Abstract:
A thermal displacement correction method includes the steps of: presetting the coordinate data of a fixed position of the workpiece on a table; finding an amount of displacement of the fixed position of the workpiece at a current cutting edge position based on the detected temperature, the coordinate data of the cutting edge position, and the coordinate data of the fixed position; computing the difference in the coordinate data between the fixed position of the workpiece and the cutting edge position; finding an amount of displacement of the workpiece between its fixed position and the cutting edge position based on the detected temperature and the difference in the coordinate data between the fixed position and the cutting edge position, and computing a sum of each amount of displacement to define an estimated value and correcting thermal displacement using an NC unit based on the estimated value.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     This application claims the benefit of Japanese Patent Application Number 2005-101479 filed on Mar. 31, 2005, the entirety of which is incorporated by reference.  
       FIELD OF THE INVENTION  
       [0002]     The present invention relates to a method for correcting thermal displacement that varies depending on a position of a tool or a workpiece in a machine tool.  
       DESCRIPTION OF THE RELATED ART  
       [0003]     In machining process of a machine tool, the machine tool and a workpiece are subject to thermal deformation due to change of environmental temperature of a room, heat emitted from the machine tool, and cutting heat. This thermal displacement leads to dimension error of machining. As a method to reduce the dimension error, from a mechanical or structural point of view, methods to keep a constant temperature of the machine and the workpiece have been proposed, for example, installation of the machine in a temperature-controlled room, and temperature control of cutting fluid. However, these methods require higher running cost and further have a problem that it is difficult to set a standard temperature of the cutting fluid. On the other hand, from a viewpoint of electrical control, a method to estimate and correct thermal displacement from temperature information or NC unit information has been proposed. As an example of this method, the applicant of the present invention discloses the Japanese Published Unexamined Patent Application No. 2001-341049. This, particular method includes the steps of detecting the coordinate data of machining point, that is, the coordinate data of the cutting edge position in machining (hereinafter, it is simply referred to as “cutting edge coordinate data”), and estimating thermal displacement in accordance with the coordinate data of the machining point and temperature information. Japanese Published Examined Patent Application No. 06-61674 discloses another method that estimates the thermal displacement in accordance with the difference between a main spindle position and a standard position, as well as temperature information. Further, a document Katagijutsu (that means “die/mold technology”), Volume 18, Issue 8, Pages 44-45 discloses another method for estimating thermal displacement generated on a table of a double-column machining center in accordance with temperature information and positional information.  
         [0004]     The above-described methods for estimating thermal displacement in accordance with temperature information or positional information from an NC unit work effectively only when a workpiece is cut on a lathe in which the fixed position of a workpiece is defined as the center of the main spindle, or only when a small workpiece is disposed on a table of a machining center and so on. However, when a relatively large workpiece such as a mold is cut, there is a problem that the thermal displacement of the workpiece varies depending on its fixed position on a table.  
         [0005]      FIG. 9  is a side schematic view of a conventional double-column machining center. Columns  6 ,  6  are disposed on opposite sides of a bed  1  (in the direction orthogonal to a drawing sheet). Between the columns  6 ,  6 , a cross rail (not shown) is bridged transversely, and a saddle  7  is mounted on the cross rail  6  movable in the Y-axis direction orthogonal to the drawing sheet. A main spindle  8  is attached on the saddle  7  movable in the Z-axis direction that is vertical. At the distal end of the main spindle  8 , a tool  9  is rotatably connected. Above the bed  1 , a table  4  is disposed movable in the X-axis direction parallel to the drawing sheet, and a workpiece  5  is fixed on the table  4 .  
         [0006]     In  FIGS. 9B and 9C , each cutting edge coordinate data X is shown at the same position. On the other hand, each coordinate data of the fixed position of the workpiece XW is shown in different positions, for example, XWa in  FIG. 9B  and XWb in  FIG. 9C .  FIG. 11  shows thermal displacement change in the X-axis direction in accordance with the fixed positions in  FIGS. 9A-9D  at a room temperature shown in  FIG. 10 . Teaching of  FIG. 11  is that change of the thermal displacement varies depending on the coordinate data of the fixed position even if the cutting edge coordinate data is unchanged. For this reason, in order to obtain the thermal displacement of the workpiece based on the cutting edge coordinate data only, it is necessary to change correction parameters in accordance with the coordinate data of the fixed position.  
         [0007]     Moreover, in machining a relatively large workpiece such as a mold, when the workpiece is disposed at a place whose environmental temperature is different, there might be another problem that the dimension and configuration of the workpiece might be different from the desired ones due to thermal deformation caused by temperature change of the workpiece even if the workpiece is machined in a uniformed environmental temperature, a temperature-controlled room for example, wherein no thermal displacement is generated on a machine tool and the workpiece.  
       SUMMARY OF THE INVENTION  
       [0008]     In order to solve the above problems, a method for correcting thermal displacement in accordance with a first aspect of the present invention includes the steps of: detecting temperature of each component of a machine tool; converting the detected temperature into numerical values, and  
         [0000]     estimating an amount of thermal displacement based on the numerical values of temperature and the coordinate data of the cutting edge position using a computing equation.  
         [0009]     Moreover, the step of estimating an amount of thermal displacement further includes the steps of:  
         [0010]     presetting the coordinate data of a fixed position of the workpiece on a table (hereinafter, it is simply referred to as “the coordinate data of the fixed position” or “the coordinate data of the fixed position of the workpiece,”); computing the following values using the coordinate data of the fixed position of the workpiece:  
         [0000]     (A) an amount of displacement of the fixed position of the workpiece at a current cutting edge position as ΔAB1,  
         [0000]     (B) an amount of displacement of the workpiece between its fixed position and the current cutting edge position as ΔC1, and  
         [0000]     computing a sum of ΔAB1 and ΔC1 to define an estimated value. 
 
