Patent Publication Number: US-2022228497-A1

Title: Rotor and compressor

Description:
TECHNICAL FIELD 
     The present invention relates to a rotor and a compressor. 
     BACKGROUND ART 
     In rotary machines such as gas turbines and compressors, the rotor blades are fixed to a rotor fixed to a rotating shaft, and the rotating shaft, the rotor, and the rotor blades rotate integrally. Here, a dovetail portion is inserted into a groove formed in the rotor, to fix the rotor blade to the rotor. A structure of the rotor blade has been proposed to prevent stress from being concentrated at the dovetail portion, which is a portion to be connected to the rotor, during rotation of the rotor, and from causing damage. 
     For example, PTL  1  describes a structure in which a blade root is formed in an S-shape that is line-symmetrical with respect to a central axis, a chamfered portion is provided on a blade root side in a part of the S-shape, and a chamfered portion is provided on a rotor side in another portion. 
     CITATION LIST 
     Patent Literature 
     [PTL 1] Japanese Unexamined Patent Application Publication No. 63-98403 
     SUMMARY OF INVENTION 
     Technical Problem 
     As described in PTL  1 , when an axial end portion of a contact surface between the groove of the rotor and the blade root of the rotor blade is chamfered to prevent the groove and the blade root from coming into contact with each other, stress concentration at the axial end portion can be suppressed, and the occurrence of damage can be suppressed. 
     Here, there is room for improvement in the structure of the contact surface between the groove of the rotor and the blade root of the rotor blade. In addition, since the groove of the rotor and the blade root of the rotor blade are rotating portions, the structure in which chamfers are provided to achieve a non-contact state therebetween may cause a turbulence of a fluid, causing a reduction in the efficiency of the rotary machine. 
     The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a rotor and a compressor capable of suppressing a cause of a turbulence of a fluid and suppressing stress concentration. 
     Solution to Problem 
     According to an aspect of the present invention, to achieve the above object, there is provided a rotor in which a groove is formed with which a rotor blade meshes, the rotor blade including a dovetail portion and a platform portion that connects the dovetail portion and a blade portion. The groove includes a contact portion that is open to a surface intersecting a rotation axis of the rotor, that extends to be inclined with respect to the rotation axis, and that increases in width toward a rotor radial inner side to be in contact with the dovetail portion, a bottom portion that is an end portion on the rotor radial inner side, a connecting portion between the contact portion and the bottom portion, a platform-facing portion located on a rotor radial outer side of the contact portion to face the platform portion, and a chamfered portion formed in an end surface of the groove in an extending direction. A chamfer dimension of the connecting portion is larger on a side on which an angle formed by the groove and the end surface is an acute angle than on a side on which an angle formed by the groove and the end surface is an obtuse angle. 
     It is preferable that a dimension of the chamfered portion of the connecting portion on the side on which the angle formed by the groove and the end surface is an acute angle is larger than a dimension of the chamfered portion of the platform-facing portion on the side on which the angle formed by the groove and the end surface is an acute angle. 
     It is preferable that a dimension of the chamfered portion of the connecting portion on the side on which the angle formed by the groove and the end surface is an acute angle is larger on an upstream side in a gas flow direction than on a downstream side in the gas flow direction. 
     It is preferable that a dimension of the chamfered portion of the connecting portion is a dimension at a position at which a distance between the chamfered portion and a facing surface of the groove is at its maximum. 
     It is preferable that the chamfered portion is formed on an entire periphery of the end surface. 
     It is preferable that a dimension of the chamfered portion of the connecting portion on the side on which the angle formed by the groove and the end surface is an acute angle is larger than dimensions of the chamfered portions of other portions. 
     It is preferable that chamfer dimensions of the contact portion and the connecting portion are larger on the side on which the angle formed by the groove and the end surface is an acute angle than on the side on which the angle formed by the groove and the end surface is an obtuse angle. 
     It is preferable that a chamfer dimension from the platform-facing portion to the connecting portion is larger on the side on which the angle formed by the groove and the end surface is an acute angle than on the side on which the angle formed by the groove and the end surface is an obtuse angle. 
     It is preferable that the platform-facing portion includes a shape facing a shank portion of the rotor blade between the platform portion and the dovetail portion. 
