JP2021049591A - On-machine measuring method in machine tool - Google Patents

Abstract

To provide an on-machine measuring method in a machine tool that enables enhancing accuracy of on-machine measurement.SOLUTION: An on-machine measuring method in a machine tool comprises: performing measurement once assuming a case of, in a machine tool, measuring a difference between a predetermined reference coordinate of the machine tool and an arbitrary coordinate to be measured on any one of X-axis, Y-axis, and Z-axis; then, performing the measurement again offsetting slightly by δ with respect to each of the directions desired to be measured; comparing a difference between a group of measurement points measured at a first time and a group of measurement points measured at a second time for each measurement point so as to determine whether any measured value that deviates from sets of other measurement points exists; and performing calibration on the spot assuming that non-linearity exists at a position with the deviating measured value.SELECTED DRAWING: Figure 7

Description

The present invention relates to high accuracy of on-machine measurement in a machine tool.

Conventionally, a machine tool (grinding machine) as shown in FIG. 1 described later has been put into practical use. That is, it has a linear X-axis, a Y-axis, and a Z-axis, and has a redundant W-axis parallel to the Z-axis. The distance of the straight U-axis to the XY plane can be adjusted by the straight Z axis, and the direction maintained parallel to the XY plane and perpendicular to the Z axis can be set by the swivel C axis.
Although not shown for any of the X, Y, Z, W, C, and U axes, it has a position detection mechanism such as a pulse coder with a built-in motor or a separate linear scale or rotary encoder, or a pulse motor. It has a position control mechanism, and the position of the grindstone as a tool can be changed according to the command of the controller.
In this type of machine tool, a probing device is connected to the controller (see, for example, Patent Document 1). The moment the probing device detects a contact, a signal is sent to the controller, and the controller that receives the signal has a function of immediately stopping the feed (hereinafter, such a function is referred to as a skip function). When stopped by this skip function, the stop position can be acquired, and the shape can be evaluated from this stop position. Measurements are made at a plurality of points and the dimensions are evaluated from the differences (see, for example, Patent Document 2).
On the other hand, there are many types of position detection mechanisms such as linear scales and rotary encoders mentioned above, but the position control mechanism is open-loop, which uses only the rotation angle of the lead screw (lead screw) for detection and control. There are loop and semi-closed loop control and full closed loop control that detects and controls the position.

Japanese Unexamined Patent Publication No. 2007-007822 Japanese Unexamined Patent Publication No. 2003-31153

Research on in-situ autonomous calibration method for geometric quantity sensors (Kiyono et al., Journal of Precision Engineering, Vol. 63, No. 10, 1997, pp. 1417-21)

Depending on the quality of the lead screw and the linear scale and the condition of assembly, the relationship between the input position command and the output displacement is often non-linear as shown in FIG. Especially for lead screws, periodic deviations tend to remain. Also, looking closely at the linear scale, there are many cases where slits, engraved lines, etc. are combined to generate a periodic signal level change according to the displacement, and interpolation is performed to ensure resolution, and the periodic deviation is It cannot be completely avoided.
These non-linearities are often used after being calibrated using a calibrator that utilizes light interference or a reference scale.
In this case, there are two well-known correction methods. There are two types, one is a correction that treats the non-linearity as a correction pulse generation at the set correction position as shown in FIG. 5, and the other is a type that corrects the non-linearity with a straight line as shown in FIG. However, in the case of the correction as shown in FIG. 5, the locality (measurement in a short period) has a large non-linearity as compared with the case where the original correction is not inserted. Although such a situation is unlikely to occur with the correction as shown in FIG. 6, even if the full closed loop control is used, the position of the tool tip is not completely controlled and the influence of the non-linearity due to the attitude change is unavoidable.
The reason for this is a slight change in posture due to the feed screw and the support mechanism (such as the distance between the balls of the bearing).
By the way, the average sensitivity in the measurement of a relatively long period can be secured to be substantially constant by the measurement of a reference block such as a block gauge, but the non-linearity may remain. In particular, when it is the result of correction pulse generation, a deviation occurs in a plurality of measurement results across the correction positions. Conventionally, even if multiple measurements are performed, the difference does not change within the range of stability. However, a large deviation seed called a large local non-linearity will be incorporated.

An object of the present invention is to provide a technique capable of improving the accuracy of on-machine measurement in a machine tool.

