Method for monitoring calibration precision of rotating shaft of multi-axis numerical control machine tool based on non-contact measuring head

Abstract

The invention discloses a rotating shaft calibration precision monitoring method for a multi-axis numerical control machine tool based on a non-contact measuring head, and the method comprises the steps: measuring a standard plane part installed in laser processing equipment through the non-contact measuring head, and obtaining the initial position data of the laser processing equipment; based on pre-calibrated calibration data of the rotating shaft, converting the initial position data to obtain spatial position data of the laser processing equipment; converting a spatial direction vector in the spatial position data into angle data of the rotating shaft, and determining theoretical point coordinates of the laser processing equipment under different spatial angles of the rotating shaft based on the angle data and the spatial position data of the laser processing equipment; and determining the calibration error of the rotating shaft according to the theoretical point position coordinates of the laser processing equipment and the actual point position coordinates measured by the corresponding non-contact measuring head. The calibration precision error of the rotating shaft of the laser processing equipment can be quickly monitored, so that whether blade positioning processing can be performed or not is identified, and the production efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of laser processing blade equipment, specifically relating to a method for monitoring the calibration accuracy of the rotary axis of a multi-axis CNC machine tool based on a non-contact probe. Background Technology

[0002] Currently, in the field of laser processing, the requirements for the processing quality of air film holes in blades are becoming increasingly stringent. The positioning accuracy of the workpiece is particularly important. If the positioning position is off, it will lead to errors in the processing hole position, which can easily cause more wall damage. The position is also related to the direction of airflow, which has a significant impact on the overall lifespan of the blade.

[0003] In the current processing industry, multi-axis CNC equipment is commonly used for positioning and machining. However, positioning requires that the equipment's accuracy meets the standards. Existing technology typically uses contact measuring instruments to measure the center and direction of the equipment's rotating axis and then directly performs positioning and machining. However, in practice, the positioning accuracy often fails to meet the requirements, making machining impossible. This necessitates extensive troubleshooting, usually due to inaccurate calibration results of the equipment's rotating axis. However, the current rotating axis calibration function of laser processing equipment is cumbersome and cannot be directly verified. It can only be deduced from the actual positioning, lacking quantitative indicators and direct representation. It requires recalibration and verification, making it difficult to quickly determine the accuracy of the rotating axis calibration results. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention provides a method for monitoring the calibration accuracy of the rotary axis of a multi-axis CNC machine tool based on a non-contact probe.

[0005] The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for monitoring the calibration accuracy of rotary axes in a multi-axis CNC machine tool based on a non-contact probe, comprising: The initial position data of the laser processing equipment is obtained by measuring a standard planar component installed in the laser processing equipment using a non-contact measuring head; the initial position data includes the initial five-axis coordinates and the initial direction vector. Based on the pre-calibrated rotation axis calibration data, the initial position data of the laser processing equipment is transformed to obtain the spatial position data of the laser processing equipment; the spatial position data includes spatial coordinates and spatial direction vectors. The spatial direction vector is converted into rotation axis angle data, and based on the angle data and the spatial position data of the laser processing equipment, the theoretical point coordinates of the laser processing equipment under different spatial angles of the rotation axis are determined. The calibration error of the rotating axis is determined based on the theoretical coordinates of the laser processing equipment at different spatial angles of the rotating axis and the actual coordinates of the corresponding non-contact measuring head.

[0006] This invention provides a method for monitoring the calibration accuracy of the rotary axis of a multi-axis CNC machine tool based on a non-contact probe. This method enables rapid verification of the rotary axis error in laser processing equipment, offering high efficiency and simple operation. Furthermore, it allows for the quantification of rotary axis error indicators for intuitive monitoring. Therefore, by rapidly monitoring the calibration accuracy error of the rotary axis in laser processing equipment, this invention can identify whether blade positioning processing can be performed, thereby improving the utilization rate of blade processing equipment and increasing production capacity.

[0007] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating a method for monitoring the calibration accuracy of a rotary axis of a multi-axis CNC machine tool based on a non-contact probe, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the process of measuring the actual point coordinates using a non-contact measuring head in an embodiment of the present invention. Detailed Implementation

[0009] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0010] This invention provides a method for monitoring the calibration accuracy of rotary axes in a multi-axis CNC machine tool based on a non-contact probe. See also... Figure 1 The method includes the following steps: S10. Measure the standard planar component installed in the laser processing equipment using a non-contact measuring head to obtain the initial position data of the laser processing equipment.

