Patent Publication Number: US-7908897-B2

Title: Spline rolling tool, and process of manufacturing spline rolling tool

Description:
TECHNICAL FIELD 
     The present invention relates to a spline rolling tool, and more particularly to such a spline rolling tool in which strength of forming teeth is so assured that durability of the forming teeth is improved and which can be manufactured at a low cost. The present invention also relates to a process of manufacturing the spline rolling tool. 
     BACKGROUND ART 
     Splines are a plurality of tooth-shaped keys provided on an outer circumferential surface of a shaft member, and are to be fitted into a member so that power (rotational force) can be transmitted through the mated members. In general, the splines are formed on an outer circumferential surface of a workpiece by a rolling operation using a rolling tool. Each of the splines can be easily broken at a longitudinal end portion of its root (at its ramped end portion). Therefore, there is a need for obtaining a torsional strength of such an easily breakable portion of the root as indicated by Japanese Application Laid-Open Publication No. JP-H11-290978 (see paragraph [0004], etc). 
     In view of the above need, the applicant of the present application invented a spline  100  as shown in  FIG. 8  (which is not publicly known at the time of filing of the present application). As shown in  FIG. 8 , a shoulder  101   a  is provided in a ramped end portion of this spline  100 , so that a root diameter defined by a root  101  of the spline  100  is changed in a direction of axis O (horizontal direction as seen in  FIG. 8 ) of a shaft member. The provision of the shoulder  101   a  assures a strength of the ramped end portion, namely, makes it possible to improve the torsional strength. 
     In a rolling tool used for rolling the spline  100 , one of widthwise end portions of each of its forming teeth is subjected to a crest removing operation (see  FIG. 2 ), for permitting the shoulder  101   a  to be provided in the root  101  when the spline  100  is formed by the rolling tool. 
     DISCLOSURE OF INVENTION 
     Object to be Solved by the Invention 
     However, in this technology, since each of the forming teeth is subjected to the crest removing operation for creating an incomplete toothed region, a periphery of the incomplete toothed region becomes a sharp edge, by which each of the forming teeth (incomplete toothed region) is easily chipped or otherwise damaged. Further, since an angular portion is formed on the spline  100 , a stress is easily concentrated in the angular portion. Consequently, there is a problem that durabilities of the rolling tool and the splined shaft are deteriorated. 
     For example, Japanese Application Laid-Open Publication No. JP-H09-308935 discloses a spline rolling tool in which a side surface of each tooth (forming tooth) is chamfered for making it possible to prevent deterioration of strength due to stress concentration. However, the chamfering is conventionally made by a handwork operation carried out by a skilled worker, thereby causing increase in time required for the handwork operation and accordingly considerable increase in cost for manufacturing the tool. Further, since the chamfering is made by the handwork operation, there is problem that a sufficient accuracy can not be obtained due to variation with respect to shape of the chamfered portion and surface roughness in the chamfered portion. 
     On the other hand, the periphery of the incomplete toothed region could be chamfered by a machining operation using a technique, as disclosed in JP-H11-290978 noted above, which is for moving a grinding wheel along a predetermined path. However, it would be necessary to extremely accurately control the feed movement of the grinding wheel through three controllable feed axes, in order to machine an entirety of the periphery of the incomplete toothed region having a stepped portion, such that the entirety of the periphery of the incomplete toothed region is round-chamfered. The necessity of the extremely accurate control of the feed movement of the grinding wheel leads to an increase in cost required for the control of the feed movement. Further, since such a machining operation with the extremely accurate control has to be made for each and every forming tooth, the required operation time is extremely increased, resulting in considerable increase in the overall cost for manufacturing the tool. 
     The present invention was developed for solving the above-described problem, and has an object to provide a spline rolling tool in which strength of forming teeth is attained so that durability of the forming teeth is improved and which can be manufactured at a low cost, and also a process of manufacturing the spline rolling tool. 
     Measures for Achieving the Object 
     For achieving the object, a first aspect of the invention is a spline rolling tool having a toothed forming face provided with a plurality of forming teeth that are to bite into an outer circumferential surface of a workpiece so as to roll splines in the outer circumferential surface of the workpiece, wherein each of the forming teeth has an incomplete toothed region which is located in one widthwise end portion thereof and which is formed by a crest removing operation, and a chamfered edge which is a periphery of the incomplete toothed region and which is formed by a chamfering operation; the incomplete toothed region has a curved surface portion located in a widthwise end portion thereof and having an arcuate cross-section, a flat surface portion contiguous to the curved surface portion and substantially parallel to a crest of each of the forming teeth, and a slant surface portion contiguous to the flat surface portion and inclined upwardly toward the other widthwise end portion of each of the forming teeth; and the chamfered edge is formed in the periphery of the incomplete toothed region to have a rounded cross-section, by rotating a wire brush having a plurality of bristles to which abrasive grains adhere and parallelly moving the wire brush in a single direction, such that the chamfered edge has a surface roughness of not larger than about 3.2 μm. 