As a result of diligent research on a method that enables high-precision on-machine measurement in a machine tool, the present inventor has made a case where, for example, the height of a work is measured using the Z-axis as the method. Assuming that the measurement is performed once, the W axis is slightly offset by δW, the measurement is performed again, and the difference between the obtained sets is calibrated on the spot using the method shown in Non-Patent Document 1. First, it can be assumed whether or not the non-linearity is likely to be within the permissible range, and it is also possible to correct the non-linearity within the range of repeatability. Also, this method is widely used in machine tools on the X-axis. , Y-axis, and Z-axis are used to measure the difference between a predetermined reference coordinate of the machine tool and an arbitrary coordinate to be measured on the axis.

That is, according to the aspect of the present invention, in the machine tool, any of the X-axis, the Y-axis, and the Z-axis is used, and the coordinates that serve as a predetermined reference and the measurement target of the machine tool on the axis are arbitrary. Assuming the case of measuring the difference between the coordinates of, once the measurement is performed, the measurement is performed again with a slight offset of δ with respect to each of the desired directions, and the group of measurement points measured the first time and 2 The difference between the groups of measurement points measured the second time is compared for each measurement point to determine whether or not there is a measurement value that deviates from the other measurement point sets, and at the location of the deviated measurement value. Given the non-linearity, an on-board measurement method characterized by in-situ calibration can be obtained. This makes it possible to first assume whether or not the non-linearity is likely to be within the permissible range. In addition, it is possible to correct the non-linearity within the range of repeatability.

According to the present invention, it is possible to provide a technique capable of improving the accuracy of on-machine measurement in a machine tool.

It is a figure which shows the basic structure of the machine tool (grinding machine) which concerns on embodiment of this invention. It is an enlarged view around the U-axis feed device and the grindstone shaft in the machine tool (grinding machine) shown in FIG. It is a block diagram which shows the outline of the control system of the machine tool (grinding machine) shown in FIG. It is a graph which shows the relationship between an input and an output, and shows the case where the non-linearity of an output is applied with respect to an input. It is a graph which shows the relationship between an input and an output, and shows the 1st case where the non-linearity of an output remains with respect to an input. It is a graph showing the relationship between an input and an output, and shows the second case in which the non-linearity of the output remains with respect to the input. This is an example of touch measurement in a direction parallel to the Z axis in the grinding machine according to the embodiment of the present invention. In the on-board measurement method according to the embodiment of the present invention, it is a figure which shows an example in which a block is measured twice in advance in order to prepare the formula or table for correction of non-linearity, and FIG. When measuring the height position of the block at predetermined intervals for the first time, in (b), after the first measurement, the height is offset by δW and the height of the block is measured at predetermined intervals for the second time. The case of measuring the position is shown. This is an example of touch measurement in a direction parallel to the X-axis in the grinding machine according to the embodiment of the present invention. FIG. 5 is a diagram showing a second example in which a block is measured twice in advance in order to prepare an equation or table for correcting nonconformity in the on-board measurement method according to the embodiment of the present invention. ) Is the first measurement of the height position of the block at predetermined intervals, and (b) is the second measurement of the block at predetermined intervals by offsetting the height by δU after the first measurement. The case of measuring the height position of is shown. This is an example of touch measurement in a direction parallel to the Y axis in the grinding machine according to the embodiment of the present invention. FIG. 5 is a diagram showing a third example in which a block is measured twice in advance in order to prepare an equation or table for correcting nonconformity in the on-board measurement method according to the embodiment of the present invention. ) Is the first measurement of the height position of the block at predetermined intervals, and (b) is the height of δU only in the state where the C axis is parallel to the Y axis after the first measurement. The case where the height position of the block is measured at predetermined intervals is shown for the second time after offsetting. This is an example of touch measurement in a direction not parallel to the X-axis and the Y-axis in the grinding machine according to the embodiment of the present invention. The case where the touch measurement example shown in FIG. 11 is calibrated in the direction to be evaluated is shown. (A) shows an example of one stage of the rotating shaft, and (b) shows an example of two stages of the rotating shaft. It is an example of a work with a plurality of circular holes, and is the first half figure for demonstrating an example of a calibration method. It is an example of a work with a plurality of circular holes, and is the latter half figure for demonstrating an example of a calibration method.

An embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a perspective view showing an example of a grinding machine to which the present invention is applied, and FIG. 2 is an enlarged view of the U-axis feed device and the periphery of the grindstone shaft. In the grinding machine 10 to which the present invention is applied, as shown in FIG. 1, a table feeding device 36 and a table 30 are supported on a bed 12 so as to be movable in the Y-axis direction (front-rear direction) via a rail 16. .. Although the column 14 is fixed to the bed 12, as described above, a relative motion can be applied to and from the feeding device 36 in the direction along the rail 16. A motor for moving the feed device 36 (not shown) is arranged at the rear of the bed 12, and the table feed device 36 is moved back and forth along the rail 16 via a ball screw (not shown) or the like. A head 18 is supported on the column 14 so as to be movable (elevable) in the W-axis direction, a grindstone shaft 20 is provided at the tip of the head 18, and a grindstone 100 (FIG. 2) is provided at the tip of the grindstone shaft 20. See) is installed. A head elevating motor (not shown) is arranged on the upper part of the column 14, and the head 18 is elevated by this motor via a ball screw (not shown) or the like. A grindstone shaft (for rotation) motor 24 (see FIG. 2) is arranged at the rear portion of the head 18, and the grindstone shaft 20 is rotated by this motor. The head elevating motor is provided with an encoder that constitutes a measuring means (not shown). The linear shaft and the rotating shaft other than the grindstone shaft are equipped with an encoder and a motor so that the feed amount or the rotation amount can be calculated and controlled even if they are not shown. From the data output from this encoder, the amount of lifting and lowering of the head 18 and the amount of cut into a workpiece (not shown) are calculated. The Z-axis is provided parallel to the W-axis direction, and the Z-axis motion can be given without hindering the movement of the head of the W-axis, the rotation of the C-axis, and the linear motion of the U-axis.

As described above, the X-axis feed device 36 is mounted on the bed 12 via the rail 16. The X-axis feed device 36 is configured to be able to linearly move back and forth in the Y direction along the direction of the rail 16. A table 30 is further supported on the X-axis feed device 36 via a rail (not shown). The table 30 is configured to be able to linearly move in the left-right direction with respect to the X-axis feed device 36. A work (not shown) is detachably installed and fixed on the upper surface. As a matter of course, a motor for moving the X-axis feed device 36 is provided on the bed 12, and the X-axis feed device 36 is moved along the rail 16 via a ball screw or the like (not shown) by this motor. There is. Similarly, the table 30 moves on the X-axis feed device 36 via a motor, a ball screw, or the like (not shown). Then, in a state where the grindstone shaft 20 is rotated by the grindstone shaft rotation motor 24, the head 18 (grindstone shaft 20) is lowered by the head elevating motor, and the grindstone 100 attached to the tip of the grindstone shaft 20 is moved. It is brought into contact with the surface of the work on the table 30. The table 30 can be freely moved in the XY directions by the above-mentioned two motors. As a result, the surface of the work is ground by the grindstone 100. The grinding machine 10 is provided with an AE (acoustic emission) sensor (not shown) as a contact detection means between the grindstone 100 and the work on the work side. Then, when the AE sensor detects the contact between the work and the grindstone 100, the feed of the grindstone 100 can be stopped by the skip signal.

As described above, the machine tool (grinding machine) 10 shown in FIG. 1 is a CNC-controlled machine tool (grinding machine) capable of simultaneously controlling at least three axes of XYZ, and further, a grindstone shaft. It has a drive shaft (rotary shaft or linear drive shaft) whose axial direction is parallel to the rotation shaft of 20. That is, the machine tool (grinding machine) 10 has a U-axis feed device 40 at the lower part of the head 18, and the U-axis feed device 40 includes a grindstone shaft 20 and a disk body 27 above the grindstone shaft 20. It is a mechanism, and is a device that linearly moves the grindstone shaft 20 and the disk body 27 above the grindstone shaft 20 within a predetermined stroke range according to the angular position of the C axis at that time, and the linear movement direction is the U axis (direction). Is defined as. That is, in the machine tool (grinding machine) 10 shown in FIG. 1, the head 18 can be linearly moved (moved up and down) in the Z-axis direction. To distinguish it from the Z-axis, it is called a W-axis feed device. Further, the U-axis feed device 40 can be swiveled with respect to the head 18 in a Z-axis linear movement and a Z-axis rotation (referred to as a C-axis). The U-axis feed device 40 can linearly move the grindstone shaft 20 in the U-axis direction. More specifically, the drive axis control of the machine tool (grinding machine) 10 is described more specifically with reference to FIGS. 2 and 3. In the machine tool (grinding machine) 10, the linear feed mechanism of the U axis is on the rotation side of the C axis. It is listed in. The U-axis feed device 40 can be linearly moved along the direction of the U-axis by the feed command of the grindstone shaft (U-axis). The center of the grindstone shaft is rotated by the rotation command of the C shaft. Further, this C-axis device can be linearly moved in the vertical direction by the Z-axis device.

