Precise modeling and predicting method suitable for riveting assembly deformation of aircraft thin-wall part

Abstract

The invention discloses a precise modeling and prediction method suitable for airplane thin-wall part riveting assembly deformation, and the method comprises the steps: carrying out the representation of a riveting surface of a thin-wall part through employing a W-M fractal function from the microstructure, and building a fractal model which accords with the actual surface statistical characteristics; then based on a fractal contact theory, establishing a micro-convex elastic-plastic contact model, expanding a microscopic contact behavior to the whole junction surface through a size distribution function, and constructing an analytical model of normal contact rigidity and contact damping; then, an equivalent modeling method based on a spring-damping unit is provided, rigidity and damping of the joint surface are distributed in a discretization mode, and accurate quantitative calculation of riveting assembly deformation is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft assembly process and structural mechanics analysis, and particularly relates to a kind of riveting assembly deformation accurate modeling and prediction method suitable for aircraft thin-walled parts. BACKGROUND

[0002] Skin, stringer and other aircraft thin-walled parts are widely used in modern aviation structures due to their light weight, good forming performance and other advantages. Riveting, as the main connection form of such components, has the characteristics of mature technology, reliable connection and convenient maintenance. However, during the riveting assembly process, the thin-walled parts are prone to plastic deformation and springback under the action of riveting force, clamping force and other multi-field loads, which seriously affects the assembly accuracy and appearance quality of the whole machine.

[0003] Currently, researchers at home and abroad mainly use theoretical analysis, experimental testing and finite element numerical simulation to study the riveting assembly deformation of aircraft thin-walled parts. Existing researches are mostly based on the macroscopic continuum hypothesis, simplifying the contact surface to an ideal smooth surface, ignoring the roughness characteristics of the actual surface at the microscale. In fact, the real contact of the riveting surface of the thin-walled part is composed of discrete micro-convex body contacts, and the real contact area is much smaller than the apparent contact area. This difference leads to significant deviations in the deformation prediction of the model based on the macroscopic smooth assumption.

[0004] Fractal theory can effectively characterize the irregular geometric features of mechanical part surfaces and has been applied to the study of contact problems such as bolt connection, gear meshing and mechanical sealing, showing good description ability for actual contact state. In view of the stress deformation and springback deformation problems existing in the riveting assembly of aircraft thin-walled parts, the present application proposes a riveting surface micro-convex body contact modeling method based on fractal contact theory: by establishing a micro-convex body elastic-plastic contact response model, combining the size distribution function to extend the micro-contact behavior to the entire riveting surface, systematically constructing the normal contact stiffness and damping model of the joint surface, and further establishing a thin-walled part riveting assembly deformation prediction method based on spring-damping discrete elements, providing a theoretical basis for accurate quantification of assembly deformation. SUMMARY

[0005] In view of the errors caused by simplifying the joint surface to an ideal smooth surface in existing riveting deformation theory, the present application proposes a riveting assembly deformation accurate modeling and prediction method suitable for aircraft thin-walled parts. The actual riveting part surface is a rough curved surface composed of a series of randomly distributed micro-convex peaks and valleys at the microscale, and its real contact area is much smaller than the nominal contact area, making it difficult for traditional macroscopic smooth assumption-based mechanical models to accurately reflect the actual contact state and deformation behavior.

[0006] The application is a kind of accurate modeling and prediction method for riveting assembly deformation of aircraft thin-walled parts, which is established by starting from micro-morphology characterization, combining fractal theory and contact mechanics, and is a riveting deformation prediction method considering surface roughness, micro-protrusion elastic-plastic deformation, contact stiffness and damping characteristics.

[0007] The application provides a kind of accurate modeling and prediction method for riveting assembly deformation of aircraft thin-walled parts, which is established by starting from micro-morphology characterization, combining fractal theory and contact mechanics, and is a riveting deformation prediction method considering surface roughness, micro-protrusion elastic-plastic deformation, contact stiffness and damping characteristics, and realizing quantitative evaluation of deformation through finite element simulation, and the specific steps are as follows:

[0008] First step: fractal quantitative description of riveting surface of aircraft thin-walled parts

[0009] Firstly, the surface profile data of the riveting area of the thin-walled part is obtained by scanning the surface morphology of the thin-walled part with a surface profiler or a white light interferometer, which provides basic data for fractal parameter calculation; and in order to characterize the randomly distributed micro-protrusions of different sizes and different heights on the surface of the thin-walled part, the W-M fractal function is used to mathematically characterize the surface profile, and a fractal geometric model reflecting the distribution characteristics of the random micro-protrusions on the surface is established;

