Component contour high-precision measurement method based on parameter calibration and error separation

Abstract

The invention discloses a component contour measurement method based on structural parameter calibration and system error separation, belongs to the technical field of high-precision measurement of complex components, and relates to a component contour high-precision measurement method based on parameter calibration and error separation. According to the method, invalid data and abnormal values in measurement data are removed through median filtering, and reliable measurement data are obtained. Empirical mode decomposition is carried out on sensor sampling data, and systematic errors caused by vibration and other disturbances are separated. And establishing a component contour measurement model considering the structure parameter error, and eliminating the measurement deviation caused by the installation error of the sensor. And reconstructing measurement data into a component surface type by adopting a least square method, so as to realize high-precision measurement of the component contour. According to the method, filtering and noise reduction processing is carried out on data, and structural parameter errors and separation systematic errors of a measurement system are calibrated. Therefore, the influence of structural parameter errors, robot vibration and other interference noise is eliminated, and high-precision measurement of the surface profile of the component is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of on-site high-precision measurement of complex components, and relates to a component contour high-precision measurement method based on parameter calibration and error separation. Background Art

[0002] Complex structural parts represented by radomes are key components of high-end equipment in the fields of aerospace, energy and power, and transportation. Realizing high-quality and efficient manufacturing of such components is of great significance to ensuring the effective operation of high-end equipment. Most of these components are thin-walled structures with weak rigidity and easy deformation. There is a large deviation between the actual surface shape of the blank and the theoretical surface shape. Therefore, it is necessary to perform high-precision conformal grinding and polishing on them based on the actual surface shape of the component to ensure that the component meets the contour and surface quality requirements, thereby ensuring the manufacturing quality of such key parts. Based on this, how to achieve high-precision and efficient measurement and contour reconstruction of complex components, so as to obtain the precise actual surface shape of the component blank, has become the key to ensuring the quality and efficiency of component grinding and polishing.

[0003] At present, the measurement methods for the contours of complex structural parts mainly include non-contact measurement and contact measurement. Among them, the non-contact measurement method represented by optical measurement must ensure the measurement accuracy by fixing the marking points on the surface of the component. Therefore, this type of measurement method is mainly used in occasions where there is no cleanliness requirement on the surface of the component. Compared with the non-contact measurement method, the contact measurement system does not require special treatment of the component surface. The robot measurement system based on the contact displacement sensor ensures that the measurement result accuracy meets the requirements without increasing the surface contamination of the component, providing a feasible solution for the contour measurement of such complex structural parts. However, the installation error of the contact displacement sensor in the robot measurement system will directly cause the measurement deviation, and the robot vibration and other interference signals introduced during the measurement process will affect the reliability of the measurement results. Therefore, it is of great significance to calibrate the structural parameters and separate the system errors for the robot contact measurement system to achieve high-precision measurement of the component contour.

[0004] Prior art document 1 “An adaptive computer-aided path planning to eliminate errors of contact probes on free-form surfaces using a 4-DOF parallel robotCMM and a turn-table”, this document proposes a parallel device combined with a trigger probe integrated measurement system, but does not take into account the probe installation error, thereby reducing the measurement accuracy; Prior art document 2 “Device for contact measurement of turbine blade geometry in robotic grinding process”, this document proposes a blade contact measurement device, but does not take into account the installation errors of multiple contact sensors and other interferences caused by the measurement process, thereby reducing the reliability of the measurement results. Summary of the invention

[0005] In order to overcome the defects of the prior art, the present invention invents a high-precision component contour measurement method based on parameter calibration and error separation. The method uses a robot contact measurement system as a measuring device to perform contact measurement on the contour of the sample. First, the median filter is used to remove invalid data and outliers in the measurement data to obtain reliability measurement data. Then, the measurement signal is subjected to empirical mode decomposition (EMD) to separate the systematic errors caused by vibration and other disturbances in the sensor measurement signal. Further, the structural parameter errors of the robot contact measurement system are calibrated to establish a component contour measurement model that takes into account the structural parameter errors, thereby effectively reducing the influence of the sensor installation error on the measurement result. The method overcomes the problems of poor measurement accuracy caused by sensor installation errors and disturbance signals such as vibration in traditional methods, and realizes high-precision measurement of component contours.

