CN112894490B - Method for realizing perpendicularity error detection of numerical control machine tool based on rotating L-shaped array - Google Patents

Abstract

The invention discloses a method for realizing the verticality error detection of a numerically controlled machine tool based on a rotating L-shaped array. First, the L-shaped reference element array is placed on a three-coordinate measuring machine, and the spindle of the three-coordinate measuring machine drives an optical angle sensor along the The L-shaped reference part array moves to calibrate the mutual positions of the reference parts in the L-shaped reference part array; then, the optical angle sensor is driven by the machine tool spindle to move along the L-shaped reference part array, and the L-shaped reference part array is used to rotate and rotate. The obtained attitude is used to obtain the coordinate position information of the measurement point. After fitting the straight line, the verticality error between the X-axis and the Y-axis of the machine tool is obtained by combining the angle relationship. Even if there is a declination error or a rotation angle error of the array of L-shaped reference parts, the verticality error of the machine tool can still be effectively obtained, and the machining accuracy of the machine tool can be improved.

Description

A method for detecting squareness error of CNC machine tool based on rotating L-shaped array

technical field

The invention relates to a method for identifying the squareness error of a numerically controlled machine tool, which mainly realizes the detection of the squareness error based on a rotating L-shaped reference piece array.

Background technique

The squareness error of CNC machine tools is a kind of geometric error item. On the one hand, there is an installation error in the machine tool itself, and on the other hand, the machine tool has a certain degree of wear and structural deformation under the working conditions of the year, which makes the movement axes of the CNC machine tool no longer have an orthogonal and vertical relationship. , a certain deviation angle is formed between the shaft and the shaft. The verticality error affects the machining accuracy of the machine tool, so in order to improve the machining accuracy of the machine tool, it is necessary to realize the detection of the verticality error of the machine tool.

In the field of machine tool squareness error detection, there are several commonly used detection methods. The square box or square ruler can be used as the measurement benchmark to detect the verticality error of the machine tool, but the measuring equipment is too cumbersome, inconvenient to operate, and the measurement accuracy is not high; the optical square and the laser interferometer can also detect the verticality error, but There are also shortcomings, which are easily affected by environmental factors, require high operation level of the measuring personnel, and the equipment cost is relatively expensive; The measurement efficiency is not high.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the machine tool squareness error detection method in the prior art, the present invention proposes a new machine tool squareness error detection method based on the rotating L-shaped reference element array.

In order to solve the above technical problems, the present invention proposes a method for detecting the verticality error of CNC machine tools based on a rotating L-shaped array. Drive the optical angle sensor to move along the L-shaped reference part array to calibrate the mutual positions of the reference parts in the L-shaped reference part array; then, drive the optical angle sensor to move along the L-shaped reference part array through the machine tool spindle, using the L-shaped reference part The coordinate position information of the measurement point is obtained by the attitude of the component array before and after the rotation, and the perpendicularity error between the X-axis and the Y-axis of the machine tool is obtained after fitting the straight line and combining the angle relationship.

Further, the method for detecting the verticality error of a numerically controlled machine tool of the present invention, wherein:

The L-shaped reference element array is composed of a plurality of reference elements arranged in an L-shaped array. In the L-shaped reference element array, the intervals of the reference elements are equal, and one of the reference elements is located at the intersection of the two directions of the L-shaped array; The top surface of the reference piece includes a plane P1 and a paraboloid P2, there is a point F on the paraboloid P2 of the reference piece, and the tangent plane of the paraboloid P2 passing through the F point is parallel to the plane P1, and the F point is recorded as a feature point; Four points are designated as measurement points A on the plane P1, and nine points are designated as measurement points M on the paraboloid P2.

