Contact Displacement Sensor Calibration Tooling and Complex Curved Surface Profile Measurement Method

Abstract

The present invention relates to a calibration tool for a contact displacement sensor and a method for measuring a complex surface profile. The present invention includes: based on the calibration tool, coaxial calibration of two contact displacement sensors is performed; based on the contact displacement sensors, measurement data of the complex surface profile is collected and processed; according to the local slope and local curvature changes, segmentation nodes are obtained, and according to the segmentation nodes, the complex surface profile is segmented to obtain a corrected fitting curve; polynomial fitting is performed on each segment in the complex surface profile to obtain the fitting error term of each segment; based on the segmentation nodes of each segment, a regularization term is constructed to enable smooth transition between segments; based on the corrected fitting curve, the fitting error term, and the regularization term, an objective function of the complex surface profile fitting curve is constructed; based on the objective function, the curve fitting result of the complex surface profile is obtained. The present invention achieves a high-precision profile fitting effect.

Description

Technical Field

[0001] The invention relates to the field of precision measurement technology, in particular to a contact displacement sensor calibration tool and a complex curved surface profile measurement method. Background Art

[0002] The measurement of complex curved surface contours is a key process to determine the machining allowance before grinding and polishing of complex curved surface parts, and to inspect the machining quality after grinding and polishing. The current mainstream measurement method is to use three-coordinate measuring equipment to measure the complex curved surface contours, but the three-coordinate measuring equipment cannot perform online measurement. If the test result is unqualified, it needs to be re-processed online. In addition, the three-coordinate measuring equipment itself is too expensive and requires a constant temperature, constant humidity and seismic isolation operating environment, resulting in low three-coordinate measurement efficiency and high measurement costs.

[0003] Existing public patents: A blade profile measurement method, device and system based on a line laser sensor, patent publication number CN111504223B, discloses a blade measurement method, device and system based on a line laser sensor, the line laser sensor measures partial contour data points of a complex surface, and then fits and splices the data points into a complete cross-sectional profile. This type of measurement method has certain limitations, such as water stains or grinding dust on complex surfaces that affect measurement accuracy; complex surfaces present a weak mirror effect after grinding and polishing, causing reflected light to scatter, resulting in the sensor being unable to collect reflected light; the large curvature of the complex surface causes the light reflection angle to be too large, which also causes the receiver to be unable to collect reflected light, seriously affecting measurement accuracy.

[0004] A contact displacement sensor is a sensor that directly contacts the object being measured and is used to measure the contour changes on the surface of the object. It has the advantages of high precision, good stability, simple structure and low cost. Existing public patents: an adjustment device, an optical device and a detection system, patent publication number CN221079022U, discloses an adjustment device, an optical device and a detection system, which designs a tooling for laser measurement sensors, with movement in three directions and rotation in two directions, and can adjust the installation posture of the laser measurement sensor at multiple angles for calibration. However, this tooling needs to be used with the calibration software that comes with the laser sensor to complete the calibration of the sensor measurement position, and cannot be used for the calibration of two independent contact displacement sensors.

[0005] During the measurement process, due to the influence of machining burrs, grinding dust, and roughness on the surface of the complex curved surface, a large amount of noise is generated in the measurement data, and there is an error between the fitted contour and the actual contour. Since the probe of the contact displacement sensor is in contact with the complex curved surface for a long time, the probe wears out, resulting in a decrease in measurement accuracy. Moreover, due to the different curved surface contours, the contact areas between the curved surface and the contact sensor are different, resulting in different wear degrees of different areas of the contact sensor probe. Therefore, adopting a suitable data fitting method and compensating the measurement results during the measurement process become the key technical points for improving and ensuring the measurement accuracy of the blade contour.

[0006] In addition, the commonly used methods for fitting measurement data currently include linear regression, least squares method, polynomial regression, neural network, and support vector machine regression, etc. The existing public patent: A data processing method, device, equipment, and medium based on linear fitting, patent publication number CN118484915A, discloses a data processing method, device, equipment, and medium based on linear fitting. It proposes a single-variable successive search strategy with three-layer loops, generates a prediction vector through linear fitting to more finely search for the optimal density difference and depth, and introduces linear fitting in the innermost layer to improve the solution efficiency and accuracy. The linear regression algorithm and the least squares method are often used to capture the linear relationship of data and perform poorly when facing non-linear data distributions. Although polynomial regression can handle non-linear relationships, when the polynomial order is too high, the model is prone to overfitting the training data, resulting in insufficient generalization ability for new data. In addition, polynomial regression requires a function that can fit complex curves, but the complex curved surface has a complex contour, with the characteristic that the outer contour changes with the cross-section position, and the contours of different parts vary greatly, making it difficult to accurately fit with a single function.

