Abstract:
A permanent-magnet motor including a rotor having permanent magnets disposed therein, and a stator, wherein an outer circumferential surface of the rotor is opposite to an inner circumferential surface of the stator, and one or both of the outer circumferential surface of the rotor and the inner circumferential surface of the stator are varied in a radial direction so as to provide a non-uniform gap between the two surfaces to approximate sinusoidal change in magnetic flux.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit of Korean Patent Application No. 2005-50534, filed on Jun. 13, 2005, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a permanent-magnet motor used in compressors of domestic refrigerators and air conditioners or other various kinds of industrial machinery, and, more particularly, to a permanent-magnet motor that is capable of approximating a back electro motive force wave to a sinusoidal wave, thereby lowering noise and increasing efficiency. 
   2. Description of the Related Art 
   Generally, a permanent-magnet motor, such as a brushless DC motor, has permanent magnets mounted at a rotor core to generate a rotary driving force. Based on how the permanent magnets are mounted at the rotor core, permanent-magnet motors are classified into surface-mounted permanent-magnet motors and embedded permanent-magnet motors. 
   The embedded permanent-magnet motor has a plurality of permanent magnets mounted in the rotor core. In the embedded permanent-magnet motor, dispersion of the permanent magnets is structurally prevented using magnet torque as well as reluctance torque. Consequently, the embedded permanent-magnet motor provides a higher efficiency than the surface-mounted permanent-magnet motor, which has permanent magnets mounted on the surface of the rotor core to create a magnetic field, and therefore, the embedded permanent-magnet motor is used when high-speed rotation is required. 
   Based on how coils are wound on a stator core, embedded permanent-magnet motors are classified into coil concentration-type motors and coil distribution-type motors.  FIG. 1  is a cross-sectional view illustrating a conventional permanent-magnet motor constructed in accordance with a coil distribution-type winding method, and  FIG. 2  is a cross-sectional view illustrating another conventional permanent-magnet motor constructed in accordance with a coil concentration-type winding method. 
   Referring to  FIGS. 1 and 2 , the conventional permanent-magnet motor comprises: a stator  1   a , 1   b  on which coils are wound; and a rotor  4   a , 4   b  rotatably disposed in the stator  1   a , 1   b.    
   The stator  1   a , 1   b  comprises: a stator core  2   a , 2   b  formed by stacking a plurality of magnetic steel sheets in the shape of a cylinder; a plurality of slots  3   a , 3   b  formed at the stator core  2   a , 2   b  while being arranged in a circumferential direction; and a plurality of coils wound on the slots  3   a , 3   b.    
   The rotor  4   a , 4   b  comprises: a rotor core  5   a , 5   b  formed by stacking a plurality of magnetic steel sheets in the shape of a cylinder, the rotor core  5   a , 5   b  being disposed in a hollow part of the stator  1   a , 1   b  while being spaced a predetermined distance from the hollow part of the stator  1   a , 1   b ; a plurality of permanent magnet insertion holes  6   a , 6   b  formed at the rotor core  5   a , 5   b  while being arranged in the circumferential direction; and a plurality of permanent magnets  7   a , 7   b inserted in the permanent magnet insertion holes  6   a , 6   b , respectively. A rotary shaft  8   a , 8   b  is inserted in a hollow part formed at the center of the rotor  4   a , 4   b , and is thereby is rotated along with the rotor  4   a , 4   b.    
   When electric current is supplied to coils wound on the slots  3   a , 3   b  of the stator  1   a , 1   b  of the conventional permanent-magnet motor with the construction described above, polarities of the coils are sequentially changed. Therefore, a rotary magnetic field is generated at teeth  9   a , 9   b  of the stator  1   a , 1   b  formed between the slots  3   a , 3   b . Consequently, a magnetic field is created at the rotor  4   a , 4   b , in which the permanent magnets  7   a , 7   b  are embedded while being adjacent to the teeth  9   a , 9   b . The magnetic field of the rotor  4   a , 4   b  follows the rotary magnetic field generated at the teeth  9   a , 9   b  of the stator  1   a , 1   b , and, therefore, the rotor  4   a , 4   b  is rotated along with the rotary shaft  8   a , 8   b  to generate a rotary driving force. 
