Bolt joint part nonlinear parameter equivalent modeling method based on virtual material

Abstract

The invention discloses a bolt joint part nonlinear parameter equivalent modeling method based on a virtual material, and belongs to the technical field of bolt joint part modeling, and the method comprises the steps: obtaining normal and tangential experimental data of a unit area of a bolt joint part, carrying out the fitting according to the experimental data, and obtaining the normal and tangential dynamic stiffness and damping of a unit area of a bolt joint surface; according to the analysis parameters of the virtual material layer of the bolt joint part, constructing a constitutive model of a stress-strain relationship; and according to the constitutive model and the normal and tangential dynamic stiffness and damping of the unit-area bolt joint surface, virtual material layer analysis parameters, equivalent thickness and equivalent density are solved. According to the method, identification and equivalent modeling can be carried out on parameters of the elastic modulus, the shear modulus, the Poisson's ratio, the equivalent density and the equivalent thickness of the bolt joint part with specific specification parameters, and through equivalent processing, in modal analysis in Ansys Workbench, the inherent frequency of an equivalent model of the method is closer to an experimental result compared with a traditional virtual material method.

Description

Technical Field

[0001] This invention relates to the field of bolt joint modeling technology, specifically to a nonlinear parameter equivalent modeling method for bolt joints based on virtual materials. Background Technology

[0002] Interconnected surfaces in machine tools are called "mating surfaces," and their stiffness and damping have a crucial impact on the overall dynamic performance of the machine. Statistics show that the contact stiffness of mating surfaces accounts for approximately 40%–60% of the overall contact stiffness of the machine, while contact damping accounts for as much as 90%. Bolted connections, as a common mechanical connection method, are widely used in important fields such as CNC machine tools, aerospace, and the automotive industry due to their simple structure, convenient assembly and disassembly, and low cost. Under dynamic excitation, the dynamic stiffness and damping of bolted joints change differently with the excitation force, and the elastic parameters of the joint, such as the elastic modulus, shear modulus, and Poisson's ratio, also change, affecting the overall dynamic performance of the joint. Currently, equivalent modeling of the nonlinear parameters of bolted joints is a technical challenge, and the accuracy of the elastic parameter modeling affects the analysis results of the dynamic characteristics of the entire joint. Summary of the Invention

[0003] The objective of this invention is to provide a nonlinear parameter equivalent modeling method for bolted joints based on virtual materials, thereby achieving accurate modeling of the elastic parameters of bolted joints and improving the dynamic characteristic analysis results of bolted joints.

[0004] To achieve the objective of this invention, the technical solution adopted by this invention is as follows: a method for equivalent modeling of nonlinear parameters of bolted joints based on virtual materials, the method comprising the following steps:

[0005] Step 1: Obtain experimental data on the normal and tangential directions of the bolt joint per unit area, including displacement data from the eddy current displacement sensor, acceleration sensor data, static force sensor data, and dynamic force and excitation frequency data from the exciter.

[0006] Step 2: Fit the experimental data from Step 1 to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows.

[0007] (1),

[0008] (2),

[0009] (3),

[0010] (4),

[0011] In the formula, and These are the normal and tangential dynamic stiffness per unit area of ​​the bolt joint surface, respectively, in units of... ; and These represent the normal and tangential damping per unit area of ​​the bolt joint surface, respectively, in units of... ; The normal surface pressure per unit area of ​​the bolt joint surface is related to the normal load borne by the bolt joint surface, and the unit is MPa; The excitation frequency is expressed in units of 1000 ppm. ; and These represent the normal and tangential dynamic displacement amplitudes of the bolt joint surface, respectively, in units of... ;

[0012] Step 3: Construct a virtual material layer for the bolted joint. Based on the analytical parameters of the virtual material layer, construct a constitutive model of the stress-strain relationship. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows:

[0013] (5),

[0014] Step 4: Solve for the analytical parameters of the virtual material layer, i.e., the elastic modulus. ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane They are as follows:

[0015] (11),

[0016] (13)

[0017] (17)

[0018] (18)

[0019] (19);

[0020] The equivalent thickness and equivalent density calculation module is used to calculate the equivalent thickness and equivalent density of the virtual material layer at the bolt joint, as follows:

[0021] The equivalent thickness of the virtual material layer is expressed by equation (21):

[0022] (twenty one),

[0023] The equivalent density of the virtual material layer is expressed as Equation (22);

[0024] (twenty two).

