JPH0790447B2 - Tracer head detection error correction method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention is to measure the dimension of a three-dimensional solid shape of a workpiece, copy a master pattern in a copying machine tool, and convert NC machining data of a numerically controlled machine tool from the master pattern copying data. Regarding the tracer head used for digitizing to be created, in particular, the physical conditions such as the length and weight of the stylus removably provided as a contact measuring element at the tip of the tracer head and the increase in the movable stroke length of the stylus should change. The present invention relates to an error correction method that can realize high detection accuracy by correcting an error in the detected displacement of the tracer head that is generated by.

[Conventional technology]

Dimensional measurement of the three-dimensional shape of the workpiece, copying control of the tool movement by copying the master mold of the desired shape to machine a workpiece with the same or similar shape as the master mold Numerical value from the machine tool or master mold copy data In a digitizing device that creates NC data for a controlled machine tool and can operate a numerically controlled machine tool using the NC data, a stylus that detects the contact of a work surface or a mother die surface is provided at the tip, A tracer head is used in which the stylus is freely supported by an elastic support mechanism so that the stylus can move in parallel in the orthogonal three-dimensional directions, and a displacement detector that takes out the following displacement of the stylus as an electric signal is built in for each axis. The most typical example of the conventional structure of such a tracer head is disclosed in Japanese Patent Publication No. 54-43230, and it is well known that a differential transformer is optimally used as the displacement detector. The tracer head disclosed in Japanese Patent Publication No. 54-43230 described above uses an elastic plate and an elastic cylinder to support the stylus, so that the stylus scans the measuring surface or the copying surface to perform mechanical displacement. It has been found to have good mechanical performance in that it eliminates the occurrence of errors due to friction. Further, an effective three-dimensional shape measuring method and apparatus using this known tracer head is disclosed in Japanese Patent Publication No. 53-03.
It is disclosed in Japanese Patent No. 935. That is, since the contact portion of the stylus with the surface to be measured is usually formed into a spherical portion, if the surface to be measured is a surface inclined with respect to the stylus axis, the point to be measured and the spherical portion are measured. In consideration of the deviation of the contact point with, the electrical correction is performed so that the apparent center of the spherical part coincides with the measured point, making it possible to realize highly accurate measurement of non-planar surfaces including inclined surfaces. Such a correction method is effectively used not only for measuring the three-dimensional shape but also for measuring the reference displacement amount in the displacement detection in the copying process of the complicated surface of the master die in the copying machine tool. There is.

[Problems to be solved by the invention]

However, the tracer head having the stylus freely supported by the elastic mechanism described above still has various problems to be solved. That is, since the conventional tracer head of this type has a free support structure using an elastic support mechanism, in principle, as described above, the three-dimensional orthogonal axial directions (X axis, Y axis, Although it is configured to perform parallel displacement on the Z axis), when the detected displacement of the stylus becomes large, the actual displacement of the stylus deviates from the one-to-one relationship with the detected displacement obtained from the displacement detector of the tracer head. As shown in FIG. 4, in the orthogonal graph display in which the horizontal axis indicates the displacement given to the stylus and the vertical axis indicates the detected displacement output of the displacement detector of the tracer head equipped with the stylus, the so-called Since non-linearity is generated, it causes an error. Further, in a copying machine tool or a digitizing device having a well-known automatic stylus changing device,
Since the length of the stylus detachably attached to the tracer head varies from short to long, the amount of displacement detected by the displacement detector of the tracer head for the same amount of displacement of the stylus is not constant. As shown in FIG.
In a graph with the horizontal axis representing the displacement with respect to the stylus and the vertical axis representing the displacement detected by the displacement detector of the tracer head, the relationship between the two is an ideal linear relationship obtained for a stylus of standard length selected in advance, As the stylus length increases, a variation that tends to lie on the side of the horizontal axis occurs, which causes a problem of deterioration in detection accuracy. In a tracer head that realizes a substantially ideal parallel movement structure by supporting a stylus with an elastic support mechanism, it is no longer possible to solve it by improving the mechanical structure. Therefore, as a solution to such a problem, conventionally, an error quick reference table according to the stylus length is created in advance, and the correction amount corresponding to the length of the stylus worn by the operator is set as the reference displacement amount of the tracer head. Although a measure was set by changing it, such correction measures due to operator intervention not only hinder automation and unmanned operation of the machine, but also in copying machine tools equipped with an automatic stylus changing device, This results in problems such as having to prepare the stylus length to a certain length and preparing it, which is troublesome and causes a high cost.