     A second aspect of the invention is a process of manufacturing a spline rolling tool having a toothed forming face provided with a plurality of forming teeth that are to bite into an outer circumferential surface of a workpiece so as to roll splines on the outer circumferential surface of the workpiece, each of the forming teeth having an incomplete toothed region which is located in one of widthwise end portions thereof and which is formed by a crest removing operation, and a chamfered edge which is a periphery of the incomplete toothed region and which is formed by a chamfering operation, comprising the steps of: forming the forming teeth in the toothed forming face of the spline rolling tool by using a grinding wheel; subjecting the forming teeth to a crest removing operation using a grinding wheel for forming the incomplete toothed region having a curved surface portion located in a widthwise end portion thereof and having an arcuate cross-section, a flat surface portion contiguous to the curved surface portion and substantially parallel to a crest of each of the forming teeth, and a slant surface portion contiguous to the flat surface portion and inclined upwardly toward the other widthwise end portion of each of the forming teeth; and subjecting the incomplete toothed region to a chamfering operation using a wire brush having a plurality of bristles to which abrasive grains adhere so as to form the chamfered edge in the periphery of the incomplete toothed region such that the chamfered edge has a rounded cross-section and a surface roughness of not larger than about 3.2 μm, wherein the chamfering step is implemented by rotating and parallelly moving the wire brush in a single direction. 
     According to a third aspect of the invention, in the process defined in the second aspect of the invention, the direction is a direction that is substantially perpendicular to a width direction of each of the forming teeth. 
     Effects of the Invention 
     In the spline rolling tool of the present invention, since the incomplete toothed region having the curved surface portion, the flat surface portion and the slant surface portion are located in one of the widthwise end portions of each of the forming teeth, roots of the respective splines can be formed such that a root diameter defined by the roots of the respective splines is changed in an axial direction of the workpiece, and a shoulder having a large diameter can be provided in a ramped end portion of each of the splines. Therefore, it is possible to roll the splines in each of which a torsional strength of the ramped end portion is improved. 
     If the incomplete toothed region is simply created on each of the forming teeth, the periphery of the incomplete toothed region would become a sharp edge whereby durabilities of the forming teeth and splines could be reduced. However, in the spline rolling tool of the present invention, the periphery of the incomplete toothed region is subjected to the chamfering operation, so that the chamfered edge is formed in the periphery of the incomplete toothed region to establish a rounded cross-section with the surface roughness of not larger than about 3.2 μm. Therefore, it is possible to restrain each of the forming teeth from being chipped or otherwise damaged and accordingly to improve the durability of the spline rolling tool per se. 
     On the other hand, when the splines are rolled in the workpiece, it is possible to restrain formation of an angular portion in the ramped end portion of each of the splines and accordingly to improve a surface smoothness of the ramped end portion. Therefore, there is an effect that the splines each having a high strength can be rolled in the workpiece. Consequently, the durability of each of the splines can be improved. 
     Further, the chamfered edge is formed by rotating the wire brush having the plurality of bristles to which abrasive grains adhere and parallelly moving the wire brush in the above noted direction. Therefore, even in a case where the incomplete toothed region has a complicated shape with the curved surface portion, the flat surface portion and the slant surface portion as in the present invention, it is possible to cause the bristles to be flexed to follow the complicated shape of the incomplete toothed region. Accordingly, it is possible to efficiently and accurately form the chamfered edge having the rounded cross-section with the surface roughness of not larger than about 3.2 μm in the periphery of the incomplete toothed region. 
     Consequently, it is possible to uniformly form the chamfered edge having the rounded cross-section, and accordingly to avoid the problem of increase in variation in the shape and surface roughness of the chamfered portion, which problem has been encountered in the conventional product requiring the handwork operation to form the chamfered portion therein. Therefore, it is possible to restrain chipping or other damage of each of the forming teeth and also to roll the splines each having a high strength, restraining formation of an angular portion in the ramped end portion of each of the splines. 
     Further, it is possible to improve accuracy in the shape of each of the forming teeth, and to avoid the problem of reduction in a non-chamfered portion of each of the forming teeth, which problem has been encountered in a conventional product in which each of the forming teeth has been likely to be chamfered too much in the chamfering operation. Therefore, there is also an effect that it is possible to roll the splines each having a high accuracy, and accordingly to improve accuracy in fitting of each of the splines. 
