Patent Publication Number: US-2016236321-A1

Title: Truing method and truing device

Description:
TECHNICAL FIELD 
     The present invention relates to a method of truing a cylindrical grindstone which is used in a grinding machine or the like, and also to a truing apparatus for realizing the truing method. 
     BACKGROUND ART 
     A cylindrical grindstone which is used in a grinding machine or the like is subjected to truing for the purposes of elimination of runout of the grinding surface, coincidence with the shape of the article to be processed, and the like. In truing, the shape of the grindstone is adjusted by using a truer provided with a diamond roll or the like which is higher in hardness than the grindstone. 
     Usually, a work of adjusting the shape of a grindstone is called truing, and that of exposing or fracturing abrasive grains of a grindstone to resharpen a grindstone is called dressing. In the application, however, both a work of adjusting the shape of a grindstone, and a work of adjusting the shape of a grindstone and exposing or fracturing abrasive grains of the grindstone are called truing. 
     For example, Patent Reference 1 describes a truing apparatus in which truing is performed by relatively moving a truer that is rotated about a truer rotation axis parallel to a grindstone rotation axis of a cylindrical grindstone, along the outer circumferential surface of the grindstone, and grindstone arcuate surfaces that are on the both sides of the outer circumferential surface of the grindstone. 
     In the truing apparatus described in Patent Reference 1, a pin portion of a crankshaft is ground by the outer circumferential surface of the cylindrical grindstone, and the arcuate surfaces in the boundaries between the outer circumferential surface and end surfaces of the grindstone, and the end surfaces of the grindstone are not used (the article to be processed does not require the end surfaces of the grindstone). 
     As shown in  FIG. 9 , therefore, a truer  170  having a roll  170 D which is rotated about a truer rotation axis TJ 1  parallel to a grindstone rotation axis XJ is used, and the truer  170  is moved relative to a grindstone  151  in a state where the truer rotation axis TJ 1  is maintained parallel to the grindstone rotation axis XJ. 
     In truing, as shown in  FIG. 9 , one outer circumference arcuate surface  151 VR is trued from a position PDR on one grindstone arcuate surface  151 ER of the grindstone  151  and in the vicinity of one grindstone end surface  151 TR, toward a grindstone outer circumferential surface  151 G, the grindstone outer circumferential surface  151 G is then trued toward the other grindstone arcuate surface  151 EL, and the other outer circumference arcuate surface  151 VL is then trued. After the truer  170  reaches a position PDL on the other grindstone arcuate surface  151 EL and in the vicinity of the other grindstone end surface  151 TL, the truer  170  is separated from the grindstone  151 . 
     PRIOR ART REFERENCE 
     Patent Reference 1: JP-A-H03-277468 
     SUMMARY OF THE INVENTION 
     Problems that the Invention is to Solve 
     In the truing apparatus described in Patent Reference 1, a region (region including the grindstone end surface  151 TR) extending from the position PDR shown in  FIG. 9  to an end surface terminal position PZR, and a region (region including the grindstone end surface  151 TL) extending from the position PDL to an end surface terminal position PZL are not trued, and therefore the apparatus cannot cope with processing of an article to be processed which requires the accuracies of the end surfaces of a grindstone. As shown in  FIG. 9 , the inner diameter side of the roll  170 D of the truer  170  is projected in the direction of the truer rotation axis TJ 1 . In the state where the truer rotation axis TJ 1  is maintained parallel to the grindstone rotation axis XJ, in a case where the grindstone end surfaces  151 TR,  151 TL shown in  FIG. 9 , and grindstone arcuate surfaces (end surface arcuate surfaces  151 UR,  151 UL in  FIG. 9 ) in the vicinity of the grindstone end surfaces are to be trued, therefore, portions which are projected from the roll  170 D interfere with the grindstone  151 , and hence truing cannot be performed. Angles θ 1 , θ 2  indicating the ranges of the end surface arcuate surfaces  151 UR,  151 UL shown in  FIG. 9  are, for example, about 10 degrees. 
     Therefore, the truing apparatus described in Patent Reference 1 cannot process an article to be processed in which requires the accuracies of the grindstone end surfaces  151 TR,  151 TL shown in  FIG. 9 , and the end surface arcuate surfaces  151 UR,  151 UL) in the vicinity of the grindstone end surfaces. 
     The invention has been conducted in view of this. It is an object of the invention to provide a grindstone truing method for adequately processing an article to be processed which requires the accuracies of grindstone end surfaces, and those of grindstone arcuate surfaces in the vicinity of the grindstone end surfaces, and to provide a truing apparatus. 
     Means for Solving the Problems 
     In order to solve the problem, the truing method and apparatus of the invention employ the following means. 
     Firstly, one aspect of the invention is a truing method which performs truing by using: first and second truers which trues a cylindrical grindstone that is rotated about a grindstone rotation axis to grind a workpiece; a moving unit which is configured to change a relative position between the first truer and the grindstone, and a relative position between the second truer and the grindstone; and a controlling unit which is configured to control the moving unit, wherein the first truer has a first roll which is rotated about a first truer rotation axis that is parallel to the grindstone rotation axis, the second truer has a second roll which is rotated about a second truer rotation axis that is perpendicular to the grindstone rotation axis, the grindstone has: a grindstone outer circumferential surface which is a surface that is parallel to the grindstone rotation axis; grindstone end surfaces which are surfaces that are perpendicular to the grindstone rotation axis; and grindstone arcuate surfaces which are surfaces in boundaries between the grindstone outer circumferential surface and the grindstone end surfaces, and which are formed into an arcuate shape, the truing method comprising: controlling the moving unit by the controlling unit, in a state where the first truer rotation axis is maintained parallel to the grindstone rotation axis, to true, by using the first truer, the grindstone outer circumferential surface, and outer circumference arcuate surfaces which are partial surfaces of the grindstone arcuate surfaces and which are continuous to the grindstone outer circumferential surface; and controlling the moving unit by the controlling unit, in a state where the second truer rotation axis is maintained in a direction perpendicular to the grindstone rotation axis, to true, by using the second truer, the grindstone end surfaces, and end surface arcuate surfaces which are remaining surfaces of the grindstone arcuate surfaces and which are continuous to the grindstone end surfaces. 
