Abstract:
A tool path-generating method for computing a tool path to process a workpiece, wherein the tool path for a designated tool when processing using the designated tool is previously established. The tool path-generating method comprises a path-computing process for computing, on the basis of the tool path for the designated tool, the tool path of a substitute tool differing from the designated tool when processing with the substitute tool. The path-computing process computes the portion that ultimately forms the machined surface when the workpiece is processed using the designated tool and sets the tool path for the substitute tool on the basis of the portion that ultimately forms the machined surface.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a U.S. National Phase patent application of International Patent Application No. PCT/JP2012/076348, filed on Oct. 11, 2012, which is hereby incorporated by reference in the present disclosure in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to a tool path generation method, a control device of a machine tool, and a tool path generation device. 
       BACKGROUND OF THE INVENTION 
       [0003]    A machine tool which performs machining, such as cutting, by moving a tool relative to a workpiece is known in a conventional technique. In such a machine tool, a numerical control-type machine tool is known which specifies a path of a tool by coordinates of a predetermined axis or the like and machines a workpiece by automatically moving the tool with respect to a workpiece. A tool used to machine a workpiece is appropriately selected depending on a machining shape of the workpiece. For example, when a groove portion is formed on a surface of a workpiece, a flat end mill or the like is used as a tool. In addition, when a plurality of types of machining is performed on a single workpiece, the machining can be performed by exchanging tools according to machining shapes of the workpiece. 
         [0004]    The patent literature 1 discloses a machine tool which selects an optimum using tool based on various condition data for machining a workpiece. The machine tool includes an automatic tool allocation determination means which allocates a tool to a tool station of edged tools and an automatic programming device of the machine tool which automatically generates a machining program. The automatic programming device determines when an optimum tool is different from a tool allocated by the machining program to a last workpiece, whether the last allocated tool can be used in place of the optimum tool. Further, it is disclosed that the automatic programming device allocates a substitute tool when the last allocated tool can be used in place of the optimum tool. 
         [0005]    Patent literature 1: Japanese Laid-open Patent Publication No. 4-25344 
       SUMMARY OF THE INVENTION 
       [0006]    A tool which machines a workpiece while moving relative to a workpiece is specified by a user or the like. A tool path when a specified tool which is specified in advance is used is calculated. Regarding a type and a size of a tool used for machining of a workpiece, it is preferable to use an optimum tool depending on a type of machining. For example, when a cylindrical cam is manufactured, a groove portion is formed on a surface of a columnar workpiece. In this case, it is preferable to use a rotary tool having a diameter identical to a groove width. When a flat end mill is used as the rotary tool, it is preferable to use a flat end mill having a tool diameter identical to a groove width. However, there are various machining shapes of the workpiece, and there is a problem that an optimum tool needs to be prepared depending on a machining shape. In addition, if an optimum tool is prepared, there is a problem that it is difficult to perform a fine adjustment of a machining dimension when the tool is worn or the like. 
         [0007]    A numerical control-type machine tool is sometimes able to perform machining using a substitute tool of which size is different from a specified tool. For example, when a rotary tool having a tool diameter smaller than that of a specified rotary tool is used, machining can be performed by generating a tool path parallely moved by a predetermined amount with respect to a tool path of the specified tool. In other words, the machining can be performed using an offset function of parallely moving a tool path by considering a difference between the tool diameters. 
         [0008]    However, depending on a tool type, it is difficult to generate a tool path when the tool is changed, and the offset function may not be used. When the offset function is used in the machining, machining accuracy may become lower or a machining time may become longer than when the machining is performed by the optimum tool. In addition, when the offset function is used, there is a problem that the tool type is unchangeable. Further, when a three-dimensional tool path is generated, a machining program needs to include a description of a normal vector perpendicular to a cutting surface. 
         [0009]    A tool path generation method of the present invention is a tool path generation method for calculating a tool path for machining a workpiece while relatively moving a tool and the workpiece, in which a tool path of a specified tool when the specified tool is used in machining is set in advance, and which includes a tool path calculation step for calculating a tool path of a substitute tool when the substitute tool different from the specified tool machines based on the tool path of the specified tool. The tool path calculation step calculates a portion which finally generates a machining surface in a machining area of the specified tool when the specified tool machines the workpiece and sets the tool path of the substitute tool based on the portion which finally generates the machining surface. 
         [0010]    According to the above-described invention, the portion which finally generates the machining surface can include a line portion or a plane portion. 
         [0011]    According to the above-described invention, machining can be performed using the substitute tool which is a same type of tool as the specified tool and is smaller than the specified tool. 
         [0012]    According to the above-described invention, the tool path calculation step can include a step for setting a virtual advancing direction when the specified tool machines the workpiece, a step for calculating the portion which finally generates the machining surface using the virtual advancing direction, a step for setting a range in which the substitute tool is disposed based on the portion which finally generates the machining surface, and a step for setting a plurality of positions on which the substitute tool is disposed within the range in which the substitute tool is disposed. 
         [0013]    A control device of a machine tool of the present invention is a control device of a machine tool which machines a workpiece while relatively moving a tool and the workpiece and comprises an input information reading unit configured to read input information including a tool path of a specified tool when the specified tool which is specified in advance machines a workpiece and a path setting unit configured to set a tool path of a substitute tool based on the input information when the substitute tool different from the specified tool performs machining. The path setting unit calculates a portion which finally generates a machining surface in a machining area of the specified tool when the specified tool machines the workpiece and sets the tool path of the substitute tool based on the portion which finally generates the machining surface. 
         [0014]    According to the above-described invention, the portion which finally generates the machining surface can include a line portion or a plane portion. 
         [0015]    According to the above-described invention, the substitute tool is a same type of tool as the specified tool and is smaller than the specified tool. 
         [0016]    According to the above-described invention, the path setting unit can include a virtual advancing direction setting unit configured to set a virtual advancing direction when the specified tool machines the workpiece based on the input information, a range setting unit configured to calculate the portion which finally generates the machining surface using the virtual advancing direction and set a range in which the substitute tool is disposed based on the portion which finally generates the machining surface, and a position setting unit configured to set a plurality of positions on which the substitute tool is disposed within the range in which the substitute tool is disposed. 
         [0017]    A tool path generation device of the present invention is a tool path generation device which generates a tool path when a workpiece is machined while relatively moving a tool and the workpiece and includes a shape data reading unit configured to read shape data of the workpiece and a path setting unit configured to set a tool path of a substitute tool based on the shape data when the substitute tool different from a specified tool which is specified in advance performs machining. The path setting unit sets a tool path of the specified tool when the specified tool machines the workpiece, calculates a portion which finally generates a machining surface in a machining area of the specified tool when the specified tool performs machining, and sets the tool path of the substitute tool based on the portion which finally generates the machining surface. 
         [0018]    According to the present invention, machining can be accurately performed using a substitute tool in place of a specified tool which is specified to perform desired machining. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1  is a schematic view of a numerical control-type machine tool in a first embodiment. 
           [0020]      FIG. 2  is a schematic view of a workpiece and a groove portion when grooving is performed using a substitute tool in the first embodiment. 
           [0021]      FIG. 3  is a schematic view of a workpiece and a groove portion when grooving is performed using a specified tool in the first embodiment. 
           [0022]      FIG. 4  is a view illustrating a trajectory of a central axis of the specified tool when grooving is performed using the specified tool in the first embodiment. 
           [0023]      FIG. 5  is a schematic view illustrating a virtual advancing direction and a portion in which a workpiece is machined when grooving is performed using the specified tool in the first embodiment. 
           [0024]      FIG. 6  is a schematic cross-sectional view illustrating when grooving is performed using the substitute tool in the first embodiment. 
           [0025]      FIG. 7  is a schematic view illustrating machining on an outward path and a return path of a first time in a grooving method of the first embodiment. 
           [0026]      FIG. 8  is a schematic view illustrating machining on an outward path and a return path of a second time in the grooving method of the first embodiment. 
           [0027]      FIG. 9  is a schematic view illustrating machining on an outward path and a return path of a third time in the grooving method of the first embodiment. 
           [0028]      FIG. 10  is a schematic cross-sectional view illustrating machining on the outward path of the first time in the grooving method of the first embodiment. 
           [0029]      FIG. 11  is a schematic cross-sectional view illustrating machining on the return path of the first time in the grooving method of the first embodiment. 
           [0030]      FIG. 12  is a schematic cross-sectional view illustrating machining on the outward path of the second time in the grooving method of the first embodiment. 
           [0031]      FIG. 13  is a schematic cross-sectional view illustrating machining on the return path of the second time in the grooving method of the first embodiment. 
           [0032]      FIG. 14  is a schematic cross-sectional view illustrating machining on the outward path of the third time in the grooving method of the first embodiment. 
           [0033]      FIG. 15  is a schematic cross-sectional view illustrating machining on the return path of the third time in the grooving method of the first embodiment. 
           [0034]      FIG. 16  is a schematic view of a machining system which machines a workpiece in the first embodiment. 
           [0035]      FIG. 17  is a flowchart illustrating control by a control device of the machine tool in the first embodiment. 
           [0036]      FIG. 18  is a schematic cross-sectional view illustrating a virtual advancing direction of the specified tool. 