     Further, since the chamfered edge is formed by parallelly moving the wire brush in the single direction, the chamfered edge can be formed in an extremely short length of time. That is, it is not necessary to carry out a complicated operation such as a machining operation with use of a numerically controlled machine tool in which a grinding wheel is fed through a three controllable axes of the machine tool so as to be moved along the periphery of the incomplete toothed region of each of the multiplicity of forming teeth provided in the toothed forming face. Thus, the chamfered edges can be formed in the multiplicity of forming teeth at a time. Consequently, it is possible to simplify the chamfering step and accordingly to reduce a time required to carry out the chamfering operation, thereby leading to reduction in the machining cost. Therefore, there is an effect that is it possible to reduce cost required for the entirety of the spline rolling tool as a product. 
     In the spline-rolling-tool manufacturing process of the present invention, since the crest removing step is implemented to form the incomplete toothed region having the curved surface portion, the flat surface portion and the slant surface portion in the one widthwise end portion of each of the forming teeth, it is possible to manufacture the spline rolling tool capable of rolling the splines in each of which a root diameter defined by roots of the respective splines is changed in an axial direction of the workpiece. That is, by using the spline rolling tool, it is possible to roll the splines in each of which a shoulder having a large diameter is provided in a ramped end portion of the spline so that a torsional strength of the ramped end portion is improved. 
     If the forming teeth are subjected to the crest removing operation performed by the grinding wheel in the crest removing step, the periphery of the incomplete toothed region would become a sharp edge whereby durabilities of the forming teeth and splines could be reduced. However, in the spline-rolling-tool manufacturing process of the present invention, the chamfering step is implemented whereby the chamfered edge is formed throughout the periphery of the incomplete toothed region to have a rounded cross-section and the surface roughness of not larger than about 3.2 μm. Therefore, it is possible to restrain each of the forming teeth from being chipped or otherwise damaged and accordingly to manufacture the spline rolling tool of high durability. 
     Since the splines are rolled in the workpiece by using the spline rolling tool having the above-described chamfered edge in the periphery of the incomplete toothed region, it is possible to restrain formation of an angular portion in the ramped end portion of each of the splines and also to improve a surface smoothness of the ramped end portion. Therefore, in the spline-rolling-tool manufacturing process of the present invention, there is an effect that it is possible to manufacture the spline rolling tool capable of rolling the splines each having a high strength in the workpiece. 
     Further, in the chamfering step, the incomplete toothed region formed in the crest removing step is subjected to the chamfering operation using the wire brush having the plurality of bristles to which the abrasive grains adhere, whereby the chamfered edge is formed in the periphery of the incomplete toothed region such that the chamfered edge has the rounded cross section and the surface roughness thereof is not larger than about 3.2 μm. 
     Therefore, even in a case where the incomplete toothed region has a complicated shape with the curved surface portion, the flat surface portion and the slant surface portion as in the present invention, it is possible to cause the bristles to be flexed to follow the complicated shape of the incomplete toothed region. Accordingly, it is possible to efficiently and accurately form the chamfered edge having the rounded cross-section with the surface roughness of not larger than about 3.2 μm in the periphery of the incomplete toothed region. 
     Consequently, it is possible to uniformly form the chamfered edge having the rounded cross-section, and accordingly to avoid the problem of increase in variation in the shape and surface roughness of the chamfered portion, which problem has been encountered in the conventional manufacturing process requiring the handwork operation to form the chamfered portion therein. Therefore, it is possible to restrain chipping or other damage of each of the forming teeth and accordingly to improve durability of the spline rolling tool. 
     Further, by using this spline rolling tool, it is possible to restrain formation of an angular portion in the ramped end portion of each of the splines and also to improve a surface smoothness of a rolled surface of the workpiece. Therefore, there is an effect that the splines each having a high strength can be rolled in the workpiece. 
     Further, in a conventional manufacturing process, there has been a problem of reduction in a non-chamfered portion of each of the forming teeth, since each of the forming teeth has been likely to be chamfered too much in the chamfering operation. However, in the manufacturing process of the present invention in which the wire brush is caused to cut an angular portion of each of the forming teeth having a relatively low rigidity, there is an effect that it is possible to assuredly obtain a non-chamfered portion of each of the forming teeth. Therefore, since accuracy in the shape of each of the forming teeth can be improved, there is an effect that it is possible to roll the splines each having a high accuracy, and accordingly to improve accuracy in fitting of each of the splines. 
