Interference fit-oriented cylinder surface system error separation and morphology modeling method
By separating and reconstructing the systematic and random errors of the shaft-hole interference fit, a combined model of Fourier basis function and radial basis function is adopted to solve the error aliasing problem, and achieve high-precision morphology reconstruction and accurate prediction of contact stress.
Patent Information
- Application Number
- CN202510889073.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-30
- Publication Date
- 2025-09-26
AI Technical Summary
Existing technologies are unable to effectively separate and decouple systematic and random errors in shaft-hole interference fit, resulting in error aliasing and distortion, and unable to accurately characterize multi-scale morphological features, affecting the accuracy of interference fit and contact stress prediction.
A method for separating systematic errors and modeling topography of cylindrical surfaces with interference fit is adopted. Through three-coordinate measurement, Fourier component analysis and finite element simulation, systematic errors and random errors are separated, and the topography is reconstructed using a combined model of Fourier basis function and radial basis function.
It achieves accurate tracing of system errors and high-precision morphology reconstruction, improves the prediction accuracy of interference fit and the accuracy of contact stress, and enhances the guiding value of process improvement.
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Figure CN120706187A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a cylindrical surface system error separation and morphology modeling method for interference fit, and belongs to the technical field of mechanical manufacturing and precision measurement. Background Art
[0002] In the field of shaft-hole interference fit, the geometric shape error of the assembly contact surface has a universal influence on the fitting accuracy. Even if the machining process meets the dimensional tolerance requirements, the mating surface will form a systematic ripple error due to deterministic factors such as the radial runout of the machine tool spindle, periodic wear of the tool, cutting thermal deformation and clamping deflection. At the same time, due to the influence of random factors such as local uneven hardness of the material and cutting micro-vibration, the surface will produce non-periodic concave and convex features. The traditional three-coordinate measurement method uses least squares cylindrical fitting, which regards the total error as a completely random distribution, resulting in some technical defects. The first is error aliasing distortion. The systematic and random errors are not separated, and the periodic ripples are masked by random noise. They cannot be traced back to process defects such as spindle runout or tool wear, and the guiding value of process improvement is lost. Secondly, modeling and representation limitations exist. Single basis function models (such as pure polynomials or Fourier series) cannot simultaneously characterize multi-scale topographic features. Polynomials can only describe overall taper / waist drum trends, while Fourier series only capture periodic textures. The fitting distortion rate for localized random bumps (abnormal protrusions >5μm) exceeds 30%. Finally, there is fit prediction distortion: interference fit simulations based on idealized smooth cylinders ignore actual topographic fluctuations, resulting in large contact interference in localized bumpy contact areas, leading to contact stress prediction errors of over 40%.
[0003] There is an urgent need to develop a method that can decouple systematic and random errors in three-dimensional space and construct a physically interpretable topography model to provide realistic geometric input for interference fits. To this end, this paper proposes a method for separating systematic errors and conducting topography modeling on cylindrical surfaces for interference fits. Through an integrated geometric-mechanical modeling architecture, this method achieves a closed-loop chain of error decoupling, topography reconstruction, and precise interference mapping in a single analytical environment. Summary of the Invention
[0004] In view of this, the present invention provides a method for separating system errors and modeling the topography of a cylindrical surface for interference fit, so as to solve or alleviate the technical problems existing in the prior art and at least provide a beneficial option.
[0005] The technical solution of the present invention is implemented as follows: a method for separating system errors and modeling the topography of a cylindrical surface for interference fit, comprising the following steps: Step 1: Measure the point cloud data of the shaft and hole cylindrical surface. Use a three-dimensional coordinate measuring machine to measure the point cloud data of the shaft and hole assembly cylindrical surface of the interference fit shaft and hole parts to be measured, and obtain the coordinates of the shaft cylindrical surface measurement data point s_shaft(x,y,z) and the hole cylindrical surface measurement data point coordinates s_hole(x,y,z) and their corresponding cylindrical coordinates s_shaft(r,θ,z) and s_hole(r,θ,z); Step 2: Iterative positioning of the reference axis. Convert the cylindrical coordinates of the point cloud data in step 1 into a Cartesian coordinate system, fit a spatial straight line as the initial reference axis, and calculate the initial reference axis through iterative optimization using the least squares method. Step 3: Partial F test is used to determine the dominant model. The initial reference axis is updated by analyzing the Fourier components of the circumferential errors of the shaft and the cylindrical surface of the hole. The partial F test is then used to determine whether the Fourier components are significant. The systematic errors are determined and added to the dominant model. Step 4: Randomness test to determine the significant model: perform serial correlation test and chi-square test on the Fourier components selected in step 3 to determine random errors, and then add them to the significant model; Step 5: Construct a cylindrical free-form surface expression. Use a combination of Fourier basis functions and radial basis functions to model the periodic errors and local details of the shaft and hole cylindrical surfaces, and collaboratively characterize the complex morphologies of the shaft and hole cylindrical surfaces. Step 6: Finite element interference fit simulation, create shafts and holes with error surfaces, assign material properties to the parts, and then establish analysis steps. The contact parts use face-to-face contact, perform finite element simulation, and view the stress distribution and deformation cloud map.