Further, according to the conventional tracer head, there is a problem that the zero point in the displacement detector of the tracer head is displaced particularly in the axial direction of the stylus due to the change in the stylus weight in addition to the change in the stylus length (see FIG. 6). As shown in the figure, the line of applied displacement-detected displacement shifts downward as the weight increases). In order to correct such a deviation of the zero point, a measure is taken in which a counterbalance device is installed in response to a change in the weight of the stylus mounted on the tracer head, and the counterbalance is manually adjusted in the axial direction of the stylus. Was there. The interposition of such a counterbalance device is an obstacle to automation, and in the case of a copying machine tool equipped with an automatic stylus changing device, a plurality of spherical parts having different diameters loaded in the automatic stylus changing device are provided. Regarding the stylus, a method of manufacturing the stylus by a method such as changing the material is adopted so that the weight of the stylus and the weight of the stylus at the same time are matched with each other in advance. Therefore, there is a problem that the processing of the stylus is extremely complicated and cost reduction is extremely difficult.

Therefore, a main object of the present invention is to provide a novel solution capable of solving the above-mentioned problems in a tracer head used for dimension measurement, copying, etc., so that the tracer head can detect displacement with higher accuracy than before. To enable.

Another object of the present invention is to provide a novel method for non-mechanically correcting the error in the detected displacement of the tracer head by using a recent high-performance microprocessor.

Still another object of the present invention is to provide a tracer head applicable to a copying machine tool or the like which is highly unmanned and can be automated.

[Solution]

That is, according to the present invention, a stylus that contacts and scans a surface to be detected such as an object to be measured or a mother die, and an elastic holding mechanism that has a centripetal effect to freely support the stylus in three orthogonal directions.
In a method for correcting an error included in a detected displacement output from a tracer head, which comprises a displacement detector for converting a given displacement given to the stylus into a detected displacement in a signal form and transmitting the detected displacement, for each length of the stylus, The relationship between the true displacement given to the stylus and the detected displacement including the error at that time is obtained in advance and stored in the reading means as a correction function, and the momentary detected displacement detected by the stylus in practical use is detected by the stylus in practical use. A method for correcting an error in the detected displacement of a tracer head, which is calculated by substituting the detected displacement term of the correction function according to the length and automatically calculating the correct displacement of the stylus, which is stored in the reading means. The correction function is as follows. The corrected displacement amount is y, the displacement amount detected by the stylus in practical use is x, and the positive coefficients determined by the length of the stylus are a and b. Then, when x ≧ 0, when y = ax ² + bx x <0, it is approximated by a quadratic function of y = −ax ² + bx, and the coefficients a and b of the function are L, the length of the stylus, If U ₁ , V ₁ , W ₁ , U ₂ , V ₂ , W ₂ are constants, a = U ₁ L ² + V ₁ L + W ₁ b = U ₂ L ² + V ₂ L + W ₂ The constants U ₁ , V ₁ , W ₁ , U ₂ , V ₂ ,
W ₂ is previously input as an experimentally obtained parameter for each tracer head, and provides a method for correcting an error in the detected displacement of the tracer head configured to be used in the calculation, thereby achieving the above-mentioned object of the invention. . Hereinafter, a more detailed description will be given based on an embodiment shown in the accompanying drawings of the present invention.

〔Example〕

FIG. 1 is a block diagram showing the configuration of the entire system showing an example in which the method is used in a digitizing device in order to explain an application example of an error correction method for a detected displacement of a tracer head according to the present invention. Further, FIG. 2 is a block diagram showing in detail the configuration of the error correction function unit provided in the copy calculation processing unit in FIG. 1, and FIG. 3 is a displacement error correction process of the displacement detector accompanying the replacement of the stylus of the tracer head. It is a flow chart which collectively explains the process and the detected displacement sending process of the displacement detector according to the measured displacement every moment.