[0025] The second objective of this invention is to provide an equivalent modeling system for nonlinear parameters of bolted joints based on virtual materials, which can accurately identify and model the nonlinear parameters of bolted joints.

[0026] Regarding the second objective, the technical solution adopted by this invention is: an equivalent modeling system for nonlinear parameters of bolted joints based on virtual materials, comprising:

[0027] The bolt joint experimental data acquisition module is used to acquire normal and tangential experimental data of bolt joints per unit area;

[0028] The fitting module is used to fit the acquired experimental data to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows.

[0029] (1),

[0030] (2),

[0031] (3),

[0032] (4),

[0033] The virtual material layer construction module for bolted joints is used to construct a virtual material layer for bolted joints. Based on the analytical parameters of the virtual material layer, a constitutive model of the stress-strain relationship is constructed. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows:

[0034] (5),

[0035] The virtual material layer analytical parameter solving module is used to solve for the analytical parameters of the virtual material layer, namely the elastic modulus. ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane They are as follows:

[0036] (11),

[0037] (13)

[0038] (17)

[0039] (18)

[0040] (19);

[0041] The equivalent thickness and equivalent density calculation module is used to calculate the equivalent thickness and equivalent density of the virtual material layer at the bolt joint, as follows:

[0042] The equivalent thickness of the virtual material layer is expressed by equation (21):

[0043] (twenty one),

[0044] The equivalent density of the virtual material layer is expressed as Equation (22);

[0045] (twenty two).

[0046] The beneficial effects of this invention are as follows: Compared with the prior art, this invention can identify and model the elastic modulus, shear modulus, Poisson's ratio, equivalent density, and equivalent thickness parameters of bolt joints with specific specifications. Through equivalent processing, in modal analysis in Ansys Workbench, the natural frequencies of the equivalent model obtained by this method are closer to the experimental results than those obtained by traditional virtual material methods. Attached Figure Description

[0047] Figure 1 A flowchart of a nonlinear parameter equivalent modeling method for bolted joints based on virtual materials;

[0048] Figure 2 This serves as a test platform for the bonding surface per unit area.

[0049] Figure 3 The experimental platform is a unit interface surface normal.

[0050] Figure 4 Tangential experimental platform for unit mating surfaces;

[0051] Figure 5 A schematic diagram of the contact between the micro-protrusions at the bolt joint and a schematic diagram of the equivalent method of the present invention;

[0052] Figure 6 This is a diagram showing the surface pressure distribution at the bolt joint.

[0053] Figure 7 To set the four-way path for bolted joints in Ansys Workbench;

[0054] Figure 8 The diagram and fitting curve of the pressure function in four directions of the bolt joint;

[0055] Figure 9 This is a virtual material method model of bolt joints;

[0056] Figure 10 The first six vibration modes of the bolted joint using the virtual material method;

[0057] Figure 11 This is a dynamic testing platform for single-bolt connected plate components. Figure 12 The MAC histogram is the corresponding graph of the experimental modality confidence matrix. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0059] Example 1: As Figure 1-12 As shown, a nonlinear parameter equivalent modeling method for bolted joints based on virtual materials is proposed. This method includes the following steps:

[0060] Step 1: Obtain experimental data on the normal and tangential directions of the bolt joint per unit area, including displacement data from the eddy current displacement sensor, acceleration sensor data, static force sensor data, and dynamic force and excitation frequency data from the exciter.

[0061] Step 2: Fit the experimental data from Step 1 to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows.

