Abstract:
The machine tool control device is provided with a calculation unit for estimating, on the basis of the tool path for machining using a tool and information on the workpiece, the portion of the tool that will form the final machined surface. The control device is provided with a feed rate-setting unit for estimating the fastest moving point, among multiple moving points contained in the portion that will form the final machined surface, for which the relative velocity of the tool with respect to the workpiece will be maximal and setting the feed rates for the machine tool movement shafts so that the relative velocity of the fastest moving point is at or below a previously specified relative velocity.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a U.S. National Phase patent application of International Patent Application No. PCT/JP2012/078050, filed on Oct. 30, 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 control device of a machine tool and the machine tool. 
       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 performs machining by automatically moving the tool with respect to a workpiece. The numerical control type machine tool can perform machining using a desired tool path at a desired feed rate by describing coordinates and a movement speed in a machining program. 
         [0004]    Patent literature 1 discloses a speed control method for moving a tip end of a tool at a given command movement speed when machining is performed by changing an angle of the tool. This patent literature discloses that a distribution moving amount of each predetermined period is calculated on condition that linear interpolation is performed using only a linear moving axis without regard to an angle change of a tool, and a position deviation caused by a rotational movement later occurring on a tip end of the tool is added to the distribution moving amount. 
       CITATIONS LIST 
       [0005]    Patent literature 1: Japanese Laid-open Patent Publication No. 6-332524 
       SUMMARY OF THE INVENTION 
       [0006]    A feed rate which is a relative movement speed of a tool to a workpiece is known to have an influence on machining accuracy of a machining surface. When the feed rate is lowered, a high precision machining surface can be generated. On the other hand, when the feed rate is lowered including a sufficient margin, a machining time is elongated. Thus, it is preferable to accurately control the feed rate to be a desired speed. 
         [0007]    In a conventional technique, it is known that a feed rate regarding a moving axis of a machine tool is input to a machining program. However, the feed rate regarding the moving axis of the machine tool sometimes does not match a speed of a machining part of a tool with respect to a machining surface of a workpiece. For example, when a cylindrical cam is manufactured, a groove portion is formed on a surface of a columnar workpiece. Since the groove portion is formed on a circumferential surface of the workpiece, the tool rotationally moves with respect to the workpiece. When the workpiece is machined in a curved shape associated with a movement of a rotational feed axis as described above, a speed in a part of an area in which the tool machines the workpiece may sometimes differ from the feed rate of the moving axis of the machine tool. Thus, the machining accuracy of the machining surface of the workpiece may sometimes be lowered than a desired accuracy. 
         [0008]    A control device of a machine tool of the present invention is a control device of a machine tool which machines a workpiece while a tool is made move relative to the workpiece and includes an arithmetic unit configured to estimate a portion of the tool which finally generates a machining surface when the tool machines the workpiece based on a tool path for the tool to perform machining and information of the workpiece. The control device includes a feed rate setting unit configured to estimate a fastest moving point at which a relative speed of the tool to the workpiece is a maximum among a plurality of moving points included in the portion which finally generates the machining surface and set a feed rate regarding a moving axis of the machine tool so that a relative speed of the fastest moving point is a preliminarily specified relative speed or less. 
         [0009]    According to the above-described invention, a plurality of relative positions of the tool to the workpiece can be specified in input numerical data to be input to the arithmetic unit, the plurality of relative positions includes a first relative position and a second relative position immediately after the first relative position, and the feed rate setting unit can estimate the fastest moving point in a movement from the first relative position to the second relative position and set the feed rate regarding the moving axis in the movement from the first relative position to the second relative position. 
         [0010]    According to the above-described invention, the feed rate setting unit can set the feed rate regarding the moving axis based on a length of time in which it takes the tool to move from the first relative position to the second relative position with respect to the workpiece. 
         [0011]    According to the above-described invention, the arithmetic unit can generate a third relative position between the first relative position and the second relative position, and the feed rate setting unit can estimate the fastest moving point in a movement between two successive relative positions and set the feed rate regarding the moving axis in the movement between the two successive relative positions. 
         [0012]    The machine tool of the present invention includes the above-described control device of the machine tool and a moving device which make the tool move relative to the workpiece based on the feed rate set by the feed rate setting unit. 
         [0013]    According to the present invention, a control device of a machine tool and the machine tool which suppress deterioration of machining accuracy on a machining surface can be provided. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is a schematic view of a numerical control type machine tool. 
           [0015]      FIG. 2  is a schematic view of a workpiece and a groove portion when grooving is performed using a substitute tool. 
           [0016]      FIG. 3  is a schematic view of a workpiece and a groove portion when grooving is performed using a specified tool. 
           [0017]      FIG. 4  is a view illustrating a trace of a central axis of the specified tool when grooving is performed using the specified tool. 
           [0018]      FIG. 5  is a schematic view illustrating a virtual advancing direction and a portion where a workpiece is machined when grooving is performed using the specified tool. 
           [0019]      FIG. 6  is a schematic cross-sectional view illustrating when grooving is performed using the substitute tool. 
           [0020]      FIG. 7  is a schematic view illustrating machining on an outward path and a return path in grooving of a first time. 
