A method and system for in-situ measurement of radial profile accuracy of a small-diameter ball head grinding wheel under high-speed rotation

Abstract

The application provides a kind of small diameter ball head grinding wheel high-speed rotation under radial profile accuracy in-situ measurement method and system, belongs to ultra-precision machining technical field, to solve the existing in-situ detection method modeling analysis difficulty, the test environment and the test personnel requirement is strict, the test precision is limited.The problems include: S1, the laser displacement sensor data sampling system is built, the starting position is determined, and the relative distance data of the radial and laser displacement sensor is collected under the rotating state of the ball head grinding wheel;S2, the low-frequency interference signal in the sampling data is filtered and denoised;S3, based on the difference of the relative distance of the ball head grinding wheel and the laser displacement sensor under different registration angles, a ball head grinding wheel circumferential profile variation model is constructed, and the radial profile accuracy of the ball head grinding wheel is solved by using the special point substitution method.The in-situ measurement of the grinding wheel profile accuracy can be realized by the method, the modeling method is simple, easy to operate, and high measurement accuracy can be achieved.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision machining technology. Specifically, it relates to a method and system for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel. Background Technology

[0002] In recent years, precision and ultra-precision grinding has been increasingly widely used in aerospace, navigation, optics, and microelectronics. However, due to factors such as grinding wheel manufacturing errors and machining wear, the radial profile accuracy of small-diameter ball-end grinding wheels deteriorates, which in turn adversely affects the surface quality and machining accuracy of hemispherical harmonic oscillators. Therefore, how to accurately obtain the radial profile accuracy of small-diameter ball-end grinding wheels under high-speed rotation has become a key issue in ultra-precision machining.

[0003] Currently, contact-based and non-contact-based in-situ inspection technologies are the two most commonly used methods for obtaining the radial profile accuracy of ball-end grinding wheels. Contact-based in-situ inspection technologies, such as dial indicators, can achieve measurements at low speeds, but this method suffers from drawbacks such as low sensitivity, easy contact point damage, and inability to be used at high speeds. Over decades of development, various sensor technologies have significantly improved the reliability of non-contact in-situ inspection. Compared to contact-based in-situ inspection, this technology avoids the aforementioned shortcomings and offers advantages such as extremely high inspection speed and the ability to measure non-contact objects such as thin-walled parts. However, this in-situ inspection method is difficult to model and analyze, has stringent requirements for the testing environment and personnel, has limited testing accuracy (not reaching the micron / submicron level), and the measurement data is easily affected by the reflective properties of the workpiece surface. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing in-situ detection methods are difficult to model and analyze, have stringent requirements for the testing environment and personnel, have limited testing accuracy, and the measurement data are easily affected by the reflective properties of the workpiece surface.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel, comprising the following steps:

[0008] S1. Set up a laser displacement sensor data sampling system, determine the starting position for data acquisition, and collect the relative distance data between the radial direction of the ball head grinding wheel and the laser displacement sensor while the ball head grinding wheel is rotating.

[0009] S2. Filter and reduce noise for low-frequency interference signals in the sampled data;

[0010] S3. Based on the difference in relative distance between the ball end grinding wheel and the laser displacement sensor under different registration angles, a model of the variation law of the circumferential profile of the ball end grinding wheel is constructed, and the radial profile accuracy of the ball end grinding wheel is solved by substituting special points.

[0011] Furthermore, the construction of the laser displacement sensor data sampling system described in S1 includes the following steps:

[0012] S11. Connect the laser displacement sensor, data acquisition card and computer in series to form a data sampling system;

[0013] S12. Install the ball-head grinding wheel at a 40° angle and install the laser displacement sensor at a 40° angle on the micro-displacement platform of the machine tool.

[0014] S13. Adjust the relative position of the laser displacement sensor and the ball head grinding wheel so that the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface contour of the grinding wheel.

[0015] Furthermore, in S1, during the acquisition of the relative distance data between the radial direction of the ball-end grinding wheel and the laser displacement sensor, the filtering mode of the laser displacement sensor is set to low-pass filtering.