   In the embedded permanent-magnet motor, a back electro motive force wave, induced at the coils wound on the stator slots  3   a , 3   b , contains many high harmonic components depending upon the location and shape of the permanent magnets  7   a , 7   b embedded in the rotor  4   a , 4   b . However, the length of a gap  94   a , 94   b  between the surface of each of the teeth  9   a , 9   b  and the outer circumferential surface of the rotor  4   a , 4   b  is uniform. As a result, a change in magnetic flux at the gap  94   a , 94   b  according to the rotation of the rotor  4   a , 4   b  is made in the shape of a non-sinusoidal wave. Therefore, the back electro motive force wave is distorted, as shown in  FIG. 3 . Consequently, a non-sinusoidal back electro motive force wave is created, and, therefore, torque ripple is increased. As a result, vibration is generated when the rotor  4   a , 4   b  is rotated, and noise is increased due to the vibration. Consequently, efficiency of the motor is lowered. 
   SUMMARY OF THE INVENTION 
   Therefore, it is an aspect of the invention to provide a permanent-magnet motor having stepped protrusions formed at the middle parts of teeth of a stator and/or stepped grooves formed at the outer circumferential surface of a rotor to approximate change in magnetic flux at a gap to a sinusoidal wave, thereby creating a sinusoidal back electro motive force wave. 
   Additional aspects and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the invention. 
   In accordance with one aspect, the present invention provides a permanent-magnet motor comprising a stator and a rotor having permanent magnets disposed therein, wherein the rotor has one or more grooves formed at the outer circumferential surface thereof, the grooves being opposite to the inner circumferential surface of the stator, to approximate sinusoidal change in magnetic flux. 
   The one or more grooves may comprise a plurality of grooves arranged on the outer circumferential surface of the rotor in a circumferential direction, the plurality of grooves being spaced a predetermined gap from the inner circumferential surface of the stator. 
   The rotor may be provided with flux barrier holes formed at opposite ends of the permanent magnets, and the grooves may be respectively provided adjacent to the flux barrier holes. 
   The flux barrier holes may be disposed in parallel with permanent magnet insertion holes, in which the permanent magnets are respectively inserted. 
   The one or more grooves may be formed in a shape of at least one step. 
   In accordance with another aspect, the present invention provides a permanent-magnet motor comprising a stator provided with a plurality of teeth, and a rotor having permanent magnets disposed therein, wherein the stator has one or more protrusions respectively formed at surfaces of the teeth, the protrusions being opposite to the outer circumferential surface of the rotor, to approximate sinusoidal change in magnetic flux. 
   The one or more protrusions may be formed at middle parts of the teeth of the stator, the teeth being spaced a predetermined gap from the outer circumferential surface of the rotor. 
   Each of the one or more protrusions may be formed in the shape of at least one step. 
   In accordance with yet another aspect, the present invention provides a permanent-magnet motor comprising a stator provided with a plurality of teeth, and a rotor having permanent magnets disposed therein, wherein the rotor has one or more rotor grooves formed at the outer circumferential surface thereof, the grooves being opposite to the inner circumferential surface of the stator, to approximate sinusoidal change in magnetic flux, and the stator has one or more stator protrusions respectively formed at the surfaces of the teeth, the protrusions being opposite to the outer circumferential surface of the rotor, to approximate the sinusoidal change in magnetic flux. 
   The one or more stator protrusions may be formed at the middle parts of the teeth of the stator in the shape of at least one step. 
   The one or more rotor grooves may comprise a plurality of rotor grooves arranged on the outer circumferential surface of the rotor in a circumferential direction, the grooves being spaced a predetermined gap from the inner circumferential surface of the stator. 
   The rotor may be provided with flux barrier holes formed at opposite ends of the permanent magnets, and the grooves may be respectively provided adjacent to the flux barrier holes. 
   The one or more rotor grooves may be formed in the shape of at least one step. 
   In accordance with yet another aspect, the present invention provides a permanent-magnet motor comprising a stator and a rotor having permanent magnets disposed therein, wherein the stator has one or more protrusions formed at an inner circumferential surface thereof, the protrusions being opposite to an outer circumferential surface of the rotor, to approximate sinusoidal change in magnetic flux. 
   In accordance with yet another aspect, the present invention provides a permanent-magnet motor comprising a stator and a rotor having permanent magnets disposed therein; wherein an outer circumferential surface of the rotor, opposite to an inner circumferential surface of the stator, varies in a radial direction so as to provide a non-uniform gap between the rotor and stator to approximate sinusoidal change in magnetic flux. 
