Patent Publication Number: US-6711829-B2

Title: Method for measuring work portion and machining method

Description:
The disclosure of Japanese Patent Application No. 2000-301323 filed on Sep. 29, 2000 including the specification, drawings and abstract are incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a measuring method for measuring the eccentricity or diameter of a work portion (i.e., a portion undergoing machining) of a workpiece, which portion is provided eccentrically with respect to the rotation center of the workpiece and has a circular cross section, as well as to a machining method capable of correcting a machining program on the basis of the measured eccentricity or diameter. 
     2. Description of the Related Art 
     When a workpiece is machined by use of a machine tool, the machining of the workpiece is sometimes effected, while the dimension or the like of the workpiece is measured by use of a measurement unit mounted on the machine tool. In particular, when a crankpin of a crankshaft serving as a workpiece is ground while the crankshaft is rotated about the journals of the crankshaft, a following-type size-measurement unit produced by, for example, Marposs S.P.A. (Italy) is typically used for measuring the diameter of the crankpin, which revolves about the journals. Such a following-type size-measurement unit is disclosed in, for example, Japanese Patent Application Laid-Open (kokai) No. 2000-127038. 
     The following-type size-measurement unit will be described with reference to FIG.  10 . FIG. 10 shows a case in which the radius of a crankpin  108  ground on a cylindrical grinder  100  which has a grinding wheel  101  is measured by use of a following-type size-measurement unit  103 . The following-type size-measurement unit  103  is attached to a support member  104  mounted on a wheel head  102  of the cylindrical grinder  100  in such a manner that the size-measurement unit  103  is swingable about a rotary shaft  105 . The size-measurement unit  103  can be moved from a standby position indicated by an alternate long and two short dashes line in FIG. 10 to a position indicated by a solid line in FIG. 10 at which the size-measurement unit  103  measures the size of the revolving crankpin  108 . 
     The measurement head of the size-measurement unit  103  has a V-block  106 . A probe  107  is supported by a shaft passing through the center of a V-groove portion of the V-block  106  and is urged forward by an unillustrated spring in such a manner that the probe  107  can be retreated. The amount of axial movement of the probe  107  is detected electrically, and an electrical signal corresponding thereto is output from the measurement head. 
     When the crankpin  108  is to be measured, as indicated by the solid line, the V-block  106  is brought into contact with the outer circumference of the crankpin  108 , so that the crankpin  108  comes into contact with the V-block  106  at two locations. At this time, the probe  107  comes into contact with the outer circumference of the crankpin  108  due to the restoration force of the unillustrated spring. Subsequently, the radius of the crankpin  108  is obtained from the geometric shape of the V-block  106  and the position of the probe  107  in contact with the crankpin  108 , which is in contact with the V-block  106 . 
     However, the conventional following-type size-measurement unit is expensive. 
     Further, since only the radius of a work portion can be measured, the diameter of the work portion must be calculated from the measured radius. In this case, a greater error is produced as compared with the case in which the diameter of the work portion is measured directly. 
     Moreover, the size of the V-groove portion of the V-block  106  and the swing support mechanism employed for supporting the V-block  106  impose limitations on the measurable workpiece diameter and measurable crankshafts, resulting in a narrow measurement range. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, an object of the present invention is to provide a measuring method which accurately measures the eccentricity and/or diameter of a work portion within a widened range at low cost. 
     Another object of the present invention is to provide a machining method capable of correcting a machining program on the basis of the eccentricity and/or diameter measured by the measuring method. 
     The present invention provides a work-portion measuring method for measuring a diameter of a cylindrical work portion of a workpiece mounted on a machine tool, the work portion being concentric with a rotation center of the workpiece, the method comprising the steps of: setting a first distance between a rotation center of the workpiece and a reference point provided on the machine tool; measuring a second distance between the reference point and an outer circumferential surface of the work portion; and obtaining the diameter of the work portion on the basis of the first and second distances. 
     The present invention provides a machining method for machining an outer circumferential surface of a cylindrical work portion of a workpiece in accordance with a machining program, the work portion being concentric with a rotation center of the workpiece, the method comprising the steps of: measuring a diameter of the work portion by the above-described work-portion measuring method; correcting the machining program based on the measured diameter of the work portion; and machining the outer circumferential surface of the work portion in accordance with the corrected machining program. 
     The present invention provides another work-portion measuring method for measuring a diameter and eccentricity of a cylindrical work portion of a workpiece mounted on a machine tool, the work portion being eccentric with respect to a rotation center of the workpiece, the method comprising the steps of: setting a first distance between a rotation center of the workpiece and a reference point provided on the machine tool; measuring a second distance between the reference point and an innermost point on an outer circumferential surface of the work portion; measuring a third distance between the reference point and an outermost point on the outer circumferential surface of the work portion; and obtaining the diameter and eccentricity of the work portion on the basis of the first, second, and third distances. 
     The present invention provides a machining method for machining an outer circumferential surface of a cylindrical work portion of a workpiece in accordance with a machining program, the work portion being eccentric with a rotation center of the workpiece, the method comprising the steps of: measuring a diameter and eccentricity of the work portion by the above-described work-portion measuring method; correcting the machining program based on the measured diameter and eccentricity of the work portion; and machining the outer circumferential surface of the work portion in accordance with the corrected machining program. 
     In the measuring method of the present invention, since the diameter and/or eccentricity is measured on the basis of distances, a measurement apparatus used in the method is required to detect distance only. Therefore, a contact-type measurement apparatus or any other simple measurement apparatus can be used in order to reduce cost. In addition, the measuring method of the present invention provides higher measurement accuracy as compared with conventional measuring methods. 
     In the machining methods of the present invention, since the machining program is corrected on the basis of the measured diameter and/or eccentricity of the work portion, the work portion can be finished to higher accuracy. 