     It is preferable that the contact portion of the groove has a multi-stage structure in which a non-contact portion is provided on the rotor radial inner side of the connecting portion and the contact portion is further provided on the rotor radial inner side of the non-contact portion. 
     According to an aspect of the present invention, to achieve the above object, there is provided a compressor including: the rotor according to any one of the above descriptions; and a rotor blade of which a blade root engages with the rotor. 
     It is preferable that the rotor blade includes a blade portion, a platform portion connected to a root side of the blade portion and having a surface parallel to a centrifugal force application direction of the blade portion, and a dovetail portion connected to the platform portion and disposed on a radial inner side of the platform portion. 
     Advantageous Effects of Invention 
     According to the present invention, a cause of a turbulence of a fluid and stress concentration can be suppressed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic view illustrating a schematic configuration of a gas turbine equipped with a rotor and a compressor according to the present embodiment. 
         FIG. 2  is a perspective view illustrating the vicinity of rotor blades of the compressor. 
         FIG. 3  is a schematic view of the compressor as seen in an axial direction. 
         FIG. 4  is a schematic view of the compressor as seen in a radial direction. 
         FIG. 5  is a schematic view of a dovetail portion and a groove as seen in the axial direction. 
         FIG. 6  is a cross-sectional view taken along line A-A in  FIG. 5 . 
         FIG. 7  is a cross-sectional view taken along line B-B in  FIG. 5 . 
         FIG. 8  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. 
         FIG. 9  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. 
         FIG. 10  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. 
         FIG. 11  is a perspective view illustrating the vicinity of rotor blades of a compressor of another example. 
         FIG. 12  is a schematic view of the compressor in  FIG. 11  as seen in the axial direction. 
         FIG. 13  is a schematic view of a dovetail portion and a groove of the compressor in  FIG. 11  as seen in the axial direction. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     An exemplary embodiment of a rotor blade body and a rotary machine according to the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention is not limited by the embodiment, and in the case of a plurality of embodiments, the present invention also includes a combination of the embodiments. 
       FIG. 1  is a schematic configuration view illustrating a gas turbine equipped with a rotor blade body according to an embodiment of the present invention. As illustrated in  FIG. 1 , a gas turbine  10  includes a compressor  11 , a combustor  12 , and a turbine  13 . A generator is connected to the gas turbine  10 , so that the generator is capable of generating electric power. 
     The compressor  11  includes an air intake port  20  that takes in air. Inside a compressor compartment  21 , an inlet guide vane (IGV)  22  is disposed, and a plurality of stator blades  23  and rotor blades  24  are alternately disposed in a front to rear direction (axial direction of a main shaft  32  to be described later), and an air bleeding chamber  25  is provided outside the compressor compartment  21 . In the combustor  12 , fuel is supplied to the compressed air compressed by the compressor  11 , and is ignited therewith to be combustible. In the turbine  13 , a plurality of stator blades  27  and rotor blades  28  are alternately disposed in the front to rear direction (axial direction of the main shaft  32  to be described later) inside a turbine compartment  26 . An exhaust chamber  30  is disposed downstream of the turbine compartment  26  via an exhaust compartment  29 , and the exhaust chamber  30  includes an exhaust diffuser  31  that is continuous with the turbine  13 . 
     In addition, the main shaft  32  is located to penetrate through central portions of the compressor  11 , the combustor  12 , the turbine  13 , and the exhaust chamber  30 . An end portion on a compressor  11  side of the main shaft  32  is rotatably supported by a bearing member  33 , and an end portion on an exhaust chamber  30  side is rotatably supported by a bearing member  34 . A plurality of rotor discs  35  in which the rotor blades  24  are mounted are placed over and fixed to the main shaft  32  in the compressor  11 , and a plurality of rotor discs  50  in which the rotor blades  28  are mounted are placed over and fixed to the main shaft  32  in the turbine  13 . A drive shaft of the generator (not illustrated) is connected to the end portion on the exhaust chamber  30  side. 
     In the gas turbine, the compressor compartment  21  of the compressor  11  is supported by legs  37 , the turbine compartment  26  of the turbine  13  is supported by legs  38 , and the exhaust chamber  30  is supported by legs  39 . 
