times..ta-
u.s
[0057] wherein X is a natural number which makes .theta. dm most
approach the value of (.phi.2-.phi.1)/2 when the following
expression is satisfied:
.theta.dm.apprxeq.(.phi.2-.phi.1)/2.apprxeq.(1/4).times.X.times..tau.s
[0058] The shapes of the permanent magnet magnetic pole sections
12a and 12b are formed into arcuate or elliptic configuration so as
to make the dimension of the gap .delta. d approach the value
determined in the above expression.
[0059] In this instance the curvature radius R1 of the magnetic
salient pole sections 9 having an open angle .alpha. 1 is set to be
smaller than curvature radius R2 of the magnetic salient pole
section 10 having an open angle .alpha. 2. When curvature radius R1
of the magnetic pole surface of the p magnetic salient pole
sections of the first group is set smaller than curvature radius R2
of the magnetic pole surface of the p magnetic salient pole
sections of the second group, the torque ripple can be reduced as
compared with the case wherein curvature radius R1 and R2 are set
at the same value. In order to increase torque, on the other hand,
curvature radii R1 and R2 may preferably be set larger than
curvature radii of the end portions of adjacent permanent magnet
magnetic pole sections and yet set at such values as to satisfy the
condition R1<R2. FIG. 6 shows the results of the content of
torque measured in the conditions of models 1-3, which were
arranged in order to recognize the effects of different conditions
on torque. As shown in FIG. 6, the value of torque ripple marked
the smallest value in the case of Model 3 wherein the condition
R1<R2 was satisfied.
[0060] In the above expression, when the value of .theta. dm is set
at 0 (.theta.dm=0.degree.), the gap formed will constitute a
general gap called "cosec gap". Such a gap configuration permits,
irrespective of the direction of the rotation of the motor, a
distribution of density of a magnetic flux from the permanent
magnets in the gap to approach a sine wave, to thereby restrain
cogging torque. Moreover, when the value of the slot pitch, .theta.
dm, is set within the range between (1/6) slot pitch and (1/2) slot
pitch, cogging torque can be reduced greatly while keeping the
distribution of density of a magnetic flux from the permanent
magnets in the gap in a state of the sine wave. In the embodiment
shown in FIG. 5, .theta. m is set at 2.degree..
[0061] In addition to satisfying the above condition, the following
expressions are satisfied in this embodiment also, while .phi. 1 is
an angle defined between the virtual center line CL3 and the
virtual line PL1 which is one of the two virtual lines PL1 and PL2
which extend from the center of the shaft through both ends of each
of the magnetic pole sections 12a, 12b and yet the virtual line on
the side of the magnetic salient pole section 10 having an open
angle .alpha. 2, and .phi. 2 is an angle defined between the
virtual center line CL3 and the virtual line PL2 which is the other
of the two virtual lines PL1 and PL2 which extend from the center
of the shaft through both ends of each of the magnetic pole
sections and yet the virtual line on the side of the magnetic
salient pole section 9 having an open angle .alpha.1:
.phi.2>.phi.1 (3)
100 2-.phi.1.apprxeq.0.5(2m-1).tau.s-(180.degree./p) (4)
.phi.2+.phi.1.apprxeq.u.multidot..tau.s (5)
.alpha.1+.alpha.2.ltoreq.(360.degree./p)-2(.phi.2+.phi.1) (6)
[0062] wherein p is the number of pole pairs and m and u are
arbitrary natural numbers. When such arrangement as shown in the
above expressions are satisfied, cogging torque can be diminished
to the minimum value. More particularly in this instance the angle
.phi. 1 may preferably be set within the range of
11.025.degree..ltoreq..phi.1.ltoreq.15.225.degree- .. The angle
.phi. 2 may preferably be set within the range of
14.775.degree..ltoreq..phi.2.ltoreq.18.975.degree.. At the same
time the angles .phi. 1 and .phi. 2 are preferably determined so as
to satisfy the following conditions:
1.65.degree..ltoreq..phi.2-.phi.1.ltoreq.5.85.degree.; and,
27.9.degree..ltoreq..phi.2+.phi.1.ltoreq.32.1.degree.
