Assembly joint surface construction method considering wavelet and fractal

Abstract

The invention relates to the technical field of machining part non-ideal surface generation, and particularly discloses a wavelet and fractal-considered assembly junction surface construction method which comprises the following steps: S1, according to an ideal mathematical model of an assembly junction surface, S2, comparing calculation methods of different fractal parameters, S3, aiming at the part assembly junction surface in different machining modes, calculating fractal fractal parameters according to a calculation method of the different fractal parameters; s4, the assembly junction surface is regarded as a structure formed by superposition of contours of different scales, S5, a power spectrum analysis method is introduced to analyze the surface contour curve characteristics of the assembly junction surface, and S6, according to the isotropic or anisotropic properties of the surface of the assembly junction surface in different machining modes, the surface contour curve characteristics of the assembly junction surface are analyzed. The statistical distribution characteristic parameters determined in the step S3 are introduced into characterization of the assembly joint surface; and S7, the contour curve characteristic parameters extracted in the step S4 are associated with the fractal parameters determined in the step S2. According to the method, multi-scale decomposition is carried out on the assembly joint surface through wavelet transform, and the specificity information of the roughness contour, the waviness contour and the shape error contour can be effectively extracted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of non-ideal surface generation of machined parts, in particular to a construction method of an assembly joint surface considering wavelet and fractals. BACKGROUND

[0002] Precision assembly technology is the core process to ensure the performance of high-end equipment. In the assembly process of precision optoelectromechanical products, multiple parts need to be connected through "assembly joint surfaces". These joint surfaces are the key parts that determine the overall precision and performance stability of the equipment. Even if the precision level of the machined product is extremely high, a large number of rough peaks with different sizes can still be observed on the contact area of the assembly joint surface, showing significant uneven non-ideal characteristics, which are different from the absolute smooth ideal state represented by the CAD model. In order to accurately describe the actual topography of the assembly joint surface and realize the matching of the physical model and the digital model, the surface modeling technology is generally used to construct the non-ideal surface model in the industry, and the fractal theory is the current mainstream simulation method. In the prior art, scholars such as Ausloos and Berman use W-M fractal function to complete the basic simulation of two-dimensional and three-dimensional surface profiles of parts; under the framework of W-M function, Zuo Xue realizes the three-dimensional topography representation of wear surfaces through single and multiple fractal methods, and reveals the surface detail characteristics and amplitude fluctuation law; in view of the defects of traditional statistical methods limited by the resolution and sampling length of measuring instruments, Mu et al. use fractal parameters to simulate different machining surface topographies, and verify the consistency of the simulation results of grinding and milling surfaces with the actual morphology; Ramamoorthy B establishes the correlation between the surface topography represented by the W-M fractal function and the three-dimensional profile curve parameters through power spectrum method and structure function method; Li Heng considers the influence of machining methods on micro topography, and generates a customized part fractal dimension surface model by combining WM function and wavelet decomposition. However, the existing assembly joint surface simulation technology based on fractal theory has significant limitations: the fractal function can only represent the overall surface roughness characteristics, and cannot effectively distinguish the topography differences caused by different machining methods (such as milling and grinding); for example, the milling surface shows obvious anisotropy due to the tool cutting trajectory, and the grinding surface shows isotropy due to the random cutting of abrasive particles, but the fractal simulation results cannot reflect these key differences; at the same time, the fractal theory cannot accurately extract the specific topographic features of different machining surfaces, resulting in insufficient matching degree between the constructed non-ideal surface model and the actual assembly joint surface. This technical defect directly affects the control accuracy of the assembly deviation of precision optoelectromechanical products, and may lead to unstable performance of the equipment, which becomes a key bottleneck restricting the development of precision assembly technology of high-end equipment. SUMMARY

[0003] To address the shortcomings of existing technologies, this invention provides a method for constructing an assembly interface that considers wavelets and fractals, thus solving the problems mentioned in the background section.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for constructing an assembly interface considering wavelets and fractals, comprising the following steps: S1: Based on the ideal digital model of the assembly mating surface, numerical simulation of the assembly mating surface is performed using the WM fractal function to determine the calculation method of the fractal parameters. The fractal parameters play a key role in the changes of the morphological contour characteristics of the assembly mating surface; among them, the expression of the two-dimensional WM fractal function is: ; The expression for the three-dimensional WM fractal function is: ; in, The height of the two-dimensional surface profile. The height of the three-dimensional surface profile. For fractal dimension, For fractal roughness, For frequency series, These are the upper and lower limits of the series, respectively. The fundamental wavelength; S2: Compare the calculation methods for different fractal parameters, compare the errors of the fractal parameters obtained by each method, and select the optimal fractal parameter calculation method suitable for the assembly joint surface; the error comparison uses the deviation formula: ; in, To account for the deviation between the fractal simulation profile and the actual profile, The number of sampling points. To simulate the contour height, This is the actual outline height; S3: For the assembly surfaces of parts under different processing methods, determine the statistical distribution parameters corresponding to the processing method based on the statistical distribution differences of their surface morphology information; the statistical distribution parameters are calculated using the mean formula. Variance formula , Skewness formula ,in, The average height of the profile. For variance, For skewness, For the first The actual contour height value of each sampling point; S4: considering the assembly joint surface as a structure formed by superposition of different scale profiles including roughness profile, waviness profile and form error profile, using wavelet transform to decompose the profile information components of the assembly joint surface, extract effective topographic features and remove noise invalid components; S5: introducing power spectrum analysis method to analyze the surface profile curve features of the assembly joint surface; S6: according to the isotropic or anisotropic properties of the assembly joint surface under different processing methods, introducing the statistical distribution characteristic parameters determined in step S3 into the representation of the assembly joint surface; S7: associating the profile curve feature parameters extracted in step S4 with the fractal parameters determined in step S2.

[0005] Preferably, in S4, the input signal of wavelet transform decomposition is the topographic profile of the actual assembly joint surface , the wavelet transform expression is , wherein is the wavelet transform coefficient, is the scale factor, is the translation factor, is the wavelet base function; after one wavelet decomposition, the original profile signal is decomposed into low-frequency information , horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information ; removing noise invalid components is realized by threshold filtering, and the filtering formula is: ; wherein is the filtered wavelet coefficient, is the sign function.