     Therefore, the air taken in from the air intake port of the compressor  11  is compressed while passing through the inlet guide vane  22 , and the plurality of stator blades  23  and rotor blades  24 , to become high-temperature and high-pressure compressed air. In the combustor  12 , a predetermined fuel is supplied to the compressed air and is combusted. High-temperature and high-pressure combustion gas (working fluid) that is a working fluid generated by the combustor  12  passes through the plurality of stator blades  27  and rotor blades  28  forming the turbine  13 , to drive and rotate the main shaft  32 , and to drive the generator connected to the main shaft  32 . On the other hand, energy of exhaust gas (combustion gas) is reduced in speed by the conversion of the exhaust gas into pressure by the exhaust diffuser  31  of the exhaust chamber  30 , and then is released to the atmosphere. 
     Next, the rotor of the present embodiment will be described with reference to  FIGS. 2 to 5 .  FIG. 2  is a perspective view illustrating the vicinity of the rotor blades of the compressor.  FIG. 3  is a schematic view of the compressor as seen in the axial direction.  FIG. 4  is a schematic view of the compressor as seen in a radial direction.  FIG. 5  is a schematic view of a dovetail portion and a groove as seen in the axial direction. 
     The rotor of the present embodiment is applied to the compressor  11  of the gas turbine  10 . The rotor of the present embodiment is a rotor disc  50  fixed to the main shaft  32 . In the present embodiment, the rotor is the rotor disc  50  that is a separate member from the main shaft  32 , and is structured to be fixed to the main shaft  32 , but is not limited thereto. The rotor may be a structure to which the rotor blades  24  are fixed and which rotates with the rotor blades  24 , and the main shaft  32  may serve as the rotor. 
     As illustrated in  FIGS. 2 to 4 , the compressor  11  includes the rotor disc  50  that can rotate integrally with the main shaft  32 , and the plurality of rotor blades  24  mounted to extend radially from an outer peripheral portion of the rotor disc  50 . The rotor blade  24  is inserted into a groove  52  formed in the rotor disc  50 . 
     The rotor blade  24  includes a blade portion  42 , a platform portion  44 , and a dovetail portion  46 . The rotor blade  24  can have a structure in which the platform portion  44  and the dovetail portion  46  are integrally formed, and the blade portion  42  is joined to the platform portion  44  by welding. In addition, the rotor blade  24  may integrally form the blade portion  42 , the platform portion  44 , and the dovetail portion  46 . 
     The blade portion  42  has a streamlined cross-sectional shape, and extends and twists gradually while ensuring the shape. The blade portion  42  includes a base end portion fixed to the platform  44  and a tip portion extending to an inner wall surface side of a casing (not illustrated), and functions to allow the compressed air to flow smoothly. 
     The platform portion  44  is connected to a root side of the blade portion  42 , and has a surface parallel to a centrifugal force application direction of the blade portion  42 . The platform portion  44  is a base that connects the blade portion  42  and the dovetail portion  46 , and is a part of an outer surface of the rotor disc  50 . A part of a side surface of the platform  44  of the present embodiment faces the groove  52  of the rotor disc  50 . Namely, the platform portion  44  overlaps a part of the rotor disc  50  in a radial direction of a rotation axis. The platform portion  44  is a parallel portion having a constant width in a rotation direction. 
     The dovetail portion  46  is connected to an end portion on a radial inner side of the platform portion  44  in a cross section in an axial view of the main shaft  32 . The dovetail portion  46  is an end portion on the radial inner side of the rotor blade  24 . The dovetail portion  46  includes a widened portion  60 , a bottom portion  62 , and a corner  64 . The widened portion  60  is a portion connected to the platform  44 . The widened portion  60  increases in width from the portion connected to the platform portion  44  toward the radial inner side in a cross section in an axial view of the main shaft  32 . The bottom portion  62  is an end portion on the radial inner side, and a surface on the radial inner side of the bottom portion  62  faces the groove  52 . The corner  64  is a connecting portion between the widened portion  60  and the bottom portion  62 , and is located on the radial inner side and in an end portion in the rotation direction. The corner  64  connects the widened portion  60  and the bottom portion  62 , which are surfaces forming different angles, with a circular arc in a cross section in an axial view of the main shaft  32 . 