[0006] Further preferably, in step 1, the coordinates of the shaft cylindrical surface measurement data points and the hole cylindrical surface measurement data points are converted into their corresponding cylindrical coordinates using the polar coordinate formula. .
[0007] Further preferably, in step 2, in a three-dimensional cylindrical coordinate system, the point cloud data is represented in the form of cylindrical coordinates (r, θ, z), where r is the radius, θ is the circumferential angle, and z is the height coordinate; in order to obtain the initial reference axis, the point cloud data is converted from the cylindrical coordinates to the Cartesian coordinate system (x, y, z), and then a spatial straight line is fitted as the initial reference axis, which is expressed by the following formula: , Where (xi, yi, zi) are the coordinates of the point cloud data in the Cartesian coordinate system; (x0, y0, z0) is the spatial starting point of the fitting axis, and (x0, y0, z0) is the average value of the Cartesian coordinate system (x, y, z) of all coordinate measurement points; (α, β, γ) are the normalized components of the axis direction vector; R is the radius of the fitting cylinder; N is the number of point cloud data. The initial reference axis is calculated through iterative optimization using the least squares method.
[0008] Further preferably, in step 3, the circumferential error of the cylinder includes systematic error and random error, and the initial reference axis is updated by analyzing the Fourier component. The Fourier component expression is as follows: , in is the amplitude of the Fourier component; is the order of the Fourier component; is the phase angle, According to the influence of the first-order Fourier component, the update formula of the initial reference axis is expressed in three-dimensional space as follows: , Where Cz is calculated by the error distribution along the axis direction; Further preferably, in step three, the initial reference axis is updated The polar coordinate formula is converted into (r, θ, z), which is then brought into the Fourier component expression to calculate the Fourier component after each update of the initial reference axis.
[0009] Further preferably, in step 3, the calculation formula of the partial F test statistic is , in, is the residual sum of squares of the current model, is the residual sum of squares of the previous model; N is the number of point cloud data, p is the number of Fourier components in the current model, and the analysis starts from the Fourier component with the heaviest weight. like The current Fourier component is considered significant and is added to the dominant model. That is, the systematic error, the final expression of the dominant model is: .
[0010] Further preferably, in step 4, the residuals of the remaining Fourier components after screening are tested for no correlation through serial correlation test, the serial correlation coefficient is calculated, the residuals are iteratively calculated starting from the Fourier component with the heaviest weight, and then the serial correlation test is performed. The formula is as follows: , in, is the residual of the i-th Fourier component, is the mean of the residuals. If the obtained |r| is approximately equal to 0, it is considered that the residuals have no correlation and a chi-square test is performed; Further preferably, in step 4, the chi-square statistic is calculated using the chi-square test formula, which is as follows: , in, is the observed frequency of the ith interval, Ei is the expected frequency, K is the number of intervals, if It is assumed that the residual follows a normal distribution and is added to the significant model, that is, random error. The final expression of the significant model is, , Further preferably, in step 5, the free-form surface models of the shaft and the cylindrical surface of the hole are expressed in the following form: , in, is the Fourier basis function, which is used to characterize the periodic characteristics in the circumferential and height directions; It is a radial basis function used to capture the complex morphological changes in local areas. The combination of Fourier basis function and radial basis function jointly describes the global trend of the axis and hole cylinder. .
[0011] Further preferably, the separation of systematic errors and random errors of the shaft cylindrical surface and the hole cylindrical surface and the construction of the free-form surface are screened and constructed according to steps two to five.