     The machining methods of the present invention preferably comprise an additional step of comparing the measured diameter or eccentricity of the work portion with a tolerance in order to judge whether the work portion is good. In this case, properness of machining can be judged easily on the machine. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various other objects, features and many of the attendant advantages of the present invention will be readily appreciated as the same becomes better understood by reference to the following detailed description of the preferred embodiments when considered in connection with the accompanying drawings, in which: 
     FIG. 1 is a schematic plan view of a grinding machine equipped with a measurement apparatus used in a work-portion measuring method according to the present invention; 
     FIG. 2 is an illustration showing a first embodiment of the work-portion measuring method of the present invention; 
     FIGS.  3 ( a ) to  3 ( f ) are illustrations showing a method for measuring distances used in the first embodiment of the work-portion measuring method of the present invention; 
     FIG. 4 is a flowchart showing the operation for grinding a crankpin of a workpiece, while measuring the eccentricity and diameter of the crankpin by the first embodiment of the work-portion measuring method of the present invention; 
     FIG. 5 is an illustration showing a second embodiment of the work-portion measuring method of the present invention; 
     FIGS.  6 ( a ) to  6 ( c ) are illustrations showing a method for measuring distances used in the second embodiment of the work-portion measuring method of the present invention; 
     FIG. 7 is a flowchart showing the operation for grinding an eccentric cylindrical portion, while measuring the cylindrical portion by the second embodiment of the work-portion measuring method of the present invention; 
     FIG. 8 is an illustration showing a method for measuring distances used in a third embodiment of the work-portion measuring method of the present invention; 
     FIG. 9 is a flowchart showing the operation for grinding journal of a crankshaft, while measuring the journal by the third embodiment of the work-portion measuring method of the present invention; and 
     FIG. 10 is a view showing a conventional follow-type size-measurement unit. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A first embodiment of the present invention will be described with reference to FIGS. 1 to  4 . The present embodiment exemplifies the case in which an outer circumferential portion of each of crankpins of a crankshaft  20  is ground by a grinding machine  1 . The crankshaft  20  (hereinafter referred to as a “workpiece”) includes journals and crankpins (work portions) eccentrically connected to the journals via crank arms. Each crankpin has a circular cross section, and its outer circumference surface is ground. FIG. 1 is a schematic plan view of the grinding machine  1  in which a measurement apparatus  25  is disposed on a wheel head  3 . The directions of movement of the wheel head  3  and a table  11  of the grinding machine  1  will be referred to as X-axis and Y-axis directions, respectively, as shown by arrows in FIG.  1 . 
     The wheel head  3  and the table  11  are mounted on a bed  2  in such a manner that the wheel head  3  is movable along the X-axis direction, and the table  11  is movable along the Y-axis direction. 
     Specifically, an X-axis motor  4  is disposed on the bed  2 . The X-axis motor  4  is drivingly coupled to the wheel head  3  via an X-axis feed screw connected to the X-axis motor  4  so as to move the wheel head  3  along slide guide surfaces which extend along the X-axis direction. An X-axis encoder  5  is attached to the X-axis motor  4 . Therefore, the position of the wheel head  3  is detected by the X-axis encoder  5 . 
     A grinding wheel  7  is rotatably supported on the wheel head  3 ; and a wheel motor  6  for rotating the grinding wheel  7  is built in the wheel head  3  together with an unillustrated bearing potion. A CBN grinding wheel is used for the grinding wheel  7 . 
     A Y-axis motor  12  is disposed on the bed  2 . The Y-axis motor  12  is drivingly coupled to the table  11  via a Y-axis feed screw connected to the Y-axis motor  12  so as to move the table  11  along slide guide surfaces which extend along the Y-axis direction. A Y-axis encoder  13  is attached to the Y-axis motor  12 . Therefore, the position of the table  11  is detected by the Y-axis encoder  13 . 
     A headstock  16  and a tailstock  14  are disposed on the table  11 . The opposite ends  20   a  and  20   b  of the workpiece  20  are supported by a center  19  of the headstock  16  and a center  15  of the tailstock  14  in such a manner that the workpiece  20  is sandwiched between the centers  15  and  19 , and is clamped and driven by a rotary chuck provided on the headstock  16 . A C-axis motor  17  for rotating the rotary chuck or the workpiece  20  is disposed on the headstock  16 . A C-axis encoder  18  is attached to the C-axis motor  17 . Further, a reference plate  29  is attached to a side surface of the headstock  16  (on the side where a measurement apparatus  25 , which will be described later, is present in FIG.  1 ). The reference plate  29  has a reference surface for determining a reference point. 
     The measurement apparatus  25  of a contact operation type is attached to the front face of the wheel head  3 . The measurement apparatus  25  includes a probe  27  and a measurement head  26 , which supports the probe  27 . The probe  27  is brought into contact with an outer circumferential surface (work surface) of the crankpin (work portion) of the workpiece  20  to be measured, and tilts as a result of the contact. The measurement head  26  outputs a contact signal (ON signal) when the probe  27  tilts by a predetermined amount. As shown in FIG. 2, the tip end of the probe  27  is formed into the shape of a sphere having a diameter P. When the workpiece  20  is being ground, in order to avoid interference with the workpiece  20  or the like, the measurement apparatus  25  can be swung about a shaft  28  to the standby position indicated by a solid line in FIG. 1 (the measurement position is shown by a broken line in FIG.  1 ). 
     Next, a control apparatus  31  for the grinding machine  1  will be described. In the present embodiment, the control apparatus  31  is a computerized numerical controller (CNC). The computerized numerical controller (hereinafter referred to as a “controller”)  31  includes a central processing unit (CPU)  32 , an X-axis drive control circuit  33 , a Y-axis drive control circuit  34 , and a C-axis control circuit  35 , and a storage unit  36  (e.g., RAM, ROM, HDD) for storing a machining operation program and data. The storage unit  36  is connected to the CPU  32  via a bus. 
     The X-axis drive control circuit  33  is connected to the X-axis motor  4  and the X-axis encoder  5 . The Y-axis drive control circuit  34  is connected to the Y-axis motor  12  and the Y-axis encoder  13 . The C-axis control circuit  35  is connected to the C-axis motor  17  and the C-axis encoder  18 . 
     The X-axis drive control circuit  33 , the Y-axis drive control circuit  34 , the C-axis control circuit  35 , and the measurement apparatus  25  are connected to the CPU  32  via an interface  37  and the bus. 
     The storage unit  36  stores a machining operation program which the grinding machine  1  requires for performing grinding operation. In addition to the machining operation program, the storage unit  36  stores ideal profile (P/F) data obtained through calculation on the basis of which trial grinding is performed; corrected profile (P/F) data which are obtained by correcting the ideal profile (P/F) on the basis of the result of the trial grinding and which are used in actual grinding operation; and re-collected profile (P/F) data which are obtained by correcting the corrected profile (P/F) in a manner as described below. 
