Patent Publication Number: US-2022212494-A1

Title: Wheel for railway vehicle

Description:
TECHNICAL FIELD 
     The present disclosure relates to a wheel used in a railway vehicle. 
     BACKGROUND ART 
     A wheel of a railway vehicle includes a boss, a rim, and a web. An axle of the railway vehicle is to be inserted into the boss. The rim forms an outer circumferential portion of the wheel and includes a tread and a flange. The tread is a surface that is to come into contact with a top surface of a rail. The flange protrudes from the tread outward in a radial direction of the wheel. The web connects the rim and the boss. 
     There have been various shapes of wheels for railway vehicles. For example, Patent Literature 1 discloses a wheel in which a web connecting a rim and a boss is bent. In Patent Literature 1, the web has a plate-thickness center line that is curvilinear when the wheel is viewed in its longitudinal section. The plate-thickness center line has a center that is an inflection point of the plate-thickness center line and symmetric about the center. 
     Patent Literatures 2 and 3 also disclose wheels including a web that is bent. In Patent Literatures 2 and 3, a plate-thickness center line of the web has a shape that is convex on an opposite side to a flange when the wheel is viewed in its longitudinal section. In other words, the plate-thickness center line is a curve with both ends being closer to the flange than a center of the plate-thickness center line is close to. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: Japanese Patent Application Publication No. 10-29401 
         Patent Literature 2: Japanese Translation of PCT International Application Publication No. 2009-545484 
         Patent Literature 3: Japanese Translation of PCT International Application Publication No. 2015-500177 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     As one type of braking device for a wheel for a railway vehicle, a tread brake is known. In a tread brake, a brake shoe is pressed against a tread of a wheel to apply a brake to a railway vehicle. During braking of the railway vehicle, frictional heat is produced between the tread and the brake shoe. As a result, a temperature of the wheel, particularly a temperature of a rim that forms an outer circumferential portion of the wheel rises, causing heat deformation of the rim. When displacement occurs in the rim due to heat deformation, traveling stability of a railway vehicle is affected. In particular, displacement of the rim in an axial direction of the wheel may induce meandering or derailing of the railway vehicle. In addition, the heat deformation of the rim and the occurrence of the thermal stress in the web during braking of the railway vehicle may cause a fatigue fracture of the wheel. It is therefore necessary to reduce the displacement of the rim in the axial direction of the wheel and to reduce the thermal stress occurring in the web during braking of the railway vehicle with the tread brake. However, with conventional wheels as exemplified by Patent Literatures 1 to 3, it is difficult to reduce both displacement of a rim and thermal stress in a web that occur during braking, at the same time. 
     An objective of the present disclosure is to provide a wheel for a railway vehicle that can reduce a displacement of its rim in an axial direction of the wheel and a thermal stress occurring in its web at the same time during braking of the railway vehicle with a tread brake. 
     Solution to Problem 
     A wheel according to the present disclosure is to be used in a railway vehicle. The wheel includes a boss, a rim, and a web. The boss forms an inner circumferential portion of the wheel. An axle of the railway vehicle is to be inserted into the boss. The rim forms an outer circumferential portion of the wheel. The rim includes a tread and a flange. The tread is to come into contact with a top surface of a rail on which the railway vehicle travels. The flange protrudes from the tread outward in a radial direction of the wheel. The web has an annular shape and connects the rim and the boss. When the wheel is viewed in its longitudinal section, the web has a linear plate-thickness center line that is inclined such that the plate-thickness center line approaches the flange side as it extends outward in the radial direction. When the wheel is viewed in its longitudinal section, an outer end of the plate-thickness center line is positioned between the flange and a center of the tread in an axial direction of the wheel. The outer end is one of both ends of the plate-thickness center line that is positioned more outward in the radial direction. 
     Advantageous Effect of Invention 
     With a wheel for a railway vehicle according to the present disclosure, it is possible to reduce a displacement of its rim in an axial direction of the wheel and a thermal stress occurring in its web at the same time during braking of the railway vehicle with a tread brake. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a longitudinal sectional view of a wheel for a railway vehicle according to an embodiment. 