In FIG. 1, the digitizing device 10 has a table 16 mounted on an upper part of a knee 14 which can move up and down (Z-axis operation) on a base 12, and a mother die 18 of a processed product is attached to the table 16, while a back part of the base 12 is mounted. A tracer head 24 is supported by a machine head 22 on a column 20 standing upright and is movably provided in two axial directions (X axis and Y axis) orthogonal to the vertical direction. The tracer head 24 is equipped with a stylus (also called a tracer) 26 having a generally spherical or hemispherical tip shape for contact-measuring the surface shape of the mother die 18 at the tip, and the body of the tracer head 24 is detachably attached. The structure is attached to. In addition, an elastic support mechanism for supporting the stylus 26 mounted inside the main body of the tracer head 24 and a displacement detector are built-in and provided, and the stylus 26 transmitted through the elastic support mechanism.
The displacement given at the time of measurement (this is referred to as a given displacement) is output by the displacement detector 25 as a detected displacement having an electrical signal form. Displacement detector 25 is X,
Three pieces are provided as shown in the drawing so that the displacements in the three Y-axis directions can be detected. A specific example of the elastic support mechanism is preferably one having the structure disclosed in Japanese Patent Publication No. 54-43230, and the displacement detector 25 can effectively use a well-known differential transformer type detector. . Tracer head 24
The detected displacement of the
It is electrically amplified by 28 and then sent to the outside. The elastic support mechanism of the stylus disclosed in Japanese Patent Publication No. 54-43230 has a tracer head as shown in FIG. 4 of the publication and as symbolically depicted in FIG. 1 of the present application. Housing, a tracer shaft having a stylus at the tip, a cylindrical hollow member that encloses the tracer shaft in the housing, and a pair of diaphragms that are provided above and below the hollow member and through which the tracer shaft is supported in the center. And an elastic cylinder that is provided so as to surround the outside of the hollow member, supports the central part of the axis of the hollow member, and has both upper and lower ends supported by the housing of the tracer head, the sum of the spring constants of the pair of diaphragms. And the spring constant of the elastic cylinder are set equal to each other, and the tracer shaft is freely supported in three orthogonal directions. Therefore, when an external force is applied to the stylus, the tracer shaft moves substantially in parallel, and when the external force is removed, the tracer shaft is again subjected to the centripetal action of returning to the axial center of the tracer head, that is, the free support position.

Further, the digitizing device 10 includes a Z-axis motor 30z for driving the vertical movement of a knee 14 having a table 16 and a machine head 2
It is provided with X-axis and Y-axis motors 30x and 30y for driving lateral movement of two orthogonal two-axis directions. Each of these drive motors 30x, etc. is usually composed of a servo motor, and the tracer head 24
Is configured to control and drive the following copying operation.

On the other hand, the digitizing device 10 is provided with a digitizing control device 40. The digitizing control device 40 is an analog interface for receiving a detected displacement signal from the signal amplification amplifier 28 of the tracer head 24.
42, an A / D converter 44 that converts an analog signal from the analog interface 42 into a digital signal, a scanning control unit 46 that performs error correction of detected displacement and scanning calculation processing,
It comprises a D / A converter 48 for converting the digital output signal of the copying control unit 46 into an analog signal again, a servo amplifier 50, a digital data creation unit 52, and the like.

Here, the scanning control unit 46 is provided to perform the error correction of the detected displacement and the scanning calculation process as described above,
In particular, the error correction processing of the detected displacement according to the present invention is performed by using a storage unit including a microprocessor unit CPU and ordinary ROM and RAM included in the copying control unit 46 as shown in FIG. The reading means 54 and the hardware means are used, and these are executed by being activated by software. The detected displacement signal sent from the copying control unit 46 is sent to the digitizing device 10 via the D / A converter 48 and the servo amplifier 50.
Feedback control is input to each of the drive motors 30x, 30y, 30z on the main body side, and the control is performed by driving these to drive the tracer head 24 to follow the surface shape of the mother die 18. On the other hand, the detected displacement signal sent from the copying control unit 46 is also converted into a position signal on the surface of the master block 18 and sent to the digital data creating section 52, where a processed product having the same or similar shape as the master block 18 is processed. Creation of digital data for NC machining is performed by a numerically controlled machine tool.

In the digitizing device 10 and the digitizing control device 40 having the above-mentioned configuration, the tracer head 24 converts the measured displacement obtained by the stylus 26 contacting and measuring the mother die 18 into the detected displacement by the built-in displacement detector 25, and sends the displacement. However, the error correction method performed here will be described below.