     An input/output unit  38 , which includes display means for displaying various data, such as a CRT, and input means such as numeric keys, is connected to the CPU  32  via an interface  39  and the bus. 
     Next, with reference to FIGS. 2 to  4 , there will be described an operation for grinding a crankpin CP 1  (work portion) of the workpiece  20 , while measuring the eccentricity and diameter of the crankpin CP 1  by a first embodiment of the work-portion measuring method of the present invention. FIG. 2 is an illustration showing the first embodiment of the work-portion measuring method of the present invention. FIGS.  3 ( a ) to  3 ( f ) are illustrations showing a method for measuring distances used in the first embodiment of the work-portion measuring method of the present invention. Notably, each of FIGS.  3 ( a ) to  3 ( f ) is a sectional view taken along line A—A in FIG.  2 . FIG. 4 is a flowchart showing the operation for grinding the crankpin CP 1  (work portion), while measuring the eccentricity and diameter of the crankpin CP 1  by the first embodiment of the work-portion measuring method of the present invention. The workpiece  20  to be machined has such a configuration that the crankpin CP 1  has a circular cross section, and the rotation center coincides with the centers of the journals and is not present in a circular area corresponding to the cross section of the crankpin CP 1 . 
     Among the X-axis, Y-axis, and Z-axis directions shown in FIGS. 2 to  4 , the X-axis and Y-axis directions are the same as those shown in FIG. 1, and the Z-axis direction is the direction of height of the grinding machine  1 . 
     A machining operation program necessary for grinding the crankpin CP 1  on the grinding machine  1  is stored in the storage unit  36  apart from the above-described profile file. 
     When this machining operation program is started, in first step S 1 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the crankpin CP 1  to be ground. 
     In next step S 2 , the workpiece  20  is rotated by the C-axis motor  17 , and the wheel head  3  is advanced to grind the crankpin CP 1 . Since the workpiece  20  is rotated with its opposite ends  20   a  and  20   b  supported, the crankpin CP 1  undergoes planetary motion. Therefore, the wheel head  3  must be advanced and retreated in synchronism with rotation of the C-axis motor  17  on the headstock  16  such that the grinding wheel  7  always remains in contact with the outer circumferential surface of the crankpin CP 1 . 
     Specifically, the corrected profile (P/F) data, which define a rotational position of the workpiece  20  and a position of the wheel head  3  for each unit rotational angle (e.g., 0.5°) of the workpiece  20 , are used in order to control rotation of the workpiece  20  and the advancement/retraction movement of the wheel head  3 . During the course of this motion control, the rotational angle of the crankpin CP 1  is detected from the output of the C-axis encoder  18 , the position of the wheel head  3  is detected from the output of the X-axis encoder  5 , and feedback control is effected in such a manner that the rotational angle of the crankpin CP 1  and the position of the wheel head  3  change according to the corrected profile (P/F) data. Thus, the wheel head  3  is advanced and retreated in synchronism with the planetary motion of the crankpin CP 1 , so that the grinding wheel  7  maintains contact with the outer circumferential surface of the revolving crankpin CP 1  and grinds the outer circumference surface of the crankpin CP 1  continuously. 
     Such motions in the C and X axes effected through 2-axis simultaneous control are continued, while the crankpin CP 1  is ground, and are superposed on a cutting feed of the wheel head  3  toward the rotational axis of the workpiece  20 , which is also effected during the grinding operation. Therefore, while being advanced gradually toward the crankpin CP 1  for effecting cutting, the grinding wheel  7  is advanced and retreated in such a manner that the contact with the crankpin CP 1  is always maintained, irrespective of the planetary angle of the crankpin CP 1 . 
     In step S 2 , the crankpin CP 1  is rough-ground at a relatively high cutting feed rate in the above-described manner. When the wheel head  3  reaches a rough-grinding end position set within the machining operation program, the cutting feed rate is switched to a relatively slow fine-grinding rate, and fine grinding is performed. When the wheel head  3  reaches a fine-grinding end position set within the machining operation program, the fine grinding is ended. Thus, the cutting feed of the wheel head  3  is stopped, and the workpiece  20  is rotated one turn or several turns in order to effect spark-out grinding. Subsequently, the wheel head  3  is retreated to the retreated position, and the workpiece  20  is stopped at such an angle position that the crankpin CP 1  is indexed to a measurement position shown in FIG.  3 ( a ). 
     Notably, the ideal profile (P/F) data are obtained through geometric calculation in consideration of various parameters such as the diameters of the crankpins CP 1  and CP 2 , the diameter of the grinding wheel, and the pin stroke; and define each rotational angle of the workpiece  20  and a position of the grinding wheel  7  corresponding to each rotational angle for grinding the crankpins CP 1  and CP 2  to a target diameter and securing a desired roundness. Meanwhile, the corrected profile (P/F) data are data which are obtained by compensating the ideal profile (P/F) data for errors which are produced due to distortion of the mechanical system and the follow delay of the servo system when the workpiece  20  is ground on a trial basis by use of the ideal profile (P/F) data. 
     In next step S 3 , an outermost-point distance M 11  and an innermost-point distance M 12  as measured from a known reference position K 1  are measured by use of the measurement apparatus  25 . 
     First, the probe  27  of the measurement apparatus  25  is swung about the shaft  28  (by about 90 degrees in FIG. 1) from the standby position indicated by the solid line in FIG. 1 to the measurement position indicated by the broken line in FIG.  1 . As shown FIG.  3 ( a ), when the workpiece  20  is indexed at the measurement position, the rotational angle of the crankshaft (workpiece)  20 ; i.e., the rotational angle of the main spindle, is adjusted in such a manner that a point on the outer circumferential surface of the crankpin CP 1  which is most remote from the center axis (hereinafter referred to as an “outermost point”) and a point on the outer circumferential surface of the crankpin CP 1  which is the closet to the center axis (hereinafter referred to as an “innermost point”) are both located on the X-axis line. The rotational angle of the crankshaft (workpiece)  20  shown in FIG.  3 ( a ) is defined as a rotational angle of 0 degrees. Further, the rotational angle of the crankshaft (workpiece)  20  shown in FIG.  3 ( c ) is referred to as a rotational angle of 270 degrees. 