         FIG. 2  is a diagram exemplifying a deformation occurring in a wheel during braking with a tread brake in an exaggerated manner. 
         FIG. 3  is a diagram illustrating wheel shapes of analytic models of Examples. 
         FIG. 4  is a diagram illustrating wheel shapes of analytic models of Comparative Examples. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A wheel according to an embodiment is used in a railway vehicle. The wheel includes a boss, a rim, and a web. The boss forms an inner circumferential portion of the wheel. An axle of the railway vehicle is to be inserted into the boss. The rim forms an outer circumferential portion of the wheel. The rim includes a tread and a flange. The tread is to come into contact with a top surface of a rail on which the railway vehicle travels. The flange protrudes from the tread outward in a radial direction of the wheel. The web has an annular shape and connects the rim and the boss. When the wheel is viewed in its longitudinal section, the web has a linear plate-thickness center line that is inclined such that the plate-thickness center line approaches the flange side as it extends outward in the radial direction. When the wheel is viewed in its longitudinal section, an outer end of the plate-thickness center line is positioned between the flange and a center of the tread in an axial direction of the wheel. The outer end is one of both ends of the plate-thickness center line that is positioned more outward in the radial direction (first configuration). 
     When a brake shoe of a tread brake is pressed against a tread of a wheel, producing frictional heat, a rim deforms by heat to be displaced in an axial direction of the wheel. In the axial direction of the wheel, when a direction toward a side on which the flange is disposed is referred to as a flange direction, and the opposite direction is referred to as a counter-flange direction, the rim generally tends to be displaced in the flange direction. In contrast, in the wheel of the first configuration, the plate-thickness center line of the web is linear and is inclined such that the plate-thickness center line approaches the flange side as it extends outward in the radial direction of the wheel when the wheel is viewed in its longitudinal section. When the rim is to be displaced in the flange direction, the web having such a plate-thickness center line resists the displacement of the rim, so that the displacement can be inhibited. It is therefore possible to reduce the displacement of the rim in the axial direction during braking of a railway vehicle with a tread brake. In addition, since the plate-thickness center line has no inflection point, stress concentration is unlikely to occur in the web. It is therefore possible to reduce thermal stress occurring in the web during braking of a railway vehicle with a tread brake. 
     With the first configuration, a displacement of the rim in the axial direction is reduced, so that the rim resists swinging with respect to the web. It is therefore possible to reduce stress occurring in a root portion of the rim in the web. In addition, by positioning the outer end of the plate-thickness center line between the flange and the center of the tread, it is possible to reduce thermal stress occurring in the web during braking of a railway vehicle. 
     A distance in the axial direction from a side face of the rim on the flange side to the outer end of the plate-thickness center line is preferably 0.3 times or more a length of the rim in the axial direction (second configuration). 
     An angle that the plate-thickness center line forms with the axial direction on the flange side is preferably 87° or less (third configuration). 
     The web preferably has a plate thickness that decreases as the web extends outward in the radial direction until a point inward from the outer end of the plate-thickness center line and has a minimum plate thickness at the point (fourth configuration). 
     An embodiment of the present disclosure will be described below with reference to the drawings. In the drawings, the same or equivalent components will be denoted by the same reference characters and repetitive description thereof will not be made. 
       FIG. 1  is a longitudinal sectional view of a wheel  100  according to the present embodiment. The longitudinal section refers to a cross section of the wheel  100  taken along a plane including a central axis X of the wheel  100 . The longitudinal section of the wheel  100  is symmetric about the central axis X, and thus  FIG. 1  illustrates the wheel  100  on one side of the central axis X only. In the present embodiment, a direction in which the central axis X of the wheel  100  extends will be referred to as an axial direction, and a radial direction of the wheel  100  will be simply referred to as a radial direction. 
     Referring to  FIG. 1 , the wheel  100  is used in a railway vehicle. The wheel  100  includes a boss  10 , a rim  20 , and a web  30 . 