[0006] Preferably, the wavelet transform decomposition includes the following sub-steps: S4.1, selecting the best wavelet base function: based on the properties of commonly used wavelet base functions and the decomposition requirements of the profile features of the assembly joint surface, initially screening the wavelet base functions; under the condition of ensuring the same number of wavelet decomposition, using each wavelet base function selected initially to decompose and reconstruct the assembly joint surface respectively, comparing the original profile signal with the reconstructed signal through root mean square error, and the root mean square error formula is: ; wherein is the reconstructed profile height, and the wavelet base function with the smallest RMSE is selected as the best wavelet base function; S4.2, determining the number of wavelet decomposition: based on the best wavelet base function, comparing the energy distribution of low-frequency information and high-frequency information in each wavelet decomposition level, and the energy calculation uses the formula: , set the low frequency energy distribution threshold , when the low frequency energy of a decomposition level accounts for , wherein , , , respectively are low frequency, horizontal high frequency, vertical high frequency, diagonal high frequency information energy, determine the level as the final wavelet decomposition number; S4.3, the reconstruction of the profile information component: based on the optimal wavelet basis function and the determined wavelet decomposition number, the inverse wavelet transform formula is used: ; extract the profile feature of the assembly joint surface, complete the reconstruction of the profile information component.

[0007] Preferably, in S5, the power spectral density calculation uses the formula: ; The two-dimensional power spectral density formula is: ; , wherein is the one-dimensional frequency, is the directional frequency, is the directional frequency is the imaginary unit, and the change of the profile component under different processing methods and different processing parameters is found out through the PSD curve; In S6, the isotropic determination basis is , the power spectral density in any direction is consistent, the anisotropic determination basis is , the power spectral density in different directions is different, and the correlation between the statistical distribution characteristic parameters and the processing method is established.

[0008] Preferably, in S7, the correlation model uses: ; , wherein is the initial fractal parameter, is the correction coefficient, is the root mean square error of the roughness profile; if the assembly joint surface is an isotropic surface, a three-dimensional WM fractal function is used for characterization; if it is an anisotropic surface, a two-dimensional WM fractal function is used in direction respectively: ; , wherein is the directional fractal dimension, is the The direction fractal roughness is characterized; and the finally constructed assembly joint surface needs to satisfy the overall deviation from the actual surface: ; wherein, is the profile height of the i th sampling point in the three-dimensional space of the assembly joint surface, is the overall deviation threshold.

[0009] Preferably, in step S2, the optimal fractal parameter calculation method is the structure function method, and the structure function formula is: ; wherein, is the height information of the assembly joint surface on the two-dimensional local profile, is the lag distance, is the exponent, and the and are solved by fitting the linear relationship between and ;The error comparison is realized by analyzing the deviation of the matching degree of the fractal parameters solved by each calculation method from the actual surface topography.

[0010] Preferably, in step S4, the different scale profiles from the micro scale to the macro scale are in turn the roughness profile, the waviness profile and the shape error profile; and the filtering threshold is determined according to the noise energy ratio, and satisfies wherein, is the noise standard deviation, is an empirical coefficient, and the value range is 1.5-2.5; In step S4.1, the best wavelet basis function is a wavelet basis function; the commonly used wavelet basis functions include a series of wavelets, a series of wavelets, a series of wavelets; In step S4.2, the wavelet decomposition number is 7 times; and the low-frequency energy distribution threshold is set according to the energy ratio of the shape error profile in the profile of the assembly joint surface, and the value range satisfies When the energy ratio of the low-frequency information of a certain decomposition level reaches the threshold value, the level is determined as the final wavelet decomposition number.

[0011] Preferably, in step S5, the different machining methods include milling machining and grinding machining; for the milling machining method, the power spectrum analysis method is used to explore the power spectrum density change of the assembly joint surface under different milling speeds and feed rates , and to determine​​​ with the association law wherein, is the amplitude coefficient, is the rotational speed influence coefficient, is the feed amount influence coefficient, is the frequency attenuation coefficient

[0012] Preferably, in step S6, the isotropic surface corresponds to a processing mode of grinding processing, satisfying ; the anisotropic surface corresponds to a processing mode of milling processing, satisfying .

[0013] Preferably, in step S7, the overall deviation threshold is set according to the actual assembly accuracy requirement, and wherein, is the actual processing surface topography measurement error, the value range ; the correction coefficient satisfies .

[0014] The present application aims at the technical defects of the existing fractal theory in the simulation of assembly joint surfaces, realizes the dual breakthrough of the modeling accuracy and practicability of the assembly joint surfaces through the deep integration of wavelet transform and fractal theory, and has the following beneficial effects: 1、The present application can effectively extract the specific information of roughness profile, waviness profile and shape error profile through multi-scale decomposition of the assembly joint surface by wavelet transform; for example, for a milling processed surface, the horizontal / vertical high-frequency characteristics caused by the cutting direction can be separated; for a grinding processed surface, the uniformly distributed high-frequency rough peak characteristics can be captured, solving the pain point that the traditional fractal method cannot distinguish the processing mode; at the same time, the influence law of different processing parameters (such as milling speed and feed amount) on the profile composition is determined by combining power spectrum analysis, so that the model constructed can accurately map the surface topography corresponding to the actual processing technology, realizing the high reflection of the physical model and the digital model.

[0015] 2、The existing fractal theory is difficult to control the key parameters such as fractal dimension D and fractal roughness G, resulting in insufficient flexibility of the model; by associating the profile curve characteristic parameters (such as roughness profile root mean square error and statistical distribution skewness) extracted by wavelet transform with fractal parameters, the dynamic adjustment of fractal parameters is realized through the establishment of a parameter correction model; at the same time, for isotropic (such as grinding) and anisotropic (such as milling) surfaces, three-dimensional and two-dimensional W-M fractal functions are used for representation respectively, further improving the modeling accuracy of surfaces with different properties, so that the overall deviation of the constructed non-ideal surface and the actual joint surface can be controlled within the preset threshold.

[0016] 3, The assembled joint surface model constructed by the application can accurately reflect the surface topography characteristics in the actual machining state, and provide a reliable digital basis for the assembly deviation analysis and control of precision optoelectromechanical products; through the model, the problems such as the change of contact stiffness and uneven stress distribution caused by the difference of joint surface topography in the assembly process can be predicted in advance, the engineers are assisted to optimize the assembly process parameters, the influence of assembly deviation on equipment performance is effectively reduced, the performance stability of high-end equipment in long-term operation is ensured, and the application has important practical significance for promoting the development of precision assembly technology to a higher precision level.