First, the tracer head 24 is usually adjusted by mounting a standard stylus whose length and weight are selected and known amounts, so that the output value from the displacement detector of each axis becomes zero in a free state without stylus displacement, so-called. Well-known automatic zero point adjustment is performed, and well-known gain automatic adjustment is performed so that the relationship between the given displacement and the displacement detected by the displacement detector when a known displacement is given to the stylus becomes a straight line with a constant slope. Be seen. Both of these automatic adjustments are not performed repeatedly,
This is a processing operation performed in a specific case such as when the tracer head 24 is used in the field. When this adjustment processing operation is performed, the detected displacement output from the displacement detector 25 of the tracer head 24 has a linear relationship with the given displacement of the stylus 26 that passes through the origin of the orthogonal coordinate system. Furthermore, if the reference displacement amount that gives a constant displacement to the stylus at the start of scanning is set in advance, the tracer head 24 normally completes the operation start preparation. However, in a specific case where the elastic coefficient of the built-in elastic support mechanism of the tracer head 24 is changed to increase the stylus movable stroke, in a region where the stylus stroke is large, the above-mentioned given displacement-detection displacement straight line is When the above-mentioned non-linearity-causing error condition is displayed and the physical conditions such as the length and weight of the stylus 26 used are different from those of the standard stylus used for the above gain adjustment, the above-mentioned displacement measurement is detected. The straight line of displacement exhibits a linear characteristic with different slopes, and has a deviation from the linear equation of the standard stylus. When the stylus weight is different, the zero point in the displacement free state moves to the position offset from the coordinate origin.

Therefore, in the present invention, a process for correcting these errors is executed to remove the error component in the detected displacement output from the displacement detector 25.

Here, referring to FIG. 3 together with FIG. 1 and FIG. 2, when the stylus 26 is replaced with another type of stylus from the standard stylus or in response to a change in the condition of the copying operation, the stylus 26 after replacement is The physical condition consisting of length data and weight data is read into the CPU. In the case of an unmanned copying machine tool equipped with a well-known automatic stylus changing device, the physical condition data of the stylus 26 is supplied as data corresponding to the stylus number from the automatic stylus changing device. In the digitizing device 10 and the three-dimensional measuring device of the present example which are not equipped with the exchange device, a person inputs and sets the data in advance (step 1). Then, when the reading of the stylus data is completed, next according to the present invention,
Non-linearity correction and deviation correction accompanying changes in stylus length are performed. Here, in the most typical embodiment of the present invention, the non-linearity due to the increase of the stylus movable stroke and the linear gradient change due to the change of the stylus length are applied to the displacement detector 25 in each axial direction in advance. For correction, it has been experimentally confirmed that the corrected displacement amount is uniquely determined from the following two equations (FIG. 7).

y = ax ² + bx (x ≧ 0) ··· (1) y = −ax ² + bx (x <0) ··· (2) where y: displacement after correction (true displacement) x : Detected displacement amount (displacement amount including error) generated in the displacement detector, a, b: Coefficient determined by stylus length. The above two formulas are the actual displacements given by the stylus of various lengths. And an amount of detection by the displacement detector 24, and an approximate expression in which the coefficients a and b are determined by the least squares method.
It is an equation that confirms that the coefficient curve of the actual detected displacement is faithfully expressed, and is preset and registered in a predetermined storage means in the copying control unit 46.

The above formulas (1) and (2) will be described a little more. The coordinates shown in FIG. 7 are obtained by plotting the detected displacement, which is the vertical axis of FIG. 4 showing the characteristics of the conventional tracer head, on the horizontal axis and the oblique straight line showing the true relationship on the vertical axis. That is, in FIG. 4, when the detected displacement and the true displacement for various given displacements are plotted on the coordinates of FIG. 7 and connected by a free curve, the free curve is expressed by the above approximate expressions (1) and (2). is there. Both equations (1) and (2) are correction functions for correcting non-linearity in a region where the stylus stroke is large. However, when this correction function is obtained for styli of various lengths,
It was found that the coefficients a and b were not uniquely determined and had a correlation with the stylus length. That is, if the relationship between the corrected displacement corresponding to each stylus length shown in FIG. 5 and the actual detected displacement is plotted in a graph, the slope of a quadratic curve passing through the origin as illustrated in FIG. Different (coefficients a, b
Of different stylus lengths (only one of which is shown in FIG. 7). Then, by plotting the values of a and b actually measured for styli of various lengths on a graph in which the vertical axis represents the values of a and b and the horizontal axis represents the stylus length L, it is possible to approximate a quadratic curve that does not pass through the origin. all right. The approximation formulas are the following formulas (3) and (4).

a = U ₁ L ² + V ₁ L + W ₁ ... (3) b = U ₂ L ² + V ₂ L + W ₂ ... (4) In these formulas (3) and (4), U ₁ , V ₁ , W ₁ , and
U ₂ , V ₂ and W ₂ are constants, and are experimentally and unambiguously obtained as a result of applying the actual a and b for various stylus lengths to the equations (3) and (4).