     In the above configuration, truing is performed by using two truers, i.e., the first truer having the first roll which is rotated about the first truer rotation axis that is parallel to the grindstone rotation axis, and the second truer having the second roll which is rotated about the second truer rotation axis that is perpendicular to the grindstone rotation axis. Moreover, the grindstone arcuate surfaces are divided into the outer circumference arcuate surfaces which are on the side close to the grindstone outer circumferential surface, and the end surface arcuate surfaces which are on the sides close to the grindstone end surfaces, the grindstone outer circumferential surface and the outer circumference arcuate surfaces are trued by the first truer, and the grindstone end surfaces and the end surface arcuate surfaces are trued by the second truer. 
     According to the configuration, the grindstone outer circumferential surface, the grindstone end surfaces, and the grindstone arcuate surfaces can be adequately trued without causing the grindstone and the first truer, and the grindstone and the second truer to interfere with each other. Therefore, it is possible to adequately process an article to be processed which requires the accuracies of grindstone end surfaces, and those of the grindstone arcuate surfaces in the vicinity of the grindstone end surfaces. 
     In one aspect of the invention, when truing is performed by using the first truer, one of the outer circumference arcuate surfaces is trued from a position remotest from the grindstone outer circumferential surface in the one outer circumference arcuate surface, toward a position closest to the grindstone outer circumferential surface in the one outer circumference arcuate surface, the grindstone outer circumferential surface is then trued from a position closest to the one outer circumference arcuate surface in the grindstone outer circumferential surface, toward a position closest to the other outer circumference arcuate surface in the grindstone outer circumferential surface, and the other outer circumference arcuate surface is then trued from a position closest to the grindstone outer circumferential surface in the other outer circumference arcuate surface, toward a position remotest from the grindstone outer circumferential surface in the other outer circumference arcuate surface. 
     When truing is performed by using the second truer, one of the end surface arcuate surfaces is trued from a position remotest from one of the grindstone end surfaces in the one end surface arcuate surface, toward a position closest to the one grindstone end surface in the one end surface arcuate surface, and the one grindstone end surface is then trued from a position closest to the one end surface arcuate surface in the one grindstone end surface, toward a position remotest from the one end surface arcuate surface in the one grindstone end surface, and the other end surface arcuate surface is trued from a position remotest from the other grindstone end surface in the other end surface arcuate surface, toward a position closest to the other grindstone end surface in the other end surface arcuate surface, and the other grindstone end surface is then turned from a position closest to the other end surface arcuate surface in the other grindstone end surface, toward a position remotest from the other end surface arcuate surface in the other grindstone end surface. 
     According to the configuration, truing is performed by using the first truer in the sequence of the one outer circumference arcuate surface, the grindstone outer circumferential surface, and the other outer circumference arcuate surface, and truing is performed by using the second truer in the sequence of the one end surface arcuate surface and the one grindstone end surface, and in the sequence of the other end surface arcuate surface and the other grindstone end surface. 
     Therefore, all the surfaces which are to be trued, i.e., the grindstone outer circumferential surface, the one grindstone end surface, the other grindstone end surface, the one outer circumference arcuate surface, the other outer circumference arcuate surface, the one end surface arcuate surface, and the other end surface arcuate surface can be trued in an adequate direction and in a shorter period of time. 
     In one aspect of the invention, at a start of truing of the one outer circumference arcuate surface, when the first truer is made relatively close to the grindstone toward the position remotest from the grindstone outer circumferential surface in the one outer circumference arcuate surface, the first truer is relatively moved from a side of the one end surface arcuate surface so as to be moved along a first virtual arc which is a virtual arc having a convex direction that is opposite to a convex direction of the grindstone arcuate surface, the first virtual arc being in contact with the grindstone arcuate surface at a boundary position between the one outer circumference arcuate surface and the one end surface arcuate surface, the first virtual arc having a first diameter. 
     Moreover, at a start of truing of the one end surface arcuate surface, when the second truer is made relatively close to the grindstone toward the position remotest from the grindstone end surface in the one end surface arcuate surface, the second truer is relatively moved from a side of the one outer circumference arcuate surface so as to be moved along a second virtual arc which is a virtual arc having a convex direction that is opposite to the convex direction of the grindstone arcuate surface, the second virtual arc being in contact with the grindstone arcuate surface at the boundary position between the one outer circumference arcuate surface and the one end surface arcuate surface, the second virtual arc having a second diameter. 
     Moreover, at a start of truing of the other end surface arcuate surface, when the second truer is made relatively close to the grindstone toward the position remotest from the grindstone end surface in the other end surface arcuate surface, the second truer is relatively moved from a side of the other outer circumference arcuate surface so as to be moved along a third virtual arc which is a virtual arc having a convex direction that is opposite to the convex direction of the grindstone arcuate surface, the third virtual arc being in contact with the grindstone arcuate surface at a boundary position between the other outer circumference arcuate surface and the other end surface arcuate surface, the third virtual arc having a third diameter. 
     According to the configuration, when truing of the one outer circumference arcuate surface is started by the first truer, the first truer is relatively moved so as to be moved along the first virtual arc; when truing of the one end surface arcuate surface is started by the second truer, the second truer is relatively moved so as to be moved along the second virtual arc; and, when truing of the other end surface arcuate surface is started by the second truer, the second truer is relatively moved so as to be moved along the third virtual arc. 