FIG. 3 is a block diagram showing an outline of the control system of the jig grinding machine shown in FIG. The jig grinding machine according to the present invention has a control device 300, an input / output device 310, each axis motor 320, each motor driver 330, a grindstone rotation motor 102A, and a grindstone motor inverter 102inv as control systems. The control device 300 includes a computer numerical control unit (CNC) 302, a programmable controller 304, and an I / O (input / output) module 306. The control system of the jig grinding machine according to the present invention also includes a keyboard, various switches, a temperature sensor and the like, a tools setter related to a skip signal, an AE sensor and the like as an input / output device 310.

Next, the on-board measurement method, which is a main part of the present invention, will be described with reference to FIGS. 7 to 17 in addition to FIGS. 1 to 3. FIG. 7 is an example of touch measurement in the direction parallel to the Z axis in the grinding machine according to the embodiment of the present invention. Here, in the machine tool shown in FIG. 1, for example, as shown in FIGS. 7 (a) and 7 (b), it is assumed that the height of the work is measured using the Z axis. First, as shown in FIG. 7 (a), the measurement is performed once, and then, as shown in FIG. 7 (b), the W axis is slightly offset by δW and the measurement is performed again. If the difference between the obtained pairs of results is calibrated in-situ using the method shown in Non-Patent Document 1 described at the beginning of the present specification, it is first determined whether or not the non-linearity is likely to be within an acceptable range. I can imagine. In addition, it is possible to correct the non-linearity within the range of repeatability. Such measurement is not limited to one point and two points, for example, as shown in FIGS. 7 (a) and 7 (b), such as measurement at three points 1, 2, and 3, and evaluation item 1 There should be a plurality of evaluation items such as the height of the work at the point 1 and the height of the work at the point 3 as the evaluation item 2. Considering the difference between the obtained set of results (before and after the offset), the coordinates of Z stopped by probing should be deviated by δW. Given the non-linearity of the W-axis, there is uncertainty on certain linearity orders. The probability of δW itself is estimated by the average. Therefore, if the data probed in the section where the linearity of the Z axis is clearly poor is mixed, the coordinates deviate significantly from the average. However, it depends on the order of linearity of the feed axis after correction. As a result, it is possible to avoid mixing the data measured in the section with clearly poor linearity. Furthermore, it is possible to perform the first-order estimation in the above-mentioned non-patent document 1 paper from the set of the average of δW and the data before and after the offset obtained by the calculation, and it is possible to estimate the result that seems to be more correct.

On the other hand, in the machine tool shown in FIG. 1, when measuring a workpiece using the XY axes, the C axis is swiveled so that the U axis is parallel to the X axis and the Y axis, so that the work is aligned with the Z axis. It can be treated in the same way. When the X direction and the Y direction are mixed in the evaluation item, set it to 45 degrees with respect to the X axis.

FIG. 8 is a diagram showing an example in which the block is measured twice in advance in order to prepare an equation or table for correcting nonconformity in the on-board measurement method according to the embodiment of the present invention. In a), when the height position of the block is measured at predetermined intervals for the first time, in (b), the height is offset by δW after the first measurement, and the predetermined interval of the block is measured for the second time. The case of measuring the height position of each is shown. In the example shown in FIG. 7 described above, since the evaluation is performed at the measurement stage, it is necessary to perform the measurement twice. However, if the block as shown in FIG. 8 is measured twice in advance, the non-linearity can be obtained. It is possible to prepare a formula or table for correction in advance.