           [0021]      FIG. 8  is a schematic view illustrating machining on the outward path and the return path in the grooving of a second time. 
           [0022]      FIG. 9  is a schematic view illustrating machining on the outward path and the return path in the grooving of a third time. 
           [0023]      FIG. 10  is a schematic cross-sectional view illustrating machining on the outward path in the grooving of the first time. 
           [0024]      FIG. 11  is a schematic cross-sectional view illustrating machining on the outward path in the grooving of the second time. 
           [0025]      FIG. 12  is a schematic cross-sectional view illustrating machining on the outward path in the grooving of the third time. 
           [0026]      FIG. 13  is a schematic view of a machining system which machines a workpiece using the substitute tool. 
           [0027]      FIG. 14  is a flowchart illustrating control by the control device of the machine tool. 
           [0028]      FIG. 15  is a schematic cross-sectional view illustrating a virtual advancing direction of the specified tool. 
           [0029]      FIG. 16  is a schematic view illustrating the virtual advancing direction of the specified tool and a range in which the substitute tool is disposed. 
           [0030]      FIG. 17  is a schematic perspective view illustrating a machining area of the specified tool and a line which finally generates a machining surface. 
           [0031]      FIG. 18  is a schematic perspective view of the specified tool and the substitute tool illustrating a position on which the substitute tool is disposed. 
           [0032]      FIG. 19  is a schematic view illustrating a scallop height when a workpiece is machined. 
           [0033]      FIG. 20  is a view illustrating a line of the substitute tool which finally generates a machining surface in the machining on the outward path in the grooving of the first time. 
           [0034]      FIG. 21  is a view illustrating a line of the substitute tool which finally generates a machining surface in the machining on the outward path in the grooving of the second time. 
           [0035]      FIG. 22  is a view illustrating a line of the substitute tool which finally generates a machining surface in the machining on the outward path in the grooving of the third time. 
           [0036]      FIG. 23  is a schematic perspective view illustrating the substitute tool disposed on a first relative position and a second relative position in a tool path of the substitute tool. 
           [0037]      FIG. 24  is a schematic view of output numerical data. 
           [0038]      FIG. 25  is a schematic perspective view illustrating the specified tool disposed on a first relative position and a second relative position in a tool path of the specified tool. 
           [0039]      FIG. 26  is a schematic view of a machining system which machines a workpiece using the specified tool. 
           [0040]      FIG. 27  is a schematic perspective view of an end cam. 
           [0041]      FIG. 28  is a schematic perspective view of a face cam. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0042]    A control device of a machine tool and the machine tool according to an embodiment are described with reference to  FIG. 1  to  FIG. 28 . As the machine tool, a horizontal machining center in which a spindle extends in a horizontal direction is described as an example. Grooving which forms a groove portion on a workpiece is described as an example. According to the present embodiment, a substitute tool smaller than a specified tool is used for grooving in place of the specified tool specified by a user. 
         [0043]      FIG. 1  is a schematic view of a numerical control type machine tool. A substitute tool  22  is mounted on a machine tool  10  illustrated in  FIG. 1  as a rotary tool performing machining. The machine tool  10  includes a moving device which relatively moves the substitute tool  22  and a workpiece  1 . The moving device includes a plurality of moving axes. The plurality of moving axes includes an X axis, a Y axis, and a Z axis, which are linear feed axes, and a B axis, which is a rotational feed axis. 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 guide rail  28  is disposed to extend in a Z-axis direction (a right and left direction in  FIG. 1 ). 
         [0044]    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  around the B axis 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 . 
         [0045]    An X-axis guide rail  36  is fixed to an upper surface of the bed  12 . The X axis 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. 
         [0046]    A Y-axis guide rail  34  is fixed to a front surface of the column  16 . The front surface faces to the workpiece  1 . The Y axis 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 . 
         [0047]    The moving device includes a Z-axis moving device which relatively moves the substitute tool  22  to the workpiece  1  in the Z-axis direction. 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. 
         [0048]    The moving device includes an X-axis moving device which makes the substitute tool  22  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. 
         [0049]    The moving device includes a Y-axis moving device which makes the substitute tool  22  move relative to the workpiece  1  in the 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  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 X-axis direction. 
         [0050]    The moving device includes a B-axis moving device which makes the substitute tool  22  move relative to the workpiece  1  around the B axis. 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 around the B axis. 
         [0051]    The substitute tool  22  is disposed on a tip end of the spindle  20 . A flat end mill as a rotary tool 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. 
         [0052]    As described above, the machine tool  10  includes the linear feed axes (the X axis, the Y axis, and the Z axis) and the rotational feed axis (the B axis) and thus can make the substitute tool  22  move relative to the workpiece  1  fixed to the table  14  by operating the column  16 , the spindle head  18 , and the table  14  along the X-axis, the Y-axis, and the Z-axis directions. Further, the machine tool  10  can drive the rotary table  42  to rotate the workpiece  1  around the B axis. The substitute tool  22  can rotationally move relative to the workpiece  1 . 
         [0053]      FIG. 2  is a schematic plan view of the workpiece  1 . 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 on the workpiece  1 , and, for example, a cylindrical cam can be manufactured. 