     A longitudinal direction of the rotor blade  24  is inclined with respect to a compressed air flow direction  56 . Namely, an angle θ formed by the longitudinal direction of the rotor blade  24  and a rotation direction  54  is not an angle of 90 degrees. Therefore, the angle θ formed in the platform portion  44  and the dovetail portion  46  by end surfaces, which are surfaces facing the groove  52 , and the rotation direction is not an angle of 90 degrees. 
     The rotor disc  50  is fixed to the main shaft  32 , and rotates integrally with the main shaft  32 . As described above, the groove  52  is formed in a surface on a radial outer side of the rotor disc  50 . A plurality of the grooves  52  are formed in the rotor disc  50  at predetermined intervals in the rotation direction. The platform portion  44  and the dovetail portion  46  of the rotor blade  24  are inserted into the groove  52 . 
     The groove  52  has a facing portion (platform-facing portion)  70 , a contact portion  72 , a bottom portion  74 , and a connecting portion  76 . The facing portion  70  is an end portion on the radial outer side of the groove  52 , and faces each of two end surfaces of the platform portion  44  in the rotation direction. The facing portion  70  is a groove having a constant width in the rotation direction and having a constant width at positions in a radial direction of the main shaft  32 . The contact portion  72  is provided on the radial inner side of the facing portion  70 , and faces each of two end surfaces of the widened portion  60  in the rotation direction. The contact portion  72  is a groove that increases in width toward the radial inner side of the main shaft  32 . When the rotor disc  50  rotates to apply a force to move the rotor blade  24  to the radial outer side, the contact portion  72  comes into contact with the widened portion  60  of the dovetail portion  46 . The bottom portion  74  is an end portion of the groove  52  on the radial inner side of the main shaft  32 . The connecting portion  76  is a connecting portion between the contact portion  72  and the bottom portion  74 , and is located on the radial inner side and at an end portion in the rotation direction. The connecting portion  76  connects the contact portion  72  and the bottom portion  74 , which are surfaces at different angles, with a circular arc in a cross section in an axial view of the main shaft  32 . The connecting portion  76  faces the corner  64  of the dovetail portion  46 . The groove  52  includes a chamfered portion  78  in each of two end surfaces in the compressed air flow direction  56 . The chamfer dimension of the chamfered portion  78  differs depending on a position in the groove  52 . The dimension of the chamfered portion  78  will be described later. 
     Here, as illustrated in  FIG. 4 , in a radial view of the main shaft  32 , an extending direction of the groove  52  is inclined along the inclination of the platform portion  44  and the dovetail portion  46  of the rotor blade  24  with respect to the compressed air flow direction  56 . Namely, an angle formed by the extending direction of the groove and the rotation direction  54  is not an angle of  90  degrees. The groove  52  has a substantially parallelogram shape in a radial view of the main shaft  32 , and is provided with four corners  80 ,  82 ,  84 , and  86 . 
     The corner  80  is located at a downstream end surface in the compressed air flow direction  56  and at a downstream end portion in the rotation direction  54 . An angle θ 1  formed at the corner  80  by the downstream end surfaces in the rotation direction  54  and in the compressed air flow direction  56  in a radial view of the main shaft  32  is an acute angle. The corner  82  is located at a downstream end surface in the compressed air flow direction  56  and at an upstream end portion in the rotation direction  54 . An angle θ 2  formed at the corner by the downstream end surfaces in the rotation direction  54  and in the compressed air flow direction  56  in a radial view of the main shaft  32  is an obtuse angle. 
     The corner  84  is located at an upstream end surface in the compressed air flow direction  56  and at an upstream end portion in the rotation direction  54 . An angle θ 1  formed at the corner  84  by the upstream end surfaces in the rotation direction  54  and in the compressed air flow direction  56  in a radial view of the main shaft  32  is an acute angle. The angle formed at the corner  84  is the same as the angle formed at the corner  80 . The corner  86  is located at an upstream end surface in the compressed air flow direction  56  and at a downstream end portion in the rotation direction  54 . An angle θ 2  formed at the corner  86  by the downstream end surfaces in the rotation direction  54  and in the compressed air flow direction  56  in a radial view of the main shaft  32  is an obtuse angle. The angle formed at the corner  86  is the same as the angle formed at the corner  82 . 