The process of calibrating the mutual positions of the reference parts in the L-shaped reference part array is as follows: the L-shaped reference part array is placed on a three-coordinate measuring machine, and the main shaft of the three-coordinate measuring machine drives the optical angle sensor along the L-shaped reference part array. Move in the X and Y directions of the reference part, respectively collect the measurement point A and the measurement point M on the reference part, and obtain the coordinates of the reference part feature point F through the coordinate vector relationship between the measurement point A and the measurement point M, and establish the calibration in the X direction. The coordinate system X ₁ -Y ₁ and the calibration coordinate system X ₂ -Y ₂ in the Y direction, the angle between the calibration coordinate system in the X direction and the calibration coordinate system in the Y direction is

The steps to obtain the coordinate position information of the measurement point by using the attitude of the L-shaped reference element array before and after rotation are as follows:

1-1) Place the L-shaped reference part array on the machine tool, and the X direction of the L-shaped reference part array is consistent with the X-axis direction of the machine tool;

1-2) The spindle of the machine tool drives the optical angle sensor to move along the X and Y directions of the L-shaped reference element array, and collects the measurement point M on the reference element, and the measurement point M is imaged in the optical angle sensor. The coordinates of the feature point F in the image coordinate system are transformed to obtain the coordinate value of the measurement point M in the machine tool coordinate system X-Y, and the coordinate position information of the measurement point of the attitude of the L-shaped reference part array before rotation is obtained;

1-3) After the L-shaped reference part array is rotated 90° counterclockwise with the intersection of the X direction and the Y direction of the array as the rotation center, the X direction of the L-shaped reference part array is consistent with the Y-axis direction of the machine tool;

1-4) Repeat step 1-2) to obtain the coordinate position information of the measuring point of the attitude of the L-shaped reference piece array after rotation.

Linear fitting is performed on the coordinate position information of the measurement points of the L-shaped reference part array before and after rotation, and the perpendicularity error between the X-axis and the Y-axis of the machine tool is obtained by combining with the angle relationship; including:

2-1) Based on the least squares method, two fitted straight lines are obtained from the measurement point M before the rotation of the L-shaped reference element array;

Assuming that the perpendicularity error α _xy between the X axis and the Y axis of the machine tool is less than 0°, according to the right angle relationship, there are:

Squareness error between machine X and Y axes:

是X₁-Y₁坐标系与X₂-Y₂坐标系之间的夹角；In formula (1) and formula (2): θ ₁ is the angle between the fitted straight line l ₁ and the X ₁ -Y ₁ coordinate system X1 axis obtained by the straight line fitting of the measuring point M in the X direction of the machine tool; θ ₂ is the angle between the fitted straight line l ₂ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the Y2 axis of the X ₂ -Y ₂ coordinate system;

is the angle between the X ₁ -Y ₁ coordinate system and the X ₂ -Y ₂ coordinate system;

2-2) Based on the least squares method, two fitting straight lines are obtained from the measuring point M after the L-shaped reference element array is rotated;

By right-angle relationship, there are:

In formula (3) and formula (4), θ ₄ is the angle between the fitted straight line l ₃ obtained by the straight line fitting of the measuring point M in the X direction of the machine tool and the X1 axis of the X ₁ -Y ₁ coordinate system; θ ₃ is the angle between the fitted straight line l4 obtained by the straight line fitting of the measuring point M in the Y direction _of the machine tool and the Y2 axis of the X1 _{- Y1} coordinate system;

2-3) From formula (2) and formula (4), we get:

Compared with the prior art, the beneficial effects of the present invention are:

The invention is based on the L-shaped reference part array, the optical angle sensor is driven by the machine tool spindle to move along the L-shaped reference part array, the coordinate position information of the measurement point is obtained by using the attitude of the L-shaped reference part array before and after the rotation, and the angle is combined after fitting the straight line. The relationship gives the squareness error between the machine axis and the axis. The method of detecting the verticality error of CNC machine tools based on the array of rotating L-shaped reference parts can effectively obtain the verticality error of the machine tool and improve the machining accuracy of the machine tool.

Description of drawings

Fig. 1 is the structural representation of the reference piece in the present invention;

Figure 2 is a schematic diagram of the measurement point collection of the reference part

Figure 3 is a schematic diagram of the L-shaped reference element array calibration;

Figure 4 is a schematic diagram of the relative position of the measurement point of the reference part;

5 is a schematic diagram of the relative position before and after the rotation of the L-shaped reference element array;

6 is a schematic diagram of the measurement principle before the rotation of the L-shaped reference element array;

Figure 7 is a schematic diagram of the measurement principle after the L-shaped reference element array is rotated;

FIG. 8 is a schematic diagram of the measurement principle of the existence of the L-shaped reference element array and the declination angle measurement;

FIG. 9 is a schematic diagram of the measurement principle of the rotation angle error of the L-shaped reference element array.