[0006] The technical solution adopted by the present invention is a high-precision component contour measurement method based on parameter calibration and error separation, which is characterized in that the method uses a robot contact measurement system as a measuring device to perform contact measurement on the sample contour to obtain measurement data; the measuring device is composed of a parallel robot 1, a sensor fixture 2, a contact displacement sensor 3, a data collector 4 and a computer 5; firstly, a median filter is used to remove invalid data and abnormal values ​​in the measurement data to obtain reliability measurement data, and then the measurement signal is subjected to empirical mode decomposition to separate the systematic error caused by vibration and other disturbances in the sensor measurement signal, and finally a component contour measurement model is established, and the structural parameters of the robot measurement system are calibrated to solve the mapping from the structural parameter error to the measurement result, and the measurement deviation caused by the sensor installation error is eliminated, and the influence of the sensor installation error on the measurement result is reduced; and the least squares method is used to reconstruct the measurement data into the component surface shape to achieve high-precision measurement of the component contour; the specific steps of the method are as follows:

[0007] Step 1, performing contact measurement on the contour of the workpiece to obtain reliable measurement data;

[0008] The workpiece to be measured is installed in the robot contact measurement system, and the contact displacement sensor 3 is used to measure the inner side profile of the workpiece to obtain the actual sensor displacement signal; the actual displacement signal collected by the displacement sensor not only contains the actual profile data, but also contains systematic errors caused by signal disturbances such as vibration and random errors such as gross noise.

[0009] Firstly, the collected original signal data is preliminarily processed and the invalid data and abnormal values ​​in the measurement data are removed by using median filtering to obtain the reliability measurement data x(t).

[0010] Step 2: Perform empirical mode decomposition on the sampled data to separate the systematic noise caused by vibration and other disturbances;

[0011] The contact displacement sensor sampling data after preliminary processing contains systematic errors caused by vibration and other disturbances. The empirical mode decomposition method is used to decompose the data, thereby obtaining all the intrinsic mode function (IMF) components of the signal x(t); then, the IMF components that are determined to play a dominant role in noise are separated, and the high-frequency IMF components representing noise are eliminated; the remaining effective signal components after removing the noise components are accumulated to complete the signal reconstruction, and finally the sensor measurement signal x′(t) after the systematic error separation is obtained;

[0012] Step 3: Establish the component contour measurement model of the robot contact measurement system

[0013] First, the robot base coordinate system {O W -X WY W Z W} as the global measurement coordinate system, according to the robot kinematic equation, solve the robot end coordinate system {O E -X E Y E Z E} to the robot base coordinate system {O W -X W Y W Z W}The conversion relationship between:

[0014]

[0015] Among them, θ4 is the robot end moving platform around its base coordinate system Z W The input angle of rotation in the axial direction, the angular displacement direction conforms to the right-hand rule, x E ,y E ,z E is the offset of the center of the robot's terminal moving platform relative to the origin of the robot's base coordinate system, W T E is the coordinate transformation matrix from the robot end coordinate system to the robot base coordinate system;

[0016] The probe center in the zero position state is taken as the origin of the probe coordinate system, and the direction of the sensor axis away from the probe is taken as the probe coordinate system Z T Axis positive direction, based on the robot end coordinate system Y E The positive axis is the probe coordinate system Y T Axis positive direction, determine X according to the right-hand rule T Axis positive direction, establish probe coordinate system {O T -X T Y T Z T Based on the sensor installation dimensions, the probe coordinate system in the zero position state is solved by coordinate transformation {O T -X T Y T Z T} to the robot end coordinate system {O E -X E Y E Z E} conversion relationship:

[0017]

[0018] Among them, d x 、h z The X coordinate of the sensor probe center relative to the center of the robot end moving platform in the robot base coordinate system W , Z W The offset distance in the direction, θ TZ is the sensor axis relative to the robot end coordinate system E The angle of the positive axis, E T T is the coordinate transformation matrix from the probe coordinate system to the robot end coordinate system;

[0019] According to the transformation matrix from the robot end coordinate system to the global measurement coordinate system W T E And the transformation matrix from the probe coordinate system to the robot end coordinate system E T T , obtained from the probe coordinate system {O T -X T Y T Z T} to the robot base coordinate system {O W -X W Y W Z W}Transformation matrix between:

[0020] W T T = W T E E T T (3)

[0021] Define the displacement measurement data set in the probe coordinate system as x(t) i , according to the transformation matrix from the probe coordinate system to the global measurement coordinate system W T T , the displacement measurement data set x(t) in the probe coordinate system i Transfer to the global measurement coordinate system to obtain the actual motion trajectory point set of the probe in the global measurement coordinate system W P i :

[0022]

[0023] Step 4: Solve the mapping relationship between structural parameter error and displacement measurement data

[0024] Since installation errors are inevitable during the sensor installation process, such as the vertical offset dimension error of the probe, the horizontal offset dimension error of the probe, and the inclination angle error of the probe axis, these structural parameter errors will directly lead to errors in the measurement data.

