An analytical method for determining the wear amount of small-diameter ball-end grinding wheels in ultra-precision grinding based on reciprocating scanning using a laser displacement sensor.

Abstract

This invention provides an analytical method for determining the wear amount of small-diameter ball-end grinding wheels in ultra-precision grinding based on reciprocating scanning using a laser displacement sensor. It relates to the field of ultra-precision machining technology and addresses the problems of existing measurement methods being susceptible to interference signals and machine tool vibrations, and the unsuitability of contact measurements for analyzing the relatively small wear of small-diameter ball-end grinding wheels. This invention uses a laser displacement sensor to calibrate the wheel axis tilt angle β; it uses the laser displacement sensor to reciprocately collect relative displacement data of the ball-end grinding wheel, and performs data filtering and noise reduction processing to fit the ball-end grinding wheel profile dimensions; by comparing the ball-end grinding wheel profile dimensions with those of a reference ball-end grinding wheel, the wear amount of the ball-end grinding wheel after ultra-precision grinding is obtained. This invention achieves real-time, in-situ monitoring of the radial profile dimensions of the ball-end grinding wheel, contributing to the realization of efficient and high-precision ultra-precision grinding processes.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ultra-precision machining, in particular to an analysis method for determining the wear of a small-diameter ball head grinding wheel in ultra-precision grinding based on laser displacement sensor reciprocating scanning. BACKGROUND

[0002] Ultra-precision grinding has the advantages of high machining quality and efficiency, strong adaptability, and low machining cost, and has become one of the mainstream methods for realizing the machining of complex thin-walled components at the present stage. With the continuous increase of the grinding period, the grinding tool such as the ball head grinding wheel will inevitably change in the radial dimension, that is, wear will occur, and if the change value of the radial dimension exceeds the threshold range, it will affect the surface type precision and surface quality of the machined part. Based on this, how to efficiently and accurately monitor the radial dimension of the grinding tool has become the key to improving the grinding efficiency and surface quality and reducing surface / subsurface damage.

[0003] At present, the measurement methods for the radial dimension of small-diameter grinding wheels include conventional measurement tools such as vernier calipers, projection measurement method, and displacement sensor measurement. Among them, the detection process of conventional tool measurement is convenient and the detection cost is low, but the detection accuracy is poor, so this detection method is mainly used in occasions where the size accuracy requirement is not strict. The projection measurement method is to obtain the three-dimensional topography of the measured object through projection, and to solve the corresponding contour size according to the topographic features, but this method is mostly used for offline measurement and the measurement cost is relatively high. In addition, the detection result is greatly affected by human subjective factors. Compared with the first two test methods, the size measurement method based on displacement sensor greatly improves the measurement efficiency while ensuring that the measurement result accuracy meets the requirements, and has become the main way for the size measurement of ball head grinding wheels at present, but the interference signals and machine tool vibration introduced in the test process will affect the authenticity of the test results, and the existing in-situ measurement is mostly contact measurement, and its resolution is not suitable for small-diameter ball head grinding wheel wear analysis. SUMMARY

[0004] The technical problem to be solved by the present application is:

[0005] The existing measurement method is susceptible to interference signals and machine tool vibration, and contact measurement is not suitable for small-diameter ball head grinding wheel wear analysis.

[0006] The technical scheme adopted by the present application to solve the above technical problems is:

[0007] The present application provides an analysis method for determining the wear of a small-diameter ball head grinding wheel in ultra-precision grinding based on laser displacement sensor reciprocating scanning, comprising the following steps:

[0008] Step one: connect the laser displacement sensor with the micro displacement platform, and fix the laser displacement sensor and the micro displacement platform in the X-Y plane of the machine tool;

[0009] Step two: clamp the unused ball head grinding wheel at the end of the tool spindle as the reference for measuring the grinding wheel wear;

[0010] Step three: control the U-axis and the Z-axis to move the ball head grinding wheel along the inclination angle direction of the grinding wheel axis by a certain distance S, and realize the calibration of the inclination angle of the grinding wheel axis through the results of the U-axis and the Z-axis at each position;

[0011] Step four: obtain the sampling starting point and the sampling ending point according to the plane where the sampling track is located and the sampling length L of the grinding wheel profile;

[0012] Step five: use the laser displacement sensor to collect the relative displacement data of the ball head grinding wheel reciprocally;

