A method for constructing an assembly joint surface considering wavelet and fractal

Abstract

The application relates to the technical field of non-ideal surface generation of machined parts, and particularly discloses a construction method of an assembly joint surface considering wavelet and fractals, which comprises the following steps: S1, according to an ideal numerical model of the assembly joint surface; S2, comparing calculation methods of different fractal parameters; S3, aiming at the assembly joint surface of parts under different machining modes; S4, regarding the assembly joint surface as a structure formed by superposition of different scale contours; S5, introducing a power spectrum analysis method to analyze the surface contour curve characteristics of the assembly joint surface; S6, according to the isotropic or anisotropic properties of the assembly joint surface under different machining modes, introducing the statistical distribution characteristic parameters determined in step S3 into the representation of the assembly joint surface; and S7, associating the contour curve characteristic parameters extracted in step S4 with the fractal parameters determined in step S2. Through multi-scale decomposition of the assembly joint surface by wavelet transform, the specific information of the roughness contour, the waviness contour and the shape error contour can be effectively extracted.

Description

TECHNICAL FIELD

[0001] The 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 wavelets and fractals. BACKGROUND

[0002] Precise assembly technology is the core process to guarantee the performance of high-end equipment. In the assembly process of precise 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 after magnification, showing significant uneven non-ideal characteristics, which are different from the absolute smooth ideal state represented by the CAD model.

[0003] 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, through single and multiple fractal methods, left snow realizes the three-dimensional topography representation of wear surfaces, and reveals the surface detail characteristics and amplitude fluctuation law; in view of the defects of the traditional statistical method, such as the limitation of the resolution of the measuring instrument and the sampling length, Mu et al. use fractal parameters to simulate different machining surface topographies, and verify the consistency of the simulation results of the 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.

[0004] 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 precise optoelectromechanical products, and may lead to unstable performance of the equipment, which becomes a key bottleneck restricting the development of precise assembly technology of high-end equipment. SUMMARY

[0005] In view of the deficiencies of the prior art, the application provides a construction method of an assembly joint surface considering wavelet and fractals, and solves the problems in the background art.

[0006] To achieve the above object, the application is implemented by the following technical scheme: a construction method of an assembly joint surface considering wavelet and fractals, comprising the following steps:

[0007] S1: according to the ideal numerical model of the assembly joint surface, the assembly joint surface is numerically simulated by using a WM fractal function to determine the calculation method of the fractal parameters, and the fractal parameters play a key role in the change of the profile characteristics of the assembly joint surface; wherein the expression of the two-dimensional WM fractal function is:

[0008] ;

[0009] the expression of the three-dimensional WM fractal function is:

[0010] ;

[0011] wherein, is the profile height of the two-dimensional surface, is the profile height of the three-dimensional surface, is the fractal dimension, is the fractal roughness, is the frequency term series, is the upper and lower limits of the series respectively, is the fundamental wave length;

[0012] S2: the calculation methods of different fractal parameters are compared, the fractal parameters solved by each calculation method are compared in error, and the optimal fractal parameter calculation method suitable for the assembly joint surface is selected; the error comparison adopts a deviation formula:

[0013] ;

[0014] wherein, 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;

[0015] S3: for the part assembly joint surface under different machining modes, the statistical distribution parameters corresponding to the machining modes are determined according to the statistical distribution difference of the surface profile information; the statistical distribution parameters are calculated by using the mean formula , the variance formula , and the skewness formula , wherein, is the mean of the profile height, is the variance, is the skewness. actual profile height value of the i-th sampling point; actual profile height value of the i-th sampling point;

[0016] S4: regarding the assembly joint surface as a structure formed by superposition of different scale profiles including roughness profile, waviness profile and form error profile, decomposing profile information components of the assembly joint surface by wavelet transform, extracting effective topographic features and removing noise invalid components;

[0017] S5: introducing power spectrum analysis method to analyze surface profile curve features of the assembly joint surface;

[0018] S6: according to isotropic or anisotropic properties of the assembly joint surface under different processing modes, introducing statistical distribution feature parameters determined in step S3 into the representation of the assembly joint surface;

[0019] S7: associating profile curve feature parameters extracted in step S4 with fractal parameters determined in step S2.

[0020] 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 a wavelet transform coefficient, is a scale factor, is a translation factor, is a 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:

[0021] ;

[0022] , wherein, is a filtered wavelet coefficient, is a sign function.

