A refined modeling method for connection structure stiffness

Abstract

The present invention discloses a method for fine-tuning the stiffness of a connection structure, comprising obtaining the fractal dimension D and fractal roughness G of the contact surface of the connection structure; and calculating the maximum contact area a of the micro-convex body on the contact surface based on D, G and the maximum contact area a of the micro-convex body on the contact surface. L Establish the expression of the total normal load P of the contact surface; obtain the value of the total normal load P of the contact surface, and obtain a according to the expression of P L ; Establish connection stiffness K n The expression of a L Substitute the connection stiffness K n The present invention improves the calculation accuracy of the connection structure stiffness and is particularly suitable for pre-tightening connection structures in mechanical systems.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical equipment connection structure mechanics, and in particular relates to a connection structure stiffness refined modeling method. Background Art

[0002] Mechanical equipment is typically a complex system with numerous connection structures. Typical examples include rotor systems in aircraft engines and gas turbines, deformable structures in aerospace equipment, and various CNC machine tools. The inherent presence of joints in these joints disrupts structural continuity and introduces numerous nonlinear factors, making the static and dynamic mechanical properties of the entire structure extremely complex and posing significant challenges in predicting the dynamic characteristics of the equipment. Research has shown that joints contribute approximately 60%-80% of the structural stiffness and 90% of the damping in mechanical systems. When subjected to dynamic loads, joints can exhibit complex mechanical behaviors such as stiffness softening and stick-slip friction, severely impacting the performance of the structure and, ultimately, the entire equipment. Therefore, accurately simulating and calculating the stiffness of joints is of great theoretical significance and engineering application value.

[0003] Currently, there are two main modeling approaches for the stiffness of the joint surfaces of connected structures: one considers that the height size of the asperities follows a statistical distribution, and the other considers that the contact area of ​​the asperities follows fractal characteristics. In terms of the modeling process, both methods first establish a contact stiffness model between individual asperities, then extend this model to the entire contact surface using statistical distribution functions or fractal geometry theory to obtain the joint stiffness of the entire joint surface. However, in reality, the size distribution of asperities on the joint surface is extremely complex, and even exhibits scale differences. Existing modeling methods have not yet considered the scale of asperities, resulting in insufficient accuracy in joint stiffness modeling and reduced practical application effectiveness. Summary of the Invention

[0004] The present invention aims to overcome these shortcomings by providing a refined modeling method for connecting structural stiffness. This method addresses the technical problem that existing modeling methods fail to consider the scale of asperities, resulting in insufficient accuracy in connecting stiffness modeling. By accounting for the scale differences of asperities on the contact surface of a connecting structure, the present invention improves the accuracy of calculating connecting structural stiffness.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0006] A method for fine-grained modeling of connection structure stiffness, comprising:

[0007] Obtain the fractal dimension D and fractal roughness G of the contact surface of the connection structure;

[0008] Based on the fractal dimension D, fractal roughness G of the contact surface of the connection structure and the maximum contact area a of the micro-asperities on the contact surface LEstablish an expression for the total normal load P on the contact surface;

[0009] Obtain the value of the normal total load P of the contact surface, and obtain the maximum contact area a of the micro-convex body on the contact surface according to the expression of the normal total load P of the contact surface L ;

[0010] Establish the connection stiffness K n The maximum contact area a of the micro-convex body on the contact surface is expressed as L Substitute the connection stiffness K n The stiffness of the connection structure is obtained from the expression of .

[0011] Furthermore, the method for obtaining the fractal dimension D and fractal roughness G of the contact surface of the connection structure includes:

[0012] Select the contact surface to be measured in the contact surface of the connection structure;

[0013] Randomly select N areas on the contact surface to be tested and measure the contour curve of each area using a surface topography instrument; N ≥ 5;

[0014] According to the contour curves of each region, the fractal dimensions D1, D2, ..., D corresponding to the N regions are obtained. N , and fractal roughness G1, G2, ..., G N ;

[0015] According to D1, D2, ..., D N The fractal dimension D of the contact surface of the connection structure is obtained according to G1, G2, ..., G N The fractal roughness G of the contact surface of the connection structure is obtained.

[0016] Furthermore, the expressions of the fractal dimension D and fractal roughness G of the contact surface of the connection structure are:

[0017]

[0018]

[0019] Among them, D i represents the fractal dimension corresponding to the i-th region, G i Represents the fractal roughness corresponding to the i-th region, 1≤i≤N.