[0062] (1),

[0063] (2),

[0064] (3),

[0065] (4),

[0066] In the formula, and These are the normal and tangential dynamic stiffness per unit area of ​​the bolt joint surface, respectively, in units of... ; and These represent the normal and tangential damping per unit area of ​​the bolt joint surface, respectively, in units of... ; The normal surface pressure per unit area of ​​the bolt joint surface is related to the normal load borne by the bolt joint surface, and the unit is MPa; The excitation frequency is expressed in units of 1000 ppm. ; and These represent the normal and tangential dynamic displacement amplitudes of the bolt joint surface, respectively, in units of... ; This represents the dynamic stiffness coefficient of the bonding surface normal. This represents the tangential dynamic stiffness coefficient of the bonding surface. Indicates the normal damping coefficient of the bonding surface. Indicates the tangential damping coefficient of the mating surface;

[0067] This represents the surface pressure coefficient of the normal dynamic stiffness of the bonding surface. This represents the surface pressure coefficient, which indicates the tangential dynamic stiffness of the bonding surface. This represents the normal damping surface pressure coefficient of the bonding surface. Indicates the tangential damping surface pressure coefficient of the joint surface;

[0068] This represents the dynamic stiffness frequency coefficient of the bonding surface normal. This represents the dynamic stiffness frequency coefficient of the bonding surface normal. This represents the normal damping frequency coefficient of the bonding surface. Indicates the tangential damping frequency coefficient of the mating surface;

[0069] This represents the dynamic displacement amplitude coefficient of the combined surface normal dynamic stiffness. This represents the dynamic displacement amplitude coefficient of the tangential dynamic stiffness of the bonding surface. This represents the coefficient of dynamic displacement amplitude of the normal damping at the interface. This represents the dynamic displacement amplitude coefficient of the tangential damping at the interface; the above parameters were obtained experimentally.

[0070] Step 3: Construct a virtual material layer for the bolted joint. Based on the analytical parameters of the virtual material layer, which includes five independent engineering elastic parameters, construct a constitutive model of the stress-strain relationship. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows:

[0071] (5),

[0072] Step 4: Solve for the analytical parameters of the virtual material layer, i.e., the elastic modulus. Elastic modulus shear modulus Poisson's ratio Compared to Poisson The solution process is as follows:

[0073] A quartic polynomial is used to describe the contact pressure distribution model of the bolt joint. The contact pressure function is fitted to a quartic polynomial related to the bolt hole spacing, expressed as Equation (6).

[0074] (6),

[0075] In the formula: and It is a constant determined by analyzing the magnitude of the bolt preload; d is the distance from the center of the bolt hole;

[0076] Referring to the metric bolt tightening torque (Q / STB 12.521.5-2000), the preload torque for a 10.9 grade M12 bolt is approximately 78-104. The relationship between torque and preload is given by equation (7), which can be used to calculate the preload of a standard bolt.

[0077] (7),

[0078] In the formula: T is the applied torque; and The coefficient of friction between the supporting surface and the threaded contact surface; and The effective radius of the supporting surface and the threaded contact surface; The thread angle; The thread lead angle, This refers to the bolt preload.

[0079] Assuming a normal load is applied to the mating surface When, the normal direction is deformed into Work done by normal load As shown in equation (8);

[0080] (8),

[0081] In the formula: For the normal stiffness of the mating surface;

[0082] After the virtual material layer is equivalent, the strain energy Represented as equation (9);

[0083] (9),

[0084] In the formula: Normal stress, The nominal contact area of ​​the mating surfaces is given by h, which represents the thickness of the specimen.

[0085] According to the functional principle Thus, equation (10) is derived.

[0086] (10)

[0087] Therefore, considering equation (1), the equivalent elastic modulus of the virtual material layer along the xoz plane is... Represented as equation (11);

[0088] (11),

[0089] In the formula, This is derived from equation (6);

[0090] With the effective elastic modulus along the Z-axis Unlike other materials, the elastic modulus along the x-axis on the xoy plane is related to the preload of the bolt connection; therefore, the actual contact area of ​​the mating surface is introduced. The concept is that the bolt joint surface will undergo microscopic micro-protrusion extrusion deformation under tangential load, resulting in macroscopic slippage of the joint surface, and its actual contact area corresponds to formula (12).

[0091] (12),

[0092] in: For lateral loads; The coefficient of friction of the connecting plate; It is a semi-vertical angle; The bolt preload is dw, where dw represents the bolt major diameter and dh represents the bolt minor diameter.

[0093] Elastic modulus along the x-axis Represented as equation (13);

[0094] (13)

[0095] in: The composite elastic modulus of the material is expressed as: , , , and These represent the elastic modulus and Poisson's ratio of the upper and lower specimens, respectively.

