Positioning device for ultra-precision bearing main load surface roughness measurement and roughness data processing method

Abstract

The positioning device for super-precision bearing main bearing surface roughness measurement and roughness data processing method belong to the technical field of super-precision machining measurement. The existing super-precision bearing main bearing surface measurement has the problems of poor clamping and positioning accuracy, poor feature measurement accuracy and single analysis dimension. The holding unit is arranged on the upper surface of the moving unit, the moving unit comprises a top platform and a bottom platform; the top platform is arranged on the upper side of the bottom platform, the lower surface of the top platform is a convex arc surface, the upper surface of the bottom platform is a concave arc surface, and the convex arc surface and the concave arc surface are matched; the second worm is inserted in the bottom platform, and the second worm rotates to drive the top platform to move along the concave arc surface of the bottom platform; the first worm is inserted in the top platform, and the direction of the first worm is perpendicular to the second worm; the first worm is used for driving the holding unit to move along the axial direction of the first worm; and the holding unit is used for holding and fixing the measurement sample block. The present application is used for bearing main bearing surface roughness measurement and data component acquisition.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision machining and measurement technology. Background Technology

[0002] Ultra-precision bearings have important applications in manufacturing, optics, aerospace, and medical equipment, requiring high-precision machining and measurement technologies to ensure the quality and performance of the main bearing surface (hereinafter referred to as the main bearing surface). Measuring the main bearing surface presents a significant challenge due to its complex shape, making clamping and positioning difficult. While increasing the Z-axis measurement range of optical equipment can address height differences, it may reduce resolution and affect the accuracy of measuring fine features. Although shims can be used to adjust the measurement surface to its optimal state, the lack of digitalization in the adjustment process makes it difficult to guarantee the consistency of repeated measurements. For example, when using a certain type of white light interferometer to measure the main bearing surface (Sa=0.05μm) of the inner raceway of a deep groove ball bearing, the scanning range of random measurement points (field of view 1×1 mm²) without a positioning device was 600μm, and the measurement time was 10 minutes, resulting in a surface roughness of Sa = 3.19μm, which is not very accurate. Furthermore, existing measurement procedures still rely on conventional surface measurement systems, and research on the compatibility of measurement methods, parameters, and signal processing methods with ultra-precision surface height data is relatively limited. Summary of the Invention

[0003] This invention addresses the problems of poor clamping and positioning accuracy, resulting in low measurement resolution, poor feature measurement accuracy, and limited analysis dimensions in existing ultra-precision bearing main bearing surface measurement. A positioning device and roughness data processing method for measuring the roughness of the main bearing surface of ultra-precision bearings are proposed.

[0004] The positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing, as described in this invention, includes a moving unit and a clamping unit;

[0005] The supporting unit is disposed on the upper surface of the moving unit. The moving unit includes a top platform (7) and a bottom platform (9). The top platform (7) is disposed on the upper side of the bottom platform (9). The lower surface of the top platform (7) is a convex arc surface, and the upper surface of the bottom platform (9) is a concave arc surface. The convex arc surface and the concave arc surface are compatible.

[0006] A second worm gear (13) is inserted into the bottom platform (9). The rotation of the second worm gear (13) causes the top platform (7) to move along the concave arc surface of the bottom platform (9).

[0007] A first worm gear (11) is inserted into the top platform (7), and the insertion direction of the first worm gear (11) is perpendicular to the insertion direction of the second worm gear (13).

[0008] The rotation of the first worm (11) causes the clamping unit to move along the axial direction of the first worm (11);

[0009] The clamping unit is used to clamp and fix the measurement sample block (2).

[0010] Furthermore, in this invention, the moving unit also includes: a lead screw (6), a translation knob (8), a rotation knob (10), and a turbine (12).

[0011] A row of T-shaped protrusions is provided along the center line of the convex arc surface of the top platform (7);

[0012] The bottom platform (9) has a groove along the centerline on its concave arc surface;

[0013] The lower surface of the T-shaped protrusion is provided with threads, and the threads of the T-shaped protrusion mesh with the threads of the second worm (13). The rotation of the second worm (13) drives the top platform (7) to move. One end of the second worm (13) is connected to the rotary knob (10).

[0014] The first worm (11) drives the lead screw (6) to rotate via the turbine (12). The rotation of the lead screw (6) drives the clamping unit to move along the axial direction of the second worm (13) on the top platform (7). One end of the first worm (11) is connected to the translation knob (8).