[0016] Furthermore, S2 performs filtering and noise reduction processing on the low-frequency interference signals in the sampled data, including the following steps:

[0017] The collected relative distance data x(t) is represented as:

[0018] x1(t)=s(t)+n(t) (1)

[0019] Where s(t) is the actual signal of relative distance data; n(t) is the low-frequency interference signal introduced during the acquisition process;

[0020] An improved empirical mode decomposition algorithm is used to denoise the data x(t), namely:

[0021] First, pairwise random white noise n with different amplitudes is added to the data x(t). i (t) and -n i (t), and ensure that the length of the added noise is consistent with the length of the original signal:

[0022]

[0023]

[0024] Secondly, the data after adding noise were analyzed separately. and EMD decomposition yields a series of IMF components: and

[0025] For the obtained IMF components and Perform aggregate averaging to obtain IMF data result C. j (t):

[0026]

[0027] The laser displacement sensor sampling data x(t) can be transformed into the following form:

[0028]

[0029] In the formula, r n (t) represents the residual signal, and n represents the number of IMF decomposition layers of the data x(t);

[0030] Finally, the corresponding frequency f is calculated based on the ball head grinding wheel speed, and the corresponding C is found based on this frequency value. j (t), at this time C j (t) is the denoised data of the sampled relative distance data x1(t) after processing by the improved empirical mode decomposition algorithm.

[0031] Furthermore, the model for the variation law of the circumferential profile of the ball-end grinding wheel described in S3 is specifically as follows:

[0032]

[0033] In the formula, R jx_out R is the radial runout of the ball-end grinding wheel. jx Dis is the radial circumferential radius of the ball-end grinding wheel. ε With Dis ξ h represents the relative distance between the ball-end grinding wheel and the laser displacement sensor sampled at registration angles θ = ε and θ = ξ after noise reduction, respectively. ξ with h ε This represents the protrusion height of the diamond abrasive grain at the radial circumference profile of the grinding wheel when the registration angles θ = ε and θ = ξ, and the registration angles ε and ξ are arbitrarily selected registration angles. This is the simplified form of equation (6). denoted as φ θ .

[0034] Furthermore, the process of solving for the radial profile accuracy of the ball-end grinding wheel based on the model, as described in S3, includes the following steps:

[0035] S31. Solve the model of the variation law of the circumferential profile of the ball-end grinding wheel by substituting special points;

[0036] Let i1 = δ, i2 = δ + β and i3 = δ - β, where β is the angular increment of the registration angle. According to formula (6), we can obtain:

[0037]

[0038]

[0039] By combining equations (7) and (8), we can obtain:

[0040]

[0041] In equation (9) Let it be X1. Let it be Y1, then:

[0042]

[0043] Since there is an error between the sampled data and the true value of the laser displacement sensor, then:

[0044]

[0045] Based on the repeatability accuracy value of the laser displacement sensor, the sampling error err is eliminated by calculating the average value of the data.

[0046]

[0047] Where, in the formula These are respectively the results of calculating the average value of the laser displacement sensor sampling data;

[0048] S32. Solving the radial runout R of a ball-end grinding wheel using cosine function fitting method. jx_out Measure the radial circumferential radius R of the grinding wheel while it is stationary. jx Further, the protrusion height h of the diamond abrasive grain is determined. θ ;

[0049] Perform a cosine function fit on equation (12) and divide the amplitude of the fit result by -4·sin(β / 2). 2 This is the radial runout R of the inner support rod. jx_out ;

[0050] Because the angle β is small, the abrasive grain protrusion height h corresponding to the angle on the grinding wheel circumference profile is... θ The height of the abrasive grains corresponding to i1, i2, and i3 will not change significantly, therefore the height of the abrasive grains corresponding to i1, i2, and i3 will be adjusted accordingly. and If we consider it as a straight line, then in equation (9) The result is 0. Further, the radius R of the circumferential profile of the ball-end grinding wheel can be calculated. jx ;

[0051] Assume h ε=a and substitute into equation (6) to solve for h. ξ By continuously changing the angle increment β, the diamond abrasive grain protrusion height h of the ball-end grinding wheel radial circumferential profile under different registration angles θ can be obtained. θ ;

[0052] S33. Solve for the radial profile accuracy of the ball-end grinding wheel;

[0053] Based on the obtained radial circumferential radius R of the ball-end grinding wheel jx And the assumed abrasive grain protrusion height h θ The radial profile dimensions of the ball-end grinding wheel under different registration angles θ are solved.