[0020] Furthermore, the method for selecting the contact surface to be measured in the contact surface of the connection structure is:

[0021] Selecting one of the two contact surfaces constituting the contact surface of the connection structure as the contact surface to be measured;

[0022] When the materials of the two contact surfaces are of the same hardness, one of the contact surfaces is selected as the contact surface to be measured; when the materials of the two contact surfaces are of different hardness, the softer contact surface is selected as the contact surface to be measured.

[0023] Furthermore, the expression of the total normal load P on the contact surface is:

[0024]

[0025] Where a represents the contact area of ​​the asperities on the contact surface, n(a) represents the distribution function of the contact area of ​​the asperities on the contact surface, and k ne k represents the stiffness of the asperity when it undergoes elastic deformation, nep It represents the stiffness of the micro-convex body when it undergoes elastic-plastic deformation, n represents the frequency index related to the size of the micro-convex body, n ce The critical elastic index of the asperity that undergoes elastic deformation, n cp The critical plasticity index of the asperity that undergoes plastic deformation, n min Represents the minimum frequency index of the asperity, n max Represents the maximum frequency index of the asperity, a ce (n) represents the critical elastic contact area of ​​the asperity with frequency index n, a cp (n) represents the critical plastic contact area of ​​the asperity with frequency index n, P ep (a) represents the contact force of the asperity in the elastic-plastic deformation stage, P p (a) represents the contact force of the asperity during the plastic deformation stage, P e (a) shows the contact force of the asperity during the elastic deformation stage;

[0026] Among them, P e (a) P ep (a), n ce 、n cp 、k nep 、k ne are the expressions of fractal dimension D or fractal roughness G, respectively.

[0027] Further, Where E represents the equivalent elastic modulus of the material, l represents the scale of the micro-convex body;

[0028] Where m represents the exponent, which is a constant and its value range is 1 <m<1.5,a ce represents the contact area when the micro-convex body undergoes maximum elastic deformation, p ce It represents the contact force when the asperity undergoes maximum elastic deformation;

[0029]

[0030] Among them, σ y represents the yield strength of the material of the contact surface to be measured, and f represents the maximum value of the contact stress field of the micro-asperity;

[0031] Among them, int means rounding down, γ represents the scale parameter of the asperity;

[0032] Where H represents the equivalent Brinell hardness of the material.

[0033] Further,

[0034]

[0035] Among them, δ ce represents the critical elastic deformation of the micro-convex body, s represents the exponent, s=m-1; where R represents the radius of curvature of the apex of the microconvex body,

[0036] Further, Among them, E1 and E2 represent the elastic modulus of the two materials at the joint of the connection structure, and v1 and v2 represent the Poisson's ratio of the two materials at the joint of the connection structure;

[0037] Among them, H1 and H2 represent the Brinell hardness of the two materials at the joint of the connection structure;

[0038] Wherein, u represents the vertical distance between a certain point inside the material to which the contact surface to be measured belongs and the contact surface to be measured, and v represents the Poisson's ratio of the material of the contact surface to be measured.

[0039] Furthermore, p p (a) = Ha; where H represents the equivalent Brinell hardness of the material;

[0040] Among them, γ represents the scale parameter of the micro-convex body, l max represents the maximum size of the asperity, l min Indicates the minimum size of the asperity.

[0041] Furthermore, the connection stiffness K n The expression is:

[0042]

[0043] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0044] (1) The present invention creatively proposes a method for fine-tuning the stiffness of a connection structure, which takes into account the scale differences of the asperities on the contact surface of the connection structure and uses fractal dimension and fractal roughness to fine-tune the modeling, which is more in line with the actual situation and improves the calculation accuracy of the stiffness of the connection structure;

[0045] (2) The connection structure stiffness modeling method proposed in the present invention takes into account the influencing factors more comprehensively, provides expressions for the total normal load on the contact surface and the connection stiffness, and each influencing parameter can be obtained through measurement, which is highly objective and improves the calculation accuracy of the connection structure stiffness.

[0046] (3) The method proposed in the present invention is particularly suitable for pre-tightened connection structures in mechanical systems. It can provide accurate input parameters for the prediction of the static and dynamic characteristics of the entire structure and even the equipment, help evaluate the performance of the entire equipment, and provide guidance for the optimal design of the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is an overall flow chart of a method for fine-tuning modeling of connection structure stiffness according to the present invention;

[0048] Figure 2 It is a two-dimensional contour map of the rough surface micromorphology;

[0049] Figure 3 Schematic diagram for the definition of asperity size parameters. DETAILED DESCRIPTION

[0050] The following detailed description of the present invention will make the features and advantages of the present invention more clear and explicit.