[0015] Furthermore, in this invention, the clamping unit includes a baffle (1), a clamp base (3), a clamp spring (4), and two clamp blades (5);

[0016] The baffle (1), clamp base (3), clamp spring (4) and clamp blade (5) are all set on the upper surface of the top platform (7);

[0017] The upper surface of the top platform (7) is also provided with a rectangular groove. The axial direction of the lead screw (6) corresponds to the length direction of the rectangular groove. The bottom of the clamp base (3) is connected to the lead screw (6) through the rectangular groove. The rotation of the lead screw (6) drives the clamp base (3) to move.

[0018] Two clamp blades (5) are fixed to the upper surface of the clamp base (3) by two bolts; the clamp base (3) drives the two clamp blades (5) to move along the axial direction of the lead screw (6); the upper surface of the top platform (7) is also provided with a baffle (1); the baffle (1) is arranged opposite to the clamping end of the two clamp blades (5); the two clamp blades (5) and the baffle (1) cooperate to fix the measuring block (2); the other end of the two clamp blades (5) is connected by a clamp spring (4).

[0019] A surface multidimensional analysis method based on measurement data of the main bearing surface of ultra-precision bearings, which is implemented based on the aforementioned positioning device for measuring the roughness of the main bearing surface of ultra-precision bearings; the method includes:

[0020] First, the positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing is used to fix the sample block of the main bearing surface of the bearing to be tested on the platform of the optical measuring equipment. The optical measuring equipment is then controlled to measure the sample block of the main bearing surface of the bearing to be tested and to obtain the surface roughness data of the sample block.

[0021] Then, based on the surface roughness data of the sample block, the multidimensional surface roughness data components of the main bearing surface of the bearing under test are obtained;

[0022] The specific method for obtaining the multidimensional surface roughness data components of the main bearing surface of the bearing under test is as follows:

[0023] Step 1: Preprocess the sample surface roughness data using the least squares fitting function and Sigma, and obtain the rough surface texture signal using the preprocessed sample surface roughness data.

[0024] Step 2: Use a two-dimensional Fourier transform to convert the texture signal from the spatial domain to the frequency domain, and use the relationship between wavelength and frequency to obtain the texture signal within the target frequency range;

[0025] Step 3: Quantitatively evaluate the texture signal within the target frequency range using the support ratio curve to obtain the prominent peak boundary P1 and the concave valley boundary P2. Use the prominent peak boundary P1 and the concave valley boundary P2 to divide the texture signal within the target frequency range into three layers in the height direction to obtain the components of the texture signal at different heights within the target frequency range.

[0026] Step 4: Decompose the rough surface texture signal using a two-dimensional wavelet analysis method, and then use inverse wavelet transform to reconstruct the decomposed signal into components in different directions to obtain the different spatial dimension components of the rough surface texture signal.

[0027] Furthermore, in this invention, the method for obtaining the surface roughness data of the sample block is as follows:

[0028] The sample is cut using a wire cutting machine to obtain a bearing surface sample to be tested. The sample is then mounted on the mounting unit of the positioning device. The positioning device with the sample is placed on the measuring platform of the optical measuring equipment. The measuring step size of the optical measuring equipment is set, and the sample is measured to obtain the surface roughness data of the sample block.

[0029] Furthermore, in this invention, the method for obtaining the texture signal of the rough surface in step one is as follows:

[0030] Using the formula:

[0031] (1)

[0032] Calculate the macroscopic morphology of the surface Where i1 and j1 are powers in the x and y directions, i1 = 1, 2, ..., m, j1 = 1, 2, ..., n, and m and n are the polynomial orders, a i1j1 These are the polynomial coefficients;

[0033] The macroscopic morphology surface is subtracted from the original surface to obtain the surface signal with the macroscopic morphology removed. ; Utilizing surface signals Obtain the texture signal of the rough surface ;

[0034] (2)

[0035] (3)

[0036] In the formula, T u T l It is the texture signal of a rough surface. Upper and lower thresholds for The average value is given by M and N, which are the number of data points in the x and y directions, respectively, and k is the noise reduction threshold.