[0054] The minimum radius R corresponding to the radial profile dimension of the ball-end grinding wheel jx_min and the maximum radius R jx_max The difference is taken as the radial profile accuracy R of the ball-end grinding wheel. jx_acc :

[0055] R jx_acc =R jx_max -R jx_min (13).

[0056] A system for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel is provided. The system has a program module corresponding to the steps of any of the above-mentioned technical solutions, and executes the steps in the above-mentioned method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel during operation.

[0057] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of the method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel as described in any of the above technical solutions.

[0058] Compared with the prior art, the beneficial effects of the present invention are:

[0059] This invention discloses an in-situ measurement method and system for the radial profile accuracy of a small-diameter ball-end grinding wheel under high-speed rotation. First, based on the difference in relative distance between the ball-end grinding wheel and a laser displacement sensor under different registration angles, a model of the circumferential profile variation of the ball-end grinding wheel is constructed, enabling in-situ measurement of the grinding wheel's profile accuracy. The modeling method of this invention is simple, easy to operate, and achieves high measurement accuracy, providing a theoretical basis for grinding wheel dressing and replacement, laying the foundation for improving the surface quality and machining accuracy of ultra-precision grinding of complex thin-walled components, and reducing the possibility of machining accidents. Second, the method of this invention has a certain degree of universality; it is not only applicable to solving the radial profile accuracy of small-diameter ball-end grinding wheels, but can also be extended to the radial profile detection of other rotary tools. Attached Figure Description

[0060] Figure 1 This is a flowchart of the in-situ measurement method for radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel in an embodiment of the present invention;

[0061] Figure 2 This is a schematic diagram of the radial profile accuracy detection of a small-diameter ball-head grinding wheel in an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram showing the relative position of the laser displacement sensor and the grinding wheel in an embodiment of the present invention;

[0063] Figure 4 This is a time-frequency domain waveform diagram of the laser displacement sensor sampling signal in an embodiment of the present invention;

[0064] Figure 5 The time-frequency domain signal image is used for denoising based on the improved empirical mode decomposition algorithm in this embodiment of the invention.

[0065] Figure 6 This is a schematic diagram illustrating the runout of a small-diameter ball-head grinding wheel during high-speed rotation in an embodiment of the present invention.

[0066] Figure 7 This is a graph showing the fitting and residual values ​​of the cftool toolbox in this embodiment of the invention;

[0067] Figure 8 This is a schematic diagram showing the protrusion height of the abrasive grains on the small-diameter ball-head grinding wheel in an embodiment of the present invention;

[0068] Figure 9 The abrasive grain protrusion heights corresponding to different registration angles in the embodiments of the present invention;

[0069] Figure 10 This is a diagram showing the radial profile dimensions and accuracy of a small-diameter ball-head grinding wheel in an embodiment of the present invention. Detailed Implementation

[0070] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0071] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0072] Specific Implementation Plan 1: (e.g.) Figure 1As shown, this invention provides a method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel, comprising the following steps:

[0073] S1. Set up a laser displacement sensor data sampling system, determine the starting position for data acquisition, and collect the relative distance data between the radial direction of the ball head grinding wheel and the laser displacement sensor while the ball head grinding wheel is rotating.

[0074] S2. Filter and reduce noise for low-frequency interference signals in the sampled data;

[0075] S3. Based on the difference in relative distance between the ball end grinding wheel and the laser displacement sensor under different registration angles, a model of the variation law of the circumferential profile of the ball end grinding wheel is constructed, and the radial profile accuracy of the ball end grinding wheel is solved according to the model.