[0013] Step six: filter and denoise the reciprocally sampled data of the laser displacement sensor;

[0014] Step seven: fit the filtered and denoised signal to obtain the profile size of the unground ball head grinding wheel;

[0015] Step eight: use the same sampling starting point and the sampling ending point as the reference ball head grinding wheel, use the laser displacement sensor to collect the relative displacement data of the ball head grinding wheel after ultra-precision grinding reciprocally, further obtain the profile size of the ball head grinding wheel by the methods of steps six to seven, compare the profile size of the ball head grinding wheel with the profile size of the reference ball head grinding wheel, and obtain the wear of the ball head grinding wheel after ultra-precision grinding.

[0016] Further, step three includes the following steps:

[0017] Step three one: control the Z-axis to adjust the distance between the laser displacement sensor and the ball head grinding wheel, so that the result of the laser displacement sensor testing the ball head grinding wheel is as large as possible, and record the corresponding (U, Z) value;

[0018] Step three two: coordinate control the U-axis and the Z-axis to move the ball head grinding wheel along the inclination angle direction by a certain distance S, repeat the operation of step three one, record the corresponding (U, Z) value, and construct the relationship between the distance S and the displacement amount of the U-axis and the Z-axis:

[0019] (1)

[0020] (2)

[0021] Step three three: repeat the operation of the above step three two to obtain a series of coordinates , where M represents the cumulative number of tests;​

[0022] Step three four: data Linear fitting, the calculated ball head grinding wheel axis tilt angle .

[0023] Further, the angle between the plane of the sampling trajectory and the horizontal plane in step four is .

[0024] Further, in step four, the grinding wheel profile sampling length L is determined according to the grinding trajectory of the small diameter ball head grinding wheel when grinding the workpiece, and the starting point and the end point are selected from the area not participating in grinding.

[0025] Further, in step five, the relative displacement data of the ball head grinding wheel is collected by the laser displacement sensor, specifically:

[0026] Based on the calibrated axial profile angle , the running track of the ball head grinding wheel during data collection is adjusted again:

[0027] (3)

[0028] (4)

[0029] The relative displacement data of the ball head grinding wheel is collected by the laser displacement sensor.

[0030] Further, in step six, the reciprocating sampling data of the laser displacement sensor is filtered and denoised, specifically: first, the Hilbert-Huang transform is used to filter and denoise the sampling data, and then the processed data is subjected to mean value operation to further eliminate sampling errors.

[0031] Further, the Hilbert-Huang transform is used to filter and denoise the sampling data, including the following steps:

[0032] (1) Calculate the local maximum points and minimum points of the signal, and connect the maximum points and minimum points of the signal with a cubic spline curve respectively to construct upper and lower envelope lines;

[0033] (2) Calculate the mean value of the upper and lower envelope lines of the reciprocating sampling data signal , denoted as , and the difference between the signal and the envelope mean value , denoted as :

[0034] (5)

[0035] (3) Determine If the two constraints of IMF component are met, go to step (4) to replace the first IMF component filtered from the signal as the original signal, and repeat steps (1)-(3) until the two constraints of IMF component are met. If the two constraints of IMF component are not met, replace with as the original signal, and repeat steps (1)-(3) until the two constraints of IMF component are met.

[0036] (6)

[0037] wherein k is the number of cycles.

[0038] The cycle filtering stopping condition is

[0039] (7)

[0040] wherein SD is the standard deviation of two adjacent components, and is set between 0.2 and 0.3.

[0041] (4) Select the IMF component meeting the IMF constraint condition to obtain a residual signal:

[0042] (8)

[0043] Replace as the new original signal, repeat steps (1)-(3) to obtain:

[0044] (9)

[0045] (5) When is a monotonic function, end the above steps, replace as the final residual term of the signal, and then the EMD decomposition process of the reciprocating sampling data can be represented as:

[0046] (10)

[0047] wherein represents the signal of the original signal after Hilbert Huang transform.

[0048] Further, the method further comprises determining the number of reciprocating cycles, specifically, performing circular fitting on the sampling data under different reciprocating cycles, calculating the fitting circle radius error rate, and further determining the number of reciprocating cycles.

[0049] Further, the calculation method of the fitting circle radius error rate is:

[0050] (11)

[0051] Further, the least square method is used for fitting the signal after filtering and denoising in step seven, to obtain the unground ball head grinding wheel profile size.