[0037] Furthermore, in this invention, the method for obtaining the texture signal within the target frequency range in step two is as follows:

[0038] The texture signal z′(x, y) is transformed from the spatial domain to the frequency domain using a two-dimensional Fourier transform to obtain the spectrum F(u, v):

[0039] (4)

[0040] Where u represents the spatial frequency in the x-direction and v represents the spatial frequency in the y-direction, the frequency corresponding to the spectral amplitude |F(u, v)| is calculated, and then the corresponding wavelength is obtained:

[0041] (5)

[0042] In the formula, (u c , v c ) = (M / 2, N / 2) represents the center of the DC component (zero frequency) of the spectrum, i.e., L x Lᵧ and Lᵧ are the sampling lengths in the x and y directions, respectively. If the sampling interval is Δ, then Lᵧ... x = M·Δ, L y = N·Δ; and These are the wavelength components in the x and y directions, respectively;

[0043] Upper limit of wavelength corresponding to the target frequency range and lower wavelength limit Substitute the weight functions of the two-dimensional Gaussian regression filter into the following:

[0044] (6)

[0045] (7)

[0046] Generate a weight function within the target frequency range, where k is the index value, k=1,2,…,2n; (x,y) are the spatial coordinates of the sampling points of the texture signal z′(x,y);

[0047] weight function , Convolving each of z′(x,y) with z′(x,y) yields wavelengths greater than [a certain value]. texture signal and greater than wavelength texture signal :

[0048] (8)

[0049] In the formula, and They are respectively and abbreviation, This represents the convolution operation.

[0050] Furthermore, in this invention, the method for obtaining the boundary P1 of the protruding peak and the boundary P2 of the concave valley in step three is as follows:

[0051] Select the measurement height z corresponding to a support ratio of 40%. a Measure the height z a The tangent line at point P1 intersects the bearing ratio curve at two points, with heights P1 and P2. The bearing ratios corresponding to P1 and P2 are Mr1 and Mr2, respectively. The distance between heights P1 and P2 is defined as the center depth S. k Height P1 serves as the boundary of the prominent peak; height P2 serves as the boundary of the concave valley.

[0052] Furthermore, in this invention, the formula for the bearing ratio curve is:

[0053] (9)

[0054] Among them, l iIndicates the actual material length of the part, l n Indicates the total measured length. Indicates the support ratio.

[0055] Furthermore, in this invention, in step four, the different spatial dimension components of the texture signal within the target frequency range include: approximate signal a j Horizontal signal d h Longitudinal signal d v and diagonal signal d d .

[0056] Furthermore, in this invention, the method for obtaining the different spatial dimension components of the texture signal of the rough surface in step four is as follows:

[0057] Using the two-dimensional wavelet transform formula:

[0058] (10)

[0059] (11)

[0060] The two-dimensional rough texture signal with dimension M × N It is decomposed into four coefficients of dimension m×n; namely: approximation coefficients. , level coefficient Vertical coefficient and Diagonal coefficients; where j2 is the scaling factor; Two-dimensional scaling functions with different coefficients. Represents a two-dimensional wavelet;

[0061] The coarse texture signal is reconstructed using inverse two-dimensional wavelet transform. :

[0062] (12)

[0063] in:

[0064] (13)

[0065] (14)

[0066] Where, ψ i2 (x, y)=φ(x )i2 1 ψ(x) i2 1 i2=h,v,d,φ i2 1 (x) represents a one-dimensional wavelet with different coefficients, ψ 1 (x) represents a one-dimensional scaling function with different coefficients; , , , These represent the approximate signal, transverse signal, longitudinal signal, and diagonal signal at scale j2, respectively; when the scale coefficient j2=1, the coefficients are reconstructed into the approximate signal a and the transverse signal d. h Longitudinal signal d v and diagonal signal d d This allows us to obtain the different spatial dimension components of the texture signal from a rough surface.

[0067] This invention standardizes the measurement process for ultra-precision main bearing surfaces, ensuring repeatability and high precision throughout the entire process from sample acquisition to data analysis. A multifunctional measurement and positioning auxiliary device is designed, enabling precise multi-dimensional adjustment and repeatable positioning, improving measurement efficiency and accuracy, and solving the problem of difficult positioning of ultra-precision main bearing surfaces. Through experimental optimization of the scanning step size and sampling frequency, the measurement parameters can be flexibly adapted to ultra-precision surfaces with different precision requirements, ensuring an optimal balance between measurement accuracy and efficiency. A multi-dimensional rough surface analysis method is proposed, combining frequency, spatial, and height information to provide a powerful analytical tool for mining texture information of ultra-precision surfaces, applicable to the processing, measurement, and evaluation of ultra-precision complex surface textures. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing, as described in this invention.

[0069] Figure 2 This is a front view of the moving unit of the positioning device used for measuring the roughness of the main bearing surface of ultra-precision bearings.

