A finite element modeling method considering multi-scale characteristics of assembly interface

Abstract

The application belongs to the field of finite element modeling, and particularly relates to a finite element modeling method considering multi-scale characteristics of an assembly interface, structural data of a rough surface is collected, a rough surface height matrix is obtained after convolution coefficient calculation; an ideal surface corresponding to the rough surface is determined, and geometric information of the ideal surface is obtained; the rough surface height matrix is modeled and superimposed on the ideal surface to obtain superimposed rough surface information; finite element modeling is performed on different superimposed rough surface information of the multi-scale surface to obtain a finite element model containing multi-scale characteristics of the assembly interface. The technical problem that existing finite element modeling software and tools cannot directly realize multi-scale modeling of the assembly interface and can only establish a model based on ideal product size, resulting in an ideal smooth contact state of the assembly interface, is solved, and the multi-scale characteristics of the assembly interface are successfully included in the product finite element model, so that the model can contain multi-scale geometric information of the actual surface of the part.

Description

Technical Field

[0001] This application belongs to the field of finite element modeling, and specifically relates to a finite element modeling method that considers the multi-scale characteristics of assembly interfaces. Background Technology

[0002] In engineering, to analyze the assembly performance of products, such as assembly accuracy and connection stiffness, it is necessary to establish a finite element model of the product and perform static or dynamic simulation analysis. Existing finite element models are usually based on the ideal dimensions of the product, meaning that the surfaces of the parts are all smooth. This results in the assembly interface between parts being a contact interface between smooth surfaces, in an ideal contact state. However, in reality, the surface of any part has processing errors at different scales and cannot be absolutely smooth. In other words, the surface of any part has multi-scale characteristics and contains geometric information at different scales. The contact interface between any two parts is actually a contact between multi-scale surfaces and naturally also possesses multi-scale characteristics. To more accurately analyze the assembly performance of a product, it is necessary to consider the multi-scale characteristics of the assembly interface in the finite element model.

[0003] Existing finite element modeling software and tools cannot directly achieve multi-scale modeling of assembly interfaces. They are based on the ideal dimensions of the product, meaning that the surfaces of the parts are smooth. This results in the assembly interfaces between parts being contact interfaces between smooth surfaces, which are in an ideal contact state.

[0004] Therefore, how to consider the multi-scale characteristics of the assembly interface in the finite element model of a product is a problem that needs to be solved. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a finite element modeling method that considers the multi-scale characteristics of assembly interfaces, thereby resolving the problem that existing finite element modeling software and tools cannot directly achieve multi-scale modeling of assembly interfaces.

[0006] The technical solution of this application is: a finite element modeling method considering the multi-scale characteristics of assembly interfaces, comprising:

[0007] Collect structural data of rough surfaces and establish autocorrelation functions. Perform a Fast Fourier Transform on the autocorrelation function and combine it with a random number sequence. The frequency response matrix is ​​obtained after calculation. ;

[0008] For the frequency response matrix Perform inverse Fourier transform to obtain the convolution coefficients The height matrix of the rough surface is obtained by calculating the convolution coefficients. ;

[0009] Determine the ideal surface corresponding to the rough surface and obtain the geometric information of the ideal surface; then, calculate the height matrix of the rough surface. The model is superimposed onto the ideal surface to obtain superimposed roughness information; finite element modeling is performed on different superimposed roughness information of multi-scale surfaces to obtain a finite element model containing multi-scale characteristics of the assembly interface.

[0010] Preferably, the autocorrelation function for:

[0011] ;

[0012] In the formula, σ is the root mean square of the height value, which is the roughness value of the rough surface. and These are the autocorrelation lengths in the x and y directions, respectively;

[0013] and All are integer sequences:

[0014] .

[0015] Preferably, a random number sequence Generated according to a two-dimensional standard normal distribution function, with dimensions of... random number sequence The spectral density is C.

[0016] Preferably, the frequency response matrix The specific calculation method is as follows:

[0017] For autocorrelation function Perform a fast Fourier transform to obtain the matrix in the frequency domain. :

[0018] ;

[0019] in, and All are integer sequences:

[0020] ;

[0021] Based on the matrix in the frequency domain Calculate the frequency response matrix :

[0022] ;

[0023] when When the distribution is a standard normal distribution, C=1.

[0024] Preferably, the convolution coefficients for:

[0025] ;

[0026] Rough surface height matrix for:

[0027] ;

[0028] Where I and J are both integer sequences:

[0029] .

[0030] Preferably, the ideal surface is set as an ideal conical surface, and in cylindrical coordinates, the three coordinates r of a point located on the ideal conical surface are... I,J , θ I,J , z I,J The following relationship must be satisfied:

[0031] ;

[0032] Where α is the cone angle, z I,J r is the height coordinate in cylindrical coordinate system. I,J Let θ be the radial coordinate in cylindrical coordinates. I,J These are the coordinates of the rotation.