   In accordance with yet another aspect, the present invention provides a permanent-magnet motor comprising a rotor having permanent magnets disposed therein, and a stator having teeth extending inward toward the rotor, wherein an inner circumferential surface of the teeth of the stator, opposite to an outer circumferential surface of the rotor, varies in a radial direction so as to provide a non-uniform gap between the rotor and stator to approximate sinusoidal change in magnetic flux. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and/or other aspects and advantages of the invention will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which: 
       FIG. 1  is a cross-sectional view illustrating a conventional permanent-magnet motor constructed in accordance with a coil distribution-type winding method; 
       FIG. 2  is a cross-sectional view illustrating another conventional permanent-magnet motor constructed in accordance with a coil concentration-type winding method; 
       FIG. 3  is a graph illustrating a back electro motive force of the conventional permanent-magnet motor; 
       FIG. 4  is a cross-sectional view illustrating a permanent-magnet motor according to an embodiment of the present invention; 
       FIG. 5  is a detailed view illustrating the teeth of the stator and the surface of the rotor shown in  FIG. 4 ; 
       FIG. 6  is a graph illustrating a back electro motive force of the permanent-magnet motor according to the embodiment of the present invention shown in  FIG. 4 ; 
       FIG. 7  is a view illustrating distribution of total harmonic distortion (THD) of the back electro motive force of the permanent-magnet motor according to the embodiment of the present invention showed in  FIG. 4  based on change in a stator protrusion angle θ s  and a rotor groove angle θ r ; 
       FIG. 8  is a cross-sectional view illustrating a permanent-magnet motor according to another embodiment of the present invention; 
       FIG. 9  is a detailed view illustrating the teeth of the stator shown in  FIG. 8 ; 
       FIG. 10  is a detailed view illustrating the surface of the rotor shown in  FIG. 8 ; 
       FIG. 11  is a graph illustrating a back electro motive force of the permanent-magnet motor according to the embodiment of the present invention shown in  FIG. 8 ; 
       FIG. 12  is a view illustrating distribution of total harmonic distortion (THD) of the back electro motive force of the permanent-magnet motor according to the embodiment of the present invention shown in  FIG. 8  based on change in a stator protrusion angle θ s2  and a rotor groove angle θ r2 ; 
       FIG. 13  is a detailed view illustrating the surface of a rotor of a permanent-magnet motor according to yet another embodiment of the present invention; 
       FIG. 14  is a view illustrating distribution of total harmonic distortion (THD) of the back electro motive force of the permanent-magnet motor according to the embodiment of the present invention shown in  FIG. 13  based on change in a rotor groove angle θ r1 ; and 
       FIG. 15  is a view illustrating a relation between an effective magnetic pole angle θ PM  of the permanent magnet and a rotor protrusion angle θ R2  of the permanent-magnet motor according to an embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. The embodiments are described below to explain the present invention by referring to the figures. 
     FIG. 4  is a cross-sectional view illustrating a permanent-magnet motor according to an embodiment of the present invention, and  FIG. 5  is a detailed view illustrating the teeth of the stator and the surface of the rotor shown in  FIG. 4 . 
   Referring to  FIG. 4 , the permanent-magnet motor comprises: a stator  10  formed by stacking a plurality of magnetic steel sheets in the shape of a cylinder; a rotor  20  formed by stacking a plurality of magnetic steel sheets in the shape of a cylinder, the rotor  20  being rotatably disposed in the stator  10  while being spaced a predetermined distance from the stator  10 ; and a rotary shaft  30  inserted in a hollow center of the rotor  20  such that the rotary shaft  30  is rotated along with the rotor  20 . 
   The stator  10  comprises: a circular stator core  11  forming the outer edge of the stator  10 ; a plurality of teeth  12  extending inward from the stator core  11  in the radial direction; a plurality of slots  13  formed between the respective teeth  12 ; and coils wound on the slots  13  to create a three-phase magnetic field. 
   As shown in  FIG. 5 , each of the teeth  12  of the stator  10  is provided at the middle part thereof with a stepped stator protrusion  12 - 1  such that the length of a gap  40  between the surface of each of the teeth  12  of the stator  10  and the outer circumferential surface of the rotor  20  is not uniform. The provision of the stepped stator protrusions  12 - 1  with outermost ends of adjacent teeth spaces apart W 1  (see  FIG. 4 ) serves to approximate the change in magnetic flux at the gap  40 , due to rotation of the rotor  20 , to a sinusoidal wave. 
   The stator protrusion  12 - 1  protrudes in a one-stepped shape in a width W 2  measured by a stator protrusion angle θ s  about the rotary shaft  30 , wherein W 2 &gt;W 1 . Preferably, though not necessarily, the stator protrusion angle θ s  is approximately 32 degrees. 