FIG. 9 is an example of touch measurement in the direction parallel to the X axis in the grinding machine according to the embodiment of the present invention. Here, in the machine tool shown in FIG. 1, for example, as shown in FIGS. 9A and 9B, the X-axis of the work is measured by measuring the difference from a certain reference coordinate using the X-axis. It is assumed that the dimensions are measured in the direction. First, as shown in FIG. 9A, as evaluation items 1, 2 and 3, after measuring the difference from a certain coordinate (reference coordinate) in the X-axis direction at points 1, 2 and 3, respectively, then , As shown in FIG. 9B, the measurement is performed again with the X-axis slightly offset by δU in a state where the U-axis is parallel to the X-axis while turning around the C-axis. If the difference between the obtained sets of results is calibrated in-situ using the method shown in Non-Patent Document 1 described at the beginning of the present specification, first of all, the non-linearity is obtained as described in FIG. It is possible to assume whether or not it is within the permissible range, and it is also possible to correct the non-linearity within the range of repeatability.

FIG. 10 is a diagram showing an example in which the block is measured twice in advance in order to prepare an equation or table for correcting non-linearity in the on-board measurement method shown in FIG. 9 (a). When the difference from the reference coordinates in the X-axis direction at predetermined intervals of the block is measured for the first time, (b) is obtained by offsetting the coordinates in the X-axis direction by δU after the first measurement. The case where the difference of the block is measured at a predetermined interval is shown at the second time. In the example shown in FIG. 9 described above, since the evaluation is performed at the measurement stage, it is necessary to perform the measurement twice. However, if the block as shown in FIG. 10 is measured twice in advance, the non-linearity can be obtained. It is possible to prepare a formula or table for correction in advance.

FIG. 11 is an example of touch measurement in the direction parallel to the Y axis in the grinding machine according to the embodiment of the present invention. Here, in the machine tool shown in FIG. 1, for example, as shown in FIGS. 11A and 11B, the Y-axis of the work is measured by measuring the difference from a certain reference coordinate using the Y-axis. It is assumed that the dimensions are measured in the direction. First, as shown in FIG. 11A, as evaluation items 1, 2 and 3, after measuring the difference from a certain coordinate (reference coordinate) in the Y-axis direction at points 1, 2 and 3, respectively, then As shown in FIG. 11B, the measurement is performed again with the Y-axis slightly offset by δU in a state where the U-axis is parallel to the Y-axis while turning around the C-axis. If the difference between the obtained sets of results is calibrated in-situ using the method shown in Non-Patent Document 1 described at the beginning of the present specification, first, as described in FIGS. 7 and 9, first It is possible to assume whether or not the non-linearity is likely to be within the permissible range, and it is also possible to correct the non-linearity within the range of repeatability.

FIG. 12 is a diagram showing an example in which the block is measured twice in advance in order to prepare an equation or table for correcting non-linearity in the on-board measurement method shown in FIG. 11 (a). When the difference from the reference coordinates in the Y-axis direction at predetermined intervals of the block is measured for the first time, (b) is obtained by offsetting the coordinates in the Y-axis direction by δU after the first measurement. The case where the difference of the block is measured at a predetermined interval is shown at the second time. In the example shown in FIG. 11 described above, since the evaluation is performed at the measurement stage, it is necessary to perform the measurement twice. However, if the block as shown in FIG. 11 is measured twice in advance, the non-linearity can be obtained. It is possible to prepare a formula or table for correction in advance.

FIG. 13 is an example of touch measurement in a direction not parallel to the X-axis and the Y-axis in the grinding machine according to the embodiment of the present invention. Here, in the machine tool shown in FIG. 1, for example, as shown in FIGS. 13 (a) and 13 (b), the difference from a certain reference coordinate is measured in a direction not parallel to the X-axis and the Y-axis. It is assumed that the dimensions of the work are measured in a direction not parallel to the X-axis and the Y-axis. First, as shown in FIG. 13A, as evaluation items 1, 2 and 3, the difference from a certain coordinate (reference coordinate) in a direction not parallel to the X-axis and Y-axis at points 1, 2 and 3, respectively, is once set. After the measurement, as shown in FIG. 13B, the U-axis direction is swiveled around the C-axis, offset slightly by δU, and the measurement is performed again. If the difference between the obtained sets of results is calibrated in-situ using the method shown in Non-Patent Document 1 described at the beginning of the present specification, it is the same as that described in FIGS. 7, 9 and 11. First, it is possible to assume whether or not the non-linearity is likely to be within the permissible range, and it is also possible to correct the non-linearity within the range of repeatability.