     Therefore, the boundary positions functioning as a place connecting a place trued by the first truer with that trued by the second truer, and between the one outer circumference arcuate surface and the one end surface arcuate surface, and between the other outer circumference arcuate surface and the other end surface arcuate surface can be trued more smoothly and more uniformly. 
     In an aspect invention of the invention, the boundary position which is between the outer circumference arcuate surface and the end surface arcuate surface in the grindstone arcuate surface is a position where a first virtual line that passes through a center of an arc of the grindstone arcuate surface before truing, and that has an angle of 45 degrees with respect to the grindstone rotation axis, intersects with the grindstone arcuate surface. 
     According to the configuration, the boundary position between the outer circumference arcuate surface and the end surface arcuate surface can be set to an adequate position. 
     The truing amounts (amounts in the arcuate direction) of the arcuate portions (grindstone arcuate surfaces) of the first truer and the second truer are the same, and therefore excellent accuracies of the arcuate portions of the grindstone (grindstone arcuate surfaces) can be attained. 
     In an aspect of the invention, the boundary position which is between the outer circumference arcuate surface and the end surface arcuate surface in the grindstone arcuate surface is a position where, in a case where a depth by which the grindstone outer circumferential surface is to be trued is indicated as ΔD, and a depth by which the grindstone end surface is to be trued is indicated as ΔW, a second virtual line intersects with the grindstone arcuate surface, the second virtual line that passes through a center of an arc of the grindstone arcuate surface before truing, and a center of the arc after truing which is a position that is further separated by ΔW in a direction separating from the grindstone end surface from a position that is moved from the center of the arc before truing by ΔD in a direction separating from the grindstone outer circumferential surface. 
     According to the configuration, the boundary position between the outer circumference arcuate surface and the end surface arcuate surface can be set to an adequate position corresponding to the machining allowance due to truing. 
     When the truing amounts (amounts in the arcuate direction) of the arcuate portions (grindstone arcuate surfaces) of the first truer and the second truer are set to values respectively corresponding to the truing depths of the first truer and the second truer, excellent accuracies of the arcuate portions of the grindstone (grindstone arcuate surfaces) can be attained. 
     An aspect of the invention is a truing apparatus comprising: a first truer which is disposed for truing a cylindrical grindstone that is rotated about a grindstone rotation axis to grind a workpiece, and which has a first roll which is rotated about a first truer rotation axis that is parallel to the grindstone rotation axis; a second truer which is disposed for truing the grindstone, and which has a second roll which is rotated about a second truer rotation axis that is perpendicular to the grindstone rotation axis; a moving unit which is configured to change a relative position between the first truer and the grindstone, and a relative position between the second truer and the grindstone; and a controlling unit which is configured to control the moving unit, wherein, by using the moving unit and the controlling unit, based on the above-described truing method, the truing apparatus trues the grindstone outer circumferential surface, the grindstone end surfaces, and the grindstone arcuate surfaces of the grindstone. 
     According to the configuration, it is possible to appropriately realize a truing apparatus which can adequately true the grindstone outer circumferential surface, the grindstone end surfaces, and the grindstone arcuate surfaces without causing the grindstone and the truers to interfere with each other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1(A)  is a plan view illustrating an example of the entire configuration of a grinding machine including the truing apparatus of the invention, and  FIG. 1(B)  is a side view of the grinding machine (a view in which a tailstock is omitted). 
         FIG. 2  is a perspective view illustrating approximate shapes and positional relationships of a grindstone (a fragmentary sectional view), a first truer, and a second truer. 
         FIG. 3  is a sectional view illustrating surfaces of a grindstone, i.e., a grindstone outer circumferential surface, grindstone end surfaces, and grindstone arcuate surfaces (outer circumference arcuate surfaces and end surface arcuate surfaces). 
         FIG. 4  is a view illustrating a truing method of a first embodiment. 
         FIG. 5  is a view illustrating the truing method of the first embodiment. 
         FIG. 6  is a view illustrating a truing method of a second embodiment. 
         FIG. 7  is a view illustrating the truing method of the second embodiment. 
         FIG. 8  is a view illustrating an example of a method for setting arc boundary positions functioning as boundaries between outer circumference arcuate surfaces and end surface arcuate surfaces. 
         FIG. 9  is a view illustrating an example of a truing method in the related art. 
     
    
    
     MODE FOR CARRYING OUT THE INVENTION 
     Hereinafter, modes for implementing the invention will be described with reference to the drawings. In the figures, in the case where the X-axis, the Y-axis, and the Z-axis are written, the X-axis, the Y-axis, and the Z-axis are perpendicular to one another, a horizontal direction which is parallel to a workpiece rotation axis WJ that is the rotation axis of a workpiece (article to be processed) W is the X-axis direction, a horizontal direction along which a grindstone  50  is cut into the workpiece W is the Z-axis direction, and a vertical upward direction is the Y-axis direction. 
     [Entire Configuration ( FIGS. 1(A) and 1(B) ) of a Grinding Machine  1 , and Approximate Shapes and Positional Relationships ( FIG. 2 ) of Grindstone  50 , First Truer  70 , and Second Truer  80 ] 
     As shown in the plan view of the grinding machine  1  of  FIG. 1(A) , and the side view of the grinding machine  1  of  FIG. 1(B) , the grinding machine  1  which includes the truing apparatus of the invention has a bed  2 , a headstock  40 , a tailstock  46 , an X-axis movement table  10 , an X-axis direction driving unit  10 M, a Z-axis movement table  20 , a Z-axis direction driving unit  20 M, a grindstone rotation driving unit  50 M, the grindstone  50 , a controlling unit  60 , the first truer  70 , the second truer  80 , etc. In  FIG. 1(B) , the illustration of the tailstock  46  is omitted. 