[0023] Preferably, wavelet transform decomposition includes the following sub-steps:

[0024] 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 decompositions, decomposing and reconstructing the assembly joint surface by using each wavelet base function initially screened, comparing the original profile signal with the reconstructed signal by root mean square error, and the root mean square error formula is:

[0025] ;

[0026] wherein, The wavelet base function with the minimum RMSE is selected as the optimal wavelet base function for reconstructing the profile height;

[0027] S4.2, determining the number of wavelet decomposition: based on the optimal wavelet base function, the energy distribution of low-frequency information and high-frequency information in each wavelet decomposition level is compared, and the energy is calculated by the formula:

[0028] , and the low-frequency energy distribution threshold is set When the low-frequency energy of a decomposition level accounts for wherein, , , , The low-frequency, horizontal high-frequency, vertical high-frequency and diagonal high-frequency information energies are respectively determined as the final wavelet decomposition number;

[0029] S4.3, reconstruction of profile information components: based on the optimal wavelet base function and the determined wavelet decomposition number, the inverse wavelet transform formula is used:

[0030] ;

[0031] The profile feature of the assembly joint surface is extracted, and the reconstruction of the profile information components is completed.

[0032] Preferably, in S5, the power spectral density is calculated by the formula:

[0033] ;

[0034] The two-dimensional power spectral density formula is:

[0035] ;

[0036] wherein, is the one-dimensional frequency, is the directional frequency, is the directional frequency is the imaginary unit, and the change of the profile components under different machining methods and different machining parameters is found out through the PSD curve;

[0037] In S6, the isotropic determination basis is , the anisotropic determination basis is , the statistical distribution characteristic parameters and the machining methods are related.

[0038] Preferably, in S7, the correlation model adopts:

[0039] ;

[0040] wherein, is the initial fractal parameter, is the correction coefficient, is the roughness profile root mean square error; 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, two-dimensional WM fractal functions are used in the direction respectively:

[0041] ;

[0042] wherein, is the fractal dimension in the direction, is the fractal roughness in the direction, for characterization; the final assembly joint surface needs to satisfy the overall deviation from the actual surface:

[0043] ;

[0044] wherein, is the profile height of the th sampling point in the three-dimensional space of the assembly joint surface, is the overall deviation threshold.

[0045] Preferably, in step S2, the optimal fractal parameter calculation method is the structure function method, and the structure function formula is:

[0046] ;

[0047] wherein, is the height information of the assembly joint surface on the two-dimensional local profile, is the lag distance, is the exponent, and and are solved by fitting the linear relationship between and ; 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.

[0048] Preferably, in step S4, the different scale profiles from microscale to macroscale are roughness profile, waviness profile and shape error profile in turn; the filtering threshold is determined according to the proportion of noise energy, satisfying wherein, is the noise standard deviation, is an experience coefficient, and the value range is 1.5-2.5;

[0049] In step S4.1, the optimal wavelet base function is Wavelet base function; commonly used wavelet base functions include Series wavelet, Series wavelet, Series wavelet;

[0050] In step S4.2, the wavelet decomposition number is 7 times; the low-frequency energy distribution threshold According to the energy proportion of the shape error profile in the assembly joint surface profile, the value range satisfies When the low-frequency information energy proportion of a decomposition level is The threshold, it is determined that the level is the final wavelet decomposition number.

[0051] Preferably, in step S5, different processing methods include milling processing and grinding processing; for the milling processing method, the power spectrum analysis method is used to determine the power spectrum density change of the lower assembly joint surface under different milling speeds , feed amount , and the association law of and is determined , wherein is an amplitude coefficient, is a speed influence coefficient, is a feed amount influence coefficient, is a frequency attenuation coefficient

[0052] Preferably, in step S6, the corresponding processing method of the isotropic surface is grinding processing, which satisfies ; the corresponding processing method of the anisotropic surface is milling processing, which satisfies .

[0053] Preferably, in step S7, the overall deviation threshold is set according to the actual assembly precision requirement, and , wherein is an actual processing surface topography measurement error, and the value range is ; the correction coefficient satisfies .

[0054] The present application aims at the technical defects of the existing fractal theory in the simulation of the assembly joint surface, realizes the dual breakthrough of the assembly joint surface modeling precision and practicability through the deep integration of wavelet transform and fractal theory, and has the following beneficial effects:

[0055] 1、The present application can effectively extract the specific information of roughness profile, waviness profile and shape error profile by multi-scale decomposition of the assembly joint surface through wavelet transform; for example, for milled surfaces, the horizontal / vertical high-frequency characteristics caused by the cutting direction can be separated; for ground surfaces, the uniformly distributed high-frequency rough peak characteristics can be captured, solving the pain point that traditional fractal methods cannot distinguish between processing methods; at the same time, the influence of different processing parameters (such as milling speed and feed rate) 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, and realize high reflection of physical model and digital model.

[0056] 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, and by establishing a parameter correction model to realize dynamic adjustment of fractal parameters, the modeling accuracy of surfaces of different properties is further improved, and the overall deviation of the constructed non-ideal surface and the actual joint surface can be controlled within a preset threshold.

[0057] 3、The assembly joint surface model constructed by the present application can accurately reflect the surface topography characteristics under actual processing conditions, providing a reliable digital basis for the assembly deviation analysis and control of precision optoelectromechanical products; through the model, changes in contact stiffness and uneven stress distribution caused by differences in joint surface topography during assembly can be predicted in advance, helping engineers optimize assembly process parameters, effectively reducing the impact of assembly deviation on equipment performance, and ensuring the performance stability of high-end equipment during long-term operation, which has important practical significance for promoting the development of precision assembly technology to higher precision levels.