[0025] Define the following parameters: The vertical offset error of the probe is Δh z , the horizontal offset error of the probe is Δd x , the horizontal tilt angle error of the probe axis is Δθ T ; Get the probe coordinate system {O T-X T Y T Z T} to the robot base coordinate system {O W -X W Y W Z W The actual transformation matrix between} is:

[0026]

[0027] Therefore, the system measurement model with structural parameter errors is:

[0028]

[0029] Where x′(t) i Collecting data sets for the end displacement sensor after coarse noise filtering and systematic error separation;

[0030] Further, the true value of the structural parameter error of the robot measurement system is determined by measurement calibration, and the actual motion trajectory point set of the probe in the global measurement coordinate system is solved based on formula (6): W P Ri ;

[0031] Step 5: Use the least squares method to reconstruct the measured data into the component surface shape

[0032] The least squares method is used to fit the measured point data of complex components after structural parameter calibration and error separation, and the surface of the complex component is reconstructed. The surface shapes before and after parameter calibration and error separation are fitted respectively, and the surface reconstruction error is further calculated. The maximum error and root mean square error results are obtained and analyzed to verify the effectiveness of the method.

[0033] The significant effects and benefits of the present invention are to scan and measure the component contour based on the contact displacement sensor, collect the relative displacement data of the probe, filter and reduce the noise of the data, and calibrate the structural parameter error of the measurement system and separate the systematic error, thereby eliminating the influence of the structural parameter error, robot vibration and other interference noise, and realizing high-precision measurement of the component surface contour. The present invention can realize high-precision measurement and reconstruction of the complex component profile with high precision and efficiency, provide a reliable surface contour for the precise grinding and polishing of the component blank, and contribute to the realization of efficient and high-precision grinding and polishing process of complex components. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 —Overall flow chart of the high-precision measurement method of component contour based on parameter calibration and error separation.

[0035] Figure 2—Schematic diagram of robot contact measurement system and coordinate transformation, in which: 1—parallel robot, 2—sensor fixture, 3—contact displacement sensor, 4—data acquisition device, 5—computer, {O W -X W Y W Z W}—parallel robot base coordinate system, {O E -X E Y E Z E}—Parallel robot 1 end coordinate system, {O T -X T Y T Z T}—Probe coordinate system.

[0036] Figure 3 —Graph of the sampling signal x(t) / mm of the contact displacement sensor 3 after filtering out the coarse noise.

[0037] Figure 4 —Frequency domain signal spectrum diagram of the sampled signal x(t), where a) IMF1-4—high-frequency interference frequency spectrum diagram, b) IMF5-8—low-frequency effective frequency spectrum diagram.

[0038] Figure 5 —Time domain signal decomposition diagram of the sampled signal x(t), where a) IMF1-4—interference signal component diagram, b) IMF5-8—effective signal component diagram.

[0039] Figure 6 —Graph of the effective sampling signal x′(t) / mm of the displacement sensor after coarse noise filtering and systematic error separation.

[0040] Figure 7 —Schematic diagram of the structural parameters of the robot contact measurement system, where {O E -X E Y E Z E} is the parallel robot terminal coordinate system, d x 、h z The X coordinate of the sensor probe center relative to the center of the robot end moving platform in the robot base coordinate system W , Z W The offset distance in the direction, θ T Z is the sensor axis relative to the robot end coordinate system E Angle of positive axis, Δh z is the vertical offset error of the probe, Δd x is the horizontal offset error of the probe, Δθ T It is the horizontal tilt angle error of the probe axis.

[0041] Figure 8 —The reconstruction results and surface reconstruction error diagram of complex component surface contour before and after structural parameter calibration and error separation. Among them, a) the reconstruction results and surface reconstruction error diagram of component surface contour before structural parameter calibration and error separation, b) the reconstruction results and surface reconstruction error diagram of component surface contour after only structural parameter calibration, c) the reconstruction results and surface reconstruction error diagram of component surface contour after structural parameter calibration and error separation.