[0070] Figure 3 Side view of the moving unit of the positioning device used for measuring the roughness of the main bearing surface of ultra-precision bearings;

[0071] Figure 4 This is a schematic diagram showing the relative positions between the positioning aid and the optical equipment.

[0072] Figure 5 A schematic diagram of the cutting process for the main bearing surface sample. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0074] Specific implementation method one: Refer to Figures 1 to 5 This embodiment is described in detail. The positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing, as described in this embodiment, includes a moving unit and a clamping unit.

[0075] The supporting unit is disposed on the upper surface of the moving unit. The moving unit includes a top platform (7) and a bottom platform (9). The top platform (7) is disposed on the upper side of the bottom platform (9). The lower surface of the top platform (7) is a convex arc surface, and the upper surface of the bottom platform (9) is a concave arc surface. The convex arc surface and the concave arc surface are compatible.

[0076] A second worm gear (13) is inserted into the bottom platform (9). The rotation of the second worm gear (13) causes the top platform (7) to move along the concave arc surface of the bottom platform (9).

[0077] A first worm gear (11) is inserted into the top platform (7), and the insertion direction of the first worm gear (11) is perpendicular to the insertion direction of the second worm gear (13).

[0078] The rotation of the first worm (11) causes the clamping unit to move along the axial direction of the first worm (11);

[0079] The clamping unit is used to clamp and fix the measurement sample block (2).

[0080] Furthermore, in this invention, the moving unit also includes: a lead screw (6), a translation knob (8), a rotation knob (10), and a turbine (12).

[0081] A row of T-shaped protrusions is provided along the center line of the convex arc surface of the top platform (7);

[0082] The bottom platform (9) has a groove along the centerline on its concave arc surface;

[0083] The lower surface of the T-shaped protrusion is provided with threads, and the threads of the T-shaped protrusion mesh with the threads of the second worm (13). The rotation of the second worm (13) drives the top platform (7) to move. One end of the second worm (13) is connected to the rotary knob (10).

[0084] The first worm (11) drives the lead screw (6) to rotate via the turbine (12). The rotation of the lead screw (6) drives the clamping unit to move along the axial direction of the second worm (13) on the top platform (7). One end of the first worm (11) is connected to the translation knob (8).

[0085] Furthermore, in this invention, the clamping unit includes a baffle (1), a clamp base (3), a clamp spring (4), and two clamp blades (5);

[0086] The baffle (1), clamp base (3), clamp spring (4) and clamp blade (5) are all set on the upper surface of the top platform (7);

[0087] The upper surface of the top platform (7) is also provided with a rectangular groove. The axial direction of the lead screw (6) corresponds to the length direction of the rectangular groove. The bottom of the clamp base (3) is connected to the lead screw (6) through the rectangular groove. The rotation of the lead screw (6) drives the clamp base (3) to move.

[0088] Two clamp blades (5) are fixed to the upper surface of the clamp base (3) by two bolts; the clamp base (3) drives the two clamp blades (5) to move along the axial direction of the lead screw (6); the upper surface of the top platform (7) is also provided with a baffle (1); the baffle (1) is arranged opposite to the clamping end of the two clamp blades (5); the two clamp blades (5) and the baffle (1) cooperate to fix the measuring block (2); the other end of the two clamp blades (5) is connected by a clamp spring (4).

[0089] Specific Implementation Method Two: The surface multidimensional analysis method based on the measurement data of the main bearing surface of ultra-precision bearings described in this implementation method is implemented based on the positioning device for measuring the roughness of the main bearing surface of ultra-precision bearings described in Specific Implementation Method One; the method includes:

[0090] First, the positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing is used to fix the sample block of the main bearing surface of the bearing to be tested on the platform of the optical measuring equipment. The optical measuring equipment is then controlled to measure the sample block of the main bearing surface of the bearing to be tested and to obtain the surface roughness data of the sample block.

[0091] Then, based on the surface roughness data of the sample block, the multidimensional surface roughness data components of the main bearing surface of the bearing under test are obtained;

[0092] The specific method for obtaining the multidimensional surface roughness data components of the main bearing surface of the bearing under test is as follows:

[0093] Step 1: Preprocess the sample surface roughness data using the least squares fitting function and Sigma, and obtain the rough surface texture signal using the preprocessed sample surface roughness data.

