Method for evaluating uncertainty of on-machine measurement of geometric parameters of cutter

Abstract

The invention discloses a cutter geometric parameter on-machine measurement uncertainty evaluation method, which comprises the following steps of: constructing an on-machine non-contact measurement system on a five-axis numerical control tool grinding machine, and realizing efficient scanning of cutter geometric parameters through linkage control of each axis; then, a cylinder is adopted as a standard part to calibrate the pose of the line laser sensor, so that the reliability of measured data is ensured; and finally, according to the GUM standard, carrying out quantitative analysis on main influence factors including repeatability errors, workpiece installation errors, calibration errors, sensor resolution errors and the like of the uncertainty of the on-machine non-contact measurement system, and calculating the synthesis standard uncertainty of the measurement system so as to establish a complete measurement uncertainty evaluation system. The method can provide reliable guarantee for high-precision measurement of geometric parameters of the cutter, provides quantitative basis for error traceability and system optimization, and has important theoretical significance and practical application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement uncertainty evaluation, and specifically relates to a method for evaluating the measurement uncertainty of tool geometric parameters during machining. Background Art

[0002] With the improvement of the service performance and reliability requirements of high-end equipment in fields such as energy, automotive, and aerospace, the requirements for the machining accuracy and surface quality of key parts in their structural compositions are also getting higher and higher. As production tools for these key parts, the manufacturing accuracy of numerous geometric parameters of complex tools such as milling cutters, taps, and drills directly affects the cutting performance and service life, thereby affecting the machining accuracy and production cost of parts. At present, most research focuses on the structural optimization design of tools, the research and development of tool materials, and the reasonable selection of coatings. However, how to ensure the precise and stable manufacturing of high-performance tools with complex structural characteristics designed is still a major problem that urgently needs to be solved.

[0003] Tool geometric parameters are usually crucial considerations during the design process, directly affecting the cutting efficiency, cutting quality, and service life of the tool. However, due to the installation deviations and manufacturing defects of the machine tool's moving axes, and the machining errors generated during multi-axis linkage machining, the tool will inevitably have machining errors. However, most traditional tool geometric parameter measurement methods are based on off-site measurement contact measurement, which not only has few measurable geometric parameters, but also easily causes problems such as secondary clamping errors of parts, surface damage, changes in machining benchmarks, and probe contact wear, making it difficult to meet the requirements for the efficient, precise, and comprehensive measurement of tool parameters.

[0004] To solve this problem, in-machine non-contact scanning technology has been introduced into tool parameter measurement. It has the advantages of high speed, high accuracy, and no need to disassemble the tool, and can directly measure the geometric parameters of the tool in real time on the processing equipment, thus significantly improving production efficiency and reducing human errors. Although non-contact measurement technology has significant advantages, the sources of uncertainty in its measurement results are complex and may be affected by multiple factors such as environmental factors, equipment performance, clamping errors, and sensor calibration accuracy. Therefore, how to accurately evaluate the uncertainty of in-machine non-contact measurement systems has become a key issue in ensuring the reliability of measurement results and improving manufacturing accuracy. Currently, most existing uncertainty evaluation methods are for off-line measurement systems or contact measurement devices, lacking a systematic evaluation method specifically for in-machine non-contact measurement systems. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for evaluating the measurement uncertainty of tool geometric parameters during machining, which can provide reliable guarantee for the high-precision measurement of tool geometric parameters and provide a quantitative basis for error tracing and system optimization.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for evaluating the uncertainty of in - machine measurement of tool geometric parameters, comprising the following steps:

[0008] Step 1: Establishment of in - machine non - contact measurement system

[0009] Based on a five - axis CNC machine tool, an in - machine non - contact measurement system is established. The tool is installed on the A - axis of the five - axis CNC machine tool, the line laser sensor is installed on the spindle of the five - axis CNC machine tool, and the spindle is locked to prevent free rotation of the spindle. Among them: the transmission chain path at the tool end is: bed → Y - axis → C - axis → A - axis → tool; the transmission chain path at the sensor end is: bed → Y - axis → X - axis → Z - axis → line laser sensor; the X - axis is used to drive the line laser sensor for translational motion, and according to the tool structure characteristics, the A - axis is used to drive the tool for indexing motion or continuous rotational motion to perform in - machine non - contact measurement of the tool.