[0042] Fig. 9 —Comparison of the maximum error and root mean square error of the model reconstruction before and after structural parameter calibration and error separation. Among them, a) the comparison of the maximum error of the model reconstruction before and after structural parameter calibration and error separation, b) the comparison of the root mean square error of the model reconstruction before and after structural parameter calibration and error separation. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions and advantages of the present invention more clear, the specific implementation modes of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0044] This embodiment provides the overall process of the component contour high-precision measurement method based on parameter calibration and error separation. Figure 1 shown.

[0045] The technical solution adopted by the method for high-precision measurement of component contour based on parameter calibration and error separation of the present invention is based on a robot contact measurement system and adopts contact measurement. First, median filtering is used to remove invalid data and outliers in the measurement data to obtain reliability measurement data, and then the measurement signal is subjected to empirical mode decomposition to separate the systematic errors caused by vibration and other disturbances in the sensor measurement signal; then a component contour measurement model is established, and the structural parameters of the robot measurement system are calibrated to solve the mapping of structural parameter errors to measurement results, eliminate the measurement deviation caused by sensor installation errors, and reduce the influence of sensor installation errors on measurement results; finally, the least squares method is used to reconstruct the measurement data into the component surface shape, and the maximum error and root mean square error results are obtained and analyzed, thereby achieving high-precision measurement of component contours. The specific steps of this method are as follows:

[0046] Step 1: Perform contact measurement on the contour of the workpiece to obtain reliable measurement data.

[0047] The workpiece to be measured is installed in the robot contact measurement system. The measurement system mainly consists of a parallel robot 1, a sensor fixture 2, a contact displacement sensor 3, a data acquisition device 4, and a computer 5. Figure 2The contact displacement sensor 3 is used to measure the inner side profile of the workpiece to obtain the actual sensor displacement signal. First, the collected original signal data is preliminarily processed to remove invalid data and abnormal values ​​in the measurement data, remove coarse noise, and obtain reliability measurement data x(t), as shown in Figure 3 shown.

[0048] Step 2: Perform empirical mode decomposition on the sampled data to separate the systematic noise caused by vibration and other disturbances.

[0049] right Figure 3 The displacement measurement signal x(t) obtained in the experiment is subjected to empirical mode decomposition to obtain 8 IMF components of the signal x(t). The frequency domain signal spectrum and time domain signal decomposition diagrams of all IMF components are shown in the following table: Figure 4 , Figure 5 Based on experience, the frequency range of effective measurement data is no higher than 50Hz. Figure 4 The frequencies of the IMF components are arranged from high frequency to low frequency. The main component frequencies corresponding to IMF1-4 components are higher than 50Hz, while the frequencies of IMF5 and later components are below 50Hz. Therefore, IMF5-8 components are initially selected as valid data components, corresponding to Figure 5 IMF5-8 components, further Figure 5 The IMF5-8 components are reconstructed into a signal to obtain the reconstructed displacement signal x′(t), as Figure 6 shown.

[0050] Step 3: Establish the component contour measurement model of the robot contact measurement system

[0051] In the robot contact measurement system, the parallel robot base coordinate system is used as the global measurement coordinate system, and the parallel robot base coordinate system {O W -X W Y W Z W}、Parallel robot terminal coordinate system {O E -X E Y E Z E}、Probe coordinate system {O T -X T Y T Z T},like Figure 2 shown.

[0052] According to the sensor installation size, the sensor probe center is relative to the origin of the parallel robot end coordinate system in the robot base coordinate system X W , Z W Distance in direction d x =15.60m / hz =133.64mm, sensor axis relative to parallel robot end coordinate system Z E Angle θ of the positive axis T =π / 4, such as Figure 7 As shown. Take a point at the end of the robot as an example, the position of this point is (x E ,y E ,z E )=(10,0,0-7)1, assuming that the robot end moving platform revolves around its base coordinate system Z W The input angle θ4 of the axis direction is counterclockwise rotation = 0°. Based on formulas (1)-(3), the probe coordinate system { T -X T Y T Z} T To the robot base coordinate system {O W -X W Y W Z W The transformation matrix between} is:

[0053]