[0011] For example, a high-precision standard planar component is pre-designed and, in conjunction with a zero-point quick-change device, is mounted on the quick-change device to facilitate its installation in the laser processing equipment. The standard planar component is the core component, and its flatness and surface roughness must be guaranteed.

[0012] Subsequently, a non-contact measuring head is used to measure the standard planar part. With both the first rotation axis (i.e., the main rotation axis) and the second rotation axis (i.e., the auxiliary rotation axis) of the laser processing equipment at (0, 0), the zero-point position of the non-contact measuring head is obtained, thereby acquiring the initial position data of the laser processing equipment. The initial position data includes the initial five-axis coordinates (x / y / z / MainAx / AssistAx) and the initial direction vector.

[0013] Specifically, the initial direction vector initDir can be preset, for example (0, 0, 1). When the parameter of the initial direction vector is empty, a preset reference direction vector can be used as the initial direction.

[0014] S20. Based on the pre-calibrated rotation axis calibration data, the initial position data of the laser processing equipment is converted to obtain the spatial position data of the laser processing equipment.

[0015] Spatial location data includes spatial coordinates and spatial direction vectors.

[0016] Optionally, step S20 may specifically include: S201. The rotation angles of the first and second rotation axes included in the initial five-axis coordinates of the laser processing equipment are converted to obtain the first rotation axis radians and the second rotation axis radians.

[0017] For example, the rotation angles MainAx of the first rotation axis and AssistAx of the second rotation axis are obtained from the initial five-axis coordinates of the laser processing equipment. Through mathematical transformation, the two angle values ​​are converted into radians respectively, with the following conversion relationship: After the transformation, we obtain the first rotation axis radian mainRad and the second rotation axis radian slaveRad, which can be used for subsequent rotation transformation calculations.

[0018] S202. Based on the pre-calibrated calibration data of the rotation axis, the first rotation axis radian and the second rotation axis radian, determine the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix.

[0019] The calibration data for the rotation axes includes first rotation axis calibration data and second rotation axis calibration data. For example, the calibration data for the rotation axes can be obtained based on laser interferometer calibration measurements according to industry standards for five-axis machining equipment. The first rotation axis calibration data is the space definition `mainAx` obtained from calibration, containing the position of the rotation center point and the rotation direction vector (i.e., the axis direction vector) of the first rotation axis; the second rotation axis calibration data is the space definition `slaveAx` obtained from calibration, containing the position of the rotation center point and the rotation direction vector (i.e., the axis direction vector) of the second rotation axis.

[0020] Optionally, step S202 may specifically include: S2021. Obtain the rotation direction vector of the first rotation axis and the rotation direction vector of the second rotation axis from the pre-calibrated calibration data of the rotation axis.

[0021] For example, since the data processing procedures for the first and second rotation axes are the same, the following explanation uses the first rotation axis as an example. The rotation center point P1 and rotation direction vector V1 are extracted from the calibration data (mainAx) of the first rotation axis.

[0022] S2022. Normalize the rotation direction vectors of the first rotation axis and the second rotation axis respectively to obtain the unit direction vectors of the first rotation axis and the second rotation axis.

[0023] For example, the rotation direction vector V1 of the first rotation axis is normalized to obtain the unit direction vector of the first rotation axis. .

[0024] S2023. Using the Rodriguez rotation formula, the unit direction vector of the first rotation axis, the unit direction vector of the second rotation axis, the radian of the first rotation axis, and the radian of the second rotation axis are calculated to obtain the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix.

[0025] For example, the first homogeneous rotation transformation matrix is ​​calculated based on the Rodriguez rotation formula. :

[0026] in, Let I be the first axis of rotation in radians, and let I be a 3×3 identity matrix. The outer product matrix of the unit direction vector u1, Unit direction vector The cross product matrix.

[0027] Received The rotation matrix based on the origin is a 3×3 matrix. In actual equipment, the rotation center point P1 in the calibration data (mainAx) of the first rotation axis changes with rotation, therefore a translation matrix needs to be added. , Finally, a 4×4 homogeneous transformation matrix is ​​obtained. .