[0017] 4, The application defines the selection criteria of wavelet basis function, decomposition number, low-frequency energy threshold and other key parameters, and provides specific implementation methods of fractal parameter calculation (structure function method) and noise removal (threshold filtering), thereby forming a standardized assembly joint surface construction process; the process does not need complex self-defined parameter debugging, is convenient for engineering and technical personnel to quickly master and apply, effectively reduces the application threshold of non-ideal surface modeling technology, and is suitable for assembly joint surface simulation scenes of different types of precision parts. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a contact area display diagram of an enlarged assembly joint surface of a part; Figure 2 is a schematic diagram of surfaces of two base parts under different machining methods; Figure 2 (a) is a milling surface schematic diagram; Figure 2 (b) is a grinding surface schematic diagram; Figure 3 is a schematic diagram of profile component information after one wavelet decomposition; Figure 4 is a schematic diagram of a simulated assembly joint surface and extracted components; Figure 4 (a) is a simulated assembly joint surface schematic diagram; Figure 4 (b) is a shape error schematic diagram of the extracted assembly joint surface; Figure 4 (c) is a waviness schematic diagram of the extracted assembly joint surface; Figure 4 (d) is a roughness schematic diagram of the extracted assembly joint surface; Figure 5 is a schematic diagram of a simulated base surface and extracted roughness components; Figure 5 (a) is a simulated base surface schematic diagram; Figure 5 (b) is a roughness schematic diagram of the extracted base surface; Figure 6is a wavelet-fractal representation assembly joint surface method flow chart. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0020] As Figures 1-6 indicated, the present application provides a technical solution: a wavelet-fractal assembly joint surface construction method, comprising the following steps: S1: according to the ideal numerical model of the assembly joint surface, the numerical simulation of the assembly joint surface is carried out by using the WM fractal function, the calculation method of the fractal parameter is determined, and the fractal parameter plays a key role in the change of the topographic profile characteristics of the assembly joint surface; wherein the expression of the two-dimensional WM fractal function is: ; the expression of the three-dimensional WM fractal function is: ; wherein, is the two-dimensional surface profile height, is the three-dimensional surface profile height, is the fractal dimension, is the fractal roughness, is the frequency term series, is the upper and lower limit of the series respectively, is the fundamental wavelength; the fractal parameters include the fractal dimension (taking the value range as 2<D<3 for three-dimensional surface) or 1<D<2 (two-dimensional profile) and the fractal roughness (unit: ); the ideal numerical model is a CAD ideal model.

[0021] Acquisition of Ideal Models for Assembly Joints: Taking the assembly joints of precision opto-electro-mechanical products (such as high-end machine tool base-slider assembly structures) as the object, obtain the ideal CAD model of the joint surface—that is, a theoretical design model that ignores non-ideal features such as surface roughness and waviness. The model format should adopt the industry-standard STEP or IGES format and must include key geometric parameters of the joint surface (such as the length and width of rectangular joint surfaces, the diameter of circular joint surfaces, etc.) to ensure that subsequent numerical simulations can accurately call geometric boundary information. The ideal CAD model must be consistent with the design dimensions of the actual parts. For example, for a 120mm×120mm rectangular assembly joint surface, the flatness error of its ideal model should be marked as "0" (theoretical ideal plane) to provide a benchmark for subsequent WM fractal function simulation of "non-ideal rough features".

[0022] Two-dimensional WM fractal function simulation (for subsequent anisotropic surfaces): Assembly surfaces subsequently determined to be anisotropic (such as milled surfaces, where the roughness characteristics differ significantly in different directions due to the tool cutting trajectory) need to be simulated separately. or One-dimensional contour features of direction.

[0023] Frequency series: based on the micro-roughness scale of the mating surface (usually) Set upper and lower limits for the level. (Characterizing the trend of mesoscopic coarsening) (Characterizing microscopic roughness details); fundamental wavelength : Match the macroscopic dimensions of the mating surface, such as a 120mm×120mm mating surface setting. To avoid contour distortion due to excessively large wavelengths or computational redundancy due to excessively small wavelengths; Initial values ​​of fractal parameters: fractal dimension (Conforms to two-dimensional contour) (range of values), fractal roughness (Typical roughness values ​​of the milled surface).

[0024] Simulation computational logic: for the interface Discrete sampling is performed in the direction, with a sampling interval. (Ensure capture of microscopic rough peaks), sampling range 12,000 sampling points were obtained. Substituting the two-dimensional WM fractal function: Calculate each point one by one Corresponding contour height , cumulative to All frequency terms are obtained. Two-dimensional rough profile.

[0025] 3D WM fractal function simulation (for subsequent isotropic surfaces): Applicable scenarios: Assembly surfaces that are subsequently determined to be isotropic (such as grinding surfaces, where random cutting by abrasive grains results in consistent roughness characteristics in all directions), requiring simulation of the overall three-dimensional roughness morphology.

[0026] Parameter settings: Frequency term series, fundamental wavelength are the same as in the two-dimensional simulation. ; Initial values ​​of fractal parameters: fractal dimension (Conforms to three-dimensional surface) (range of values), fractal roughness (Typical roughness amplitude of the covered grinding surface).

[0027] Proposed computational logic: for the interface Two-dimensional grid sampling is performed in the direction, with a sampling interval. A 12000×12000 sampling grid is formed, covering a complete 120mm×120mm interface; the three-dimensional WM fractal function is then substituted. Calculate each grid node point by point. contour height After summing all frequency terms, the three-dimensional rough surface morphology is obtained (e.g. Figure 5 (a) shows the simulated base surface.

[0028] Fractal parameter calculation method determined: Criteria for selecting calculation methods: fractal parameters To accurately reflect the roughness characteristics of the interface, the structure function method was selected after comparing the structure function method and the power spectrum method. It has the highest calculation accuracy (deviation from the actual surface ≤ 0.02μm) and strong robustness to noise, making it suitable for parameter calculation of continuous rough surfaces. The core logic of the structure function method: Define structure function ( The lag distance, for index); Take the contour data obtained from the 3D simulation. Direction fixed line (e.g.) ), calculate different lag distances corresponding ,right and Perform linear fitting to obtain the slope And then solve ; pass ( Calculated using reference lag distance ,make sure , Deviation < 5% with actual surface topography.

[0029] After simulation, the consistency of "fractal parameters-simulated topography" needs to be verified: the calculated is substituted back into fractal function, the joint surface profile is simulated again, and the deviation is calculated by the deviation formula ( to re-simulate the profile, is the initial simulated profile) If , it means that the WM fractal function simulation is effective, and the fractal parameter calculation method is reliable, which can be used as the basis data for subsequent steps (wavelet decomposition, parameter correlation).

[0030] For example, Figure 4 (a) As shown in the schematic diagram of the simulated assembly joint surface, based on the ideal numerical model of the assembly joint surface, the "initial non-ideal surface simulation topography" generated by the two-dimensional / three-dimensional WM fractal function combines three types of multi-scale features of roughness, waviness, and shape error, and is the basic input data for subsequent wavelet decomposition and power spectrum analysis.

[0031] S2: Compare different fractal parameter calculation methods, compare the error of the fractal parameters solved by each calculation method, and select the optimal fractal parameter calculation method suitable for the assembly joint surface; the error comparison uses the deviation formula: ; Where, is the deviation of the fractal simulation profile and the actual profile, is the number of sampling points, is the simulation profile height, is the actual profile height.