[0010] Step 2: Calibration of sensor pose

[0011] Calibrate the pose of the line laser sensor relative to the Z - axis to obtain the rotation matrix R and translation matrix T from the line laser sensor coordinate system to the Z - axis coordinate system.

[0012] Step 3: Evaluation of measurement uncertainty

[0013] The sources of uncertainty in the in - machine non - contact measurement system include the uncertainty u1 caused by measurement repeatability error, the uncertainty u2 caused by workpiece installation error, the uncertainty u3 caused by calibration error, and the uncertainty u4 caused by sensor resolution. Then the combined standard uncertainty u is:

[0014]

[0015] Further, in the above - mentioned step 2, the method steps for sensor pose calibration are as follows:

[0016] 21) Obtain calibration data

[0017] Taking a standard cylinder as a standard part, install the standard part on the A - axis; control the movement of the X - axis and Y - axis to position the standard part at three or more different spatial positions; at each positioned spatial position of the standard part, use the line laser sensor to collect the cross - sectional contour data of the standard part multiple times to obtain calibration data.

[0018] 22) Solve the cross - section center coordinates

[0019] Due to the existence of installation errors, the intersection of the laser plane and the cylinder will form an elliptical cross - section; use the random sample consensus algorithm to fit the elliptical expression to obtain the cross - section center coordinates.

[0020] 23) Establish a coordinate transformation relationship

[0021] The transformation relationship between the coordinate system of the line laser sensor and the Z - axis coordinate system is expressed as:

[0022]

[0023] Where: (x si , y si , z si ) and (x zi , y zi , z zi ) respectively represent the elliptical center coordinates of the i - th elliptical cross - section in the coordinate system of the line laser sensor and the Z - axis coordinate system;

[0024] 24) Solve the rotation matrix R and the translation matrix T.

[0025] Furthermore, in step 24), the solution methods for the rotation matrix R and the translation matrix T are as follows:

[0026] 241) Construct an anti - symmetric matrix S composed of three independent coefficients a, b, and c, and express the rotation matrix R as:

[0027] R=(I + S)(I - S) -1

[0028] Where: I represents the identity matrix;

[0029] 242) Construct the i - th point pair with the elliptical center coordinates of any i - th elliptical cross - section in the coordinate system of the line laser sensor and the Z - axis coordinate system; Substitute m groups of point pairs into the transformation relation between the coordinate system of the line laser sensor and the Z - axis coordinate system, and eliminate the translation matrix T by pairwise subtraction to obtain a system of equations containing only the coefficients a, b, and c; m is the number of calibration data;

[0030] 243) Use the least - squares method to solve the coefficients a, b, and c to obtain the rotation matrix R;

[0031] 244) Substitute the obtained R back into the transformation relation between the coordinate system of the line laser sensor and the Z - axis coordinate system to calculate the translation matrix T.

[0032] Furthermore, in step three, the uncertainty u1 caused by the repeatability error is:

[0033]

[0034] Where: S p is the standard deviation of the assumed measured parameter; m is the number of calibration data, that is, the number of repeated measurements.

[0035] Further, in the third step, the uncertainty u2 caused by the workpiece installation error is as follows:

[0036]

[0037] where: e is the installation error; k2 is the error factor when the installation error is assumed to follow a uniform distribution.