     Further, since the chamfering step is performed by rotating and parallelly moving the wire brush in the single direction, the chamfered edge can be formed in an extremely short length of time. That is, it is not necessary to carry out a complicated operation such as a machining operation with use of a numerically controlled machine tool in which a grinding wheel is fed through a three controllable axes of the machine tool so as to be moved along the periphery of the incomplete toothed region of each of the multiplicity of forming teeth provided in the toothed forming face. Thus, the chamfered edges can be formed in the multiplicity of forming teeth at one time. Consequently, it is possible to simplify the chamfering step and accordingly to reduce a time required to carry out the chamfering operation, thereby leading to reduction in the machining cost. Therefore, there is an effect that is it possible to reduce cost required for manufacturing the spline rolling tool. 
     In the spline-rolling-tool manufacturing process of the present invention, in addition to the effects provided by the spline-rolling-tool manufacturing process noted above, there is an effect that it is possible to cause each of the bristles of the wire brush to be appropriately brought into contact with the periphery of the incomplete toothed region and accordingly to highly efficiently and reliably carry out the chamfering operation even in a case where the incomplete toothed region has a complicated shape with the curved surface portion, the flat surface portion and the slant surface portion as in the present invention, since the wire brush is moved in the direction (the single direction) that is substantially perpendicular to the width direction of each of the forming teeth. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  A set of views showing a spline rolling tool according to an embodiment of the present invention, wherein views (a) and (b) are upper and side views of the spline rolling tool, respectively. 
         FIG. 2A  A cross sectional view of the spline rolling tool, taken along line  2 A- 2 A of view (a) of  FIG. 1 . 
         FIG. 2B  A side view of the spline rolling tool, as seen from a direction of arrow  2 B of  FIG. 2A . 
         FIG. 3  A perspective view of forming teeth that are ground to be formed in a teeth forming step. 
         FIG. 4  A perspective view of the forming teeth in each of which an incomplete toothed region is formed by a crest removing operation in a crest removing step. 
         FIG. 5  A perspective view of the forming teeth in each of which a chamfering edge is formed by a chamfering operation in a chamfering step. 
         FIG. 6  A bottom view of a wire brush. 
         FIG. 7  A schematic view schematically showing the chamfering operation performed on the forming tooth by the wire brush. 
         FIG. 8  A cross sectional view of a spline having a shoulder. 
     
    
    
     EXPLANATION OF REFERENCE SIGNS 
     
         
           1  spline rolling tool 
           11  toothed  1  forming face 
           12  forming teeth 
           30  incomplete toothed region 
           30   a  curved surface portion 
           30   b  flat surface portion 
           30   c  inclined surface portion 
           40  chamfered edge 
           70  wire brush 
           72   a  bristle 
           100  spline 
         L single direction 
       
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     Hereinafter, a preferred embodiment of the present invention will be described with reference to the drawings.  FIG. 1  is a set of views for explaining a spline rolling tool  1  according to an embodiment of the present invention, wherein views (a) and (b) are upper and side views of the spline rolling tool  1 , respectively. It is noted that incomplete toothed regions  30  and chamfered edges  40  are not shown in  FIG. 1 . 
     Referring first to  FIG. 1 , an overall construction of the spline rolling tool  1  is described first. The spline rolling tool  1  is a tool that is to be used for causing plastic deformation on an outer circumferential surface of a workpiece provided by a cylindrical material so as to roll splines  100  (see  FIG. 8 ) in each of which a shoulder  101   a  is provided in a ramped end portion of a root  101  of the spline  100 . 
     In  FIG. 1 , one of a pair of spline rolling tools  1  that are to be fixed to a rolling apparatus (not shown) is shown, while the other of the spline rolling tools  1  that is to be parallelly moved relative to the one of the spline rolling tools  1  is not shown. 
     The spline rolling tool  1  has a generally elongated, rectangular-parallelepiped body, as shown in  FIG. 1 , which is made of alloy tool steel, high speed tool steel or other metallic material that is suitable for a rolling work. In an upper surface (which is located in a top side of a drawing sheet of view (a) of  FIG. 1  and which is located in an upper side in view (b) of  FIG. 1 ), a toothed forming face  11  is provided to roll the splines  100  (see  FIG. 8 ) in the outer circumferential surface of the workpiece. 
     The toothed forming face  11  has a biting portion  11   a , a finishing portion  11   b  and a relief portion  11   c , as shown in  FIG. 1 , which are arranged in this order as seen in a direction from a rolling initiation or leading end (right end in  FIG. 1 ) of the spline rolling tool  1  toward a trailing end (left end in  FIG. 1 ). 