[0094] Step 2: Use a two-dimensional Fourier transform to convert the texture signal from the spatial domain to the frequency domain, and use the relationship between wavelength and frequency to obtain the texture signal within the target frequency range;

[0095] Step 3: Quantitatively evaluate the texture signal within the target frequency range using the support ratio curve to obtain the prominent peak boundary P1 and the concave valley boundary P2. Use the prominent peak boundary P1 and the concave valley boundary P2 to divide the texture signal within the target frequency range into three layers in the height direction to obtain the components of the texture signal at different heights within the target frequency range.

[0096] Step 4: Decompose the rough surface texture signal using a two-dimensional wavelet analysis method, and then use inverse wavelet transform to reconstruct the decomposed signal into components in different directions to obtain the different spatial dimension components of the rough surface texture signal.

[0097] Furthermore, in this invention, the method for obtaining the surface roughness data of the sample block is as follows:

[0098] The sample is cut using a wire cutting machine to obtain a bearing surface sample to be tested. The sample is then mounted on the mounting unit of the positioning device. The positioning device with the sample is placed on the measuring platform of the optical measuring equipment. The measuring step size of the optical measuring equipment is set, and the sample is measured to obtain the surface roughness data of the sample block.

[0099] Furthermore, in this invention, the method for obtaining the texture signal of the rough surface in step one is as follows:

[0100] Using the formula:

[0101] (1)

[0102] Calculate the macroscopic morphology of the surface Where i1 and j1 are powers in the x and y directions, i1 = 1, 2, ..., m, j1 = 1, 2, ..., n, and m and n are the polynomial orders, a i1j1 These are the polynomial coefficients;

[0103] The macroscopic morphology surface is subtracted from the original surface to obtain the surface signal with the macroscopic morphology removed. Using surface signals Obtain the texture signal of the rough surface ;

[0104] (2)

[0105] (3)

[0106] In the formula, T uT l It is the texture signal of a rough surface. Upper and lower thresholds for The average value is given by M and N, which are the number of data points in the x and y directions, respectively, and k is the noise reduction threshold.

[0107] Furthermore, in this invention, the method for obtaining the texture signal within the target frequency range in step two is as follows:

[0108] The texture signal z′(x, y) is transformed from the spatial domain to the frequency domain using a two-dimensional Fourier transform to obtain the spectrum F(u, v):

[0109] (4)

[0110] Where u represents the spatial frequency in the x-direction and v represents the spatial frequency in the y-direction, the frequency corresponding to the spectral amplitude |F(u, v)| is calculated, and then the corresponding wavelength is obtained:

[0111] (5)

[0112] In the formula, (u c , v c ) = (M / 2, N / 2) represents the center of the DC component (zero frequency) of the spectrum, i.e., L x Lᵧ and Lᵧ are the sampling lengths in the x and y directions, respectively. If the sampling interval is Δ, then Lᵧ... x = M·Δ, L y = N·Δ; and These are the wavelength components in the x and y directions, respectively;

[0113] Upper limit of wavelength corresponding to the target frequency range and lower wavelength limit Substitute the weight functions of the two-dimensional Gaussian regression filter into the following:

[0114] (6)

[0115] (7)

[0116] Generate a weight function within the target frequency range, where k is the index value, k=1,2,…,2n; (x,y) are the spatial coordinates of the sampling points of the texture signal z′(x,y);

[0117] weight function , Convolve each value with z′(x, y) to obtain wavelengths greater than [value]. texture signal and greater than wavelength texture signal :

[0118] (8)

[0119] In the formula, and They are respectively and abbreviation, This represents the convolution operation.

[0120] Furthermore, in this invention, the method for obtaining the boundary P1 of the protruding peak and the boundary P2 of the concave valley in step three is as follows:

[0121] Select the measurement height z corresponding to a support ratio of 40%. a Measure the height z a The tangent line at point P1 intersects the bearing ratio curve at two points, with heights P1 and P2. The bearing ratios corresponding to P1 and P2 are Mr1 and Mr2, respectively. The distance between heights P1 and P2 is defined as the center depth S. k Height P1 serves as the boundary of the prominent peak; height P2 serves as the boundary of the concave valley.

[0122] Furthermore, in this invention, the formula for the bearing ratio curve is:

[0123] (9)

[0124] Among them, l i Indicates the actual material length of the part, l n Indicates the total measured length. Indicates the support ratio.

[0125] Furthermore, in this invention, in step four, the different spatial dimension components of the texture signal within the target frequency range include: approximate signal a j Horizontal signal d h Longitudinal signal d v and diagonal signal d d .