FIG. 14 is a diagram showing an example in which the block is measured twice in advance in order to prepare an equation or table for correcting non-linearity in the on-board measurement method shown in FIG. 13 (a). When the difference from the reference coordinates in the direction not parallel to the X-axis and the Y-axis at predetermined intervals of the block is measured for the first time, (b) is set to the X-axis and the Y-axis after the first measurement. The case where the coordinates in the non-parallel directions are offset by δU and the difference between the blocks at predetermined intervals is measured for the second time is shown. In the example shown in FIG. 13 described above, since the evaluation is performed at the measurement stage, two measurements are unavoidable. However, if the block as shown in FIG. 14 is measured twice in advance, the non-linearity can be obtained. It is possible to prepare a formula or table for correction in advance. That is, in the example shown in FIG. 14, it is possible to calibrate the touch measurement example shown in FIG. 13 in the direction to be evaluated.

However, the U-axis need only be offset in the specified direction, and does not have to be a linear axis. It may be composed of a combination of rotating shafts or rotating shafts, and as a result, an offset similar to that of the U-axis described above may be obtained. An example of this is shown in FIG. FIG. 15A shows an example of one stage of the rotating shaft. That is, as shown in FIG. 15A, in the example where the rotation axis is one step, the locus is offset by δU'(a locus on an arc with a minute rotation angle) by slightly rotating with a certain radius from the center of rotation. Therefore, it can be approximated as an almost linear movement). However, for example, a structure having a two-stage rotation axis on the mechanism is within the scope of the present invention as long as an offset can be obtained in the same manner. An example of this (an example of two stages of rotating shafts) is shown in FIG. 15 (b). As shown in FIG. 15B, in a device having such a structure, for example, the stylus can be rotated around the second turning center, and the second turning center can be rotated around the first turning center. That is, as shown in FIG. 15B, in the example where the rotation axis has two stages, it rotates (slightly) with a constant first radius from the first turning center and also rotates around the first turning center. An offset of δU'' can be obtained by rotating (slightly) with a constant second radius from the possible second turning center. In this case, the first and second turns may be NC-controlled, respectively, or the structure may be such that when one of them is moved by a structure such as a gear, the other direction is determined.

FIG. 16 is an example of a work having a plurality of circular holes, and is a first half view for explaining an example of a calibration method. First, it is assumed that a plurality of circular holes are formed in the work in the positional relationship as shown in FIG. 16A. Here, in a machine tool that processes the work, it is assumed that the relationship between the position command displacement of the X-axis is as shown in FIG. 16 (b). First, as shown in FIG. 16C, it is assumed that the holes at the lower left are installed so that X = 50 and Y = 50. As for the measurement coordinates, only those whose normal direction of touch is in the X direction are extracted. FIG. 16D shows the coordinates when the U0 and C axes are set so that the U axis is parallel to the X axis and measured. On the other hand, FIG. 16E shows the coordinates when the U0.002 and the C-axis are set so that the U-axis is parallel to the X-axis and measured.

FIG. 17 is an example of a work having a plurality of circular holes, and is a latter half view for explaining an example of a calibration method. That is, as shown on the left and right of FIG. 17 (f), the coordinates shown in FIG. 16 (d) and the coordinates shown in FIG. 16 are compared, and before the shift [see FIG. 16 (d)] and after the shift [FIG. 16 (e)] If the difference between the measurement pairs is taken, the side of the graph in FIG. 17 (g) is taken from the group group shown by connecting two intersecting curves on the left and right in FIG. 17 (f). As shown by enclosing it in an ellipse on the axis, a pair whose difference is different from the difference of other group groups was found (in this case, the value on the vertical axis is 0.000 (near 0), but it is not necessarily 0. This does not mean that points 7 and 8 have used the part of the machine tool where the X-axis linearity is extremely poor for measurement.

According to the present invention, in a machine tool, it is possible to improve the accuracy of the on-machine measurement. In the above-described embodiment, examples of measuring the dimensions of the work have been given, but the present invention is not limited to these, and the present invention is used when measuring the machine coordinates apart from the work within the range described in the claims. Is also applicable. Further, in the above-described embodiment, the U-axis is assumed to be linear, but the U-axis does not necessarily have to be linear.