     The biting portion  11   a  is used so that the toothed forming surface  11  bites into an outer circumferential surface of the workpiece. As shown in view (b) of  FIG. 1 , the biting portion  11   a  is upwardly inclined with an inclination angle k 1  as it extends from the leading end (right end in  FIG. 1 ) of the spline rolling tool  1  to the finishing portion  11   b  left end in  FIG. 1 ). 
     The finishing portion  11   b  is a portion serving for finishing the splines  100  (see  FIG. 8 ) that are rolled in the workpiece by the biting portion  11   a . As shown in view (b) of  FIG. 1 , the finishing portion  11   b  is substantially parallel with a supported surface (lower surface of the spline rolling tool  1 . 
     The relief portion  11   c  is is a portion serving for releasing the workpiece from the toothed forming surface  11 . As shown in view (b) of  FIG. 1 , the relief portion  11   c  is downwardly inclined with an inclination angle k 2  as it extends from a terminal end of the finishing portion  11   b  to the trailing end (left end in  FIG. 1 ) of the spline rolling tool  1 . 
     On the toothed forming surface  11  constituted by the leading end portion  11   a , the finishing portion  11   b  and the relief portion  11   c , there are formed a plurality of tooth profiles (hereinafter referred to as “forming teeth”)  12 . The plurality of forming teeth  12  are successively arranged in a rolling feed direction (longitudinal direction of the rectangular-parallelepiped body of the spline rolling tool  1  corresponding to a horizontal direction as seen in  FIG. 1 ) at a constant pitch that is dependent upon an outer circumferential dimension of the workpiece. Each of the forming teeth  12  is arranged to extend in a direction (vertical direction as seen in view (a) of  FIG. 1 ) that is substantially perpendicular to the rolling feed direction. The workpiece is rolled and moved relative to the toothed forming surface  11  from the leading end toward the trailing end, whereby the splines  100  (see  FIG. 8 ) are formed on the outer circumferential surface of the workpiece. 
     Referring next to  FIGS. 2A and 2B , there will be described a construction of each of the forming teeth  12  in detail.  FIG. 2A  shows a cross sectional view of the spline rolling tool  1 , taken along line  2 A- 2 A of view (a) of  FIG. 1 , while  FIG. 2B  shows a side view of the spline rolling tool, as seen from a direction of arrow  2 B of  FIG. 2A . It is noted that  FIG. 2A  corresponds to a cross sectional view taken along a tooth root line  12   b  of each of the forming teeth  12 . 
     As described above, each of the forming teeth  12  is a portion that is to bite into the outer circumferential surface of the workpiece, so as to plastically deform the outer circumferential surface of the workpiece, for thereby rolling the splines  100 . As shown in  FIGS. 2A and 2B , each of the forming teeth  12  includes an incomplete toothed region  30  which is located in an end portion (right end in  FIGS. 2A and 2B ) as viewed in a width direction of the forming tooth  12  (horizontal direction in  FIG. 2A ) and which is formed by a crest removing operation. Each of the forming teeth  12  further includes a chamfered edge  40  which is a periphery of an incomplete-toothed region surface in the incomplete toothed region  30  and which is formed by a chamfering operation. 
     The incomplete toothed region  30  is a region in which a height of the tooth is relatively low, so that the shoulder  101   a  can be formed in the root  101  of the spline  100  (see  FIG. 8 ). As shown in  FIGS. 2A and 2B , in the incomplete toothed region  30 , a crest of each forming tooth  12  is removed such that an upper end of each forming tooth  12  is defined by the incomplete-toothed region surface that is constituted principally by a curved surface portion  30   a , a flat surface portion  30   b  and an inclined surface portion  30   c.    
     As shown in  FIGS. 2A and 2B , the curved surface portion  30   a  is located in an end portion (right end in  FIG. 2A ) as viewed in a width direction of the forming tooth  12  (horizontal direction in  FIG. 2A ), and is formed to have an arcuate cross-section. The flat surface portion  30   b  is contiguous to the curved surface portion  30   a , and is formed to be substantially parallel to the crest of the forming tooth  12 . The slant surface portion  30   c  is contiguous to the flat surface portion  30   b , and is formed to be inclined upwardly as it extends from the flat surface portion  30   b  to another end portion (left end in  FIG. 2B ) as viewed in the width direction of the forming tooth  12 . 
     Where the splines are rolled in the workpiece by this spline rolling tool  1 , each of the splines can be formed such that a root diameter defined by the roots of the respective splines is changed in a direction of an axis of the workpiece and such that a shoulder having a large diameter is formed in a ramped end portion of each of the splines (see  FIG. 8 ). Consequently, it is possible to roll the splines in each of which a torsional strength of the ramped end portion is improved. 