[0010] Second step: calculation of fractal parameters of riveting surface of aircraft thin-walled parts

[0011] The surface profile data is processed by using the structure function method to calculate the fractal dimension D and fractal roughness parameter G of the surface of the thin-walled part, so as to realize quantitative description of the surface morphology;

[0012] Third step: contact modeling of single micro-protrusion on riveting surface

[0013] The micro-protrusions on the surface of the thin-walled part are simplified as spherical models, and the relationship among contact force, deformation and contact area in the elastic and plastic stages is established respectively to determine the critical contact state and the corresponding criterion;

[0014] Fourth step: contact area modeling of riveting surface

[0015] Based on the fractal distribution function, the contact size distribution of the micro-protrusions is derived, and the real contact area in the nominal contact area is calculated;

[0016] Fifth step: normal contact stiffness modeling of riveting surface

[0017] The normal contact stiffness K of the micro-protrusions on the riveting surface of the thin-walled part is calculated by integration n Contact stiffness, combined with size distribution function, to establish a theoretical model of macroscopic normal contact stiffness of the bonding surface;

[0018] Step 6: Equivalent model of contact damping at the riveting surface:

[0019] Based on the principle of energy dissipation, the contact damping loss factor is calculated by combining elastoplastic strain energy, and a normal contact damping model is established.

[0020] Step 7: Quantitative Calculation of Riveting Deformation of Thin-Walled Aircraft Components

[0021] The equivalent contact stiffness and damping are distributed to the spring-damping element and embedded in the finite element model to simulate the riveting process. Based on the riveting force, material parameters, and micro- and macro-morphological parameters of the riveting surface, the riveting deformation of the thin-walled aircraft parts is obtained, thus achieving accurate prediction of the assembly deformation of the thin-walled parts.

[0022] Preferably, in the first step, the WM fractal function is used to characterize the surface profile of the thin-walled part as follows:

[0023]

[0024] In the formula, z(x) represents the two-dimensional profile height curve of the rough surface of a thin-walled part, x is the measurement distance, D is the surface fractal dimension, G is the surface fractal roughness, γ is the frequency density in the surface profile (usually γ = 1.5), and n is the frequency exponent, whose lower limit is determined by... OK, L is the sampling length.

[0025] Preferably, the structure function in the second step is defined as:

[0026]

[0027] In the formula, ξ represents the data step size in the horizontal direction, z(x) represents the measured value of the surface profile, C is the correlation coefficient, and D... s Let D represent the fractal dimension of the cross-sectional profile on the rough surface, and D s The relationship between the rough surface fractal dimension D and the fractal dimension D is D = D s +1;

[0028] Taking the logarithm of both sides of the equivalent structure function, i.e.:

[0029] logH(ξ)=(4-2D s )logξ+logC

[0030] logH(ξ) and logξ are linearly related, and the slope of the line formed by logH(ξ) and logξ is b, with an intercept of c; the fractal dimension D can be calculated from the slope of the line, and the fractal roughness G can be calculated from the intercept of the line. Therefore, the expression is:

[0031]

[0032] Since the two thin-walled parts have different surface morphologies, their structure functions for the rough surfaces are H1(ξ) and H2(ξ), respectively. The fractal parameters of the equivalent rough thin-walled surface of the riveting surface of the two thin-walled parts can be obtained by the following formula:

[0033]

[0034] Preferably, in the third step, when the micro-protrusion is simplified to a spherical model, the peaks of the micro-protrusions are opposite each other when there is no riveting force; when the rivet is subjected to riveting force, the rivet shank deforms and applies a load to the thin-walled part, at which time the micro-protrusion is subjected to the load and undergoes contact deformation; the state of contact deformation of the micro-protrusion after being subjected to riveting force is equivalent to the contact between a micro-protrusion and a smooth plane;

[0035] Suppose that the contact area of ​​any single pair of micro-protrusions under riveting force is a = πr. 2 r is the radius of the contact area of ​​the micro-protrusion, r = (3FR / 4E) 13 The radius of curvature of the equivalent micro-convex body is R, R = a 0.5D G 1-D The deformation of the micro-protrusion is:

[0036] δ=G (D-1) a (2-D)2 ;

[0037] When a single pair of micro-protrusions is in the critical state of elastic deformation and plastic deformation, the expression for the critical deformation amount of the micro-protrusion is:

[0038]

[0039] In the formula, the proportionality constant k = H / σ s , It is related to the elastic modulus E of the interface and the yield strength σ of the softer material. s The relevant coefficients,

[0040] When δ=δ c At that time, the critical contact area a of the micro-protrusion c The expression is:

[0041]

[0042] According to Hertzian theory, when the contact area of ​​the micro-convex body satisfies a > a c At this time, when a single pair of micro-protrusions is in the elastic deformation stage, the expression for the elastic contact load is:

[0043]

[0044] When the contact area of ​​the micro-protrusion satisfies a < a cAt this time, when a single pair of micro-protrusions is in the plastic deformation stage, the expression for the plastic contact load is:

[0045] f p =Ha

[0046] In the formula, H is the hardness of the softer material in the two thin-walled parts;

[0047] Since the contact between each pair of micro-convexities is considered as the contact between spheres, applying the method for calculating the contact stiffness between spheres in Hertz theory, the expression for the contact stiffness of any equivalent spherical micro-convexity in contact with a rigid plane is obtained as follows:

[0048]

[0049] When a thin-walled component is subjected to riveting force and the micro-protrusions undergo elastic deformation, the elastic strain energy of a single pair of micro-protrusions can be obtained by integrating the elastic contact load with respect to the deformation:

[0050]

[0051] When a micro-protrusion undergoes plastic deformation, the plastic strain energy of a single pair of micro-protrusions can be obtained by integrating the plastic contact load with respect to the deformation amount:

[0052]

[0053] Preferably, in the fourth step, the modeling of the contact area of ​​the riveting surface is as follows: Using the island area distribution theory, the expression for the number of micro-protrusions on the surface of the thin-walled part with a contact area greater than 'a' is obtained as follows:

[0054]

[0055] Using fractal contact theory, the expression for the size distribution function n(a) of the contact area of ​​the micro-convex body is obtained:

[0056]

[0057] ψ is the domain expansion factor for the contact area distribution of the micro-convex body, and it is also a function related to the fractal dimension D. Its expression is:

[0058]

[0059] The actual contact area formed by the deformation of all micro-protrusions on the riveting surface is A. r Its expression is:

[0060]

[0061] Preferably, in the fifth step, the normal contact stiffness K of the micro-protrusions on the riveting surface of the thin-walled part is... nThis can be obtained by extending the micro-protrusion size distribution function n(a) to the entire mating surface:

[0062]

[0063] Solving for the total strain energy of the riveting surface of thin-walled parts requires starting from the elastoplastic strain energy of a single micro-protrusion and extending it to the entire riveting surface through the micro-protrusion size distribution function n(a). The total elastic strain energy of the riveting surface is the critical contact area a. c Up to the maximum contact area is a l Integral of the elastic strain energy of a single micro-convexity:

[0064]

[0065] The total plastic strain energy of the riveted surface is the minimum contact area a s To the critical contact area a c Integral of the plastic strain energy of a single micro-protrusion:

[0066]

[0067] Preferably, in step six, the damping loss factor η of the riveting surface can be obtained through the total elastic strain energy and the total plastic strain energy:

[0068]

[0069] The mass of the thin-walled part is M, C c It is the critical damping coefficient, and Normal contact damping value C of the riveting surface of thin-walled parts n The expression is:

[0070]

[0071] During the riveting assembly process, the contact stress area between the two thin-walled parts is mainly around the rivet holes, and the area of ​​the contact stress area tends to a constant value after riveting. Within this range, the contact stress value varies greatly; beyond this range, the contact stress value varies very little. Therefore, spring-damping units are placed on the circumference of this area. Then, based on the number and arrangement of the spring-damping units, the normal contact stiffness and normal contact damping values ​​of the thin-walled part mating surfaces are evenly distributed to each spring-damping unit. Based on the above formulas, the expressions for the contact stiffness and contact damping of each spring-damping unit are obtained:

[0072]

[0073] Beneficial effects of this invention:

[0074] 1. High prediction accuracy of the present invention: The present invention introduces a micro-contact description method based on fractal theory for the first time in the modeling of riveting deformation of thin-walled aircraft parts. It fully considers the actual surface roughness and micro-protrusion contact mechanism, overcomes the model deviation caused by the traditional macro-smoothness assumption, and significantly improves the accuracy and reliability of deformation prediction.