     The boss  10  forms an inner circumferential portion of the wheel  100 . The boss  10  has a substantially cylindrical shape the axial centerline of which is the central axis X. An axle of the railway vehicle (not illustrated) is to be inserted into the boss  10 . 
     The rim  20  forms an outer circumferential portion of the wheel  100 . The rim  20  is disposed outside the boss  10  in the radial direction. In addition, the rim  20  is positioned so as to be outward from the boss  10  in a track-width direction. In other words, a rim-width center C 20  illustrated by a two-dot chain line in  FIG. 1  is positioned outward from a boss-width center C 10  illustrated similarly by a two-dot chain line on a track. 
     The rim  20  includes a tread  21  and a flange  22 . The tread  21  faces outward in the radial direction. The tread  21  is to come into contact with a top surface of a rail on which the railway vehicle travels. A diameter of the tread  21  gradually increases toward the flange  22 . A shape of the tread  21  is not limited to a particular shape. For example, the tread  21  may be a conical tread or may be an arc tread. 
     The flange  22  is provided at one end of the rim  20  in the axial direction. In the axial direction of the wheel  100 , a direction toward a side on which the flange  22  is disposed will be referred to as a flange direction, and the opposite direction will be referred to as a counter-flange direction. The flange  22  protrudes from the tread  21  outward in the radial direction. When the railway vehicle travels on right and left rails, the flange  22  is positioned inward from the rails. The flange  22  includes side faces  221  and  222 . When the wheel  100  is viewed in its longitudinal section, the side faces  221  and  222  each have a curve shape including one or more types of arcs. 
     The side face  221  is disposed on a side close to the tread  21  in the axial direction. The side face  221  is connected to the tread  21  via a throat  23 . When the wheel  100  is viewed in its longitudinal section, the throat  23  has a curve shape including one or more types of arcs and connects the side face  221  to the tread  21  smoothly. A curvature of a surface of the rim  20  changes at a boundary  24  between the throat  23  and the tread  21 . A portion of the tread  21  adjacent to the boundary  24  has a curvature the absolute value of which is significantly smaller than absolute values of curvatures of the side face  221  of the flange  22  and the throat  23 . 
     The side face  222  is disposed on an opposite side to the side face  221  in the axial direction. The side face  222  is connected to a side face  25 , which is one of both side faces  25  and  26  of the rim  20 . 
     The web  30  has an annular shape. The web  30  connects the boss  10  and the rim  20 . The web  30  has a plate thickness that is smaller as a whole than thicknesses of the boss  10  and the rim  20 . The thicknesses of the boss  10  and the rim  20  refer to lengths of the boss  10  and the rim  20  in the axial direction, respectively. The plate thickness of the web  30  is a length of the web  30  in the axial direction. The plate thickness of the web  30  is large on its boss  10  side and small on its rim  20  side. 
     The web  30  includes side faces  31  and  32 . The side face  31  is a face disposed on a flange  22  side in the axial direction. The side face  32  is positioned on an opposite side to the side face  31  in the axial direction. When the wheel  100  is viewed in its longitudinal section, the side faces  31  and  32  are connected to the rim  20  via arcs  41  and  42 , respectively. The side faces  31  and  32  are connected to the boss  10  via arcs  43  and  44 , respectively. 
     In the present embodiment, one of an end  411  of the arc  41  on the web  30  side and an end  421  of the arc  42  on the web  30  side that is positioned more inward than the other in the radial direction is defined to be an outer circumference end of the web  30 . In addition, one of an end  431  of the arc  43  on the web  30  side and an end  441  of the arc  44  on the web  30  side that is positioned more outward than the other in the radial direction is defined to be an inner circumference end of the web  30 . The outer circumference end of the web  30  can be regarded as a root of the rim  20  for the web  30 . The inner circumference end of the web  30  can be regarded as a root of the boss  10  for the web  30 . In the present embodiment, the end  421  of the arc  42  and the end  441  of the arc  44  are the outer circumference end and the inner circumference end of the web  30 , respectively. 
     The plate thickness of the web  30  decreases as the web  30  extends outward in the radial direction until a position inward from the outer circumference end  421  and is minimized at the position. In other words, the web  30  has its minimum plate thickness at a portion inward from the outer circumference end  421  in the radial direction and in a vicinity of the outer circumference end  421 . A position at which the plate thickness of the web  30  is minimized substantially coincides with a position at which a bending stress produced in the web  30  by a bending load received by the wheel  100  from a rail when the railway vehicle passes a curve is minimized. For example, the plate thickness of the web  30  can be minimized at a position that is 5 mm to 30 mm inward from the outer circumference end  421  in the radial direction. 