   The rotor  20  comprises: a rotor core  21  approximately formed in the shape of a cylinder; a plurality of permanent magnet insertion holes  22  formed at the edge of the rotor core  21  while being arranged in the circumferential direction; and a plurality of permanent magnets  23  inserted in the permanent magnet insertion holes  22 , respectively. 
   The permanent magnets  23  are inserted in the respective permanent magnet insertion holes  22  such that neighboring magnetic poles have opposite polarities. At opposite ends of each permanent magnet  23  are formed flux barrier holes  24  to prevent a short and/or leakage of magnetic flux. The flux barrier holes  24  are disposed in parallel with the permanent magnet insertion holes  22 , or on the same line as the permanent magnet insertion holes  22 . 
   On the outer circumferential surface of the rotor  20  are formed stepped rotor grooves  20 - 1 , which are adjacent to the flux barrier holes  24  and arranged in the circumferential direction, as shown in  FIG. 5 , such that the length of the gap  40  between the surface of each of the teeth  12  of the stator  10  and the outer circumferential surface of the rotor  20  is not uniform. The provision of the stepped rotor grooves  20 - 1  serves to approximate the change in magnetic flux at the gap  40 , due to rotation of the rotor  20 , to a sinusoidal wave. 
   Each of the stepped rotor grooves  20 - 1  is depressed in a one-stepped shape in a width measured by a rotor groove angle θ r  about the rotary shaft  30 . Preferably, though not necessarily, the rotor groove angle θ r  is approximately 22 degrees. 
   When electric current is supplied to the coils wound on the slots  13  of the stator  10  of the permanent-magnet motor with the construction described above, polarities of the coils are sequentially changed, and, therefore, a rotary magnetic field is generated at the teeth  12  formed between the slots  13 . Consequently, a magnetic field is created at the rotor  20 , in which the permanent magnets  23  are embedded while being adjacent to the teeth  12 . The magnetic field of the rotor  20  follows the rotary magnetic field generated at the teeth  12  of the stator  10 , and, therefore, the rotor  20  is rotated along with the rotary shaft  30  to generate a rotary driving force. 
   At this time, a back electro motive force wave induced at the coils of the stator  10  contains many high harmonic components due to magnetic flux concentration at opposite ends of the teeth  12  of the stator  10 , and bridge parts  24   a  of the rotor  20 . According to this embodiment of the present invention, the one-stepped stator protrusions  12 - 1  are formed at the middle parts of the teeth  12  of the stator  10 , and the one-stepped rotor grooves  20 - 1  are formed on the outer circumferential surface of the rotor  20  so as to be adjacent to the bridge parts  24   a  of the rotor  20 . As a result, the length of the gap  40  between the surface of each of the teeth  12  of the stator  10  and the outer circumferential surface of the rotor  20  is not uniform, and, therefore, the change in magnetic flux at the gap  40  due to rotation of the rotor  20  is approximated to a sinusoidal wave. Consequently, a sinusoidal back electro motive force wave is created. 
   The back electro motive force (BEMF) of the permanent-magnet motor of this embodiment of the present invention is illustrated in  FIG. 6 . 
   As shown in  FIG. 6 , all of the high harmonic components except the first high harmonic are reduced by forming the one-stepped stator protrusions  12 - 1  at the middle parts of the teeth  12  of the stator  10 , and the one-stepped rotor grooves  20 - 1  at the outer circumferential surface of the rotor  20 . Consequently, the back electro motive force wave is approximated to a sinusoidal wave. 
   As a result, torque ripple is decreased, and, therefore, vibration generated during rotation of the rotor  20  is minimized, and noise is also decreased. Consequently, reliability of the motor is improved. 
     FIG. 7  illustrates the simulation results of total harmonic distortion (THD) of a back electro motive force generated when the stator protrusion angle θ s  is changed within a range of 28 to 36 degrees, and the rotor groove angle θ r  is changed within a range of 14 to 22 degrees. 
   As can be seen from  FIG. 7 , the total harmonic distortion (THD) of the back electro motive force of the permanent-magnet motor according to this embodiment of the present invention, which is characterized in that the one-stepped stator protrusions  12 - 1  are formed at the middle parts of the teeth  12  of the stator  10 , and the one-stepped rotor grooves  20 - 1  are formed at the outer circumferential surface of the rotor  20 , is approximately 2.9 to 3%, which is less than the total harmonic distortion (approximately 15%) of the back electro motive force of the conventional permanent-magnet motor. 