         [0054]    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 around the B axis. 
         [0055]    In the grooving 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  has an approximately quadrangular cross section, a side surface  66   a  on one side, and a side surface  66   b  on the other side. The groove portion  66  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. 
         [0056]    A grooving method 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 moved relative 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 , the spindle  20  is moved in the Y-axis direction. The workpiece  1  is moved relative to the substitute tool  22  in the Y-axis direction as indicated by an arrow  92 . Further, the workpiece  1  is moved relative 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. 
         [0057]    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 moved relative to the direction in which the groove portion  66  extends, and the groove portion  66  is formed. 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. 
         [0058]    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 a desired shape, and insufficient 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 . Insufficient 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 . 
         [0059]      FIG. 3  is a schematic plan view of the workpiece  1  when machining is performed using the specified tool. A specified tool  81  is a rotary tool having a diameter identical to the groove width of the groove portion  66 . The specified tool  81  is a flat end mill. The specified tool  81  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 , the workpiece  1  is rotated around the B axis while the spindle  20  is moved in the Y-axis direction. The workpiece  1  is moved relative 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. 
         [0060]      FIG. 4  is a schematic view illustrating a trace 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 so that the central axis  81   a  of the specified tool  81  faces a radial direction of the workpiece  1 . In other words, the specified tool  81  is disposed so that the central axis  81   a  intersects with the central axis  1   a  of the workpiece  1 . 
         [0061]    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 trace  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 end point. A development view  72  is a view that a circumferential area of the workpiece  1  which passes the tool tip end point is developed as indicated by arrows  97 . A trace  72   a  of the tool tip end point is depicted in the development view  72 . 
         [0062]    When comparing the trace  71   a  of points on the tool central axis  81   a  on the surface of the workpiece  1  with the trace  72   a  of the tool tip end points, it is understood that shapes of these traces 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 traces 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 . 
         [0063]      FIG. 5  is a schematic view illustrating a direction to which the central axis  81   a  moves when the specified tool  81  is moved relative 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 . 
         [0064]    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 line finally generating a machining surface of the workpiece when the workpiece is machined, which is described below. In the example illustrated in  FIG. 5 , the line of the contact portion  81   b  is not 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. 
         [0065]    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 disposed so that a central axis  22   a  is parallel to the central axis  81   a  of the specified tool  81 . Further, the substitute tool  22  can be disposed in a manner that a surface of the substitute tool  22  is in contacts 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 , insufficient cutting part is generated in some areas in the depth direction of the groove portion  66 . The grooving of the present embodiment 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. Accordingly, 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 the side surface of the groove portion  66 . 
         [0066]      FIG. 6  is a schematic cross-sectional view illustrating the grooving using the substitute tool  22 . In the grooving, 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. 
         [0067]    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 . 
         [0068]    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 . 
         [0069]    In the grooving method, 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 the example illustrated in  FIG. 6 , the substitute tool  22  is disposed on a position  85   a  in the machining of the side surface  66   a  of a first time. Then, as indicated by an arrow  103 , the substitute tool  22  is moved relative 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 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 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 contacts a position of the surface of the specified tool  81  when the specified tool  81  is used. 
         [0070]    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 . 
         [0071]    In the present embodiment, the machining is performed 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. 
         [0072]      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. 
         [0073]      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. 
         [0074]      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, similar to the machining of the first time and the second time, the substitute tool  22  is also disposed on the position  85   c  on the outward path to perform the machining on the side surface  66   a  on one side and is disposed on the position  86   c  on the return path to perform the machining on the side surface  66   b  on the other side. 
         [0075]      FIG. 10  is a schematic cross-sectional view illustrating when the machining of the first time is performed on the outward path.  FIG. 11  is a schematic cross-sectional view illustrating when the machining of the second time is performed on the outward path.  FIG. 12  is a schematic cross-sectional view illustrating when the machining of the third time is performed on the outward path. Each drawing illustrates a machining surface  67  having a shape desired by a user. The machining is performed for a plurality of times to match the side surface  66   a  of the groove portion  66  with the machining surface  67 . 
         [0076]    With reference to  FIG. 10 , 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  in the machining on the outward path of the first time. 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 insufficient cutting part is generated. With reference to  FIG. 11 , 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  in the machining on the outward path of the second time. With reference to  FIG. 12 , the insufficient cutting part on the lower portion of the side surface  66   a  on one side can be cut in the machining on the outward path of the third time. Accordingly, the groove portion  66  can match the machining surface  67  having the desired shape. In the machining on the return path, similar to the machining on the outward path, the side surface  66   b  on the other side of the groove portion  66  can match the machining surface  67  by the machining performed for a plurality of times. 
         [0077]    As described above, the grooving method 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 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 enables the machining of a groove portion to be performed with high accuracy without using a rotary tool having a diameter identical to a groove width. 
         [0078]    Next, the control device of the machine tool is described which perform the grooving method according to the present embodiment. 
         [0079]      FIG. 13  is a schematic view of a machining system which includes the machine tool  10  and a device for generating input numerical data  54  input to the machine tool  10 . 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 . 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 . 