     The headstock  40  is fixed onto the bed  2 , and includes a main spindle  41 . 
     The main spindle  41  includes a chuck  42  which is rotated about the workpiece rotation axis WJ based on a control signal output from the controlling unit  60  (for example, a numerical control apparatus), and which can grip and release the workpiece W. 
     The tailstock  46  is fixed onto the bed  2 , and includes a center  47 . 
     The center  47  is disposed rotatably about the workpiece rotation axis WJ, movable along the direction (X-axis direction) of the main spindle  41 , and urged in the direction toward the main spindle  41 . 
     The workpiece W is, for example, a crankshaft for a vehicle, gripped by the chuck  42  of the main spindle  41 , pressed toward the main spindle  41  and supported by the center  47 , and rotated about the workpiece rotation axis WJ which is parallel to the X-axis, by rotation of the main spindle  41 . 
     The X-axis movement table  10  is reciprocally moved in the X-axis direction with respect to the bed  2  along guide rails  10 L that are disposed on the bed  2  along the X-axis direction. 
     The X-axis direction driving unit  10 M (for example, an electric motor) rotates a ball screw which is not shown, based on the control signal output from the controlling unit  60  to reciprocally move the X-axis movement table  10  coupled to the ball screw, in the X-axis direction. The moving distance is controlled based on a detection signal output from an encoder  10 E which is disposed in the X-axis direction driving unit  10 M. 
     The Z-axis movement table  20  is reciprocally moved in the Z-axis direction with respect to the X-axis movement table  10  along guide rails  20 L that are disposed on the X-axis movement table  10  along the Z-axis direction. 
     The Z-axis direction driving unit  20 M (for example, an electric motor) rotates a ball screw which is not shown, based on the control signal output from the controlling unit  60  to reciprocally move the Z-axis movement table  20  coupled to the ball screw, in the Z-axis direction. The moving distance is controlled based on a detection signal output from an encoder  20 E which is disposed in the Z-axis direction driving unit  20 M. 
     The X-axis direction driving unit  10 M and the Z-axis direction driving unit  20 M correspond to the moving unit which changes the relative position between the grindstone  50  and the workpiece W, that between the grindstone  50  and the first truer  70 , and that between the grindstone  50  and the second truer  80 . 
     The grindstone rotation driving unit  50 M (for example, an electric motor) generates a rotating driving force for the grindstone, and the generated rotating driving force is transmitted to the grindstone  50  through a power transmitting unit such as a pulley and a belt. 
     The grindstone  50  is supported rotatably about the grindstone rotation axis XJ which is parallel to the X-axis. Also the grindstone rotation axis XJ is located on a virtual plane VM which is an XZ-plane including the workpiece rotation axis WJ (see  FIG. 1(B) ). 
     As described above, the controlling unit  60  receives the detection signals output from the encoders  10 E,  20 E, a rotation angle signal of the main virtual plane VM spindle  41 , and the like, and outputs the control signal for rotating the main spindle  41 , that for driving the X-axis direction driving unit  10 M, and that for driving the Z-axis direction driving unit  20 M. 
     The first truer  70  has a first roll  70 D (a diamond roll or the like) which is rotated about a first truer rotation axis TJ 1  parallel to the grindstone rotation axis XJ, and a roll driving unit  70 M (for example, an electric motor, see  FIG. 2 ) which rotates the first roll  70 D, and is fixed to, for example, the headstock  40 . 
     The second truer  80  has a second roll  80 D (a diamond roll or the like) which is rotated about a second truer rotation axis TJ 2  perpendicular to the grindstone rotation axis XJ, and a roll driving unit  80 M (for example, an electric motor, see  FIG. 2 ) which rotates the second roll  80 D, and is disposed so as to be movable, for example, along guide rails  80 L in the Z-axis direction with respect to the bed  2 . In the case where the workpiece W is supported between the main spindle  41  and the center  47 , the second truer  80  is moved by the controlling unit  60  in the direction separating from the grindstone  50  so as not to interfere with the workpiece W, and, in the case where the workpiece W is not supported between the main spindle  41  and the center  47 , and the grindstone  50  is to be trued, the second truer  80  is moved by the controlling unit  60  in the direction approaching the grindstone  50 . 
     As shown in  FIGS. 1(B)  and  2 , then, the first truer rotation axis TJ 1  and the second truer rotation axis TJ 2  are located on the virtual plane VM which is an XZ-plane including the workpiece rotation axis WJ. 
     Therefore, all the workpiece rotation axis WJ, the grindstone rotation axis XJ, the first truer rotation axis TJ 1 , and the second truer rotation axis TJ 2  are on the virtual plane VM (virtual plane which is parallel to the X-axis and the Z-axis), all the workpiece rotation axis WJ, the grindstone rotation axis XJ, and the first truer rotation axis TJ 1  are parallel to the X-axis, and the second truer rotation axis TJ 2  is parallel to the Z-axis (perpendicular to the X-axis). 
     Referring to  FIG. 2 , the grindstone  50  is configured by a grindstone portion  51  which contains bonding parts and abrasive grains, and which is formed into a cylindrical shape, and a disk-like base portion  52  which holds the grindstone portion  51 . 
     Then, a place in which the outer circumferential surface of the grindstone  50 , and the virtual plane VM are in contact with each other, and truing is performed by using the first truer  70  is indicated as a to-be-trued place T 70 , that in which the end surface of the grindstone  50 , and the virtual plane VM are in contact with each other, and truing is performed by using the second truer  80 , and which corresponds to the right side in  FIG. 2  is indicated as a to-be-trued place T 80 R, and that in which the end surface of the grindstone  50 , and the virtual plane VM are in contact with each other, and truing is performed by using the second truer  80 , and which corresponds to the left side in  FIG. 2  is indicated as a to-be-trued place T 80 L. 