[0076] This invention defines the registration angle θ as the angle between the line connecting the geometric center O1 of the ball-end grinding wheel and the actual center O2 during high-speed rotation, and the horizontal line; for example... Figure 6 As shown, due to factors such as installation and manufacturing errors, the geometric center O1 and the actual center O2 of the ball-end grinding wheel may not coincide during high-speed rotation. Therefore, to better describe the position of the actual center O2, this invention constructs a model of the variation law of the circumferential profile of the ball-end grinding wheel based on the difference in the relative distance between the ball-end grinding wheel and the laser displacement sensor under different registration angles.

[0077] By measuring different radial profile accuracies of ball-end grinding wheels in place, the worst-case radial profile accuracy region of the ball-end grinding wheel was determined. This information was then used to analyze the main factors affecting the radial profile accuracy of the grinding wheel. For example, if the worst-case radial profile accuracy region appears in the area of ​​most severe wear, it means that the main factor affecting the radial profile accuracy is grinding wheel wear; if the worst-case radial profile accuracy region appears at the position of maximum / minimum equivalent radius, it means that the grinding wheel speed has the greatest impact on the radial profile accuracy, etc. This provides a basis for optimizing the subsequent ultra-precision grinding process.

[0078] Specific Implementation Plan Two: (e.g.) Figure 2 As shown, the construction of the laser displacement sensor data sampling system described in S1 includes the following steps:

[0079] S11. Connect the laser displacement sensor, data acquisition card and computer in series to form a data sampling system;

[0080] S12. Install the ball-head grinding wheel at a 40° angle and install the laser displacement sensor at a 40° angle on the micro-displacement platform of the machine tool.

[0081] S13. Adjust the relative position of the laser displacement sensor and the ball-end grinding wheel so that the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface contour of the grinding wheel. The rest of this implementation scheme is the same as in specific implementation scheme one.

[0082] like Figure 3 As shown, adjust the relative position of the ball-end grinding wheel and the laser displacement sensor. By adjusting the positions of the X, Y, and Z axes of the machine tool, ensure that the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface of the ball-end grinding wheel. At this point, fix the laser displacement sensor in the XY plane of the machine tool with screws.

[0083] Specific Implementation Scheme 3: During the acquisition of the relative distance data between the radial direction of the ball-end grinding wheel and the laser displacement sensor in S1, the filtering mode of the laser displacement sensor is set to low-pass filtering. All other aspects of this implementation scheme are the same as Specific Implementation Scheme 1.

[0084] In this implementation scheme, the LK-H020 laser displacement sensor is used. Due to the high rotation speed of the ball head grinding wheel (114,000 rpm), in order to ensure the accuracy and quantity of the sampled data and reduce the interference of external noise signals on the sampling process, the relevant parameters of the laser displacement sensor need to be set before data acquisition. The specific results are shown in Table 1.

[0085] Table 1

[0086]

[0087] Acquire the radial profile signal x(t) of the ball-end grinding wheel. Turn on the laser displacement sensor and preheat for 30 minutes, then control the U-axis and Z-axis to move the small-diameter ball-end grinding wheel to the measurement position. Subsequently, during the high-speed rotation of the ball-end grinding wheel, as... Figure 4 As shown, a laser displacement sensor is used to collect data on its radial profile.

[0088] Specific implementation plan four: In S2, low-frequency interference signals in the sampled data are filtered and denoised, including the following steps:

[0089] The collected relative distance data x(t) is represented as:

[0090] x1(t)=s(t)+n(t) (1)

[0091] Where s(t) is the actual signal of relative distance data; n(t) is the low-frequency interference signal introduced during the acquisition process;

[0092] An improved empirical mode decomposition algorithm is used to denoise the data x(t), namely:

[0093] First, pairwise random white noise n with different amplitudes is added to the data x(t). i (t) and -n i (t), and ensure that the length of the added noise is consistent with the length of the original signal:

[0094]

[0095]

[0096] Secondly, the data after adding noise were analyzed separately. and EMD decomposition yields a series of IMF components: and

[0097] For the obtained IMF components and Perform aggregate averaging to obtain IMF data result C. j (t):

[0098]

[0099] The laser displacement sensor sampling data x(t) can be transformed into the following form:

[0100]

[0101] In the formula, r n (t) represents the residual signal, and n represents the number of IMF decomposition layers of the data x(t);

[0102] Finally, the corresponding frequency f is calculated based on the ball head grinding wheel speed, and the corresponding C is found based on this frequency value. j (t), at this time C j (t) is the denoised data of the sampled relative distance data x1(t) after processing by the improved empirical mode decomposition algorithm. The rest of this implementation scheme is the same as that of specific implementation scheme one.