[0007] Although the neural network is a powerful non-linear model and is good at dealing with complex pattern recognition and fitting problems, it requires a large amount of data and computing resources. In addition, the internal structure of the neural network is complex, the decision-making process and prediction results are difficult to interpret, and it is impossible to achieve high-precision measurement of complex curved surfaces. The performance of support vector machine regression highly depends on hyperparameters (such as the selection of parameters such as the kernel function γ), the parameter tuning process is complex and requires a large number of cross-validation experiments to determine the optimal parameters. And in unbalanced datasets, the support vector machine regression method tends to the majority class and ignores the minority class, resulting in inaccurate fitting.

[0008] Considering the diversity and complexity of the contour function of the surface to be measured, the error between the actual surface and the theoretical model, and the requirement of high-precision measurement, there is an urgent need to design a lightweight and adaptive data fitting algorithm that can adapt to different surface contours to effectively process the measurement data of the complex surface contour collected. Summary of the Invention

[0009] To this end, the present invention provides a calibration tooling for a contact displacement sensor and a complex surface profile measurement method. The precise adjustment of the position and attitude of the sensor is achieved through the calibration tooling, ensuring the coaxial installation of two contact displacement sensors to improve the measurement accuracy. For different complex surface profiles, an adaptive segmented fitting, compensation, and smooth transition strategy is adopted to achieve a high-precision profile fitting effect.

[0010] To solve the above technical problems, the present invention provides a calibration tooling for a contact displacement sensor, including:

[0011] Based on the calibration tooling for the contact displacement sensor, coaxial calibration of two contact displacement sensors is performed;

[0012] Based on the contact displacement sensor, measurement data of the complex surface profile is collected;

[0013] The measurement data is denoised and filtered to obtain the processed measurement data;

[0014] Based on the processed measurement data, segmentation nodes are obtained according to the local slope and local curvature changes. According to the segmentation nodes, the complex surface profile is segmented;

[0015] Based on the processed measurement data, an initial fitting curve and a residual are obtained. The residual is polynomially fitted to obtain a polynomial form. Based on the polynomial form, a design matrix is constructed. Based on the design matrix, polynomial coefficients are obtained. Based on the polynomial coefficients, a compensation polynomial is obtained. Based on the compensation polynomial and the initial fitting curve, a corrected fitting curve is obtained;

[0016] Each segment of the complex surface profile is polynomially fitted to obtain the fitting error term for each segment;

[0017] Based on the segmentation nodes of each segment, a regularization term is constructed to enable smooth transition between segments;

[0018] Based on the corrected fitting curve, the fitting error term, and the regularization term, an objective function for the complex surface profile fitting curve is constructed. Based on the objective function, the curve fitting result of the complex surface profile is obtained;

[0019] Wherein, the calibration tooling for the contact displacement sensor includes:

[0020] A base;

[0021] An adjustment seat, adjustably connected to the base along a first direction;

[0022] A main bracket, pivoting on the adjustment seat with a second direction as the axis;

[0023] Auxiliary bracket, adjustably connected to the main bracket along the second direction;

[0024] Sensor mounting plate, pivotally mounted on the auxiliary bracket with the first direction as the axis. The sensor mounting plate is used to mount a contact displacement sensor, and the probe of the contact displacement sensor can be adjusted to extend along the third direction;

[0025] Wherein, the first direction, the second direction, and the third direction are perpendicular to each other in pairs.

[0026] In an embodiment of the present invention, it further includes a first support shaft, a second support shaft, and a first adjustment spring;

[0027] The first support shaft is installed on the base, and the adjustment seat is slidably connected to the base along the first direction through the first support shaft. Two first adjustment springs are sleeved on the first support shaft, and both ends of each first adjustment spring are limited by the adjustment seat and the base respectively;

[0028] A first locking member capable of abutting against the first support shaft is connected to the adjustment seat along the third direction to lock the relative position between the adjustment seat and the base;

[0029] The second support shaft is installed on the adjustment seat along the second direction, and the main bracket is rotatably connected to the adjustment seat through the second support shaft;

[0030] A first adjusting member connected to the second support shaft is connected to the middle end face of the adjustment seat along the second direction to adjust the angle between the main bracket and the adjustment seat.

[0031] In an embodiment of the present invention, it further includes a third support shaft and a second adjustment spring;

[0032] The third support shaft is installed on the main bracket, the auxiliary bracket is slidably connected to the third support shaft along the second direction, the second adjustment spring is sleeved on the third support shaft and both ends are limited by the auxiliary bracket and the main bracket respectively;

[0033] A second adjusting member abutting against the auxiliary bracket is connected to the main bracket along the second direction to adjust the relative position between the auxiliary bracket and the main bracket;

[0034] A second locking member abutting against the auxiliary bracket is connected to the main bracket along the first direction to lock the relative position between the auxiliary bracket and the main bracket.