[0052] Compared with the prior art, the beneficial effects of the present application are:

[0053] The present application is a kind of based on laser displacement sensor reciprocating scanning determination ultra-precision grinding processing small diameter ball head grinding wheel wear analysis method, based on the relative displacement data of the reciprocating movement of the grinding wheel along the axis direction of the grinding wheel is collected by the non-contact laser displacement sensor, data filtering and denoising processing is carried out, the influence of machine vibration and interference noise in data is eliminated;The wear is determined by comparing the fitting of the grinding wheel profile size before and after grinding, and the radial profile size of the ball head grinding wheel is realized in real time in situ.The present application can judge the wear degree of grinding wheel in time, greatly simplify the grinding wheel wear test process, and help to realize the efficient and high-precision machining process of ultra-precision grinding.

[0054] The method of the present application can also be used to study the influence of feed rate a p , grinding wheel spindle rotation rate v s , grinding wheel feed rate f, abrasive grain size Z and abrasive grain concentration ρ on the wear of ball head grinding wheel, so as to provide a theoretical basis for subsequent ultra-precision grinding process parameter optimization and grinding wheel manufacturing.

[0055] The method of the present application has certain universality, and can be applied to the wear detection of ball head grinding wheel in all ultra-precision / precision grinding processes. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 The flow chart of the analysis method for determining the wear of small diameter ball head grinding wheel in ultra-precision grinding process based on laser displacement sensor reciprocating scanning in the embodiment of the present application is shown in the figure.

[0057] Figure 2 The schematic diagram of the radial size test system of small diameter ball head grinding wheel in the embodiment of the present application is shown in the figure.

[0058] Figure 3 The schematic diagram of the radial size scanning track of ball head grinding wheel in the embodiment of the present application is shown in the figure.

[0059] Figure 4 The fitting result of U and Z value measurement data in the embodiment of the present application is shown in the figure.

[0060] Figure 5 The schematic diagram of the grinding track of small diameter ball head grinding wheel in the embodiment of the present application is shown in the figure.

[0061] Figure 6A comparison chart of fitting results of the same test profile circle of the ball head grinding wheel in the embodiment of the present application is shown in the figure;

[0062] Figure 7 A time-frequency domain signal chart of the reciprocating sampling signal x(t) before filtering and noise reduction in the embodiment of the present application is shown in the figure;

[0063] Figure 8 A time-frequency domain signal chart of the reciprocating sampling signal x(t) after filtering and noise reduction in the embodiment of the present application is shown in the figure;

[0064] Figure 9 A trend chart of the ball head grinding wheel fitting circle radius value under different reciprocating cycle numbers in the embodiment of the present application is shown in the figure;

[0065] Figure 10 A reciprocating scanning data chart after Hilbert Huang filtering in the embodiment of the present application is shown in the figure;

[0066] Figure 11 A profile size comparison chart of the ground ball head grinding wheel and the unground ball head grinding wheel in the embodiment of the present application is shown in the figure;

[0067] Figure 12 A comparison of the method and the simulation modeling result in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0068] In the description of the present application, it should be explained that the terms "first", "second", "third" mentioned in the embodiments of the present application are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second", "third" can explicitly or implicitly include one or more features.

[0069] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0070] Specific implementation scheme one: as shown in the figure, the present application provides an analysis method for determining the wear of a small-diameter ball head grinding wheel in ultra-precision grinding based on laser displacement sensor reciprocating scanning, which comprises the following steps: Figure 1

[0071] Step one: connect the laser displacement sensor with the micro-displacement platform, and fix the laser displacement sensor and the micro-displacement platform in the X-Y plane of the machine tool;

[0072] Step two: clamp the unused ball head grinding wheel at the end of the tool spindle as the reference for measuring the wear of the grinding wheel;

[0073] ​Step three: control the U-axis and the Z-axis to move the ball head grinding wheel along the angle direction of the grinding wheel axis by a distance S, and realize the calibration of the angle of the grinding wheel axis through the results of the U-axis and the Z-axis at each position.