           [0037]      FIG. 19  is a schematic view illustrating the virtual advancing direction of the specified tool and a range in which the substitute tool is disposed in the first embodiment. 
           [0038]      FIG. 20  is a schematic perspective view illustrating a machining area of the specified tool and a portion which finally generates a machining surface in the first embodiment. 
           [0039]      FIG. 21  is a schematic perspective view of the specified tool and the substitute tool illustrating a position on which the substitute tool is disposed in the first embodiment. 
           [0040]      FIG. 22  is a schematic view illustrating a scallop height when a workpiece is machined in the first embodiment. 
           [0041]      FIG. 23  is a first schematic perspective view of the substitute tool in which a portion which finally generates a machining surface is indicated in the first embodiment. 
           [0042]      FIG. 24  is a second schematic perspective view of the substitute tool in which a portion which finally generates a machining surface is indicated in the first embodiment. 
           [0043]      FIG. 25  is a third schematic perspective view of the substitute tool in which a portion which finally generates a machining surface is indicated in the first embodiment. 
           [0044]      FIG. 26  is a schematic view of another machining system in the first embodiment. 
           [0045]      FIG. 27  is a schematic perspective view of an end cam in the first embodiment. 
           [0046]      FIG. 28  is a view illustrating a portion which finally generates a machining surface. 
           [0047]      FIG. 29  is a schematic cross-sectional view of a workpiece when machining is performed by a substitute tool in a second embodiment. 
           [0048]      FIG. 30  is a schematic plan view of a workpiece when machining is performed by the substitute tool in the second embodiment. 
           [0049]      FIG. 31  is a schematic cross-sectional view of a workpiece when machining is performed by a specified tool in the second embodiment. 
           [0050]      FIG. 32  is a schematic plan view of a workpiece when machining is performed by the specified tool in the second embodiment. 
           [0051]      FIG. 33  is a flowchart illustrating control for setting a position on which the substitute tool is disposed in the second embodiment. 
           [0052]      FIG. 34  is a schematic perspective view of the specified tool in the second embodiment. 
           [0053]      FIG. 35  is a schematic bottom view of the specified tool in the second embodiment. 
           [0054]      FIG. 36  is a schematic view illustrating a scallop height when a workpiece is machined in the second embodiment. 
           [0055]      FIG. 37  is a view illustrating judgment of a scallop height in the second embodiment. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     First Embodiment 
       [0056]    A tool path generation method, a control device of a machine tool, and a tool path generation device according to the first embodiment are described with reference to  FIG. 1  to  FIG. 28 . As the machine tool of the present embodiment, a horizontal machining center in which a spindle extends in a horizontal direction is described as an example. In the present embodiment, grooving which forms a groove portion on a workpiece is described as an example. When a workpiece is machined, it is preferable to use a tool having an optimum type and optimum size to machine the workpiece into a desired shape. A user can specify the optimum tool as a specified tool. In the present embodiment, a substitute tool smaller than the specified tool is used for grooving in place of the specified tool which is specified by the user. 
         [0057]      FIG. 1  is a schematic view of a numerical control-type machine tool according to the present embodiment. A substitute tool  22  is mounted as a tool on a machine tool  10  illustrated in  FIG. 1 . The machine tool  10  of the present embodiment includes a moving device which relatively moves the substitute tool  22  and a workpiece  1 . The machine tool  10  includes a bed  12  disposed on a floor of a factory or the like. A Z-axis guide rail  28  is fixed to an upper surface of the bed  12 . The Z axis of the present embodiment is the horizontal direction. The Z-axis guide rail  28  is disposed to extend in a Z-axis direction (a right and left direction in  FIG. 1 ). 
         [0058]    A table  14  is disposed on an upper surface of the Z-axis guide rail  28 . The table  14  is slidably disposed to the Z-axis guide rail  28 . The table  14  moves along the Z axis. A numerical control-type rotary table  42  for rotating the workpiece  1  in a B-axis direction is disposed on an upper surface of the table  14 . The workpiece  1  is fixed to an upper surface of the rotary table  42  via a workpiece holding member  40 . 
         [0059]    An X-axis guide rail  36  is fixed to an upper surface of the bed  12 . An X axis of the present embodiment is perpendicular to the Z axis and extends in the horizontal direction (a vertical direction of a paper surface of  FIG. 1 ). The X-axis guide rail  36  is formed to extend along the X axis. A column  16  is slidably disposed on the X-axis guide rail  36 . The column  16  moves along the X axis. 
         [0060]    A Y-axis guide rail  34  is fixed to a front surface of the column  16 . The front surface faces to the workpiece  1 . A Y axis of the present embodiment extends in a direction perpendicular to the X axis and the Z axis. The Y-axis guide rail  34  extends along the Y axis. A spindle head  18  is disposed on the Y-axis guide rail  34 . The spindle head  18  is slidably formed to the Y-axis guide rail  34 . The spindle head  18  moves along the Y axis. The spindle head  18  is formed to rotatably support a spindle  20 . 
         [0061]    The moving device of the present embodiment includes a Z-axis moving device which relatively moves the substitute tool  22  to the workpiece  1  in the Z-axis direction. In the present embodiment, a Z-axis feed screw  24  is disposed below the table  14  inside the bed  12 . The Z-axis feed screw  24  extends in the Z-axis direction. A nut  26  is fixed to a lower surface of the table  14 . The nut  26  is screwed to the Z-axis feed screw  24 . One end of the Z-axis feed screw  24  is connected to a Z-axis servomotor  25 . The Z-axis servomotor  25  is driven to rotate the Z-axis feed screw  24 , and thus the nut  26  moves in the Z-axis direction. The table  14  moves along the Z-axis guide rail  28  in conjunction with the movement of the nut  26 . Accordingly, the workpiece  1  moves in the Z-axis direction. 
         [0062]    The machine tool  10  of the present embodiment includes an X-axis moving device which makes the substitute tool  22  to move relative to the workpiece  1  in the X-axis direction. The X-axis moving device includes an X-axis feed screw disposed below the column  16  inside the bed  12 , similar to the Z-axis moving device. The X-axis feed screw is formed to extend in the X-axis direction. A nut  37  screwed to the X-axis feed screw is fixed to a lower surface of the column  16 . One end of the X-axis feed screw is connected to an X-axis servomotor  38 . The X-axis servomotor  38  is driven to rotate the X-axis feed screw, and thus the nut  37  moves in the X-axis direction. The column  16  moves along the X-axis guide rail  36  in conjunction with the movement of the nut  37 . Accordingly, the substitute tool  22  moves in the X-axis direction. 
         [0063]    The machine tool  10  of the present embodiment includes a Y-axis moving device which makes the substitute tool  22  to move relative to the workpiece  1  in a Y-axis direction. A Y-axis feed screw  32  is disposed inside the column  16 . The Y-axis feed screw  32  is formed to extend in the Y-axis direction. A nut  30  which is screwed to the Y-axis feed screw  32  is fixed to a back surface of the spindle head  18 . An upper end of the Y-axis feed screw  32  is connected to a Y-axis servomotor  31 . The Y-axis servomotor  31  is driven to rotate the Y-axis feed screw  32 , and thus the nut  30  moves in the Y-axis direction. The spindle head  18  moves along the Y-axis guide rail  34  in conjunction with the movement of the nut  30 . Accordingly, the substitute tool  22  moves in the Y-axis direction. 
         [0064]    The machine tool  10  of the present embodiment includes a B-axis moving device which makes the substitute tool  22  to move relative to the workpiece  1  in the B-axis direction. The rotary table  42  includes a B-axis servomotor  43  which rotate the workpiece  1 . The B-axis servomotor  43  is driven, and thus the workpiece  1  rotates in the B-axis direction. 
         [0065]    The substitute tool  22  is disposed on a tip end of the spindle  20 . In the present embodiment, an end mill is mounted as the substitute tool  22 . The spindle  20  is connected to a motor  23  which rotates the substitute tool  22 . The motor  23  is driven, and the substitute tool  22  rotates on a central axis of the spindle  20  as a rotation axis. 
         [0066]    The machine tool  10  of the present embodiment includes linear feed axes (the X axis, the Y axis, and the Z axis) and a rotational feed axis (the B axis), operates the column  16 , the spindle head  18 , and the table  14  in the respective X-axis, Y-axis, and Z-axis directions while rotating the substitute tool  22 , and thus can cut the workpiece  1  fixed to the table  14  into a desired shape. Further, the machine tool  10  can drive the rotary table  42  to rotate the workpiece  1  around the B axis. The machine tool  10  of the present embodiment functions as a four-axis machine tool including the B axis. 
         [0067]      FIG. 2  is a schematic plan view of the workpiece  1  in the present embodiment. In the present embodiment, a groove portion  66  is formed on a circumferential surface of the columnar workpiece  1 . The groove portion  66  spirally extends on the surface of the workpiece  1 . Grooving for forming the groove portion  66  is performed, and, for example, a cylindrical cam or the like can be manufactured. 