[0058] 4、The present application defines the selection criteria for key parameters such as wavelet basis function, decomposition number and low-frequency energy threshold, and provides specific implementation methods for fractal parameter calculation (structure function method) and noise removal (threshold filtering), forming a standardized assembly joint surface construction process; this process does not require complex custom parameter debugging, making it easy for engineering and technical personnel to quickly master and apply, effectively reducing the application threshold of non-ideal surface modeling technology, and being suitable for assembly joint surface simulation scenarios of different types of precision parts. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is a contact area display diagram of enlarged assembly joint surface of parts;

[0060] Figure 2 is a schematic diagram of surfaces of two base parts under different processing methods;

[0061] Figure 2 (a) is a milling surface schematic diagram;

[0062] Figure 2 (b) is a grinding surface schematic diagram;

[0063] Figure 3 is a profile component information schematic diagram after one wavelet decomposition;

[0064] Figure 4 is a simulated assembly joint surface and extracted component schematic diagram;

[0065] Figure 4 (a) is a simulated assembly joint surface schematic diagram;

[0066] Figure 4 (b) is an assembly joint surface extracted shape error schematic diagram;

[0067] Figure 4 (c) is an assembly joint surface extracted waviness schematic diagram;

[0068] Figure 4 (d) is an assembly joint surface extracted roughness schematic diagram;

[0069] Figure 5 is a simulated base surface and extracted roughness component schematic diagram;

[0070] Figure 5 (a) is a simulated base surface schematic diagram;

[0071] Figure 5 (b) is a base surface extracted roughness schematic diagram;

[0072] Figure 6 is a wavelet-fractal assembly joint surface characterization method flow schematic diagram. DETAILED DESCRIPTION

[0073] 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 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 of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0074] As shown in Figures 1-6 , the present application provides a technical solution: a wavelet and fractal considering assembly joint surface construction method, comprising the following steps:

[0075] S1: According to the ideal numerical model of the assembly joint surface, the WM fractal function is used to simulate the assembly joint surface, and the calculation method of the fractal parameter is determined, which plays a key role in the change of the profile characteristics of the assembly joint surface; the two-dimensional WM fractal function expression is:

[0076] ;

[0077] The three-dimensional WM fractal function expression is:

[0078] ;

[0079] , 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;

[0080] The fractal parameters include the fractal dimension (taking the value range of 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.

[0081] Obtaining the ideal numerical model of the assembly joint surface: taking the assembly joint surface of a precision optoelectromechanical product (such as a high-end machine tool base-sliding block assembly structure) as the object, the CAD ideal model of the joint surface is obtained, that is, the theoretical design model ignoring the non-ideal characteristics such as surface roughness and waviness, the model format adopts the industry common STEP or IGES format, and needs to include the key geometric parameters of the joint surface (such as the length, width of the rectangular joint surface, the diameter of the circular joint surface, etc.), to ensure that the geometric boundary information can be accurately called in subsequent numerical simulation. The CAD ideal model needs to be consistent with the design size of the actual part, for example, for a 120mm×120mm rectangular assembly joint surface, the flatness error of its ideal model needs to be marked as “0” (theoretically ideal plane), which provides a reference for the subsequent WM fractal function simulation of “non-ideal roughness characteristics”.

[0082] Two-dimensional WM fractal function simulation (for subsequent anisotropic surfaces): the subsequent assembly joint surface determined to be anisotropic (such as a milling surface, which has significant differences in roughness characteristics in different directions due to the tool cutting trajectory), needs to simulate the one-dimensional profile characteristics of or direction separately.

[0083] Frequency term series: according to the micro-roughness scale of the joint surface (usually Set upper and lower limits for the level. (Characterizing the trend of mesoscopic coarsening) (Characterizing microscopic roughness details);

[0084] 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;

[0085] Initial values ​​of fractal parameters: fractal dimension (Conforms to two-dimensional contour) (range of values), fractal roughness (Typical roughness values ​​of the milled surface).

[0086] 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.

[0087] 3D WM fractal function simulation (for subsequent isotropic surfaces):

[0088] 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.

[0089] Parameter settings: Frequency term series, fundamental wavelength are the same as in the two-dimensional simulation. ;

[0090] 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).

[0091] 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. profile height , after accumulating all frequency terms, the three-dimensional rough surface topography (such as Figure 5 (a) shows the simulated base surface).