An amount of correction of the coordinate data of the cutting edge position=−(Δ AB 1 +ΔC 1)  [Equation 1]
 
 wherein, 
 
 ΔAB1: an amount of displacement of the fixed position of the workpiece at a current cutting edge position 
 
 ΔC1: an amount of displacement of the workpiece between its fixed position and the cutting edge position 
 
         [0011]     In addition, a method for correcting thermal displacement in accordance with a second aspect of the present invention is characterized by the following steps of:  
         [0012]     computing an amount of displacement of the fixed position of the workpiece at the positive end position of moving distance of a cutting edge with respect to a table (hereinafter, it is simply referred to as “stroke” or “cutting stroke”) as ΔAB2, and an amount of displacement of the fixed position of the workpiece at the negative end position of cutting stroke as ΔAB3 instead of ΔAB1 described above; computing an amount of displacement of the workpiece between the fixed position and the positive end position of the cutting stroke as ΔC2, and an amount of displacement of the workpiece between the fixed position and the negative end position of the cutting stroke as ΔC3 instead of ΔC1 described above;  
         [0000]     computing a sum of ΔAB2 and ΔC2 to define an estimated value at the positive end of the cutting stroke, and a sum of ΔAB3 and ΔC3 to define an estimated value at the negative end of the cutting stroke, and  
         [0000]     using two-point correction function of a servo system. 
 