[0012] The embodiment of the present invention adopts the above technical solution, which has the following advantages: The present invention realizes the decoupling and separation of systematic error and random error over the entire cylindrical surface, eliminates the first-order eccentricity component through iterative positioning of the axis, and screens the significant Fourier component through the partial F test, thereby realizing the decoupling and separation of systematic error and random error over the entire cylindrical surface, and greatly improving the accuracy of tracing the source of systematic error; at the same time, a hybrid model of Fourier basis function plus radial basis function is proposed, which realizes high-fidelity reconstruction of multi-scale morphology, and high-precision restoration of local random concave-convex errors, periodic textures and overall trends. Compared with the existing single model, the morphology restoration degree is greatly improved.
[0013] The above summary is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments and features described above, further aspects, embodiments and features of the present invention will be readily apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS
[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.
[0015] Figure 1 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION
[0016] In the following, only certain exemplary embodiments are briefly described. As those skilled in the art would realize, the described embodiments may be modified in various different ways without departing from the spirit or scope of the present invention.
[0017] The embodiments of the present invention are described in detail below.
[0018] The embodiment of the present invention provides a method for separating system errors and modeling the topography of a cylindrical surface for interference fit, comprising the following steps: Step 1: Measure the point cloud data of the shaft and hole cylindrical surface. Use a three-dimensional coordinate measuring machine to measure the point cloud data of the shaft and hole assembly cylindrical surface of the interference fit shaft and hole parts to be measured, and obtain the coordinates of the shaft cylindrical surface measurement data point s_shaft(x,y,z) and the hole cylindrical surface measurement data point coordinates s_hole(x,y,z) and their corresponding cylindrical coordinates s_shaft(r,θ,z) and s_hole(r,θ,z); Step 2: Iterative positioning of the reference axis. Convert the cylindrical coordinates of the point cloud data in step 1 into a Cartesian coordinate system, fit a spatial straight line as the initial reference axis, and calculate the initial reference axis through iterative optimization using the least squares method. Step 3: Partial F test is used to determine the dominant model. The initial reference axis is updated by analyzing the Fourier components of the circumferential errors of the shaft and the cylindrical surface of the hole. The partial F test is then used to determine whether the Fourier components are significant. The systematic errors are determined and added to the dominant model. Step 4: Randomness test to determine the significant model: perform serial correlation test and chi-square test on the Fourier components selected in step 3 to determine random errors, and then add them to the significant model; Step 5: Construct a cylindrical free-form surface expression. Use a combination of Fourier basis functions and radial basis functions to model the periodic errors and local details of the shaft and hole cylindrical surfaces, and collaboratively characterize the complex morphologies of the shaft and hole cylindrical surfaces. Step 6: Finite element interference fit simulation, create shafts and holes with error surfaces, assign material properties to the parts, and then establish analysis steps. The contact parts use face-to-face contact, perform finite element simulation, and view the stress distribution and deformation cloud map.
[0019] .
[0020] In one embodiment, in step 1, the coordinates of the shaft cylindrical surface measurement data points and the hole cylindrical surface measurement data points are converted into their corresponding cylindrical coordinates using the polar coordinate formula. The original point cloud data of the assembly cylindrical surface of the interference fit shaft and hole is obtained and converted into Cartesian coordinates and cylindrical coordinates to provide basic data for subsequent error analysis and modeling. The three-dimensional coordinate measuring instrument can collect three-dimensional space point coordinates with high precision, ensuring the accuracy of the original data, which is the prerequisite for error separation; the cylindrical coordinates (r, θ, z) directly correspond to the radial, circumferential and height directions of the cylindrical surface, facilitating the subsequent analysis of errors in various directions, such as radial errors affecting the amount of interference and circumferential errors affecting the uniformity of fit; Cartesian coordinates (x, y, z) are suitable for spatial linear fitting, while cylindrical coordinates facilitate subsequent Fourier analysis. The combination of the two coordinate systems can take into account both spatial geometric calculations and cylindrical surface characteristic analysis.