[0033] Preferably, the rough surface height matrix The model is superimposed onto the ideal surface, specifically as follows:

[0034] rough surface height matrix Superimposed on the ideal conical surface, the new coordinates r_new of the conical surface containing roughness information I,J θ_new I,J , z_new I,J Calculate using the following formula:

[0035] .

[0036] Preferably, when performing finite element modeling, the information of different superimposed rough surfaces on multi-scale surfaces is combined to form the geometric envelope of the part, which is a geometric model of the part containing multi-scale information; the geometric model of the part containing multi-scale information is assembled to obtain a multi-scale assembly model; the multi-scale assembly model is meshed to obtain a finite element model containing the multi-scale characteristics of the assembly interface.

[0037] The finite element modeling method for considering the multi-scale characteristics of assembly interfaces in this application has the following advantages:

[0038] This invention solves the technical problem that existing finite element modeling software and tools cannot directly realize multi-scale modeling of assembly interfaces and can only build models based on the ideal dimensions of the product, resulting in the assembly interface being in an ideal smooth contact state. It successfully incorporates the multi-scale characteristics of the assembly interface into the product finite element model, allowing the model to contain multi-scale geometric information of the actual surface of the parts. It retains the basic geometric features of the ideal surface and incorporates the rough surface geometric information reflecting the processing error, thus restoring the actual multi-scale contact interface state between parts. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the rough conical surface modeling in this application;

[0040] Figure 2 This is a schematic diagram of the overall structure of the finite element model of this application, which includes the multi-scale characteristics of the assembly interface.

[0041] Figure 3 This is a partial structural diagram of the finite element model of the assembly interface in this application, which includes multi-scale characteristics of the assembly interface. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0043] The first aspect of this application provides a finite element modeling method that considers the multi-scale characteristics of the assembly interface. The model can include multi-scale geometric information of the actual surface. The calculation results obtained by finite element simulation based on such a model are more accurate and more in line with the actual situation.

[0044] like Figures 1-3 Specifically, it includes the following steps:

[0045] Step S100: Collect structural data of the rough surface and establish an autocorrelation function. Perform a Fast Fourier Transform on the autocorrelation function and combine it with a random number sequence. The frequency response matrix is ​​obtained after calculation. .

[0046] Preferably, the autocorrelation function for:

[0047] ;

[0048] In the formula, σ is the root mean square of the height value, which is the roughness value of the rough surface. and These are the autocorrelation lengths in the x and y directions, respectively;

[0049] and All are integer sequences:

[0050] .

[0051] random number sequence Generated using a random number generation algorithm, following a preset probability distribution function with a dimension of [missing information]. random number sequence ,Right now It is a dimension of The matrix. Preferably, the sequence is obtained using a two-dimensional standard normal distribution function. .

[0052] Preferably, the frequency response matrix The specific calculation method is as follows:

[0053] For autocorrelation function Perform a fast Fourier transform to obtain the matrix in the frequency domain. :

[0054] ;

[0055] in, and All are integer sequences:

[0056] ;

[0057] Based on the matrix in the frequency domain Calculate the frequency response matrix :

[0058] ;

[0059] when When the distribution is a standard normal distribution, C=1.

[0060] Step S200, for the frequency response matrix Perform inverse Fourier transform to obtain the convolution coefficients Through convolution coefficients The rough surface height matrix is ​​obtained after calculation. .

[0061] Preferably, the convolution coefficient for:

[0062] ;

[0063] Rough surface height matrix for:

[0064] ;

[0065] Where I and J are both integer sequences:

[0066] .

[0067] The above method can be used to generate a specific surface roughness σ and a specific autocorrelation length. and The height coordinates corresponding to the discrete point array of the fractal rough surface: , where I and J are the indexes of the points.

[0068] Step S300: Determine the ideal surface corresponding to the rough surface and obtain the geometric information of the ideal surface; convert the rough surface height matrix... The model is superimposed onto the ideal surface to obtain superimposed roughness information.

[0069] rough surface height matrix The model is superimposed onto an ideal surface to obtain the actual surface corresponding to that ideal surface. For example, we can... By superimposing these elements onto a conical surface, a "rough conical surface" can be obtained. This conical surface contains the geometric information of both the rough surface and the ideal surface, and it is multi-scale.

[0070] The following explanation uses a conical surface as an example:

[0071] In cylindrical coordinates, the three coordinates r of a point located on the surface of an ideal cone are... I,J , θ I,J , z I,J The following relationship must be satisfied:

[0072] ;

[0073] Where α is the cone angle, z I,J r is the height coordinate in cylindrical coordinate system. I,J Let θ be the radial coordinate in cylindrical coordinates. I,J These are the coordinates of the rotation.