In the picture:

P1 is a plane, P2 is a paraboloid, F is a feature point, M is a paraboloid measurement point, and A is a plane measurement point;

1 is the L-shaped reference part array, 2 is the spindle of the CMM, and 3 is the optical angle sensor;

l ₁ is the fitted straight line of the measuring point in the X direction of the machine tool before rotation;

l ₂ is the fitted straight line of the measuring point in the Y direction of the machine tool before rotation;

l ₃ is the fitting straight line of the measuring point in the X direction of the machine tool after rotation;

l ₄ is the fitting straight line of the measuring point in the Y direction of the machine tool after rotation;

X ₁ -Y ₁ is the calibration coordinate system formed when calibrating the X direction of the L-shaped reference element array;

X ₂ -Y ₂ is the calibration coordinate system formed when calibrating the Y direction of the L-shaped reference element array;

l _x is the actual motion trajectory of the machine tool in the X direction;

l _y is the actual motion trajectory of the machine tool in the Y direction;

l ₅ is the fitting straight line of the measuring point in the X direction of the machine tool when the L-shaped reference element array has a deviation angle;

l ₆ is the fitting straight line of the measuring point in the Y direction of the machine tool when the L-shaped reference element array has a placement deviation angle;

l ₇ is the fitting straight line of the measuring point in the Y direction of the machine tool when the L-shaped reference piece has a rotation error angle;

l ₈ is the fitting straight line of the measuring point in the X direction of the machine tool when the L-shaped reference piece has a rotation error angle.

Detailed ways

The design idea of the method for realizing the verticality error detection of CNC machine tools based on the rotating L-shaped array of the present invention is as follows: the detection of the verticality error is mainly realized based on the rotating L-shaped reference part array, and the optical angle sensor is driven by the machine tool spindle to move along the L-shaped reference part array. , using the attitude of the L-shaped reference element array before and after rotation to obtain the coordinate position information of the measurement point, and after fitting the straight line and combining the angle relationship, the perpendicularity error between the machine tool axis and the axis is obtained. By analyzing the actual measurement conditions, even if there is a declination error or a rotation angle error of the L-shaped reference element array placement, this method can still be used to effectively obtain the verticality error of the machine tool and improve the machining accuracy of the machine tool.

The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments do not limit the present invention by any means.

Example:

In the present invention, the reference pieces combined with the plane P1 and the paraboloid P2 are arranged to form an L-shaped reference piece array, the interval between each reference piece is 50mm, and 9 reference pieces are installed in each column (that is, in the X direction and the Y direction respectively). At the same time, the concept of feature point F is introduced, and the tangent plane of the point located on the paraboloid P2 is parallel to the plane, so that the relative position between the reference parts can be easily evaluated. Using the attitude of the L-shaped reference part array before and after rotation, the perpendicularity error between the CNC to the machine tool axis and the axis is obtained after analysis and processing. The main contents are: first, place the L-shaped reference part array on the CMM, The main shaft of the coordinate measuring machine drives the optical angle sensor to move along the L-shaped reference part array to calibrate the mutual positions of the reference parts in the L-shaped reference part array; then, the optical angle sensor is driven along the L-shaped reference part by the machine tool spindle. The coordinate position information of the measurement point is obtained by using the attitude of the L-shaped reference part array before and after rotation, and the perpendicularity error between the X-axis and the Y-axis of the machine tool is obtained after fitting the straight line and combining the angle relationship.