[0028] This ultimately generates a 4×4 first homogeneous rotation transformation matrix that rotates the object by a specified number of radians (mainRad) around a specific spatial axis (mainAx). And generate a 4×4 second homogeneous rotation transformation matrix that rotates a specified number of radians (slaveRad) around a specific spatial axis (slaveAx). .

[0029] S203. Perform matrix multiplication on the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix to obtain the first combined rotation transformation matrix; and perform inversion on the first combined rotation transformation matrix to obtain the inverse matrix of the first combined rotation transformation.

[0030] For example, the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix are multiplied to obtain the first combined rotation transformation matrix trsf, where the transformation order is the first homogeneous rotation transformation first, followed by the second homogeneous rotation transformation. Then, the first combined rotation transformation matrix is ​​inverted to obtain the first combined rotation transformation inverse matrix trsf.Inverted(), which represents the mapping relationship from the machine tool coordinate system to the space coordinate system.

[0031] S204. Multiply the initial position data of the laser processing equipment with the inverse matrix of the first combined rotation transformation to obtain the spatial position data of the laser processing equipment.

[0032] For example, the three-dimensional linear coordinates xyz are extracted from the initial position data of the laser processing equipment, represented in homogeneous coordinate form, and multiplied with the inverse matrix of the first combined rotation transformation, i.e., pnt = pos.xyz.Transformed(trsf), to calculate the three-dimensional coordinates pnt of the machine tool coordinate point in the spatial coordinate system, and thus obtain the spatial coordinates N1 (x1 / y1 / z1). The initial direction vector (initDir) is multiplied with the inverse matrix of the first combined rotation transformation, i.e., dir = ininitDir.Transformed(trsf), where the transformation of the initial direction vector only applies the rotation transformation component and ignores the translation component, thus obtaining the spatial direction vector dir in the spatial coordinate system. dir is an array of different spatial directions in the three-dimensional spatial coordinate system based on the standard detection origin. For example, the direction vector (0.707, 0.707, 1) corresponds to the point at 45 degrees in the rotation axis direction.

[0033] S30. Convert the spatial direction vector into rotation axis angle data, and based on the angle data and the spatial position data of the laser processing equipment, determine the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis.

[0034] Optionally, step S30 may specifically include: S301. Transform the spatial direction vector from the spatial coordinate system to the machine tool rotation axis direction to obtain the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis.

[0035] Optionally, step S301 may specifically include: S3011. Based on the spatial direction vector and the preset first rotation axis direction vector, determine the first angle array corresponding to the first rotation axis.

[0036] For example, a numerical tolerance threshold eps (typically 1×10) can be set. -6), used to handle boundary conditions and singular positions in numerical calculations. In addition, the first rotation axis direction vector (U)_mainDir (corresponding to X-axis (1,0,0) / Y-axis (0,1,0)) and the second rotation axis direction vector (V)_assistDir (corresponding to C-axis (0,0,1)) can be obtained in advance.

[0037] Two different strategies can be used to determine the method for calculating the first angle array a2{} corresponding to the first rotation axis based on the type of the first rotation axis. The first angle array a2{} includes multiple first rotation angles. .

[0038] Strategy 1: When the first rotation axis is the X-axis or Y-axis, the Z component of the spatial direction vector dir can be used. Calculate the first rotation angle Specifically, it can be calculated using the inverse cosine function: The `clamp` function (a numerical range clamping function) ensures that the input value is within the range [-1, 1], preventing the inverse cosine function parameter from exceeding its domain due to floating-point errors. The geometric principle of Strategy 1 is: when the U-axis is the X or Y axis, rotation around the U-axis directly affects the Z-axis component, and the Z-component is equal to the first rotation angle. The cosine value.

[0039] Strategy 2: When the first rotation axis is the C-axis (around the Z-axis), the first rotation angle can be calculated using the projection of the spatial direction vector dir onto the XY plane. Specifically, it is calculated using the arctangent function in the four quadrants: The geometric principle of Strategy 2 is as follows: when the U-axis is the Z-axis, the rotation only changes the azimuth angle of the direction in the XY plane, and does not change the Z component.

[0040] S3012. Based on the first rotation axis direction vector and the rotation angle of the first rotation axis, construct the first rotation transformation matrix and calculate the inverse matrix of the first rotation transformation matrix to obtain the first inverse transformation matrix.