[0038] Further, in the third step, the solution method for the uncertainty u3 caused by the calibration error is as follows:

[0039] The uncertainty of each element of the rotation matrix R is characterized by the uncertainties u a 、u b and u c of a, b, and c through the uncertainty propagation equation, expressed as:

[0040]

[0041] where: f ij is a function of each element of the rotation matrix R expressed as parameters a, b, and c; r ij is each element in the rotation matrix R; i and j represent the row and column respectively;

[0042] The uncertainties u(t1), u(t2), and u(t3) of each element in the translation matrix T are expressed as:

[0043]

[0044] where: m is the number of calibration data;

[0045] Then the coordinate uncertainty of each point in the tool coordinate system is approximately:

[0046]

[0047] The uncertainty u3 caused by the calibration error is:

[0048]

[0049] where: (x wi ,y wi ,z wi ) represents the point coordinates in the tool coordinate system; u(x wi ), u(y wi ), and u(z wi ) respectively represent the coordinate uncertainties of the points in the tool coordinate system on the X-axis, Y-axis, and Z-axis; u(x zi ), u(y zi ), and u(z zi ) respectively represent the coordinate uncertainties of the points in the Z-axis coordinate system on the X-axis, Y-axis, and Z-axis.

[0050] Further, in the third step, the uncertainty u4 caused by the sensor resolution is as follows:

[0051]

[0052] Where: r x and r z respectively represent the resolutions of the line laser sensor in the X-axis and Z-axis directions; k4 is the resolution factor when assuming the resolution follows a uniform distribution.

[0053] Further, in the third step, a confidence interval is introduced to obtain the expanded uncertainty:

[0054] U = k × u

[0055] Where: U is the expanded uncertainty; k is the confidence factor.

[0056] The beneficial effects of the present invention are as follows:

[0057] The method for evaluating the uncertainty of the in-machine measurement of the cutting tool geometric parameters of the present invention builds an in-machine non-contact measurement system on a five-axis CNC tool grinder. Through the coordinated control of each axis, the efficient scanning of the cutting tool geometric parameters is realized; then, a cylinder is used as a standard part to calibrate the pose of the line laser sensor to ensure the reliability of the measurement data; finally, according to the "Guide to the expression of uncertainty in measurement (GUM)" standard, the main influencing factors of the uncertainty of the in-machine non-contact measurement system, including repeatability error, workpiece installation error, calibration error, and sensor resolution error, are quantitatively analyzed, and the combined standard uncertainty of the measurement system is calculated, thereby establishing a complete measurement uncertainty evaluation system. The method of the present invention can provide a reliable guarantee for the high-precision measurement of the cutting tool geometric parameters, and provide a quantitative basis for error tracing and system optimization, having important theoretical significance and practical application value. Description of the Drawings

[0058] In order to make the objectives, technical solutions, and beneficial effects of the present invention clearer, the following drawings are provided by the present invention for illustration:

[0059] Figure 1 is a schematic structural diagram of the in-machine non-contact measurement system;

[0060] Figure 2 is a schematic diagram of the calibration of the installation pose of the line laser sensor;

[0061] Figure 3 is a physical diagram of the in-machine non-contact measurement system;

[0062] Figure 4It is a physical diagram for the pose calibration of the sensor. Specific implementation mode

[0063] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited do not limit the present invention.

[0064] The method for evaluating the uncertainty of the in-machine measurement of the tool geometric parameters in this embodiment includes the following steps.

[0065] Step 1: Establishment of an in-machine non-contact measurement system

[0066] Based on a five-axis CNC machine tool, an in-machine non-contact measurement system is established. The tool is installed on the A axis of the five-axis CNC machine tool, and the line laser sensor is installed on the spindle of the five-axis CNC machine tool, and the spindle is locked to prevent the spindle from rotating freely; among them: the transmission chain path at the tool end is: bed → Y axis → C axis → A axis → tool; the transmission chain path at the sensor end is: bed → Y axis → X axis → Z axis → line laser sensor; the X axis is used to drive the line laser sensor for translational motion, and according to the tool structure characteristics, the A axis is used to drive the tool for indexing motion or continuous rotation motion to perform in-machine non-contact measurement of the tool.