     Subsequently, the table  11  is moved along the Y-axis direction by the Y-axis motor  12 , and the wheel head  3  is moved along the X-axis direction by the X-axis motor  4  until the measurement apparatus  25  outputs an ON signal. Thus, the probe  27  of the measurement apparatus  25  is brought into contact with the reference surface of the reference plate  29  provided on the side surface of the headstock  16  (FIG.  3 ( a )). This position will be used as a reference point. At this point, the X-axis position of the wheel head  3  is detected from the output of the X-axis encoder  5  and is stored in the storage unit  36 . 
     In the case of the measurement apparatus  25  used in the present embodiment, the center of the probe  27  is used as a measurement position. Therefore, the distance between the main spindle center  19  of the headstock  16  and the reference position K 1  as measured along the X-axis direction is the distance (reference distance) between the main spindle center  19  of the headstock  16  and the center of the probe  27  in contact with the reference point of the reference plate  29 . This reference distance is a known value which is stored in the storage unit  36  as K 1 . 
     Subsequently, the wheel head  3  and the table  11  are moved by the X-axis motor  4  and the Y-axis motor  12 , respectively, such that the probe  27  comes into contact with the outermost point (a point which is most remote from the center axis) on the outer circumferential surface of the crankpin CP 1 . The advance movement of the wheel head  3  is stopped at a position where the measurement apparatus  25  outputs an ON signal (FIG.  3 ( b )). Notably, the “outermost point” is not necessarily a point which is most remote from the center axis; the term “outermost point” encompasses a point which is not most remote from the center axis. At this time, the amount of movement from the reference point to the outermost point along the X-axis direction is detected from the output of the X-axis encoder  5 . The distance from the reference point to the outermost point along the X-axis direction is stored in the storage unit  36  as the outermost-point distance M 11 . 
     Subsequently, the probe  27  is separated from the crankpin CP 1 , and the workpiece  20  is rotated by the C-axis motor  17  in such a manner that the crankpin CP 1  becomes lower in position than the main spindle center  19  (FIG.  3 ( c )). In the present embodiment, the workpiece  20  is rotated clockwise from the position shown in FIG.  3 ( a ) by about 90 degrees. 
     In this state, the wheel head  3  is advanced along the X-axis direction by the X-axis motor  4  (FIG.  3 ( c )). 
     When the probe  27  has completely passed over the crankpin CP 1 , the wheel head  3  is stopped. 
     Next, the crankpin CP 1  is returned to the initial position shown in FIG.  3 ( a ). In the present embodiment, the workpiece  20  is rotated counterclockwise by 90 degrees (FIG.  3 ( d )). 
     Subsequently, the wheel head  3  is retracted by the X-axis motor  4 , such that the probe  27  comes into contact with the innermost point (a point which is the closest to the center axis) on the outer circumferential surface of the crankpin CP 1 . The retraction movement of the wheel head  3  is stopped at a position where the measurement apparatus  25  outputs an ON signal (FIG.  3 ( e )). Notably, the “innermost point” is not necessarily a point which is the closet to the center axis; the term “innermost point” encompasses a point which is not the closest to the center axis. At this time, the amount of movement from the reference point to the innermost point along the X-axis direction is detected from the output of the X-axis encoder  5 . The distance from the reference point to the innermost point along the X-axis direction is stored in the storage unit  36  as the innermost-point distance M 12 . 
     Subsequently, the probe  27  is separated from the crankpin CP 1 , and the workpiece  20  is rotated by the C-axis motor  17  in such a manner that the crankpin CP 1  becomes lower in position than the main spindle center  19 . For example, the workpiece  20  is rotated clockwise by 90 degrees. In this state, the wheel head  3  is retracted along the X-axis direction by the X-axis motor  4  (FIG.  3 ( f )). When the probe  27  has completely passed over the crankpin CP 1 , the wheel head  3  is stopped. 
     In subsequent step S 4 , the diameter D 11  and eccentricity (the amount of offset from the journals) ST 11  of the crankpin CP 1  are obtained on the basis of the outermost-point distance M 11  and the innermost-point distance M 12 , which were measured in step S 3 , and the reference distance K 1  and the spherical diameter P of the probe  27 , which are previously stored values. The diameter D 11  of the crankpin CP 1  can be obtained by, for example, the formula D 11 =M 12 −M 11 −P. The offset amount (eccentricity) ST 11  of the crankpin CP 1  can be obtained by, for example, the formula ST 11 =K 1 −M 11 −(D 11 +P)/2. 
     The diameter D 1  and the offset amount (eccentricity) ST 11  obtained in step S 4  are used in step S 6  in order to re-correct the corrected profile (P/F) data used for the above-described rough grinding and fine grinding. 
     Before the re-correction processing, in step S 5 , the diameter of the grinding wheel is calculated. Specifically, the error between the diameter D 11  of the crankpin CP 1  obtained in step S 4  and a target diameter of the crankpin CP 1  to be obtained through fine grinding is obtained, and the diameter of the grinding wheel set in a calculation formula which is used for preparing the corrected profile (P/F) data is corrected by the error, so that the corrected diameter of the grinding wheel is calculated. 
     Further, in step S 5 , a corrected eccentricity is calculated. Specifically, the error between the actual eccentricity ST 11  of the crankpin CP 1  obtained in step S 4  and a target eccentricity is obtained, and the eccentricity set in the calculation formula which is used for preparing the corrected profile (P/F) data is corrected by the error, so that the corrected eccentricity is calculated. 
     The thus-obtained corrected wheel diameter and corrected eccentricity are regarded as values which are determined in total consideration of deformation of the workpiece  20  during the grinding operation, elastic deformation and thermal deformation of the structure and feed mechanism of the grinding machine  1 , and delay of the feed serve system. 
     In step S 6 , the corrected wheel diameter and corrected eccentricity are substituted into the calculation formula for preparing the corrected profile (P/F) data to thereby create the re-corrected profile (P/F) data (re-corrected C-X data), which are then stored in a re-corrected P/F data area of the storage unit  36 . 
     In subsequent step S 7 , the crankpin CP 1  is subjected to finish grinding (micro grinding, grinding without cutting) performed in accordance with the re-corrected profile (P/F) data obtained in step S 6 . 
     When the wheel head  3  is returned to the retreated position after completion of the finish grinding, in step S 8 , the reference position K 1 , the outermost-point distance M 11 , and the innermost-point distance M 12  are determined in the same manner as that in step S 3 . 
     In subsequent step S 9 , the diameter D 12  and eccentricity ST 12  of the crankpin CP 1  are obtained in the same manner as that in step S 4 . 