         [0068]    With reference to  FIG. 1  and  FIG. 2 , when the groove portion  66  is formed on the workpiece  1 , the workpiece  1  is fixed to the rotary table  42  in a manner that a central axis  1   a  of the workpiece  1  becomes parallel to the Y axis. Further, the workpiece  1  is fixed in a manner that the central axis  1   a  coincides with a rotation axis of the rotary table  42 . In the machining of the workpiece  1 , the workpiece  1  is linearly moved in the X-axis direction and the Y-axis direction and rotated in the B-axis direction. 
         [0069]    In a grooving method of the present embodiment, cutting is performed using the substitute tool  22  having a diameter smaller than a groove width of the groove portion  66 . The groove portion  66  of the present embodiment has an approximately quadrangular cross section, a side surface  66   a  on one side, and a side surface  66   b  on the other side. 
         [0070]    The groove portion  66  of the present embodiment is formed to have constant depth and groove width. When such a groove portion  66  is to be formed, control is performed to change respective positions of the X axis, the Y axis, and the B axis along the surface of the workpiece  1  without changing a relative position (a position of the Z axis) in a depth direction of the substitute tool  22  in cutting. 
         [0071]    The grooving method of the present embodiment includes a reciprocation step for reciprocating the substitute tool  22  along a shape of the groove portion  66 . On an outward path of the reciprocation step, the side surface  66   a  on one side of the groove portion  66  is machined. As indicated by an arrow  95 , the substitute tool  22  is relatively moved to a direction in which the groove portion  66  extends, and the side surface  66   a  on one side of the groove portion  66  is machined. In the machine tool  10  of the present embodiment, the spindle  20  is moved in the Y-axis direction. The workpiece  1  is relatively moved to the substitute tool  22  in the Y-axis direction as indicated by an arrow  92 . Further, the workpiece  1  is relatively moved to the substitute tool  22  by rotating the workpiece  1  around the central axis  1   a  as indicated by an arrow  91 . When the substitute tool  22  reaches a predetermined end of the groove portion  66 , the substitute tool  22  is moved in the X-axis direction and the Y-axis direction to be disposed on a position of a return path. Then, a direction of the relative movement is changed, and machining on the return path is performed. 
         [0072]    On the return path of the reciprocation step, the side surface  66   b  on the other side of the groove portion  66  is machined. The substitute tool  22  is relatively moved to the direction in which the groove portion  66  extends, and the groove portion  66  is formed. In the present embodiment, the workpiece  1  is rotated as indicated by an arrow  93  while being relatively moved to the substitute tool  22  as indicated by an arrow  94 , so that the relative movement between the workpiece  1  and the substitute tool  22  is performed. 
         [0073]    When the substitute tool  22  having a diameter smaller than the groove width of the groove portion  66  performs once the machining on the side surfaces  66   a  and  66   b  of the groove portion  66 , the groove portion  66  is hardly to be formed into the desired shape, and incomplete cutting part is generated in any portion in a depth direction of the side surfaces  66   a  and  66   b  of the groove portion  66 . The incomplete cutting part is described which is generated when the substitute tool  22  having a diameter smaller than the groove width of the groove portion  66  machines the side surface of the groove portion  66 . 
         [0074]      FIG. 3  is a schematic plan view of the workpiece  1  when machining is performed using the specified tool. A specified tool  81  has a diameter identical to the groove width of the groove portion  66 . The specified tool  81  of the present embodiment is a rotary tool optimum to form the groove portion  66 . When the specified tool  81  is used, as indicated by the arrow  95 , the groove portion  66  can be formed by relatively moving the specified tool  81  once along the direction in which the groove portion  66  extends. In the machine tool  10  of the present embodiment, the spindle  20  is moved in the Y-axis direction, and the workpiece  1  is rotated around the B axis. The workpiece  1  is relatively moved to the specified tool  81  in the Y-axis direction as indicated by the arrow  92  and rotated around the central axis  1   a  as indicated by the arrow  91 , accordingly the groove portion  66  can be formed. When the specified tool  81  is used, the side surface  66   a  on one side and the side surface  66   b  on the other side can be both formed by one-time machining. 
         [0075]      FIG. 4  is a schematic view illustrating a trajectory of a central axis  81   a  of the specified tool  81  when the specified tool  81  is used. In the example illustrated in  FIG. 4 , the specified tool  81  is disposed in a manner that the central axis  81   a  of the specified tool  81  becomes parallel to a radial direction of the workpiece  1 . In other words, the central axis  1   a  of the workpiece  1  is disposed on the extension of the central axis  81   a.    
         [0076]    The specified tool  81  rotates on the central axis  81   a  as indicated by an arrow  98 . One end of the specified tool  81  is inserted into the workpiece  1 . A development view  71  is a view that the circumferential surface of the workpiece  1  is developed as indicated by arrows  96 . A trajectory  71   a  that the central axis  81   a  passes is depicted on the circumferential surface of the workpiece  1 . The specified tool  81  has a point of a tip end on the central axis  81   a , namely a tool tip point. A development view  72  is a view that a circumferential plane of the workpiece  1  which passes the tool tip point is developed as indicated by arrows  97 . A trajectory  72   a  of the tool tip point is depicted in the development view  72 . 
         [0077]    When comparing the trajectory  71   a  of points on the tool central axis  81   a  on the surface of the workpiece  1  with the trajectory  72   a  of the tool tip points, it is understood that shapes of these trajectories are different from each other. When the workpiece  1  rotates with respect to the specified tool  81 , radii of rotation are different from each other, so that the respective trajectories of points are different. Thus, a relative advancing direction of the specified tool  81  to the workpiece  1  is different depending on a depth direction of the groove portion  66 . 
         [0078]      FIG. 5  is a schematic view illustrating a direction to which the central axis  81   a  moves when the specified tool  81  is moved with respect to the workpiece  1 . An arrow  101  indicates a virtual advancing direction of the specified tool  81  at a predetermined point in the depth direction. The virtual advancing direction is a virtual advancing direction of a tool when it is assumed that the workpiece  1  is stopped and the tool moves. It is understood that the virtual advancing direction varies in a direction to which the central axis  81   a  extends. In other words, it is understood that the virtual advancing direction varies in the depth direction of the groove portion  66 . 
         [0079]    An arrow  102  indicates a direction perpendicular to a direction of the arrow  101  indicating the virtual advancing direction. An intersection point of the arrow  102  and the surface of the specified tool  81  is a contact portion  81   b . The contact portion  81   b  is a portion forming the side surfaces  66   a  and  66   b  of the groove portion  66 . In addition, the contact portion  81   b  is equivalent to a portion finally generating a machining surface of the workpiece when the workpiece is machined, which is described below. In the present embodiment, a line of the contact portion  81   b  has characteristics of not being parallel to the central axis  81   a  of the specified tool  81 . In the example illustrated in  FIG. 5 , the line of the contact portion  81   b  is curved; however, a contact portion may be linear. 
         [0080]    When the substitute tool  22  having a tool diameter smaller than that of the specified tool  81  is used, the substitute tool  22  can be obliquely disposed so that a central axis  22   a  of the substitute tool  22  is parallel to the central axis  81   a  of the specified tool  81 . In other words, the substitute tool  22  can be disposed in a manner that the central axis  22   a  is approximately parallel to the central axis  81   a  of the specified tool  81 . Further, the substitute tool  22  can be disposed in a state in which a surface of the substitute tool  22  is in contact with a position of the surface of the specified tool  81 , when the specified tool  81  is used. In this case, the central axis  22   a  of the substitute tool  22  is on a position shifted from the central axis  81   a  of the specified tool  81 . No matter how a position of the central axis  22   a  is selected, it is impossible for the surface of the substitute tool  22  to pass through all of the contact portions  81   b  in one-time machining. Thus, when cutting is performed by disposing the substitute tool  22 , incomplete cutting part is generated in some areas in the depth direction of the groove portion  66 . The substitute tool  22  has characteristics that if it intends to form the side surface  66   a  or the side surface  66   b  of the groove portion  66  in one-time machining using the substitute tool  22 , a desired side surface shape is not gained. 
         [0081]    In the grooving method of the present embodiment, machining is performed for a plurality of times by changing a relative position of the substitute tool  22  to the workpiece  1  in order to form a side surface of the groove portion  66 . 
         [0082]      FIG. 6  is a schematic cross-sectional view illustrating the grooving method of the present embodiment. In the grooving method of the present embodiment, the substitute tool  22  is used of which diameter is smaller than the groove width of the groove portion  66  indicated by an arrow  99 . In other words, the substitute tool  22  is used in place of the specified tool  81 .  FIG. 6  illustrates machining of the side surface  66   a  on one side of the groove portion  66  as an example. 
         [0083]    In the grooving method of the present embodiment, a tilt of the substitute tool  22  is set so that the central axis  22   a  of the substitute tool  22  is parallel to the depth direction of the groove portion  66 . In other words, the tilt of the substitute tool  22  is set so that a central axis of a circle  84  for disposing the substitute tool  22  is parallel to a rotation axis of the substitute tool  22 . 