         [0080]    In the CAM apparatus  53 , the input numerical data  54  as input information to be input to the control device  55  of the machine tool  10  is generated based on the shape data  52 . The input numerical data  54  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 . 
         [0081]    The numerical control type machine tool  10  includes the control device  55 . The control device  55  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. 
         [0082]    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 . The output numerical data  62  includes numerical data for relatively moving the substitute tool  22  to the workpiece  1 . 
         [0083]    The control device  55  includes a numerical data reading unit  56  serving as an input information reading unit and an arithmetic unit  57 . The numerical data reading unit  56  has a function of reading the input numerical data  54 . The arithmetic unit  57  includes a virtual advancing direction setting unit  58 , a range setting unit  59 , and a position setting unit  60 . The arithmetic unit  57  sets a position on which the substitute tool  22  is disposed based on the read input numerical data  54 . In other words, the arithmetic unit  57  sets a tool path of the substitute tool. Further, the arithmetic unit  57  estimates a line of the substitute tool  22  which finally generates a machining surface. A feed rate setting unit  61  calculates a relative speed of the substitute tool  22  to the workpiece  1  based on the tool path and the line which finally generates the machining surface calculated by the arithmetic unit  57 . In other words, the feed rate regarding each of the moving axes of the machine tool  10  is determined. The feed rate setting unit  61  generates the output numerical data  62 . 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 . 
         [0084]      FIG. 14  is a flowchart illustrating control by the control device  55  of the machine tool  10 . With reference to  FIG. 13  and  FIG. 14 , 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  includes data indicating a path of the tool tip end point when the specified tool  81  is used. In other words, the tool path of the specified tool  81  is included. 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. 
         [0085]    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 includes the coordinate values of the XYZ axes and the rotational angles of the ABC axes. 
         [0086]    Next, the arithmetic 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 arithmetic 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. 
         [0087]      FIG. 15  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. 15 , the workpiece  1  is rotated in a direction indicated by an 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 end point  81   c  of the specified tool  81  is a direction indicated by the arrow  101 . The virtual advancing direction is set by, for example, a vector of a unit length on the XYZ axes. 
         [0088]      FIG. 16  is a schematic plan view illustrating when the grooving is performed. The virtual advancing direction of a point on a predetermined height of the specified tool  81  is indicated by the arrow  101 . The virtual advancing direction indicates a direction when the specified tool  81  having the diameter identical to the diameter of the circle  84  advances along the direction in which the groove portion  66  extends. 
         [0089]    With reference to  FIG. 13  and  FIG. 14 , 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. 
         [0090]    In step  125 , the range setting unit  59  reads machining setting data. The machining setting data includes information of the workpiece, such as the groove width of the groove portion  66  and depth of the groove portion  66 , the tool diameter of the substitute tool  22 , and the like. The machining setting data further includes a feed rate of the tool on a machining surface set by a user. In other words, a relative speed of the tool to the workpiece is set. A desired relative speed of a tool to a workpiece may be input by a user to the CAM apparatus  53  and be included in the input numerical data  54 . Alternatively, the desired relative speed may be automatically specified by the CAM apparatus  53 . 
         [0091]    The machining setting data may include data limiting a position where a tool contacts with a workpiece. For example, in the machining by the substitute tool  22 , one of two side surfaces of the groove portion  66  is machined. When a position in which the substitute tool  22  contacts the workpiece is not restricted, it may be judged that the substitute tool  22  machines both side surfaces of the groove portion at once. In such a case, the substitute tool can be specified to contact only one side surface. 
         [0092]    In step  126 , the range setting unit  59  sets the range in which the substitute tool  22  is disposed using the machining setting data and the virtual advancing direction. The range setting unit  59  estimates a line of the specified tool  81  which finally generates a machining surface based on the virtual advancing direction. The range setting unit  59  sets the range in which the substitute tool  22  is disposed based on the line which finally generates the machining surface. The line which finally generates the machining surface is described below. 
         [0093]      FIG. 17  is a schematic perspective view of the specified tool.  FIG. 17  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. 17  is equivalent to an upper end of a groove portion. As described above, the virtual advancing direction indicated by the arrow  101  gradually changes depending on a position in a height direction of the central axis  81   a  of the specified tool  81 . 
         [0094]    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, a line  132  of the specified tool  81  which finally generates the machining surface is obtained. 
         [0095]    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 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, in the example illustrated in  FIG. 17 , the line  132  which finally generates the machining surface is curved. 
         [0096]    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 . The specified tool  81  includes a machining area  131  for forming a machining surface of the workpiece. The 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 groove portion  66  can be formed by cutting the workpiece  1  in the machining area  131 . An end of the machining area  131  becomes a portion which finally generates the machining surface. In this example, a portion finally performing the machining is the line  132  which finally generates the machining surface. 
         [0097]    The line  132  which finally generates the machining surface can be estimated by calculation. As indicated by arrows  110  and  111 , a line perpendicular to the calculated virtual advancing direction is set. Moving 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 estimated. 
         [0098]    Next, the range in which the substitute tool  22  is disposed is set based on the line  132  which finally generates the machining surface. 