[0067] As Figure 1 shown, an in-machine non-contact measurement system is established on a five-axis CNC tool grinder in this embodiment. The in-machine non-contact measurement system is composed of a line laser sensor, a bed, a tool, a workbench, three linear axes (X, Y, Z) and two rotary axes (A, C). The tool end starts from the bed and is successively composed of the Y axis, the C axis, the A axis and the workpiece; the sensor end starts from the bed and is successively composed of the Y axis, the X axis, the Z axis and the line laser sensor. The in-machine non-contact measurement system adopts a multi-axis (multi-coordinate) linkage measurement method, among which: O W -X W Y W Z W represents the workpiece coordinate system; O A -X A Y A Z A 、O X -X X Y X Z X 、O Y -X Y Y Y Z Y and O Z -X Z Y Z Z Z respectively represent the coordinate systems of the A axis, the X axis, the Y axis and the Z axis; O M -X M YM Z M represents the machine tool coordinate system; O S -X S Y S Z S represents the line laser measurement coordinate system. In terms of the installation method, the sensor is installed at the end of the spindle through a special fixture. During installation, ensure that the installation surface is parallel to the axis of the spindle installation hole, and lock the spindle to prevent free rotation. During the measurement process, the X-axis is responsible for driving the sensor to perform translational motion, and the A-axis drives the measured component to perform indexing motion or continuous rotational motion according to the structural characteristics of the measured tool, so as to achieve high-precision measurement.

[0068] Step 2: Sensor pose calibration

[0069] To ensure the accuracy of the measurement data, it is necessary to calibrate the pose of the line laser sensor relative to the Z-axis to obtain the rotation matrix R and translation matrix T of the line laser sensor coordinate system O S -X S Y S Z S to the Z-axis coordinate system O Z -X Z Y Z Z Z .

[0070] In this embodiment, the method steps for sensor pose calibration are as follows:

[0071] 21) Obtain calibration data

[0072] As Figure 2 shown, in this embodiment, a high-precision cylinder is used as the standard part for calibration. Install the standard part on the A-axis; control the movement of the X-axis and Y-axis to position the standard part at three or more different spatial positions, and collect the cross-sectional contour data of it respectively. In addition, to ensure the calibration accuracy, at each positioned spatial position of the standard part, use the line laser sensor to collect the cross-sectional contour data of the standard part multiple times to obtain high-precision calibration data.

[0073] 22) Solve the cross-section center coordinates

[0074] First, filter the measured cylinder cross-section data to eliminate the interference of noise on data fitting. Due to the existence of installation errors, the intersection of the laser plane and the cylinder will form an elliptical cross-section; use the Random Sample Consensus algorithm (RANSAC) to fit the elliptical expression to obtain the cross-section center coordinates.

[0075] 23) Establish a coordinate transformation relationship

[0076] The line laser sensor coordinate system O S -X S Y S ZS to the Z-axis coordinate system O Z -X Z Y Z Z Z The conversion relationship is expressed as:

[0077]

[0078] Where: (x si , y si , z si ) and (x zi , y zi , z zi ) represent the elliptical center coordinates of the i-th elliptical cross-section in the on-line laser sensor coordinate system and the Z-axis coordinate system, respectively. (x zi , y zi , z zi ) can be calculated based on the machine tool coordinate values, the dimensions of the on-line laser sensor, and the fixture dimensions.

[0079] 24) Solve the rotation matrix R and the translation matrix T.

[0080] Specifically, in this embodiment, the rotation matrix R and the translation matrix T are solved based on the Rodrigues matrix method. The method is as follows:

[0081] 241) Construct an anti-symmetric matrix S composed of three independent coefficients a, b, and c, and represent the rotation matrix R as:

[0082] R = (I + S)(I - S) -1

[0083] Where: I represents the identity matrix.

[0084] 242) Construct the i-th point pair from the elliptical center coordinates of any i-th elliptical cross-section in the on-line laser sensor coordinate system and the Z-axis coordinate system; substitute m groups of point pairs into the conversion relationship between the on-line laser sensor coordinate system and the Z-axis coordinate system, and eliminate the translation matrix T by pairwise subtraction to obtain a system of equations containing only the coefficients a, b, and c; m is the number of calibration data.

[0085] 243) Use the least squares method to solve the coefficients a, b, and c to obtain the rotation matrix R.