[0035] In an embodiment of the present invention, it further includes a fourth support shaft and a rotary adjustment block;

[0036] The fourth support shaft is installed on the auxiliary bracket along the first direction, and the sensor mounting plate is rotatably connected to the auxiliary bracket through the fourth support shaft;

[0037] The rotation adjustment block is connected to the auxiliary bracket, and the rotation adjustment block is connected with a third adjustment member capable of abutting against the sensor mounting plate to adjust the angle between the sensor mounting plate and the auxiliary bracket.

[0038] In an embodiment of the present invention, the coaxial calibration of two contact displacement sensors includes:

[0039] Place the calibration block at the middle position between the two contact displacement sensors, and make the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block;

[0040] Rotate and adjust each contact displacement sensor around the y-axis to make its measured value reach the minimum;

[0041] Rotate and adjust each contact displacement sensor around the z-axis to make its measured value reach the minimum again, so that the probe axes of the two contact displacement sensors are parallel to the reference plane of the calibration block;

[0042] Place the calibration ball at the middle position between the two contact displacement sensors, horizontally move the probes of each contact displacement sensor along the y-axis direction to find the minimum value on the same horizontal plane;

[0043] Move the probes of each contact displacement sensor along the z-axis direction to find the minimum value in different height directions, so that the probe axes of the two contact displacement sensors are coaxial.

[0044] After the adjustment is completed, fix the positions of the two contact displacement sensors.

[0045] In an embodiment of the present invention, based on the processed measurement data, according to the local slope and local curvature changes, segmented nodes are obtained, and according to the segmented nodes, the complex surface contour is segmented, including:

[0046] Calculate the slope of each data point in the processed measurement data, and obtain the slope difference between the slopes of adjacent data points;

[0047] If the slope difference is greater than a preset slope change threshold, the corresponding data point is used as a segmented node;

[0048] Calculate the curvature of each data point in the processed measurement data;

[0049] If the curvature is greater than a preset curvature change threshold, the corresponding data point is also used as a segmented node;

[0050] Among them, the slope is calculated as follows:

[0051] ,

[0052] The slope difference is calculated as follows:

[0053] ,

[0054] The curvature is calculated as follows:

[0055] ,

[0056] Among them, is the slope of the i-th data point, and are the ordinate and abscissa of this point respectively, and are the ordinate and abscissa of the next point respectively, and are the ordinate and abscissa of the next-next data point respectively.

[0057] In an embodiment of the present invention, based on the processed measurement data, an initial fitting curve and a residual are obtained. The residual is polynomially fitted to obtain a polynomial form. Based on the polynomial form, a design matrix is constructed. Based on the design matrix, polynomial coefficients are obtained. Based on the polynomial coefficients, a compensation polynomial is obtained. Based on the compensation polynomial and the initial fitting curve, a corrected fitting curve is obtained, including:

[0058] Calculate the residual of each data point in the processed measurement data, that is, the difference between the actual value and the fitted value. Among them, the residual is defined as:

[0059] ,

[0060] Among them, is the actual data point, and are the ordinate and abscissa of the data point respectively, is the value of the initial fitting curve at the point , and the initial fitting curve is fitted by the spline interpolation method;

[0061] Perform polynomial fitting on the residual . For each data point , the polynomial form is:

[0062] , n is a positive integer;

[0063] For m data points, construct the design matrix X, specifically:

[0064] ,

[0065] Calculate the polynomial coefficients , specifically:

[0066] ,

[0067] where ; T is the transpose of the matrix;

[0068] Generate the compensation polynomial:

[0069] ,

[0070] where , ..., are the polynomial coefficients and n is a positive integer;

[0071] Modify the fitting curve to be the sum of the initial fitting curve and the compensation polynomial :

[0072] .

[0073] In one embodiment of the present invention, polynomial fitting is performed on each segment in the complex surface contour to obtain the fitting error term of each segment, including:

[0074] Within each segment, use the least squares method to solve the coefficients of the polynomial, gradually increase the order of the polynomial, and calculate the fitting error at each order ;

[0075] Adopt the mean square error MSE as the evaluation criterion, start fitting from the low-order polynomial until the decrease in the error is not greater than a preset threshold, where:

[0076] ,

[0077] where n is the number of data points, is the fitting error term.

[0078] In one embodiment of the present invention, the expression of the objective function is:

[0079] ,

[0080] where is the regularization term;

[0081] and are the derivatives of the k-th and (k + 1)-th segments at the boundary point respectively; K is a positive integer; is the fitting error term;

[0082] is the preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when is relatively small, the fitting error term dominates, and the curve is closer to the data points; when is relatively large, the regularization term dominates, and the curve is smoother.