         [0084]    In the grooving method of the present embodiment, the machining is performed for a plurality of times by gradually changing a position of the substitute tool  22  to the side surface  66   a  on one side of the groove portion  66 . In other words, the side surface  66   a  on one side is formed by gradually changing a path of the substitute tool  22 . In the example illustrated in  FIG. 6 , the substitute tool  22  is disposed on a position  85   a  in the machining of a first time. Then, as indicated by an arrow  103 , the substitute tool  22  is relatively moved along the direction in which the groove portion  66  extends. In the machining of the side surface  66   a  of a second time, the substitute tool  22  is disposed on a position  85   b  and is relatively moved along the direction in which the groove portion  66  extends. Further, in the machining of the side surface  66   a  of a third time, the substitute tool  22  is disposed on a position  85   c  and is relatively moved along the direction in which the groove portion  66  extends. Each of the positions  85   a ,  85   b , and  85   c  is set to be inscribed to the circle  84  of which diameter is the groove width of the groove portion  66 . In other words, the substitute tool  22  is disposed so that the surface of the substitute tool  22  is in contact with a position of the surface of the specified tool  81  when the specified tool  81  is used. 
         [0085]    In the machining on a return path, similar to the machining on the outward path, the machining is performed for a plurality of times by changing the position of the substitute tool  22  to form the side surface  66   b  on the other side of the groove portion  66 . In the present embodiment, the machining is performed for three times by changing the position of the substitute tool  22  on the outward path and the return path. An arbitrary number of times can be selected as the number of machining times for forming a side surface. When the number of machining times increases, a scallop height can be reduced as described below. In other words, machining accuracy of a groove portion can be improved. 
         [0086]      FIG. 7  is a schematic cross-sectional view illustrating positions of the substitute tool  22  on the outward path and on the return path in the machining of the first time. An arrow  100  indicates a rotating direction of the substitute tool  22 , and the same rotation direction is used on both of the outward path and the return path. In the machining on the outward path of the first time, the substitute tool  22  is disposed on the position  85   a . The substitute tool  22  is moved along an extending shape of the groove portion  66  as indicated by the arrow  103 , and the machining is performed on the side surface  66   a  on one side. In the machining on the return path of the first time, the substitute tool  22  is disposed on a position  86   a . The substitute tool  22  is moved along the extending shape of the groove portion  66  as indicated by an arrow  104 , and the machining is performed on the side surface  66   b  on the other side. 
         [0087]      FIG. 8  is a schematic cross-sectional view illustrating positions of the substitute tool  22  on the outward path and on the return path in the machining of the second time. In the machining of the second time, the substitute tool  22  is disposed on the position  85   b  on the outward path and moved in a direction indicated by the arrow  103 , so that the side surface  66   a  on one side is machined. On the return path, the substitute tool  22  is disposed on a position  86   b  and moved in a direction indicated by the arrow  104 , so that the side surface  66   b  on the other side is machined. 
         [0088]      FIG. 9  is a schematic cross-sectional view illustrating positions of the substitute tool  22  on the outward path and on the return path in the machining of the third time. In the machining of the third time, the substitute tool  22  is also disposed on the position  85   c  on the outward path, and the machining is performed on the side surface  66   a  on one side similar to the machining of the first time and the second time. On the return path, the substitute tool  22  is disposed on a position  86   c , and the machining is performed on the side surface  66   b  on the other side. 
         [0089]    In the grooving method of the present embodiment, the positions  85   a ,  85   b , and  85   c  of the substitute tool  22  on the outward path and the positions  86   a ,  86   b , and  86   c  of the substitute tool  22  on the return path are respectively in symmetrical positions. For example, in the machining of the first time, the position  85   a  on the outward path and the position  86   a  on the return path are in positions symmetrical to a center point  84   a  of the circle  84 . In other words, the tool tip point of the position  85   a  and the tool tip point of the position  86   a  are set to positions symmetrical to each other with respect to the center point  84   a  of the circle  84 . 
         [0090]      FIG. 10  is a schematic cross-sectional view illustrating when the side surface  66   a  on one side is machined on the outward path in the machining of the first time.  FIG. 11  is a schematic cross-sectional view illustrating when the side surface  66   b  on the other side is machined on the return path in the machining of the first time. Each drawing illustrates a machining surface  67  having a shape desired by a user. The machining is performed for a plurality of times so as to match the side surfaces  66   a  and  66   b  of the groove portion  66  with the machining surface  67 . 
         [0091]    On the outward path in the machining of the first time, an upper portion of the side surface  66   a  on one side can be cut so as to be almost identical to the machining surface  67 . However, at a central portion and a lower portion of the side surface  66   a  on one side, it is difficult to perform the machining up to the machining surface  67 , and incomplete cutting part is generated. On the return path of the machining of the first time, the lower portion of the side surface  66   b  on the other side can be cut up to the machining surface  67 . However, at a central portion and an upper portion of the side surface  66   b  on the other side, it is difficult to perform the machining up to the machining surface  67 , and incomplete cutting part is generated. 
         [0092]      FIG. 12  is a schematic cross-sectional view illustrating when the machining of the second time is performed on the outward path.  FIG. 13  is a schematic cross-sectional view illustrating when the machining of the second time is performed on the return path. On the outward path in the machining of the second time, the machining can be performed so as to bring the central portion of the side surface  66   a  on one side close to the machining surface  67 . On the return path in the machining of the second time, the machining can be performed so as to bring the central portion of the side surface  66   b  on the other side close to the machining surface  67 . 
         [0093]      FIG. 14  is a schematic cross-sectional view illustrating when the machining of the third time is performed on the outward path.  FIG. 15  is a schematic cross-sectional view illustrating when the machining of the third time is performed on the return path. On the outward path and the return path of the machining of the third time, the incomplete cutting part on the side surface  66   a  on one side and the side surface  66   b  on the other side can be cut. Accordingly, the groove portion  66  can match the machining surface  67  having the desired shape. 
         [0094]    As described above, the grooving method of the present embodiment includes a machining step for machining the workpiece  1  by relatively moving the substitute tool  22  in the tool path along the direction in which the groove portion  66  extends. In the machining step, the substitute tool  22  is disposed so as to be inscribed to the circle  84  of which diameter is the groove width of the groove portion  66  to be formed on the workpiece  1 . The machining is performed for a plurality of times by changing the relative position of the substitute tool  22  to the workpiece  1 . Adopting the method makes it possible to form a groove portion of which groove width is greater than a diameter of a rotary tool in a short time. Further, machining of a groove portion can be performed with high accuracy without using a rotary tool having a diameter identical to a groove width. Furthermore, there is no need to change a tool when a groove width of a groove portion to be generated is changed, and the groove portion can be formed by a rotary tool having a diameter smaller than the groove width. 
         [0095]    As a comparative example, when a groove portion having a large groove width is formed, a dedicated tool head (an eccentric holder) can be used which causes a rotary tool to make a planetary rotary motion. However, the dedicated tool head performing the planetary rotary motion has low rigidity, and therefore it is impossible to increase a cutting amount. Therefore, it is preferable to set a feed rate of the tool head to a small value. Therefore, there is a problem that when the tool head performing the planetary rotary motion is used, a machining time becomes longer. In contrast, the grooving method of the present embodiment can increase a cutting amount of a workpiece, and grooving can be performed in a short time. 
         [0096]    When the rotary tool makes the planetary rotary motion, there are many areas in which the rotary tool is not in contact with the workpiece, and machining takes a long time. In contrast, the grooving method of the present embodiment can set a path of the rotary tool in an area necessary for forming the groove portion  66 , and grooving can be performed in a short time. 
         [0097]    For example, as illustrated in  FIG. 6 , a range inscribed to the circle  84  of which diameter is the groove width of the groove portion  66  includes a range in which the side surface of the groove portion  66  is machined and a range in which the side surface of the groove portion  66  is not machined. In ranges close to the side surfaces of the groove portion, the side surfaces of the groove portion  66  are machined, however, ranges other than that, namely areas indicated by arrows  105  do not contribute to machining of the side surfaces of the groove portion  66 . Thus, the machining time can be shortened by disposing the substitute tool  22  avoiding the areas indicated by the arrows  105 . In the present embodiment, a range in which the substitute tool  22  is disposed to form the groove portion  66  is calculated, which is described below. Therefore, the grooving can be performed in a short period of time. 
         [0098]    Next, the control device of the machine tool and the tool path generation device are described which perform the grooving method of the present embodiment. 
         [0099]      FIG. 16  is a schematic view of a machining system which includes the machine tool  10  and a device for generating input numerical data  54  which is input to the machine tool  10  according to the present embodiment. In the present embodiment, a CAD (Computer Aided Design) apparatus  51  designs a shape of the workpiece  1 . The CAD apparatus  51  supplies shape data  52  of the workpiece  1  to a CAM (Computer Aided Manufacturing) apparatus  53 . The shape data  52  includes shape data of the groove portion  66  to be formed on the workpiece  1 . A user can input information of the specified tool  81  to the CAM apparatus  53 . In the present embodiment, the information of the specified tool  81  having a diameter identical to the groove width of the groove portion  66  is input. The specified tool  81  may be automatically specified by the CAM apparatus  53 . 
         [0100]    In the CAM apparatus  53 , the input numerical data  54  is generated based on the shape data  52  as input information to be input to the control device  55  of the machine tool  10 . The input numerical data  54  of the present embodiment is numerical data for forming a groove portion using the specified tool  81  having the diameter identical to the groove width of the groove portion  66 . 