[0086] 244) Substitute the obtained R back into the conversion relationship between the on-line laser sensor coordinate system and the Z-axis coordinate system to calculate the translation matrix T.

[0087] Step Three: Evaluation of Measurement Uncertainty

[0088] Analyze the uncertainty of the in - machine non - contact measurement system according to the "Guide to the expression of uncertainty in measurement (GUM)". The sources of uncertainty of the in - machine non - contact measurement system include the uncertainty u1 caused by measurement repeatability error, the uncertainty u2 caused by workpiece installation error, the uncertainty u3 caused by calibration error, and the uncertainty u4 caused by sensor resolution.

[0089] (1) Uncertainty u1 caused by repeatability error

[0090] Assume that the standard deviation of the measured parameter is S p , and the number of repeated measurements is n. Then the uncertainty u1 caused by repeatability error is:

[0091]

[0092] Where: S p is the assumed standard deviation of the measured parameter; m is the number of calibration data, that is, the number of repeated measurements.

[0093] (2) Uncertainty u2 caused by workpiece installation error

[0094] During the workpiece installation process, even if a dial indicator is used for centering, it is inevitable to introduce an installation error e due to manual operation and low precision. When evaluating the measurement uncertainty, it can be considered that this error follows a uniform distribution, and its coverage factor is k2. In this embodiment, the uncertainty u2 caused by workpiece installation error is:

[0095]

[0096] Where: e is the installation error; k2 is the error factor when the installation error is assumed to follow a uniform distribution.

[0097] (3) Uncertainty u3 caused by calibration error

[0098] In this embodiment, the solution method for the uncertainty u3 caused by calibration error is:

[0099] During the sensor pose calibration process, the uncertainties of the rotation matrix R and the translation vector T will directly lead to measurement errors of coordinate points, and thus affect the calculation accuracy of tool geometric parameters. In order to accurately evaluate the measurement uncertainty u3, it is necessary to quantitatively analyze the uncertainty of coordinate points caused by calibration errors. From the solution process of R in step two, each element of R can be expressed as a function f of parameters a, b, c ij , so the uncertainty of each element of the rotation matrix R is determined by the uncertainties u a , u b and uc Characterized by the uncertainty propagation equation, expressed as:

[0100]

[0101] Where: f ij Each element of the rotation matrix R is expressed as a function of the parameters a, b, and c; r ij Each element in the rotation matrix R; i and j represent the row and column respectively.

[0102] The uncertainties u(t1), u(t2), and u(t3) of the elements in the translation matrix T are expressed as:

[0103]

[0104] Where: m is the number of calibration data.

[0105] The uncertainties of the elements of the rotation matrix R and the translation matrix T can be calculated by the above process. Since the conversion between O Z -X Z Y Z Z Z and O W -X W Y W Z W only involves translational transformation, the propagation of conversion error between them can be ignored. Therefore, the coordinate uncertainty of each point in the tool coordinate system O W -X W Y W Z W is approximately:

[0106]

[0107] Then the uncertainty u3 caused by the calibration error is:

[0108]

[0109] Where: (x wi , y wi , z wi ) represents the point coordinates in the tool coordinate system; u(x wi ), u(y wi ), and u(z wi ) represent the coordinate uncertainties of the points in the tool coordinate system on the X-axis, Y-axis, and Z-axis respectively; u(x zi ), u(y zi ), and u(z zi ) represent the coordinate uncertainties of the points in the Z-axis coordinate system on the X-axis, Y-axis, and Z-axis respectively.

[0110] (4) Uncertainty u4 caused by sensor resolution

[0111] The resolutions of the sensor in the X-axis and Z-axis directions are r x and r z . The error caused by the resolution can be considered to follow a uniform distribution, and its coverage factor is k4. Therefore, the uncertainty u4 caused by the sensor resolution is:

[0112]

[0113] where: r x and r z respectively represent the resolutions of the line laser sensor in the X-axis and Z-axis directions; k4 is the resolution factor when the resolution is assumed to follow a uniform distribution.