[0051] The word "exemplary" is used exclusively herein to mean "serving as an example, example, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0052] The present invention proposes a method for fine-tuning the modeling of connection structure stiffness, which improves the calculation accuracy of the connection stiffness and provides accurate input parameters for the prediction of the static and dynamic characteristics of the entire structure and even the equipment.

[0053] The present invention proposes a method for fine-tuning the stiffness modeling of a connection structure, comprising the following steps:

[0054] (1) Obtain the fractal dimension D and fractal roughness G of the contact surface of the connection structure;

[0055] (2) Establish the calculation expression of the total normal load P of the contact surface;

[0056] (3) Obtain the value of the total normal load P on the contact surface and calculate the maximum contact area a of the micro-convex body on the contact surface L ;

[0057] (4) Establish connection stiffness K n The calculation expression of the connection stiffness can be accurately simulated and calculated;

[0058] Among them, the connection stiffness K n The calculation expression is as follows:

[0059]

[0060] Where a represents the contact area of ​​the micro-asperity, n(a) represents the distribution function of the contact area of ​​the micro-asperity on the contact surface, and k ne k represents the stiffness of the asperity when it undergoes elastic deformation, nep It represents the stiffness of the micro-convex body when it undergoes elastic-plastic deformation, n represents the frequency index related to the size of the micro-convex body, n ce The critical elastic index of the asperity that undergoes elastic deformation, n cp The critical plasticity index of the asperity that undergoes plastic deformation, n min Represents the minimum frequency index of the asperity, a ce (n) represents the critical elastic contact area of ​​the asperity with frequency index n, a cp (n) represents the critical plastic contact area of ​​the asperity with frequency index n.

[0061] In a preferred embodiment, the overall process of the connection structure stiffness refinement modeling method of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0062] (1) Obtain the fractal dimension D and fractal roughness G of the contact surface of the connection structure;

[0063] First, N areas (N≥5) are randomly selected on the contact surface of the selected joint of the connection structure, and the contour curves of each area are measured using a surface topography instrument, such as Figure 2 Then, the power spectrum method or structure function method is used to fit and calculate the fractal dimensions D1, D2, ..., D corresponding to N points respectively. N , and fractal roughness G1, G2, ..., G N ; The calculation expressions of the fractal dimension D and fractal roughness G of the entire contact surface are as follows:

[0064]

[0065]

[0066] Wherein, the subscript i represents the i-th region. The selected contact surface is the contact surface of the softer material of the two contact surfaces constituting the bonding portion.

[0067] The power spectrum method and structure function method have high fitting accuracy for the fractal dimension D and fractal roughness G of the rough surface, and the calculation results are relatively accurate. At present, there are clear principles and mature implementation methods. Therefore, the present invention is not limited to them.

[0068] (2) Establish the calculation expression of the total normal load P of the contact surface;

[0069] The calculation expression of the normal total load P on the contact surface of the connection structure is:

[0070]

[0071] p e It represents the contact force of the asperity in the elastic deformation stage, and its expression is:

[0072]

[0073] Where l represents the scale of the micro-convex body, such as Figure 3 As shown, Figure 3 Where δ is the deformation of the micro-convex body, and δ increases with the increase of pressure. E represents the equivalent elastic modulus of the material, and its calculation expression is:

[0074]

[0075] Wherein, E1 and E2 represent the elastic moduli of the two materials at the junction, and v1 and v2 represent the Poisson's ratio of the two materials at the junction.

[0076] p p It represents the contact force of the asperity in the plastic deformation stage, and its expression is:

[0077] p p (a)=Ha

[0078] Among them, H represents the equivalent Brinell hardness of the material, and its calculation expression is:

[0079]

[0080] Among them, H1 and H2 represent the Brinell hardness of the two materials at the bonding point.

[0081] p ep It represents the contact force of the asperity in the elastic-plastic deformation stage, and its expression is:

[0082]

[0083] Where m represents the exponent, which is a constant and its value range is 1 <m<1.5。

[0084] Among them, a ce It represents the contact area when the micro-convex body undergoes maximum elastic deformation, and its expression is:

[0085]

[0086] Among them, σ y Represents the yield strength of the softer material. When the materials of the two contact surfaces are the same, σ y represents the yield strength of the material of any contact surface, and f represents the maximum value of the contact stress field of the asperity, which is expressed as follows:

[0087]

[0088] Wherein, u represents the vertical distance between a certain point inside the material of the contact surface to be measured and the contact surface to be measured. In a preferred embodiment, it represents the vertical distance between a certain point inside the softer material and the contact surface, and v represents the Poisson's ratio of the softer material.