このときSmは平均感度を表し、g(x)は非線形成分を表す。
いま、サンプリング点x_iを線形性の判断をしたい入力範囲になるべく均等に配置して、そのときの出力をv_iとすると第0次近似として、次式（２）を得る。

また、その点でΔxだけ離れた2点の出力の差分である下記の数式（３）

を用いて、非線形性分g(x)の導関数の第0次近似が、次式（４）で与えられる。ここで、繰り返し性の範囲内で入力のx_i同士の差は一定でオフセットだけ与えられるとする。このために冗長軸を使う。

これを数値積分すると、g(x)の第０次近似g₀(x)が得られる。
このg₀(x)を用いると、x_iが次式（５）のように修正される。

このx_1iを用いると、g’(x)、g(x)の近似精度が改善される。
一般に、j番目の近似値x_jiを用いて表したg’(x)およびそれを積分したg(x)の近似関数が次式（６）のように得られる。

これを用いて、j+1番目のxの近似が次式（７）により得られる。

繰り返し回数jを増すとxの近似が正確な値に収束するものと期待される。逆に収束しなければ、本方法が使えないほど、線形性が悪いか雑音などの影響で測定の繰り返し性が悪いことが疑われるので処理を打ち切る。非線形性の評価の説明は以上である。 According to the reference (Non-Patent Document 1), the evaluation of non-linearity is as follows.
The input / output relationship of the sensor is expressed as the following formula (1) with x as the input and v as the output.

At this time, Sm represents the average sensitivity, and g (x) represents the non-linear component.
Now, if the sampling points x _i are arranged as evenly as possible in the input range for which the linearity is to be judged and the output at that time is v _i , the following equation (2) is obtained as the 0th approximation.

In addition, the following formula (3), which is the difference between the outputs of two points separated by Δx at that point.

The 0th-order approximation of the derivative of the nonlinear component g (x) is given by Eq. (4). Here, it is assumed that _{the difference between the inputs x i} is constant and only the offset is given within the range of repeatability. A redundant axis is used for this.

Numerical integration of this gives a 0th-order approximation of g (x), _{g 0 (x).}
Using this g ₀ (x), x _i is modified as in the following equation (5).

Using this x _1i improves the approximation accuracy of g'(x) and g (x).
In general, an approximate function of g'(x) expressed using the j-th approximate value x _ji and g (x) obtained by integrating it is obtained as shown in the following equation (6).

Using this, an approximation of the j + 1th x can be obtained by the following equation (7).

It is expected that the approximation of x will converge to an accurate value as the number of iterations j is increased. On the contrary, if it does not converge, it is suspected that the linearity is so bad that this method cannot be used, or the repeatability of the measurement is poor due to the influence of noise, etc., so the process is discontinued. This concludes the explanation of the evaluation of non-linearity.

Here, depending on the measurement target of the work, _{when it is difficult to arrange the sampling points x i} as evenly as possible in the input range for which the linearity is to be judged, the inclination as shown in FIGS. 8, 10 and 12 It is conceivable to plan a shape that gives input and perform pre-evaluation.
In addition, basically, the work is measured, and the measurement is performed in the input range where the points of the shape that give the tilt input as shown in FIGS. 8, 10 and 12 are insufficient by limiting only the section where the points are sparse. It may be a hybrid.
The operation of increasing the number of iterations j as described above can be easily performed on a general computer, but it is troublesome to implement it in an NC program. In that case, it is appropriate to set j = 1, that is, to apply an abbreviated calculation that detects defects related to non-linearity by using the difference before and after the offset as it is.

10 grinding machine, 12 beds, 14 columns, 16 rails, 18 heads, 20 grindstone shafts, 24 grindstone shafts (for rotation) motors, 30 tables, 36 table feed devices, 100 grindstones

Claims (2)

The machine tool has an X-axis, a Y-axis, a Z-axis, and one or more redundant linear or swivel axes, and any of the above axes is used as a predetermined reference for the machine tool on the axis. In a machine tool that measures the difference between the coordinates to be measured and the arbitrary coordinates to be measured, after the measurement is performed once, the X-axis, the Y-axis, the Z-axis, and one or more axes are redundant with respect to the respective desired directions. The difference between the group of measurement points measured the first time and the group of measurement points measured the second time is measured by offsetting one or a combination of these linear axes or swirling axes by a slight δ and measuring again. Compare each point to determine if there is a measurement value that deviates from the set of other measurement points, and calibrate it on the spot, assuming that there is non-linearity at the location of the measurement value that deviates. An on-machine measurement method for a characteristic machine tool. According to the on-machine measurement method according to claim 1, it is assumed that the non-linearity is likely to be within the permissible range, and then the non-linearity is corrected within the repeatability range. Top measurement method.

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