     The web  30  has a plate-thickness center line A. The plate-thickness center line A is a line that passes midpoints between the side faces  31  and  32  and extends from the boss  10  side to the rim  20  side. When the wheel  100  is viewed in its longitudinal section, the plate-thickness center line A has a linear shape. A linear shape herein includes not only a perfect straight line but also a very gentle arc having a curvature radius of, for example, 1000 mm or more, or even a polygonal chain. In other words, the plate-thickness center line A is any line that can be recognized as a substantially straight line when the wheel  100  is viewed in its longitudinal section. Since the plate-thickness center line A has a linear shape when the wheel  100  is viewed in its longitudinal section, the web  30  has a substantially flat disk shape and is not bent in the axial direction. 
     When the wheel  100  is viewed in its longitudinal section, the plate-thickness center line A is inclined with respect to the radial direction such that the plate-thickness center line A approaches the flange  22  side as it extends outward in the radial direction. Of both ends Aa and Ab of the plate-thickness center line A, the end Aa, which is positioned outward in the radial direction, will be referred to as an outer end of the plate-thickness center line A, and the end Ab, which is positioned inward in the radial direction, will be referred to as an inner end of the plate-thickness center line A. The outer end Aa of the plate-thickness center line A is a point at which the plate-thickness center line A is connected to a straight line that passes the outer circumference end  421  of the web  30  and extends in the axial direction. The inner end Ab of the plate-thickness center line A is a point at which the plate-thickness center line A is connected to a straight line that passes the inner circumference end  441  of the web  30  and extends in the axial direction. 
     In the axial direction, the outer end Aa of the plate-thickness center line A is positioned within a range R between the flange  22  and a center  211  of the tread  21 . In other words, the outer end Aa is disposed on the counter-flange direction side with respect to the side face  221  of the flange  22 . In addition, the outer end Aa is disposed on the flange direction side with respect to the center  211  of the tread  21 . The center  211  of the tread  21  refers to a middle position in the axial direction between the boundary  24  between the tread  21  and the throat  23  and the side face  26  of the rim  20 . 
     By disposing the outer end Aa of the plate-thickness center line A between the flange  22  and the center  211  of the tread  21 , a distance in the axial direction between the web  30  and the side face  25  of the rim  20  on the flange  22  side is kept. Suppose a distance in the axial direction from the side face  25  of the rim  20  to the outer end Aa of the plate-thickness center line A is denoted by a web position Pw. The web position Pw is determined as appropriate in accordance with specifications of a tread brake used for the wheel  100  or the like. For example, the web position Pw [mm] is preferably 0.3 times or more a width Wr [mm] of the rim  20  (Pw/Wr≥0.3). The web position Pw [mm] is preferably 0.6 times or less the width Wr [mm] of the rim  20  (Pw/Wr≤0.6). The width Wr of the rim  20  is a length of the rim  20  in the axial direction, and is a maximum distance from the side face  25  on the flange  22  side to the side face  26  on the opposite side in the axial direction. 
     When the wheel  100  is viewed in its longitudinal section, the plate-thickness center line A forms an angle θ with the axial direction on the flange  22  side. In a case where the plate-thickness center line A is a very gentle curve, the angle θ is determined to be an angle formed by a tangential line at a center of the plate-thickness center line A (midpoint between the outer end Aa and the inner end Ab) with the axial direction. In a case where the plate-thickness center line A is a polygonal chain, the angle θ is determined to be an angle formed by the longest segment among segments included in the plate-thickness center line A with the axial direction. 
     The angle θ is less than 90°. The angle θ is preferably 87° or less, which however depends on specifications of a tread brake used for the wheel  100  or the like. The angle θ is preferably 75° or more. 
     Advantageous Effects of Embodiment 