[0041] For example, the first rotation angle calculated according to step S3011 Using the preset first rotation axis direction vector, construct the first rotation transformation matrix trsfU around the U-axis. Then, calculate the inverse transformation matrix trsfU to obtain the first inverse transformation matrix invU. Here, trsfU represents rotating the workpiece coordinate system around the U-axis. Angle transformation, invU represents rotation in the opposite direction.

[0042] S3013. Determine the first intermediate vector based on the spatial direction vector and the first inverse transformation matrix.

[0043] For example, the spatial direction vector dir is transformed by applying the first inverse transformation matrix invU to obtain the first intermediate vector intermediate. This process involves rotating in the opposite direction from the target orientation. Angle, so that the target direction is aligned with the coordinate system after the U-axis rotation.

[0044] S3014. Determine the second intermediate vector based on the preset reference direction vector and the first rotation transformation matrix.

[0045] For example, the preset reference direction vector (usually the Z-axis direction of the coordinate system, Dir.DZ) is transformed using the first rotation transformation matrix trsfU to obtain the second intermediate vector m. This indicates that the Z-axis rotates only around the U-axis. The direction behind the angle.

[0046] S3015. Determine the second angle array corresponding to the second rotation axis based on the first intermediate vector and the second intermediate vector.

[0047] For example, first, the dot product between the second intermediate vector m and the first intermediate vector intermediate is calculated: Then, the angle between the two vectors is calculated using the inverse cosine function: This allows us to obtain the value of the second rotation angle corresponding to the second rotation axis.

[0048] Next, determine the sign (direction) of the second rotation angle. Specifically, calculate the cross product of the second intermediate vector m and the first intermediate vector intermediate: And determine the rotation direction based on the calculation results: if Then keep If it is positive; Then Take the negative value. Where... Let V be the unit direction vector of the second rotation axis V.

[0049] In this embodiment, the rotation direction is determined by the sign of the dot product between the cross product direction and the V-axis direction, which conforms to the right-hand rule.

[0050] Furthermore, singular positions need to be handled, i.e., when m and intermediate are nearly collinear (i.e. Special handling is required: if If it is a singular location, then it is determined to be a singular location; if (The two vectors are basically in the same direction), set ;like (The two vectors are in basically opposite directions), set Next, we further verify the singular positions: calculate the magnitude of the cross product vector `cross`, if it is close to zero (i.e., ... This has been identified as a singular location. At singular locations, the rotation direction is not unique; a uniform setting is used. .

[0051] Finally, the radian system and Convert to angle system: It returns angle pairs (uAngle, vAngle), and finally we can obtain the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis.

[0052] This embodiment aligns the reference direction (Z-axis) with the target direction (spatial direction vector) through two rotational transformations. First, it rotates around the U-axis. The angle is rotated such that the Z-axis direction is rotated to a position where it has the same projection relationship with the target direction on a plane perpendicular to the V-axis; then, by rotating about the V-axis... The angle is calculated by aligning the center direction perfectly with the target direction. Its core principle lies in separating the effects of the two rotations through an inverse transformation method, thus achieving decoupled angle calculation.

[0053] S302. Based on the first angle array corresponding to the first rotation axis, the second angle array corresponding to the second rotation axis, and the spatial coordinates of the laser processing equipment, determine the theoretical point coordinates of the laser processing equipment under different spatial angles of the rotation axis.

[0054] Optionally, step S302 may specifically include: S3021. Construct a second combined rotation transformation matrix based on the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis.

[0055] For example, the input parameters include: spatial coordinates point(N1), a first angle array uAngle(a2{}), and a second angle array vAngle(a1{}). }), Initial calibration results of the rotating axis The coordinate offset of the non-contact measuring head. Specifically, the non-contact measuring head can be used to measure the reference position of the center of the rotation axis of the laser processing equipment, obtaining the position of the non-contact measuring head relative to the center of the rotation axis of the laser processing equipment, and then obtaining the offset (x / y / z). Afterwards, the calibration data of the rotation axis is... The corresponding first and second rotation axes undergo relative position transformations.

[0056] Among them, the calibration data for the rotation axis of the non-contact measuring head:

[0057] Convert the first angle array uAngle from degrees to radians to obtain Convert the second angle array vAngle from degrees to radians to obtain... Then, construct the second combined rotation transformation matrix. The specific construction process can be referred to in step S20 for the specific process of the first combined rotation transformation matrix, which will not be repeated here.