     At this time, in the case where the rotation direction of the grindstone  50  is a rotation direction  50 K shown in  FIG. 2 , when the to-be-trued place T 70  is to be trued, the first roll  70 D is rotated in a rotation direction  70 K; when the to-be-trued place T 80 R is to be trued, the second roll  80 D is rotated in a rotation direction  80 KR; and, when the to-be-trued place T 80 L is to be trued, the second roll  80 D is rotated in a rotation direction  80 KL. 
     When truing is to be performed, therefore, the rotation direction of the grindstone  50  and that of the first roll are identical to each other, the rotation direction of the grindstone  50  and that of the second roll are identical to each other, and the grindstone  50  is trued by the rotation difference. 
     [Shape ( FIG. 3 ) of Section Including to-be-Trued Places of Grindstone  50 ] 
     Next, the shape of a section including the to-be-trued places of the grindstone  50 , and the like will be described with reference to  FIG. 3 .  FIG. 3  is a sectional view of the grindstone  50  taken along an XZ-plane including the grindstone rotation axis XJ. 
     Referring to  FIG. 3 , a surface which is the outer surface (surface which is to be in contact with the workpiece W) of the grindstone  50  (grindstone portion  51 ), and which is parallel to the grindstone rotation axis XJ is indicated as a grindstone outer circumferential surface  51 G. Moreover, a surface which is perpendicular to the grindstone rotation axis XJ, and which is on the right side in  FIG. 3  is indicated as a grindstone end surface  51 TR, and that which is perpendicular to the grindstone rotation axis XJ, and which is on the left side in  FIG. 3  is indicated as a grindstone end surface  51 TL. Furthermore, a surface which is a surface at a boundary between the grindstone outer circumferential surface  51 G and the grindstone end surface  51 TR, and which is formed into an arcuate shape in  FIG. 3  is indicated as a grindstone arcuate surface  51 ER, and that which is a surface at a boundary between the grindstone outer circumferential surface  51 G and the grindstone end surface  51 TL, and which is formed into an arcuate shape in  FIG. 3  is indicated as a grindstone arcuate surface  51 EL. 
     Moreover, the center of the arc of the grindstone arcuate surface  51 ER is indicated as the arc center OR, and that of the arc of the grindstone arcuate surface  51 EL is indicated as the arc center OL. 
     Then, the boundary position between the grindstone end surface  51 TR and the grindstone arcuate surface  51 ER is indicated as an end surface boundary position PTR, and that between the grindstone outer circumferential surface  51 G and the grindstone arcuate surface  51 ER is indicated as an outer circumferential boundary position PGR. 
     Similarly, the boundary position between the grindstone end surface  51 TL and the grindstone arcuate surface  51 EL is indicated as an end surface boundary position PTL, and that between the grindstone outer circumferential surface  51 G and the grindstone arcuate surface  51 EL is indicated as an outer circumferential boundary position PGL. 
     Moreover, a position which, in the grindstone end surface  51 TR, is remotest from the grindstone arcuate surface  51 ER is indicated as an end surface terminal position PZR. 
     Similarly, a position which, in the grindstone end surface  51 TL, is remotest from the grindstone arcuate surface  51 EL is indicated as an end surface terminal position PZL. 
     Referring to  FIG. 3 , then, a point where a first virtual line VTR which has an angle θR (predetermined angle) with respect to the grindstone rotation axis XJ, and which passes through the arc center OR, and the grindstone arcuate surface  51 ER intersect with each other is indicated as an arc boundary position PER, and that where a first virtual line VTL which has an angle θL (predetermined angle) with respect to the grindstone rotation axis XJ, and which passes through the arc center OL, and the grindstone arcuate surface  51 EL intersect with each other is indicated as an arc boundary position PEL. The angles θR, θL are angles which are adequately set, and, for example, 45 degrees. 
     Then, a surface which is a partial surface of the grindstone arcuate surface  51 ER, which is continuous to the grindstone outer circumferential surface  51 G, and which extends from the outer circumferential boundary position PGR to the arc boundary position PER is indicated as an outer circumference arcuate surface  51 FR. Moreover, a surface which is the remaining surface of the grindstone arcuate surface  51 ER, which is continuous to the grindstone end surface  51 TR, and which extends from the end surface boundary position PTR to the arc boundary position PER is indicated as an end surface arcuate surface  51 SR. That is, the grindstone arcuate surface  51 ER is divided at the arc boundary position PER into the outer circumference arcuate surface  51 FR and the end surface arcuate surface  51 SR. 
     Similarly, a surface which is a partial surface of the grindstone arcuate surface  51 EL, which is continuous to the grindstone outer circumferential surface  51 G, and which extends from the outer circumferential boundary position PGL to the arc boundary position PEL is indicated as an outer circumference arcuate surface  51 FL. Moreover, a surface which is the remaining surface of the grindstone arcuate surface  51 EL, which is continuous to the grindstone end surface  51 TL, and which extends from the end surface boundary position PTL to the arc boundary position PEL is indicated as an end surface arcuate surface  51 SL. That is, the grindstone arcuate surface  51 EL is divided at the arc boundary position PEL into the outer circumference arcuate surface  51 FL and the end surface arcuate surface  51 SL. 
     [Truing Method ( FIGS. 4 and 5 ) of First Embodiment] 
     Next, a truing method of a first embodiment will be described with reference to  FIGS. 4 and 5 . 