An amount of correction at the positive end of the cutting stroke=−(Δ AB 2 +ΔC 2)  [Equation 2]
 
An amount of correction at the negative end of the cutting stroke=−(Δ AB 3 +ΔC 3)  [Equation 3]
 
 wherein: 
 
 ΔAB2: an amount of displacement of the fixed position of the workpiece at the positive end position of the cutting stroke 
 
 ΔAB3: an amount of displacement of the fixed position of the workpiece at the negative end position of the cutting stroke 
 
 ΔC2: an amount of displacement of the workpiece between the fixed position and the positive end position of the cutting stroke 
 
 ΔC3: an amount of displacement of the workpiece between the fixed position and the negative end position of the cutting stroke 
 
         [0013]     It should be noted that the present invention can be easily embodied, for example, by providing an NC machine tool (a machining center) shown in  FIG. 1  which is an object of thermal displacement correction, with the following: a temperature sensor; a temperature measuring device; a parameter storage device that stores each parameter, and a correction device for computing a correction value based on detected temperature and information of an NC unit. In the parameter storage device, various values are set, such as, the X-coordinates of the fixed position of the workpiece Xw, a coefficient of linear thermal expansion α, a standard temperature, the X-coordinates of the positive end position of the cutting stroke Xlp, and the X-coordinates of the negative end position of the cutting stroke Xlm.  
         [0014]     Here, as a more concrete method, an amount of displacement ΔAB1 is obtained from Equation 4 by computing a sum of ΔA1, an amount of displacement of a scale at the cutting edge position (shown in A 1  in  FIG. 2 ) and ΔB, an amount of displacement of a table (shown in B in  FIG. 2 ). (a third aspect of the present invention) 
 
Δ AB 1=(Δ A 1 +ΔB )  [Equation 4]
 
 wherein, 
 
Δ A 1=(a temperature for estimating thermal displacement that is obtained based on a temperature of a scale and a standard temperature)×(the coordinate data of the cutting edge position−the coordinate data of the scale detector position)×(a coefficient of linear thermal expansion of the scale)  [Equation 5]
 
Δ B =(a temperature for estimating thermal displacement that is obtained based on a temperature of a table and a standard temperature)×(the coordinate data of the scale detector position−the coordinate data of the fixed position of the workpiece)×(a coefficient of linear thermal expansion of the table)  [Equation 6]
 
         [0015]     Further, an amount of displacement ΔC 1  (shown in C in  FIG. 2 ) is obtained Equation 7. (a fourth aspect of the present invention) 
 
Δ C 1=(a temperature for estimating thermal displacement that is obtained based on a temperature of the workpiece and a standard temperature)×(the coordinate data of the fixed position of the workpiece−the coordinate data of the cutting edge position)×(a coefficient of linear thermal expansion of the workpiece)  [Equation 7]
 
         [0016]     Still further, an amount of displacement ΔAB2 is obtained from Equation 8 by computing a sum of ΔA2, an amount of displacement of the scale at the positive end of the cutting stroke (shown in A 2  in  FIG. 3A ) and ΔB described above (shown in B in  FIG. 3A ). (a fifth aspect of the present invention) 
 
Δ AB 2=(Δ A 2 +ΔB )  [Equation 8]
 
 wherein, 
 
Δ A 2=(a temperature for estimating thermal displacement that is obtained based on a temperature of a scale and a standard temperature)×(the coordinate data of the positive end position of the cutting stroke−the coordinate data of the scale detector position)×(a coefficient of linear thermal expansion of the scale)  [Equation 9]
 
         [0017]     Similarly, an amount of displacement ΔAB3 is obtained from Equation 10 by computing a sum of ΔA3, an amount of displacement of the scale at the negative end of the cutting stroke (shown in A 3  in  FIG. 3B ) and ΔB described above (shown in B in  FIG. 3B ) (a fifth aspect of the present invention) 
 
Δ AB 3=(Δ A 3 +ΔB )  [Equation 10]
 
 wherein, 
 
Δ A 3=(a temperature for estimating thermal displacement that is obtained based on a temperature of a scale and a standard temperature)×(the coordinate data of the negative end position of the cutting stroke−the coordinate data of the scale detector position)×(a coefficient of linear thermal expansion of the scale)  [Equation 11]
 
         [0018]     Still further, an amount of displacement ΔC2 (shown in D in  FIG. 3A ) and an amount of displacement ΔC3 (shown in E in  FIG. 3B ) are obtained from equations below. (a sixth aspect of the present invention) 
 