[0074] Step four: obtain the starting point and the ending point of sampling according to the plane where the sampling track is located and the sampling length L of the grinding wheel profile;

[0075] Step five: collect the relative displacement data of the ball head grinding wheel by the laser displacement sensor in a reciprocating manner;

[0076] Step six: filter and denoise the reciprocating sampling data of the laser displacement sensor;

[0077] Step seven: fit the signal after filtering and denoising to obtain the profile size of the ball head grinding wheel before grinding;

[0078] Step eight: collect the relative displacement data of the ball head grinding wheel after ultra-precision grinding by the laser displacement sensor in a reciprocating manner using the same starting point and ending point as the reference ball head grinding wheel, further obtain the profile size of the ball head grinding wheel by the method of steps six to seven, and compare the profile size of the ball head grinding wheel with the profile size of the reference ball head grinding wheel to obtain the wear of the ball head grinding wheel after ultra-precision grinding.

[0079] As shown in Figure 2 , the embodiment is based on a hemispherical resonator ultra-precision five-axis linkage machine tool, and the movement axes are mainly distributed in two regions, which are located on the gantry of the machine tool and directly below the gantry; the gantry is provided with a linear axis Z-axis, a rotating axis C-axis and a feed axis U-axis, the Z-axis is arranged in the vertical direction, the rotating shaft C-axis is connected with the Z-axis through an adapter, and the U-axis is located below the C-axis, the moving axis thereof is located in the same plane as the rotating shaft C-axis, and single degree of freedom movement can be realized. The workbench is arranged in the region below the gantry, and the X-axis and the Y-axis are connected below the workbench to realize the movement of the workbench in the plane. When the ball head grinding wheel circumferential topography profile is measured, the angle between the grinding wheel spindle and the horizontal plane is β.

[0080] Specific embodiment two: step three includes the following steps:

[0081] Step three one: control the Z-axis to adjust the distance between the laser displacement sensor and the ball head grinding wheel, so that the result of the laser displacement sensor testing the ball head grinding wheel is as large as possible, and record the corresponding (U, Z) value;

[0082] Step three two: coordinate control the U-axis and the Z-axis to move the ball head grinding wheel along the angle direction by a distance S, repeat the operation of step three one, record the corresponding (U, Z) value, and construct the relationship between the distance S and the displacement amount of the U-axis and the Z-axis:

[0083] (1)​

[0084] (2)

[0085] Step three three: repeat the operation of step three two, to get a series of coordinates , wherein M represents the cumulative number of tests; the specific data results are shown in Table 1;

[0086] Table 1

[0087]

[0088] Step three four: as shown in Figure 4 , the data in Table 1 is linearly fitted using the cftool package of MATLAB, according to the geometric relationship, the slope K (0.724) of the straight line is equal to , that is , the calculated ball head grinding wheel axis tilt angle is equal to 35.9045°. The other embodiments of the present embodiment are the same as the first embodiment.

[0089] Specific embodiment three: as shown in Figure 3 , the angle between the plane where the sampling trajectory in step four is located and the horizontal plane is , and the sampling trajectory in other dotted line directions often has different degrees of error. The other embodiments of the present embodiment are the same as the first embodiment.

[0090] Specific embodiment four: in step four, the grinding wheel profile sampling length L is determined according to the grinding trajectory when the small-diameter ball head grinding wheel grinds the workpiece, and the sampling starting point and the sampling ending point are selected from the region not participating in grinding. The other embodiments of the present embodiment are the same as the third embodiment.

[0091] Since the ball head part and the rod diameter of the ball head grinding wheel adopt a fillet transition, if the profile data sampling length is too long, the profile size data of the fillet region will be introduced, affecting the subsequent circle fitting result; on the contrary, if the profile data sampling length is too short, the entire grinding area cannot be covered, and the subsequent wear analysis of the ball head grinding wheel cannot be performed.

[0092] Figure 5 As shown in , the grinding trajectory when the small-diameter ball head grinding wheel grinds the complex thin-walled part can be known, the grinding length range is -1.88219mm~1.2213mm, therefore the sampling length L cannot be less than this value, therefore, in the present embodiment, the sampling length L is defined as 3.20mm, the sampling starting point is -1.9mm, and the sampling ending point is 1.3mm.

[0093] Specific embodiment five: in step five, the relative displacement data of the ball head grinding wheel is collected by the laser displacement sensor, specifically:

[0094] Based on the calibrated axial profile angle Readjust the trajectory of the ball-end grinding wheel during data acquisition:

[0095] (3)

[0096] (4)

[0097] A laser displacement sensor is used to repeatedly collect relative displacement data of the ball-end grinding wheel. This implementation scheme is otherwise identical to specific implementation scheme one.