     When truing of the grindstone  50  is instructed, the controlling unit controls the grindstone rotation driving unit  50 M to rotate the grindstone  50 , the first truer  70  to rotate the first roll  70 D, and the moving unit (the X-axis direction driving unit  10 M, the Z-axis direction driving unit  20 M, and the like) to move the relative position of the first truer  70  with respect to the grindstone  50 , thereby starting truing by the first truer. 
     When the truing by the first truer  70  is ended, then, the controlling unit controls the second truer  80  to rotate the second roll  80 D, and the moving unit (the X-axis direction driving unit  10 M, the Z-axis direction driving unit  20 M, and the like) to move the relative position of the second truer  80  with respect to the grindstone  50 , thereby starting truing by the second truer. 
     When the grindstone outer circumferential surface  51 G is to be trued, as shown in  FIG. 4 , the controlling unit controls the moving unit to relatively move the first truer  70  with respect to the grindstone  50  in a state where the first truer rotation axis TJ 1  is maintained parallel to the grindstone rotation axis XJ, thereby truing the outer circumference arcuate surface  51 FR which is a partial surface of the grindstone arcuate surface  51 ER, and which is continuous to the grindstone outer circumferential surface  51 G, the grindstone outer circumferential surface  51 G, and the outer circumference arcuate surface  51 FL which is a partial surface of the grindstone arcuate surface  51 EL, and which is continuous to the grindstone outer circumferential surface  51 G. 
     When the grindstone end surface  51 TR is to be trued, as shown in  FIG. 5 , the controlling unit controls the moving unit to relatively move the second truer  80  with respect to the grindstone  50  in a state where the second truer rotation axis TJ 2  is maintained in a direction perpendicular to the grindstone rotation axis XJ, thereby truing the end surface arcuate surface  51 SR which is the remaining surface of the grindstone arcuate surface  51 ER, and which is continuous to the grindstone end surface  51 TR, and the grindstone end surface  51 TR. 
     When the grindstone end surface  51 TL is to be trued, as shown in  FIG. 5 , the controlling unit controls the moving unit to relatively move the second truer  80  with respect to the grindstone  50  in a state where the second truer rotation axis TJ 2  is maintained in a direction perpendicular to the grindstone rotation axis XJ, thereby truing the end surface arcuate surface  51 SL which is the remaining surface of the grindstone arcuate surface  51 EL, and which is continuous to the grindstone end surface  51 TL, and the grindstone end surface  51 TL. 
     Moreover, the positions and sequence of truing by using the first truer  70  will be described more correctly. As shown in  FIG. 4 , the controlling unit trues the outer circumference arcuate surface  51 FR from the arc boundary position PER that is the position which, in the outer circumference arcuate surface  51 FR (corresponding to the one outer circumference arcuate surface), is remotest from the grindstone outer circumferential surface  51 G, toward the outer circumferential boundary position PGR that is the position which, in the outer circumference arcuate surface  51 FR, is closest to the grindstone outer circumferential surface  51 G. 
     Then, the controlling unit trues the grindstone outer circumferential surface  51 G from the outer circumferential boundary position PGR that is the position which, in the grindstone outer circumferential surface  51 G, is closest to the outer circumference arcuate surface  51 FR, toward the outer circumferential boundary position PGL that is the position which, in the grindstone outer circumferential surface  51 G, is closest to the outer circumference arcuate surface  51 FL (corresponding to the other outer circumference arcuate surface). 
     Then, the controlling unit trues the outer circumference arcuate surface  51 FL from the outer circumferential boundary position PGL that is the position which, in the outer circumference arcuate surface  51 FL, is closest to the grindstone outer circumferential surface  51 G, toward the arc boundary position PEL that is the position which, in the outer circumference arcuate surface  51 FL, is remotest from the grindstone outer circumferential surface  51 G. 
     Moreover, the positions and sequence of truing by using the second truer  80  will be described more correctly. As shown in  FIG. 5 , the controlling unit trues the end surface arcuate surface  51 SR from the arc boundary position PER that is the position which, in the end surface arcuate surface  51 SR (corresponding to the one end surface arcuate surface), is remotest from the grindstone end surface  51 TR (corresponding to the one grindstone arcuate surface), toward the end surface boundary position PTR that is the position which, in the end surface arcuate surface  51 SR, is closest to the grindstone end surface  51 TR. 
     Then, the controlling unit trues the grindstone end surface  51 TR from the end surface boundary position PTR that is the position which, in the grindstone end surface  51 TR, is closest to the end surface arcuate surface  51 SR, toward the end surface terminal position PZR that is the position which, in the grindstone end surface  51 TR, is remotest from the end surface arcuate surface  51 SR. 
     As shown in  FIG. 5 , similarly, the controlling unit trues the end surface arcuate surface  51 SL from the arc boundary position PEL that is the position which, in the end surface arcuate surface  51 SL (corresponding to the other end surface arcuate surface), is remotest from the grindstone end surface  51 TL (corresponding to the other grindstone end surface), toward the end surface boundary position PTL that is the position which, in the end surface arcuate surface  51 SL, is closest to the grindstone end surface  51 TL. 
     Then, the controlling unit trues the grindstone end surface  51 TL from the end surface boundary position PTL that is the position which, in the grindstone end surface  51 TL, is closest to the end surface arcuate surface  51 SL, toward the end surface terminal position PZL that is the position which, in the grindstone end surface  51 TL, is remotest from the end surface arcuate surface  51 SL. 