Δ C 2=(a temperature for estimating thermal displacement that is obtained based on a temperature of the workpiece and a standard temperature)×(the coordinate data of fixed position of the workpiece−the coordinate data of the positive end position of the cutting stroke)×(a coefficient of linear thermal expansion of the workpiece)  [Equation 12]
 
Δ C 3=(a temperature for estimating thermal displacement that is obtained based on a temperature of the workpiece and a standard temperature)×(the coordinate data of fixed position of the workpiece−the coordinate data of the negative end position of the cutting stroke)×(a coefficient of linear thermal expansion of the workpiece)  [Equation 13]
 
         [0019]     It should be noted that a standard temperature is set to be a temperature that requires dimensional accuracy of the workpiece, for example, an environmental temperature capable of measuring the dimensional accuracy of the workpiece, or an environmental temperature capable of assembling a product using the workpiece. With this setting, it is possible to machine the workpiece with dimension suitable for an environmental temperature that requires dimensional accuracy even if machining process is conducted in a different environment. (a seventh aspect of the present invention)  
         [0020]     Moreover, workpiece information, such as the coordinate data of the fixed position of the workpiece, a coefficient of linear thermal expansion of the workpiece, and a standard temperature (that requires dimensional accuracy of the workpiece) are preferably set for each workpiece by providing a setting screen on an NC unit or set by means of NC program. (an eighth to a thirteenth aspects of the present invention)  
         [0021]     By setting the workpiece information such as the coordinate data of the fixed position of the workpiece, a coefficient of linear thermal expansion of the workpiece, and a standard temperature of the workpiece, it is possible to apply correction suitable for environment according to the fixed position of the workpiece, the workpiece material, and a location of a machine. Moreover, by setting the workpiece information via an operation panel, the setting operation becomes easy. Further, by setting the workpiece information using NC program, correction can be applied to unattended machining process of the workpiece. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0022]      FIG. 1  is an example of a device used for embodying the present invention.  
         [0023]      FIG. 2  is a diagram showing relationship between an amount of displacement of a scale and an amount of displacement of a table at the coordinate data of cutting edge position.  
         [0024]      FIG. 3A  is a diagram showing relationship between an amount of displacement of a scale and an amount of displacement of a table at the coordinate data of the positive end position of cutting stroke.  
         [0025]      FIG. 3B  is a diagram showing relationship between an amount of displacement of a scale and an amount of displacement of a table at the coordinate data of the negative end position of the cutting stroke.  
         [0026]      FIG. 4  is a setting screen of an NC machine tool showing the coordinate data of the fixed position of a workpiece, a coefficient of linear thermal expansion of the workpiece, and a standard temperature.  
         [0027]      FIG. 5  is a graph showing the temperature of a workpiece, table, and bed as an example, which are subject to correction of the thermal displacement according to the present invention.  
         [0028]      FIG. 6  is a flow chart of an embodiment of the present invention.  
         [0029]      FIG. 7  is a flow chart of another embodiment of the present invention.  
         [0030]      FIG. 8  is a graph showing a result of measuring the thermal displacement in a condition that correction of the thermal displacement according to the present invention is conducted.  
         [0031]      FIGS. 9A-9D  are diagrams showing relationship between the coordinate data of the fixed position of the workpiece and the coordinate data of the cutting edge position according to prior art.  
         [0032]      FIG. 10  is a graph showing a room temperature change in measuring the thermal displacement.  
         [0033]      FIG. 11  is a graph showing a result of measuring the thermal displacement according to the prior art.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0034]      FIG. 1  is an embodiment of a device of the present invention. The device consists of an NC machine tool (machining center) that conducts thermal displacement correction, a temperature sensor, a temperature measuring device, a storage device that stores each parameter, a correction device that computes a correction value based on the detected temperature and NC unit information, and an NC unit that conducts a numerical control on the machine tool. Here, the thermal displacement in X-axis direction where the dimension of a workpiece and moving distance are large will be explained as an example.  
         [0035]      FIG. 1  is a side schematic view of a double-column machining center. Columns  6 ,  6  are disposed on opposite sides of a bed  1  (in the direction orthogonal to a drawing sheet). Between the columns  6 ,  6 , a cross rail (not shown) is bridged transversely, and a saddle  7  is mounted on the cross rail movable in the Y-axis direction orthogonal to the drawing sheet. A main spindle  8  is attached on the saddle  7  movable in the Z-axis direction that is vertical. At the distal end of the main spindle  8 , a tool  9  is rotatably connected. Above the bed  1 , a table  4  is disposed movable in the X-axis direction parallel to the drawing sheet, and a workpiece  5  is fixed on the table  4 . The position of the table  4  in the X-axis direction is determined by a scale  2  disposed on the bed  1  and a scale detector  3  fixed on the table  4 .  
         [0036]     The temperature sensors are preferably disposed on each component of the machine tool, in particular, a component that relatively moves a cutting edge and a workpiece in the axial direction to be corrected. In this embodiment, a temperature sensor  10   a  is disposed on the bed  1  near a scale to measure a temperature of the scale, a temperature sensor  10   b  is disposed on the table  4  to measure a temperature of the table, a temperature sensor  10   c  is disposed on the workpiece  5  to measure a temperature of the workpiece.  
         [0037]     Hereinafter, correction of the thermal displacement in the X-axis direction at the coordinate data of the fixed position of the workpiece shown in  FIG. 1  using the temperature of the workpiece, table, and bed shown in  FIG. 5  will be explained. In  FIG. 1 , the X-coordinates of the positive end position of cutting stroke Xlp, the X-coordinates of the negative end position of cutting stroke Xlm, and the X-coordinates of the fixed position of the workpiece Xw are as follows. 
 