     Next, the chamfered portion  78  of the groove  52  will be described with reference to  FIGS. 6 and 7  in addition to  FIGS. 4 and 5 .  FIG. 6  is a cross-sectional view taken along line A-A in  FIG. 5 .  FIG. 7  is a cross-sectional view taken along line B-B in  FIG. 5 . As described above, the chamfered portion  78  is provided in each of an upstream end surface and a downstream end surface of the groove  52  in the compressed air flow direction  56 . Hereinafter, the chamfered portion  78  on a downstream end surface side of the groove  52  in the compressed air flow direction  56  will be described. 
     As illustrated in  FIGS. 4 to 7 , the chamfered portion  78  is formed on the entire periphery of the groove  52 , namely, in the facing portion  70 , the contact portion  72 , the bottom portion  74 , and the connecting portion  76 . As illustrated in  FIGS. 6 and 7 , the chamfered portion  78  has a rounded cross section. Since the chamfered portion  78  has a rounded cross section, the rotor blade  24  can be easily inserted into the groove  52 . However, the chamfered portion  78  is not limited to having a rounded shape, and may have a cutout shape. 
     The dimension of the chamfered portion  78  differs between the corner  80  on an acute angle side and the corner  82  on an obtuse angle side. Specifically, a chamfer dimension C 2  of the chamfered portion  78  of the connecting portion  76  on a corner  82  side is larger than a chamfer dimension C 1  of the chamfered portion  78  of the connecting portion  76  on a corner  80  side. The chamfer dimension of the connecting portion  76  is larger on a side on which the angle formed by the groove and the end surface is an acute angle than on a side on which the angle formed by the groove and the end surface is an obtuse angle. A radius of the rounded shape is set to different values to make the chamfered portion  78  of the present embodiment have different chamfer dimensions. A radius R 1  of a curved surface of the chamfered portion  78  of the connecting portion  76  on the corner  80  side is larger than a radius R 2  of a curved surface of the chamfered portion  78  of the connecting portion  76  on the corner  82  side. 
     In addition, the chamfer dimension of the chamfered portion  78  of the facing portion  70  and the contact portion  72  on the corner  80  side is larger than the chamfer dimension of the chamfered portion  78  of the facing portion  70  and the contact portion  72  on the corner side. In addition, the chamfer dimension of the chamfered portion  78  of the bottom portion  74  decreases from the corner  80  toward the corner  82 . The chamfer dimension of the chamfered portion  78  changes gradually. Therefore, in the chamfered portion  78 , the chamfer dimension on the corner  80  side is larger than the chamfer dimension at the corner  82 , and the chamfer dimension of the bottom portion  74  changes. 
     The chamfered portion  78  on a downstream end surface side of the groove  52  in the compressed air flow direction  56  has the same structure. Namely, the dimension of the chamfered portion  78  on the downstream end surface side of the groove  52  in the compressed air flow direction  56  differs between the corner  84  on the acute angle side and the corner  86  on the obtuse angle side. Specifically, a chamfer dimension C 3  of the chamfered portion  78  of the connecting portion  76  on a corner  84  side is larger than a chamfer dimension C 4  of the chamfered portion  78  of the connecting portion  76  on a corner  86  side. 
     Since the rotor disc (rotor)  50  has a structure in which in the groove  52 , the chamfer dimension C 2  of the chamfered portion  78  of the connecting portion  76  on the corner  82  side is larger than the chamfer dimension C 1  of the chamfered portion  78  of the connecting portion  76  on the corner  80  side, the stress of the groove  52  can be prevented from being concentrated at the connecting portion  76  on the corner  80  side during rotation. In addition, since the chamfer dimension C 2  of the connecting portion  76  on the corner  82  side is reduced, a gap between an upstream end surface of the dovetail portion  46  in the rotation direction at which the angle is an acute angle and the connecting portion  76  can be reduced, and the occurrence of a turbulence in an air flow on the corner  82  side at an obtuse angle during rotation can be reduced. In addition, since the connecting portion  76  on the corner side forms the chamfered groove portion  78  on a downstream side in the rotation direction, and a radial cross section of the corner  64  facing the connecting portion  76  is at an obtuse angle, the occurrence of a turbulence can be reduced. 