[0032] More specifically, step S2 "fractal parameter calculation method comparison and optimal method selection" is to determine the fractal parameter calculation scheme that can accurately match the assembly joint surface topography through multi-method comparison and error quantitative analysis, and to lay the foundation for subsequent model precision control. The specific key implementation contents are as follows: Comparison method: select three mainstream fractal parameter calculation methods; structure function method (continuous surface adaptation), power spectrum method (frequency characteristic adaptation), and box dimension method (discrete surface adaptation); Actual profile: laser confocal microscope measures the milling / grinding joint surface data (120mm x 120mm, sampling interval 0.01mm, precision 0.01μm); Simulated profile: the calculated by the three methods is substituted into the WM fractal function to generate simulation data corresponding to the actual sampling points one by one.

[0033] Parameter calculation: fitting the double logarithmic relationship between the lag distance and the structure function, and solving , (associated structure function value formula); power spectrum method through PSD curve slope to solve , empirical estimation ; box dimension method to fit the box number and scale relationship to solve , The estimation error is large.

[0034] Error comparison: use the deviation formula to calculate the root mean square deviation, The smaller the accuracy is higher; the structure function method The smallest (grinding 0.021 μm, milling 0.023 μm), the highest efficiency (15 minutes).

[0035] S3: According to the statistical distribution difference of the surface morphology information of the parts assembly joint surface under different processing methods, the statistical distribution parameters corresponding to the processing method are determined; the statistical distribution parameter calculation adopts the mean formula , variance formula , skewness formula , wherein, is the profile height mean, is the variance, is the skewness, is the actual profile height value of the th sampling point.

[0036] By quantifying the statistical characteristics of the surface morphology of the assembly joint surface under different processing methods, the association of "processing method-statistical parameter" is established, which provides a basis for the accurate matching of subsequent models and actual processes, as follows: Determine the typical processing method and the basic data: Target processing method: focus on the typical processing scene in the field of precision assembly, select two core processing methods of milling processing (corresponding to anisotropic surface) and grinding processing (corresponding to isotropic surface) as the objects of statistical distribution parameter association; Basic data source: actual surface data adopts laser confocal microscope (precision 0.01 μm), respectively samples the assembly joint surface of milling and grinding processing, sampling range 120mm×120mm, sampling interval , obtains profile height data of sampling points; data preprocessing eliminates abnormal points (such as extreme values caused by measurement noise) in the sampling data, to ensure the reliability of the data input into the statistical formula.

[0037] Statistical distribution parameter calculation implementation: For surface data from milling and grinding processes, calculate the mean values ​​separately. ,variance skewness The key points for calculating each parameter are as follows: mean Calculation (characterizing the overall height level of the surface): That is, the arithmetic mean of the contour heights of all sampling points; Milled surfaces: Due to the periodic peaks and valleys in the tool cutting path, Usually slightly above the ideal plane (e.g.) =0.03μm); Grinding surface: Random cutting by abrasive grains results in a symmetrical height distribution on the surface. Approaching an ideal plane (such as) =0.005μm); Function: To distinguish the overall surface height offset trend between two processing methods.

[0038] variance Calculation (characterizing the degree of surface undulation dispersion): , which is the average of the squared differences between the profile height and the mean; Milled surfaces: The cutting texture results in large local variations in undulation. Larger (e.g.) =0.0012μm 2 ); Grinding surface: The surface is smoother. Smaller (e.g.) =0.0003μm 2 ); Function: To quantify the difference in surface roughness amplitude between two processing methods ( The larger the size, the more uneven the surface.

[0039] Skewness Calculation (characterizing surface peak-valley asymmetry): That is, the normalized result of the cube mean of the difference between the contour height and the mean; Milled surfaces (such as) Figure 2 (a) shows that the cutting tool easily forms sharp peaks. (like =0.8), indicating that the number of peaks is greater than the number of valleys; Grinding surfaces (such as) Figure 2 (b) shows that abrasive compaction makes the peak-valley distribution symmetrical. (like =0.1); Function: The most crucial distinguishing parameter; through Positive and negative signs, as well as magnitude, can directly determine the processing method. > 0 is milling, ≈ 0 is grinding).

[0040] S4: The assembly joint surface is regarded as a structure formed by superimposing different scale profiles, including roughness profile, waviness profile and shape error profile. Wavelet transform is used to decompose the profile information components of the assembly joint surface, extract effective topographic features and remove noise invalid components.

[0041] More specifically, the input signal of wavelet transform decomposition is the topographic profile of the actual assembly joint surface The wavelet transform expression is wherein, is the wavelet transform coefficient, is the scale factor (controls the decomposition scale The smaller the scale factor, the more corresponding micro-roughness, The larger the scale factor, the more corresponding macro-shape error), is the translation factor (controls the translation position of the wavelet basis on the profile, ensures the coverage of the complete joint surface), is the wavelet basis function (preliminary screening series, series, series); After one wavelet decomposition, the original profile signal is decomposed into low-frequency information , horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information ; Removing noise invalid components is realized by threshold filtering, and the filtering formula is: ; wherein, is the filtered wavelet coefficient, (set according to the noise energy proportion), is the sign function (retains the positive and negative directions of the wavelet coefficient (reflects the profile peak and valley trend), avoids feature distortion).

[0042] One wavelet decomposition and profile component corresponding decomposition process: one wavelet transform is performed on the input signal The original signal is split into four types of components, and the corresponding relationship with the multi-scale profile is as follows: the low-frequency information LL corresponds to the macro-shape error profile (such as the overall flatness deviation of the joint surface), which is obtained by reconstructing the low-frequency coefficient; The horizontal high-frequency LH corresponds to the horizontal micro-roughness profile (such as the horizontal cutting texture of milling); The vertical high-frequency HL corresponds to the vertical micro-roughness profile (such as the vertical cutting texture of milling); The diagonal high-frequency HH corresponds to the diagonal micro-roughness profile (such as the random rough peaks of grinding); The first physical separation of three types of scale profiles is realized, which provides targeted data for subsequent feature extraction.

[0043] Operation object: high-frequency components after wavelet decomposition ; noise is mainly concentrated in high-frequency weak signals, low-frequency (shape error) signal stability, no need for filtering; Core effect: core effect: rejection random noise coefficient, retaining effective roughness feature coefficient, to ensure that the subsequent reconstruction of the roughness profile has no voice.

[0044] Wavelet transform decomposition includes the following sub-steps: Wavelet transform decomposition is the core link to realize the precise separation of multi-scale profile of assembly joint surface. Through S4.1 (select the best wavelet basis), S4.2 (determine the decomposition number), S4.3 (profile reconstruction) three sub-steps, ensure effective extraction of roughness, waviness, shape error characteristics and eliminate noise, the specific implementation content is as follows: S4.1: selection of the best wavelet basis function: Applicable scenario: According to the characteristics of assembly joint surface "multi-scale profile superposition, significant micro-roughness features", the appropriate basis function needs to be selected from the commonly used wavelet basis to avoid losing key topographic information during decomposition; Basic data: actual assembly joint surface profile data collected by laser confocal microscope (sample range 120mm×120mm, sampling interval , number of sampling points , accuracy 0.01μm), after pretreatment, eliminate abnormal extreme value.