     In subsequent step S 10 , the CPU  32  judges whether the diameter D 12  and the eccentricity ST 12  obtained in step S 9  fall within tolerances set for the respective target values to be attained after completion of the grinding operation. When both the diameter D 12  and the eccentricity (stroke) ST 12  obtained in step S 9  fall within the respective tolerances, the CPU  32  proceeds to step S 11 . When either one of the diameter D 12  and the eccentricity (stroke) ST 12  falls outside the respective tolerances, the CPU  32  proceeds to step S 12 . 
     In step S 12 , the CPU  32  feeds to the input/output unit  38  an NG signal indicating that the ground crankpin CP 1  is NG; i.e., unsatisfactory. Upon receipt of the NG signal, the input/output unit  38  displays on the display means a message reporting that the ground crankpin CP 1  is NG Further, the CPU  32  transmits a machining stop command to the grinding machine  1 , so that grinding of a subsequent crankpin CP 2  is stopped. 
     In step S 11 , the CPU  32  judges whether all crankpins have been ground. When no other crankpins to be ground are present, the CPU  32  ends the processing. When any crankpin to be ground is present, the CPU  32  proceeds to step S 13 . 
     In step S 13 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the next crankpin CP 2  to be ground. 
     In next step S 14 , the crankpin CP 2  is subjected to rough grinding and fine grinding performed in the same manner as that in step S 2 . In subsequent step S 15 , the crankpin CP 2  is subjected to finish grinding (micro grinding, grinding without cutting) performed in accordance with the re-corrected profile (P/F) data obtained in step S 6  when the crankpin CP 1  was ground. 
     Upon completion of the finish grinding, the CPU  32  proceeds to step S 11 . In a modified embodiment, the CPU  32  is programmed to proceed from step S 15  to step S 8  as indicated by line L 1 , so that the processing in steps S 8 , S 9 , and S 10  is performed. 
     Next, a second embodiment of the work-portion measuring method of the present invention will be described with reference to FIGS. 5 to  7 . FIG. 5 is an illustration showing the second embodiment of the work-portion measuring method of the present invention. FIGS.  6 ( a ) to  6 ( c ) are illustrations showing a method for obtaining distance used in the second embodiment of the work-portion measuring method of the present invention. Notably, each of FIGS.  6 ( a ) to  6 ( c ) is a sectional view taken along line B—B in FIG.  5 . FIG. 7 is a flowchart showing the operation for grinding an eccentric cylindrical portion, while measuring the cylindrical portion by use of the measurement apparatus  25 . In the present embodiment, a shaft (workpiece)  21  to be machined has eccentric cylindrical portions CA 1  and CA 2 , each having a circular cross section and being eccentric with the rotation center axis of the shaft  21 . 
     A machining operation program which is required to grind the outer circumferential surfaces of the eccentric cylindrical portions CA 1  and CA 2  of the shaft  21  on the grinding machine  1  is stored in the storage unit  36  in advance. 
     When the machining operation program shown in FIG. 7 is started, in first step S 21 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the eccentric cylindrical portion CA 1  to be ground first. 
     In next step S 22 , the workpiece  21  is rotated by the C-axis motor  17 , and the wheel head  3  is advanced to grind the eccentric cylindrical portion CA 1 . Although the workpiece  21  is rotated about its center axis, the center of the eccentric cylindrical portion CA 1  is eccentric with respect to the center axis (rotation center) of the workpiece  21 . Therefore, the wheel head  3  is advanced and retreated in synchronism with rotation of the C-axis motor  17  on the headstock  16  such that the grinding wheel  7  is always in contact with the outer circumferential surface of the eccentric cylindrical portion CA 1 . This advancement/retreat motion is continuously effected in accordance with the corrected profile (P/F) data, while the wheel head  3  is advanced for cutting in accordance with the machining operation program. Specifically, in step S 22 , the wheel head  3  is fed toward the workpiece  21  for effecting cutting feed, while being advanced and retreated in synchronism with the rotation of the workpiece  21 . First, rough grounding is performed at a relatively high cutting-feed rate. When the wheel head  3  reaches a rough-grinding end position, the cutting feed rate is reduced to a relatively low feed rate in order to perform fine grinding. When the wheel head  3  reaches a fine-grinding end position, the cutting feed of the wheel head  3  is stopped, and the workpiece  21  is rotated one turn or several turns in order to effect spark-out grinding. Subsequently, the wheel head  3  is retreated to the retreated position. 
     In step S 23 , by means of a function of stopping the main spindle at a constant position, the workpiece  21  is stopped at an angular position which is determined such that the eccentric cylindrical portion CA 1  is located at an angular position suitable for measurement. In the present embodiment, as shown in FIG.  6 ( a ), the workpiece  21  is stopped at such an angular position that a point on the outer circumferential surface of the eccentric cylindrical portion CA 1  which is the closet to the center axis (hereinafter referred to as an “innermost point”) and a point on the outer circumferential surface of the eccentric cylindrical portion CA 1  which is most remote from the center axis (hereinafter referred to as an “outmost point”) are both located on the X-axis line. The rotational angle at which the eccentric cylindrical portion CA 1  is oriented as shown in FIG.  6 ( a ) is defined as a rotational angle of 0 degrees. Further, the rotational angle at which the eccentric cylindrical portion CA 1  is oriented as shown in FIG.  6 ( c ) is referred to as a rotational angle of 180 degrees. 
     In subsequent step S 24 , the probe  27  of the measurement apparatus  25  is swung from the standby position indicated by the solid line in FIG. 1 to the measurement position indicated by the broken line in FIG.  1 . Subsequently, the table  11  is moved by the Y-axis motor  12  to a position at which the probe  27  faces the reference surface of the reference plate  29 . In this state, the wheel head  3  is advanced by the X-axis motor  4 , and is stopped when the measurement apparatus  25  outputs an ON signal due to contact with the reference plate  29 . The stopped position is detected from the output of the X-axis encoder  5  and is stored in the storage unit  36  as a reference point K 2 . 
     In step S 25 , the wheel head  3  and the table  11  are moved by the X-axis motor  4  and the Y-axis motor  12 , respectively, such that the probe  27  comes into contact with the innermost point of the eccentric cylindrical portion CA 1  (FIG.  6 ( a )). The advance movement of the wheel head  3  is stopped at a position where the measurement apparatus  25  outputs an ON signal. At this time, the distance from the reference point K 2  to the innermost point along the X-axis direction is detected from the output of the X-axis encoder  5  and is stored in the storage unit  36  as the innermost-point distance M 21 . 