[0075] 2. By establishing a micro-convex elastoplastic contact model and size distribution function, this invention achieves a scientific transition from microscopic single-point contact behavior to macroscopic overall mechanical properties of the joint surface. It can more fundamentally reflect the formation mechanism of contact stiffness, damping and energy dissipation during riveting, providing a theoretical basis for deformation control.

[0076] 3. The spring-damped unit equivalent model constructed in this invention is easy to integrate with mainstream simulation tools such as the finite element method, realizing multi-scale joint modeling. This method can not only be used for deformation prediction, but also provide quantitative references for optimizing assembly process parameters, demonstrating good engineering applicability.

[0077] 4. This invention uses the structure function method to calculate fractal parameters. This process is based on actual surface scanning data, which reduces human assumptions and parameter arbitrariness, making the model input parameters more objective and repeatable, and enhancing the scientific rigor and credibility of the entire method. Attached Figure Description

[0078] The accompanying drawings, which are provided to further illustrate the invention and constitute a part of this invention, are illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention.

[0079] Fig. 1 This is a schematic diagram of the contact process of the micro-protrusions on the riveting surface of the thin-walled component of the present invention;

[0080] Fig. 2 This is a schematic diagram of the equivalent rough joint surface of the riveting surface spring-damping unit of the present invention;

[0081] Fig. 3 This is a schematic diagram of the arrangement scheme of the spring-damping unit on the riveting surface of the present invention. Detailed Implementation

[0082] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the drawings is to supplement the textual description with graphics, so that people can intuitively and vividly understand each technical feature and overall technical solution of the present invention, but they should not be construed as limiting the scope of protection of the present invention.

[0083] Example 1

[0084] Reference Figs. 1-3This invention provides a method for accurate modeling and prediction of deformation in the riveting assembly of thin-walled aircraft parts. Starting from microscopic morphology characterization and combining fractal theory and contact mechanics, this method establishes a riveting deformation prediction method that comprehensively considers surface roughness, elastoplastic deformation of micro-protrusions, contact stiffness, and damping characteristics. Furthermore, it achieves quantitative evaluation of deformation through finite element simulation. The specific steps are as follows:

[0085] Step 1: Fractal quantitative description of the riveting surfaces of thin-walled aircraft components

[0086] First, the surface morphology of the area to be riveted on the thin-walled part is scanned by a surface profilometer or white light interferometer to obtain surface profile data, which provides basic data for fractal parameter calculation. In order to characterize the randomly distributed micro-protrusions of different sizes and heights on the surface of the thin-walled part, the WM fractal function is used to mathematically characterize the surface profile and establish a fractal geometric model that can reflect the distribution characteristics of random micro-protrusions on the surface.

[0087] Specifically, the WM fractal function is used to characterize the surface profile of a thin-walled part as follows:

[0088]

[0089] In the formula, z(x) represents the two-dimensional profile height curve of the rough surface of a thin-walled part, x is the measurement distance, D is the surface fractal dimension, G is the surface fractal roughness, γ is the frequency density in the surface profile (usually γ = 1.5), and n is the frequency exponent, whose lower limit is determined by... OK, L is the sampling length.

[0090] Step 2: Calculation of fractal parameters for riveting surfaces of thin-walled aircraft components

[0091] The structure function method is used to process surface contour data, calculate the fractal dimension D and fractal roughness parameter G of the thin-walled part surface, and realize a quantitative description of the surface morphology.

[0092] Specifically, the structure function is defined as:

[0093]

[0094] In the formula, ξ represents the data step size in the horizontal direction, z(x) represents the measured value of the surface profile, C is the correlation coefficient, and D... s Let D represent the fractal dimension of the cross-sectional profile on the rough surface, and D s The relationship between the rough surface fractal dimension D and the fractal dimension D is D = D s +1;

[0095] Taking the logarithm of both sides of the equivalent structure function, i.e.:

[0096] logH(ξ)=(4-2D s)logξ+logC

[0097] logH(ξ) and logξ are linearly related, and the slope of the line formed by logH(ξ) and logξ is b, with an intercept of c; the fractal dimension D can be calculated from the slope of the line, and the fractal roughness G can be calculated from the intercept of the line. Therefore, the expression is:

[0098]

[0099] Since the two thin-walled parts have different surface morphologies, their structure functions for the rough surfaces are H1(ξ) and H2(ξ), respectively. The fractal parameters of the equivalent rough thin-walled surface of the riveting surface of the two thin-walled parts can be obtained by the following formula:

[0100]

[0101] Step 3: Modeling the contact of a single micro-protrusion on the riveting surface

[0102] The micro-protrusions on the surface of thin-walled parts are simplified into spherical models. The relationships between contact force, deformation and contact area in the elastic and plastic stages are established to determine the critical contact state and corresponding criteria.