The method of obtaining the constant is to obtain three types of lengths in equation (3).
Value of a obtained experimentally for the stylus of L ₁ , L ₂ and L _3.
A system of three-dimensional equations can be obtained from a ₁ , a ₂ , and a ₃ (a ₁ , a ₂ ,
a ₃ , L ₁ , L ₂ , L ₃ are known quantities, U ₁ , V ₁ , W ₁ are unknowns).

a ₁ ＝ U ₁ L ₁₂ ＋ V ₁ L ₁ ＋ W ₁ a ₂ ＝ U ₁ L ₂₂ ＋ V ₁ L ₂ ＋ W ₁ a ₃ ＝ U ₁ L ₃₂ ＋ V ₁ L ₃ ＋ W ₁ By solving this simultaneous equation, the constant U ₁ , V ₁ and W ₁ are required.

Further, in the equation (4), the following three-dimensional simultaneous equations can be obtained from the values b ₁ , b ₂ and b _{3 of} b experimentally obtained for three types of stylus of length L ₁ , L ₂ and L _3. (B ₁ , b ₂ , b ₃ , L ₁ , L ₂ ,
L ₃ is a known amount, U ₂ , V ₂ and W ₂ are unknowns).

b ₁ = U ₂ L ₁₂ ＋ V ₂ L ₁ ＋ W ₂ b ₂ ＝ U ₂ L ₂₂ ＋ V ₂ L ₂ ＋ W ₂ b ₃ ＝ U ₂ L ₃₂ ＋ V ₂ L ₃ ＋ W ₂ By solving this simultaneous equation, the constant U ₂ , V ₂ , W ₂ are required.

In this way, the non-linearity can be corrected in the region where the stylus stroke is large by the formulas (1), (2), (3) and (4).

Then, U ₁ , V ₁ , W ₁ and U ₂ , V ₂ , W obtained as a result of applying the actual coefficients a and b for the predetermined stylus length L to the above equations (3) and (4) _When the six values of ₂ are set and registered as system parameters in the RAM of the storage means of the scanning control unit 46 and the length L is designated at the time of exchanging the stylus, the CPU makes the expressions (3) and (4) above. Is calculated (step 2), and the corresponding coefficient values of a and b are determined. (Step 3). If the coefficients a and b are determined, the coefficient values are calculated by the correction condition reading means.
Registered within 54. Since the offset value of the zero point must be changed according to the weight of the stylus 26, the value of the displacement detector when the zero point adjustment signal is issued is read and set and registered in the correction condition reading means 54. (Step 4). Thus, during the practical use of the stylus 26 in which the length L and the weight are designated, the actual detected displacement amount of the displacement detector 24 corrected by the above equations (1) and (2) is the value of each axis (X,
It is obtained for the Y and Z axes) (step 5), and offset correction is also performed. In this way, the detected displacement is sent out for each axis (step 6). The steps (5) and (6) are repeatedly performed for each measured displacement. Therefore, the scanning control unit 46 performs various predetermined scanning calculation processes such as calculating a combined displacement from the detected displacement of the tracer head 24 sent via the correction condition reading means 54 for each axis. The D / A converter 48 shown in FIG. The detected displacement thus copied is
As described above, the tracer head 24 is used for copying control and for creating NC machining data by digitizing.

Although the above description has been given with reference to the example of the digitizing device 10, the error correcting method according to the present invention is similarly applied to a tracer head in a copying machine tool having an automatic stylus changing device or a three-dimensional dimension measuring device. Needless to say, is applicable.