     Further, the CPU  32  calculates the smaller radius (the distance between the rotation center and the innermost point) U on the basis of the known reference distance K 2  and the measured innermost-point distance M 21  and stores it in the storage unit  36 . The smaller radius U can be obtained by, for example, the formula U=K 2 −M 21 −P/2. 
     In step S 26 , the wheel head  3  is retreated in order to separate the probe  27  from the eccentric cylindrical portion CA 1  (probe retraction) (FIG.  6 ( b )), and the workpiece  21  is rotated by 180 degrees (workpiece half-turn rotation) (FIG.  6 ( c )). 
     In subsequent step S 27 , the wheel head  3  is moved by the X-axis motor  4  such that the probe  27  comes into contact with the outermost point of the eccentric cylindrical portion CA 1 . The advance movement of the wheel head  3  is stopped at a position where the measurement apparatus  25  outputs an ON signal. At this time, the distance between the reference point K 2  and the outermost point along the X-axis direction is stored in the storage unit  36  as the outermost-point distance M 22 . 
     Further, the CPU  32  calculates the larger radius (the distance between the rotation center and the outermost point) V on the basis of the reference distance K 2  and the measured innermost-point distance M 22  and stores it in the storage unit  36 . The larger radius V can be obtained by, for example, the formula V=K 2 −M 22 −P/2. After completion of tie measurement of the innermost-point distance M 22 , the wheel head  3  is returned to the retreated position, and the probe  27  is returned to the standby position. 
     In subsequent step S 28 , the radius R of the eccentric cylindrical portion CA 1  is obtained from the smaller radius U and the larger radius V obtained in steps S 25  and S 27 . The radius R can be obtained by, for example, the formula R=(U+V)/2. 
     In step S 29 , the eccentricity T of the eccentric cylindrical portion CA 1  with respect to the rotation center of the workpiece  21  is obtained from the larger radius V and the radius R of the eccentric cylindrical portion CA 1 , and is stored in the storage unit  36 . The eccentricity T can be obtained by, for example, the formula T=V−R. 
     In step S 30 , the calculated eccentricity T is compared with a target eccentricity. When the error exceeds the tolerance, profile data which are used for performing simultaneous two-axis control (for the C axis and the X axis) so as to form the eccentric cylindrical portion CA 1  on the center shaft are judged to be inaccurate, and the profile data are corrected on the basis of the error. More specifically, the profile data are calculated again, while the eccentricity input value used in the previous calculation is corrected by an amount corresponding to the error. Thus, re-corrected profile (P/F) data which enable attainment of an eccentricity closer to the target eccentricity are obtained and stored in the re-corrected P/F data area of the storage unit  36 . 
     The re-corrected profile (P/F) data are used in step S 31  in order to finish-grind the eccentric cylindrical portion CA 1 . The advancement/retraction motion of the wheel head  3 —which is performed in synchronism with rotation of the workpiece  21  and is superposed on the cutting feed for the finish grinding—is controlled on the basis of the re-corrected profile (P/F) data. Thus, the eccentric cylindrical portion CA 1  is ground to have the target finish diameter and the target eccentricity. 
     In subsequent step S 32 , the CPU  32  judges whether all eccentric cylindrical portions have been ground. When no other eccentric cylindrical portions to be ground are present, the CPU  32  ends the processing. When any eccentric cylindrical portion to be ground is present (e.g., an eccentric cylindrical portion CA 2  as shown in FIG.  5 ), the CPU  32  proceeds to step S 33 . 
     In step S 33 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the second eccentric cylindrical portion CA 2  to be ground. In next step S 34 , the second eccentric cylindrical portion CA 2  is subjected to rough grinding and fine grinding performed in the same manner as in step S 22 . Since a phase difference of 180 degrees is present between the eccentric cylindrical portions CA 1  and CA 2 , before start of the rough grinding, the workpiece  21  is oriented or indexed to an index angle which is shifted by half a turn from the index angle at which the rough grinding of the eccentric cylindrical portion CA 1  was started, so that the smallest radius portion of the eccentric cylindrical portion CA 2  is caused to face the grinding wheel  7 . The rough grinding is started from such an index angle. During the rough grinding and fine grinding subsequent thereto, in accordance with the re-corrected profile (P/F) data which have been obtained in step S 30  through grinding of the first eccentric cylindrical portion CA 1 , the wheel head  3  is advanced and retracted in synchronism with rotation of the workpiece  21  in such a manner that the advancement/retraction motion of the wheel head  3  is superposed on the cutting feed motion toward the workpiece  21 . 
     Subsequent to the fine grinding, finish grinding is performed in step S 35 . In this finish grinding as well, the wheel head  3  is advanced and retracted in synchronism with rotation of the workpiece  21  and in accordance with the re-corrected profile (P/F) data. At the end of the finish grinding, the cutting feed of the wheel head  3  is stopped, and the workpiece  21  is rotated one turn or several turns in order to effect spark-out grinding. In this manner, the second eccentric cylindrical portion CA 2  has undergone the rough grinding, the fine grinding, and the finish grinding. In the case of the workpiece  21 , which has two eccentric cylindrical portions as shown in FIG. 5, in step S 32 , the CPU  32  judges that all the eccentric cylindrical portions have been ground, and ends the present machining operation program. 
     Next, a third embodiment of the work-portion measuring method of the present invention will be described with reference to FIGS. 8 and 9. FIG. 8 is an illustration showing the third embodiment of the work-portion measuring method of the present invention. FIG. 9 is a flowchart showing the operation for grinding a journal portion, while measuring the journal portion by use of the measurement apparatus  25 . 
     A machining operation program which is required to grind the outer circumferential surface of a journal J 1  (work portion) of a crankshaft (workpiece)  20  on the grinding machine  1  is stored in the storage unit  36  in advance. 
     When the machining operation program shown in FIG. 9 is started, in first step S 41 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the first journal J 1 . 
     In next step S 42 , the workpiece  20  is rotated by the C-axis motor  17  on the headstock  16 , and the wheel head  3  is advanced by the X-axis motor  4  in such a manner that the grinding wheel  7  cuts into the journal J 1  to thereby perform rough grinding and fine grinding. At the end of the fine grinding, the cutting feed of the wheel head  3  is stopped, and the workpiece  20  is rotated one turn or several turns in order to effect spark-out grinding. Subsequently, the fine grinding is ended. 