Xlp=6000 mm 
 
Xlm=0 mm 
 
Xw=1500 mm 
 
       First Embodiment  
       [0038]     The first embodiment will be explained based on a flowchart of  FIG. 6 . At S 1 , a temperature measuring device  11  converts the analog signals into numerically expressed digital signals representing the temperatures of each sensor  10   a - 10   c  with a predetermined interval (10 seconds) by a well-known method. In a parameter storage device  13 , the X-coordinates of the fixed position of the workpiece Xw, a coefficient of linear thermal expansion α, and a standard temperature are preset.  
         [0039]     At S 2 , the X-coordinates of a current cutting edge position is detected by an NC unit  14 . At S 3 , with a correction amount computing unit  12 , an amount of displacement of the scale ΔA1, an amount of displacement of the table ΔB, and an amount of displacement of the workpiece ΔA2 are computed a using Equations 5, 6, and 7, respectively.  
         [0040]     Here, as a computing method for obtaining a temperature for estimating the thermal displacement shown in the first term on the right-hand side of Equation 5, there is provided an exponential smoothing filter as shown in the Japanese Published Unexamined Patent Application No. 9-225781 filed by the present applicant. Accordingly, Equation 5 can be expressed as follows. 
 
 X   7n   =Y   7n ·( X−Xs )· K   7   [Equation 5a]
 
 wherein, 
 
 Y   7n   =Y   7n-1 +( T   70n   −Y   7n-1 )·α 7  
 
 T   70   =T   7   −T   0  
 
T 0 =20 
 
 wherein, 
 
 X n : nth amount of displacement 
 
 Y n : nth temperature for estimating the thermal displacement 
 
 T n : nth input temperature 
 
 α: a coefficient of a filter (α 7 =3.2×10 −2 ) 
 
 X: the X-coordinates 
 
 Xs: the X-coordinates of a scale detector (=6000 mm) 
 
 K: a coefficient of linear thermal expansion (K 7 =11×10 −6 ) 
 
 Subscript 7: a scale value 
 
 Subscript 0: a standard value 
 
         [0041]     Similarly, Equations 6 and 7 can be expressed as follows. 
 