[0092] Fractal parameter calculation method is determined:

[0093] The calculation method is screened according to the fractal parameter Need to accurately reflect the roughness characteristics of the joint surface, compared with the structure function method, power spectrum method, select the structure function method; Its calculation accuracy is the highest (deviation from the actual surface ≤0.02 μm), and it is robust to noise, suitable for parameter calculation of continuous rough surface;

[0094] The core logic of the structure function method:

[0095] Define the structure function ( is the lag distance, is exponent);

[0096] For the three-dimensional simulation of the profile data, take fixed line (such as ), calculate the corresponding of different lag distance , linear fitting for and , get the slope , and then solve ;

[0097] Calculate ( is the reference lag distance) through , ensure that , and the actual surface topography match the deviation ≤5%.

[0098] After simulation, the consistency of "fractal parameter-simulated topography" needs to be verified: the calculated is re-substituted into fractal function, and the joint surface profile is simulated again. Calculate the deviation through the deviation formula ( is the re-simulated 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 the subsequent steps (wavelet decomposition, parameter correlation).

[0099] As Figure 4(a) Based on the ideal model of the assembly joint surface, the "initial non-ideal surface simulation topography" generated by the two-dimensional / three-dimensional WM fractal function simulates the assembly joint surface shown in the schematic diagram, and fuses three types of multi-scale features of roughness, waviness, and shape error, which is the basic input data for subsequent wavelet decomposition and power spectrum analysis.

[0100] S2: Compare the calculation methods of different fractal parameters, compare the errors 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:

[0101] ;

[0102] Wherein, the deviation of the fractal simulation profile and the actual profile, the number of sampling points, the simulation profile height, the actual profile height.

[0103] 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 lay the foundation for subsequent model precision control. The specific key implementation contents are as follows:

[0104] Comparison method: select three main fractal parameters calculation methods; structure function method (continuous surface adaptation), power spectrum method (frequency characteristic adaptation), and box dimension method (discrete surface adaptation);

[0105] Actual profile: laser confocal microscope measures the milling / grinding joint surface data (120mm x 120mm, sampling interval 0.01mm, precision 0.01μm);

[0106] Simulation profile: the calculated by the three methods is substituted into the WM fractal function to generate simulation data corresponding to the actual sampling points.

[0107] Parameter calculation: fit the lag distance and the double logarithm relationship of the structure function by the structure function method, and solve , (formula associated structure function value); the power spectrum method solves by the slope of the PSD curve, and is estimated by experience; the box dimension method fits the number of boxes and the scale relationship to solve , The estimated error is large.

[0108] Error comparison: calculate the root mean square deviation by the deviation formula , The smaller the precision is, the higher the accuracy is; structure function method The smallest (grinding 0.021 μm, milling 0.023 μm), the highest efficiency (15 minutes).

[0109] S3: For the assembly joint surface of parts under different machining methods, the statistical distribution parameters corresponding to the machining methods are determined according to the statistical distribution difference of the surface topography information; the statistical distribution parameters are calculated by using the mean formula , the variance formula , and the skewness formula , wherein, is the mean value of the profile height, is the variance, is the skewness, is the actual profile height value of the i-th sampling point.

[0110] By quantifying the statistical characteristics of the surface topography of the assembly joint surface under different machining methods, the association of "machining method-statistical parameter" is established, which provides a basis for the accurate matching of the subsequent model and the actual process, as follows:

[0111] Determine the typical machining method and the basic data:

[0112] Target machining method: focus on the typical machining scene in the field of precision assembly, select two core machining methods of milling processing (corresponding to anisotropic surface) and grinding processing (corresponding to isotropic surface) as the objects of statistical distribution parameter association;

[0113] Basic data source: the actual surface data is obtained by using a laser confocal microscope (precision 0.01 μm), and the assembly joint surfaces of milling and grinding processing are sampled respectively, the sampling range is 120 mm x 120 mm, the sampling interval is , the profile height data of sampling points are obtained ; the data preprocessing eliminates the 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.

[0114] Statistical distribution parameter calculation implementation:

[0115] For the surface data of milling and grinding, the mean value , the variance , and the skewness are calculated respectively, and the calculation of each parameter is as follows:

[0116] Mean value calculation (representing the overall height level of the surface): , that is, the arithmetic mean value of the profile height of all sampling points;

[0117] ​Milling surface: periodic peaks and valleys due to tool cutting trajectory, Generally slightly above ideal plane (e.g. = 0.03 pm);

[0118] Grinding surface: random cutting by abrasive particles makes surface height distribution symmetric, Close to ideal plane (e.g. = 0.005 pm);

[0119] Purpose: to distinguish the overall height shift trend of surfaces processed by two methods.

[0120] Variance Calculation (characterizes the dispersion of surface undulation): i.e. the average of squared differences between profile height and mean value;

[0121] Milling surface: cutting texture leads to large local undulation difference, Larger (e.g. = 0.0012 pm 2 );

[0122] Grinding surface: surface is smoother, Smaller (e.g. = 0.0003 pm 2 );

[0123] Purpose: to quantify the difference in surface roughness amplitude of two processing methods (the larger, the more uneven the surface). Skewness

[0124] Calculation (characterizes the asymmetry of surface peaks and valleys): i.e. the normalized result of cubic average of differences between profile height and mean value; Milling surface (e.g. shown in (a) of the drawings): tool cutting easily forms sharp peaks,

[0125] (e.g. = 0.8), indicating that the number of peaks is more than that of valleys; Figure 2 Grinding surface (e.g. shown in (b) of the drawings): abrasive particles rolling makes peak-valley distribution symmetric, (e.g. = 0.1);

[0126] Purpose: the most critical distinguishing parameter; by Figure 2 positive and negative and size, the processing method can be directly determined (> 0 is probably milling, = 0 is grinding).