     In this case, the workpiece  20  deflects during the rough grinding and the fine grinding, so that the finished journal J 1  of the workpiece  20  may come to have an elliptical cross section. In order to eliminate an elliptical component, the wheel head  3  may be advanced and retreated over a small distance in synchronism with rotation of the workpiece  20 . In the case in which such elliptical-component correction motion is to be imparted to the wheel head  3 , first trial grinding is performed in order to obtain the relationship between each rotational angular position of the workpiece  20  and a corresponding correction amount (increase or decrease amount) by which the corresponding movement amount of the wheel head  3  is to be corrected in order to eliminate the elliptical component. The thus-obtained relationship is stored in the storage unit  36  as correction profile (P/F) data. During each grinding step, the correction amount is added to the cutting feed amount of the wheel head  3  in accordance with the correction profile (P/F) data. 
     In subsequent step S 43 , the probe  27  of the measurement apparatus  25  is brought into contact with the reference surface of the reference plate  29  provided on the headstock  16 . When the measurement apparatus  25  outputs an ON signal, the position of the wheel head  3  is detected from the output of the X-axis encoder  5  and is stored in the storage unit  36  as a reference point K 3 . 
     Next, the probe  27  is brought into contact with the first journal J 1  having been ground. When the measurement apparatus  25  outputs an ON signal, the position of the wheel head  3  is detected, and the distance in the X-axis direction between the reference point K 3  and the position at which the measurement apparatus  25  has output the ON signal is obtained as an outer-circumferential-surface distance M 31 . 
     In step S 44 , the CPU  32  calculates the diameter JD 11  of the journal J 1  on the basis of the known reference distance K 3  and the measured outer-circumferential-surface distance M 31 . The diameter JD 11  of the journal J 1  can be obtained by, for example, the formula JD=(K 3 −M 31 −P/2)×2. 
     In subsequent step S 45 , the measured actual diameter JD of the journal J 1  after fine grinding is compared with a target diameter after fine grinding. When the error therebetween is in excess of a preset tolerance, the set value for the wheel diameter is corrected, or the coordinate of the wheel head  3  is corrected. 
     In the method in which the set value for the wheel diameter is corrected, the main purpose of correction is to compensate thermal deformation of a metal core member of, for example, a CBN grinding wheel and a measurement error in measurement of a wheel diameter, which is performed manually by use of a measurement tool. However, errors stemming from thermal deformation of all mechanical elements which constitute the grinding machine and follow delay of the feed servo system are regarded as errors in setting the wheel diameter; and the set value for the wheel diameter is corrected on the basis of the errors. Specifically, when the actual diameter JD after fine grinding is smaller than the corresponding target diameter, the set value for the wheel diameter is judged to be smaller than an ideal value by an amount corresponding to the difference between the actual diameter and the target diameter. In such a case, the set value for the wheel diameter is reset to a value which is greater than the previous value by an amount corresponding to the difference, and thus, the cutting-feed end position of the wheel head  3  in finish grinding is corrected so as to be shifted rearward or toward the retracted position. When the actual diameter JD after fine grinding is greater than the corresponding target diameter, the set value for the wheel diameter is reset to a value which is smaller than the previous value by an amount corresponding to the difference, and thus, the cutting-feed end positron of the wheel head  3  in finish grinding is corrected to be shifted forward or toward the center of the workpiece  20 . 
     In the method in which the coordinate of the wheel head  3  is corrected, errors due to thermal deformation, measurement errors, and follow delay of the feed servo system are regarded as an error in initial setting of the coordinate of the wheel head  3 . In this method, when the actual diameter JD after fine grinding is smaller than the corresponding target diameter, the coordinate of the wheel head  3  is corrected to be shifted forward in the cutting feed direction; and when the actual diameter JD after fine grinding is greater than the corresponding target diameter, the coordinate of the wheel head  3  is corrected to be shifted rearward in the cutting feed direction. 
     In subsequent step S 46 , the journal J 1  having undergone rough grinding and fine grinding in step S 43  is subjected to finish grinding. At the end of the finish grinding, spark-out grinding is performed in the same manner as that performed at the end of the fine grinding. In the case in which the set value for the wheel diameter has been corrected in step S 45 , during the finish grinding, the wheel head  3  is fed to a cutting-feed end position for finish grinding which is re-calculated on the basis of the corrected wheel diameter. Thus, the journal J 1  is finished to have the target finish diameter. 
     In the case in which the present position coordinate of the wheel head  3  has been corrected in step S 45 , the coordinate which is contained in the numerical control program and which designates the cutting-feed end position for finish grinding is not changed. However, since the present position coordinate of the wheel head  3  has been corrected, the position of the wheel head  3  at the cutting-feed end position for finish grinding is changed consequently, so that the journal J 1  is finished to have the target finish diameter. 
     After completion of the finish grinding, in step S 47 , the probe  27  is brought into contact with the journal J 1  in a manner similar to that in step S 43 . When the measurement apparatus  25  outputs an ON signal, the position of the wheel head  3  is detected, and the distance in the X-axis direction between the reference point K 3  and the position at which the measurement apparatus  25  has output the ON signal is obtained as an outer-circumferential-surface distance M 32 . 
     In step S 48 , the CPU  32  calculates the diameter JD 12  of the journal J 1  in the same manner as in step S 44 . 
     In step S 49 , the CPU  32  judges whether the obtained diameter JD 12  falls within the tolerances set for the target value to be attained after completion of the grinding operation. When the diameter JD 12  falls within the tolerance, the CPU  32  proceeds to step S 50 . When the diameter JD 12  falls outside the tolerance, the CPU  32  proceeds to step S 51 . 
     In step S 51 , the CPU  32  feeds to the input/output unit  38  an NG signal indicating that the ground journal J 1  is NG; i.e., unsatisfactory. Upon receipt of the NG signal, the input/output unit  38  displays on the display means a message reporting that the ground journal J 1  is NG Further, the CPU  32  transmits a machining stop command to the grinding machine  1 , so that grinding of a subsequent journal J 2  is stopped. 
     In step S 50 , the CPU  32  judges whether all journals have been ground. When no other journals to be ground are present, the CPU  32  ends the processing. When any journal to be ground is present (e.g., journals J 2  and J 3 ), the CPU  32  proceeds to step S 52 . 