 X   8n   =Y   8n ·( Xs−Xw )· K   8   [Equation 6a]
 
 wherein, 
 
 Y   8n   =Y   8n-1 +( T   80n   −Y   8n-1 )·α 8  
 
 T   80   =T   8   −T   0  
 
T 0 =20 
 
 X   2n   =Y   2n ·( Xw−X )· K   2   [Equation 7a]
 
 wherein, 
 
 Y   2n   =Y   2-1 +( T   20n   −Y   2n-1 )·α 2  
 
 T   20   =T   8   −T   0  
 
T 0 =20 
 
 wherein, 
 
 X an : nth amount of displacement 
 
 Y n : nth temperature for estimating the thermal displacement 
 
 T n : nth input temperature 
 
 X: the X-coordinates 
 
 Xs: the X-coordinates of a scale detector (=6000 mm) 
 
 α: a coefficient of a filter (α 8 =3.2×10 −2 , α 2 =8.3×10 −3 ) 
 
 K: a coefficient of linear thermal expansion (K 8 =11×10 −6 , K 2 =11×10 −6 ) 
 
 Subscript 8: a table value 
 
 Subscript 2: a workpiece value 
 
 Subscript 0: a standard value 
 
         [0042]     Then, from Equations 1 and 4, the amount of correction at the X-coordinates XC is computed. 
 
 XC =−( X   7   +X   8   +X   2 ) 
 
         [0043]     At S 4 , the NC unit carries out correction of the thermal displacement, moving by the amount of correction XC in the axis direction. At S 5 , it returns to S 1  when correction is continued, or the process is finished when the correction is discontinued.  
       Second Embodiment  
       [0044]     Another embodiment of the present invention will be explained based on a flowchart of  FIG. 7 . At S 11 , the temperature measuring device  11  converts the analog signals into numerically expressed digital signals representing the temperatures of each sensor  10   a - 10   c  with a predetermined interval (10 seconds) by a well-known method. In the parameter storage device, the X-coordinates of the positive end position of the cutting stroke Xlp, the X-coordinates of the negative end position of the cutting stroke Xlm, the X-coordinates of the fixed position of the workpiece Xw, and a standard temperature are preset.  
         [0045]     At S 12 , with the correction amount computing unit  12 , a correction amount XCP at the coordinate data of the positive end position of the cutting stroke is computed based on an amount of displacement of the scale ΔA2 (from Equation 9), an amount of displacement of the table ΔB (from Equation 6), an amount of displacement the workpiece ΔC2 (from Equation 12) using Equations 1 and 8. 
 
 XCP =−( X   9   +X   8   +X   5 )  [Equation 1b]
 
 X   9n   =Y   9n ·( Xlp−Xs )· K   9   [Equation 9b]
 
 X   8n   =Y   8n ·( Xs−Xw )· K   8   [Equation 6b]
 
 X   5n   =Y   5n ·( Xw−Xlp )· K   8   [Equation 12b]
 
 wherein, 
 
 Y   9n   =Y   9n-1 +( T   90n   −Y   9n-1 )·α 9  
 
 T   90   =T   9   −T   0  
 
T 0 =20 
 
 Y   8n   =Y   8n-1 +( T   80n   −Y   8n-1 )·α 8  
 
 T   80   =T   8   −T   0  
 
T 0 =20 
 
 Y   5n   =Y   5n-1 +( T   50n   −Y   5n-1 )·α 5  
 
 T   50   =T   5   −T   0  
 
T 0 =20 
 
 wherein, 
 
 X n : nth amount of displacement 
 
 Y n : nth temperature for estimating the thermal displacement 
 
 T n : nth input temperature 
 
 α: a coefficient of a filter (α 9 =3.2×10 −2 , α 8 =3.2×10 −2 , α 5 =8.3×10 −3 ) 
 