     In addition, since the dimension of the chamfered portion  78  of the connecting portion  76  on the corner  80  side at an acute angle is larger than the dimension of the chamfered portion  78  of the platform-facing portion  70  on the corner  82  side at an obtuse angle, stress concentration can be suppressed. In addition, since the chamfer dimension of the platform-facing portion  70  on the corner  82  side at an obtuse angle is reduced, the occurrence of a turbulence in an air flow on the corner  82  side at an obtuse angle can be reduced. 
     Here, it is preferable that the chamfer dimensions Ci and C 3  of the connecting portions  76  of the corners  80  and on the acute angle side are 1.8 mm or more. It is preferable that the chamfer dimensions C 2  and C 4  of the connecting portions  76  of the corners  82  and  86  on the obtuse angle side are 1.7 mm or less. 
     Here, it is preferable that the dimension of the chamfered portion  78  of the connecting portion  78  is a dimension at a position at which a distance between the chamfered portion  78  and a facing surface of the groove  52  is at its maximum. Accordingly, stress concentration at the connecting portion  78  can be more suitably suppressed. 
     In addition, when the chamfered portion  78  is formed on the entire periphery of the end surface as in the present embodiment, the rotor blade  24  can be easily inserted into the groove  52 . 
     In addition, as in the present embodiment, when the chamfered portion  78  has the structure in which the chamfer dimension from the facing portion to the connecting portion is larger on the corner  80  side at an acute angle than on the corner  82  side at an obtuse angle, the chamfered portion  78  can be easily processed. 
       FIG. 8  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. A chamfered portion  78   a  is formed in a groove portion  52   a  illustrated in  FIG. 8 . The groove portion  52   a  has the same structure as that of the groove portion  52  except for a structure of the chamfered portion  78   a.  The chamfer dimensions of the chamfered portions  78   a  of the contact portion  72  and the connecting portion  76  are larger on the corner  80  side at an acute angle than on the corner  82  side at an obtuse angle. In addition, the chamfer dimensions of the chamfered portions  78   a  of the connecting portion  76  and the contact portion  74  at the corner  80  having an acute angle is larger than the chamfer dimension of the chamfered portion  78   a  of the facing portion  70  at the corner  80  having an acute angle. In addition, in the present embodiment, the chamfer dimension of the chamfered portion  78   a  of the facing portion  70  at the corner  80  having an acute angle is the same as the chamfer dimension of the chamfered portion  78   a  of the facing portion  70  at the corner  82  having an obtuse angle. 
     Since the chamfer dimensions of the chamfered portions  78   a  of the contact portion  72  and the connecting portion  76  are larger on the corner  80  side at an acute angle than on the corner  82  side at an obtuse angle, the occurrence of a turbulence in an air flow can be reduced while suppressing stress concentration. In addition, as in the present embodiment, when the chamfer dimensions of the connecting portion  76  and the contact portion  74  at the corner  80  having an acute angle is set to be larger than the chamfer dimension of the facing portion  70  at the corner  80  having an acute angle, namely, when the chamfer dimension of the facing portion  70  at the corner  80  having an acute angle is set to be smaller than the chamfer dimension of the connecting portion  76 , an air flow at the facing portion  70  can be prevented from being turbulent. 
     It is preferable that the chamfered portion  78   a  has a structure in which the dimension of the connecting portion  78  on the corner  80  side at an acute angle is larger than the dimensions of other portions. Accordingly, stress concentration at the connecting portion  78  can be more suitably suppressed. In addition, in the above embodiment, the dimension of the contact portion  74  on the corner  80  side at an acute angle is the same as the dimension of the connecting portion  78  on the corner  80  side at an acute angle, but may be set to a dimension smaller than the dimension of the connecting portion  78  on the corner  80  side at an acute angle, or may decrease gradually as a distance from the connecting portion  78  increases. 