     At the start of the truing of the outer circumference arcuate surface  51 FR, as shown in  FIG. 4 , when, in the case where the first truer  70  is made relatively close to the grindstone  50  toward the arc boundary position PER, the first truer is relatively moved from the side of the end surface arcuate surface  51 SR so as to be moved along a first virtual arc VE 1  which is a virtual arc having a convex direction that is opposite to a convex direction of the grindstone arcuate surface  51 ER, which is in contact with the grindstone arcuate surface  51 ER at the arc boundary position PER, and which has a first diameter, the truing from the arc boundary position PER can be started more smoothly. Therefore, this is more preferable. The value of the first diameter is appropriately set. 
     At the end of the truing of the outer circumference arcuate surface  51 FL, when, in the case where the first truer  70  is relatively separated from the arc boundary position PEL with respect to the grindstone  50 , the first truer is relatively moved to the side of the end surface arcuate surface  51 SL so as to be moved along a fourth virtual arc VEZ which is a virtual arc having a convex direction that is opposite to a convex direction of the grindstone arcuate surface  51 EL, which is in contact with the grindstone arcuate surface  51 EL at the arc boundary position PEL, and which has a fourth diameter, the truing in the arc boundary position PEL can be ended more smoothly. Therefore, this is more preferable. The value of the fourth diameter is appropriately set. 
     At the start of the truing of the end surface arcuate surface  51 SR, as shown in  FIG. 5 , when, in the case where the second truer  80  is made relatively close to the grindstone  50  toward the arc boundary position PER, the second truer is relatively moved from the side of the outer circumference arcuate surface  51 FR so as to be moved along a second virtual arc VE 2  which is a virtual arc having a convex direction that is opposite to the convex direction of the grindstone arcuate surface  51 ER, which is in contact with the grindstone arcuate surface  51 ER at the arc boundary position PER, and which has a second diameter, the truing from the arc boundary position PER can be started more smoothly. Therefore, this is more preferable. The value of the second diameter is appropriately set. 
     At the start of the truing of the end surface arcuate surface  51 SL, as shown in  FIG. 5 , when, in the case where the second truer  80  is made relatively close to the grindstone  50  toward the arc boundary position PEL, the second truer is relatively moved from the side of the outer circumference arcuate surface  51 FL so as to be moved along a third virtual arc VE 3  which is a virtual arc having a convex direction that is opposite to the convex direction of the grindstone arcuate surface  51 EL, which is in contact with the grindstone arcuate surface  51 EL at the arc boundary position PEL, and which has a third diameter, the truing from the arc boundary position PEL can be started more smoothly. Therefore, this is more preferable. The value of the third diameter is appropriately set. 
     [Truing Method ( FIGS. 6 and 7 ) of Second Embodiment] 
     Next, a truing method of a second embodiment will be described with reference to  FIGS. 6 and 7 . 
     The truing method of the second embodiment shown in  FIG. 6  is different from that of the first embodiment shown in  FIG. 4  in that the path in the case where the first truer  70  is made close to the arc boundary position PER, and that in the case where the first truer is separated from the arc boundary position PEL are not paths which extend along the virtual arcs, but those which extend along virtual lines parallel to the grindstone rotation axis XJ. 
     The truing method of the second embodiment shown in  FIG. 7  is different from that of the first embodiment shown in  FIG. 5  in that the path in the case where the second truer  70  is made close to the arc boundary position PER, and that in the case where the second truer is made close to the arc boundary position PEL are not paths which extend along the virtual arcs, but those which extend along virtual lines perpendicular to the grindstone rotation axis XJ. 
     Hereinafter, description will be made with emphasis on these different points. 
     At the start of the truing of the outer circumference arcuate surface  51 FR, as shown in  FIG. 6 , when, in the case where the first truer  70  is made relatively close to the grindstone  50  toward the arc boundary position PER, the first truer  70  is relatively moved with respect to the grindstone  50  so as to be moved along a virtual line VTA which is parallel to the grindstone rotation axis XJ, and which passes through the arc boundary position PER. According to the configuration, the first truer  70  can be made relatively close to the grindstone  50  through the simple path. 
     At the end of the truing of the outer circumference arcuate surface  51 FL, as shown in  FIG. 6 , when, in the case where the first truer  70  is relatively separated from the grindstone  50  from the arc boundary position PEL, the first truer  70  is relatively moved with respect to the grindstone  50  so as to be moved along a virtual line VTB which is parallel to the grindstone rotation axis XJ, and which passes through the arc boundary position PEL. According to the configuration, the first truer  70  can be relatively separated from the grindstone  50  through the simple path. 
     At the start of the truing of the end surface arcuate surface  51 SR, as shown in  FIG. 7 , when, in the case where the second truer  80  is made relatively close to the grindstone  50  toward the arc boundary position PER, the second truer  80  is relatively moved with respect to the grindstone  50  so as to be moved along a virtual line VTC which is perpendicular to the grindstone rotation axis XJ, and which passes through the arc boundary position PER. According to the configuration, the second truer  80  can be made relatively close to the grindstone  50  through the simple path. 
     At the start of the truing of the end surface arcuate surface  51 SL, as shown in  FIG. 7 , when, in the case where the second truer  80  is made relatively close to the grindstone  50  toward the arc boundary position PEL, the second truer  80  is relatively moved with respect to the grindstone  50  so as to be moved along a virtual line VTD which is perpendicular to the grindstone rotation axis XJ, and which passes through the arc boundary position PEL. According to the configuration, the second truer  80  can be made relatively close to the grindstone  50  through the simple path. 
     [Example ( FIG. 8 ) of Method for Setting Boundary Positions (Arc Boundary Positions PER, PEL) Between Outer Circumference Arcuate Surface and End Surface Arcuate Surfaces] 
     In the description of  FIG. 3 , the angles θR, θL (predetermined angles) of the first virtual lines VTR, VTL with respect to the grindstone rotation axis XJ in the case where the arc boundary positions PER, PEL are to be set are, for example, 45 degrees. However, the below-described setting of angles θR′, θL′ (predetermined angles) shown in  FIG. 8  is more preferable. 