     Where the forming teeth  12  are subjected to the crest removing operation to form the respective incomplete toothed regions  30 , the periphery of each incomplete toothed region  30  would become a sharp edge whereby durabilities of the forming teeth  12  and splines could be reduced. In view of this, in the spline rolling tool  1  of the present invention, the periphery of each incomplete toothed region  30  is subjected to a chamfering operation, as described below, whereby the chamfered edge  40  is formed in the periphery of each incomplete toothed region  30 . 
     Owing to the formation of the chamfered edge  40 , it is possible to restrain chipping or other damage of each of the forming teeth  12  and accordingly to improve durability of the spline rolling tool  1 . Further, by using this spline rolling tool  1 , it is possible to restrain formation of an angular portion in the ramped end portion of each of the splines, so that the splines each having a high strength can be rolled in the workpiece. 
     The chamfered edge  40  is formed in the periphery of the incomplete-toothed region surface of the incomplete toothed region  30  to have a rounded cross-section (see  FIG. 5 ), by a wire brush  70  (see  FIG. 6 ) having a plurality of bristles  72   a  to which abrasive grains adhere, as described below. 
     Further, the chamfered edge  40  is formed to have a surface roughness of not larger than about 3.2 μm. Therefore, by using this spline rolling tool  1 , it is possible to improve a surface smoothness of the ramped end portion of each of the splines, so that the splines each having a high strength can be rolled in the workpiece. Consequently, the durability of each of the splines can be improved. 
     Referring next to  FIGS. 3-5 , there will be described a process of manufacturing the spline rolling tool  1 .  FIG. 3  is a perspective view of the forming teeth  12  that have been ground in a teeth forming step.  FIG. 4  is a perspective view of the forming teeth  12  in each of which the incomplete toothed region  30  that has been formed in a crest removing step.  FIG. 5  is a perspective view of the forming teeth  12  in each of which the chamfering edge  40  has been formed in a chamfering step. 
     For manufacturing the spline rolling tool  1 , a die material made of a metallic material such as alloy tool steel and high-speed tool steel is first cut to have a substantially rectangular parallelepiped shape, and is then subjected to a heat treatment. Then, the forming teeth  12  are formed in a surface of the die material that has been subjected to the heat treatment, by a grinding operation using a grinding wheel (teeth forming step). 
     That is, in the teeth forming step, by rotating the grinding wheel having a disk shape while parallelly moving the grinding wheel in a direction of arrow W shown in  FIG. 3  (width direction of the spline rolling tool  1 , i.e., vertical direction in view (a) of  FIG. 1 ), the multiplicity of forming teeth  12  are formed in the toothed forming face  11  (see  FIG. 1 ), as shown in  FIG. 3 . 
     The grinding wheel used in the teeth forming step has a cross section that is configured to correspond to a cross sectional shape of one or two forming teeth  12  (one or two grooves between the forming teeth  12 ) (i.e., shape defined by arcuate portions of teeth roots and crests, and straight line portions connecting the arcuate portions). In common case, one or two forming teeth  12  (one or two grooves between the forming teeth  12 ) are formed by one stroke movement of the grinding wheel in the direction of arrow W. 
     In the present embodiment, a total of 243 forming teeth  12  (188 forming teeth in the leading portion  11   a,  43 forming teeth in the finishing portion  11   b , and  12  forming teeth in the relief portion  11   c ) are formed. Each forming tooth  12  has a height of about 0.975 mm as a maximum value. A pitch between the forming teeth  12  (as measured in the rolling direction) is about 2.503 mm. 
     After the teeth forming step, the crest removing step is implemented to carry out a crest removing operation on the forming teeth  12 . In the crest removing step, as in the teeth forming step, a grinding wheel having a disk shape is rotated and parallelly moved in a direction of arrow L shown in  FIG. 4  (direction substantially perpendicular to the width direction of each forming tooth  12 , i.e., direction substantially perpendicular to the vertical direction in view (a) of  FIG. 1 ), for thereby carrying out the crest removing operation in the end portion as viewed in the width direction of the forming tooth  12 , so as to form the incomplete toothed regions  30  in the respective forming teeth  12 , as shown in  FIG. 4 . 
     The grinding wheel used in the crest removing step has a cross section that is configured to correspond to a shape of a cross section of each forming tooth  12  in the incomplete toothed region  30  (i.e., a shape of a cross section created by a plane cutting each forming tooth  12  in the incomplete toothed region  30  and parallel to the width direction of the forming tooth  12 ). In common case, the plurality of forming teeth  12  are successively subjected to the crest removing operation, by one stroke movement of the grinding wheel in the direction of arrow L, so as to form the incomplete toothed region  30  (in which the upper end of each forming tooth  12  is defined by the incomplete-toothed region surface that includes the curved surface portion  30   a , the flat surface portion  30   b  and the inclined surface portion  30   c ) in each forming tooth  12 , as shown in  FIG. 4 . 