         [0099]      FIG. 18  is a schematic perspective view illustrating the range in which the substitute tool is disposed. With reference to  FIG. 16  and  FIG. 18 , 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 moving point  183  of an upper end and the moving 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. The range in which the substitute tool  22  is disposed is indicated by an arrow  176 . 
         [0100]    With reference to  FIG. 13  and  FIG. 14 , next, 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. 
         [0101]      FIG. 19  is a schematic view illustrating the scallop height. The positions  85   a ,  85   b , and  85   c  of the substitute tool  22  are set 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. 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. 
         [0102]    With reference to  FIG. 13  and  FIG. 14 , 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 and the like. The number of positions on which the substitute tool  22  is disposed can be calculated based on the scallop height. In the process of the present embodiment, the machining is set to three times. 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. The position of the substitute tool  22  can be output as, for example, the coordinate values of the XYZ axes and the angle of the rotational feed axis at the tool tip end point or a difference from the coordinate value sequence output in step  122 . 
         [0103]    Next, in step  129 , the feed rate setting unit  61  sets the relative speed of the substitute tool  22  to the workpiece  1 . In other words, the feed rate regarding the moving axis of the machine tool is set. In the present embodiment, a movement speed in the Y-axis direction and a rotational speed around the B axis are set. In step  129 , a fastest moving point at which a relative speed of the substitute tool  22  to the workpiece  1  is the maximum is estimated among a plurality of moving points included in the line which finally generates the machining surface. Then, the feed rate regarding the moving axis of the machine tool is set so that the relative speed of the fastest moving point is a preliminarily specified relative speed or less. In this example, the relative speed is set for each block described in the input numerical data. 
         [0104]      FIG. 20  is a schematic perspective view of the substitute tool  22  when the machining of the first time is performed on the outward path.  FIG. 21  is a schematic perspective view of the substitute tool  22  when the machining of the second time is performed on the outward path.  FIG. 22  is a schematic perspective view of the substitute tool  22  when the machining of the third time is performed on the outward path. When the substitute tool  22  is used, a line of the substitute tool  22  which finally generates a machining surface is also generated. With reference to  FIG. 20 , 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. 21 , 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. 22 , 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. 
         [0105]    When the lines  132   a ,  132   b , and  132   c , respectively illustrated in  FIG. 20  to  FIG. 22 , 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. 
         [0106]      FIG. 23  is a schematic perspective view of the substitute tool  22  disposed on a predetermined position in the machining on the outward path of the first time. The input numerical data input to the arithmetic unit includes a plurality of relative positions of the tool to the workpiece.  FIG. 23  illustrates the substitute tool  22  disposed on a first relative position  201  and a second relative position  202  in the tool path. The first relative position  201  is a position described in a specific block in the coordinate value sequence output in step  122  in  FIG. 14 . The second relative position  202  is a position described in a block immediately behind the specific block. In other words, two positions of the substitute tool  22  are equivalent to positions described in the two successive blocks. 
         [0107]      FIG. 23  illustrates a movement of the substitute tool  22  with respect to the workpiece  1  when it is assumed that the workpiece  1  is stopped. The substitute tool  22  moves from the first relative position  201  to the second relative position  202 , and thus a tool tip end point  22   c  of the substitute tool  22  moves as indicated by an arrow  195 . Together with the movement of the substitute tool  22 , the line  132   a  which finally generates the machining surface moves. At that time, a plurality of moving points can be set on the line  132   a . A movement speed of the plurality of moving points is different from each other depending on a position on the line  132   a.    
         [0108]    In the example illustrated in  FIG. 23 , points on both ends of the line  132   a  which finally generates the machining surface are set as the moving points  183  and  185 . The moving point  183  moves as indicated by an arrow  191 . The moving point  185  moves as indicated by an arrow  192 . The grooving includes a rotational movement, and the moving points  183  and  185  have curved moving paths, however, the arrows  191  and  192  indicate positions before and after the movement by straight lines. 
         [0109]    A relative speed of the moving point  183  to the workpiece  1  and a relative speed of the moving point  185  to the workpiece  1  are different from each other. The relative speed of the moving point becomes larger as a distance from a rotation center of the B axis is greater. In the example, the relative speed of the moving point  183  is greater than the relative speed of the moving point  185 . Thus, the fastest moving point, at which the relative speed of the tool to the workpiece  1  is the fastest, is the moving point  183  among the plurality of moving points on the line  132   a  which finally generates the machining surface. The fastest moving point can be estimated as described above. Alternatively, a moving point of which moving distance from the first relative position to the second relative position is the longest can be estimated as the fastest moving point. 
         [0110]    In the grooving according to the present embodiment, relative speeds on the outward path of the second time and of the third time are the same as a relative speed on the outward path of the first time. With reference to  FIG. 21 , a relative speed of a moving point  186  is greater than a relative speed of a moving point  187  on the line  132   b  which finally generates the machining surface in the machining on the outward path of the second time. Further, with reference to  FIG. 22 , a relative speed of a moving point  188  is greater than a relative speed of the moving point  184  on the line  132   c  which finally generates the machining surface in the machining on the outward path of the third time. The moving points  186  and  188  are the fastest moving points in the respective machining. 