[0127] Purpose: the most critical distinguishing parameter; by positive and negative and size, the processing method can be directly determined (> 0 is probably milling, = 0 is grinding).

[0128] ​​​​​S4: The assembly joint surface is regarded as a structure formed by superposition of 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.

[0129] 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 ; The removal of noise invalid components is realized by threshold filtering, and the filtering formula is:

[0130] ;

[0131] 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).

[0132] One wavelet decomposition and profile component corresponding decomposition process: for the input signal Perform one wavelet transform, and the original signal is split into four types of components. 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 processing); The vertical high-frequency HL corresponds to the vertical micro-roughness profile (such as the vertical cutting texture of milling processing); The diagonal high-frequency HH corresponds to the diagonal micro-roughness profile (such as the random rough peaks of grinding processing); The first implementation of three types of scale profile physical separation provides targeted data for subsequent feature extraction.

[0133] Operation object: for the high-frequency components after wavelet decomposition ; noise is mainly concentrated in high frequency weak signal, low frequency (shape error) signal stability, no need for filtering;

[0134] Core effect: core effect: rejection random noise coefficient, keep effective roughness characteristic coefficient, to ensure the roughness profile of subsequent reconstruction without voice.

[0135] 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, to ensure the effective extraction of roughness, waviness, shape error characteristics and eliminate noise, the specific key implementation content as follows:

[0136] S4.1: selection of the best wavelet basis function:

[0137] Applicable scenario: according to the characteristics of assembly joint surface "multi-scale profile superposition, micro roughness characteristics significant", need to select the adaptive basis function from the commonly used wavelet basis, to avoid losing key topographic information during decomposition;

[0138] Basic data: actual assembly joint surface profile data collected by laser confocal microscope (sample range 120mm x 120mm, sampling interval , the number of sampling points , accuracy 0.01μm), after pretreatment, eliminate abnormal extreme value.

[0139] Based on the profile characteristics of assembly joint surface (continuous smooth, containing micro high frequency rough peak) and the properties of wavelet basis function, three kinds of mainstream wavelet basis are preliminarily selected:

[0140] db series wavelet: strong compact support, high computational efficiency, but poor smoothness, easy to lose micro profile details;

[0141] sym series wavelet: compact support and smoothness, reconstruction error is small, suitable for multi-scale decomposition of continuous surface;

[0142] coif series wavelet: good symmetry, good fitting for low frequency signal, but the resolution of high frequency roughness characteristics is insufficient.

[0143] 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 three kinds of wavelet basis to decompose and reconstruct , the reconstruction accuracy is quantified by root mean square error (RMSE);

[0144] RMSE formula application:

[0145] The root mean square error formula is , wherein is the profile height after reconstruction of different wavelet bases, and the smaller the RMSE is, the higher the matching degree of the reconstructed profile and the original profile is;

[0146] Screening results and best choice: the RMSE of the combined surface data of milling and grinding is calculated, and the results are shown in the following table:

[0147]

[0148] By comparison, the RMSE of sym5 wavelet base is the smallest in the two processing scenarios, and the reconstructed micro-rough peak characteristics (such as milling cutting texture and grinding random rough peak) can be completely retained, so the sym5 wavelet base is determined as the "best wavelet base function".

[0149] S4.2: Wavelet decomposition number determination:

[0150] Core target: 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;

[0151] Basic parameters: sym5 wavelet base determined based on S4.1, preset decomposition number range is 1-10 times, low frequency energy distribution threshold According to the energy ratio requirement of the shape error profile, it is set to 0.7-0.8 (when the LL energy ratio , LL can completely represent the shape error).

[0152] Energy calculation method: use the formula to calculate the signal energy of each decomposition level, wherein 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 respectively.

[0153] Low frequency energy ratio calculation: the low frequency energy ratio formula is , the value of after 1-10 times of decomposition is calculated, when first reaches , the corresponding level is the final decomposition number.

[0154] The decomposition result of 120mmx120mm combined surface data shows that when the decomposition number is 7 times, (falls into (range), at which point the LL energy percentage is sufficient to represent the shape error, and It can completely preserve roughness features; if the number of decompositions is less than 7, (Shape error extraction is incomplete); if the number of decompositions is greater than 7, (Excessive decomposition leads to the loss of roughness features); therefore, the wavelet decomposition order is determined to be 7.