[0096] The work done by the tangential load when the mating surface is subjected to a tangential load. Represented as equation (14):

[0097] (14)

[0098] After the virtual material layer is equivalent, the strain energy Represented as equation (15):

[0099] (15)

[0100] According to the functional principle shear modulus Represented as equation (16):

[0101] (16)

[0102] Therefore, considering equation (2), the equivalent shear modulus of the virtual material layer along the xoz plane is... Represented as equation (17):

[0103] (17)

[0104] According to the definition of Poisson's ratio, the equivalent virtual material of the fixed joint is... Plane edge The Poisson's ratio for axial tension and compression is expressed as equation (18);

[0105] (18)

[0106] According to the definition of Poisson's ratio, the fixed joint is equivalent to a transversely isotropic virtual material. Plane edge The Poisson's ratio for axial tension and compression is expressed as equation (19).

[0107] (19);

[0108] Step 5: Based on the virtual material layer of the bolt joint, solve for its equivalent thickness and equivalent density, as follows:

[0109] The thickness of the virtual material is obtained using the equivalent stiffness method, assuming the thickness is over the entire nominal contact area. The average pressure distribution on it is Preload and virtual material deformation The functional relationship between the dynamic stiffness of the bolt joint and the bolt joint can be expressed as equation (20);

[0110] (20)

[0111] Therefore, the equivalent thickness of the virtual material layer is expressed as equation (21):

[0112] (twenty one),

[0113] The equivalent density of the virtual material layer is expressed as Equation (22);

[0114] (twenty two).

[0115] Thus, the formulas for the elastic modulus, shear modulus, Poisson's ratio, equivalent density, and equivalent thickness of the virtual material layer at the bolt joint are derived. By building an experimental platform, the specific specifications of the experimental specimen can be obtained, and then the elastic parameters of the virtual material layer can be solved.

[0116] The above method was simulated using Ansys Workbench. The effectiveness of the equivalent model was verified by combining Ansys Workbench simulation with experiments. The natural frequencies of the traditional virtual material method and the method of this invention were calculated using the modal analysis module. Then, the natural frequencies of the bolted joint under real-world conditions were experimentally determined, and the error magnitudes were compared and analyzed. The conclusion is that after equivalent modeling the bolted connection area, the obtained natural frequencies are highly consistent with the experimental values, with a maximum relative error of only 4.86% and an average error of 2.61%. In contrast, the maximum relative error of the natural frequencies obtained using the traditional virtual material method is 10.46%. Therefore, the equivalent method of this invention is more accurate and can effectively model the actual working conditions of the bolted joint.

[0117] Example 2: A system for equivalent modeling of nonlinear parameters of bolted joints based on virtual materials is provided, which can accurately identify and model the nonlinear parameters of bolted joints, including:

[0118] The bolt joint experimental data acquisition module is used to acquire normal and tangential experimental data of bolt joints per unit area;

[0119] The fitting module is used to fit the acquired experimental data to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows.

[0120] (1),

[0121] (2),

[0122] (3),

[0123] (4),

[0124] The virtual material layer construction module for bolted joints is used to construct a virtual material layer for bolted joints. Based on the analytical parameters of the virtual material layer, a constitutive model of the stress-strain relationship is constructed. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows:

[0125] (5),

[0126] The virtual material layer analytical parameter solving module is used to solve for the analytical parameters of the virtual material layer, namely the elastic modulus. ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane They are as follows:

[0127] (11),

[0128] (13)

[0129] (17)

[0130] (18)

[0131] (19);

[0132] The equivalent thickness and equivalent density calculation module is used to calculate the equivalent thickness and equivalent density of the virtual material layer at the bolt joint, as follows:

[0133] The equivalent thickness of the virtual material layer is expressed by equation (21):

[0134] (twenty one),

[0135] The equivalent density of the virtual material layer is expressed as Equation (22);

[0136] (twenty two),

[0137] The specific experimental procedure is as follows: Figure 2 The diagram shows a dynamic characteristic test bench for a unit interface, which includes a control front-end, a data acquisition front-end, a power amplifier, control software, a vibrator, a charge amplifier, and data acquisition software. The control software can control the vibrator to output different excitation forces and frequencies. The vibrator, through excitation... Figure 3 , Figure 4 The test platform for the normal and tangential mating surfaces allows for different vibration conditions between the mating surfaces, simulating the actual machining conditions of the machine tool. The acceleration sensor, displacement sensor, static force, and dynamic force signals in the test platform are collected by the acquisition software, and then the normal and tangential dynamic stiffness and damping are solved by the formulas of the mating surfaces (1)-(4).