         [0101]    The numerical control type machine tool  10  of the present embodiment includes the control device  55 . The control device  55  of the present embodiment includes an arithmetic processing device. The arithmetic processing device includes a microprocessor (CPU) performing arithmetic processing and the like, a ROM (Read Only Memory) and a RAM (Random Access Memory) as storage devices, and other peripheral circuits. 
         [0102]    The control device  55  generates output numerical data  62  using the input numerical data  54 . The output numerical data  62  includes an instruction issued to a machine when the substitute tool  22  having a tool diameter smaller than that of the specified tool  81  is used. The output numerical data  62  includes information of tool paths on which machining is performed for a plurality of times to form the groove portion  66 . In the present embodiment, the output numerical data  62  includes numerical data for relatively moving the substitute tool  22  to the workpiece  1 . 
         [0103]    The control device  55  of the present embodiment includes a numerical data reading unit  56  serving as an input information reading unit and a path setting unit  57 . The numerical data reading unit  56  has a function of reading the input numerical data  54 . The path setting unit  57  generates the output numerical data  62  based on the read input numerical data  54 . The path setting unit  57  of the present embodiment includes a virtual advancing direction setting unit  58 , a range setting unit  59 , and a position setting unit  60 . The output numerical data  62  is input to a numerical control unit  63 . The numerical control unit  63  drives an individual axis servomotor  64  based on the output numerical data  62 . The individual axis servomotor  64  includes the X-axis servomotor  38 , the Y-axis servomotor  31 , the Z-axis servomotor  25 , and the B-axis servomotor  43 . 
         [0104]      FIG. 17  is a flowchart illustrating control by the control device of the machine tool of the present embodiment. With reference to  FIG. 16  and  FIG. 17 , the input numerical data  54  generated by the CAM apparatus  53  is input to the numerical data reading unit  56  of the control device  55 . The input numerical data  54  of the present embodiment includes data indicating a path of the tool tip point when the specified tool  81  is used. The input numerical data  54  includes, for example, coordinate values of the XYZ axes and rotational angles of ABC axes. The input information to be input to the control device  55  is not limited to the above-described numerical data pieces, and input information indicating a path of an arbitrary portion of the specified tool can be adopted. 
         [0105]    First, in step  121 , the control device  55  reads the input numerical data  54  by the numerical data reading unit  56 . In step  122 , a coordinate value sequence is output. The coordinate value sequence of the control includes the coordinate values of the XYZ axes and the rotational angles of the ABC axes. 
         [0106]    Next, the path setting unit  57  sets a tool path on which machining is performed using the substitute tool  22  having a diameter smaller than that of the specified tool  81 . In step  123 , the virtual advancing direction setting unit  58  of the path setting unit  57  reads data of the machine tool  10 . The data of the machine tool  10  includes an axis constitution and a coordinate system of the machine tool  10  and so on. Next, in step  124 , the virtual advancing direction setting unit  58  calculates the virtual advancing direction. 
         [0107]      FIG. 18  is a schematic cross-sectional view illustrating the virtual advancing direction. The virtual advancing direction is an advancing direction of the specified tool  81  with respect to the workpiece  1  when it is assumed that the workpiece  1  is stopped. For the virtual advancing direction, directions that a plurality of points advances on each height of the specified tool  81  can be adopted. In the example illustrated in  FIG. 18 , the workpiece  1  is rotated in a direction indicated by the arrow  91  without changing the position of the specified tool  81 . In other words, the central axis  81   a  of the specified tool  81  is in a stopped state, and the workpiece  1  is rotated. If it is assumed that the workpiece  1  is stopped in this state, the virtual advancing direction of a tool tip point  81   c  of the specified tool  81  is a direction indicated by the arrow  101 . The virtual advancing direction can be set by, for example, a vector of a unit length on the XYZ axes. 
         [0108]      FIG. 19  is a schematic plan view illustrating when the grooving is performed according to the present embodiment. The virtual advancing direction of a point on a predetermined height of the specified tool  81  is indicated by the arrow  101 . Thus, the virtual advancing direction indicates a direction when the specified tool  81  having the diameter identical to a diameter of the circle  84  advances along the direction in which the groove portion  66  extends. 
         [0109]    With reference to  FIG. 16  and  FIG. 17 , up to step  124 , the virtual advancing direction is calculated on the assumption that the specified tool  81  is used. Next, a tool path of the substitute tool  22  is set based on the virtual advancing direction of the specified tool  81 . The range setting unit  59  of the control device  55  sets a range in which the substitute tool  22  is disposed. 
         [0110]    In step  125 , the range setting unit  59  reads machining setting data. The machining setting data includes the groove width and depth of the groove portion  66 , the tool diameter of the substitute tool  22 , and the like. In step  126 , the range in which the substitute tool  22  is disposed is set using the machining setting data and the virtual advancing direction. 
         [0111]    In the present embodiment, a portion which finally generates a machining surface is calculated based on the virtual advancing direction. The range in which the substitute tool is disposed is set based on the portion which finally generates the machining surface. The portion which finally generates the machining surface in the present embodiment is described below. 
         [0112]      FIG. 20  is a schematic perspective view of the specified tool according to the present embodiment.  FIG. 20  illustrates a portion of the specified tool  81  where actually performs machining. For example, an upper end of the specified tool  81  illustrated in  FIG. 20  is equivalent to an upper end of a groove portion. As described above, in the present embodiment, the virtual advancing direction gradually changes depending on a position in a height direction of the central axis  81   a  of the specified tool  81 . 
         [0113]    An intersection point of a direction of a point on the central axis  81   a  perpendicular to the virtual advancing direction and the surface of the specified tool  81  is a point on which the specified tool  81  is finally in contact with the workpiece  1  when machining the workpiece  1 . When the points are connected, the portion of the specified tool  81  which finally generates the machining surface is obtained. The portion which finally generates the machining surface in the present embodiment is indicated by a line  132 . 
         [0114]    As illustrated in  FIG. 5 , the virtual advancing direction changes in an axial direction of the specified tool  81 , and thus the line  132  which finally generates the machining surface of the present embodiment is not approximately parallel to the central axis  81   a  of the specified tool  81  but twisted with respect to the central axis  81   a . Further, the line  132  is curved. 
         [0115]    When the specified tool  81  moves to the virtual advancing direction indicated by the arrow  101 , cutting of the workpiece can be performed on a partial area on the surface of the specified tool  81 . A machining area  131  in which the workpiece is actually machined is set on a side to which the virtual advancing direction advances than the line  132 . The specified tool  81  includes the machining area  131  for forming a machining surface of the workpiece. In the machining area  131 , the groove portion  66  can be formed by cutting the workpiece  1 . An end of the machining area  131  is the portion which finally generates the machining surface. In the present embodiment, the portion which finally generates the machining surface is configured by a line; however, the portion which finally generates the machining surface is not limited to the above-described embodiment and may be a plane or dots. 
         [0116]    The line  132  which finally generates the machining surface can be set by calculation. As indicated by arrows  110  and  111 , a line perpendicular to the calculated virtual advancing direction is set. Points  183  and  184  are calculated which are intersection points of the line and the surface of the specified tool  81 . Similarly, a point on the surface of the specified tool  81  is calculated regarding each of a plurality of points on the central axis  81   a , so that the line  132  which finally generates the machining surface can be calculated. 
         [0117]    Next, the range in which the substitute tool  22  is disposed is set based on the calculated line  132  which finally generates the machining surface. 
         [0118]      FIG. 21  is a schematic perspective view illustrating the range in which the substitute tool is disposed. With reference to  FIG. 19  and  FIG. 21 , the substitute tool  22  is disposed in a manner that the surface of the substitute tool  22  is in contact with the surface of the specified tool  81  when the specified tool  81  is used. The substitute tool  22  is disposed to correspond to the line  132  of the specified tool  81  which finally generates the machining surface. An area between the point  183  of an upper end and the point  184  of a lower end of the line  132  which finally generates the machining surface can be set as the range in which the substitute tool  22  is disposed. In  FIG. 19 , the range in which the substitute tool  22  is disposed is indicated by an arrow  176 . 
         [0119]    With reference to  FIG. 16  and  FIG. 17 , the position setting unit  60  sets a position on which the substitute tool  22  is disposed within the range in which the substitute tool  22  is disposed. In step  127 , the position setting unit  60  reads the machining setting data. The machining setting data read here includes a scallop height, the tool diameter of the substitute tool, and the like. 
         [0120]      FIG. 22  is a schematic view illustrating the scallop height according to the present embodiment. In the present embodiment, the positions  85   a ,  85   b , and  85   c  of the substitute tool  22  are set so as to be inscribed to the circle  84 . Thus, the scallop height indicated by an arrow  106  is determined according to the number of the positions on which the substitute tool  22  is disposed. The scallop height also depends on the diameter of the substitute tool  22 . For example, the number of positions on which the substitute tool  22  is disposed is increased within the range in which the substitute tool  22  is disposed. In addition, an interval between positions on which the substitute tool  22  is disposed is decreased, so that the scallop height can be lessened. In other words, when the number of times to machine the side surface of the groove portion is increased, the scallop height can be lessened. 