In the case of the digitizing device 10, as described above, the correction of the detection error of the tracer head, in particular, the correction of the non-linearity when the stylus stroke is increased is performed. Even when the stylus 26 of FIG. 2 causes an overshoot (corresponding to a large stroke variation) due to a rapid shape change of the mother die 18, the overshoot amount is accurately copied as a detected displacement amount sent by the displacement detector 24. Arithmetic processing unit
Therefore, the stylus 26 can accurately obtain the data imitating the master block 18 by subtracting the overshoot amount in the process of creating the NC machining data by the digital data creating unit 52. Based on this, NC processing data can be created, and digitizing can be made even more precise.

〔The invention's effect〕

The present invention has been described above based on the embodiments, but from these explanations, according to the present invention, the stylus as the contact probe provided at the tip of the tracer head is replaced,
Even when the conditions such as length and weight are changed, or when the physical conditions such as increasing the stylus stroke are changed, the displacement detector, which mainly consists of the differential transformer type displacement detector, causes an error. Automatically compensated, the stylus outputs the detected displacement that has a true relationship to the measured displacement caused by contact scanning of the surface of the master block or the object to be measured. Guaranteed
As a result, the accuracy of the copying machine tool is improved and the accuracy of the NC machining data created by the digitizing device is guaranteed, and the machining accuracy of the numerically controlled machine tool can be improved. Also, in copying machine tools equipped with an automatic stylus changing device,
Even if the stylus length fluctuates, the detection displacement accuracy of the tracer head is maintained at a high level, so that it is possible to significantly improve the performance of the copying machine tool by unmanning and further improve the practicability. At the same time, by releasing the trouble of unifying the length and weight of the stylus, it is possible to obtain the effect of reducing the cost of the copying machine tool with the automatic stylus changing device of this kind. Furthermore, since the detection error in the area where the stylus stroke is large can be corrected, high detection accuracy can be obtained even in the situation where the tracer head must be used in the area where the stylus stroke is large by correcting the stylus weight (offset correction). To be

[Brief description of drawings]

FIG. 1 is a block diagram showing the configuration of the entire system showing an example in which the method is used in a digitizing device in order to explain an application example of an error correction method for a detected displacement of a tracer head according to the present invention. FIG. 1 is a block diagram showing in detail the configuration of an error correction function unit provided in the scanning calculation processing unit in FIG. 1, and FIG. 3 is a displacement error correction processing process of the displacement detector accompanying the stylus replacement of the tracer head and the moment. Flowchart for collectively explaining the detected displacement sending process of the displacement detector according to the stylus displacement, FIG. 4, FIG.
6 and 6 are graphs showing the characteristics of the conventional tracer head, and FIG. 7 is a graph showing the relationship between the corrected displacement and the actual detected displacement according to the present invention. 10 …… Digitizing device 24 …… Tracer head 25 …… Displacement detector 26 …… Stylus 40 …… Digitizing control device 46 …… Copying control unit 54 …… Correction condition reading means

Claims (1)

[Claims] 1. A stylus for contacting and scanning a surface to be detected such as an object to be measured or a mother die, an elastic holding mechanism for centripetally supporting the stylus in three orthogonal directions, and providing the stylus with the stylus. A method for correcting an error contained in a detected displacement output from a tracer head, which comprises a displacement detector for converting and transmitting the given displacement to a detected displacement in a signal form, wherein a true value given to the stylus for various lengths of the stylus is provided. The relationship between the given displacement and the detected displacement including the error at that time is obtained in advance and stored in the reading means as a correction function, and the momentary detected displacement detected by the stylus in practical use is determined according to the stylus length in practical use. A method for correcting an error in the detected displacement of a tracer head, which is calculated by substituting it into the detected displacement term of the correction function to automatically obtain the correct displacement amount of the stylus, The correction function stored in the reading means is such that when the corrected displacement amount is y, the displacement amount detected by the stylus in practical use is x, and the positive coefficients determined by the length of the stylus are a and b, when x ≧ 0 , Y = ax ² + bx x <0, it is approximated by a quadratic function of y = −ax ² + bx, and the coefficients a and b of the function are L, the length of the stylus, U ₁ ,
When V ₁ , W ₁ , U ₂ , V ₂ , and W ₂ are constants, a = U ₁ L ² + V ₁ L + W ₁ b = U ₂ L ² + V ₂ L + W ₂ is approximated by the following function, and the constant U ₁ , V ₁ , W ₁ , U ₂ , V ₂ , W ₂
Is a method for correcting an error in the detected displacement of the tracer head, which is configured such that it is inputted as parameters experimentally obtained for each tracer head in advance and is used in the calculation.