 Xs: the X-coordinates of a scale detector (=6000 mm) 
 
 K: a coefficient of linear thermal expansion (K 9 =11×10 −6 , K 8 =11×10 −6 , K 5 =11×10 −6 ) 
 
 Subscript 9: a scale value 
 
 Subscript 8: a table value 
 
 Subscript 5: a workpiece value 
 
 Subscript 0: a standard value 
 
         [0046]     Similarly, a correction amount at the coordinate data of the negative end position of the cutting stroke XCM is computed based on an amount of displacement of the scale ΔA3 (from Equation 11), an amount of displacement of the table ΔB (from Equation 6), an amount of displacement the workpiece ΔC3 (from Equation 13) using Equations 1 and 10. 
 
 XCM =−( X   10   +X   8   +X   6 )  [Equation 1c]
 
 X   10n   =Y   10n ·( Xlm−Xs )· K   10   [Equation 11c]
 
 X   8n   =Y   8n ·( Xs−Xw )· K   8   [Equation 6c]
 
 X   6n   =Y   6n ·( Xw−Xlm )· K   6   [Equation 13c]
 
 wherein, 
 
 Y   10n   =Y   10n-1 +( T   100n   −Y   10n-1 )·α 10  
 
 T   100   =T   10   −T   0  
 
T 0 =20 
 
 Y   8n   =Y   8n-1 +( T   80n   −Y   8n-1 )·α 8  
 
 T   80   =T   8   −T   0  
 
T 0 =20 
 
Y 6n   =Y   6n-1 +( T   60n   −Y   6n-1 )·α 6  
 
 T   60   =T   6   −T   0  
 
T 0 =20 
 
 wherein, 
 
 X n : nth amount of displacement 
 
 Y n : nth temperature for estimating the thermal displacement 
 
 T n : nth input temperature 
 
 α: a coefficient of a filter (α 9 =3.2×10 −2 , α 8 =3.2×10 −2 , α 5 =8.3×10 −3 ) 
 
 Xs: the X-coordinates of a scale detector (=6000 mm) 
 
 K: a coefficient of linear thermal expansion (K 9 =11×10 −6 , K 8 =11×10 −6 , K 5 =11×10 −6 ) 
 
 Subscript 9: a scale value 
 
 Subscript 8: a table value 
 
 Subscript 5: a workpiece value 
 
 Subscript 0: a standard value 
 
         [0047]     At S 13 , the computed correction amounts are transmitted to a servo system. In this servo system, the correction amounts at both ends of the cutting stroke are processed with a linear interpolation method and correction is carried out in accordance with the coordinate data of the cutting edge position using a well-known two-point correction method. At S 14 , it returns to S 11  when correction is continued, or the process is finished when the correction is discontinued.  
         [0048]      FIG. 8  shows a result of thermal displacement correction in the X-axis direction at each machining position of  FIGS. 9A-9D  using the methods of the first and second aspects of the present invention. This result shows that the thermal displacement is controlled irrespective of the cutting edge position and the fixed position of the workpiece. Although in this figure the thermal displacement in the X-axis direction is explained, the thermal displacement in the Y-axis direction can be corrected by using the temperature of the cross rail instead of the temperature of the bed. Likewise, the thermal displacement in the Z-axis direction can be corrected by using the temperature of the column instead of the bed, and the temperature of the main spindle instead of the table.  
       Third Embodiment  
       [0049]     Moreover, it is required that workpiece information, such as the coordinate data of the fixed position of the workpiece, a coefficient of linear thermal expansion of the workpiece, and a standard temperature (that requires dimensional accuracy of the workpiece) are set for each workpiece to be machined. For this reason, by providing a setting screen as shown in  FIG. 4  to set the information with an operation panel, the setting operation becomes easy. Further, by setting the workpiece information using NC program, the workpiece information can be set in unattended machining process of the workpiece, for example, with an automatic pallet changer.