[0098] Specific Implementation Scheme Six: The filtering and noise reduction processing of the laser displacement sensor's reciprocating sampling data described in step six is ​​as follows: First, the Hilbert-Huang transform is used to filter and reduce noise in the sampling data. Then, the processed data is averaged to further eliminate sampling errors. The rest of this implementation scheme is the same as Specific Implementation Scheme One.

[0099] The sampling error when using the LK-H020 laser displacement sensor for data sampling is ±1.2μm, and the repeatability is 0.1μm. Figure 6 As shown, discrepancies arise between different data sampling results, leading to inconsistent fitting radius results when fitting the same measurement trajectory data of a ball-end grinding wheel using the least squares method. To address this issue, this implementation plan proposes using a laser displacement sensor to collect ball-end grinding wheel contour data via reciprocating scanning, forming periodic data. Subsequently, the data is filtered for noise reduction and averaged to eliminate the impact of sampling errors.

[0100] Specific implementation plan seven: The step of using Hilbert-Huang transform to filter and reduce noise in the sampled data includes the following steps:

[0101] (1) Calculate the local maxima and minima of the signal, and use cubic spline curves to connect the maxima and minima of the signal to construct the upper and lower envelopes;

[0102] (2) Calculate the reciprocating sampling data signal The mean of the upper and lower envelopes is denoted as And find the signal and envelope mean The difference is denoted as :

[0103] (5)

[0104] (3) Judgment Does it meet the two constraints of the IMF component? If it does, proceed to step (4) to... The first IMF component selected from the signal is denoted as ; if not, replace with as the original signal, and repeat steps (1)-(3) until the two IMF components meet the two prerequisites.

[0105] (6)

[0106] where k is the number of cycles.

[0107] The condition for stopping the cycle selection is

[0108] (7)

[0109] where SD is the standard deviation of two adjacent components, and is set between 0.2 and 0.3.

[0110] (4) Select the IMF component that meets the IMF constraint condition to obtain the residual signal:

[0111] (8)

[0112] Take as the new original signal, repeat steps (1)-(3) to obtain:

[0113] (9)

[0114] (5) When is a monotonic function, end the above steps, take as the final residual term of the signal, and the EMD decomposition process of the data can be expressed as:

[0115] (10)

[0116] where represents the signal of the original signal after Hilbert Huang transform. The other aspects of this embodiment are the same as Embodiment Six.

[0117] The Hilbert-Huang transform can adaptively decompose any complex signal into a series of intrinsic mode functions (IMF) with decreasing frequency; the obtained IMF component can be regarded as a single frequency signal, and needs to meet the following constraint prerequisites:

[0118] (I) The number of all extreme points is equal to the number of zero points or only differs by 1.

[0119] (II) At any given time, the upper and lower envelopes formed by the local extreme points must be symmetrical about the time axis, that is, the mean of the upper and lower envelopes is 0.

[0120] In this implementation scheme, the sampling frequency of the laser displacement sensor is fs = 1000Hz, and the cutoff frequency is f_zz = 0.1Hz. Based on the given scanning parameters, sampling length L and sampling rate v, the frequency f corresponding to the reciprocating signal x(t) can be derived to be 0.02Hz. Figure 7 The result shown is the Fourier transform of the sampled data x(t). It can be seen that in addition to the required signal frequency f, there are also a series of random frequency components in the frequency domain. Therefore, the signal needs to be filtered and denoised before data analysis.

[0121]

[0122] Because the Hilbert-Huang transform can achieve maximum noise reduction while preserving signal characteristics. Based on this, such as... Figure 8 As shown, this implementation scheme uses Hilbert-Huang transform to perform filtering and noise reduction analysis on the reciprocating signal x(t) sampled by the laser displacement sensor, achieving a significant degree of filtering and noise reduction.

[0123] like Figure 10 As shown, the data after Hilbert-Huang transform processing consists of multiple periodic signals, let f(x1), f(x2), ..., f(x3) be located inside the rectangle. n-1 f(x) n To improve the reliability of the measurement data, the above signals are summed and averaged to obtain the corresponding signal f(x); the mean-averaging process is as follows:

[0124]

[0125] Specific Implementation Scheme Eight: The method further includes determining the number of reciprocating cycles, specifically by performing circle fitting on the sampling data under different reciprocating cycles, calculating the error rate of the fitted circle radius, and further determining the number of reciprocating cycles. This implementation scheme is otherwise the same as Specific Implementation Scheme One.