[0054] Define the robot end (x E ,y E ,z E ) The displacement measurement data of the corresponding measuring point in the probe coordinate system is x(t) i =2.6mm, according to the transformation matrix from the probe coordinate system to the global measurement coordinate system W T T , the displacement measurement data x(t) of the measuring point in the probe coordinate system i Transfer to the global measurement coordinate system and use formula (4) to obtain the actual motion trajectory of the probe in the global measurement coordinate system: W P i ,for:

[0055]

[0056] Step 4: Solve the mapping relationship between structural parameter error and displacement measurement data

[0057] Assuming that the sensor installation error is measured and calibrated, the sensor installation error includes: the vertical offset error of the probe is Δh z =0.50mm, the horizontal offset error of the probe is Δd x =0.80mm, the horizontal tilt angle error of the probe axis is Δθ T =5°, such as Figure 7 Taking the above error parameters into account, the probe coordinate system {O T -X T YT Z} T To the robot base coordinate system {O W -X W Y W Z} W The actual transformation matrix between is:

[0058]

[0059] According to step 2, obtain the corresponding measurement point data x′(t) of the contact displacement sensor i = 2.54 mm, and then the actual motion trajectory of the probe in the global measurement coordinate system is solved based on formula (6): W P Ri ,for:

[0060]

[0061] The calculation method for other measuring points is the same. Take the measurement data of a certain layer on the component and calculate the positions of the measuring points before and after the structural parameter error calibration and error separation of this layer.

[0062] Step 5: Use the least squares method to reconstruct the measured data into the component surface shape

[0063] The least square method is used to calibrate the complex component measurement point data after structural parameter calibration and error separation. W P i , W P Ri Fitting is performed to reconstruct the complex component surface. The surface shapes before and after parameter calibration and error separation are fitted respectively, and the surface reconstruction error is further calculated. Figure 8 a) is the surface reconstruction result and reconstruction error map before structural parameter calibration and error separation. Figure 8 b) is the surface reconstruction result and reconstruction error diagram of only parameter calibration. Figure 8 c) is the model reconstruction result and reconstruction error diagram after structural parameter calibration and error separation. Fig. 9 a) is the comparison diagram of the maximum error of the model reconstruction before and after structural parameter calibration and error separation. Fig. 9b) is a comparison of the root mean square error of the model reconstruction before and after structural parameter calibration and error separation. The figure shows that before structural parameter calibration and error separation, the maximum error is 1.12mm and the root mean square error is 1.00mm; after only structural parameter calibration, the maximum error is 0.21mm and the root mean square error is 0.09mm; after structural parameter calibration and error separation, the maximum error is 0.14mm and the root mean square error is 0.08mm. Further, after structural parameter calibration, the maximum error is reduced from 1.12mm to 0.21mm, a decrease of 81.3%, and the root mean square error is reduced from 1.00mm to 0.09mm, a decrease of 91.0%; after structural parameter calibration and error separation, the maximum error is reduced from 1.12mm to 0.14mm, a decrease of 87.5%, and the root mean square error is reduced from 1.00mm to 0.08mm, a decrease of 92.0%, which verifies the effectiveness of this method.