[0103] In this implementation scheme, although a low-pass filter is set in S1, low-frequency interference signals n(t) caused by environmental factors and machine tool vibrations are inevitably introduced during laser displacement sensor sampling. To ensure the reliability of subsequent analysis results, the sampled signal needs to be processed to obtain the true signal s(t) reflecting the radial profile of the small-diameter ball-end grinding wheel. The improved empirical mode decomposition algorithm is effective in denoising signals, especially nonlinear and non-stationary signals. Therefore, this implementation scheme uses the improved empirical mode decomposition algorithm to denoise the sampled signal x(t), and the results are as follows. Figure 5 As shown.

[0104] Specific implementation plan five: The model of the variation law of the circumferential profile of the ball-end grinding wheel described in S3 is as follows:

[0105]

[0106]

[0107] In the formula, R jx_out R is the radial runout of the ball-end grinding wheel. jx Dis is the radial circumferential radius of the ball-end grinding wheel. ε With Dis ξ h represents the relative distance between the ball-end grinding wheel and the laser displacement sensor when the registration angles θ = ε and θ = ξ, respectively. ξ with h ε This represents the protrusion height of the diamond abrasive grain at the radial circumferential profile of the grinding wheel when the registration angles θ = ε and θ = ξ. The registration angles ε and ξ are arbitrarily chosen. To simplify the calculation process, the registration angle θ used in the analysis process usually has a certain correlation, that is, the solution is achieved based on special points. At the same time, to simplify the writing of formula (6), the following is used: denoted as φ θ This implementation plan is otherwise the same as Specific Implementation Plan One.

[0108] Specific Implementation Scheme Six: The process described in S3 for solving the radial profile accuracy of the ball-end grinding wheel based on the model includes the following steps:

[0109] S31. Solve the model of the variation law of the circumferential profile of the ball-end grinding wheel by substituting special points;

[0110] Since the calculation process of equation (6) includes trigonometric functions, the calculation method based on the substitution of special points can effectively simplify the calculation process and better realize the solution of the model of the change law of the circumferential profile of the ball head grinding wheel.

[0111] Let i1 = δ, i2 = δ + β and i3 = δ - β, where β is the angular increment of the registration angle. According to formula (6), we can obtain:

[0112]

[0113]

[0114] By combining equations (7) and (8), we can obtain:

[0115]

[0116] In equation (9) Let it be X1. Let it be Y1, then:

[0117]

[0118] Because there is an error between the sampled data and the true value of the laser displacement sensor, the single sampling accuracy of the LK-H020 laser displacement sensor is ±1.2μm. Therefore:

[0119]

[0120] Since the sampling error err significantly affects the reliability of subsequent analysis results, and given that the repeatability of the LK-H020 laser displacement sensor is ±0.01μm, the sampling error err is eliminated based on the data mean calculation method, according to the repeatability value of the laser displacement sensor.

[0121]

[0122] Where, in the formula These are respectively the results of calculating the average value of the laser displacement sensor sampling data;

[0123] S32. Solving the radial runout R of a ball-end grinding wheel using cosine function fitting method. jx_out Measure the radial circumferential radius R of the grinding wheel while it is stationary. jx Further, the protrusion height h of the diamond abrasive grain is determined. θ ;

[0124] According to equation (12), From cosine trigonometric functions -4·R jx_out ·cosδ·sin(β / 2) 2 It consists of the residual value X1+Y1, therefore, as Figure 7 As shown, the cosine function of equation (12) is fitted using the cftool toolbox in MATLAB, and the amplitude of the fitting result is divided by -4·sin(β / 2). 2 The result is the radial runout R of the inner support rod. jx_out The minimum value corresponds to an angle δ of 0°.