[0103] Specifically, when the micro-protrusion is simplified to a sphere model, the peaks of the micro-protrusions are opposite each other when there is no riveting force. When the rivet is subjected to riveting force, the rivet shank deforms and applies a load to the thin-walled part. At this time, the micro-protrusion is subjected to the load and undergoes contact deformation. The state of contact deformation of the micro-protrusion after being subjected to riveting force is equivalent to the contact between a micro-protrusion and a smooth plane.

[0104] Suppose that the contact area of ​​any single pair of micro-protrusions under riveting force is a = πr. 2 r is the radius of the contact area of ​​the micro-protrusion, r = (3FR / 4E) 13 The radius of curvature of the equivalent micro-convex body is R, R = a 0.5D G 1-D The deformation of the micro-protrusion is:

[0105] δ=G (D-1) a (2-D)2 ;

[0106] When a single pair of micro-protrusions is in the critical state of elastic deformation and plastic deformation, the expression for the critical deformation amount of the micro-protrusion is:

[0107]

[0108] In the formula, the proportionality constant k = H / σ s , It is related to the elastic modulus E of the interface and the yield strength σ of the softer material.s The relevant coefficients,

[0109] When δ=δ c At that time, the critical contact area a of the micro-protrusion c The expression is:

[0110]

[0111] According to Hertzian theory, when the contact area of ​​the micro-convex body satisfies a > a c At this time, when a single pair of micro-protrusions is in the elastic deformation stage, the expression for the elastic contact load is:

[0112]

[0113] When the contact area of ​​the micro-protrusion satisfies a < a c At this time, when a single pair of micro-protrusions is in the plastic deformation stage, the expression for the plastic contact load is:

[0114] f p =Ha

[0115] In the formula, H is the hardness of the softer material in the two thin-walled parts;

[0116] Since the contact between each pair of micro-convexities is considered as the contact between spheres, applying the method for calculating the contact stiffness between spheres in Hertz theory, the expression for the contact stiffness of any equivalent spherical micro-convexity in contact with a rigid plane is obtained as follows:

[0117]

[0118] When a thin-walled component is subjected to riveting force and the micro-protrusions undergo elastic deformation, the elastic strain energy of a single pair of micro-protrusions can be obtained by integrating the elastic contact load with respect to the deformation:

[0119]

[0120] When a micro-protrusion undergoes plastic deformation, the plastic strain energy of a single pair of micro-protrusions can be obtained by integrating the plastic contact load with respect to the deformation amount:

[0121]

[0122] Step 4: Modeling the contact area of ​​the riveting surfaces:

[0123] The contact size distribution of micro-protrusions is derived based on the fractal distribution function, and the actual contact area within the nominal contact region is calculated.

[0124] Specifically, the modeling of the contact area of ​​the riveting surface is as follows: Using the island area distribution theory, the expression for the number of micro-protrusions on the surface of a thin-walled part with a contact area greater than 'a' is obtained as follows:

[0125]

[0126] Using fractal contact theory, the expression for the size distribution function n(a) of the contact area of ​​the micro-convex body is obtained:

[0127]

[0128] ψ is the domain expansion factor for the contact area distribution of the micro-convex body, and it is also a function related to the fractal dimension D. Its expression is:

[0129]

[0130] The actual contact area formed by the deformation of all micro-protrusions on the riveting surface is A. r Its expression is:

[0131]

[0132] Step 5: Modeling the normal contact stiffness of the riveting surface

[0133] The normal contact stiffness K of the micro-protrusions on the riveting surface of the thin-walled component is calculated by integration. n Contact stiffness: Based on the size distribution function, a theoretical model of the macroscopic normal contact stiffness of the interface surface is established.