         [0121]    With reference to  FIG. 16  and  FIG. 17 , in step  128 , the position of the substitute tool  22  can be set based on the input machining setting data, such as the scallop height. In the present embodiment, the number of positions on which the substitute tool is disposed can be calculated based on the scallop height. Thus, when an allowable value of the scallop height is specified, a plurality of positions of the substitute tool  22  can be set within the range in which the substitute tool  22  is disposed. In the present embodiment, the machining is performed three times. The position of the substitute tool  22  can be expressed by, for example, coordinate values of the XYZ axes. Alternatively, for example, a difference from the coordinate value sequence output in step  122  can be output. 
         [0122]      FIG. 23  is a schematic perspective view of the substitute tool when the substitute tool performs the machining of the first time.  FIG. 24  is a schematic perspective view of the substitute tool when the substitute tool performs the machining of the second time.  FIG. 25  is a schematic perspective view of the substitute tool when the substitute tool performs the machining of the third time.  FIG. 23  to  FIG. 25  illustrate states when the substitute tool moves in the outward path to form a side surface on one side of a groove portion according to the present embodiment. With reference to  FIG. 23 , a portion which finally generates a machining surface is also generated in the substitute tool  22 . In the machining of the first time by the substitute tool  22 , a line  132   a  of the substitute tool  22  which finally generates the machining surface is formed on an upper area of the groove portion. With reference to  FIG. 24 , in the machining of the second time by the substitute tool  22 , a line  132   b  of the substitute tool  22  which finally generates the machining surface is formed on a center area of the groove portion. With reference to  FIG. 25 , in the machining of the third time by the substitute tool  22 , a line  132   c  of the substitute tool  22  which finally generates the machining surface is formed on a lower area of the groove portion. 
         [0123]    When the lines  132   a ,  132   b , and  132   c , respectively illustrated in  FIG. 23  to  FIG. 25 , which finally generate the machining surface are combined, a line can be formed which corresponds to the line  132  which finally generates the machining surface when the specified tool  81  performs the machining. In the entire depth direction of the groove portion  66 , the groove portion can be formed to accurately match the desired shape. In other words, the groove portion can be formed which is approximately identical to the groove portion  66  formed by the specified tool  81 . 
         [0124]    With reference to  FIG. 16  and  FIG. 17 , next, the position setting unit  60  outputs the output numerical data  62  in step  129 . The output numerical data  62  can be set by, for example, the coordinates of the XYZ axes and a relative angle between the substitute tool  22  and the workpiece  1  on the ABC axes. 
         [0125]    As described above, the control device  55  of the present embodiment generates the output numerical data  62 . The numerical control unit  63  drives the individual axis servomotor  64  based on the output numerical data  62 . Accordingly, the position relative to workpiece  1  and the substitute tool  22  can be adjusted. 
         [0126]    The control device of the machine tool  10  of the present embodiment comprises the path setting unit. The path setting unit calculates the portion which finally generates the machining surface in the machining area  131  of the specified tool  81  when the specified tool  81  machines the workpiece  1  and sets a tool path of the substitute tool  22  based on the portion which finally generates the machining surface. According to the configuration, the machining can be performed using the substitute tool in place of the specified tool. In addition, the machining can be accurately performed. 
         [0127]    The path setting unit  57  further includes the virtual advancing direction setting unit  58  which sets the virtual advancing direction when the specified tool  81  machines the workpiece  1  based on the input numerical data  54 , the range setting unit  59  which calculates the portion which finally generates the machining surface using the virtual advancing direction and sets a range in which the substitute tool is disposed based on the portion which finally generates the machining surface, and the position setting unit  60  which sets a plurality of positions on which the substitute tool  22  is disposed within the range in which the substitute tool  22  is disposed. Adopting the configuration makes it possible to set tool paths of the substitute tool  22  for a plurality of times in a simple configuration. 
         [0128]    As described above, the tool path generation method of the present embodiment is a generation method of a tool path for calculating a tool path of the substitute tool  22 , and a tool path of the specified tool  81  when machining is performed by the specified tool  81  is set in advance. The method includes a tool path calculation step for calculating the tool path of the substitute tool  22  based on the tool path of the specified tool  81  when the machining is performed by the substitute tool  22  different from the specified tool  81 . In the tool path calculation step, the portion is calculated which finally generates the machining surface in the machining area of the specified tool  81  when the specified tool  81  machines the workpiece, and the tool path of the substitute tool is set based on the portion which finally generates the machining surface. Adopting the method enables the machining to be performed using the substitute tool in place of the specified tool. In addition, the tool path for accurately performing machining can be generated. 
         [0129]    Further, in the tool path generation method, the tool path calculation step includes a step for setting the virtual advancing direction when the specified tool  81  machines the workpiece  1  and a step for calculating the portion which finally generates the machining surface using the virtual advancing direction. Following these steps, the tool path calculation step can include a step for setting the range in which the substitute tool  22  is disposed based on the portion which finally generates the machining surface and a step for setting a plurality of positions on which the substitute tool  22  is disposed within the range in which the substitute tool  22  is disposed. 
         [0130]    In the above descriptions of the present embodiment, the CAM apparatus generates the input numerical data when the specified tool is used based on the shape data output from the CAD apparatus. The control device of the machine tool generates the output numerical data to be the tool path of the substitute tool using the input numerical data. However, it is not limited to the above-described embodiment, and the output numerical data can be generated in the CAM apparatus using the shape data output from the CAD apparatus. 
         [0131]      FIG. 26  is a schematic view of a machining system which includes the CAD apparatus and the tool path generation device of the present embodiment. The shape data  52  is generated in the CAD apparatus  51  similar to the machining system illustrated in  FIG. 16 . A tool path generation device  75  of the present embodiment has functions of the CAM apparatus. The tool path generation device  75  further has a function of generating the output numerical data  62  of the tool path on which machining is performed using the substitute tool based on the shape data  52 . 
         [0132]    The tool path generation device  75  of the present embodiment comprises a shape data reading unit  76  and a path setting unit  77 . The shape data reading unit  76  of the present embodiment reads the shape data  52  after the workpiece  1  is machined. The path setting unit  77  sets a tool path for a relative movement to the direction in which the groove portion  66  extends using the substitute tool  22  having a diameter smaller than that of the specified tool  81  based on the shape data  52  of the workpiece  1 . 
         [0133]    The path setting unit  77  has functions of, for example, the CAM apparatus  53 , the numerical data reading unit  56 , and the path setting unit  57  of the machining system illustrated in  FIG. 16 . The path setting unit  77  generates the input numerical data  54  indicating a path of the specified tool  81  based on, for example, the shape data  52 . The path setting unit  77  generates the output numerical data  62  indicating a path of the substitute tool  22  using the input numerical data  54 . At that time, the path setting unit  77  can calculate the line  132  which finally generates the machining surface in the machining area  131  of the specified tool  81  and set the tool path of the substitute tool  22  based on the line  132  which finally generates the machining surface. 
         [0134]    The output numerical data  62  is input to the machine tool  10 . The control device  55  of the machine tool  10  drives the individual axis servomotor  64  using the output numerical data  62 . The control device  55  can relatively move the substitute tool  22  to the workpiece  1 . 
         [0135]    The tool path generation device of the present embodiment can also generates the tool path using the substitute tool in place of the specified tool. 
         [0136]    The moving device which relatively moves the substitute tool  22  and the workpiece  1  in the present embodiment is configured to move the substitute tool  22  with respect to the workpiece  1  regarding the X axis and the Y axis, and move the workpiece  1  with respect to the substitute tool  22  regarding the Z axis and the B axis. However, the moving device is not limited to the above-described embodiment as long as the moving device can move at least one of the workpiece and the rotary tool with respect to each axis. 
         [0137]    In the present embodiment, the virtual advancing direction of the specified tool is calculated, and a range and a position to which the substitute tool is disposed are set based on the virtual advancing direction. However, it is not limited to the above-described embodiment, and the position on which the substitute tool is disposed may be set without using the virtual advancing direction. For example, the position of the substitute tool may be set by estimating the portion of the specified tool which finally generates the machining surface based on the direction in which the groove portion extends. 
         [0138]    In the present embodiment, grooving of a cylindrical cam in which a depth and a groove width of the groove portion are constant is described as an example. However, the present invention is not limited to the above-described embodiment and can be applied to arbitrary machining. 
         [0139]      FIG. 27  is a schematic perspective view of an end cam. An end cam  136  includes an end face  136   a . The end face  136   a  is in contact with a cam follower  135 . The cam follower  135  is formed in a columnar shape and rotatably supported. The cam follower  135  is in contact with the end face  136   a  on a circumferential surface thereof. The end cam  136  and the cam follower  135  move by rotating around a central axis  137 , so that top and bottom positions of the cam follower  135  can be changed. 
         [0140]    In machining of the end face  136   a  of the end cam  136 , it is preferable to use a rotary tool having a tool diameter identical to a diameter of the cam follower  135 . It is preferable that a rotation axis of the cam follower  135  when rotating and a rotation axis of the rotary tool match each other to perform machining. 
         [0141]    For example, the end face  136   a  can be formed by rotating a workpiece around the central axis  137  to perform cutting using an end mill having a diameter identical to the diameter of the cam follower  135 . According to the above-described method, the end face  136   a  having a desired shape can be formed. 