[0083] The above technical solution of the present invention has the following advantages compared with the prior art:

[0084] The contact displacement sensor calibration tooling and the complex surface profile measurement method described in the present invention adjust the positions and angles of two contact displacement sensors through the calibration tooling and corresponding calibration steps to make them in a coaxial installation state, so that the theoretical measurement points coincide with the actual measurement points. And an adaptive piecewise fitting method is proposed, which uses the adaptive piecewise polynomial interpolation algorithm combined with the regularization algorithm to fit the measurement data, and adaptively compensates the measurement results based on the error between the actual profile and the fitted profile of the complex surface, improving the accuracy and stability of the complex surface profile measurement.

[0085] The present invention adaptively divides the overall data set into multiple curves that can be represented by different polynomial functions according to the slope change amplitude of the measurement data in different regions. Based on the error between the actual profile and the fitted profile, a polynomial compensation function is used to provide a bias for the measurement data on the basis of the initial fitting function to make up for the measurement error caused by the wear of the sensor probe. The polynomial interpolation algorithm is used for data fitting within each segment, and the least squares method is used to solve the polynomial coefficients to ensure the local fitting accuracy. A regularization term is introduced between the curves of each segment, and an objective function is constructed by combining the fitting error term and the regularization term to achieve the balance of smooth transition and closeness to the actual measurement data, realizing a high-precision profile fitting effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to make the content of the present invention easier to be clearly understood, the present invention will be further described in detail below according to the specific embodiments of the present invention and in conjunction with the accompanying drawings.

[0087] Figure 1 is the overall structural schematic diagram of the contact displacement sensor calibration tooling of the present invention.

[0088] Figure 2 is the exploded structural schematic diagram of the contact displacement sensor calibration tooling of the present invention.

[0089] Figure 3It is the adjustment direction diagram of the calibration tooling for the contact displacement sensor of the present invention.

[0090] Figure 4 It is the flow chart of the complex curved surface contour measurement method of the present invention.

[0091] Figure 5 It is the schematic diagram when the contact displacement sensor is installed non-coaxially.

[0092] Figure 6 It is the schematic diagram of coaxial calibration (using a calibration block) of the contact displacement sensor.

[0093] Figure 7 It is the schematic diagram of coaxial calibration (using a calibration ball) of the contact displacement sensor.

[0094] Explanation of the reference numerals in the specification drawings:

[0095] 1. Base; 11. First support shaft; 12. First adjustment spring; 13. First hole position;

[0096] 2. Adjusting seat; 21. Second support shaft; 22. Second hole position;

[0097] 3. Main support; 31. Third support shaft; 32. Second adjustment spring; 33. Third hole position; 34. Fourth hole position;

[0098] 4. Sub-support; 41. Fourth support shaft;

[0099] 5. Sensor mounting plate;

[0100] 6. Rotary adjustment block; 61. Fifth hole position. Detailed implementation manners

[0101] 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 embodiments cited are not intended to limit the present invention.

[0102] In the present invention, when directions (up, down, left, right, front and back) are described, it is only for the convenience of describing the technical solution of the present invention, rather than indicating or implying that the technical features referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0103] In the present invention, the meaning of "several" is one or more, the meaning of "multiple" is two or more, and understandings such as "greater than", "less than", "exceeding", etc. do not include the corresponding number; understandings such as "above", "below", "within" etc. include the corresponding number. In the description of the present invention, if there is a description of "first" and "second", it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence relationship of the indicated technical features.

[0104] In the present invention, unless otherwise clearly defined, words such as "arranged", "installed", "connected", etc. should be understood in a broad sense. For example, they can be directly connected, or indirectly connected through an intermediate medium; they can be fixedly connected, or detachably connected, or integrally formed; they can be mechanically connected, or electrically connected or capable of communicating with each other; they can be the communication inside two components or the interaction relationship between two components. Those skilled in the art can reasonably determine the specific meaning of the above words in the present invention in combination with the specific content of the technical solution.

[0105] Refer to Figures 1 to 3 As shown, a calibration tool for a contact displacement sensor includes:

[0106] Base 1;

[0107] Adjusting seat 2, which is adjustably connected to the base 1 along the first direction;

[0108] Main bracket 3, which pivots on the adjusting seat 2 with the second direction as the axis;

[0109] Auxiliary bracket 4, which is adjustably connected to the main bracket 3 along the second direction;

[0110] Sensor mounting plate 5, which pivots on the auxiliary bracket 4 with the first direction as the axis. The sensor mounting plate 5 is used to mount a contact displacement sensor, and the probe of the contact displacement sensor can be adjusted to extend along the third direction;

[0111] Wherein, the first direction, the second direction and the third direction are perpendicular to each other in pairs.