[0155] S4.3: Reconstruction of contour information components:

[0156] 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;

[0157] 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;

[0158] Scale-based reconstruction logic:

[0159] 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.

[0160] 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.

[0161] Roughness profile: Substituting high-frequency coefficients (LH+HL+HH from the 6th-7th decomposition) into the formula, the micro-roughness is reconstructed. );

[0162] 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.

[0163] 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, The random rough peaks of the abrasive particles can be completely reserved, and the reconstruction accuracy meets the requirements.

[0164] As Figure 4 (b) the extracted shape error profile, (c) the extracted waviness profile, and Figure 4 (d) the extracted roughness profile, the simulated profile of (a) is decomposed by wavelet transform (sym5 wavelet basis, 7th decomposition), and three types of single-scale profiles of "shape error, waviness, and roughness" are reconstructed respectively, directly verifying the technical effect of wavelet transform in "separating multi-scale features and removing noise". Figure 4

[0165] S5: Introducing power spectrum analysis method to analyze the surface profile curve characteristics of the assembly joint surface;

[0166] The power spectral density calculation uses the formula:

[0167] ;

[0168] The two-dimensional power spectral density formula is:

[0169] ;

[0170] wherein, 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 machining methods and different machining parameters are investigated through the PSD curve.

[0171] The frequency distribution characteristics of the surface profile are quantified by power spectral density (PSD), and the correlation between "machining method, machining parameter, and profile composition" is established, which provides frequency dimension basis for subsequent surface property determination (S6) and parameter correlation (S7). The specific implementation contents are as follows:

[0172] For the assembly joint surface profile data reconstructed in step S4, including:

[0173] One-dimensional profile data: profile height of typical direction line (such as direction =60mm line, direction =60mm line) extracted from three-dimensional profile or ;

[0174] Three-dimensional profile data: complete three-dimensional topography data of the assembly joint surface ​(Sampling range 120mm×120mm, sampling interval) Number of sampling points );

[0175] Data preprocessing: Zero-mean subtraction is performed on the contour data (mean is subtracted). This eliminates the interference of overall height offset on PSD calculation; at the same time, it removes local abnormal extreme values ​​(such as abrupt changes caused by measurement noise) to ensure the reliability of input data.

[0176] One-dimensional power spectral density Calculation (for a single-direction profile):

[0177] Analyze the contour frequency characteristics of the assembly mating surface in a specific direction (such as the cutting direction or perpendicular cutting direction in milling) to determine the frequency distribution differences of roughness and waviness in that direction.

[0178] The formula for one-dimensional power spectral density is: ;

[0179] in, 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;

[0180] Calculation operation: for one-dimensional contour data Perform Fast Fourier Transform The frequency domain coefficients are obtained. Taking the square of the modulus of the frequency domain coefficients, i.e. This yields a one-dimensional PSD curve;

[0181] 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).

[0182] Two-dimensional power spectral density Calculation (for 3D surfaces):

[0183] The frequency distribution characteristics of the whole assembly joint surface are analyzed to determine the isotropy / anisotropy of the surface (to provide basis for S6), and the profile component differences in different directions are found out; the two-dimensional power spectral density formula is:

[0184] ;

[0185] wherein, are the frequencies in the x and y directions (unit: ); is a complex exponential term of two-dimensional Fourier transform, which realizes the conversion from the time domain three-dimensional profile to the frequency domain;

[0186] Calculation operation: two-dimensional fast Fourier transform is performed on the three-dimensional profile data to obtain two-dimensional frequency domain coefficients ; the square of the modulus of the two-dimensional frequency domain coefficients, i.e. , is obtained to obtain the two-dimensional PSD spectrum (the horizontal coordinate , the vertical coordinate , and the color / height represent the PSD value); Frequency range setting:

[0187] The highest frequency in the x and y directions is , and the lowest frequency is , which is consistent with the one-dimensional PSD to ensure data comparability. Through the PSD curve (one-dimensional) or spectrum (two-dimensional), the profile characteristics of the two typical machining methods of milling and grinding can be directly distinguished, and the specific differences are as follows:

[0188]

[0189] S6: According to the isotropy or anisotropy properties of the surface 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;

[0190] The isotropy determination basis is

[0191] , the power spectral density in any direction is consistent, the anisotropy determination basis is , the power spectral density in different directions is different, and the correlation between the statistical distribution characteristic parameters and the machining method is established. The isotropy / anisotropy properties of the assembly joint surface are determined by the power spectral density (PSD), and the statistical distribution parameters of step S3 are deeply bound with the machining method to provide "process-feature" matching basis for subsequent fractal representation (S7), and the specific key implementation contents are as follows:

[0192]

[0193] ​​PSD data: two-dimensional power spectral density data calculated in step S5 (over the range of 120 mm x 120 mm of the assembly joint, The frequency range is ;

[0194] Statistical parameter data: three types of statistical distribution parameters calculated in step S3; mean , variance , skewness (laser confocal measured milling / grinding joint profile data);

[0195] Processing mode object: typical processing scenarios in the field of focused precision assembly, taking milling processing (preset to correspond to anisotropic surface) and grinding processing (preset to correspond to isotropic surface) as the core related objects.