         [0111]    As described above, the relative speeds of the moving points on the lines  132   a ,  132   b , and  132   c  which finally generate the machining surface become larger as distances from the rotation center of the B axis are greater. In other words, the moving point  183  can be estimated that the relative speed to the workpiece  1  is the fastest among the relative speeds of the moving points  183 ,  186 , and  188 . Thus, in the machining on the outward path of the second time and of the third time, the feed rate regarding the moving axis of the machine tool can be set using the relative speed of the moving point  183  in the machining on the outward path of the first time on the corresponding positions  85   a ,  85   b , and  85   c  illustrated in  FIG. 6 . The feed rate regarding the moving axis of the machine tool may be set based on the relative speeds of the moving points  186  and  188  which are respectively the fastest moving points in the machining of the second time and the third time. 
         [0112]    Next, the feed rate regarding the moving axis is set so that a speed of the moving point  183  is the preliminarily specified relative speed or less. In the present embodiment, the feed rate is set so that the relative speed of the moving point  183  coincides with the preliminarily specified relative speed. Further, the feed rate is set based on the length of time in which it takes the substitute tool  22  to move from the first relative position  201  to the second relative position  202 . At that time, the feed rate is set by an inverse of the time length in each block. In other words, an inverse time command is described in the output numerical data. 
         [0113]    With reference to  FIG. 18 , the moving point  183  of the substitute tool  22  matches the moving point  183  of the specified tool  81 . With reference to  FIG. 14 ,  FIG. 18 , and  FIG. 23 , in step  128 , coordinate values of the moving point  183  can be calculated when the position of the substitute tool  22  is set. The coordinate values of the moving point  183  at the first relative position  201  and the coordinate values of the moving point  183  at the second relative position  202  are calculated. Next, a distance between the moving point  183  at the first relative position  201  and the moving point  183  at the second relative position  202  is calculated. The distance is calculated by approximating to a linear moving distance as indicated by the arrows  191  and  192 . 
         [0114]    Next, a calculation method of the feed rate regarding the moving axis of the moving device is described. A speed of a tool on a machining surface input by a user on an input screen, namely a preliminarily specified relative speed of the tool to a workpiece is denoted by F [mm/min]. Machine coordinate values of the substitute tool  22  at the first relative position  201  are denoted by p 1 , and machine coordinate values of the substitute tool  22  at the second relative position  202  are denoted by p 2 . The coordinate values include values of the three-dimensional XYZ coordinates and a rotational movement coordinate. In other words, the coordinate values include information of an angle of the tool to the workpiece. 
         [0115]    A speed of the fastest moving point when the substitute tool  22  moves from the coordinate value p 1  to the coordinate value p 2  by taking, for example, a time t [min] is denoted by f(t) [mm/min]. In this case, a distance that the fastest moving point moves during the time t [min] is expressed as f(t)·t. Thus, an inverse time command value I [1/min] is calculated by the following expression (1). 
         [0000]        I=F /( f ( t )· t )  (1)
 
         [0116]    An arbitrary value can be adopted to the time t as a variable. When 1 [min] is substituted for the time t, the inverse time command value I is deformed to the following expression (2). 
         [0000]        I=F/f (1)  (2)
 
         [0117]    With reference to  FIG. 23 , in the present embodiment, the moving distance between the moving point  183  at the first relative position  201  and the moving point  183  at the second relative position  202  is substituted in f(1). By substituting the moving distance of the fastest moving point in f(1), the inverse time command value I when the moving point moves from the first relative position to the second relative position can be calculated. 
         [0118]    According to the present embodiment, the first relative position and the second relative position are equivalent to the two successive blocks, so that the inverse time command can be calculated for each block. 
         [0119]    As described above, the feed rate regarding the moving axis in a movement from the first relative position to the second relative position can be set based on the information of the tool path and the workpiece. 
         [0120]    With reference to  FIG. 13  and  FIG. 14 , the feed rate setting unit  61  calculates the feed rate regarding each moving axis in step  129 , and then generates the output numerical data  62  in step  130 . The output numerical data  62  can be set by, for example, the coordinates of the XYZ axes and relative angles between the substitute tool  22  and the workpiece  1  on the ABC axes. 
         [0121]      FIG. 24  is an example of the output numerical data  62  generated by the feed rate setting unit  61 . Coordinate values in a row correspond to a block. The feed rate regarding the moving axis is specified for each block. The feed rate is specified by the inverse time command. The coordinates of the X axis, the Y axis, and the Z axis indicate a position of the tool tip end point  22   c  of the substitute tool  22 . An angle of the B axis indicates a rotational angle of the workpiece  1 . 
         [0122]    A mark “G93” of the output numerical data  62  indicates that subsequent speed commands are performed by the inverse time command. The feed rate is determined so that a linear feed movement in the Y-axis direction and a rotational movement around the B axis are performed within a predetermined time period. For example, when the inverse time command is “F10”, it means moving to a position of a predetermined Y coordinate and an angle of the B axis by a time of 1/10 [min]. 