In the present invention, the L-shaped reference element array is composed of a plurality of reference elements arranged in an L-shaped array. In the L-shaped reference element array, the intervals of the reference elements are equal, and one of the reference elements is located in two directions of the L-shaped array. The intersection; as shown in Figure 1, the top surface of the reference piece includes a plane P1 and a paraboloid P2, there is a point F on the paraboloid P2 of the reference piece, and the tangent plane of the paraboloid P2 passing the point F is parallel to the plane P1, The F point is recorded as a feature point; as shown in Figure 2, 4 points are designated as the measurement point A on the plane P1, and 9 points are designated as the measurement point M on the paraboloid P2.

Step 1. As shown in Fig. 3, after the reference parts are installed, the mutual positions of the reference parts in the L-shaped reference part array 1 should be calibrated first. Place the L-shaped reference part array 1 on a three-coordinate measuring machine, record the position coordinates of the reference part at the intersection of the two directions of the L-shaped reference part array 1 as (0, 0), and use this as a benchmark to obtain the difference between the reference parts. relative positional relationship. Before calibration, adjust the X direction of the L-shaped reference element array 1 to be parallel to the X axis of the CMM, and adjust the measurement beam of the laser interferometer to be consistent with the X axis movement direction of the CMM. The optical angle sensor 3 is installed on the main shaft 2, and the main shaft 2 of the coordinate measuring machine drives the optical angle sensor 3 to move along the X direction of the L-shaped reference part array 1, and respectively collects the measurement point A and the measurement point M on the reference part, Through the coordinate vector relationship between the measurement point A and the measurement point M, the coordinates of the feature point F of the reference part are obtained, and the calibration coordinate system X ₁ -Y ₁ in the X direction is established;

Step 2. After calibrating the X direction of the L-shaped reference element array, repeat the process of the above step 1 to calibrate the Y direction of the L-shaped array. The main axis of the CMM drives the optical angle sensor along the Y of the L-shaped reference element array. Move in the direction, collect the measurement point A and the measurement point M on the reference part respectively, and then obtain the coordinates of the feature point F of the reference part through the coordinate vector relationship between the measurement point A and the measurement point M, and establish the calibration coordinate system X ₂ - Y ₂ ;

Step 3. Combine steps 1 and 2 to establish the respective calibration coordinate systems. Due to the extremely small error of the CMM itself, the calibration coordinate systems in the X and Y directions are not strictly coincident, and the angle between the calibration coordinate system in the X direction and the calibration coordinate system in the Y direction is

Step 4. Place the L-shaped reference part array on the machine tool, try to make the X direction of the L-shaped reference part array consistent with the X-axis direction of the machine tool, the machine tool spindle drives the angle sensor to move along the X direction of the reference part array, and on the reference part The measurement point M is collected on the paraboloid P2 of the reference part; the position of the reference part array is kept stationary, the machine tool spindle drives the angle sensor to move along the Y direction of the reference part array, and the measurement point M is collected on the paraboloid P2 of the reference part. The spot coordinates of the measurement point M imaged in the optical angle sensor, combined with the coordinates of the feature point F in the image coordinate system, are transformed to obtain the coordinate value of the measurement point M in the machine tool coordinate system X-Y, and the attitude of the L-shaped reference part array before rotation is obtained. The coordinate position information of the measurement point M; the process is as follows:

As shown in Figure 4, the measurement point M is taken on the calibrated reference part, and the relative position coordinates of the reference part measurement points M in the X direction under the machine tool coordinate system are obtained from the vector relationship of the vectors:

Wherein, M ₁ and M _i are the measurement points on the first reference piece and the i-th reference piece, respectively, and F ₁ and F _i are the feature points on the first reference piece and the i-th reference piece, respectively.

Convert the vector form to the form of the coordinate difference,

X _Mi -X _M1 =X _F1 -X _M1 +X _Fi -X _F1 +X _Mi -X _Fi

There is a quantitative relationship between the point on the same reference piece and the coordinate difference between the machine tool coordinate system and the image coordinate system. Substitute it to get:

X _Mi -X _M1 =m(x _M1 -x _F1 )+Δ _i +m(x _Mi -x _Fi )

Thereby, the relative positional relationship between the measurement points M on the reference member is obtained.