     In addition, it is preferable that the groove  52  has a structure in which the dimension of the chamfered portion  78   a  of the connecting portion on a side on which the angle formed by the groove  52  and the end surface is an acute angle is larger on an upstream side in the compressed air flow direction  56  than on a downstream side in the compressed air flow direction  56 . Namely, it is preferable that the dimension C 3  is set to be larger than the dimension C 1 . Accordingly, the occurrence of a turbulence of air can be reduced while reducing stress concentration. 
       FIG. 9  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. A rotor blade  124  illustrated in  FIG. 9  includes a blade portion  142 , a platform portion  144 , and a dovetail portion  146 . The blade portion  142  and the dovetail portion  146  are the same as the blade portion  42  and the dovetail portion  46  of the rotor blade  24 , respectively. The platform portion  144  includes a parallel portion having a constant width in the rotation direction, and a shank portion  92 . The shank portion  92  is provided on a dovetail portion  146  side of the platform  144 . The shank portion  92  is provided with a concavity having a width narrower than that of the parallel portion in a cross-sectional view seen in the axial direction. The dovetail portion  146  includes a widened portion  160 , a bottom portion  162 , and a corner  164 . 
     A groove  152  includes a facing portion  170 , a contact portion  172 , a bottom portion  174 , and a connecting portion  176 . The contact portion  172 , the bottom portion  174 , and the connecting portion  176  have the same structures as the contact portion  72 , the bottom portion  74 , and the connecting portion  76  of the groove  52 , respectively. The facing portion  170  has a structure in which the facing portion  170  changes in width at a position facing the shank portion  92  of the platform portion  144 , and has a convex shape in a cross-sectional view seen in the axial direction. 
       FIG. 10  is a schematic view of a dovetail portion and a groove of another example as seen in the axial direction. A rotor blade  224  illustrated in  FIG. 10  includes a blade portion  242 , a platform portion  244 , and a dovetail portion  246 . The blade portion  242  and the dovetail portion  246  are the same as the blade portion  42  and the dovetail portion  46  of the rotor blade  24 . The platform portion  244  includes a shank portion  294  and a parallel portion  296  having a constant width in the rotation direction. The shank portion  294  is provided on a dovetail portion  246  side of the platform  244 . The shank portion  294  is provided with a concavity that decreases in width in a cross-sectional view seen in the axial direction. The parallel portion  296  is disposed outside the shank portion  294  in the radial direction, and protrudes outward from a rotor disc  250  in the radial direction. The dovetail portion  246  includes a widened portion  260 , a bottom portion  262 , and a corner  264 . 
     A groove  252  includes a facing portion  270 , a contact portion  272 , a bottom portion  274 , and a connecting portion  276 . The contact portion  272 , the bottom portion  274 , and the connecting portion  276  have the same structures as the contact portion  72 , the bottom portion  74 , and the connecting portion  76  of the groove  52 , respectively. The facing portion  270  has a structure in which the facing portion  270  changes in width at a position facing the shank portion  292  of the platform portion  244 , and has a convex shape in a cross-sectional view seen in the axial direction. 
     As illustrated in  FIGS. 9 and 10 , the compressor  11  and the rotor disc may have a structure in which the platforms  144  and  244  are provided with the shank portions  92  and  294 , respectively. The structure of the platform and the dovetail portion  46  can be various structures, and in the case of any structure, when a structure is adopted in which each portion at the corner on the acute angle side and each portion at the corner on the obtuse angle side satisfy the above relationship, the above effect can be obtained. 
       FIG. 11  is a perspective view illustrating the vicinity of rotor blades of a compressor of another example.  FIG. 12  is a schematic view of the compressor in  FIG. 11  as seen in the axial direction.  FIG. 13  is a schematic view of a dovetail portion and a groove of the compressor in  FIG. 11  as seen in the axial direction. In the compressor illustrated in  FIGS. 11 to 13 , a rotor blade  324  is inserted into a groove  352  of a rotor disc  350 . 
     The rotor blade  324  includes a blade portion  342 , a platform portion  344 , and a dovetail portion  346 . The rotor blade  324  has a so-called Christmas tree structure in which an increase and a reduction in the width of the dovetail portion  346  are repeated a plurality of times. The blade portion  342  is the same as the blade portion  42  of the rotor blade  24 . 