     In the shape of the grindstone  50  (grindstone portion  51 ) after truing of the grindstone  50  (grindstone portion  51 ) before truing, as shown in  FIG. 8 , the truing depth (machining allowance due to truing) in a direction perpendicular to the grindstone rotation axis XJ is set as ΔD, and the truing depth (machining allowance due to truing) in the direction parallel to the grindstone rotation axis XJ is set as ΔW. 
     As shown in  FIG. 8 , then, the center of the arc of the right grindstone arcuate surface before truing is indicated as the arc center OR, and that of the arc of the left grindstone arcuate surface before truing is indicated as the arc center OL. 
     Then, a position which is further moved by ΔW in the direction separating from the right grindstone end surface, from a position that is moved by ΔD from the position of the arc center OR in the direction separating from the grindstone outer circumferential surface is set as a new arc center OR′ which is the center of the arc of the right grindstone arcuate surface after truing. 
     Then, the intersection of a second virtual line VTR 2  which passes through the arc center OR and the arc center OR′, and the right grindstone arcuate surface before truing is set as the arc boundary position PER before truing, and that of the second virtual line VTR 2  and the right grindstone arcuate surface after truing is set as the arc boundary position PER′ after truing. 
     From the above, an angle θR′ of the second virtual line VTR 2  with respect to the grindstone rotation axis XJ is given by the following expression: 
       Angle θ R ′=tan −1 (Δ D/ΔW ).
 
     Similarly, a position which is further moved by ΔW in the direction separating from the left grindstone end surface, from a position that is moved by ΔD from the position of the arc center OL in the direction separating from the grindstone outer circumferential surface is set as a new arc center OL′ which is the center of the arc of the left grindstone arcuate surface after truing. 
     Then, the intersection of a second virtual line VTL 2  which passes through the arc center OL and the arc center OL′, and the right grindstone arcuate surface before truing is set as the arc boundary position PEL before truing, and that of the second virtual line VTL 2  and the right grindstone arcuate surface after truing is set as the arc boundary position PEL′ after truing. 
     An angle θL′ is identical with the angle θR′, and therefore its description is omitted. 
     Although, in the above description of the embodiments, the truing methods for truing the grindstone by using the first truer and the second truer have been described, it is possible to realize a truing apparatus including: a first truer having a first roll which is rotated about a first truer rotation axis that is parallel to the grindstone rotation axis XJ; a second truer having a second roll which is rotated about a second truer rotation axis that is perpendicular to the grindstone rotation axis XJ; a moving unit; and a controlling unit, the apparatus truing the grindstone outer circumferential surface, grindstone end surfaces, and grindstone arcuate surfaces of the grindstone, based on the truing methods which have been described in the embodiments. 
     In the truing methods which have been described in the embodiments, the grindstone end surfaces, and the grindstone arcuate surfaces (end surface arcuate surface) which are continuous to the grindstone end surfaces can be adequately trued, the fracturability of the abrasive grains is improved, and the sharpness of the grindstone is improved. The improvement of the sharpness can adequately prevent grinding burn from occurring, and contribute to cost reduction. 
     Moreover, truing is performed in appropriate sequence and route. Therefore, truing can be performed in a shorter period of time, and this can contribute to shortening of the process time and energy saving. 
     Furthermore, the invention can cope with processing which is applied to, for example, a crankshaft for a special vehicle, and in which accuracies of grindstone end surfaces are required, reduce the friction resistance of the crankshaft, and contribute to improvement of fuel efficiency of the vehicle. 
     In the truing method of the invention, various changes, additions, and deletions may be made without changing the spirit of the invention. The configuration, structure, shape, and the like of the truing apparatus of the invention may be variously modified, added, or deleted without changing the spirit of the invention. 
     Moreover, the configuration, structure, shape, and the like of the grinding machine  1  which have been described in the embodiments may be variously modified, added, or deleted without changing the spirit of the invention. 
     The application is based on Japanese Patent Application (No. 2013-215492) filed Oct. 16, 2013, and its disclosure is incorporated herein by reference. 
     INDUSTRIAL APPLICABILITY 
     According to the invention, it is possible to adequately process an article to be processed in which the accuracies of grindstone end surfaces, and those of grindstone arcuate surfaces in the vicinity of the grindstone end surfaces are required. 
     DESCRIPTION OF THE REFERENCE NUMERALS AND SIGNS 
     
         
           1  grinding machine 
           2  bed 
           10  X-axis movement table 
           10 M X-axis direction driving unit 
           20  Z-axis movement table 
           20 M Z-axis direction driving unit 
           40  headstock 
           41  main spindle 
           46  tailstock 
           47  center 
           50  grindstone 
           51  grindstone portion 
           51 ER,  51 EL grindstone arcuate surface 
           51 FR,  51 FL outer circumference arcuate surface 
           51 G grindstone outer circumferential surface 
           51 SR,  51 SL end surface arcuate surface 
           51 TR,  51 TL grindstone end surface 
           60  controlling unit 
           70  first truer 
           70 D first roll 
           80  second truer 
           80 D second roll 
         OR, OL arc center 
         PER, PEL arc boundary position 
         PGR, PGL outer circumferential boundary position 
         PTR, PTL end surface boundary position 
         PZR, PZL end surface terminal position 
         TJ 1  first truer rotation axis 
         TJ 2  second truer rotation axis 
         VE 1  first virtual arc 
         VE 2  second virtual arc 
         VE 3  third virtual arc 
         VM virtual plane 
         VTR, VTL first virtual line 
         VTR 2 , VTL 2  second virtual line 
         W workpiece 
         WJ workpiece rotation axis 
         XJ grindstone rotation axis