[0058] S3022. Based on the second combined rotation transformation matrix, the spatial coordinates of the laser processing equipment are transformed to obtain the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis.

[0059] For example, the second combined rotation transformation matrix is ​​applied to the spatial coordinates N1 of the laser processing equipment, through... The method calculates the transformed theoretical point coordinates pos, and can create and return a Coordinate5Ax object containing the theoretical point coordinates pos, a first angle array uAngle, and a second angle array vAngle.

[0060] S40. Determine the calibration error of the rotating axis based on the theoretical coordinates of the laser processing equipment at different spatial angles of the rotating axis and the actual coordinates of the corresponding non-contact measuring head.

[0061] Optionally, the process of measuring the actual point coordinates with a non-contact measuring head may specifically include: Using a non-contact measuring head, the actual coordinates of the points measured by the non-contact measuring head at different spatial angles of the rotating axis are obtained by executing the preset CNC program of the laser processing equipment according to the theoretical coordinates of the measuring points.

[0062] For example, the specific process of obtaining the actual point coordinates N3 measured by the non-contact measuring head can be referred to Figure 2 .

[0063] Optionally, step S40 may specifically include: S401. Calculate the difference between the theoretical coordinates of the laser processing equipment at different spatial angles of the rotation axis and the actual coordinates of the corresponding non-contact measuring head to obtain the initial deviation value.

[0064] For example, the difference between the theoretical coordinates N2 of the laser processing equipment at different spatial angles of the rotation axis and the actual coordinates N3 measured by the corresponding non-contact measuring head is calculated to obtain the initial deviation value, which is used to determine the correctness of the rotation axis center. Theoretically, the initial deviation value is zero. If the initial deviation value is greater than zero, it indicates that there is a deviation in the rotation axis center.

[0065] S402. Using trigonometric functions, calculate the initial deviation value, the spatial coordinates of the laser processing equipment, and the angle data of the rotating axis to obtain the calibration error of the rotating axis.

[0066] For example, in actual practice, due to assembly and measurement errors in the laser processing equipment during the calibration of the rotation axis center, the calibration error of the rotation axis is obtained by using the trigonometric functions sin(a) and cos(c) for the initial deviation value, expressed as:

[0067]

[0068] in, express Z-axis coordinate value in express The Z-axis coordinate value in the data.

[0069] If the calibration error is too large, it is necessary to use a laser interferometer to compensate for the error values ​​of each axis of the laser processing equipment.

[0070] Subsequently, the calculated calibration error of the rotating shaft can be sent to the monitoring equipment in real time for display, so that users can monitor it intuitively.

[0071] This invention discloses a method for monitoring the calibration accuracy of the rotary axis of a multi-axis CNC machine tool based on a non-contact probe. This method enables rapid verification of the rotary axis error in laser processing equipment, offering high efficiency, simple operation, and lower operating costs compared to laser interferometers. Furthermore, it allows for the quantification of rotary axis error indicators for intuitive monitoring. Therefore, by rapidly monitoring the calibration accuracy error of the rotary axis in laser processing equipment, this invention identifies whether blade positioning processing can be performed, thereby improving the utilization rate of blade processing equipment and increasing production capacity.

[0072] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0073] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0074] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0075] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for monitoring the calibration accuracy of rotary axes in a multi-axis CNC machine tool based on a non-contact probe, characterized in that, include: The initial position data of the laser processing equipment is obtained by measuring a standard planar component installed in the laser processing equipment using a non-contact measuring head. The initial position data includes initial five-axis coordinates and initial direction vectors; Based on the pre-calibrated rotation axis calibration data, the initial position data of the laser processing equipment is transformed to obtain the spatial position data of the laser processing equipment; the spatial position data includes spatial coordinates and spatial direction vectors; The spatial direction vector is converted into rotation axis angle data, and based on the angle data and the spatial position data of the laser processing equipment, the theoretical point coordinates of the laser processing equipment under different spatial angles of the rotation axis are determined. The calibration error of the rotating axis is determined based on the theoretical coordinates of the laser processing equipment at different spatial angles of the rotating axis and the actual coordinates of the corresponding non-contact measuring head.

2. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 1, characterized in that, The initial position data of the laser processing equipment is transformed based on the calibration data of the pre-calibrated rotation axis to obtain the spatial position data of the laser processing equipment, including: The rotation angles of the first and second rotation axes included in the initial five-axis coordinates of the laser processing equipment are converted to obtain the first rotation axis radians and the second rotation axis radians. Based on the pre-calibrated rotation axis calibration data, the first rotation axis radian and the second rotation axis radian, a first homogeneous rotation transformation matrix and a second homogeneous rotation transformation matrix are determined; the rotation axis calibration data includes the first rotation axis calibration data and the second rotation axis calibration data; Perform matrix multiplication on the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix to obtain the first combined rotation transformation matrix; and perform inversion on the first combined rotation transformation matrix to obtain the inverse matrix of the first combined rotation transformation. The initial position data of the laser processing equipment is multiplied by the inverse matrix of the first combined rotation transformation to obtain the spatial position data of the laser processing equipment.

3. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 2, characterized in that, The determination of the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix based on the pre-calibrated rotation axis calibration data, the first rotation axis radian, and the second rotation axis radian includes: From the pre-calibrated calibration data of the rotation axes, obtain the rotation direction vectors of the first rotation axis and the second rotation axis respectively; The rotation direction vectors of the first rotation axis and the second rotation axis are normalized respectively to obtain the unit direction vectors of the first rotation axis and the second rotation axis. Using the Rodriguez rotation formula, the unit direction vector of the first rotation axis, the unit direction vector of the second rotation axis, the radian of the first rotation axis, and the radian of the second rotation axis are calculated to obtain the first homogeneous rotation transformation matrix and the second homogeneous rotation transformation matrix.

4. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 1, characterized in that, The step of converting the spatial direction vector into rotation axis angle data, and determining the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis based on the angle data and the spatial coordinates of the laser processing equipment, includes: Transform the spatial direction vector from the spatial coordinate system to the machine tool rotation axis direction to obtain the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis. Based on the first angle array corresponding to the first rotation axis, the second angle array corresponding to the second rotation axis, and the spatial coordinates of the laser processing equipment, the theoretical point coordinates of the laser processing equipment under different spatial angles of the rotation axis are determined.

5. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 4, characterized in that, The step of transforming the spatial direction vector from the spatial coordinate system to the machine tool rotation axis direction to obtain the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis includes: Based on the spatial direction vector and the preset first rotation axis direction vector, determine the first angle array corresponding to the first rotation axis; Based on the first rotation axis direction vector and the rotation angle of the first rotation axis, a first rotation transformation matrix is ​​constructed, and the inverse matrix of the first rotation transformation matrix is ​​calculated to obtain the first inverse transformation matrix; The first intermediate vector is determined based on the spatial direction vector and the first inverse transformation matrix; The second intermediate vector is determined based on the preset reference direction vector and the first rotation transformation matrix; Based on the first intermediate vector and the second intermediate vector, determine the second angle array corresponding to the second rotation axis.

6. The method for monitoring the calibration accuracy of the rotary axis of a multi-axis CNC machine tool based on a non-contact probe according to claim 4 or 5, characterized in that, The step of determining the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis based on the first angle array corresponding to the first rotation axis, the second angle array corresponding to the second rotation axis, and the spatial coordinates of the laser processing equipment includes: Based on the first angle array corresponding to the first rotation axis and the second angle array corresponding to the second rotation axis, a second combined rotation transformation matrix is ​​constructed. Based on the second combined rotation transformation matrix, the spatial coordinates of the laser processing equipment are transformed to obtain the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis.

7. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 1, characterized in that, The process of measuring the actual point coordinates with the non-contact measuring head includes: Using a non-contact measuring head, the measured point positions are determined according to the theoretical coordinates of the laser processing equipment. The preset CNC program of the laser processing equipment is executed to obtain the actual coordinates of the measured points at different spatial angles of the rotation axis.

8. The method for monitoring the calibration accuracy of rotary axes of a multi-axis CNC machine tool based on a non-contact probe according to claim 1, characterized in that, The determination of the calibration error of the rotating axis based on the theoretical coordinates of the laser processing equipment at different spatial angles of the rotating axis and the corresponding actual coordinates measured by the non-contact measuring head includes: Calculate the difference between the theoretical point coordinates of the laser processing equipment at different spatial angles of the rotation axis and the actual point coordinates measured by the corresponding non-contact measuring head to obtain the initial deviation value; The calibration error of the rotating axis is obtained by calculating the initial deviation value, the spatial coordinates of the laser processing equipment, and the angle data of the rotating axis using trigonometric functions.

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