     The platform portion  344  includes an insertion portion  394  and a parallel portion  396  having a constant width in the rotation direction. The insertion portion  394  is provided on a dovetail portion  346  side of the platform  344 . The insertion portion  394  has a structure in which the insertion portion  394  decreases in width toward the radial inner side in a cross-sectional view seen in the axial direction. The parallel portion  396  is disposed outside the insertion portion  394  in the radial direction, and protrudes outward from the rotor disc  350  in the radial direction. 
     The dovetail portion  346  includes a widened portion  360 , a bottom portion  362 , a corner  364 , and a reduced portion  396 . The widened portions  360 , the corners  364 , and the reduced portions  396  are provided in the dovetail portion  346  at a plurality of positions in the radial direction. The widened portion  360  has a structure in which the widened portion  360  increases in width toward the radial inner side. The reduced portion  396  has a structure in which the reduced portion  396  decreases in width toward the radial inner side. The corner  364  connects an end portion on the radial inner side of the widened portion  360  and an end portion on the radial outer side of the reduced portion  396 . In addition, the corner  364  connects the widened portion  360  and the bottom portion  362 . 
     In the dovetail portion  346 , from the radial outer side toward the radial inner side, the widened portion  360 , the corner  364 , the reduced portion  396 , the widened portion  360 , the corner  364 , and the reduced portion  396  are disposed in order, and end portions of the widened portion  360 , the corner  364 , and the bottom portion  362  on the radial inner side are disposed in order. 
     The groove  352  includes a facing portion  370 , a contact portion  372 , a bottom portion  374 , a connecting portion  376 , and a non-contact portion  398 . A plurality of the contact portions  372 , the connecting portions  376 , and the non-contact portions  398  are disposed in the radial direction of the main shaft  32 . The facing portion  370  is disposed at a position to face the insertion portion  394  of the platform  344 . The contact portion  372  is disposed at a position to face the widened portion  360  of the dovetail portion  346 . The bottom portion  374  is disposed at a position to face the bottom portion  362  of the dovetail portion  346 . The connecting portion  376  is disposed at a position to face the corner  364 . The non-contact portion  398  is disposed at a position to face the reduced portion  396 . Namely, the groove  352  has a multi-stage structure in which the non-contact portion  398  is provided inside the connecting portion  376  in the radial direction of the main shaft  32 , the contact portion  372  is provided inside the non-contact portion  398  in the radial direction of the main shaft  32 , and the plurality of contact portions  372  are disposed in the radial direction. 
     The groove portion  352  is provided with a chamfered portion  378 . 
     Similarly to the above embodiment, the chamfer dimension of the chamfered portion  378  differs between a corner  380  on the acute angle side and a corner  382  on the obtuse angle side. Specifically, at least the chamfer dimension of the chamfered portion  378  of the connecting portion  376  at the corner  380  on the acute angle side is larger than the chamfer dimension of the chamfered portion  378  of the connecting portion  376  at the corner  382  on the obtuse angle side. Namely, in the groove portion  352 , the chamfer dimension at the position of a concave portion on a corner  380  side on the acute angle side is relatively large, and the chamfer dimension at the position of a concave portion on a corner  382  side on the obtuse angle side is relatively small, so that the occurrence of a turbulence in an air flow can be reduced while suppressing stress concentration. 
     In addition, in the above-described embodiment, the rotor according to the present invention has been described as being applied to the compressor  11  of the gas turbine, but may be applied to the turbine  13 . In addition, the present invention is not limited to being applied to the gas turbine, and can be applied to other rotary machines such as steam turbines. 
     REFERENCE SIGNS LIST 
       11 : Compressor 
       12 : Combustor 
       13 : Turbine 
       24 : Rotor blade 
       32 : Main shaft 
       42 : Blade portion 
       44 : Platform portion 
       46 : Dovetail portion 
       50 : Rotor disc (rotor) 
       52 : Groove 
       54 : Rotation direction 
       56 : Compressed air flow direction 
       60 : Widened portion 
       62 : Bottom portion 
       64 : Corner 
       70 : Facing portion (platform-facing portion) 
       72 : Contact portion 
       74 : Bottom portion 
       76 : Connecting portion 
       78 : Chamfered portion 
       80 ,  82 ,  84 ,  86 : Corner