         [0123]    With reference to  FIG. 13 , the numerical control unit  63  drives the individual axis servomotor  64  based on the output numerical data  62 . Accordingly, the relative position between the workpiece  1  and the substitute tool  22  can be adjusted. 
         [0124]    As described above, the arithmetic unit of the control device estimates the line which finally generates the machining surface in the machining area of the substitute tool when machining a workpiece. Further, the feed rate setting unit estimates the fastest moving point included in the line which finally generates the machining surface and sets the feed rate regarding the moving axis of the machine tool so that the relative speed of the fastest moving point is the preliminarily specified relative speed or less. By adopting this configuration, a machining speed on an arbitrary point of a machining surface can be set to a desired speed or less. Desired machining accuracy or more can be obtained in the entire machining surface. The machining accuracy can be prevented from being deteriorated on a part of the machining surface because that the relative speed of the tool with respect to the workpiece exceeds the desired relative speed on the part of the machining surface. 
         [0125]    According to the present embodiment, the relative speed of the fastest moving point on the line which finally generates the machining surface is controlled to be equal to the preliminarily specified relative speed. However, the present invention is not limited to the above-described embodiment as long as the relative speed of the fastest moving point is set to be the preliminarily specified relative speed or less. 
         [0126]    The feed rate setting unit estimates the fastest moving point in the movement from the first relative position to the second relative position and sets the feed rate regarding the moving axis in the movement from the first relative position to the second relative position. By adopting this configuration, the feed rate regarding the individual moving axis can be set for each of the output numerical data blocks. 
         [0127]    Further, the feed rate setting unit sets the feed rate regarding the moving axis based on the length of time in which it takes the tool to move from the first relative position to the second relative position with respect to the workpiece. By adopting this configuration, the feed rate can be easily set to the desired speed in a relative movement including a rotational movement. In numerical data for controlling the moving device, a linear movement can be specified on the XYZ coordinates; however, a rotational angle is to be specified in a rotational movement. A unit of linear movement and a unit of rotational movement are different, thus calculation of the feed rate of each moving axis is complicated. In contrast, since the feed rate regarding the individual moving axis is set for each block using the time length, the feed rate can be easily controlled in the case of the relative movement including the rotational movement. 
         [0128]    In the above-described embodiment, the tool path of the specified tool  81  is converted into the tool path of the substitute tool  22  to perform grooving. If the specified tool  81  having a tool diameter identical to a groove width can be prepared when forming the groove portion  66 , the machining can be performed using the specified tool  81  as illustrated in  FIG. 3 . In this case, the fastest moving point on the line of the specified tool  81  which finally generates the machining surface is estimated, and the control can be performed so that the relative speed of the fastest moving point is the preliminarily specified relative speed or less. 
         [0129]      FIG. 25  is a schematic perspective view of the specified tool  81  disposed on the first relative position  201  and the second relative position  202 . The specified tool  81  moves from the first relative position  201  to the second relative position  202 , and thus the tool tip end point  81   c  moves as indicated by an arrow  196 . The line  132  which finally generates the machining surface is estimated at each of the first relative position  201  and the second relative position  202 , and the fastest moving point at which the relative speed to the workpiece is the maximum is estimated from among the moving points included in the line  132  of the specified tool  81  which finally generates the machining surface. 
         [0130]    In the example illustrated in  FIG. 25 , the moving point  183  and the moving point  184  are specified as the moving points included in the line  132  which finally generates the machining surface. The moving point  183  and the moving point  184  are points on both ends of the line  132  which finally generates the machining surface. The specified tool  81  moves from the first relative position  201  to the second relative position  202 , and thus the moving point  183  moves as indicated by an arrow  193 , and the moving point  184  moves as indicated by an arrow  194 . The relative speed of the moving point  183  on the upper end of the line  132  which finally generates the machining surface to the workpiece  1  is compared with the relative speed of the moving point  184  on the lower end of the line  132  which finally generates the machining surface to the workpiece  1 . 
         [0131]    When the relative speed of the moving point  183  is compared with the relative speed of the moving point  184 , the relative speed of a point farther from the rotation axis, namely the moving point  183  of which distance from the B axis is larger, is faster. The moving point  183  can be estimated as the fastest moving point. Thus, the feed rate regarding the moving axis is set so that the relative speed of the moving point  183  is the preliminarily specified relative speed or less. For example, a moving distance of the moving point  183  indicated by the arrow  193  is calculated, and the inverse time command can be set for each block based on the calculated moving distance. 
         [0132]      FIG. 26  is a schematic view of a machining system which machines a workpiece using the specified tool  81 . With reference to  FIG. 13  and  FIG. 26 , when the machining is performed using the specified tool  81  having a tool diameter identical to a groove width, the tool path of the specified tool  81  is not necessary to be converted into the tool path of the substitute tool  22 . Thus, the arithmetic unit  57  calculates the virtual advancing direction of the specified tool  81  by the virtual advancing direction setting unit  58  and then can estimate the line  132  of the specified tool  81  which finally generates the machining surface by a machining line setting unit  68 . The feed rate setting unit  61  can set the feed rate regarding the individual moving axis based on the relative speed of the fastest moving point included in the line  132  which finally generates the machining surface. The output numerical data  62  includes information of the tool path of the specified tool  81  and the relative speed of the specified tool  81  to the workpiece  1 . 