[0112] Specifically, it further includes a first support shaft 11, a second support shaft 21, and a first adjustment spring 12;

[0113] The first support shaft 11 is installed on the base 1, and the adjusting seat 2 is slidably connected to the base 1 along the first direction through the first support shaft 11. Two first adjustment springs 12 are sleeved on the first support shaft 11, and both ends of each first adjustment spring 12 are limited by the adjusting seat 2 and the base 1 respectively;

[0114] On the adjusting seat 2 (on the first hole position 13), a first locking member capable of abutting against the first support shaft 11 is connected along the third direction to lock the relative position between the adjusting seat 2 and the base 1; the first locking member can be a screw;

[0115] The second support shaft 21 is installed on the adjusting seat 2 along the second direction, and the main bracket 3 is rotatably connected to the adjusting seat 2 through the second support shaft 21;

[0116] On the middle end face of the adjusting seat 2 (on the second hole position 22), a first adjusting member connected to the second support shaft 21 is connected along the second direction to adjust the angle between the main bracket 3 and the adjusting seat 2. The first adjusting member can be a bolt;

[0117] Specifically, a third support shaft 31 and a second adjusting spring 32 are further included;

[0118] The third support shaft 31 is installed on the main bracket 3, the sub-bracket 4 is slidably connected to the third support shaft 31 along the second direction, and the second adjusting spring 32 is sleeved on the third support shaft 31 and its two ends are respectively limited by the sub-bracket 4 and the main bracket 3;

[0119] On the main bracket 3 (on the third hole position 33), a second adjusting member abutting against the sub-bracket 4 is connected along the second direction to adjust the relative position between the sub-bracket 4 and the main bracket 3; the second adjusting member can be a bolt;

[0120] On the main bracket 3 (on the fourth hole position 34), a second locking member abutting against the sub-bracket 4 is connected along the first direction to lock the relative position between the sub-bracket 4 and the main bracket 3; the second locking member can be a screw;

[0121] Specifically, a fourth support shaft 41 and a rotary adjustment block 6 are further included;

[0122] The fourth support shaft 41 is installed on the sub-bracket 4 along the first direction, and the sensor mounting plate 5 is rotatably connected to the sub-bracket 4 through the fourth support shaft 41;

[0123] The rotary adjustment block 6 is connected to the sub-bracket 4, and a third adjusting member capable of abutting against the sensor mounting plate 5 is connected to the rotary adjustment block 6 (on the fifth hole position 61) to adjust the angle between the sensor mounting plate 5 and the sub-bracket 4. The third adjusting member can be a bolt, and there are two of them, which are respectively installed on both sides of the rotary adjustment block 6 in the rotation direction of the sensor mounting plate 5.

[0124] It should be noted that in this embodiment, the first direction, the second direction, and the third direction are the y-axis, the z-axis, and the x-axis respectively.

[0125] Referring to Figure 4 as shown, this embodiment also provides a method for measuring the complex surface profile. Based on the coaxial relative installation of two contact displacement sensors, the complex surface profile is measured, including:

[0126] S1. Based on the calibration tooling of the contact displacement sensors, coaxial calibration of the two contact displacement sensors is performed.

[0127] Referring to Figure 5 as shown, since two independent contact displacement sensors are used for measurement, only relying on machining and installation accuracy cannot ensure the coaxial installation of the sensors, resulting in a position deviation between the theoretical measurement point and the actual measurement point. Therefore, it is necessary to calibrate the positions and postures of the two measurement sensors to improve the measurement accuracy.

[0128] Referring to Figure 6 and Figure 7 as shown, the calibration steps include:

[0129] Place the calibration block at the middle position between the two contact displacement sensors, so that the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block;

[0130] Rotate and adjust each contact displacement sensor around the y-axis to make its measured value reach the minimum;

[0131] Rotate and adjust each contact displacement sensor around the z-axis to make its measured value reach the minimum again, so that the probe axes of the two contact displacement sensors are parallel to the reference plane of the calibration block;

[0132] Place the calibration sphere at the middle position between the two contact displacement sensors, horizontally move the probes of each contact displacement sensor along the y-axis direction, and find the minimum value on the same horizontal plane;

[0133] Move the probes of each contact displacement sensor along the z-axis direction, find the minimum values in different height directions, and make the probe axes of the two contact displacement sensors coaxial.

[0134] After the adjustment is completed, fix the positions of the two contact displacement sensors.

[0135] S2. Based on the contact displacement sensors, collect the measurement data of the complex surface profile.

[0136] It should be noted that for the complex surface, only a simple linear movement between the two contact displacement sensors is required. By contacting different positions of the complex surface with the probes of the contact displacement sensors and according to the change of the contour amplitude, the probes expand and contract within the measurement range, and the contour of the complex surface can be measured to obtain the measurement data.