     In the present embodiment, an amount of removal of an upper portion of each forming tooth  12  (i.e., a distance between the crest of each forming tooth  12  and the flat surface portion  30   b ) is about 0.238 mm. A radius of curvature of the curved surface portion  30   a  is about 5.5 mm. An inclination angle of the inclined surface portion  30   c  (i.e., an angle defined between the flat surface portion  30   b  and an extension of the inclined surface portion  30   c ) is about 12°. A length of the incomplete toothed region  30  (as measured in the widthwise direction of each forming tooth  12 ) is about 7.5 mm. 
     Where the forming teeth  30  are subjected to the crest removing operation in the crest removing step, the periphery of the incomplete-toothed region surface of the incomplete toothed region  30  would become a sharp edge, and burrs could be left in the periphery, whereby the forming teeth  12  could be easily chipped or otherwise damaged. Further, an angular portion could be formed in each of the splines  100  that are rolled by such forming teeth  12 , so that each spline  100  could suffer from a stress concentrated at the angular portion. 
     For avoiding such a problem, after the crest removing operation in the crest removing step, the chamfering step is implemented to carry out the chamfering operation on the forming teeth  12 . The chamfering operation is carried out by using the wire brush  70 . Referring now to  FIGS. 6  and  7 , there will be described a construction of the wire brush  70  in detail. 
       FIG. 6  is a bottom view of the wire brush  70 . In  FIG. 6 , only some of a multiplicity of bristle clusters  72  is illustrated by solid lines, while the other bristle clusters  72  are schematically illustrated by two-dot chain lines. 
     As shown in  FIG. 6 , the wire brush  70  is constituted to have the multiplicity of bristle clusters  72  disposed on a bottom surface of a substrate member  71 . In the present embodiment, the substrate member  71  is provided by a disk-shaped body made of aluminum alloy and having a diameter of about 150 mm. The bristle clusters  72  are arranged in two lines extending along respective two virtual circles that are coaxial with an axis of the disk-shaped substrate member  71 . The bristle clusters  72  arranged in a radially inner one of the two lines are disposed in a total of 20 portions that are circumferentially spaced apart from each other by an angular pitch of about 18°. The bristle clusters  72  arranged in a radially outer one of the two lines are disposed in a total of 30 portions that are circumferentially spaced apart from each other by an angular pitch of about 12°. 
     Each of the bristle clusters  72  consists of total of 30 bristles  72   a  that are densely located within a virtual circle having a diameter of about 10 mm. Each of the bristles  72   a  is provided by a line-shaped resin material such as nylon, to which abrasive grains adhere (or which contain the abrasive grains). Each of the bristles  72   a  has a diameter of about 1 mm, and a length (i.e., dimension of its projection from the bottom surface of the substrate member  71 ) of about 13 mm. The abrasive grains are provided by GC (Green Carbon Random) as grain material, and has a grain size of # 120 . 
       FIG. 7  is a schematic view schematically showing the chamfering operation performed on the forming teeth  12  by the wire brush  70 . The wire brush  70  is rotated about the axis of the disk-shaped substrate member  71 , and is moved in the direction indicated by arrow L shown in  FIG. 7 . In this instance, the bristles  72   a  are moved while being flexed to have an arcuate shape, as shown in  FIG. 7 , so as to follow the complicated shape of the incomplete-toothed region surface of the incomplete toothed region  30 . Therefore, the periphery of the incomplete-toothed region surface of the incomplete toothed region  30  can be chamfered to have an arcuate cross sectional shape that is constant over an entirety of the periphery of the incomplete-toothed region surface of the incomplete toothed region  30 ′. 
     If the chamfering is performed by a handwork operation as conventionally practiced, the forming teeth  12  could be chamfered too much, thereby resulting in problematic reduction in a non-chamfered portion of each of the forming teeth  12 . In the present invention, however, since it is possible to cause the bristles  72  of the wire brush  70  to cut an angular portion of each of the forming teeth  12  having a relatively low rigidity, it is possible to assuredly obtain the non-chamfered portion of each of the forming teeth  12 . Consequently, it is possible to improve accuracy in fitting of each of the splines that is rolled in the workpiece. 