[0021] In one embodiment, in step 2, in a three-dimensional cylindrical coordinate system, the point cloud data is represented in cylindrical coordinate form (r, θ, z), where r is the radius, θ is the circumferential angle, and z is the height coordinate. To obtain an initial reference axis, the point cloud data is converted from cylindrical coordinates to a Cartesian coordinate system (x, y, z), and then a spatial straight line is fitted as the initial reference axis, which is expressed by the following formula: , Where (xi, yi, zi) are the coordinates of the point cloud data in the Cartesian coordinate system; (x0, y0, z0) is the spatial starting point of the fitting axis, (x0, y0, z0) is the average value of the Cartesian coordinate system (x, y, z) of all coordinate measurement points; (α, β, γ) is the normalized component of the axis direction vector; R is the radius of the fitted cylindrical surface; N is the number of point cloud data, and the initial reference axis is calculated by iterative optimization using the least squares method; the initial reference axis of the cylindrical surface is determined by fitting a spatial straight line using the least squares method, providing a benchmark for error separation; the shape error of the cylindrical surface, such as roundness and straightness, needs to be analyzed based on the axis, and the axis positioning accuracy directly affects the error separation result; with the goal of minimizing the sum of the squares of the distance from the point cloud to the axis, the starting point of the axis (x0, y0, z0) and direction vectors (α, β, γ) can suppress the influence of measurement noise and improve the accuracy of axis fitting; after converting cylindrical coordinates into Cartesian coordinates, spatial straight line fitting is easier to handle mathematically, such as vector operations and distance calculations, which conforms to the optimization logic of the least squares method.
[0022] In one embodiment, in step 3, the circumferential error of the cylinder includes systematic error and random error. The initial reference axis is updated by analyzing the Fourier component. The Fourier component expression is as follows: , in is the amplitude of the Fourier component; is the order of the Fourier component; is the phase angle.
[0023] According to the influence of the first-order Fourier component, the update formula of the initial reference axis is expressed in three-dimensional space as follows: , Where Cz is calculated by the error distribution along the axis direction; In step 3, the initial reference axis is updated The polar coordinate formula is converted into (r, θ, z), which is then brought into the Fourier component expression to calculate the Fourier component after each update of the initial reference axis.
[0024] In step 3, the partial F test statistic is calculated as , in, is the residual sum of squares of the current model, is the residual sum of squares of the previous model; N is the number of point cloud data, p is the number of Fourier components in the current model, and the analysis starts from the Fourier component with the heaviest weight. like The current Fourier component is considered significant and is added to the dominant model. That is, the systematic error, the final expression of the dominant model is: , The circumferential error is analyzed by Fourier analysis, and the significant Fourier components are screened using the partial F test to determine the systematic error and update the reference axis. The periodic error characterization of Fourier analysis shows that the circumferential error of the cylindrical surface, such as polyhedralism and eccentricity, is periodic and can be decomposed into Fourier components of different orders, such as the first order corresponding to eccentricity and the second order corresponding to ellipticity, which is convenient for quantitative description. The test starts from the Fourier component with the heaviest weight, and by comparing the changes in the sum of squares of the model residuals, it is judged whether the current component has a significant contribution to the error, avoiding the introduction of irrelevant components that lead to model redundancy. The first-order Fourier component, such as eccentricity, will affect the axis position. By iteratively updating the axis, the interference of low-order errors on the benchmark can be eliminated, making subsequent analysis more accurate.
[0025] In one embodiment, in step 4, the residuals of the remaining Fourier components after screening are tested for correlation by serial correlation, and the serial correlation coefficient is calculated. The residuals are iteratively calculated starting from the Fourier component with the heaviest weight, and then the serial correlation test is performed. The formula is as follows: , in, is the residual of the i-th Fourier component, is the mean of the residuals. If the obtained |r| is approximately equal to 0, it is considered that the residuals have no correlation and a chi-square test is performed; In step 4, the chi-square statistic is calculated using the chi-square test formula, which is as follows: , in, is the observed frequency of the ith interval, Ei is the expected frequency, K is the number of intervals, if It is assumed that the residual follows a normal distribution and is added to the significant model, that is, random error. The final expression of the significant model is, .
[0026] The filtered Fourier components are subjected to serial correlation test and chi-square test to identify random errors and add them to the model; systematic errors, such as periodic polyhedralism, can be characterized by Fourier components, while random errors, such as surface roughness and measurement noise, are irregular and need to be identified through statistical tests; if there is correlation in the residuals, it means that the model does not fully capture the systematic errors; if |r|≈0, the residuals are independent and the randomness can be further tested; if the residuals obey the normal distribution and are judged by the chi-square test, they are considered to be random errors and need to be added to the model to improve the integrity of the morphology modeling and avoid missing local details.