[0137] S3. Denoise and filter the measurement data to obtain the processed measurement data. Specifically, it includes:

[0138] First, use the mean filter method to clean the measurement data and remove outliers or noise. Set the window size for denoising to δ , and calculate the average value within around δ each data point. The formula is as follows:

[0139] ,

[0140] where is the processed data. Use a low-pass filter to filter the measurement data and remove high-frequency noise. The formula is as follows:

[0141] ,

[0142] where is the transfer function of the filter, is the frequency, is the cut-off frequency, is the order of the filter.

[0143] S4. According to the distribution characteristics of the processed measurement data, determine the number of segments of the overall contour and the initial node of each segment. Specifically: Based on the processed measurement data, obtain the segmentation nodes according to the local slope and local curvature changes, and segment the complex surface contour according to the segmentation nodes.

[0144] More specifically, it includes:

[0145] Calculate the local slope, that is, calculate the slope of each data point in the processed measurement data. The change trend of the curve is reflected by the slope. If the slope changes significantly, it indicates that there may be a mutation point or a transition point in the curve in this area;

[0146] Set the slope change threshold , and obtain the slope difference between adjacent data point slopes by traversing the slope sequence;

[0147] If the slope difference is greater than the preset slope change threshold , it is considered that there is a significant trend change at this point, and the corresponding data point is used as the segmentation node.

[0148] Subsequently, set k i as the curvature at point i, and set the curvature change threshold ;

[0149] Calculate the curvature of each data point in the processed measurement data ;

[0150] If the curvature is greater than a preset curvature change threshold , it indicates that there is a significant geometric shape change in this area, and the corresponding data points are also taken as segmentation nodes;

[0151] Among them, the slope is calculated as follows:

[0152] ,

[0153] The slope difference is calculated as follows:

[0154] ,

[0155] The curvature is calculated as follows:

[0156] ,

[0157] Among them, is the slope of the i-th data point, and are the ordinate and abscissa of this point respectively, and are the ordinate and abscissa of the next point respectively, and are the ordinate and abscissa of the next-next data point respectively.

[0158] It should be noted that the starting point of each segment is the end point of the previous segment, and the end point is the next detected segmentation node or the end point of the curve.

[0159] S5. Due to the diversity of complex surfaces, the wear degrees of different regions are different when the probe is measuring, so data compensation is required. The specific steps are as follows: Based on the processed measurement data, an initial fitting curve and a residual are obtained, the residual is polynomially fitted to obtain a polynomial form, based on the polynomial form, a design matrix is constructed, based on the design matrix, polynomial coefficients are obtained, based on the polynomial coefficients, a compensation polynomial is obtained, and based on the compensation polynomial and the initial fitting curve, a corrected fitting curve is obtained.

[0160] More specifically, it includes:

[0161] Calculate the residual of each data point in the processed measurement data, that is, the difference between the actual value and the fitted value. Among them, the residual is defined as:

[0162] ,

[0163] Among them, is the actual data point, is the value of the initial fitting curve at the point , and the initial fitting curve is fitted by spline interpolation;

[0164] For the residual perform polynomial fitting. For each data point , the polynomial form is:

[0165] , n where n is a positive integer;

[0166] For m data points, construct the design matrix:

[0167] ,

[0168] Calculate the polynomial coefficients , specifically:

[0169] ,

[0170] where, ;

[0171] Generate the compensation polynomial:

[0172] ,

[0173] where, , ..., are the polynomial coefficients and n is a positive integer;

[0174] Modify the fitting curve to be the superposition of the initial fitting curve and the compensation polynomial :

[0175] .

[0176] S6. Perform piecewise polynomial differential interpolation on the obtained modified curve F(x). Each segment is fitted using a polynomial. Use the least squares method to solve for the polynomial coefficients within each segment to ensure local fitting accuracy. Calculate the fitting error within each segment. Start fitting from a low-order polynomial and gradually increase the order until the decrease in error is no longer significant. The polynomial order selected at this time can avoid overfitting while ensuring fitting accuracy.

[0177] Specifically, perform polynomial fitting on each segment in the complex surface contour to obtain the fitting error terms for each segment, including:

[0178] Within each segment, the least squares method is used to solve for the coefficients of the polynomial. The order of the polynomial is gradually increased, and the fitting error at each order is calculated.

[0179] The mean squared error (MSE) is used as the evaluation criterion. Starting from a low-order polynomial, fitting is performed until the decrease in the error is no greater than a preset threshold, where:

[0180] ,

[0181] where, n is the number of data points, and is the fitting error term. When the decrease in MSE is no longer significant, the increase in the polynomial order can be stopped. The criterion for no longer being significant is set manually as a parameter.

[0182] S7. Based on the segment nodes of each segment, a regularization term is constructed to enable smooth transition between segments.