[0126] In this implementation scheme, a larger number of reciprocating sampling periods n of the laser displacement sensor results in higher reliability of the fitting results. However, an excessively large number of reciprocating sampling periods n will significantly increase the sampling duration T, and the maximum data storage capacity of the laser displacement sensor is limited. Conversely, a small number of sampling periods will affect the reliability of the fitting results. Therefore, the number of reciprocating sampling periods should be reduced as much as possible while ensuring the accuracy of the fitting results. Table 2 shows the results of circular fitting of the filtered and denoised signal using the least squares method when the sampling length L = 3.20 mm and the sampling rate v = 0.32 mm / s.

[0127] Table 2

[0128]

[0129] As Figure 9 shown in the figure, the curve of the fitting circle radius value changing with the number of reciprocating cycles shows that when the number of reciprocating cycles exceeds 20, the circle radius value is stable. At the same time, the fitting circle radius error rate err at this time is not more than 1%, so the sampling reciprocating cycle number n in the test process is 24.

[0130] Specific embodiment nine: the calculation method of the fitting circle radius error rate is:

[0131] (11)

[0132] The other parts of the embodiment are the same as those of specific embodiment eight.

[0133] Specific embodiment ten: the least square method is used to fit the signal after filtering and noise reduction in step seven to obtain the unground ball head grinding wheel profile size. The other parts of the embodiment are the same as those of specific embodiment nine.

[0134] As Figure 11 shown, the ball head grinding wheel profile size is compared with the reference ball head grinding wheel profile size to obtain the super-precision grinding ball head grinding wheel wear amount. The present application assumes that the unground grinding wheel has consistent circumferential radius, and the area near the sampling starting point and the sampling ending point does not participate in grinding, so the profile size of the unground area is used as the reference to obtain the corresponding ball head grinding wheel wear amount, which has high reliability.

[0135] To verify the reliability of the wear amount result of the present application, the obtained ball head grinding wheel wear amount is compared with the theoretical simulation modeling result. In the simulation modeling process: the micro-grinding volume dv1 and dv2 of the ball head grinding wheel and the workpiece at the grinding point position are obtained by analysis, and then the relationship between them is established according to the grinding ratio, and the relationship between the grinding wheel wear aw and the grinding process parameters and the grinding ratio is obtained after simplifying the equation. As Figure 12 shown, the method proposed in the present application is consistent with the simulation modeling in the wear amount analysis trend, and the wear amount error rate is controlled within 5%, which indirectly proves the reliability of the method proposed in the present application. At the same time, compared with the simulation modeling process, the present application has great simplification in calculation efficiency and modeling analysis, so it can be used as the main method for subsequent small-diameter ball head grinding wheel wear amount measurement.

[0136] Although the present application discloses as above, the protection scope of the present application is not limited to this. The person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application, and these changes and modifications will fall within the protection scope of the present application.

Claims

1. An analysis method for determining the wear of a super-precision grinding machining small-diameter ball head grinding wheel based on the reciprocating scanning of a laser displacement sensor, characterized in that, It comprises the following steps: Step one: connect the laser displacement sensor with the micro-displacement platform, and fix the laser displacement sensor and the micro-displacement platform in the X-Y plane of the machine tool; Step two: clamp the unused ball head grinding wheel at the end of the tool spindle as the reference for measuring the grinding wheel wear; Step three: control the U-axis and the Z-axis to move the ball head grinding wheel along the grinding wheel axis line in the direction of the inclination angle by a certain distance S, and realize the calibration of the inclination angle of the grinding wheel axis line through the results of the U-axis and the Z-axis at each position . Step four: obtain the sampling starting point and the ending point according to the plane where the sampling track is located and the grinding wheel profile sampling length L; Step five: collect the relative displacement data of the ball head grinding wheel by the laser displacement sensor; Step six: filter and denoise the data collected by the laser displacement sensor; Step seven: fit the filtered and denoised signal to obtain the profile size of the ball head grinding wheel before grinding; Step eight: collect the relative displacement data of the ball head grinding wheel after super-precision grinding by the laser displacement sensor using the same sampling starting point and ending point as the reference ball head grinding wheel, and further obtain the profile size of the ball head grinding wheel by the method of steps six to seven, compare the profile size of the ball head grinding wheel with the profile size of the reference ball head grinding wheel to obtain the wear of the ball head grinding wheel after super-precision grinding; Step three comprises the following steps: Step three one: control the Z-axis to adjust the distance between the laser displacement sensor and the ball head grinding wheel, so that the result of the laser displacement sensor testing the ball head grinding wheel is as large as possible, and record the corresponding (U, Z) value; Step three two: coordinate control the U-axis and the Z-axis to move the ball head grinding wheel along its tilt angle direction by a certain distance S, repeat the operation of step three one, record the corresponding (U, Z) value, and construct the relationship between the distance S and the displacement amount of the U-axis and the Z-axis: （1） （2） Step three three: repeat the operation of the above step three two, get a series of coordinates where M is the number of cumulative tests. Step three four: data Linear fitting is performed to calculate the axis tilt angle of the ball head grinding wheel .