[0138] (1),

[0139] (2),

[0140] (3),

[0141] (4),

[0142] like Figure 5 As shown, the bolt joint micro-protrusions are in contact and are constructed as a virtual material layer. The left side of the figure is a schematic diagram of the bolt joint micro-protrusions in contact, and the right side is an equivalent schematic diagram of the virtual material layer.

[0143] from Figure 6 As can be seen, the surface pressure of the bolt preload on the mating surface exhibits a characteristic of gradually decreasing from the center of the hole to the edge. A fourth-order polynomial function is proposed to fit this nonlinear change. The analytical model of the bolt joint is obtained through finite element modeling, as shown below. Figure 7As shown, the upper bolt connection plate 100 is connected to the lower bolt connection plate 120 through a virtual material layer 110, and paths in four directions from the hole center to the edge are set to detect and export its pressure change data. The pressure change function is as follows: Figure 8 As shown, the four sets of data are averaged and fitted with a fourth-order polynomial to obtain the pressure distribution function as shown in equation (5).

[0144] (5),

[0145] In the formula, r is the distance from the center of the bolt hole;

[0146] Assuming a normal load is applied to the mating surface When, the normal direction is deformed into Work done by normal load As shown in equation (6);

[0147] (6),

[0148] In the formula: For the normal stiffness of the mating surface;

[0149] After the virtual material layer is equivalent, the strain energy It can be expressed as equation (7);

[0150] (7),

[0151] In the formula: Normal stress, The nominal contact area of ​​the mating surfaces;

[0152] According to the functional principle Equation (8) can be derived:

[0153] (8),

[0154] Therefore, considering equation (1), the equivalent elastic modulus of the virtual material layer along the xoz plane is... It can be expressed as equation (9);

[0155] (9),

[0156] In the formula, the normal surface pressure It can be derived from equation (5);

[0157] Equivalent elastic modulus along the xoz plane Unlike other materials, the elastic modulus along the xoy plane is related to the preload of the bolt connection; therefore, the actual contact area of ​​the mating surface is introduced. The concept of . When the bolt joint surface is subjected to tangential load, microscopic micro-protrusion extrusion deformation will occur, resulting in macroscopic slippage of the joint surface, and its actual contact area corresponds to formula (10);

[0158] (10)

[0159] Elastic modulus along the xoy plane It can be expressed as equation (11):

[0160] (11),

[0161] in: The composite elastic modulus of the material; can be expressed as ;

[0162] The work done by the tangential load when the mating surface is subjected to a tangential load. It can be expressed as equation (12):

[0163] (12),

[0164] After the virtual material layer is equivalent, the strain energy It can be expressed as equation (13):

[0165] (13)

[0166] According to the functional principle shear modulus It can be expressed as equation (14):

[0167] (14)

[0168] Therefore, considering equation (2), the equivalent shear modulus of the virtual material layer along the xoz plane is... It can be expressed as equation (15):

[0169] (15)

[0170] According to the definition of Poisson's ratio, the equivalent virtual material of the fixed joint is... Plane edge The Poisson's ratio for axial tension and compression can be expressed as equation (16);

[0171] (16)

[0172] According to the definition of Poisson's ratio, the fixed joint is equivalent to a transversely isotropic virtual material. Plane edge The Poisson's ratio for axial tension and compression can be expressed as equation (17);

[0173] (17)

[0174] This invention uses the equivalent stiffness method to obtain the thickness of the virtual material, assuming the thickness over the entire nominal contact area. The average pressure distribution on it is , force and virtual material deformation The functional relationship between the dynamic stiffness of the bolt joint and the bolt joint can be expressed as equation (18);

[0175] (19)

[0176] Therefore, the equivalent thickness of the virtual material layer can be expressed as Equation (20);

[0177] (20)

[0178] The equivalent density of the virtual material layer can be expressed as Equation (21);

[0179] (twenty one).