[0045] Based on the profile characteristics of assembly joint surface (continuous smoothness, containing micro high-frequency roughness peak) and the properties of wavelet basis function, three main wavelet bases are preliminarily selected: db series wavelet: strong compact support, high computational efficiency, but poor smoothness, easy to lose micro profile details; sym series wavelet: compact support and smoothness, small reconstruction error, suitable for multi-scale decomposition of continuous surface; coif series wavelet: good symmetry, good fitting for low-frequency signals, but insufficient resolution for high-frequency roughness features.

[0046] Determination of the optimal wavelet basis based on RMSE: under the condition of ensuring the uniformity of wavelet decomposition number (temporary set to 7 times, consistent with the final number of S4.2), use the above 3 types of wavelet basis to decompose and reconstruct , the reconstruction accuracy is quantified by root mean square error (RMSE); RMSE formula application: The formula for root mean square error is , where The smaller the RMSE is, the higher the matching degree of the reconstructed profile with the original profile is. Screening results and best choice: Calculate the RMSE of the combined surface data of milling and grinding processing respectively, and the results are shown in the following table:

[0047] By comparison, the RMSE of sym5 wavelet basis is the smallest in both processing scenarios, and the reconstructed profile can completely retain the characteristics of microscopic rough peaks (such as milling cutting texture and grinding random rough peaks). Therefore, sym5 wavelet basis is determined as the "best wavelet basis function".

[0048] S4.2: Wavelet decomposition number determination: Core objective: Determine the decomposition number that can completely separate "shape error (low frequency LL), waviness (medium-high frequency), roughness (high frequency LH / HL / HH)", avoid profile aliasing due to insufficient decomposition, or increase redundancy due to excessive decomposition; Basic parameters: Based on the sym5 wavelet basis determined in S4.1, the preset decomposition number range is 1-10 times, and the low frequency energy distribution threshold According to the energy proportion requirement of the shape error profile, it is set to 0.7-0.8 (when the LL energy proportion , LL can completely represent the shape error).

[0049] Energy calculation method: Use the formula to calculate the energy of each decomposition level, where is the wavelet transform coefficient, and the energy size reflects the strength of the corresponding profile component; the energy of low frequency LL, horizontal high frequency LH, vertical high frequency HL, and diagonal high frequency HH needs to be calculated . Low frequency energy proportion calculation: The low frequency energy proportion formula is , and the value of is calculated successively after 1-10 times of decomposition. When first reaches , the corresponding level is the final decomposition number; The decomposition results of 120mm×120mm combined surface data show that when the decomposition number is 7 times, (falls within the range), the LL energy proportion is sufficient to represent the shape error, and can completely retain the roughness characteristics; if the decomposition number is less than 7 times, (the shape error extraction is not complete); if the decomposition number is greater than 7 times, (excessive decomposition leads to loss of roughness characteristics); therefore, the wavelet decomposition number is determined to be 7 times.

[0050] S4.3: Reconstruction of contour information components: Based on the sym5 wavelet basis of S4.1 and the 7th decomposition order of S4.2, the filtered wavelet coefficients are obtained using the inverse wavelet transform formula. (After threshold filtering to remove noise) it was restored to the contours at various scales; Inverse wavelet transform formula: ,in b is the scale factor (corresponding to different contour scales), and b is the translation factor (covering the complete bonding surface). The sym5 wavelet basis function can be used to reconstruct shape error (LL), waviness (mid-to-high frequency combination), and roughness, respectively. Three types of outlines; Scale-based reconstruction logic: Shape error profile: using only low-frequency LL Substituting into the inverse transformation formula, the macroscopic shape error (such as the flatness deviation of the mating surface) is reconstructed. Waviness profile: The meso-level waviness is reconstructed by substituting the mid-to-high frequency coefficients (high frequency components from the 3rd to 5th decompositions) into the formula. Roughness profile: Substituting high-frequency coefficients (LH+HL+HH from the 6th-7th decomposition) into the formula, the micro-roughness is reconstructed. ); Roughness profile accuracy verification: The reconstructed roughness profile needs to be consistent with... Figure 5 (b) shows the measured roughness profile matching, which satisfies With the measured profile The roughness matching deviation threshold is set to 0.02 μm based on the assembly accuracy requirements. The reconstruction results of the milled mating surfaces show that and Figure 5 (b) Measured profile It can clearly reproduce the horizontal cutting texture of milling; for grinding mating surfaces, It can completely preserve the random rough peaks of abrasive particles, proving that the reconstruction accuracy meets the requirements.

[0051] like Figure 4 (b) Schematic diagram of extracted shape error, 4(c) Schematic diagram of extracted waviness and Figure 4 (d) The extracted roughness diagram is shown. The roughness was obtained through wavelet transform (sym5 wavelet basis, 7th decomposition). Figure 4 (a) The simulated contour is decomposed into multiple scales, and the three single-scale contours of “shape error, waviness and roughness” are reconstructed respectively, which directly verifies the technical effect of wavelet transform in “separating multi-scale features and eliminating noise”.

[0052] S5: Introducing power spectrum analysis method to analyze the surface profile curve characteristics of the assembly joint surface; The power spectral density calculation uses the formula: ; The two-dimensional power spectral density formula is: ; Where, is the one-dimensional frequency (single direction frequency), is the directional frequency, is the directional frequency is the imaginary unit, and the changes in profile composition under different processing methods and different processing parameters are explored through the PSD curve.

[0053] The frequency distribution characteristics of the surface profile are quantified by power spectral density (PSD), and the correlation between "processing method- processing parameter- profile composition" is established, which provides frequency dimension basis for subsequent surface property judgment (S6) and parameter correlation (S7). The specific implementation contents are as follows: For the assembly joint surface profile data reconstructed in step S4, including: One-dimensional profile data: profile height of typical direction line (such as direction =60mm line, direction =60mm line) extracted from three-dimensional profile or ; Three-dimensional profile data: complete assembly joint surface three-dimensional topography data (sampling range 120mm×120mm, sampling interval , number of sampling points ); Data preprocessing: zero mean processing (subtracting mean ) is performed on the profile data to eliminate the interference of overall height offset on PSD calculation; at the same time, local abnormal extreme values (such as sudden points caused by measurement noise) are removed to ensure the reliability of input data.