[0125] Because the angle β is small, the abrasive grain protrusion height h corresponding to the angle on the grinding wheel circumference profile is... θ It will not change significantly, therefore, as Figure 8 As shown, the abrasive grain protrusion heights corresponding to i1, i2, and i3 are... and If we consider them as three points on a straight line y = kx + b, then in equation (9) The result is 0. Further, the radius R of the circumferential profile of the ball-end grinding wheel can be calculated. jx The result was 1783.5 μm;

[0126] Based on the foregoing analysis, the radial circumferential radius R of the ball-end grinding wheel jx Circumferential radial runout R jx_out All are known, let h ε =10 and substitute it into equation (6) to solve for h. ξ ,like Figure 9As shown, by continuously changing the angle increment β, the diamond abrasive grain protrusion height h of the radial circumferential profile of the ball-end grinding wheel under different registration angles θ can be obtained. θ ;

[0127] S33. Solve for the radial profile accuracy of the ball-end grinding wheel;

[0128] Based on the obtained radial circumferential radius R of the ball-end grinding wheel jx And the assumed abrasive grain protrusion height h θ The radial profile dimensions of the ball-end grinding wheel under different registration angles θ were solved, and the results are as follows: Figure 10 As shown in (a);

[0129] like Figure 10 As shown in (b), the radial circumferential radius R jx and abrasive grain protrusion height h θ By converting the sum to polar coordinates, the minimum radius R corresponding to the radial profile dimension of the ball-end grinding wheel can be determined. jx_min and the maximum radius R jx_max The difference between the two is the radial profile accuracy R of the ball-end grinding wheel. jx_acc ;

[0130] R jx_acc =R jx_max -R jx_min (13).

[0131] This implementation plan is otherwise the same as Specific Implementation Plan Five.

[0132] This implementation scheme considers the sampling error err of the laser displacement sensor. The existence of sampling error err seriously affects the reliability of subsequent analysis results. The single sampling accuracy of the LK-H020 laser displacement sensor is ±1.2μm. Since the repeatability accuracy of the LK-H020 laser displacement sensor is ±0.01μm, the sampling error err is eliminated by calculating the average of the data.

[0133] Specific Implementation Scheme Seven: A system for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel. This system has a program module corresponding to the steps of any of the above implementation schemes, and executes the steps in the above-described method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel during operation.

[0134] Specific implementation scheme eight: A computer-readable storage medium storing a computer program configured to, when called by a processor, implement the steps of the method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel as described in any of the above implementation schemes.

[0135] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel, characterized in that, Includes the following steps: S1. Set up a laser displacement sensor data sampling system, determine the starting position for data acquisition, and collect the relative distance data between the radial direction of the ball head grinding wheel and the laser displacement sensor while the ball head grinding wheel is rotating. S2. Filter and reduce noise for low-frequency interference signals in the sampled data; S3. Based on the difference in relative distance between the ball end grinding wheel and the laser displacement sensor under different registration angles, a model of the variation law of the circumferential profile of the ball end grinding wheel is constructed, and the radial profile accuracy of the ball end grinding wheel is solved by substituting special points. The construction of the laser displacement sensor data sampling system described in S1 includes the following steps: S11. Connect the laser displacement sensor, data acquisition card and computer in series to form a data sampling system; S12. Install the ball-head grinding wheel at a 40° angle and install the laser displacement sensor at a 40° angle on the micro-displacement platform of the machine tool. S13. Adjust the relative position of the laser displacement sensor and the ball head grinding wheel so that the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface contour of the grinding wheel. The model of the variation law of the circumferential profile of the ball-end grinding wheel described in S3 is as follows: （6） In the formula, This refers to the radial runout of the ball-end grinding wheel. The radial circumferential radius of the ball-end grinding wheel. and These represent the registration angles after noise reduction. and The relative distance between the ball-head grinding wheel and the laser displacement sensor is sampled in real time. and This indicates the registration angle. and The protrusion height of the diamond abrasive grains at the radial circumferential profile of the grinding wheel, and the registration angle. and For any chosen registration angle, and for the simplified form of (6), the following will be used: Recorded as .