[0196] Determination tool and index setting: use MATLAB R2023b to draw two-dimensional map (representing PSD value size with color gradient), and calculate one-dimensional PSD curve 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 all , then it is determined that the "power spectral density is consistent", otherwise it is "different".

[0197] Isotropic determination (corresponding to grinding processing): two-dimensional power spectral density satisfies (any direction power spectral density is consistent);

[0198] Specific determination operation: from the two-dimensional map, extract one-dimensional PSD curves of four typical directions 0° , 45°, 90° , 135°; calculate the relative deviation of PSD curves in each direction and the PSD curve in 0° direction:

[0199] ;

[0200] If the of all directions is , and the two-dimensional map is "approximately concentric" (no obvious directional preference), then the surface is determined to be isotropic;

[0201] The determination of the grinding processing joint shows that the of the four directions is , which meets the isotropic determination standard and matches the preset processing mode.

[0202] Anisotropy determination (corresponding to milling processing): determine according to two-dimensional power spectral density satisfying (difference exists in different directions power spectral density);

[0203] Specific determination operation: same as isotropic determination step, extract one-dimensional PSD curve of four typical directions; calculate relative deviation , if there is at least one direction , and two-dimensional spectrum along a certain direction (such as milling cutting direction) appears "high PSD value strip area" (direction preference is significant), it is determined that the surface is anisotropic;

[0204] The determination of milling processing joint surface (cutting direction 0°) shows that the maximum of 90° direction (perpendicular to cutting direction) is 18.5%>5%, and the spectrum along 0° direction presents high PSD band, which meets the anisotropy determination standard and matches the preset processing mode.

[0205] Correlation between statistical distribution parameters and processing mode: based on the surface anisotropy determination result, the statistical distribution parameters of step S3 are bound with milling / grinding processing mode to form the exclusive correlation relationship of "processing mode-anisotropy-statistical parameter", and the specific correlation results are shown in the following table:

[0206]

[0207] S7: according to the wavelet-fractal characterization process shown in Figure 6 , the contour curve feature parameters extracted in step S4 are associated with the fractal parameters determined in step S2;

[0208] The correlation model adopts:

[0209] ;

[0210] Wherein, is the initial fractal parameter, is the correction coefficient, is the root mean square error of roughness profile (used to quantify the deviation degree of the micro-roughness profile of the assembly joint surface from the reference benchmark (such as the actual measured profile, the reconstructed profile)) If the assembly joint surface is isotropic surface, three-dimensional WM fractal function is used for characterization; if it is anisotropic surface, two-dimensional WM fractal function is used in direction respectively:

[0211] ;

[0212] Wherein, is the direction fractal dimension, is The direction fractal roughness is characterized; the finally constructed assembly joint surface needs to meet the overall deviation from the actual surface:

[0213] ;

[0214] 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, and meets (a) the matching degree of the simulated base surface morphology meets the requirements, and the construction of the assembly joint surface is completed. Figure 5 The basic data are the initial fractal parameters of step S2,

[0215] the roughness of S4, the skewness of S3, and the surface isotropy judgment result (isotropic / anisotropic) of S6; The preset parameters are the correction coefficient

[0216] , the overall deviation threshold (because , therefore ), and the function parameters.

[0217] The fractal parameters are corrected, and the corrected parameters are calculated by using the correlation model:

[0218] (such as grinding ); (such as grinding ).

[0219] Isotropic (grinding): a three-dimensional function is used;

[0220] Anisotropic (milling): the directions are respectively represented by two-dimensional functions .

[0221] The overall deviation is calculated, needs to meet , and meets Figure 5 (a) the macroscopic morphology deviation of the simulated base surface is less than or equal to 0.05 mm.

[0222] Step S7 realizes the precise construction of the assembly joint surface model through the process of "parameter correlation-direction characterization-deviation control": the correlation model solves the pain point of "uncontrollable" traditional fractal parameters, so that ​​The actual profile characteristics can be dynamically adjusted according to actual profile characteristics; the anisotropy / isotropy surface process matching is ensured, the milling model can restore the cutting texture, and the grinding model can reflect random rough peaks; deviation control The model precision is much higher than the measurement error, which provides a reliable digital basis for subsequent precise assembly analysis, and finally completes the construction of the assembly joint surface which is highly consistent with the actual process and actual morphology.

[0223] More specifically, in step S2, the optimal fractal parameter calculation method is the structure function method, and the structure function formula is:

[0224] ;

[0225] Wherein, is the height information of the assembly joint surface on the two-dimensional local profile, is the hysteresis distance, is exponent, which is 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 and the actual surface topography.