       FIG. 2  is a diagram illustrating only a section of the wheel  100  illustrated in  FIG. 1  and exemplifying a deformation occurring in the wheel  100  during braking with a tread brake in an exaggerated manner. Referring to  FIG. 2 , when a brake shoe of the tread brake is pressed against the tread  21  of the wheel  100 , the rim  20  is subjected to heat deformation by friction and tends to be displaced toward the flange  22  side in the axial direction (in the flange direction). However, in the wheel  100  according to the present embodiment, it is possible to reduce such displacement of the rim  20 . In the wheel  100 , the plate-thickness center line A of the web  30  has a linear shape when the wheel  100  is viewed in its longitudinal section. In addition, the plate-thickness center line A is inclined such that the plate-thickness center line A approaches the flange  22  side as it extends outward in the radial direction. As a result, even though the rim  20  is to be displaced in the flange direction during braking of a railway vehicle with tread brakes, the web  30  resists the displacement of the rim  20 , so that the displacement can be inhibited. It is therefore possible to reduce the displacement of the rim  20  in the axial direction. 
     In the wheel  100  according to the present embodiment, since the plate-thickness center line A is linear when the wheel  100  is viewed in its longitudinal section, the web  30  has substantially no inflection point. As a result, stress concentration is unlikely to occur in the web  30  during braking of the railway vehicle with a tread brake. It is therefore possible to reduce not only the displacement of the rim  20  in the axial direction but also the thermal stress occurring in the web  30 . 
     In the present embodiment, the web position Pw is preferably 0.3 times or more the width Wr of the rim  20 . It is thereby possible to further reduce the displacement of the rim  20  in the axial direction. 
     In the present embodiment, the angle θ that the plate-thickness center line A forms with the axial direction on the flange  22  side is preferably set at 87° or less. It is thereby possible to reduce the displacement of the rim  20  in the axial direction and the thermal stress occurring in the web  30  more reliably. 
     In the present embodiment, the plate thickness of the web  30  decreases as the web  30  extends outward in the radial direction until a point inward from the outer end Aa of the plate-thickness center line A and is minimized at the point. More specifically, in the web  30 , the position at which the bending stress produced by a bending load received from a rail when the railway vehicle passes a curve is made to substantially coincide with the position at which the plate thickness is minimized. With this configuration, it is possible to prevent fatigue fracture of the web  30 , increasing a life of the wheel  100 . 
     An embodiment according to the present disclosure is described above, but the present disclosure is not limited to the above embodiment, and various modifications may be made without departing the gist and scope of the present disclosure. 
     EXAMPLE 
     The present disclosure will be described below more in detail with reference to EXAMPLE. However, the present disclosure should not be construed to be limited to the EXAMPLE described below. 
     To evaluate effects brought by a wheel for a railway vehicle according to the present disclosure, a numerical analysis by the finite element method (FEM analysis) was conducted. In the FEM analysis, an analytic model having the same shape as that of the wheel  100  according to the above-described embodiment ( FIG. 1 ) was created, and evaluation was conducted on the analytic model while the angle of the plate-thickness center line A (plate angle) θ [°] and the web position Pw [mm] were changed. For the purpose of comparison, the evaluation was conducted on analytic models each having a wheel shape that is generally used in Europe or North America. 
       FIG. 3  is a diagram illustrating wheel shapes (outlines in ½ section) of analytic models of Examples 1 to 4. The wheel shapes of the analytic models of Examples 1 to 4 are all such that their bosses are positioned closer to a center of a track (closer to a center of a wheelset) than their rims.  FIG. 4  is a diagram illustrating wheel shapes (outlines in ½ section) of analytic models of Comparative Examples 1 to 5. Referring to  FIG. 3  and  FIG. 4 , in Examples 1 to 4 and Comparative Examples 1 to 3, their plate-thickness center lines A were linear. However, in Examples 1 to 4, their plate angles θ were less than 90°, but in Comparative Examples 1 to 3, their plate angles θ were 90° or more. As illustrated in  FIG. 4 , in Comparative Example 4 and Comparative Example 5, their plate-thickness center lines A bend unlike Examples 1 to 4 and Comparative Examples 1 to 3. The analytic model of Comparative Example 4 has a wheel shape that is generally used in Europe. The analytic model of Comparative Example 5 has a wheel shape that is generally used in North America. Shape parameters of each analytic model are shown in Table 1. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Plate angle θ 
                 Web position Pw 
                 Web position Pw/ 
               