[0089] Among them, p ce It represents the contact force when the asperity undergoes maximum elastic deformation, and its expression is:

[0090]

[0091] Among them, n min It represents the minimum frequency index of the asperity, and its calculation expression is:

[0092]

[0093] Where γ represents the scale parameter of the asperity, which is usually 1.5; l max It represents the maximum size of the asperity. Its value is the sampling length for surface topography measurement. The sampling length is a measurement parameter that can be set in the instrument. It is equivalent to the size of the measured area. When the measurement area is a square, the sampling length is the side length of the square.

[0094] Among them, n max It represents the maximum frequency index of the asperity, and its calculation expression is:

[0095]

[0096] Among them, l min It represents the minimum size of a micro-protrusion, and its value is the resolution of the surface topography measurement instrument.

[0097] Among them, n ceThe critical elastic index of the asperity that undergoes elastic deformation is expressed as follows:

[0098]

[0099] Among them, int means round down.

[0100] Among them, n cp The critical plasticity index of the asperity that undergoes plastic deformation is expressed as follows:

[0101]

[0102] (3) Obtain the value of the total normal load P on the contact surface and calculate the maximum contact area a of the micro-convex body on the contact surface L ;

[0103] The normal total load P of the contact surface of the connection structure is obtained by direct measurement. According to the calculation expression of the normal total load P in step (2), an equation is constructed. By solving the equation, the maximum contact area a of the micro-convex body is calculated. L .

[0104] (4) Establish connection stiffness K n The calculation expression of is used to accurately simulate and calculate the connection stiffness.

[0105] Connection stiffness K n The calculation expression is:

[0106]

[0107] Among them, k ne It represents the stiffness of the convex body when it undergoes elastic deformation, and its calculation expression is:

[0108]

[0109] k nep It represents the stiffness of the convex body when it undergoes elastic-plastic deformation, and its calculation expression is:

[0110]

[0111] Among them, δ ce It represents the critical elastic deformation of the micro-convex body, indicating that the elastic deformation of the micro-convex body ends and enters the elastic-plastic deformation. Its calculation expression is:

[0112]

[0113] Where R represents the curvature radius of the apex of the microconvex body, and its calculation expression is:

[0114]

[0115] Where s represents the exponent, and its calculation expression is:

[0116] s=m-1

[0117] The above content describes in detail the process of the proposed method for fine-grained modeling of connection structure stiffness. This method carefully considers two practical aspects:

[0118] (1) The deformation state of a single micro-convex body will undergo elastic, elastoplastic and plastic deformation processes as the normal pressure increases. Therefore, given a preloaded connection structure, there are three types of deformation states of the micro-convex body on the contact surface of the joint, namely elastic deformation state, elastoplastic deformation state and plastic deformation state.

[0119] (2) Asperities on rough surfaces vary in size, even across scales. Asperities of different scales have significantly different contact mechanical properties and contributions to the mechanical properties of the entire contact surface. Therefore, meticulously considering the contact conditions of asperities of various scales allows for a more accurate model of the connection stiffness of the entire contact surface, which can then be used to analyze the static and dynamic mechanical properties of the entire structure.

[0120] The above content also gives in detail the parameters used in the proposed refined modeling method of connection structure stiffness and their acquisition methods, which can more conveniently calculate the connection structure stiffness.

[0121] The present invention has been described in detail above with reference to specific embodiments and exemplary examples. However, these descriptions should not be construed as limiting the present invention. Those skilled in the art will appreciate that various equivalent substitutions, modifications, or improvements may be made to the technical solutions and implementations of the present invention without departing from the spirit and scope of the present invention, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be determined by the appended claims.