2. The method according to claim 1, wherein the laser displacement sensor reciprocating scanning based analysis method for determining the wear of the ultra-precision grinding machining small-diameter ball head grinding wheel is characterized in that, The angle of the plane in which the sampling trajectory described in step four lies with the horizontal is .

3. The method according to claim 2, wherein the laser displacement sensor reciprocating scanning based analysis method for determining the wear of the ultra-precision grinding machining small-diameter ball head grinding wheel is characterized in that, In step four, the grinding wheel profile sampling length L is determined according to the grinding track of the small-diameter ball head grinding wheel when grinding a workpiece, and the sampling starting point and the ending point are selected from the region not participating in grinding.

4. The method according to claim 1, wherein the method is characterized in that, In step five, the laser displacement sensor is used to collect the relative displacement data of the ball head grinding wheel, specifically: based on the calibrated axial profile angle re-adjusting the running path of the ball head grinding wheel during data acquisition: （3） （4） The laser displacement sensor is used to collect the relative displacement data of the ball head grinding wheel.

5. The method according to claim 1, wherein the method is characterized in that, In step six, the laser displacement sensor is used to collect the relative displacement data of the ball head grinding wheel, specifically:

6. The analytical method for determining the wear of a super-precision grinding machining small-diameter ball head grinding wheel based on the reciprocating scanning of a laser displacement sensor according to claim 5, characterized in that, First, the Hilbert-Huang transform is used to filter and denoise the sampling data, and then the processed data is subjected to mean value operation to further eliminate sampling errors. The laser displacement sensor is used to collect the relative displacement data of the ball head grinding wheel. (2) Reciprocal sampling data signal The mean value of the upper and lower envelope lines is denoted as and the difference between the signal and the envelope mean value is denoted as : (5) (3) Judgment Does it meet the two constraints of the IMF component? If it does, proceed to step (4) to... As a signal The first IMF component selected from the pool is denoted as If it does not meet the requirements, then... replace As the original signal, steps (1) to (3) are repeated until the two preconditions of the IMF are met; (6) The cycle selection stopping condition is Wherein, SD is the standard deviation of two adjacent components, which is set between 0.2 and 0.3; (7) (4) select the IMF component that meets the IMF constraint condition to obtain the residual signal: The method further comprises determining the number of reciprocating cycles, specifically, performing circular fitting on the sampling data under different reciprocating cycles, calculating the fitting circle radius error rate, and further determining the number of reciprocating cycles. (8) The As a new original signal, repeat steps (1)-(3) to obtain: (9) (5) When is a monotonic function, the above steps are ended, and is taken as the final residual term of the signal, and then the data is collected in a reciprocating manner. The EMD decomposition process is represented as: (10) wherein represents the original signal the signal after the Hilbert-Huang transformation.

7. The method according to claim 1, wherein the method is characterized in that, The fitting circle radius error rate is calculated by:

8. The analytical method for determining the wear of a super-precision grinding machining small-diameter ball head grinding wheel based on the reciprocating scanning of a laser displacement sensor according to claim 7, characterized in that, In step seven, the least square method is used to fit the filtered and denoised signal to obtain the profile size of the ball head grinding wheel before grinding. （11）。 9. The method according to claim 8, wherein the method is characterized in that, ​

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