2. The method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel according to claim 1, characterized in that, In S1, during the acquisition of the relative distance data between the radial direction of the ball head grinding wheel and the laser displacement sensor, the filtering mode of the laser displacement sensor is set to low-pass filtering.

3. The method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel according to claim 1, characterized in that, S2 performs filtering and noise reduction processing on low-frequency interference signals in the sampled data, including the following steps: For the collected relative distance data Represented as: （1） in, This represents the actual signal of the relative distance data; Low-frequency interference signals introduced during the acquisition process; An improved empirical mode decomposition algorithm is used to analyze the data. Noise reduction processing is performed, that is: First, in the data Add paired random white noise with different amplitudes and And ensure that the length of the added noise is consistent with the length of the original signal: （2） （3） Secondly, the data after adding noise were analyzed separately. and EMD decomposition yields a series of IMF components: and ; For the obtained IMF components and Perform aggregate averaging to obtain the IMF data results. : （4） Data sampled by laser displacement sensor Transform it into the following form: （5） In the formula, For residual signals, For data The number of IMF decomposition layers; Finally, the corresponding frequency f is calculated based on the ball head grinding wheel speed, and the corresponding frequency value is found based on this frequency value. ,at this time That is, the relative distance data sampled. Noise-reduced data after processing with an improved empirical mode decomposition algorithm.

4. The method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel according to claim 1, characterized in that, The process of solving for the radial profile accuracy of the ball-end grinding wheel as described in S3 includes the following steps: S31. Solve the model of the variation law of the circumferential profile of the ball-end grinding wheel by substituting special points; make , and β is the angular increment of the registration angle, which can be obtained according to formula (6): （7） （8） By combining equations (7) and (8), we can obtain: （9） In equation (9) Recorded as , Recorded as ,but: （10） Since there is an error between the sampled data and the true value of the laser displacement sensor, then: （11） Based on the repeatability accuracy value of the laser displacement sensor, the sampling error err is eliminated by calculating the average value of the data. （12） Where, in the formula These are respectively the results of calculating the average value of the laser displacement sensor sampling data; S32. Solving the radial runout of a ball-end grinding wheel using cosine function fitting. Measure the radial circumference of the grinding wheel while it is stationary. Further determine the protrusion height of the diamond abrasive grains. ; Perform a cosine function fit on equation (12), and divide the amplitude of the fit result by... This is the radial runout of the inner support rod. ; Due to the angle Smaller, the abrasive grain protrusion height corresponding to the angle on the grinding wheel's circumferential profile. It will not change significantly, therefore... , and Corresponding abrasive grain protrusion height , and If we consider it as a straight line, then in equation (9) The result is 0. Further, the radius of the circumferential profile of the ball-end grinding wheel can be calculated. ; Assumption Substituting this into equation (6), we can then solve for the solution. Then continuously change the angle increment As a result, the radial circumferential profile of the ball-end grinding wheel can be obtained at different registration angles. The protrusion height of the diamond abrasive grains below ; S33. Solve for the radial profile accuracy of the ball-end grinding wheel; Based on the obtained radial circumference radius of the ball-end grinding wheel and the assumed abrasive grain protrusion height For different registration angles of ball-end grinding wheels The radial profile dimensions are solved. The minimum radius corresponding to the radial profile dimension of the ball-end grinding wheel and maximum radius The difference is used as the radial profile accuracy of the ball-end grinding wheel. : （13）。 5. A system for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel, characterized in that, The system has a program module corresponding to the steps of any one of the claims 1 to 4 above, and executes the steps in the above-described method for measuring the radial profile accuracy under high-speed rotation of a small-diameter ball-head grinding wheel.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for in-situ measurement of radial profile accuracy under high-speed rotation of a small-diameter ball-end grinding wheel as described in any one of claims 1 to 4.

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