[0183] The regularization term is added to the objective function to control the smoothness of the entire fitting curve. The regularization term can be based on the first or second derivative of the curve, and smoothness is achieved by penalizing excessive derivative changes. Among them, the regularization term based on the first derivative restricts the slope change of the curve to ensure that the fitting curve is not too steep or undergoes drastic changes. Its function is:

[0184] ,

[0185] In the formula, and are the derivatives of the k-th and (k + 1)-th segments at the boundary point respectively. This regularization term penalizes the sudden change in the derivative at the segment boundary, enabling the fitting curve to maintain smooth transition between segments.

[0186] S8. Based on the corrected fitting curve, the fitting error term, and the regularization term, an objective function for the complex surface contour fitting curve is constructed. Based on the objective function, the curve fitting result of the complex surface contour is obtained.

[0187] Specifically, the expression of the objective function is:

[0188] ,

[0189] where, is the regularization term;

[0190] and are the derivatives of the k-th and (k + 1)-th segments at the boundary point respectively; is the fitting error term;

[0191] is a preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when is relatively small, the fitting error term dominates, and the curve is closer to the data points; when is relatively large, the regularization term dominates, and the curve is smoother. For the objective function, iterative optimization methods (such as gradient descent or quadratic optimization algorithms) can be used to solve it.

[0192] This objective function achieves the balance between fitting accuracy and curve smoothness. It combines the fitting error term and the regularization term to ensure that the fitting curve is close to the actual measurement data and has a smooth transition at the segmented boundaries.

[0193] This measurement method adjusts the position and attitude of the sensor through a calibration tooling, realizes the coaxial installation and measurement of two contact displacement sensors, and improves the measurement accuracy; and based on different complex surface profiles, adopts an adaptive segmented fitting, compensation and smooth transition method for the measurement data to achieve a high-precision profile fitting effect.

[0194] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0195] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0196] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device realizes the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1The functions specified in one or more boxes.

[0197] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide for implementing the steps of the functions specified in one or more processes and / or boxes Figure 1 One process or more processes and / or boxes Figure 1 The steps of the functions specified in one or more boxes.

[0198] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the examples, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A complex surface profile measurement method, characterized in that: include: Based on the contact displacement sensor calibration fixture, coaxial calibration of two contact displacement sensors is performed; Based on the contact displacement sensor, collecting measurement data of complex curved surface contours; Performing denoising and filtering processing on the measurement data to obtain processed measurement data; Based on the processed measurement data, segmentation nodes are obtained according to changes in local slope and local curvature, and segmentation processing is performed on the complex surface contour according to the segmentation nodes; Based on the processed measurement data, an initial fitting curve and residuals are obtained, polynomial fitting is performed on the residuals to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve; Perform polynomial fitting on each segment in the complex surface profile to obtain the fitting error term of each segment; Based on the segment nodes of each segment, a regularization term is constructed to make a smooth transition between segments; Based on the corrected fitting curve, the fitting error term and the regularization term, an objective function of the complex surface profile fitting curve is constructed, and based on the objective function, a curve fitting result of the complex surface profile is obtained; Wherein, the contact displacement sensor calibration tool comprises: Base (1); An adjustment seat (2) adjustably connected to the base (1) along a first direction; A main bracket (3) is pivoted on the adjustment seat (2) with the second direction as an axis; A secondary support (4) adjustably connected to the main support (3) along the second direction; A sensor mounting plate (5) is pivoted on the auxiliary bracket (4) with the first direction as an axis, the sensor mounting plate (5) being used to mount a contact displacement sensor, the probe of the contact displacement sensor being capable of being adjusted to extend along a third direction; The first direction, the second direction and the third direction are perpendicular to each other.

2. A complex curved surface profile measurement method according to claim 1, characterized in that: The contact displacement sensor calibration tool further comprises a first support shaft (11), a second support shaft (21), and a first adjustment spring (12); The first support shaft (11) is mounted on the base (1); the adjustment seat (2) is slidably connected to the base (1) along the first direction via the first support shaft (11); two first adjustment springs (12) are sleeved on the first support shaft (11), and two ends of each first adjustment spring (12) are respectively limited by the adjustment seat (2) and the base (1); A first locking member capable of abutting against the first supporting shaft (11) is connected to the adjustment seat (2) along the third direction to lock the relative position of the adjustment seat (2) and the base (1); The second support shaft (21) is mounted on the adjustment seat (2) along the second direction, and the main bracket (3) is rotatably connected to the adjustment seat (2) via the second support shaft (21); A first adjustment member connected to the second support shaft (21) is connected to the middle end surface of the adjustment seat (2) along the second direction to adjust the angle between the main support (3) and the adjustment seat (2).