[0027] In one embodiment, in step five, the free-form surface models of the shaft and the cylindrical surface of the hole are expressed in the following form: , in, is the Fourier basis function, which is used to characterize the periodic characteristics in the circumferential and height directions; It is a radial basis function used to capture the complex morphological changes in local areas. The combination of Fourier basis function and radial basis function jointly describes the global trend of the axis and hole cylinder. .
[0028] In order to reflect the periodic characteristics of the cylindrical circumferential error, the Fourier basis function is constructed based on the analysis results of the significant model in step 2, and its expression is:
[0029] in, is the amplitude of the Fourier component; is the order of the Fourier component; is the phase angle. is the number of Fourier components that dominate the model, The systematic error function expression uses the Fourier components in the dominant model as the input of the Fourier basis function after screening, retaining the periodic components that have a significant impact on the shaft hole surface, thereby achieving accurate fitting of the periodic error of the point cloud data; In local areas, there may be more complex details and changes in the morphology, which are modeled by radial basis functions. The expression of the radial basis function is: , Among them, (w_j) is the weight coefficient of the radial basis function, is the Gaussian radial basis function, Specific form for, ,r represents the distance between the predicted point and the center point; σ represents the scale parameter of the radial basis function, which is calculated based on the statistical optimization of the distance between the point cloud data. (xj = (Θ, z)) represents the central node position of the radial basis function. K is the number of centers of the radial basis function, which is consistent with the number of point cloud data collected by the data points. The Gaussian radial basis function can well capture the complex morphological changes of local areas in the point cloud data, and is particularly suitable for fitting modeling of non-uniformity or local anomalies. It should be noted that the separation of systematic errors and random errors of the shaft-cylinder surface and the hole-cylinder surface, as well as the construction of free-form surfaces, are all screened and constructed according to steps two to five. A combined model of Fourier basis functions and radial basis functions is used to collaboratively characterize the global periodic errors and local detailed morphologies of the cylindrical surface. The significant Fourier components screened in steps three and four can accurately describe the periodic errors in the circumferential and height directions, such as roundness and waviness, to ensure the correctness of the global trend. The Gaussian radial basis function can fit non-uniform and locally abnormal morphologies, such as scratches and bumps, through the weight coefficients wj and the central nodes xj. Its flexibility is suitable for complex local features, making up for the shortcomings of Fourier analysis in local details. The combination of global and local models can not only ensure the accuracy of the main errors in interference fit analysis, such as periodic shape errors, but also reflect the influence of local defects on contact stress, thereby improving the engineering practicality of the model. Import shaft and hole models with error surfaces into finite element analysis to simulate stress distribution and deformation under interference fit and verify the impact of error on assembly performance; after theoretical modeling, simulation is required to evaluate the impact of error on actual assembly, such as stress concentration and deformation, to provide data support for part design and tolerance allocation; face-to-face contact settings can simulate the actual contact state of shaft-hole interference fit, and stress cloud maps can intuitively display local stress anomalies caused by errors, such as high stress areas caused by excessive local interference, to help optimize the assembly process; assigning material properties such as elastic modulus and yield strength and setting analysis steps can ensure that the simulation results conform to actual physical laws, directly linking error modeling with engineering applications.
[0030] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various modifications and substitutions within the technical scope disclosed in the present invention, and such modifications and substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.
Claims
1. A method for separating systematic errors and modeling topography of cylindrical surfaces for interference fit, characterized by: The following steps are included: Step 1: Measure the point cloud data of the shaft and hole cylindrical surface. Use a three-dimensional coordinate measuring machine to measure the point cloud data of the shaft and hole assembly cylindrical surface of the interference fit shaft and hole parts to be measured, and obtain the coordinates of the shaft cylindrical surface measurement data point s_shaft(x,y,z) and the hole cylindrical surface measurement data point coordinates s_hole(x,y,z) and their corresponding cylindrical coordinates s_shaft(r,θ,z) and s_hole(r,θ,z); Step 2: Iterative positioning of the reference axis. Convert the cylindrical coordinates of the point cloud data in step 1 into a Cartesian coordinate system, fit a spatial straight line as the initial reference axis, and calculate the initial reference axis through iterative optimization using the least squares method. Step 3: Partial F test is used to determine the dominant model. The initial reference axis is updated by analyzing the Fourier components of the circumferential errors of the shaft and the cylindrical surface of the hole. The partial F test is then used to determine whether the Fourier components are significant. The systematic errors are determined and added to the dominant model. Step 4: Randomness test to determine the significant model: perform serial correlation test and chi-square test on the Fourier components selected in step 3 to determine random errors, and then add them to the significant model; Step 5: Construct a cylindrical free-form surface expression. Use a combination of Fourier basis functions and radial basis functions to model the periodic errors and local details of the shaft and hole cylindrical surfaces, and collaboratively characterize the complex morphologies of the shaft and hole cylindrical surfaces. Step 6: Finite element interference fit simulation, create shafts and holes with error surfaces, assign material properties to the parts, and then establish analysis steps. The contact parts use face-to-face contact, perform finite element simulation, and view the stress distribution and deformation cloud map.
2. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 1, the coordinates of the shaft cylindrical surface measurement data points and the hole cylindrical surface measurement data points are converted into their corresponding cylindrical coordinates using the polar coordinate formula. 。 3. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 2, in a 3D cylindrical coordinate system, the point cloud data is expressed in cylindrical coordinate form (r, θ, z), where r is the radius, θ is the circumferential angle, and z is the height coordinate. To obtain the initial reference axis, the point cloud data is converted from cylindrical coordinates to a Cartesian coordinate system (x, y, z), and then a spatial straight line is fitted as the initial reference axis, expressed by the following formula: ， Where (xi, yi, zi) are the coordinates of the point cloud data in the Cartesian coordinate system; (x0, y0, z0) is the spatial starting point of the fitting axis, and (x0, y0, z0) is the average value of the Cartesian coordinate system (x, y, z) of all coordinate measurement points; (α, β, γ) are the normalized components of the axis direction vector; R is the radius of the fitting cylinder; N is the number of point cloud data. The initial reference axis is calculated through iterative optimization using the least squares method.
4. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 3, the circumferential error of the cylinder includes systematic error and random error. The initial reference axis is updated by analyzing the Fourier component. The Fourier component expression is as follows: ， in is the amplitude of the Fourier component; is the order of the Fourier component; is the phase angle; According to the influence of the first-order Fourier component, the update formula of the initial reference axis is expressed in three-dimensional space as follows: ， Where Cz is calculated by the error distribution along the axis.
5. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 4, characterized in that: In step 3, the initial reference axis is updated The polar coordinate formula is converted into (r, θ, z), which is then brought into the Fourier component expression to calculate the Fourier component after each update of the initial reference axis.
6. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 3, the partial F test statistic is calculated as ， in, is the residual sum of squares of the current model, is the residual sum of squares of the previous model; N is the number of point cloud data, p is the number of Fourier components in the current model, and the analysis starts from the Fourier component with the heaviest weight. like The current Fourier component is considered significant and is added to the dominant model. That is, the systematic error, the final expression of the dominant model is: 。 7. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 4, the residuals of the remaining Fourier components after screening are tested for no correlation through serial correlation test, and the serial correlation coefficient is calculated. The residuals are iteratively calculated starting from the Fourier component with the heaviest weight, and then the serial correlation test is performed. The formula is as follows: ， in, is the residual of the i-th Fourier component, is the mean of the residuals. If the obtained |r| is approximately equal to 0, it is considered that the residuals have no correlation, and a chi-square test is performed.
8. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 7, characterized in that: In step 4, the chi-square statistic is calculated using the chi-square test formula, which is as follows: ， in, is the observed frequency of the ith interval, Ei is the expected frequency, K is the number of intervals, if It is assumed that the residual follows a normal distribution and is added to the significant model, that is, random error. The final expression of the significant model is, .
9. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claim 1, characterized in that: In step 5, the free-form surface model of the shaft and hole cylindrical surface is expressed in the following form: ， in, is the Fourier basis function, which is used to characterize the periodic characteristics in the circumferential and height directions; It is a radial basis function used to capture the complex morphological changes in local areas. The combination of Fourier basis function and radial basis function jointly describes the global trend of the axis and hole cylinder. .
10. The method for separating system errors and modeling topography of cylindrical surfaces for interference fit according to claims 1 to 8, characterized in that: The separation of systematic errors and random errors of the shaft cylindrical surface and the hole cylindrical surface and the construction of the free-form surface are all screened and constructed according to steps two to five.