     FIG. 8  is a cross-sectional view illustrating a permanent-magnet motor according to another embodiment of the present invention,  FIG. 9  is a detailed view illustrating the teeth of the stator shown in  FIG. 8 , and  FIG. 10  is a detailed view illustrating the surface of the rotor shown in  FIG. 8 . Components of this preferred embodiment of the present invention, which may be identical to those of the previously discussed embodiment of the present invention, may be indicated by the same reference numerals as those of the previously discussed embodiment of the present invention, and a detailed description thereof will not be given. 
   Referring to  FIGS. 8 and 9 , each of teeth  14  of the stator  10  is provided at the middle part thereof with a stepped stator protrusion  14 - 1  such that the length of the gap  40  between the surface of each of the teeth  14  of the stator  10  and the outer circumferential surface of a rotor  26  is not uniform. 
   The stator protrusion  14 - 1  protrudes in a width measured by a first stator protrusion angle θ s1  about the rotary shaft  30 , and further protrudes in a width measured by a second stator protrusion angle θ s2  about the rotary shaft  30 . Consequently, the stator protrusion  14 - 1  is formed in a two-stepped shape. Preferably, though not necessarily, the first stator protrusion angle θ s1  is approximately 34 degrees, and the second stator protrusion angle θ s2  is approximately 28 degrees. 
   Referring to  FIGS. 8 and 10 , the rotor  26  is provided at the outer circumferential surface thereof with stepped rotor grooves  26 - 1 , which are adjacent to the flux barrier holes  24  and arranged in the circumferential direction, such that the length of the gap  40  between the surface of each of the teeth  14  of the stator  10  and the outer circumferential surface of the rotor  26  is not uniform. 
   Each of the stepped rotor grooves  26 - 1  is depressed in a width measured by a second rotor groove angle θ r2  about the rotary shaft  30 , and is further depressed in a width measured by a first rotor groove angle θ r1  about the rotary shaft  30 . Consequently, each of the stepped rotor grooves  26 - 1  is formed in a two-stepped shape. Preferably, though not necessarily, the second rotor groove angle θ r2  is approximately 22 degrees, and the first rotor groove angle θ r1  is approximately 16 degrees. 
   When electric current is supplied to the coils wound on the slots  13  of the stator  10  of the permanent-magnet motor with the construction described above, polarities of the coils are sequentially changed, and, therefore, a rotary magnetic field is generated at the teeth  14  formed between the slots  13 . Consequently, a magnetic field is created at the rotor  26 , in which the permanent magnets  23  are embedded while being adjacent to the teeth  14 . The magnetic field of the rotor  26  follows the rotary magnetic field generated at the teeth  14  of the stator  10 , and, therefore, the rotor  26  is rotated along with the rotary shaft  30  to generate a rotary driving force. 
   At this time, a back electro motive force wave induced at the coils of the stator  10  contains many high harmonic components due to magnetic flux concentration at opposite ends of the teeth  14  of the stator  10 , and bridge parts  24   a  of the rotor  26 . According to this embodiment of the present invention, the two-stepped stator protrusions  14 - 1  are formed at the middle parts of the teeth  12  of the stator  10 , and the two-stepped rotor grooves  26 - 1  are formed on the outer circumferential surface of the rotor  26  so as to be adjacent to the bridge parts  24   a  of the rotor  26 . As a result, the length of the gap  40  between the surface of each of the teeth  14  of the stator  10  and the outer circumferential surface of the rotor  26  is not uniform, and, therefore, the change in magnetic flux at the gap  40  due to rotation of the rotor  26  is approximated to a sinusoidal wave. Consequently, a sinusoidal back electro motive force wave is created. 
   The back electro motive force of the permanent-magnet motor of this embodiment of the present invention is illustrated in  FIG. 11 . 
   As shown in  FIG. 11 , all of the high harmonic components except the first high harmonic are reduced by forming the two-stepped stator protrusions  14 - 1  at the middle parts of the teeth  14  of the stator  10 , and the two-stepped rotor grooves  26 - 1  at the outer circumferential surface of the rotor  26 . Consequently, the back electro motive force wave is approximated to a sinusoidal wave. 
   As a result, torque ripple is decreased, and, therefore, vibration generated during rotation of the rotor  26  is minimized, and noise is also decreased. Consequently, reliability of the motor is improved. 