         [0142]    On the other hand, when a rotary tool having a tool diameter different from the diameter of the cam follower  135  is used as the rotary tool to machine the end face  136   a , the end face  136   a  may not be a smooth surface. Accordingly, when the end cam  136  is driven, movement of the cam follower  135  may not be smooth. 
         [0143]    However, it is sometimes difficult to prepare a rotary tool having a tool diameter identical to the diameter of the cam follower  135 . Thus, when an end mill having a diameter smaller than, for example, a desired tool diameter is used, an eccentric holder, which revolves the end mill while rotating it, is used. However, there is a need to prepare the eccentric holder, and it may elongate a machining time. 
         [0144]    When such an end face  136   a  of the end cam  136  is manufactured, a method and a device similar to grooving in the present embodiment can be applied to. In other words, the end face  136   a  of the end cam  136  can be formed similar to a side surface of a groove portion. For example, machining can be performed using a rotary tool having a diameter smaller than the diameter of the cam follower  135  while rotating the end cam  136  around the central axis  137 . 
         [0145]    In this case, a rotary tool having a tool diameter identical to the diameter of the cam follower  135  can be specified as a specified tool. In addition, a rotary tool having a tool diameter smaller than the diameter of the cam follower  135  can be specified as a substitute tool. A portion of the specified tool which finally generates a machining surface is calculated, and a tool path of the substitute tool is calculated based on the portion which finally generates the machining surface. The substitute tool performs the machining using the calculated tool path and can form a smooth end face  136   a . Adopting the method and the device in the present embodiment makes it possible to machine the end face  136   a  into a desired shape. Accordingly, movement of the cam follower  135  can be smooth. 
         [0146]      FIG. 28  is a schematic diagram illustrating a portion of a tool which finally generates a machining surface when various workpieces are machined.  FIG. 28  is a schematic cross-sectional view of an example of a tool  181  having a circular cross sectional shape. The tool  181  rotates around a tool center point  181   a . A surface of the tool  181  machines a workpiece. On the surface of the tool  181 , a portion which finally generates a machining surface can be calculated by the following method. 
         [0147]    An arbitrary point p is set on the surface of the tool  181 . A normal direction of the surface of the tool  181  on the point p is set as N(p). A virtual advancing direction on the point p at a predetermined time t 1  is set as V(p, t 1 ). A virtual advancing direction on the point p at a time t 2  later than the time t 1  is set as V(p, t 2 ). In this case, in machining performed in a period from the time t 1  to the time t 2 , the portion of the tool  181  which finally generates the machining surface is defined by the following expression. In the following expression, an inner product of N(p) and V(p, t 1 ) and an inner product of N(p) and V(p, t 2 ) are used. 
         [0000]        N ( p )· V ( p,t 1)≧0  (1)
 
         [0000]        N ( p )· V ( p,t 2)≦0  (2)
 
         [0148]    The mathematical symbol “·” indicates an inner product. An area satisfying both of the above expressions (1) and (2) corresponds to the portion which finally generates the machining surface in the period from the time t 1  to the time t 2 . In  FIG. 28 , an area satisfying the above expression (1) is indicated by an arrow  173 . An area satisfying the above expression (2) is indicated by an arrow  174 . An area indicated by an arrow  175 , where the area indicated by the arrow  173  and the area indicated by the arrow  174  overlap with each other, corresponds to the portion which finally generates the machining surface. For example, a plurality of points p is generated on an entire surface of the tool  181 , and a portion where the points p satisfying the above-described expressions (1) and (2) exist is the portion which finally generates the machining surface. 
         [0149]    The estimation of the portion which finally generates the machining surface based on the expressions (1) and (2) is not limited to a tool having a circular cross sectional shape and can be applied to a tool having an arbitrary shape. In addition, a machining shape of a workpiece is not limited to a groove, and an arbitrary shape can be adopted. 
         [0150]    The numerical control-type machine tool of the present embodiment includes one rotational feed axis and a plurality of linear feed axes. However, the present invention is not limited to the above-described embodiment and can be applied to numerical control-type machine tools performing arbitrary machining. Further, the specified tool and the substitute tool of the present embodiment are flat end mills. In other words, the substitute tool of the present embodiment is a similar type tool to the specified tool. However, the substitute tool is not limited to the above-described embodiment and may be a different type of tool from the specified tool. Further, when a tool other than the rotary tool is used, an instruction regarding a rotation phase of the spindle may be added to a setting of a tool position. 
         [0151]    In the machining of the present embodiment, a feed rate for relatively advancing a rotary tool to a workpiece while rotating the rotary tool is approximately constant. However, the feed rate is not limited to the above-described embodiment and may be changed depending on a cutting amount of the workpiece. The above-described control can shorten a machining time and elongate a tool life. 
       Second Embodiment 
       [0152]    A tool path generation method, a control device of a machine tool, and a tool path generation device according to the second embodiment are described with reference to  FIG. 29  to  FIG. 37 . Processing in the present embodiment, a recess portion is generated on a surface of a workpiece. In the present embodiment, a specified tool is also specified in advance, and a substitute tool is used in actual machining in place of the specified tool. 
         [0153]      FIG. 29  is a schematic cross-sectional view of a workpiece when machining is performed by a substitute tool  151  according to the present embodiment.  FIG. 30  is a schematic plan view of the workpiece  1  when machining is performed by the substitute tool  151  according to the present embodiment.  FIG. 29  illustrates a specified tool  140  in addition to the substitute tool  151 . With reference to  FIG. 29  and  FIG. 30 , a recess portion  141  having a circular arc cross sectional shape is formed on a surface of the workpiece  1  in the present embodiment. The surface of the workpiece  1  of the present embodiment is a planar shape. As a tool to cut the workpiece  1 , a ball end mill having a hemispherical tip end is used. The substitute tool  151  forms the recess portion  141  by performing machining for a plurality of times. 
         [0154]      FIG. 31  is a schematic cross-sectional view illustrating when the recess portion is formed on the workpiece using the specified tool  140 .  FIG. 32  is a schematic plan view illustrating when the recess portion is formed on the workpiece using the specified tool  140 . In the present embodiment, the specified tool  140  is also an optimum tool to form a desired recess portion  141 . The specified tool  140  is a ball end mill. A shape of a tip end portion of the specified tool  140  matches with a shape of the desired recess portion  141 . Thus, as indicated by an arrow  171 , when the specified tool  140  is moved to a direction for approaching the workpiece  1  while rotating and is pressed against the workpiece  1 , the recess portion  141  having a desired shape can be formed. In other words, the workpiece  1  is cut by a part of a hemispherical portion on the tip end of the specified tool  140 , and the recess portion  141  can be formed. 
         [0155]    With reference to  FIG. 29  and  FIG. 30 , in the present embodiment, the substitute tool  151  is used in place of the specified tool  140 . The substitute tool  151  is a ball end mill having a tool diameter smaller than that of the specified tool  140 . In other words, the substitute tool  151  is a tool which is the same type as that of the specified tool  140  and smaller than the specified tool  140 . 
         [0156]    In the present embodiment, a tool path of the substitute tool  151  is also set so as to form a machining surface of the workpiece  1  into a desired shape. Similar to the first embodiment, the tool path of the substitute tool  151  is set based on a portion of the specified tool  140  which finally generates a machining surface. In the present embodiment, the portion of the specified tool  140  which finally generates the machining surface is also calculated, and a range in which the substitute tool  151  is disposed is set based on the portion which finally generates the machining surface. Further, a position on which the substitute tool  151  is disposed is set within the range. 
         [0157]    In the present embodiment, the machining can also be performed using the machine tool described in the first embodiment. With reference to  FIG. 1 , in the present embodiment, the substitute tool  151  is attached in place of the substitute tool  22 . The workpiece  1  is fixed to the rotary table  42 . After setting positions in the X-axis direction and the Y-axis direction, and around the B axis of the substitute tool  151  to the workpiece  1 , the substitute tool  151  is fixed not to move in the X-axis direction and the Y-axis direction, and around the B axis. In the state, the substitute tool  151  is relatively moved to the workpiece  1  in the Z-axis direction. In the present embodiment, the workpiece  1  is moved in the Z-axis direction, and thus the substitute tool  151  can be moved to a direction for approaching the workpiece  1 . 
         [0158]    In the present embodiment, the machining can also be performed using the machining system illustrated in  FIG. 16  and the control illustrated in  FIG. 17  of the first embodiment. With reference to  FIG. 16  and  FIG. 17 , the input numerical data  54  when the specified tool  140  is used is generated by the CAD apparatus  51  and the CAM apparatus  53 . 
         [0159]    Next, the numerical data reading unit  56  reads the input numerical data  54 . The numerical data reading unit  56  outputs the coordinate value sequence. Next, the virtual advancing direction setting unit  58  reads the machine tool data. The virtual advancing direction setting unit  58  calculates the virtual advancing direction. In the present embodiment, the substitute tool  151  does not move in the X-axis direction and the Y-axis direction, and around the B axis during a machining period, and thus the virtual advancing direction is a direction that the substitute tool  151  is relatively moved to the workpiece  1  in the Z-axis direction. With reference to  FIG. 31 , the virtual advancing direction of the specified tool  140  is indicated by the arrow  171 . 