3. A complex curved surface profile measurement method according to claim 1, characterized in that: The contact displacement sensor calibration tool further comprises a third support shaft (31) and a second adjustment spring (32); The third support shaft (31) is mounted on the main support (3), the auxiliary support (4) is slidably connected to the third support shaft (31) along the second direction, and the second adjustment spring (32) is sleeved on the third support shaft (31) and has two ends respectively limited by the auxiliary support (4) and the main support (3); The main support (3) is connected to a second adjusting member along the second direction and abuts against the auxiliary support (4) so ​​as to adjust the relative position between the auxiliary support (4) and the main support (3); The main bracket (3) is connected to a second locking piece along the first direction and abuts against the auxiliary bracket (4) so ​​as to lock the relative position between the auxiliary bracket (4) and the main bracket (3).

4. A complex surface profile measurement method according to claim 1, characterized in that: The contact displacement sensor calibration tool further comprises a fourth support shaft (41) and a rotation adjustment block (6); The fourth support shaft (41) is mounted on the auxiliary bracket (4) along the first direction, and the sensor mounting plate (5) is rotatably connected to the auxiliary bracket (4) via the fourth support shaft (41); The rotation adjustment block (6) is connected to the auxiliary bracket (4), and the rotation adjustment block (6) is connected to a third adjustment member capable of abutting against the sensor mounting plate (5) so as to adjust the angle between the sensor mounting plate (5) and the auxiliary bracket (4).

5. The complex surface profile measurement method according to claim 1, characterized in that: Perform a coaxial calibration of two contact displacement sensors, including: Place the calibration block in the middle of the two contact displacement sensors so that the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block; Rotate and adjust each contact displacement sensor around the y-axis to minimize its measured value; Rotate and adjust each contact displacement sensor around the z-axis so that its measured value reaches the minimum again, and make the probe axes of the two contact displacement sensors parallel to the reference plane of the calibration block; Place the calibration ball in the middle of the two contact displacement sensors, move the probes of each contact displacement sensor horizontally along the y-axis direction, and find the minimum value on the same horizontal plane; Move the probes of each contact displacement sensor along the z-axis direction to find the minimum value in different height directions, so that the probe axes of the two contact displacement sensors are coaxial; After the adjustment is completed, fix the positions of the two contact displacement sensors.

6. A complex surface profile measurement method according to claim 1, characterized in that: Based on the processed measurement data, segmentation nodes are obtained according to the local slope and local curvature changes, and segmentation processing is performed on the complex surface contour according to the segmentation nodes, including: Calculating the slope of each data point in the processed measurement data, and obtaining the slope difference between the slopes of adjacent data points; If the slope difference is greater than a preset slope change threshold, the corresponding data point is used as a segmentation node; calculating the curvature of each data point in the processed measurement data; If the curvature is greater than a preset curvature change threshold, the corresponding data point is also used as a segmentation node; Wherein, the slope is calculated as follows: ， The slope difference is calculated as follows: ， The curvature is calculated as follows: ， in, i represents a sequence of data points, It is i The slope of the data point, and are the ordinate and abscissa of the point, respectively. is the slope of the next data point, and They are the ordinate and abscissa of the next data point respectively; and They are the ordinate and abscissa of the next data point respectively.

7. A complex curved surface profile measurement method according to claim 6, characterized in that: Based on the processed measurement data, an initial fitting curve and a residual are obtained, a polynomial fitting is performed on the residual to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve, including: The residual of each data point in the processed measurement data is calculated, that is, the difference between the actual value and the fitted value, wherein the residual is defined as: ， in, is a data point, and are the ordinate and abscissa of the data point, respectively. is the initial fitting curve At the point The value at which the initial fitting curve Fitting by spline interpolation; Perform polynomial fitting, for each data point , the polynomial form is: , n is a positive integer; for m data points, construct the design matrix X, specifically: ， Calculate polynomial coefficients , specifically: ,in ; T is the transpose of the matrix; Generate the compensation polynomial: ,in is the polynomial coefficient, n is a positive integer; correct the fitting curve is the initial fitting curve With the compensation polynomial The superposition of .

8. A complex curved surface profile measurement method according to claim 7, characterized in that: Perform polynomial fitting on each segment in the complex surface profile to obtain the fitting error term of each segment, including: In each segment, the least squares method is used to solve the coefficients of the polynomial, gradually increasing the order of the polynomial and calculating the fitting error term at each order. ; Using mean square error (MSE) as the evaluation criterion, fitting starts from a low-order polynomial until the error decreases to no more than a preset threshold, where: , in, n is the number of data points, is the fitting error term.

9. A complex surface profile measurement method according to claim 8, characterized in that: The expression of the objective function is: ， in, is the regularization term; and The kth and k+1th segments are at the boundary points The derivative at ; k is a positive integer; is the fitting error term; is the preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when When it is small, the fitting error term dominates and the curve is closer to the data point; When it is larger, the regularization term dominates and the curve is smoother.

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