     Referring back to  FIG. 5 , the chamfering operation is described. In the chamfering operation, the wire brush  70  constructed as described above is parallelly moved in the direction indicated by arrow L shown in  FIG. 5  (the same direction as the direction of arrow L in  FIG. 4 ) while being rotated, whereby the chamfering operation is performed on the forming teeth  12  by the abrasive grains adhering to the bristles  72   a  of the wire brush  70 . Thus, the chamfered edge  40  is formed in the periphery of the incomplete-toothed region surface of the incomplete toothed region  30 , as shown in  FIG. 5 . 
     In the chamfering operation, the plurality of forming teeth  12  (the peripheries of the incomplete-toothed region surface of the incomplete toothed regions  30 ) are successively subjected to the crest removing operation, by one stroke movement of the wire brush  70  in the direction of arrow L, thereby making it possible to complete the chamfering step in an extremely short length of time. 
     That is, the chamfering operation can be performed successively on the multiplicity of forming teeth  12  provided in the toothed forming face  11 , without having to carry out a complicated operation such as a machining operation with use of a numerically controlled machine tool in which a grinding wheel is fed through a three controllable axes of the machine tool so as to be moved along the periphery of the incomplete-toothed region surface of the incomplete toothed region  30  of every one of the multiplicity of forming teeth  12  of the toothed forming face  11 . Consequently, it is possible to simplify the chamfering step and accordingly to remarkably reduce a time required to carry out the chamfering operation, thereby leading to reduction in the machining cost and consequent reduction in cost for manufacturing the spline rolling tool  1 . 
     Further, since the direction (direction of arrow L) of the parallel movement of the wire brush  70  is substantially perpendicular to the width direction of each of the forming teeth  12 , it is possible to cause each of the bristles  72   a  of the wire brush  70  to be appropriately brought into contact with the periphery of the incomplete-toothed region surface of the incomplete toothed region  30 . Accordingly, it is possible to efficiently and reliably carry out the chamfering operation, even in a case where the incomplete-toothed region surface of the incomplete toothed region  30  is a complicated shape having the curved surface portion  30   a , the flat surface portion  30   b  and the slant surface portion  30   c  as in the present invention. 
     Further, since the direction (direction of arrow L) of the parallel movement of the wire brush  70  coincides with the direction (direction of arrow L) of the movement of the grinding wheel for the crest removing operation performed on the forming teeth  12 , it is possible to suitably remove burrs by the bristles  72   a  of the wire brush  70 , if the burrs are left in the peripheries of the incomplete-toothed region surfaces of the respective incomplete toothed regions  30  after the crest removing operation. 
     If the wire brush  70  were parallelly moved in a direction (direction of the width of each forming tooth  12 ) substantially perpendicular to the direction of arrow L, a direction of displacement of each of the bristles  72   a  as a result of rotation of the wire brush  70  would be substantially perpendicular to the width direction of each forming tooth  12 , so that the burrs removed by the bristles  72   a  would be slid, together with the bristles  72   a , on the incomplete-toothed region surfaces and the chamfered edges  40  in the incomplete toothed regions  30 , thereby damaging the surfaces of the incomplete-toothed region surfaces and the chamfered edges  40 . 
     On the other hand, since the wire brush  70  is parallelly moved in the direction of arrow L, the direction of displacement of each of the bristles  72   a  as a result of rotation of the wire brush  70  coincides with the width direction of each forming tooth  12 , thereby making it possible for the bristles  72   a  to carry the removed burrs away from the forming teeth  12 . Thus, the chamfering operation can be performed to form the chamfered edges  40 , without damaging the incomplete-toothed region surfaces and the chamfered edges  40  by the removed burrs. 
     The wire brush  70  is fixed in a height position permitting distal ends of the respective bristles  72   a  to be aligned with lower ends of the respective incomplete-toothed region surfaces of the curved surface portion  30   a , and is parallelly moved in the direction of arrow L shown in  FIG. 5  while being fixedly held in such a height position. In the present embodiment, while the wire brush  70  is held in the height position, the distal ends of the respective bristles  72   a  are positioned to be lower than the crests of the forming teeth  12 , by about 5.738 mm that corresponds to a sum of about 0.238 mm as the amount of removal of the upper portions of the respective forming teeth  12  and about 5.5 mm as the radius of curvature of the curved surface portions  30   a.    
     While the present invention has been described based on the embodiment, it is to be easily imagined that the present invention is not at all limited to the details of the above-described embodiment but may be subjected to various improvements and modifications within a range that is not deviated from the gist of the invention. 
     For example, numerical values described above in the description of the embodiment are merely examples, and the numerical values may be changed as needed. 
     Further, the present invention is not limited to the above-described embodiment in which the crest removing operation is performed on only the one widthwise end portion of each forming tooth  12 . That is, the crest removing operation may be performed on widthwise opposite end portions of each forming tooth  12 .