[0074] Based on the above formula, we can obtain the array coordinates (r) of discrete points on an ideal conical surface according to the given cone angle, height range, and rotation angle range. I,J , θ I,J , z I,J ).

[0075] Of course, the ideal surface in reality may also be a cylindrical surface, a spherical surface, etc., and all of them can be calculated according to the above method.

[0076] rough surface height matrix Superimposed on the ideal conical surface, the new coordinates r_new of the conical surface containing roughness information I,J θ_new I,J , z_new I,J Calculate using the following formula:

[0077] .

[0078] Step S400: Perform finite element modeling on the different superimposed roughness information of the multi-scale surface to obtain a finite element model containing the multi-scale characteristics of the assembly interface.

[0079] Preferably, when performing finite element modeling, the information of different superimposed rough surfaces on multi-scale surfaces is combined to form the geometric envelope of the part, which is a geometric model of the part containing multi-scale information; the geometric model of the part containing multi-scale information is assembled to obtain a multi-scale assembly model; the multi-scale assembly model is meshed to obtain a finite element model containing the multi-scale characteristics of the assembly interface.

[0080] In summary, this application has the following advantages:

[0081] This invention solves the technical problem that existing finite element modeling software and tools cannot directly realize multi-scale modeling of assembly interfaces and can only build models based on the ideal dimensions of the product, resulting in the assembly interface being in an ideal smooth contact state. It successfully incorporates the multi-scale characteristics of the assembly interface into the product finite element model, allowing the model to contain multi-scale geometric information of the actual surface of the parts. It retains the basic geometric features of the ideal surface and incorporates the rough surface geometric information reflecting the processing error, thus restoring the actual multi-scale contact interface state between parts.

[0082] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A finite element modeling method considering the multi-scale characteristics of assembly interfaces, characterized in that, include: Collect structural data of rough surfaces and establish autocorrelation functions. Perform a Fast Fourier Transform on the autocorrelation function and combine it with a random number sequence. The frequency response matrix is ​​obtained after calculation. ; For the frequency response matrix Performing an inverse Fourier transform yields the convolution coefficients. Through convolution coefficients The rough surface height matrix is ​​obtained after calculation. ; Determine the ideal surface corresponding to the rough surface and obtain the geometric information of the ideal surface; then, calculate the height matrix of the rough surface. The model is superimposed onto the ideal surface to obtain superimposed roughness information; Finite element modeling is performed on the different superimposed roughness information of multi-scale surfaces to obtain a finite element model that includes the multi-scale characteristics of the assembly interface.

2. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 1, characterized in that, The autocorrelation function for: ； In the formula, σ is the root mean square of the height value, which is the roughness value of the rough surface. and These are the autocorrelation lengths in the x and y directions, respectively; and All are integer sequences: 。 3. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 1, characterized in that, random number sequence Generated according to a two-dimensional standard normal distribution function, with dimensions of... random number sequence The spectral density is C.

4. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 3, characterized in that, Frequency response matrix The specific calculation method is as follows: For autocorrelation function Perform a fast Fourier transform to obtain the matrix in the frequency domain. : ； in, and All are integer sequences: ； Based on the matrix in the frequency domain Calculate the frequency response matrix : ； when When the distribution is a standard normal distribution, C=1.

5. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 1, characterized in that, The convolution coefficients for: ； Rough surface height matrix for: ； Where I and J are both integer sequences: 。 6. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 1, characterized in that, The ideal surface is set as an ideal cone. In cylindrical coordinates, the three coordinates r of a point located on the ideal cone are... I,J , θ I,J , z I,J The following relationship must be satisfied: ； Where α is the cone angle, z I,J r is the height coordinate in cylindrical coordinate system. I,J Let θ be the radial coordinate in cylindrical coordinates. I,J These are the coordinates of the rotation.

7. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 6, characterized in that, rough surface height matrix The model is superimposed onto the ideal surface, specifically as follows: rough surface height matrix Superimposed on the ideal conical surface, the new coordinates r_new of the conical surface containing roughness information I,J θ_new I,J , z_new I,J Calculate using the following formula: 。 8. The finite element modeling method considering the multi-scale characteristics of the assembly interface as described in claim 1, characterized in that, When performing finite element modeling, the information of different superimposed rough surfaces on multi-scale surfaces is combined to form the geometric envelope of the part, which is a geometric model of the part containing multi-scale information. The geometric model of the part containing multi-scale information is assembled to obtain a multi-scale assembly model. The multi-scale assembly model is meshed to obtain a finite element model containing the multi-scale characteristics of the assembly interface.

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