[0126] Furthermore, in this invention, the method for obtaining the different spatial dimension components of the texture signal of the rough surface in step four is as follows:

[0127] Using the two-dimensional wavelet transform formula:

[0128] (10)

[0129] (11)

[0130] The two-dimensional rough texture signal with dimension M × N It is decomposed into four coefficients of dimension m×n; namely: approximation coefficients. , level coefficient Vertical coefficient and Diagonal coefficients; where j2 is the scaling factor; Two-dimensional scaling functions with different coefficients. Represents a two-dimensional wavelet;

[0131] The coarse texture signal is reconstructed using inverse two-dimensional wavelet transform. :

[0132] (12)

[0133] in:

[0134] (13)

[0135] (14)

[0136] Where, ψ i2 (x, y)=φ(x )i2 1 ψ(x) i2 1 i2=h,v,d,φ i2 1 (x) represents a one-dimensional wavelet with different coefficients, ψ 1 (x) represents a one-dimensional scaling function with different coefficients; , , , These represent the approximate signal, transverse signal, longitudinal signal, and diagonal signal at scale j2, respectively; when the scale coefficient j2=1, the coefficients are reconstructed into the approximate signal a and the transverse signal d. h Longitudinal signal d v and diagonal signal d d This allows us to obtain the different spatial dimension components of the texture signal from a rough surface.

[0137] Specific implementation: A white light interferometer was used to perform complete measurement and data processing on the outer ring (hereinafter referred to as the outer ring) of the 6008 deep groove ball bearing.

[0138] Step 1: Use a wire EDM machine to cut the outer ring radially. The measuring block (2) in the (x, y, z directions) is within the size limits of the measuring device and the positioning device, and is not cut in other directions to avoid mechanical and thermal deformation of the measuring surface.

[0139] Step 2: Place the positioning aid on the optical testing platform (e.g., Figure 1 The measuring block is clamped and positioned. The measuring block is manually pressed and clamped. The worm gear on the translation knob is rotated. Through the worm gear transmission, the worm and lead screw (6) are rotated, so that the fixture base is translated until the other end of the measuring block is in contact with the baffle. After clamping, the XYZ direction is adjusted using a white light interferometer to find the measurement point. By rotating the worm gear on the knob, the top platform is rotated by a certain angle φ through the worm gear transmission, so that the measurement range is optimal during the measurement process, and the accurate positioning of the four data (X, Y, Z, φ) is completed.

[0140] Step 3: Set the sampling frequency of the white light interferometer to 1μm. -1 The scanning step size was set to 0.38 μm. Following the operating procedures of the white light interferometer, the measurement points were measured to obtain their height data. .

[0141] Step 4: Using equations (1), (2), and (3) to... Perform operations to remove macroscopic morphology and spike noise to obtain .

[0142] Step 5: Inputting equations (4) and (5), the wavelength range is obtained as (1.414, 564.271). Seven upper and lower cutoff parameters are set. The values ​​are (0.025, 5), (5, 25), (25, 125), (125, 250), (250, 350), (350, 450), and (450, 600), respectively. The first value (0.025, 5) is used as the cutoff point. Substituting into equation (6) yields the weight function. Normalize it to obtain and to Perform two-dimensional convolution, extract the central portion of the convolution result and remove it to obtain detailed topographic data after removing large-scale features. The cutoff point is (0.025, 5). Substituting into equation (7) yields the weight function. Normalize it to obtain and to Two-dimensional convolution is performed, and the central portion of the convolution result is extracted to obtain target topography data between (0.025, 5) wavelengths. The same procedure applies to other wavelength ranges to achieve [the desired effect]. In-depth mining of frequency dimension information.

[0143] Step 6: Surface The tangent to the bearing ratio curve intersects the bearing ratio at heights P1 and P2, respectively, which are (0.0714, -0.0627). Based on this, in the height dimension... Divided into three layers, to achieve... In-depth mining of high-dimensional information.

[0144] Step 7: Use the db6 wavelet analysis method to analyze the data using equations (10) and (11). Perform a level 1 decomposition, perform inverse wavelet transform on the detailed features of the decomposition, and reconstruct the multi-scale signals a and d using equations (12), (13), and (14) with different coefficients. h d v and d d To achieve In-depth mining of spatial dimension information.

[0145] This completes the in-depth mining of information in three dimensions: frequency, altitude, and space. These three dimensions can be used in parallel and in series to perform targeted and quantitative information mining on the original surface and the surface after service.