               
                   
                 [°] 
                 [mm] 
                 Rim width Wr 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Example 1 
                 85 
                 36 
                 0.26 
               
               
                 Example 2 
                 85 
                 52 
                 0.37 
               
               
                 Example 3 
                 85 
                 66 
                 0.47 
               
               
                 Example 4 
                 87 
                 66 
                 0.47 
               
               
                 Comparative 
                 90 
                 52 
                 0.37 
               
               
                 Example 1 
                   
                   
                   
               
               
                 Comparative 
                 100 
                 52 
                 0.37 
               
               
                 Example 2 
                   
                   
                   
               
               
                 Comparative 
                 110 
                 52 
                 0.37 
               
               
                 Example 3 
                   
                   
                   
               
               
                 Comparative 
                 — 
                 72 
                 0.51 
               
               
                 Example 4 
                   
                   
                   
               
               
                 Comparative 
                 — 
                 93 
                 0.66 
               
               
                 Example 5 
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     The FEM analysis was conducted with general-purpose software (ABAQUS Ver.6.12, from Dassault Systemes SE). In the analysis, to simulate braking of a railway vehicle with a tread brake, heat flux was provided to a region of a tread of a wheel that is to come into contact with a brake shoe of the tread brake. Braking duration was set at 1200 seconds, and an inner circumferential portion of a wheel was fully constrained. In addition, to evaluate a stress occurring in a wheel when a railway vehicle travels on a rail (mechanical stress), a load was applied to a tread of the wheel at a position at which the tread is to come into contact with the rail. At this time, the load was set at 40 t for each wheelset. 
     Results of the FEM analysis are shown in Table 2. In Table 2, Rim displacement [mm] indicates a maximum displacement of a rim in the axial direction during braking, where a displacement in the flange direction is indicated as negative, and a displacement in the counter-flange direction is indicated as positive. The rim displacement was evaluated at a position at a diameter of 890 mm of a wheel on a side face of a rim on its flange side. Web thermal stress indicates a maximum stress in a web during braking. Web mechanical stress indicates a maximum value of a stress amplitude of a web that occurs while a wheel makes one revolution on a rail (½ of stress range). Table 2 shows, for each of Examples and Comparative Examples, a web thermal stress is expressed in a form of its ratio to a web thermal stress of Example 1, and a web mechanical stress is expressed in a form of its ratio to a web mechanical stress of Example 1. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Rim 
                 Web 
                 Web 
               
               
                   
                 displacement 
                 thermal stress 
                 mechanical stress 
               
               
                   
                 [mm] 
                 [—] 
                 [—] 
               
               
                   
               
             
            
               
                 Example 1 
                 −1.5 
                 1.00 
                 1.00 
               
               
                 Example 2 
                 −0.7 
                 0.96 
                 1.00 
               
               
                 Example 3 
                 −0.2 
                 0.86 
                 0.91 
               
               
                 Example 4 
                 −0.4 
                 0.75 
                 0.99 
               
               
                 Comparative 
                 −2.0 
                 0.78 
                 1.05 
               
               
                 Example 1 
                   
                   
                   