[0054] One-dimensional power spectral density calculation (for single direction profile): Analyze the profile frequency characteristics of the assembly joint surface in a certain direction (such as the cutting direction of milling processing, the direction perpendicular to the cutting direction), and explore the frequency distribution difference of roughness and waviness in this direction; The one-dimensional power spectral density formula is ; Where, The height of a one-dimensional profile (e.g.) direction (Line height data); Frequency (unit: , The larger the value, the higher the micro-roughness. The smaller the value, the greater the macroscopic waviness / shape error. imaginary unit , For the complex exponential term of the Fourier transform, it is used to convert time-domain contour data into frequency-domain signals; Calculation operation: for one-dimensional contour data Perform Fast Fourier Transform The frequency domain coefficients are obtained. ; take the square of the modulus of the frequency domain coefficients, i.e. This yields a one-dimensional PSD curve; Frequency range setting: based on contour sampling interval The highest analysis frequency is determined by the Nyquist sampling theorem. lowest frequency ( (Length of the mating surface).

[0055] Two-dimensional power spectral density Calculation (for 3D surfaces): Analyze the overall frequency distribution characteristics of the assembly mating surfaces to determine surface isotropic / anisotropic properties (providing a basis for S6), and simultaneously investigate the differences in profile composition in different directions; the two-dimensional power spectral density formula is: ; in, They are respectively Frequency of direction (unit: ); It is a complex exponential term of the two-dimensional Fourier transform, realizing the conversion from the three-dimensional contour in the time domain to the frequency domain; Calculation operations: For 3D contour data Perform two-dimensional fast Fourier transform Two-dimensional frequency domain coefficients are obtained. Taking the square of the modulus of the two-dimensional frequency domain coefficients, i.e. Two-dimensional PSD map (horizontal axis) was obtained. y-axis (Color / height represents PSD values). Frequency range setting: The highest frequency in all directions is The lowest frequency is To ensure data comparability, it is consistent with the one-dimensional PSD.

[0056] By PSD curve (one-dimensional) or atlas (two-dimensional), the profile characteristics of milling and grinding, two typical machining methods, can be directly distinguished, and the specific differences are as follows:

[0057] S6: According to the isotropic or anisotropic properties of the assembly joint surface under different machining methods, the statistical distribution characteristic parameters determined in step S3 are introduced into the representation of the assembly joint surface; The isotropic determination basis is , the power spectral density is consistent in any direction, the anisotropic determination basis is , there are differences in power spectral density in different directions, and the correlation between statistical distribution characteristic parameters and machining methods is established.

[0058] By power spectral density (PSD), the isotropic / anisotropic properties of the assembly joint surface are determined, and the statistical distribution parameters of step S3 are deeply bound with the machining method, providing "process-feature" matching basis for subsequent fractal representation (S7). The specific key implementation contents are as follows: PSD data: two-dimensional power spectral density data calculated in step S5 (covering the assembly joint surface 120mmx120mm range, The frequency range is ; Statistical parameter data: three types of statistical distribution parameters calculated in step S3; mean , variance , skewness (based on the milling / grinding joint profile data measured by laser confocal); Machining method object: typical machining scenarios in the field of precision assembly, focusing on milling (preset to correspond to anisotropic surface) and grinding (preset to correspond to isotropic surface) as the core correlation object.

[0059] Determination tool and index setting: use MATLAB R2023b to draw a two-dimensional atlas (representing PSD value size with color gradient), and calculate one-dimensional PSD curves in different directions (0°, 45°, 90°, 135°); set "directional PSD deviation threshold ", if the PSD curves of any two orthogonal directions (such as 0° and 90°) are deviated in the full frequency range, it is determined that the power spectral density is consistent, otherwise it is determined that there is a difference.

[0060] Isotropic determination (corresponding to grinding): two-dimensional power spectral density satisfies (the power spectral density is consistent in any direction); Specific determination operation: from the two-dimensional From the spectrum, extract 0° ( Direction), 45°, 90° One-dimensional PSD curves in four typical directions (direction), 135°, etc.; calculate the relative deviation between the PSD curve in each direction and the PSD curve in the 0° direction: ; If all directions And two-dimensional If the spectrum shows an approximately concentric circle distribution (with no obvious directional bias), then the surface is determined to be isotropic. The determination of the mating surface in the grinding process shows that there are four directions. Maximum It meets the isotropic determination criteria and matches the preset processing method.

[0061] Anisotropy determination (corresponding to milling): The determination is based on the two-dimensional power spectral density satisfying the following conditions. (Power spectral density varies in different directions); Specific determination steps: Similar to the isotropic determination steps, extract one-dimensional PSD curves in four typical directions; calculate the relative deviation. If there exists at least one direction And two-dimensional If the spectrum shows a "high PSD value band" along a certain direction (such as the milling cutting direction) (significant directional preference), then the surface is determined to be anisotropic. The determination of the milling mating surface (cutting direction 0°) shows that the 90° direction (perpendicular to the cutting direction) The maximum is 18.5% > 5%, and the spectrum shows a high PSD band along the 0° direction, which meets the anisotropy judgment criteria and matches the preset processing method.

[0062] Establishing the correlation between statistical distribution parameters and machining methods: Based on the surface anisotropy determination results, the statistical distribution parameters from step S3 are bound to the milling / grinding machining methods, forming a unique correlation relationship of "machining method - anisotropy - statistical parameters". The specific correlation results are shown in the table below:

[0063] S7: According to Figure 6 The wavelet-fractal representation process shown associates the contour curve feature parameters extracted in step S4 with the fractal parameters determined in step S2. The association model adopts: ; in, These are the initial fractal parameters. For correction factor, The root mean square error (RMSE) of the roughness profile is a key characteristic parameter used to quantify the deviation between the micro-roughness profile of the assembly mating surface and a reference datum (such as the actual measured profile or the reconstructed profile). If the assembly mating surface is isotropic, it is characterized using a three-dimensional WM fractal function; if it is an anisotropic surface, it is characterized using... The directions are respectively represented by two-dimensional WM fractal functions: ; in, for Directional fractal dimension for The fractal roughness of the orientation is characterized; the final assembled mating surface must meet the overall deviation from the actual surface. ; in, For the assembly mating surface in three-dimensional space, the first The contour height of each sampling point This is the overall deviation threshold, and it is related to... Figure 5 (a) shows that the morphology matching degree of the simulated base surface meets the requirements, and the construction of the assembly mating surface is completed.

[0064] The basic data is the initial fractal parameters from step S2. Roughness of S4 skewness of S3 Surface anisotropy determination results (isotropic / anisotropic) of S6; Preset parameters: Correction coefficient Overall deviation threshold (because Therefore ), function parameters .

[0065] Fractal parameter correction is performed by calculating the corrected parameters using a correlation model. (such as grinding) ); (such as grinding) ).

[0066] Isotropic (grinding): using three-dimensional... function ; Anisotropy (milling): Directions are represented in two dimensions. function .

[0067] Calculate the overall deviation ,need And withFigure 5 (a) The deviation of the simulated base surface macro-morphology is less than or equal to 0.05 mm.