     In step S 52 , the table  11  is moved by the Y-axis motor  12  to a position at which the grinding wheel  7  faces the second journal J 2 . 
     In next step S 53 , the journal J 2  is subjected to rough grinding and fine grinding performed in the same manner as in step S 42 . 
     In subsequent step  54 , in the same manner as in step S 46 , the wheel head  3  is advanced to the cutting-feed end position for finish grinding which has been corrected through wheel diameter correction or wheel-head coordinate correction in step S 45 . Thus, the journal J 1  is subjected to finish grinding (micro grinding, grinding without cutting). 
     Upon completion of the finish grinding, the CPU  32  proceeds to step S 50  and ends the grinding work. 
     In a modification of the third embodiment, the CPU  32  calculates the diameter JD of the journal J 1  after completion of the finish grinding. In this case, the CPU  32  is programmed to proceed from step S 54  to step S 47  as indicated by line L 2 , so that the processing in step S 47  and subsequent steps is performed. 
     As described above, the work-portion measuring method according to the present invention enables accurate measurement of the diameter of the work portion at low cost. Further, the eccentricity of the work portion with respect to the center axis can be measured. Therefore, when the measuring method of the present invention is employed in a grinding machine, a workpiece can be ground with improved finish accuracy. 
     The present invention is not limited to the above-described embodiments, and the embodiments may be modified in various ways without departing from the scope of the present invention. 
     For example, in the embodiments, the present invention is applied to the grinding machine. However, the present invention can be applied to various machine tools other than the grinding machine. 
     In the embodiments, distance is measured along a single axis (e.g., the X axis). However, the diameter or eccentricity of each work portion can be measured on the basis of distances which are measured two-dimensionally or three-dimensionally. 
     Further, the operation for grinding a work portion of the workpiece  20  or  21  while measuring the work portion is not limited to these shown in the flowcharts of FIGS. 4,  7 , and  9 , and may be modified in various manners. 
     Machining and measurement of crankpins, eccentric cylindrical portions, and journals of a crankshaft have been described. However, no limitation is imposed on the type or shape of the workpiece or work portion, insofar as the workpiece is a rotary object having a center axis (i.e., a shaft-shaped workpiece). 
     Although in the embodiments a CBN grinding wheel is used for the grinding wheel  7 , grinding wheels of other types, such as WA grinding wheel, may be used, and a cutting tool such as a cutter or turning tool may be used. 
     The measuring method is not limited to those shown in FIGS. 3,  6 , and  8 , and may be modified in various manners. 
     In the embodiments, the reference plate  29  is provided on the side surface of the headstock  16 . However, the position and shape of the reference plate  29  can be changed freely, insofar as the reference plate  29  enables determination of a reference position with respect to the axis of the main spindle center  19 . 
     In the embodiments, each of work portions of workpieces has a circular cross section. However, the measuring method according to the present invention can be applied to work portions whose cross sections have a shape other than circular. 
     The two points on the outer circumferential surface of a work portion at which the probe  27  of the measurement apparatus  25  is brought into contact with the surface are freely determined in such a manner that the selected two points are located at diametrically opposite positions with respect to the rotation center (the selected two points are separated from each other by 180 degrees in the circumferential direction). 
     The measurement apparatus  25  used in the above-described embodiments is of a contact operation type; i.e., the measurement apparatus  25  outputs an ON signal when the probe  27  inclines by a predetermined angle due to contact with a work portion to be measured. However, measurement apparatuses of other types may be used. For example, a measurement apparatus which can detect movement of a probe within a relatively small range but with a high resolution of, for example, 0.1 or 1 micrometer. When such an measurement apparatus is used, the reference point on the reference plate  29  is memorized as follows. The wheel head  3  is advanced by a predetermined movement amount in order to bring the probe into contact with the reference plate  29 , and the amount of movement of the probe at that time is detected from the output of the measurement apparatus, and the sum of the predetermined amount of movement of the wheel head  3  and the detected amount of movement of the probe is obtained and is stored as a reference point. Further, the distance between the reference point and the surface of each work portion (e.g., M 11 , M 12  in FIG. 2) is obtained as follows. The wheel head  3  is advanced by a predetermined amount of movement in order to bring the probe into contact with the work portion, and the amount of movement of the probe at that time is detected from the output of the measurement apparatus, and the sum of the predetermined amount of movement of the wheel head  3  and the detected amount of movement of the probe is obtained and stored as the distance between the reference point and the surface of the work portion. 
     In place of the measurement apparatus  25 , other types of measurement apparatuses such as an ultrasonic sensor and an optical sensor may be used, insofar as the selected measurement apparatus can accurately detect the surface of the reference plate  29  or the surface of a work portion to be measured. 
     Further, the measuring method of the present invention can be applied to a grinding machine for grinding a camshaft. Specifically, the measuring method of the present invention can be used to measure the shape of a cam after completion of grinding operation; in particular, the radius of the base circle of the cam, and the radius of the top portion as measured from the center of the base circle or to measure the position of the surface of a ground cam at a plurality of positions to thereby check the cam profile. Similarly, the measuring method of the present invention can be used to measure the position of the surface of a ground cylindrical portion at a plurality of positions to thereby measure the roundness of the ground cylindrical portion on the machine. Moreover, when the measuring method of the present invention is used to measure a concentric cylindrical portion, an eccentric cylindrical portion, or a crankpin portion of a workpiece set on the grinding machine before performance of grinding operation, it becomes possible to check beforehand whether grinding allowance is sufficient and/or whether each workpiece is defective, thereby enabling ejection of defective workpieces before start of grinding operation. 
     In the above-described embodiment, the probe  27  is formed into the shape of a sphere having a diameter P. However, the shape, material, length, number, etc. of the probe may be changed. 
     In the above-described embodiment, the center of the probe  27  is used as a measurement position of the measurement apparatus. However, any other position within the probe  27  may be used as a measurement position. The measurement apparatus  25  is preferably mounted on a tool head such as the wheel head  3 . 
     In the above-described embodiment, the control apparatus  31  is a computerized numerical controller (CNC). However, a controller of any other type may be sued. In the above-described embodiment, ideal profile (P/F) data, corrected (or correction) profile (P/F) data, and re-corrected profile (P/F) data are stored in the storage unit  36 . However, the types of data and programs stored in the storage unit  36  are not limited thereto.