[0226] More specifically, in step S4, the profiles of different scales from microscale to macroscale are in turn roughness profile (wavelength , microscale, affecting surface contact performance), waviness profile (wavelength , mesoscale, affecting assembly gap) and shape error profile (wavelength , macroscale, affecting overall assembly accuracy); the filtering threshold is determined according to the noise energy ratio, which satisfies Wherein, is the standard deviation of noise, is an empirical coefficient, with a value range of 1.5-2.5;

[0227] The calculation formula is: Wherein is the standard deviation of measurement noise (obtained by actual measurement of the noise-free area), is an empirical coefficient (value 1.5-2.5, balancing noise elimination and feature retention); only the high-frequency component is filtered, and the low-frequency (shape error) does not need to be processed.

[0228] In step S4.1, the best wavelet base function is wavelet base function; common wavelet base functions include Daubechies series wavelet, Coiflet series wavelet,​​ series wavelet; The calculation needs to be based on Figure 5 (a) the complete sampling data of the simulated base surface shown, with a sampling interval , and a sampling range ;

[0229] In step S4.2, the wavelet decomposition number is 7 times; the low-frequency energy distribution threshold value is set according to the energy proportion of the shape error profile in the assembly joint surface profile, and the value range satisfies When the low-frequency information energy proportion of a certain decomposition level reaches the threshold value, the level is determined as the final wavelet decomposition number;

[0230] The low-frequency energy distribution threshold value is set according to the shape error profile energy proportion, and the value is 0.7-0.8;

[0231] The energy proportion formula is: is the low-frequency energy, is the high-frequency energy);

[0232] Decomposition number determination: based on the sym5 wavelet base, when decomposed 7 times, the first time to reach the range, it is determined that 7 times is the final decomposition number.

[0233] More specifically, in step S5, different machining methods include milling machining and grinding machining; for the milling machining method, the power spectrum density variation of the assembly joint surface under different milling speeds (unit: m / min), feed rates (unit: mm / r) is explored by power spectrum analysis method, and the association law of and is clarified , wherein is the amplitude coefficient, is the speed influence coefficient, is the feed rate influence coefficient, is the frequency attenuation coefficient.

[0234] Association of milling machining parameters and PSD: select the milling speed (unit: m / min, value range 80-150 m / min), feed rate (unit: mm / r, value range 0.08-0.2 mm / r) as variables, and other machining parameters (such as cutting depth, tool diameter) are fixed (cutting depth 0.2 mm, tool diameter 10 mm); for the milling joint surface under different combinations, laser confocal microscopy sampling (sampling range ), obtain contour data ;

[0235] Calculation and correlation patterns. Substituting into the two-dimensional power spectral density formula:

[0236] Calculate the combination of parameters Values; establish through data fitting. Quantitative correlation model: ,in:

[0237] The amplitude coefficient (range of values ​​after fitting) ); The rotational speed influence coefficient (value obtained after fitting) Negative coefficients indicate When it increases reduce); The feed rate influence coefficient (value obtained after fitting) Positive coefficients indicate (rise) The frequency attenuation coefficient (value obtained after fitting) ,express (It decreases with increasing frequency).

[0238] More specifically, in step S6, the isotropic surface is processed by grinding, satisfying... The corresponding machining method for anisotropic surfaces is milling, which satisfies... .

[0239] Based on the two-dimensional... Atlas, satisfying (Power spectral density is consistent in all directions), and there is no difference in fractal parameters in the x and y directions; the fractal dimension is calculated using the structure function method determined in step S2. fractal roughness , must meet (three-dimensional surface) ), This ensures that the surface has no orientation bias.

[0240] Anisotropic surfaces (corresponding to milling): based on the two-dimensional model in step S5 Atlas, satisfying (The power spectral density varies significantly in different directions), and There are clear differences in the directional fractal parameters;

[0241] Fractal parameter requirements: Calculated using the same structure function method. The directional fractal parameters must satisfy:

[0242] Fractal dimension difference (like direction , direction (difference ≥ 0.05)

[0243] Fractal roughness difference: (like direction , direction Difference ).

[0244] 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: .

[0245] 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.

[0246] Correction coefficient Sure:

[0247] 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;

[0248] 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 , Increase by 0.002-0.003);

[0249] Similarly, the fitting obtains Value range (As when Every increase of 0.1, Increase ), the actual application can be adjusted within the range according to the specific processing method (milling takes a large value, grinding takes a small value).

[0250] More specifically, the wavelet inverse transform reconstruction needs to cover Figure 6 The "contour extraction-parameter association" link in the process, to ensure With the original signal The , and the reconstructed waviness, shape error profile respectively with Figure 5 (a) The simulated surface mesoscopic, macroscopic features are consistent.

[0251] 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. The 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. The 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. The method for constructing an assembly interface considering wavelets and fractals 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. The 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. The 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. The method for constructing an assembly interface considering wavelet and fractal as described in 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. The method for constructing an assembly interface considering wavelet and fractal as described in 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 wavelets and fractals 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 factor satisfy .

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