               
               
                 Comparative 
                 −3.8 
                 0.99 
                 0.78 
               
               
                 Example 2 
                   
                   
                   
               
               
                 Comparative 
                 −3.8 
                 0.92 
                 1.00 
               
               
                 Example 3 
                   
                   
                   
               
               
                 Comparative 
                 −0.2 
                 1.29 
                 0.99 
               
               
                 Example 4 
                   
                   
                   
               
               
                 Comparative 
                 −2.4 
                 0.77 
                 1.14 
               
               
                 Example 5 
               
               
                   
               
            
           
         
       
     
     In Comparative Example 5, its plate-thickness center line A was formed in a substantially S shape, and in its web, a root portion of its boss was separated from a root portion of its rim in the axial direction ( FIG. 4 ). With such a wheel shape, reduction in the web thermal stress can be designed, but the rim displacement cannot be reduced. Actually, in Comparative Example 5, its rim displacement was −2.4 mm, and the result was that its rim is significantly displaced in the flange direction. In contrast, in Examples 1 to 4, in which their plate-thickness center lines A were linear, their rim displacements were −1.5 mm to −0.2 mm, which were reduced as compared with Comparative Example 5. 
     In Comparative Examples 1 to 3, their plate-thickness center lines A were linear as in Examples 1 to 4. However, although the plate angles θ of Examples 1 to 4 were less than 90°, the plate angles θ of Comparative Examples 1 to 3 were 90° or more. In Comparative Examples 1 to 3, their rim displacements were −2.0 mm to −3.8 mm. In contrast, in Examples 1 to 4, in which their plate angles θ were less than 90°, their rim displacements were −1.5 mm to −0.2 mm, which were small as compared with Comparative Examples 1 to 3. In particular, in Examples 2 to 4, in which ratios of their web positions Pw [mm] to their rim widths Wr [mm] were 0.3 or more, the results were that their rim displacements fell within a tolerated range according to European standards EN 13979-1 (−1.0 mm to 3.0 mm). 
     In Comparative Example 4, its web was provided with two inflection points ( FIG. 4 ). With such a wheel shape, reduction in the rim displacement can be designed, but the web thermal stress cannot be reduced. Actually, in Comparative Example 4, a ratio of its web thermal stress (to that of Example 1) was as high as 1.29. In contrast, in Examples 1 to 4, in which their plate-thickness center lines A were linear, ratios of their web thermal stresses (to that of Example 1) were reduced to 0.75 to 1.00. In Examples 2 to 4, in which their web positions Pw were relatively large, their web thermal stresses were further reduced. 
     Web thermal stresses of Comparative Examples 1 to 3 were also reduced as compared with Comparative Example 4. In particular, the web thermal stress of Comparative Example 1, in which its plate angle θ was 90°, was smaller than the web thermal stresses of Examples 1 to 3. However, in Comparative Example 1, its web mechanical stress was large as compared with Examples. Therefore, considering the web mechanical stress, the plate angle θ needs to be less than 90°. 
     It was thus confirmed that, in a wheel for a railway vehicle, by making its plate-thickness center line A linear, inclining the plate-thickness center line A such that the plate-thickness center line A approaches a flange side as the plate-thickness center line A extends outward in a radial direction, and making its plate angle θ less than 90°, it is possible to reduce a rim displacement and a web thermal stress at the same time. According to the analysis results of Examples 1 to 4, by making the plate angle θ 87° or less, it is possible to reduce the rim displacement and the web thermal stress more reliably. In addition, according to the analysis results of Examples 2 to 4, when a ratio of the web position Pw to the rim width Wr is 0.3 or more, it is possible to further reduce the rim displacement. 
     REFERENCE SIGNS LIST 
     
         
         
           
               100 : wheel 
               10 : boss 
               20 : rim 
               21 : tread 
               22 : flange 
               30 : web 
             A: plate-thickness center line