         [0133]    In the above-described embodiment, both end points of the line which finally generates the machining surface are set as the moving points. However, the present invention is not limited to the embodiment, and an arbitrary point included in the line which finally generates the machining surface can be set as a moving point. However, it is preferable that the moving points on the both ends on the line which finally generates the machining surface are included since one of the moving points on the both ends moves at the maximum speed in many types of machining. 
         [0134]    In the above-described embodiment, the movement speed is calculated for each block included in the input numerical data. However, the present invention is not limited to the embodiment, and the feed rate setting unit may calculates a change in the relative speed of the moving point during a period of the movement from the first relative position to the second relative position. During the period when the tool moves from the first relative position to the second relative position, a relative speed of a predetermined moving point may sometimes be changed. For example, when machining is performed in such a manner that the tool moves toward the rotation axis and then moves away from the rotation axis, the relative speed of the tool to the workpiece becomes slower as the moving point approaches the rotation axis. In such case, a change in the movement speed of the moving point when the tool moves from the first relative position to the second relative position can be calculated by functions or the like. A greatest relative speed when the predetermined moving point moves from the first relative position to the second relative position may be calculated using these functions. 
         [0135]    The arithmetic unit may add a third position between the first relative position and the second relative position. In this case, the arithmetic unit estimates a line of the tool which finally generates the machining surface on the third position. The feed rate setting unit estimates the fastest moving point in the movement from the first relative position to the third relative position and sets the feed rate regarding the moving axis in the movement from the first relative position to the third relative position. Further, the fastest moving point in the movement from the third relative position to the second relative position is estimated and the feed rate regarding the moving axis in the movement from the third relative position to the second relative position is set. 
         [0136]    As described above, the feed rate setting unit can estimate the fastest moving point in the movement between two successive relative positions and set the feed rate regarding the moving axis in the movement between the two successive relative positions. Accordingly, blocks more than the number of the blocks in the input numerical data can be output to the output numerical data. By adopting this configuration, the maximum speed of the moving point on the line which finally generates the machining surface can be more accurately calculated, and the machining accuracy can be improved. 
         [0137]    In addition, a plurality of positions may be set between the first relative position and the second relative position. In other words, a plurality of positions, such as the third position and a fourth position, may be added between the first relative position and the second relative position. In this way, an interval between the first relative position and the second relative position can be divided into arbitrary minute sections, so that the machining accuracy can be improved. 
         [0138]    The numerical control type machine tool according to the above-described embodiment performs machining using a rotation 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 a control device of a machine tool which performs machining in a curved line. For example, the present invention can be applied to a machine tool which performs machining associated with the rotational movement and machining moving in a curved line by combining a plurality of linear movements. 
         [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  contacts with a cam follower  135 . The cam follower  135  is formed in a columnar shape and rotatably supported. The end cam  136  rotates around a central axis  137 , so that positions of the cam follower  135  in a top and bottom direction 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. For example, cutting is performed using an end mill having a diameter identical to the diameter of the cam follower  135  while rotating a workpiece around the central axis  137 , and thus the end face  136   a  can be formed. On the other hand, when a rotary tool having a tool diameter smaller than the diameter of the cam follower  135  is used as a rotary tool to machine the end face  136   a , the end face  136   a  of the end cam  136  can be formed by a machining method similar to that of the above-described machining of a side surface of the groove portion. In this case, the rotary tool having the 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. In the machining of this case, the line which finally generates the machining surface can be estimated, and the feed rate regarding the moving axis of the machine tool can be set based on the fastest moving point included in the line which finally generates the machining surface. 
         [0141]      FIG. 28  is a schematic perspective view of a face cam. In manufacturing of a face cam, the groove portion  66  is formed on a surface of a plate member. The groove portion  66  of the face cam may sometimes include a linear portion  66   c  and a curved portion  66   d . When machining including such a curved portion  66   d  is performed, the present invention can be suitably applied. When a rotary tool having a tool diameter identical to the groove width of the groove portion  66  is used, the line which finally generates the machining surface is generated on the machining area in which the side surface  66   a  on one side is machined, and the line which finally generates the machining surface is also generated on the machining area in which the side surface  66   b  on the other side is machined. Regarding moving points included in both of the lines which finally generate the machining surfaces, the fastest moving point at which the relative speed of the tool to the workpiece is the maximum is estimated. The feed rate regarding the moving axis of the machine tool can be set so that the relative speed of the fastest moving point is the preliminarily specified relative speed or less. 
         [0142]    The tool according to the present embodiment is a rotary tool which rotates. However, the present invention is not limited to the above-described embodiment and can be applied to arbitrary tools. 
         [0143]    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 
           22  substitute tool 
           54  input numerical data 
           55  control device 
           57  arithmetic unit 
           58  virtual advancing direction setting unit 
           61  feed rate setting unit 
           62  output numerical data 
           68  machining line setting unit 
           131  machining area 
           132 ,  132   a  line which finally generates a machining surface 
           183  to  188  moving point 
           201  first relative position 
           202  second relative position