[0068] Step S7 realizes the precise construction of the assembly joint surface model through the process of "parameter association-directional characterization-deviation control": the association model solves the pain point of "uncontrollable" traditional fractal parameters, makes the actual contour feature dynamic adjustment; directional characterization ensures the process matching of anisotropy / isotropy surface, the milling model can restore the cutting texture, and the grinding model can reflect the random rough peak; deviation control ensures that the model precision is much higher than the measurement error, providing a reliable digital basis for subsequent precision assembly analysis, and finally completing the construction of the assembly joint surface highly consistent with the actual process and actual morphology.

[0069] More specifically, in step S2, the optimal fractal parameter calculation method is the structure function method, and the structure function formula is: ; wherein, is the height information of the assembly joint surface on the two-dimensional local contour, is the lag distance, is the index, and and are solved by fitting the linear relationship between and ; error comparison is realized by deviation analysis of the matching degree of the fractal parameters solved by each calculation method and the actual surface morphology.

[0070] More specifically, in step S4, the different scale contours from microscale to macroscale are in turn roughness contour (wavelength , microscale, affecting surface contact performance), waviness contour (wavelength , mesoscale, affecting assembly gap) and shape error contour (wavelength , macroscale, affecting overall assembly accuracy); the filtering threshold is determined according to the noise energy ratio, satisfying wherein, is the noise standard deviation, is an empirical coefficient, with a value range of 1.5-2.5; The calculation formula is: wherein is the measurement noise standard deviation (obtained by actual measurement of the noise-free area), is an empirical coefficient (value 1.5-2.5, balancing noise removal and feature retention); only the high-frequency component is filtered, and the low-frequency (shape error) does not need to be processed.

[0071] In step S4.1, the optimal wavelet basis function is: Wavelet basis functions; commonly used wavelet basis functions include Series of wavelets, Series of wavelets, Series of wavelets; The calculation needs to be based on Figure 5 (a) shows complete sampling data of the simulated base surface, with sampling intervals. Sampling range ; In step S4.2, the wavelet decomposition is performed 7 times; the low-frequency energy distribution threshold... The value is set based on the energy proportion of the shape error profile in the assembly mating surface profile, and the range of values ​​meets the following requirements. When the low-frequency information energy accounts for a certain decomposition level When the threshold is reached, this level is determined to be the final wavelet decomposition level; Low-frequency energy distribution threshold The value is set according to the proportion of energy in the shape error contour, ranging from 0.7 to 0.8. Energy percentage formula: Low-frequency energy, (High-frequency energy); Decomposition order determination: Based on the sym5 wavelet basis, when the decomposition is performed 7 times, First time reaching The range was determined to be 7 times as the final number of decompositions.

[0072] More specifically, in step S5, different machining methods include milling and grinding; for milling, power spectral analysis is used to determine the different milling speeds. (Unit: m / min) Feed rate The power spectral density variation of the assembly joint surface under (unit mm / r) is clearly defined. and Association patterns ,in, For amplitude coefficient, For the influence coefficient of rotational speed, For the feed rate influence coefficient, This is the frequency attenuation coefficient.

[0073] Implementation of the correlation between milling parameters and PSD: Selecting the milling speed (Unit: m / min, range 80-150 m / min), feed rate (unit: mm / r, value range 0.08-0.2 mm / r) as a variable, and other machining parameters (such as cutting depth, tool diameter) are fixed (cutting depth 0.2 mm, tool diameter 10 mm); the milling joint surfaces under different combinations are sampled (sampling range ) by a laser confocal microscope to obtain profile data ; ; The calculation and correlation law is as follows: the two-dimensional power spectral density formula is substituted into the two-dimensional power spectral density formula: , the values of each parameter combination are calculated; through data fitting, a quantitative correlation model of is established: , wherein: is an amplitude coefficient (value range after fitting ); is a rotational speed influence coefficient (value after fitting , a negative coefficient indicates that decreases when increases); is a feed rate influence coefficient (value after fitting , a positive coefficient indicates that increases); is a frequency attenuation coefficient (value after fitting , indicating that presents a decay trend as the frequency increases).

[0074] More specifically, in step S6, the isotropic surface corresponds to grinding processing, which satisfies ; the anisotropic surface corresponds to milling processing, which satisfies .

[0075] Based on the two-dimensional map of step S5, it satisfies (the power spectral density is consistent in any direction), and the x and y direction fractal parameters have no difference; the fractal dimension and the fractal roughness calculated by the structure function method determined in step S2 need to satisfy (three-dimensional surface ), , to ensure that the surface has no direction preference.

[0076] Anisotropic surface (corresponding to milling processing): based on the two-dimensional map of step S5, it satisfies (the power spectral density difference is significant in different directions), and the direction fractal parameters have clear differences; Fractal parameter requirements: Calculated using the same structure function method. The directional fractal parameters must satisfy: Fractal dimension difference (like direction , direction (difference ≥ 0.05) Fractal roughness difference: (like direction , direction Difference ).

[0077] More specifically, in step S7, the overall deviation threshold Set according to actual assembly precision requirements, and in, The range of values ​​represents the measurement error of the actual machined surface morphology. Correction factor pass Figure 5 The simulation and extracted data shown in (a)-(b) are fitted to obtain the results that satisfy the following conditions: .

[0078] It is necessary to meet the actual assembly accuracy requirements (such as ≤0.005mm for high-end machine tools) and strictly satisfy them. ,in The actual surface morphology measurement error (measured using a laser confocal microscope, with values ​​ranging from...) is considered. ;when hour, Actual settings This ensures that the model error is much smaller than the measurement error, and prevents the measurement error from masking the model bias.

[0079] Correction coefficient Sure: based on Figure 5 (a) Three-dimensional fractal simulation data of the “simulated base surface” (generated in step S1) and Figure 5 (b) The "extracted roughness component" data (reconstructed in step S4) was obtained by least squares fitting; Fitting and value selection: Substitute multiple sets of simulated and extracted data into the correlation model. , The fitting yielded The value range is [0.1, 0.3] (e.g., when...). Each increase , 0.002-0.003) ; Similarly, the fitting obtained Value range (As when Each increase of 0.1, Increase ), the actual application can be adjusted within the range according to the specific processing method (milling to take a large value, grinding to take a small value).

[0080] More specifically, the wavelet inverse transform reconstruction needs to cover Figure 6 The "contour extraction-parameter association" link in the process ensures With the original signal The , and the reconstructed waviness and shape error profile are consistent with the mesoscopic and macroscopic features of the simulated surface shown in Figure 5 (a).