[0114] (5) Combined standard uncertainty u

[0115] Then the combined standard uncertainty u is:

[0116]

[0117] Introducing the confidence interval, when the confidence interval is 95% and the coverage factor is k, the expanded uncertainty is obtained:

[0118] U = k × u

[0119] where: U is the expanded uncertainty; k is the confidence factor.

[0120] The following combines specific examples to detail the specific implementation manner of the method for evaluating the uncertainty of the cutting tool geometric parameters in this embodiment during machining.

[0121] 1. Setup of the in-machine non-contact measurement system

[0122] Referring to Step 1, set up the in-machine non-contact measurement system as shown Figure 3 in a five-axis CNC tool grinder.

[0123] 2. Calibration of the sensor pose

[0124] Referring to Step 2, calibrate the installation pose of the line laser sensor, and collect eight groups of cross-sectional data at different positions of the standard part. The rotation matrix R and the translation matrix T can be solved by the least squares method. The on-site calibration diagram is as shown Figure 4 . The rotation matrix R and the translation matrix T are respectively:

[0125]

[0126] 3. Evaluation of measurement uncertainty

[0127] Referring to Step 3, the measurement uncertainty of the built-in non-contact measurement system is evaluated. In this example, the basic major diameter d of the M8 screw tip tap is taken as an example for uncertainty analysis. It is repeatedly measured 10 times, and the average parameter value of d measured is 8.43 mm. According to Step 3, the uncertainties u1 caused by the repeatability error of the system, u2 caused by the workpiece installation error, u3 caused by the calibration error, and u4 caused by the sensor resolution are 3.2 μm, 1.4 μm, 1.1 μm, and 2.8 μm respectively. Furthermore, the combined standard uncertainty u = 4.6 μm is calculated, and the coverage factor k is taken as 2, and the expanded uncertainty U is 9.2 μm.

[0128] Therefore, the basic major diameter d of the M8 screw tip tap is expressed as (8.43 ± 0.0092) mm, meeting the measurement requirements. In addition, the uncertainties caused by measurement repeatability and sensor resolution dominate in this uncertainty, and the accuracy can be improved by replacing the sensor with a higher resolution.

[0129] The above-described embodiments are merely preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

1. A method for evaluating the uncertainty of on-machine measurement of tool geometric parameters, characterized by: The steps include: Step 1: On-machine non-contact measurement system construction Based on the five-axis CNC machine tool, a non-contact measurement system is built on the machine. The tool is installed on the A-axis of the five-axis CNC machine tool, and the line laser sensor is installed on the spindle of the five-axis CNC machine tool, and the spindle is locked to prevent the spindle from rotating freely. Among them: the transmission chain path of the tool end is: bed → Y-axis → C-axis → A-axis → tool; the transmission chain path of the sensor end is: bed → Y-axis → X-axis → Z-axis → line laser sensor; the X-axis is used to drive the line laser sensor for translational motion, and the A-axis is used to drive the tool for indexing motion or continuous rotation motion according to the tool structure characteristics, so as to measure the tool non-contactly on the machine; Step 2: Sensor pose calibration Calibrate the position and posture of the line laser sensor relative to the Z axis, and obtain the rotation matrix R and translation matrix T from the line laser sensor coordinate system to the Z axis coordinate system; Step 3: Measurement uncertainty assessment The sources of uncertainty in the on-machine non-contact measurement system include the uncertainty u1 caused by measurement repeatability error, the uncertainty u2 caused by workpiece installation error, the uncertainty u3 caused by calibration error and the uncertainty u4 caused by sensor resolution; the combined standard uncertainty u is:

2. The method for evaluating the uncertainty of tool geometric parameters on-machine measurement according to claim 1, characterized in that: In step 2, the method steps for calibrating the sensor posture are as follows: 21) Obtain calibration data Take the standard cylinder as the standard part and install it on the A axis; control the movement of the X axis and the Y axis to position the standard part at three or more different spatial positions; use a line laser sensor to collect the cross-sectional profile data of the standard part multiple times at each spatial position of the standard part to obtain calibration data; 22) Solve the coordinates of the center of the cross section Due to the existence of installation errors, the intersection of the laser plane and the cylinder will form an elliptical section. The random sample consistency algorithm is used to fit the elliptical expression to obtain the center coordinates of the section. 23) Establish coordinate transformation relationship The conversion relationship between the line laser sensor coordinate system and the Z-axis coordinate system is expressed as: Where: (x si ,y si ,z si ) and (x zi ,y zi ,z zi ) represent the coordinates of the center of the ellipse of the i-th elliptical cross section in the online laser sensor coordinate system and the Z-axis coordinate system respectively; 24) Solve the rotation matrix R and translation matrix T.

3. The method for evaluating the uncertainty of tool geometric parameters on-machine measurement according to claim 2, characterized in that: In step 24), the solution method of the rotation matrix R and the translation matrix T is: 241) Construct an antisymmetric matrix S consisting of three independent coefficients a, b and c, and express the rotation matrix R as: R=(I+S)(I-S) -1 Where: I represents the identity matrix; 242) The i-th point pair is constructed by using the ellipse center coordinates of any i-th elliptical cross section in the line laser sensor coordinate system and the Z-axis coordinate system; m groups of point pairs are substituted into the transformation relationship between the line laser sensor coordinate system and the Z-axis coordinate system, and the translation matrix T is eliminated by pairwise subtraction to obtain a set of equations containing only coefficients a, b and c; m is the number of calibration data; 243) Solve the coefficients a, b and c using the least squares method to obtain the rotation matrix R; 244) Substitute the solved R back into the transformation relationship between the line laser sensor coordinate system and the Z-axis coordinate system to calculate the translation matrix T.

4. The method for evaluating the uncertainty of on-machine measurement of tool geometric parameters according to claim 1, characterized in that: In step 3, the uncertainty u1 caused by the repeatability error is: Where: S p is the standard deviation of the assumed measured parameter; m is the number of calibration data, that is, the number of repeated measurements.

5. The method for evaluating the uncertainty of on-machine measurement of tool geometric parameters according to claim 1, characterized in that: In step 3, the uncertainty u2 caused by the workpiece installation error is: Where: e is the installation error; k2 is the error factor when the installation error is assumed to obey a uniform distribution.

6. The method for evaluating the uncertainty of on-machine measurement of tool geometric parameters according to claim 3 is characterized in that: In step 3, the solution method for the uncertainty u3 caused by the calibration error is: The uncertainty of each element of the rotation matrix R is given by the uncertainty u of a, b, and c a 、u b and u c It is characterized by the uncertainty propagation equation, expressed as: Where: f ij Each element of the rotation matrix R is expressed as a function of parameters a, b and c; r ij is each element in the rotation matrix R; i and j represent rows and columns respectively; The uncertainty u(t1), u(t2) and u(t3) of each element in the translation matrix T is expressed as: Where: m is the number of calibration data; Then the coordinate uncertainty of each point in the tool coordinate system is approximately: The uncertainty u3 caused by the calibration error is: Where: (x wi ,y wi ,z wi ) represents the point coordinates in the tool coordinate system; u(x wi )、u(y wi ) and u(z wi ) represent the coordinate uncertainty of the tool coordinate system point on the X-axis, Y-axis and Z-axis respectively; u(x zi )、u(y zi ) and u(z zi ) represent the coordinate uncertainty of the point in the Z-axis coordinate system on the X-axis, Y-axis and Z-axis respectively.

7. The method for evaluating the uncertainty of on-machine measurement of tool geometric parameters according to claim 1, characterized in that: In step 3, the uncertainty u4 caused by the sensor resolution is: Where: r x and r z They represent the resolution of the line laser sensor in the X-axis and Z-axis directions respectively; k4 is the resolution factor when the resolution is assumed to obey a uniform distribution.

8. The method for evaluating the uncertainty of on-machine measurement of tool geometric parameters according to claim 1, characterized in that: In step 3, the confidence interval is introduced to obtain the expanded uncertainty: U=k×u Where: U is the expanded uncertainty; k is the confidence factor.

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