[0134] Specifically, the normal contact stiffness K of the micro-protrusions on the riveting surface of thin-walled parts n This can be obtained by extending the micro-protrusion size distribution function n(a) to the entire mating surface:

[0135]

[0136] Solving for the total strain energy of the riveting surface of thin-walled parts requires starting from the elastoplastic strain energy of a single micro-protrusion and extending it to the entire riveting surface through the micro-protrusion size distribution function n(a). The total elastic strain energy of the riveting surface is the critical contact area a. c Up to the maximum contact area is a l Integral of the elastic strain energy of a single micro-convexity:

[0137]

[0138] The total plastic strain energy of the riveted surface is the minimum contact area a s To the critical contact area a c Integral of the plastic strain energy of a single micro-protrusion:

[0139]

[0140] Step 6: Equivalent model of contact damping at the riveting surface:

[0141] Based on the principle of energy dissipation, the contact damping loss factor is calculated by combining elastoplastic strain energy, and a normal contact damping model is established.

[0142] Specifically, the damping loss factor η of the riveted surface can be obtained through the total elastic strain energy and the total plastic strain energy:

[0143]

[0144] The mass of the thin-walled part is M, C c It is the critical damping coefficient, and Normal contact damping value C of the riveting surface of thin-walled parts n The expression is:

[0145]

[0146] During the riveting assembly process, the contact stress area between the two thin-walled parts is mainly around the rivet holes, and the area of ​​the contact stress area tends to a constant value after riveting. Within this range, the contact stress value varies greatly; beyond this range, the contact stress value varies very little. Therefore, spring-damping units are placed on the circumference of this area. Then, based on the number and arrangement of the spring-damping units, the normal contact stiffness and normal contact damping values ​​of the thin-walled part mating surfaces are evenly distributed to each spring-damping unit. Based on the above formulas, the expressions for the contact stiffness and contact damping of each spring-damping unit are obtained:

[0147]

[0148] Step 7: Quantitative Calculation of Riveting Deformation of Thin-Walled Aircraft Components

[0149] The equivalent contact stiffness and damping are distributed to the spring-damping element and embedded in the finite element model to simulate the riveting process. Based on the riveting force, material parameters, and micro- and macro-morphological parameters of the riveting surface, the riveting deformation of the thin-walled aircraft parts is obtained, thus achieving accurate prediction of the assembly deformation of the thin-walled parts.

[0150] As can be seen from the implementation steps of this invention: This invention utilizes fractal contact theory to construct a fractal model of the riveting surface of a thin-walled part that conforms to the actual contact conditions of the riveting surface. Characteristic parameters of the equivalent riveting surface morphology are obtained using the structure function method. Furthermore, this invention constructs a micro-protrusion contact model of the riveting surface, and obtains the normal contact stiffness and normal contact damping of the riveting surface of the thin-walled part through the expansion of the micro-protrusion size distribution function, proposing a thin-walled part riveting assembly model based on the spring-damping method. Therefore, this invention effectively solves the key problem that traditional riveting deformation models based on the macroscopic smoothness assumption cannot truly reflect the microscopic rough contact state, thus leading to insufficient prediction accuracy of deformation in thin-walled part riveting assembly.

[0151] Specifically:

[0152] (1) This invention solves the problem of distorted surface morphology representation: Traditional methods idealize the bonding surface as a smooth surface, ignoring the decisive influence of micro-roughness on the contact mechanism. This invention accurately quantifies the surface morphology through fractal theory, solving the problems of distorted surface representation and large deviations in contact area calculation in macroscopic modeling.

[0153] (2) This invention solves the problem of inaccurate modeling of contact mechanical behavior: This invention establishes an elastoplastic contact model of micro-convexity and extends it to the entire joint surface, accurately describing nonlinear mechanical behavior such as contact stiffness and damping, and overcoming the shortcomings of traditional models that cannot reflect micro-deformation and energy dissipation mechanisms.

[0154] (3) This invention solves the problem of connecting multi-scale simulation modeling: the proposed spring-damped unit equivalent model successfully transforms microscopic contact parameters into macroscopic element properties that can be used for finite element simulation, achieving an effective leap from microscopic statistical characteristics to macroscopic assembly deformation prediction, and solving the connection problem in multi-scale modeling. In summary, this invention provides a theoretically rigorous and reliable technical means for the accurate prediction of deformation in the riveting assembly of thin-walled aircraft parts, and has a significant effect on improving aircraft assembly quality and control accuracy.