     FIG. 12  illustrates the simulation results of total harmonic distortion of a back electro motive force generated when the second stator protrusion angle θ s2  is changed within a range of 30 to 42 degrees, and the second rotor groove angle θ r2  is changed within a range of 14 to 30 degrees. 
   As can be seen from  FIG. 12 , the total harmonic distortion of the back electro motive force of the permanent-magnet motor according to this embodiment of the present invention, which is characterized in that the two-stepped stator protrusions  14 - 1  are formed at the middle parts of the teeth  14  of the stator  10 , and the two-stepped rotor grooves  26 - 1  are formed at the outer circumferential surface of the rotor  26 , is approximately 2.2%, which is less than the total harmonic distortion (approximately 15%) of the back electro motive force of the conventional permanent-magnet motor. 
     FIG. 13  is a detailed view illustrating the surface of a rotor  27  of a permanent-magnet motor according to yet another embodiment of the present invention. 
   As shown in  FIG. 13 , the rotor  27  is provided at the outer circumferential surface thereof with stepped rotor grooves  27 - 1 , which are adjacent to the flux barrier holes  24  and arranged in the circumferential direction, such that the length of the gap  40  between the surface of each of the teeth  14  of the stator  10  and the outer circumferential surface of the rotor  27  is not uniform. 
   Each of the rotor grooves  27 - 1  is depressed in a width measured by a second rotor groove angle θ r2  about the rotary shaft  30 , and is further depressed in a width measured by a first rotor groove angle θ r1  about the rotary shaft  30 . Consequently, each of the rotor grooves  27 - 1  is formed in a two-stepped shape. Preferably, though not necessarily, the second rotor groove angle θ r2  is approximately 22 degrees, and the first rotor groove angle θ r1  is approximately 2 to 18 degrees. 
   As shown in  FIG. 14 , total harmonic distortion of a back electro motive force generated when the first rotor groove angle θ r1  is changed within a range of 2 to 18 degrees is less than approximately 2%, which is less than the total harmonic distortion (approximately 15%) of the back electro motive force of the conventional permanent-magnet motor. 
     FIG. 15  is a view illustrating a relation between an effective magnetic pole angle θ PM  of the permanent magnet and a rotor protrusion angle θ R2  of the permanent-magnet motor according to an embodiment of the present invention. 
   On the assumption that an angle θ R2  between the second rotor groove angle θ r2  and the next second rotor groove angle θ r2  of the embodiment shown in  FIG. 8  is a rotor protrusion angle, reduction of the total harmonic distortion of the back electro motive force and reduction of cogging torque are changed based on the rotor protrusion angle θ R2  and effective magnetic pole angle θ PM  of the permanent magnet. 
   If the rotor protrusion angle θ R2  is greater than the effective magnetic pole angle θ PM  of the permanent magnet, for example, the total harmonic distortion (THD) of the back electro motive force is further reduced than the cogging torque. On the other hand, if the rotor protrusion angle θ R2  is less than the effective magnetic pole angle θ PM  of the permanent magnet, the cogging torque is further reduced than the total harmonic distortion (THD) of the back electro motive force. 
   According to the present invention, the permanent-magnet motor is designed such that the rotor protrusion angle θ R2  is greater than or equal to the effective magnetic pole angle θ PM  of the permanent magnet in order to maximally reduce the total harmonic distortion (THD) of the back electro motive force. 
   In the illustrated embodiments, the stator protrusions  12 - 1 , 14 - 1  are formed at the middle parts of the teeth  12 , 14  of the stator  10  in the one- or two-stepped shape, and the rotor grooves  20 - 1 , 26 - 1 , 27 - 1  are formed at the outer circumferential surface of the rotor  20 , 26 , 27  in the one- or two-stepped shape, but the present invention is not limited to these embodiments. For example, the stator may have one-stepped stator protrusions while the rotor has two-stepped rotor grooves, or the stator may has two-stepped stator protrusions while the rotor has one-stepped rotor grooves, which may achieve the same aspects and advantages as the illustrated embodiments of the present invention. 
   As apparent from the above description, the present invention provides a permanent-magnet motor having stepped protrusions formed at the middle parts of teeth of a stator and/or stepped grooves formed at the outer circumferential surface of a rotor, to approximate change in magnetic flux at a gap to a sinusoidal wave, thereby creating a sinusoidal back electro motive force wave. As a result, torque ripple is decreased, and, therefore, vibration generated during rotation of the rotor is minimized, and noise is also decreased. Consequently, the reliability of the motor is improved. 
   Although a few embodiments of the present invention have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.