Among them, X _M1 and X _Mi are the coordinates of the measurement point M of the first reference piece and the i-th reference piece respectively in the machine tool coordinate system, and x _M1 and x _Mi are the first reference piece and the i-th reference piece respectively. The coordinates of the measurement point M in the image coordinate system, x _F1 and x _Fi are the coordinates of the feature point F of the first reference part and the i-th reference part in the image coordinate system, respectively, m is the displacement measurement of the optical angle sensor Coefficient, that is, a pixel corresponds to the actual displacement in the machine tool coordinate system, and Δ _i is the distance of the feature point of the reference part in the machine tool coordinate system.

Similarly, the Y coordinate of the measuring point M in the machine tool coordinate system is obtained by calculation, and the relative position information between the measuring points M of the reference piece is obtained from the X coordinate and the Y coordinate.

Step 5. After the L-shaped reference part array is rotated 90° counterclockwise with the intersection of the X direction and the Y direction of the array as the rotation center, as shown in Figure 5, the X direction of the L-shaped reference part array is the same as that of the machine tool. The Y-axis directions are the same, that is, use the X direction of the original L-shaped reference part array to collect the measurement point M when the machine tool moves on the Y-axis, and use the Y direction of the original L-shaped reference part array to collect the measurement point M when the machine tool moves along the X-axis. The spindle of the machine tool drives the optical angle sensor to collect data along the X and Y directions respectively, and repeats step 4 to obtain the coordinate position information of the measurement point after the rotation of the L-shaped reference element array.

Step 6: As shown in Figure 6, the coordinates of the measurement points obtained in the X direction and the Y direction of the L-shaped reference part array are respectively fitted with a straight line to the measurement point coordinate position information of the L-shaped reference part array before and after the rotation. And combined with the angle relationship, the verticality error between the X-axis and the Y-axis of the machine tool is obtained; including:

6-1) The optical angle sensor is driven by the spindle of the machine tool to move along the original X direction of the L-shaped reference element array, that is, the measurement points during the movement of the machine tool Y-axis are collected in the original X direction of the L-shaped reference element array, and fitted by the measurement points The actual trajectory of the machine tool Y-axis movement is displayed.

Based on the least squares method, two fitting straight lines are obtained from the measurement point M before the rotation of the L-shaped reference element array;

Taking the verticality error α _xy between the X axis and the Y axis of the machine tool less than 0° as an example, from the right angle relationship, there are:

Squareness error between machine X and Y axes:

是X₁-Y₁坐标系与X₂-Y₂坐标系之间的夹角；In formula (1) and formula (2): θ ₁ is the angle between the fitted straight line l ₁ and the X ₁ -Y ₁ coordinate system X1 axis obtained by the straight line fitting of the measuring point M in the X direction of the machine tool; θ ₂ is the angle between the fitted straight line l ₂ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the Y2 axis of the X ₂ -Y ₂ coordinate system;

is the angle between the X ₁ -Y ₁ coordinate system and the X ₂ -Y ₂ coordinate system;

6-2) As shown in Figure 7, for the same reason, use the original Y direction of the L-shaped reference element array to collect the measurement points during the X-axis movement of the machine tool, and fit the actual trajectory of the X-axis movement of the machine tool from the measurement points.

Based on the least squares method, two fitting straight lines are obtained from the measurement point M after the L-shaped reference element array is rotated;

By right-angle relationship, there are:

In formula (3) and formula (4), θ ₄ is the angle between the fitted straight line l ₃ obtained by the straight line fitting of the measuring point M in the X direction of the machine tool and the X1 axis of the X ₁ -Y ₁ coordinate system; θ ₃ is the angle between the fitted straight line l4 obtained by the straight line fitting of the measuring point M in the Y direction _of the machine tool and the Y2 axis of the X1 _{- Y1} coordinate system;

2-3) Combined with the situation that the L-shaped reference element array does not rotate in the above steps, the perpendicularity error α _xy between the X-axis and the Y-axis of the machine tool is calculated by formulas (2) and (4) as:

As shown in Figure 8, but under actual conditions, after the L-shaped reference part array is placed on the machine tool, the X direction of the L-shaped reference part array may not be strictly consistent with the X-axis direction of the machine tool, and there is a placement error. It can be known that the coordinate position of the measurement point will be changed, and the fitted straight line will deviate from the actual motion trajectory of the machine tool. Since the reference part array is L-shaped, the deviation angle β1 between the two sides of the L _- shaped reference part array and the actual motion trajectory of the machine tool is equal.