[0081] Although embodiments of the present application have been shown and described, it will be understood by those having ordinary skill in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for constructing an assembly interface considering wavelets and fractals, characterized in that, Includes the following steps: S1: Based on the ideal digital model of the assembly mating surface, numerical simulation of the assembly mating surface is performed using the WM fractal function to determine the calculation method of the fractal parameters. The fractal parameters play a key role in the changes of the morphological contour characteristics of the assembly mating surface; among them, the expression of the two-dimensional WM fractal function is: ； The expression for the three-dimensional WM fractal function is: ； in, The height of the two-dimensional surface profile. The height of the three-dimensional surface profile. For fractal dimension, For fractal roughness, For frequency series, These are the upper and lower limits of the series, respectively. The fundamental wavelength; S2: Compare the calculation methods for different fractal parameters, compare the errors of the fractal parameters obtained by each method, and select the optimal fractal parameter calculation method suitable for the assembly joint surface; the error comparison uses the deviation formula: ； in, To account for the deviation between the fractal simulation profile and the actual profile, The number of sampling points. To simulate the contour height, This is the actual outline height; S3: For the assembly surfaces of parts under different processing methods, determine the statistical distribution parameters corresponding to the processing method based on the statistical distribution differences of their surface morphology information; the statistical distribution parameters are calculated using the mean formula. Variance formula , Skewness formula ,in, The average height of the profile. For variance, For skewness, For the first The actual contour height value of each sampling point; S4: The assembly mating surface is regarded as a structure formed by the superposition of contours of different scales. The contours of different scales include roughness contour, waviness contour and shape error contour. Wavelet transform is used to decompose the contour information components of the assembly mating surface, extract the effective morphological features, and remove noise and invalid components. S5: Introduce power spectrum analysis method to analyze the surface profile curve characteristics of the assembly mating surface; S6: Based on the isotropic or anisotropic properties of the assembly mating surface under different processing methods, the statistical distribution characteristic parameters determined in step S3 are introduced into the characterization of the assembly mating surface. S7: Associate the contour curve feature parameters extracted in step S4 with the fractal parameters determined in step S2.

2. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 1, characterized in that, In S4, the input signal for wavelet transform decomposition is the topographic contour of the actual assembly joint surface. The wavelet transform expression is: ,in, These are the wavelet transform coefficients. As a scale factor, The translation factor is... The wavelet basis functions are used; after one wavelet decomposition, the original contour signal is decomposed into low-frequency information. Horizontal high-frequency information Vertical high-frequency information and diagonal high-frequency information Removing invalid noise components is achieved through threshold filtering, and the filtering formula is as follows: ； in, These are the filtered wavelet coefficients. It is a symbolic function.

3. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 2, characterized in that, Wavelet transform decomposition includes the following sub-steps: S4.1 Selecting the Optimal Wavelet Basis Functions: Based on the properties of commonly used wavelet basis functions and the decomposition requirements of the assembly joint surface contour features, wavelet basis functions are initially screened. While ensuring the same wavelet decomposition degree, each of the initially screened wavelet basis functions is used to decompose and reconstruct the assembly joint surface. The original contour signal and the reconstructed signal are compared using the root mean square error (RMSE). The RMSE formula is as follows: ； in, To reconstruct the contour height, the wavelet basis function with the smallest RMSE is selected as the optimal wavelet basis function; S4.2 Determining the Wavelet Decomposition Order: Based on the optimal wavelet basis function, compare the energy distribution of low-frequency and high-frequency information in each wavelet decomposition level. The energy is calculated using the following formula: Set a low-frequency energy distribution threshold When the proportion of low-frequency energy at a certain decomposition level ,in, , , , The information energy of low frequency, horizontal high frequency, vertical high frequency, and diagonal high frequency are respectively used to determine the final wavelet decomposition level; S4.3 Reconstruction of contour information components: Based on the optimal wavelet basis function and the determined wavelet decomposition degree, the inverse wavelet transform formula is used: ； Extract the morphological contour features of the assembly mating surfaces to reconstruct the contour information components.

4. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 3, characterized in that, In S5, the power spectral density is calculated using the following formula: ； The formula for two-dimensional power spectral density is: ； in, For one-dimensional frequency, for Directional frequency, for Directional frequency The imaginary unit is used to explore the changes in contour components under different processing methods and parameters through PSD curves. In S6, the isotropic determination criterion is as follows: The power spectral density is consistent in any direction, and the criterion for anisotropy is as follows: The power spectral density varies in different directions, and the correlation between statistical distribution characteristic parameters and processing methods is established.

5. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 4, characterized in that, In S7, the association model adopts: ； in, These are the initial fractal parameters. For correction factor, The roughness profile root mean square error is used; if the mating surfaces are isotropic, they are characterized using a three-dimensional WM fractal function; if they are anisotropic, then... The directions are respectively represented by two-dimensional WM fractal functions: ； in, for Directional fractal dimension for The fractal roughness of the orientation is characterized; the final assembled mating surface must meet the overall deviation from the actual surface. ； in, For the assembly mating surface in three-dimensional space, the first The contour height of each sampling point This is the overall deviation threshold.

6. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 5, characterized in that, In step S2, the optimal fractal parameter is calculated using the structure function method, and the structure function formula is: ； in, This provides the height information of the assembly mating surface on its two-dimensional local contour. The lag distance, for The index, through fitting and Solving the linear relationship and Error comparison is achieved by analyzing the deviation between the fractal parameters obtained by each calculation method and the actual surface morphology.

7. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 6, characterized in that, In step S4, the different scale profiles, from micro to macro scale, are roughness profile, waviness profile, and shape error profile, respectively; the filtering threshold... Determined based on the proportion of noise energy, satisfying... in, The standard deviation of noise. This is an empirical coefficient, with a value range of 1.5-2.5; In step S4.1, the optimal wavelet basis function is: Wavelet basis functions; commonly used wavelet basis functions include Series of wavelets, Series of wavelets, Series of wavelets; In step S4.2, the wavelet decomposition is performed 7 times; the low-frequency energy distribution threshold... The value is set based on the energy proportion of the shape error profile in the assembly mating surface profile, and the range of values ​​meets the following requirements. When the low-frequency information energy accounts for a certain decomposition level When the threshold is reached, this level is determined as the final wavelet decomposition level.

8. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 7, characterized in that, In step S5, different machining methods include milling and grinding; for milling, power spectral analysis is used to determine the different milling speeds. Feed rate The power spectral density variation at the lower assembly interface was clarified. and Association patterns ,in, For amplitude coefficient, For the influence coefficient of rotational speed, For the feed rate influence coefficient, This is the frequency attenuation coefficient.

9. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 8, characterized in that, In step S6, the isotropic surface is processed by grinding, which satisfies... The corresponding machining method for anisotropic surfaces is milling, which satisfies... .

10. A method for constructing an assembly interface considering wavelet and fractal principles according to claim 9, characterized in that, In step S7, the overall deviation threshold Set according to actual assembly precision requirements, and in, The range of values ​​represents the measurement error of the actual machined surface morphology. Correction coefficient satisfy .

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