Claims

1. A high-precision component contour measurement method based on parameter calibration and error separation, characterized in that: The method uses a robot contact measurement system to perform contact measurement on the contour of the sample to obtain measurement data; the measurement equipment in the robot contact measurement system consists of a parallel robot 1, a sensor fixture 2, a contact displacement sensor 3, a data collector 4, and a computer 5; firstly, a median filter is used to remove invalid data and abnormal values ​​in the measurement data to obtain reliability measurement data; and the measurement signal is subjected to empirical mode decomposition to separate the systematic errors caused by vibration and other disturbances in the sensor measurement signal, and finally a component contour measurement model is established, and the structural parameters of the robot measurement system are calibrated to solve the mapping from the structural parameter error to the measurement result, and the measurement deviation caused by the sensor installation error is eliminated to reduce the influence of the sensor installation error on the measurement result; and the least squares method is used to reconstruct the measurement data into the component surface shape to achieve high-precision measurement of the component contour; the specific steps of the method are as follows: Step 1, performing contact measurement on the contour of the workpiece to obtain reliable measurement data; The workpiece to be measured is installed in the robot contact measurement system, and the contact displacement sensor 3 is used to measure the inner side profile of the workpiece to obtain the actual sensor displacement signal; the actual displacement signal collected by the displacement sensor not only contains the actual profile data, but also contains the systematic error caused by signal disturbances such as vibration and random errors such as gross noise; firstly, the collected original signal data is preliminarily processed, and the invalid data and abnormal values ​​in the measurement data are removed by using the median filter to obtain the reliability measurement data x(t); Step 2: Perform empirical mode decomposition on the sampled data to separate the systematic noise caused by vibration and other disturbances; The contact displacement sensor sampling data after preliminary processing contains systematic errors caused by vibration and other disturbances. The empirical mode decomposition method is used to decompose the data, thereby obtaining all the intrinsic mode function (IMF) components of the signal x(t); then, the IMF components that are determined to play a dominant role in noise are separated, and the high-frequency IMF components representing noise are eliminated; the remaining effective signal components after removing the noise components are accumulated to complete the signal reconstruction, and finally the sensor measurement signal x′(t) after the systematic error separation is obtained; Step 3: Establish the component contour measurement model of the robot contact measurement system First, the robot base coordinate system {O W -X W Y W Z W } as the global measurement coordinate system, according to the robot kinematic equation, solve the robot end coordinate system {O E -X E Y E Z E } to the robot base coordinate system {O W -X W Y W Z W }The conversion relationship between: Among them, θ4 is the robot end moving platform around its base coordinate system Z W The input angle of rotation in the axial direction, the angular displacement direction conforms to the right-hand rule, x E ,y E ,z E is the offset of the center of the robot's terminal moving platform relative to the origin of the robot's base coordinate system, W T E is the coordinate transformation matrix from the robot end coordinate system to the robot base coordinate system; The probe center in the zero position state is taken as the origin of the probe coordinate system, and the direction of the sensor axis away from the probe is taken as the probe coordinate system Z T Axis positive direction, based on the robot end coordinate system Y E The positive axis is the probe coordinate system Y T Axis positive direction, determine X according to the right-hand rule T Axis positive direction, establish probe coordinate system {O T -X T Y T Z T }; Based on the sensor installation dimensions, the probe coordinate system in the zero position state is solved by coordinate transformation {O T -X T Y T Z T } to the robot end coordinate system {O E -X E Y E Z E } conversion relationship: Among them, d x 、h z The X coordinate of the sensor probe center relative to the center of the robot end moving platform in the robot base coordinate system W , Z W The offset distance in the direction, θ T Z is the sensor axis relative to the robot end coordinate system E The angle of the positive axis, E T T is the coordinate transformation matrix from the probe coordinate system to the robot end coordinate system; According to the transformation matrix from the robot end coordinate system to the global measurement coordinate system W T E And the transformation matrix from the probe coordinate system to the robot end coordinate system E T T , obtained from the probe coordinate system {O T -X T Y T Z T } to the robot base coordinate system {O W -X W Y W Z W }Transformation matrix between: W T T = W T E E T T (3) Define the displacement measurement data set in the probe coordinate system as x(t) i , according to the transformation matrix from the probe coordinate system to the global measurement coordinate system W T T , the displacement measurement data set x(t) in the probe coordinate system i Transfer to the global measurement coordinate system to obtain the actual motion trajectory point set of the probe in the global measurement coordinate system W P i : Step 4: Solve the mapping relationship between structural parameter error and displacement measurement data Since there are inevitably installation errors in the sensor installation process, such as the vertical offset size error of the probe, the horizontal offset size error of the probe, and the tilt angle error of the probe axis, these structural parameter errors will directly lead to errors in the measurement data; Define the following parameters: The vertical offset error of the probe is Δh z , the horizontal offset error of the probe is Δd x , the horizontal tilt angle error of the probe axis is Δθ T ; Get the probe coordinate system {O T -X T Y T Z T } to the robot base coordinate system {O W -X W Y W Z W The actual transformation matrix between} is: Therefore, the system measurement model with structural parameter errors is: Where x′(t) i Collecting data sets for the end displacement sensor after denoising and systematic error separation; Further, the true value of the structural parameter error of the robot measurement system is determined by measurement calibration, and the actual motion trajectory point set of the probe in the global measurement coordinate system is solved based on formula (6): W P Ri ; Step 5: Use the least squares method to reconstruct the measured data into the component surface shape The least squares method is used to fit the measured point data of complex components after structural parameter calibration and error separation, and the surface of the complex component is reconstructed. The surface shapes before and after parameter calibration and error separation are fitted respectively, and the surface reconstruction error is further calculated. The maximum error and root mean square error results are obtained and analyzed to verify the effectiveness of the method.

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