[0155] Without causing conflict, those skilled in the art can freely combine and use the above-mentioned additional technical features.

[0156] The above description is only a preferred embodiment of the present invention. Any technical solution that achieves the purpose of the present invention by essentially the same means is within the protection scope of the present invention.

Claims

1. A method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts, characterized in that: The method, starting from microscopic morphology characterization and combining fractal theory and contact mechanics, establishes a riveting deformation prediction method that comprehensively considers surface roughness, elastoplastic deformation of micro-protrusions, contact stiffness, and damping characteristics. The deformation is then quantitatively evaluated through finite element simulation. The specific steps are as follows: Step 1: Fractal quantitative description of the riveting surfaces of thin-walled aircraft components First, the surface morphology of the area to be riveted on the thin-walled part is scanned by a surface profilometer or white light interferometer to obtain surface profile data, which provides basic data for fractal parameter calculation. In order to characterize the randomly distributed micro-protrusions of different sizes and heights on the surface of the thin-walled part, the WM fractal function is used to mathematically characterize the surface profile and establish a fractal geometric model that can reflect the distribution characteristics of random micro-protrusions on the surface. Step 2: Calculation of fractal parameters for riveting surfaces of thin-walled aircraft components The structure function method is used to process surface contour data, calculate the fractal dimension D and fractal roughness parameter G of the thin-walled part surface, and realize a quantitative description of the surface morphology. Step 3: Modeling the contact of a single micro-protrusion on the riveting surface The micro-protrusions on the surface of thin-walled parts are simplified into spherical models. The relationships between contact force, deformation and contact area in the elastic and plastic stages are established to determine the critical contact state and corresponding criteria. Step 4: Modeling the contact area of ​​the riveting surfaces: The contact size distribution of micro-protrusions is derived based on the fractal distribution function, and the actual contact area within the nominal contact region is calculated. Step 5: Modeling the normal contact stiffness of the riveting surface The normal contact stiffness K of the micro-protrusions on the riveting surface of the thin-walled component is calculated by integration. n Contact stiffness: Based on the size distribution function, a theoretical model of the macroscopic normal contact stiffness of the interface surface is established. Step 6: Equivalent model of contact damping at the riveting surface: Based on the principle of energy dissipation, the contact damping loss factor is calculated by combining elastoplastic strain energy, and a normal contact damping model is established. Step 7: Quantitative Calculation of Riveting Deformation of Thin-Walled Aircraft Components The equivalent contact stiffness and damping are distributed to the spring-damping element and embedded in the finite element model to simulate the riveting process. Based on the riveting force, material parameters, and micro- and macro-morphological parameters of the riveting surface, the riveting deformation of the thin-walled aircraft parts is obtained, thus achieving accurate prediction of the assembly deformation of the thin-walled parts.

2. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: In the first step, the WM fractal function is used to characterize the surface profile of the thin-walled part as follows: In the formula, z(x) represents the two-dimensional profile height curve of the rough surface of a thin-walled part, x is the measurement distance, D is the surface fractal dimension, G is the surface fractal roughness, γ is the frequency density in the surface profile (usually γ = 1.5), and n is the frequency exponent, whose lower limit is determined by... OK, L is the sampling length.

3. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: The structure function in the second step is defined as follows: H(ξ)=[z(x+ξ)-z(x)] 2 =Cξ (4-2Ds) In the formula, ξ represents the data step size in the horizontal direction, z(x) represents the measured value of the surface profile, C is the correlation coefficient, and D... s Let D represent the fractal dimension of the cross-sectional profile on the rough surface, and D s The relationship between the rough surface fractal dimension D and the fractal dimension D is D = D s +1; Taking the logarithm of both sides of the equivalent structure function, i.e.: logH(ξ)=(4-2D s )logξ+logC logH(ξ) and logξ are linearly related, and the slope of the line formed by logH(ξ) and logξ is b, with an intercept of c; the fractal dimension D can be calculated from the slope of the line, and the fractal roughness G can be calculated from the intercept of the line. Therefore, the expression is: Since the two thin-walled parts have different surface morphologies, their structure functions for the rough surfaces are H1(ξ) and H2(ξ), respectively. The fractal parameters of the equivalent rough thin-walled surface of the riveting surface of the two thin-walled parts can be obtained by the following formula:

4. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: In the third step, when the micro-protrusion is simplified to a spherical model, the peaks of the micro-protrusions are opposite each other when there is no riveting force. When the rivet is subjected to riveting force, the rivet shank deforms and applies a load to the thin-walled part. At this time, the micro-protrusion is subjected to the load and undergoes contact deformation. The state of contact deformation of a micro-protrusion after being subjected to riveting force is equivalent to the contact between a micro-protrusion and a smooth surface; Suppose that the contact area of ​​any single pair of micro-protrusions under riveting force is a = πr. 2 r is the radius of the contact area of ​​the micro-protrusion, r = (3FR / 4E) 13 The radius of curvature of the equivalent micro-convex body is R, R = a 0.5D G 1-D The deformation of the micro-protrusion is: δ=G (D-1) a (2-D)2 ; When a single pair of micro-protrusions is in the critical state of elastic deformation and plastic deformation, the expression for the critical deformation amount of the micro-protrusion is: In the formula, the proportionality constant k = H / σ s , It is related to the elastic modulus E of the interface and the yield strength σ of the softer material. s The relevant coefficients, When δ=δ c At that time, the critical contact area a of the micro-protrusion c The expression is: According to Hertzian theory, when the contact area of ​​the micro-convex body satisfies a > a c At this time, when a single pair of micro-protrusions is in the elastic deformation stage, the expression for the elastic contact load is: When the contact area of ​​the micro-protrusion satisfies a < a c At this time, when a single pair of micro-protrusions is in the plastic deformation stage, the expression for the plastic contact load is: f p =Ha In the formula, H is the hardness of the softer material in the two thin-walled parts; Since the contact between each pair of micro-convexities is considered as the contact between spheres, applying the method for calculating the contact stiffness between spheres in Hertz theory, the expression for the contact stiffness of any equivalent spherical micro-convexity in contact with a rigid plane is obtained as follows: When a thin-walled component is subjected to riveting force and the micro-protrusions undergo elastic deformation, the elastic strain energy of a single pair of micro-protrusions can be obtained by integrating the elastic contact load with respect to the deformation: When a micro-protrusion undergoes plastic deformation, the plastic strain energy of a single pair of micro-protrusions can be obtained by integrating the plastic contact load with respect to the deformation amount:

5. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: In the fourth step, the contact area modeling of the riveting surface is as follows: Using the island area distribution theory, the expression for the number of micro-protrusions on the thin-walled part surface with a contact area greater than 'a' is obtained as follows: Using fractal contact theory, the expression for the size distribution function n(a) of the contact area of ​​the micro-convex body is obtained: ψ is the domain expansion factor for the contact area distribution of the micro-convex body, and it is also a function related to the fractal dimension D. Its expression is: The actual contact area formed by the deformation of all micro-protrusions on the riveting surface is A. r Its expression is:

6. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: In the fifth step, the normal contact stiffness K of the micro-protrusions on the riveting surface of the thin-walled part is... n This can be obtained by extending the micro-protrusion size distribution function n(a) to the entire mating surface: Solving for the total strain energy of the riveting surface of thin-walled parts requires starting from the elastoplastic strain energy of a single micro-protrusion and extending it to the entire riveting surface through the micro-protrusion size distribution function n(a). The total elastic strain energy of the riveting surface is the critical contact area a. c Up to the maximum contact area is a l Integral of the elastic strain energy of a single micro-convexity: The total plastic strain energy of the riveted surface is the minimum contact area a s To the critical contact area a c Integral of the plastic strain energy of a single micro-protrusion:

7. The method for accurate modeling and prediction of deformation in riveting assembly of thin-walled aircraft parts according to claim 1, characterized in that: In step six, the damping loss factor η of the riveted surface can be obtained from the total elastic strain energy and the total plastic strain energy: The mass of the thin-walled part is M, C c It is the critical damping coefficient, and Normal contact damping value C of the riveting surface of thin-walled parts n The expression is: During the riveting assembly process, the contact stress area between the two thin-walled parts is mainly around the rivet holes, and the area of ​​the contact stress area tends to a constant value after riveting. Within this range, the contact stress value varies greatly; beyond this range, the contact stress value varies very little. Therefore, spring-damping units are placed on the circumference of this area. Then, based on the number and arrangement of the spring-damping units, the normal contact stiffness and normal contact damping values ​​of the thin-walled part mating surfaces are evenly distributed to each spring-damping unit. Based on the above formulas, the expressions for the contact stiffness and contact damping of each spring-damping unit are obtained:

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