[0063] In this embodiment the angle .phi. 1 is set at
13.125.degree. and .phi. 2 is set at 16.875.degree.. These values
of these angles are obtained, when the following values are put in
the above expressions (4) and (5): .tau.s=7.5 p=4 m=7 u=4
.phi.2-.phi.1.apprxeq.0.5(2m-1).tau.s-(180.degree./p) (4)
.phi.2+.phi.1.apprxeq.u.multidot..tau.s (5)
.phi.2-.phi.1=0.5(2m-1).tau.s-(180.degree./p)=0.5.times.(2.times.7-1).time-
s.7.5-(180/4)=3.75.degree.
.phi.2+.phi.1.apprxeq.u.multidot..tau.s=4.times.7.5=30.degree.
[0064] By solving the above two expressions, .phi. 1 and .phi. 2
are determined as 13.125.degree. and 16.875.degree.,
respectively.
[0065] Based on the values of the above angles .phi. 1 and .phi. 2,
the optimal values of the .theta. dm and .theta. m to make the
value of cogging torque the minimum are obtained in the
expressions:
.theta.dm=(.phi.2-.phi.1)/2=(16.875-13.125)/2=1.875.degree.
[0066] Therefore, when .theta. dm is 1.875(.theta.dm=1.875), the
value of cogging torque becomes the minimum. Then X in the
expression
.theta.dm.apprxeq.(.phi.2-.phi.1)/2.apprxeq.(1/4).times.X.times.X.tau.s
is obtained. The value of X to satisfy
(1/4).times.X.times..tau.s=1.875 is 1.
[0067] Now by substituting 1 for X(X=1) and 7.5 for
.tau.s(.tau.s=7.5) in the above mentioned expression
(1/6).times.X.times..tau.s.ltoreq..theta.d-
m.ltoreq.(1/2).times.X.times..tau.s, the optimum range of .theta.
dm is determined as
1.25.degree..ltoreq..theta.dm.ltoreq.3.75.degree..
[0068] As shown in FIG. 7, the width in the peripheral direction of
the grooves 11a and 11b (open angles) are set at 2.25.degree. and
1.5.degree., respectively. Also, as shown in FIG. 7 a first and a
second non-magnetic sections 13a, 13b formed on the rotor core 7
are configured in different shapes.
[0069] In this embodiment the value of torque ripple can be made
the minimum, when .alpha. 1, .alpha. 2, .phi. 1 and .phi. 2 are
determined to satisfy the following expressions (7) and (8).
(180.degree./2P)+(.alpha.1/2)-.phi.2=(1/4)(2v1-1).tau.s (7)
(180.degree./2P)+(.alpha.2/2)-.phi.1=(1/4)(2v2-1).tau.s (8)
[0070] wherein v1 and v2 are arbitrary natural numbers.
[0071] In this instance, the angles at different portions are set
to satisfy the above expressions of (7) and (8).
[0072] The conditions for the angles at different portions to make
the torque ripple the minimum are obtained by solving the
simultaneous equations of (3), (4), (5) and (6). FIG. 8 shows the
relationship between .phi. 2, .phi. 1 and m which make the value of
cogging torque the minimum in a synchronous motor with eight pole
pairs (P=8), 48 slots and distributed windings.
[0073] The values along the axis of ordinates show the values of
.phi. 2 and the values along the axis of abscissas show the values
of .phi. 1. In FIG. 8, the points shown by small circles are the
values which make the torque ripple the minimum when substituting
the determined values of m and u.
[0074] FIG. 9 shows the relationship between .alpha. 1, .alpha. 2
and n which are obtained by solving the above expressions (7) and
(8). In the embodiments of the present invention, when the values
of .alpha. 1 and .alpha. 2 are determined to satisfy the
relationship shown in FIG. 9, the torque ripple can be reduced to
the minimum.
[0075] According to the present invention cogging torque and torque
pulsation can be restrained in an interior permanent magnet
synchronous motor.
[0076] While preferred embodiments of the invention have been
described with a certain degree of particularity with reference to
the drawings, obvious modifications and variations are possible in
light of the above teachings. It is therefore to be understood that
within the scope of the appended claims, the invention may be
practiced otherwise than as specifically described.
* * * * *