[0122] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for fine-tuning the stiffness modeling of a connection structure, characterized in that: include: Obtain the fractal dimension D and fractal roughness G of the contact surface of the connection structure; Based on the fractal dimension D, fractal roughness G of the contact surface of the connection structure and the maximum contact area a of the micro-convex body on the contact surface L Establish an expression for the total normal load P on the contact surface; Obtain the value of the normal total load P of the contact surface, and obtain the maximum contact area a of the micro-convex body on the contact surface according to the expression of the normal total load P of the contact surface L ; Establish the connection stiffness K n The maximum contact area a of the asperity on the contact surface is expressed as L Substitute the connection stiffness K n The stiffness of the connection structure is obtained from the expression of The expression of the total normal load P on the contact surface is: Where a represents the contact area of ​​the asperities on the contact surface, n(a) represents the distribution function of the contact area of ​​the asperities on the contact surface, and k ne k represents the stiffness of the asperity when it undergoes elastic deformation, nep It represents the stiffness of the micro-convex body when it undergoes elastic-plastic deformation, n represents the frequency index related to the size of the micro-convex body, n ce The critical elastic index of the asperity that undergoes elastic deformation, n cp The critical plasticity index of the asperity that undergoes plastic deformation, n min Represents the minimum frequency index of the asperity, n max Represents the maximum frequency index of the asperity, a ce (n) represents the critical elastic contact area of ​​the asperity with frequency index n, a cp (n) represents the critical plastic contact area of ​​the asperity with frequency index n, P ep (a) represents the contact force of the asperity in the elastic-plastic deformation stage, P p (a) represents the contact force of the asperity during the plastic deformation stage, P e (a) shows the contact force of the asperity during the elastic deformation stage; Among them, P e (a) P ep (a), n ce 、n cp 、k nep 、k ne are the expressions of fractal dimension D or fractal roughness G respectively; Where E represents the equivalent elastic modulus of the material, l represents the scale of the micro-convex body; Where m represents the exponent, which is a constant and its value range is 1 <m<1.5,a ce represents the contact area when the micro-convex body undergoes maximum elastic deformation, p ce It represents the contact force when the asperity undergoes maximum elastic deformation; Among them, σ y represents the yield strength of the material of the contact surface to be measured, and f represents the maximum value of the contact stress field of the micro-asperity; Among them, int means rounding down, γ represents the scale parameter of the asperity; Where H represents the equivalent Brinell hardness of the material.

2. A method for fine-tuning the stiffness of a connection structure according to claim 1, characterized in that: The method for obtaining the fractal dimension D and fractal roughness G of the contact surface of the connection structure includes: Select the contact surface to be measured in the contact surface of the connection structure; Randomly select N areas on the contact surface to be tested and measure the contour curve of each area using a surface topography instrument; N ≥ 5; According to the contour curves of each region, the fractal dimensions D1, D2, ..., D corresponding to the N regions are obtained. N , and fractal roughness G1, G2, ..., G N ; According to D1, D2, ..., D N The fractal dimension D of the contact surface of the connection structure is obtained according to G1, G2, ..., G N The fractal roughness G of the contact surface of the connection structure is obtained.

3. A method for fine-tuning the stiffness modeling of a connection structure according to claim 2, characterized in that: The expressions of fractal dimension D and fractal roughness G of the contact surface of the connection structure are: Among them, D i represents the fractal dimension corresponding to the i-th region, G i Represents the fractal roughness corresponding to the i-th region, 1≤i≤N.

4. The method for fine-tuning the stiffness modeling of a connection structure according to claim 2, characterized in that: The method for selecting the contact surface to be measured in the connection structure contact surface is: Selecting one of the two contact surfaces constituting the contact surface of the connection structure as the contact surface to be measured; When the materials of the two contact surfaces are of the same hardness, one of the contact surfaces is selected as the contact surface to be measured; when the materials of the two contact surfaces are of different hardness, the softer contact surface is selected as the contact surface to be measured.

5. The method for fine-tuning the stiffness modeling of a connection structure according to claim 1, characterized in that: Among them, δ ce represents the critical elastic deformation of the micro-convex body, s represents the exponent, s=m-1; where R represents the radius of curvature of the apex of the microconvex body, 6. A method for fine-tuning the stiffness modeling of a connection structure according to claim 5, characterized in that: Among them, E1 and E2 represent the elastic modulus of the two materials at the joint of the connection structure, and v1 and v2 represent the Poisson's ratio of the two materials at the joint of the connection structure; Among them, H1 and H2 represent the Brinell hardness of the two materials at the joint of the connection structure; Wherein, u represents the vertical distance between a certain point inside the material to which the contact surface to be measured belongs and the contact surface to be measured, and v represents the Poisson's ratio of the material of the contact surface to be measured.

7. The method for fine-tuning the stiffness modeling of a connection structure according to claim 1, characterized in that: p p (a) = Ha; where H represents the equivalent Brinell hardness of the material; Among them, γ represents the scale parameter of the micro-convex body, l max represents the maximum size of the asperity, l min Indicates the minimum size of the asperity.

8. The method for fine-tuning the stiffness modeling of a connection structure according to claim 1, characterized in that: Connection stiffness K n The expression is:

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