         [0160]    Next, the range setting unit  59  reads the machining setting data. The machining setting data of the present embodiment includes a diameter in a plane view of the recess portion  141 , a depth of the recess portion  141 , the tool diameter of the substitute tool  151 , and the like. Next, the range in which the substitute tool  151  is disposed is calculated. In the present embodiment, an area forming the recess portion  141  on the tip end of the specified tool  140  is the range in which the substitute tool  151  is disposed. With reference to  FIG. 31 , a ball end mill includes a boundary  143  between a hemispherical portion on a tip end and a cylindrical portion. In the present embodiment, a center of a circle forming the hemispherical tip end of the tool is referred to as a tool center  140   a . The virtual advancing direction is parallel to a direction to which the central axis of the specified tool  140  extends, as indicated by the arrow  171 . 
         [0161]    At the tool center  140   a , an angle θm to the virtual advancing direction is calculated based on a shape of the recess portion  141 . A surface of the specified tool  140  within a range of the calculated angle θm is indicated by an arrow  172 . The range indicated by the arrow  172  is the portion of the specified tool  140  which finally generates the machining surface. In the present embodiment, the portion of the specified tool  140  which finally generates the machining surface is configured by a plane. Further, in the present embodiment, the portion of the specified tool  140  which finally generates the machining surface is the range in which the substitute tool  151  is disposed. 
         [0162]    In the present embodiment, the virtual advancing direction is calculated, and the portion which finally generates the machining surface is calculated based on the virtual advancing direction. However, it is not limited to the above-described embodiment, and the portion which finally generates the machining surface may be calculated without using the virtual advancing direction. 
         [0163]    With reference to  FIG. 16  and  FIG. 17 , next, the position setting unit  60  reads the machining setting data including a scallop height and the like. The position setting unit  60  further sets the position on which the substitute tool  151  is disposed. 
         [0164]      FIG. 33  is a flowchart illustrating control for setting the position on which the substitute tool  151  is disposed in the present embodiment. In step  161 , the range in which the substitute tool  151  is disposed is read.  FIG. 34  is a schematic perspective view of the specified tool  140 . A part of the tip end of the specified tool  140  is the portion which finally generates the machining surface and equivalent to a range  142  in which the substitute tool  151  is disposed. 
         [0165]    With reference to  FIG. 33 , next, in step  162 , a plurality of points p is set on the portion which finally generates the machining surface. The points p are points to contact with the substitute tool  151  later. 
         [0166]      FIG. 35  is a schematic view of the specified tool  140  seen from the tip end. In other words,  FIG. 35  is a bottom view of the specified tool  140 . The range  142  in which the substitute tool  151  is disposed is set to a central part of the specified tool  140 . The plurality of points p is set within the range  142 . A plurality of predetermined numbers of points p can be set. In the setting of the points p, the points p are generated, for example, at irregular positions. Then, the points p can be moved so that intervals between the points p become as even as possible by using a simulation apparatus. For example, regarding an arbitrary point p, a repulsive force is applied to intervals between other points or a boundary of the range  142 . The point p can be moved by setting so that a greater force is applied as the distance is smaller. The above-described simulation is continued for a predetermined time period, and a state becomes in approximate equilibrium. All of the points p can be disposed approximately evenly. 
         [0167]    Next, it is determined whether the scallop height is an allowable value or less when the substitute tool  151  is brought into contact with the set point p. In the present embodiment, the number of positions on which the substitute tool  151  is disposed is set so that the scallop height of the recess portion  141  is a predetermined allowable value or less. 
         [0168]      FIG. 36  is a schematic cross-sectional view illustrating the scallop height according to the present embodiment. In the present embodiment, irregularity is generated on a surface of the recess portion  141  depending on the number of positions on which the substitute tool  151  is disposed. A height indicated by the arrow  106  is the scallop height. In the present embodiment, the scallop height can also be reduced by increasing the number of positions on which the substitute tool  151  is disposed. In the present embodiment, the scallop height after machining is determined using an angle around the tool center  140   a  of the specified tool  140 . 
         [0169]      FIG. 37  is a schematic view illustrating the specified tool  140  and the substitute tool  151  according to the present embodiment. The points p are points which are randomly set in step  162  and in contact with the substitute tool  151 . An arbitrary point x different from the point p is set in the range  142  in which the substitute tool  151  is disposed. A plurality of points x is set. From the plurality of points p, one of the point p nearest to the points x can be selected. In this case, an angle θx between a line connecting the tool center  140   a  and the point p and a line connecting the tool center  140   a  and the point x can be calculated. The smaller a maximum value of a distance between the point x and the point p is at the plurality of points x, the smaller the scallop height becomes. Thus, when many points x are generated, and the angles θx regarding all of the points x are a predetermined allowable angle or less, the scallop height can be the allowable value or less. 
         [0170]    With reference to  FIG. 33 , in step  163 , an angle judgment value is calculated. The angle judgment value can be calculated based on an allowable value H of the scallop height, a tool diameter R of the specified tool, and a tool diameter r of the substitute tool, which are criteria of judgment. 
         [0171]    Next, in step  164 , the point x is generated within the range  142  in which the substitute tool is disposed. In the present embodiment, a predetermined number of the points x is generated. Regarding the setting of the point x, a method similar to the setting of the position of the point p can be adopted. 
         [0172]    Next, in step  165 , the angle θx relating to the point x and the point p nearest to the point x is calculated. The calculation is executed on all of the points x. A maximum angle θxmax is selected from a plurality of calculated angles θx. 
         [0173]    Next, in step  166 , it is determined whether the calculated maximum angle θxmax is the angle judgment value or less. In step  166 , when the calculated maximum angle θxmax is greater than the angle judgment value, it can be determined that a generated scallop height becomes larger than the allowable value. In this case, the processing is shifted to step  167 . In step  167 , the number of points p is increased. For example, a predetermined number of points is added to the number of current points p. Then, the processing returns to step  162 , and the positions of the points p are newly set. As described above, the control to increase the number of positions on which the substitute tool is disposed is performed until the scallop height of the recess portion becomes the allowable value or less. 
         [0174]    In step  166 , when the calculated maximum angle is the angle judgment value or less, it can be determined that the scallop height is the allowable value or less. In other words, it can be determined that a desired scallop height is achieved. In this case, the processing is shifted to step  168 . 
         [0175]    In step  168 , the position of the substitute tool  151  is set. The substitute tool  151  is set to be in contact with the point p. The point p is set on a surface of the portion which finally generates the machining surface. In the present embodiment, positions of the X-axis direction, the Y-axis direction, and the Z-axis direction are set. As described above, the position on which the substitute tool  151  is disposed can be set. The machine tool of the present embodiment can set the number of position to dispose the substitute tool  151  within the range in which the substitute tool  151  is disposed so that the scallop height is a desired height or less. 
         [0176]    With reference to  FIG. 16  and  FIG. 17 , next, the position setting unit  60  can generate the output numerical data  62  based on the calculated position of the substitute tool  151 . The output numerical data  62  includes the tool path of the substitute tool  151 . Next, similar to the first embodiment, the numerical control unit  63  can drive the individual axis servomotor  64  based on the output numerical data  62 . 
         [0177]    Similar to the tool path generation method of the first embodiment, the tool path generation method of the present embodiment includes the tool path calculation step for calculating the tool path of the substitute tool  151 . In the tool path calculation step, the portion which finally generates the machining surface can be calculated in the machining area of the specified tool  140  when the specified tool  140  machines the workpiece  1 , and the tool path of the substitute tool  151  can be set based on the portion which finally generates the machining surface. 
         [0178]    In the tool path generation device of the present embodiment, the tool path of the substitute tool  151  can also be formed similar to the tool path generation device of the first embodiment. With reference to  FIG. 26 , the tool path generation device  75  reads the shape data of the workpiece  1  by the shape data reading unit  76 . Next, the path setting unit  77  can set the tool path of the substitute tool  151  when the substitute tool  151  performs the machining which is different from the specified tool  140  specified in advance. In this case, the path setting unit  77  can set the tool path of the specified tool  140  when the workpiece  1  is machined by the specified tool  140 , calculate the portion which finally generates the machining surface in the machining area of the specified tool  140  when the specified tool  140  performs the machining, and set the tool path of the substitute tool  151  based on the portion which finally generates the machining surface. 
         [0179]    The other configurations, functions, and effects are similar to those in the first embodiment, and the descriptions thereof are not repeated. 
         [0180]    The above-described embodiments can be appropriately combined with each other. In the above-described drawings, the same reference numerals are attached to the same or corresponding portions. The above-described embodiments are merely examples and are in no way intended to limit the invention. Further, the above-described embodiments include modifications indicated in the scope of claims. 
       REFERENCE SIGNS LIST 
       [0000]    
       
           1  workpiece 
           10  machine tool 
           20  spindle 
           22 ,  151  substitute tool 
           55  control device 
           57  path setting unit 
           58  virtual advancing direction setting unit 
           59  range setting unit 
           60  position setting unit 
           75  tool path generation device 
           76  shape data reading unit 
           77  path setting unit 
           81 ,  140  specified tool