[0146] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A surface multidimensional analysis method based on measurement data of the main bearing surface of ultra-precision bearings, wherein the method is based on a positioning device for measuring the roughness of the main bearing surface of ultra-precision bearings; characterized in that, The method includes: First, the positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing is used to fix the sample block of the main bearing surface of the bearing to be tested on the platform of the optical measuring equipment. The optical measuring equipment is then controlled to measure the sample block of the main bearing surface of the bearing to be tested and to obtain the surface roughness data of the sample block. Then, based on the surface roughness data of the sample block, the multidimensional surface roughness data components of the main bearing surface of the bearing under test are obtained; The specific method for obtaining the multidimensional surface roughness data components of the main bearing surface of the bearing under test is as follows: Step 1: Preprocess the sample surface roughness data using the least squares fitting function and Sigma, and obtain the rough surface texture signal using the preprocessed sample surface roughness data. Step 2: Use a two-dimensional Fourier transform to convert the texture signal from the spatial domain to the frequency domain, and use the relationship between wavelength and frequency to obtain the texture signal within the target frequency range; Step 3: Quantitatively evaluate the texture signal within the target frequency range using the support ratio curve to obtain the prominent peak boundary P1 and the concave valley boundary P2. Use the prominent peak boundary P1 and the concave valley boundary P2 to divide the texture signal within the target frequency range into three layers in the height direction to obtain the components of the texture signal at different heights within the target frequency range. The method for obtaining the boundary of the prominent peak P1 and the boundary of the concave valley P2 is as follows: Select the measurement height z corresponding to a support ratio of 40%. a Measure the height z a The tangent line at point P1 intersects the bearing ratio curve at two points, with heights P1 and P2. The bearing ratios corresponding to P1 and P2 are Mr1 and Mr2, respectively. The distance between heights P1 and P2 is defined as the center depth S. k Height P1 serves as the boundary of the prominent peak; height P2 serves as the boundary of the concave valley. Step 4: Decompose the rough surface texture signal using a two-dimensional wavelet analysis method, and then use inverse wavelet transform to reconstruct the decomposed signal into components in different directions to obtain the different spatial dimension components of the rough surface texture signal.

2. The surface multidimensional analysis method based on the measurement data of the main bearing surface of an ultra-precision bearing according to claim 1, characterized in that, In step one, the method for obtaining the texture signal of the rough surface is as follows: Using the formula: Calculate the macroscopic morphology of the surface Where i1 and j1 are powers in the x and y directions, i1 = 1, 2, ..., m, j1 = 1, 2, ..., n, and m and n are the polynomial orders, a i1j1 These are the polynomial coefficients; The macroscopic morphology surface is subtracted from the original surface to obtain the surface signal with the macroscopic morphology removed. ; Utilizing surface signals Obtain the texture signal of the rough surface ; In the formula, T u T l It is the texture signal of a rough surface. Upper and lower thresholds for The average value is given by M and N, which are the number of data points in the x and y directions, respectively, and k is the noise reduction threshold.

3. The surface multidimensional analysis method based on the measurement data of the main bearing surface of an ultra-precision bearing according to claim 1, characterized in that, In step two, the method for obtaining the texture signal within the target frequency range is as follows: The texture signal z′(x, y) is transformed from the spatial domain to the frequency domain using a two-dimensional Fourier transform to obtain the spectrum F(u, v): Where u represents the spatial frequency in the x-direction and v represents the spatial frequency in the y-direction, the frequency corresponding to the spectral amplitude |F(u,v)| is calculated, and then the corresponding wavelength is obtained: In the formula, (u c ,v c )=(M / 2, N / 2) represents the center of the zero frequency of the DC component of the spectrum, that is, L x Let L and Lᵧ be the sampling lengths in the x and y directions, respectively. If the sampling interval is Δ, then L... x = M·Δ,L y =N·Δ; and These are the wavelength components in the x and y directions, respectively; Upper limit of wavelength corresponding to the target frequency range and lower wavelength limit Substitute the weight functions of the two-dimensional Gaussian regression filter into the following: Generate a weight function within the target frequency range, where k is the index value, k=1,2,…,2n; (x,y) are the spatial coordinates of the sampling point of the texture signal z′(x,y); weight function , Convolve each value with z′(x, y) to obtain wavelengths greater than [value]. texture signal and greater than wavelength texture signal : In the formula, and They are respectively and ** is an abbreviation for convolution operation.