From the angle relationship,

In formula (6) and formula (7), θ ₅ is the angle between the fitted straight line l ₅ obtained by the straight line fitting of the measurement point M in the X direction of the machine tool and the actual motion trajectory l _x of the machine tool X direction; θ ₆ is The angle between the fitting straight line l ₆ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the actual motion trajectory l _y in the Y direction of the machine tool.

As shown in Figure 9, under actual conditions, when the L-shaped reference element array is rotated counterclockwise, it is difficult to accurately ensure that the rotation angle is 90°. The motion trajectory also produces deviations. However, the deviation angle β ₂ between the two sides of the L-shaped reference element array and the actual motion trajectory of the machine tool is equal.

The angle relationship is as follows:

In formula (8) and formula (9), θ ₇ is the angle between the fitted straight line l ₇ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the actual motion trajectory l _y in the Y direction of the machine tool; θ ₈ is _The included angle between the fitted straight line l8 obtained by the straight line fitting of the measuring point M in the X direction of the machine tool and the actual motion trajectory lx in the _X direction of the machine tool;

Combining formulas (7) and (9), the verticality error between the X axis and Y of the machine tool can be obtained as:

It can be seen from the above analysis that even if the L-shaped reference element array may have a placement error in actual conditions, or the rotation angle is not exactly 90°, the measurement point information before and after rotation can still be used to effectively obtain the motion axis of the machine tool. verticality error.

Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the inspiration of the present invention, many modifications can be made without departing from the spirit of the present invention, which all belong to the protection of the present invention.

Claims (4)

1. a method for realizing the verticality error detection of a CNC machine tool based on a rotating L-shaped array, is characterized in that, at first, the L-shaped reference element array is placed on a three-coordinate measuring machine, and the optical angle sensor is driven by the main shaft of the three-coordinate measuring machine. Move along the L-shaped reference part array to calibrate the mutual positions of the reference parts in the L-shaped reference part array; then, drive the optical angle sensor to move along the L-shaped reference part array through the machine tool spindle, and use the L-shaped reference part array to rotate the front and The rotated attitude obtains the coordinate position information of the measurement point, and after fitting the straight line, the verticality error between the X axis and the Y axis of the machine tool is obtained by combining the angle relationship; The steps to obtain the coordinate position information of the measurement point M by using the attitude of the L-shaped reference element array before and after rotation are as follows: 1-1) Place the L-shaped reference part array on the machine tool, and the X direction of the L-shaped reference part array is consistent with the X-axis direction of the machine tool; 1-2) The spindle of the machine tool drives the optical angle sensor to move along the X and Y directions of the L-shaped reference element array, and collects the measurement point M on the reference element, and the measurement point M is imaged in the optical angle sensor. The coordinates of the feature point F in the image coordinate system are transformed to obtain the coordinate value of the measurement point M in the machine tool coordinate system X-Y, and the coordinate position information of the measurement point of the attitude of the L-shaped reference part array before rotation is obtained; 1-3) After the L-shaped reference part array is rotated 90° counterclockwise with the intersection of the X direction and the Y direction of the array as the rotation center, the X direction of the L-shaped reference part array is consistent with the Y-axis direction of the machine tool; 1-4) Repeat step 1-2) to obtain the coordinate position information of the measuring point of the attitude after the rotation of the L-shaped reference piece array; Linear fitting is performed on the coordinate position information of the measurement points of the L-shaped reference part array before and after rotation, and the perpendicularity error between the X-axis and the Y-axis of the machine tool is obtained by combining with the angle relationship; including: 2-1) Based on the least squares method, two fitted straight lines are obtained from the measurement point M before the rotation of the L-shaped reference element array; Assuming that the perpendicularity error α _xy between the X axis and the Y axis of the machine tool is less than 0°, according to the right angle relationship, there are:

Squareness error between machine X and Y axes:

In formula (1) and formula (2): θ ₁ is the angle between the fitted straight line l ₁ and the X ₁ -Y ₁ coordinate system X1 axis obtained by the straight line fitting of the measuring point M in the X direction of the machine tool; θ ₂ is the angle between the fitted straight line l ₂ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the Y2 axis of the X ₂ -Y ₂ coordinate system;

is the angle between the X ₁ -Y ₁ coordinate system and the X ₂ -Y ₂ coordinate system; 2-2) Based on the least squares method, two fitting straight lines are obtained from the measuring point M after the L-shaped reference element array is rotated; By right-angle relationship, there are:

In formula (3) and formula (4), θ ₄ is the angle between the fitted straight line l ₃ obtained by the straight line fitting of the measuring point M in the X direction of the machine tool and the X1 axis of the X ₁ -Y ₁ coordinate system; θ ₃ is the angle between the fitted straight line l4 obtained by the straight line fitting of the measuring point M in the Y direction _of the machine tool and the Y2 axis of the X1 _{- Y1} coordinate system; 2-3) From formula (2) and formula (4), we get:

2. The method for realizing the verticality error detection of a CNC machine tool based on a rotating L-shaped array according to claim 1, wherein the L-shaped reference part array is composed of a plurality of reference parts arranged in an L-shaped array, and the L-shaped reference part array is arranged in an L-shaped array. In the reference piece array, the reference pieces are equally spaced, and one reference piece is located at the intersection of two directions of the L-shaped array; the top surface of the reference piece includes a plane P1 and a paraboloid P2, and the paraboloid P2 of the reference piece has a A point F, and the tangent plane of the paraboloid P2 passing through the point F is parallel to the plane P1, record the point F as the feature point; designate 4 points on the plane P1 as the measurement point A, and designate 9 points on the paraboloid P2 as the measurement point Click M. 3. the method for realizing the verticality error detection of CNC machine tool based on the rotating L-shaped array according to claim 2, is characterized in that, the process of carrying out the mutual position calibration between the reference parts in the L-shaped reference part array is: the L-shaped reference The component array is placed on a CMM, and the main shaft of the CMM drives the optical angle sensor to move along the X and Y directions of the L-shaped reference component array to collect the measurement point A and the measurement point M on the reference component, respectively. Through the coordinate vector relationship between the measurement point A and the measurement point M, the coordinates of the feature point F of the reference part are obtained, and the calibration coordinate system X ₁ -Y ₁ in the X direction and the calibration coordinate system X ₂ -Y ₂ in the Y direction are established. The angle between the calibration coordinate system in the X direction and the calibration coordinate system in the Y direction is

4. The method for realizing the verticality error detection of CNC machine tools based on the rotating L-shaped array according to claim 1, it is characterized in that, if the deviation angle of the two right-angle sides of the L-shaped reference part array and the actual motion track of the machine tool is β ₁ , The angle relationship is as follows,

In formula (6) and formula (7), θ ₅ is the angle between the fitted straight line l ₅ obtained by the straight line fitting of the measurement point M in the X direction of the machine tool and the actual motion trajectory l _x of the machine tool X direction; θ ₆ is The angle between the fitted straight line l ₆ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the actual motion trajectory l _y in the Y direction of the machine tool; If the L-shaped reference part array is rotated 90 counterclockwise, the deviation angle between the two right-angled sides of the L-shaped reference part array and the actual motion trajectory of the machine tool is β ₂ , The angle relationship is as follows:

In formula (8) and formula (9), θ ₇ is the angle between the fitted straight line l ₇ obtained by the straight line fitting of the measuring point M in the Y direction of the machine tool and the actual motion trajectory l _y in the Y direction of the machine tool; θ ₈ is _The included angle between the fitted straight line l8 obtained by the straight line fitting of the measuring point M in the X direction of the machine tool and the actual motion trajectory lx in the _X direction of the machine tool; Combining formulas (7) and (9), the perpendicularity error between the X-axis and the Y-axis of the machine tool is obtained as:

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