4. The surface multidimensional analysis method based on the measurement data of the main bearing surface of an ultra-precision bearing according to claim 3, characterized in that, The formula for the bearing ratio curve is: Among them, l i Indicates the actual material length of the part, l n Indicates the total measured length. Indicates the support ratio.

5. The surface multidimensional analysis method based on the measurement data of the main bearing surface of an ultra-precision bearing according to claim 3, characterized in that, In step four, the different spatial dimension components of the texture signal within the target frequency range include: approximate signal a j Horizontal signal d h Longitudinal signal d v and diagonal signal d d .

6. The surface multidimensional analysis method based on the measurement data of the main bearing surface of an ultra-precision bearing according to claim 5, characterized in that, In step four, the method for obtaining the different spatial dimension components of the texture signal of the rough surface is as follows: Using the two-dimensional wavelet transform formula: The two-dimensional rough texture signal with dimension M × N It is decomposed into four coefficients of dimension m×n; They are: approximation coefficients , level coefficient Vertical coefficient and Diagonal coefficients; where j2 is the scaling factor; Two-dimensional scaling functions with different coefficients. Represents a two-dimensional wavelet; The coarse texture signal is reconstructed using inverse two-dimensional wavelet transform. : in: in, Let i2 represent the two-dimensional scaling function at scale j2, where i2 = h, v, d. This represents a two-dimensional wavelet at the j2 scale. , , , These represent the approximate signal, transverse signal, longitudinal signal, and diagonal signal at scale j2, respectively; when the scale coefficient j2=1, the coefficients are reconstructed into the approximate signal a and the transverse signal d. h Longitudinal signal d v and diagonal signal d d This allows us to obtain the different spatial dimension components of the texture signal from a rough surface.

7. A positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing, the device being used to implement the method described in claim 1, characterized in that, Includes a mobile unit and a support unit; The supporting unit is disposed on the upper surface of the moving unit. The moving unit includes a top platform (7) and a bottom platform (9). The top platform (7) is disposed on the upper side of the bottom platform (9). The lower surface of the top platform (7) is a convex arc surface, and the upper surface of the bottom platform (9) is a concave arc surface. The convex arc surface and the concave arc surface are compatible. A second worm gear (13) is inserted into the bottom platform (9). The rotation of the second worm gear (13) causes the top platform (7) to move along the concave arc surface of the bottom platform (9). A first worm gear (11) is inserted into the top platform (7), and the insertion direction of the first worm gear (11) is perpendicular to the insertion direction of the second worm gear (13). The rotation of the first worm (11) causes the clamping unit to move along the axial direction of the first worm (11); The clamping unit is used to clamp and fix the measurement sample block (2).

8. The positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing according to claim 7, characterized in that, The moving unit also includes: a lead screw (6), a translation knob (8), a rotation knob (10), and a turbine (12); A row of T-shaped protrusions is provided along the center line of the convex arc surface of the top platform (7); The bottom platform (9) has a groove along the centerline on its concave arc surface; The lower surface of the T-shaped protrusion is provided with threads, and the threads of the T-shaped protrusion mesh with the threads of the second worm (13). The rotation of the second worm (13) drives the top platform (7) to move. One end of the second worm (13) is connected to the rotary knob (10). The first worm (11) drives the lead screw (6) to rotate via the turbine (12). The rotation of the lead screw (6) drives the clamping unit to move along the axial direction of the second worm (13) on the top platform (7). One end of the first worm (11) is connected to the translation knob (8).

9. The positioning device for measuring the roughness of the main bearing surface of an ultra-precision bearing according to claim 8, characterized in that, The clamping unit includes a baffle (1), a clamp base (3), a clamp spring (4), and two clamp blades (5); The baffle (1), clamp base (3), clamp spring (4) and clamp blade (5) are all set on the upper surface of the top platform (7); The upper surface of the top platform (7) is also provided with a rectangular groove. The axial direction of the lead screw (6) corresponds to the length direction of the rectangular groove. The bottom of the clamp base (3) is connected to the lead screw (6) through the rectangular groove. The rotation of the lead screw (6) drives the clamp base (3) to move. Two clamp blades (5) are fixed to the upper surface of the clamp base (3) by two bolts; the clamp base (3) drives the two clamp blades (5) to move along the axial direction of the lead screw (6); the upper surface of the top platform (7) is also provided with a baffle (1); the baffle (1) is arranged opposite to the clamping end of the two clamp blades (5); the two clamp blades (5) and the baffle (1) cooperate to fix the measuring block (2); the other end of the two clamp blades (5) is connected by a clamp spring (4).

Images