[0180] Thus, the formulas for the elastic modulus, shear modulus, Poisson's ratio, equivalent density, and equivalent thickness of the virtual material layer in the bolt joint are derived. By building an experimental platform, the specific specifications of the experimental specimen can be obtained, and then the elastic parameters of the virtual material layer can be solved.

[0181] This invention establishes, in the finite element method, as follows Figure 9 The analysis model shown mainly consists of three parts: an upper connecting plate, a lower connecting plate, and a virtual material layer. The upper and lower connecting plates are both made of HT300 material, and their material parameters are set. The material properties of the virtual material layer are specific parameters established by the method of this invention, including the elastic modulus of the xoy plane, the elastic modulus of the xoz plane, the shear modulus of the xoz plane, the Poisson's ratio of the xoy plane, the Poisson's ratio of the xoz plane, the equivalent density, and the equivalent thickness.

[0182] In the finite element method, a specific working condition is simulated by fixing one end and applying an 80N tangential force to the other end. Then, the natural frequencies of its first six modalities are analyzed, and the mode shapes are as follows: Figure 10 As shown;

[0183] Build such Figure 11The experimental setup shown includes M+P SmartOffice, a vibrator, an M+P data acquisition unit, a single-bolt connecting plate, and a triaxial accelerometer. The connecting screws on both sides of the vibrator 1 are symmetrically hung on the crossbeam at the top of the U-shaped suspension 3 via two elastic ropes 2. The output end of the vibrator 1 is connected to the upper bolt connecting plate 4 via a vibration rod. A triaxial accelerometer 5 is installed on the upper bolt connecting plate 4. The lower end of the upper bolt connecting plate 4 overlaps the upper end of the lower bolt connecting plate 7 and is fixedly connected by an M12 bolt 6. The lower end of the lower bolt connecting plate 7 is fixedly connected to a vise 8, which clamps the upper end of the lower bolt connecting plate 8. The triaxial accelerometer 5 is connected to the M+P data acquisition unit, which is connected to a host computer. The host computer has M+P SmartOffice installed. The vibrator provides a fixed-frequency vibration signal to the specimen. The triaxial accelerometer is used to measure the specific acceleration signal of the connecting plate, and the M+P data acquisition unit is used to acquire the signal. SmartOffice is used to analyze and process acceleration signals to obtain the natural frequency of the specimen.

[0184] Table 1 shows the experimental modal confidence matrix, and its corresponding MAC histogram is as follows: Figure 12 As shown, the results were used to analyze the consistency of the modal results. The analysis results show that the autocorrelation MAC value of each order modal vector is 1, indicating that the consistency of modes of the same order fully meets the accuracy requirements; while the maximum cross-correlation MAC value between different order modal vectors is only 0.0278 (occurring between the 3rd and 4th order modal vectors). This result shows that different orders of modes have good independence and orthogonality, thus verifying the reliability and validity of the dynamic test data obtained in this experiment.

[0185]

[0186] The simulated natural frequencies of traditional virtual materials and the method of this invention were analyzed in Ansys Workbench, and the actual natural frequencies were obtained with reference to experiments. The deviations are shown in Table 2. It can be seen that the natural frequencies obtained by the method of this invention are highly consistent with the experimental values, with a maximum relative error of only 4.86% and an average error of 2.61%. In contrast, the natural frequencies obtained by the traditional virtual material method have a maximum relative error of 10.46%. The RMSE comparison in Table 5 shows that when using the method of this invention, the first 6 natural frequencies of the model are closer to the experimental values. Therefore, it can be concluded that the equivalent method of this invention is more accurate and can be used to perform equivalent modeling of the actual working conditions of bolted joints.

[0187]

[0188]

[0189] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection of the claims.

Claims

1. A method for equivalent modeling of nonlinear parameters of bolted joints based on virtual materials, characterized in that, The method includes the following steps: Step 1: Obtain experimental data on the normal and tangential directions of the bolt joint per unit area, including displacement data from the eddy current displacement sensor, acceleration sensor data, static force sensor data, and dynamic force and excitation frequency data from the exciter. Step 2: Fit the experimental data from Step 1 to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows. （1）， （2）， （3）， （4）， In the formula, and These are the normal and tangential dynamic stiffness per unit area of ​​the bolt joint surface, respectively, in units of... ; and These represent the normal and tangential damping per unit area of ​​the bolt joint surface, respectively, in units of... ; The normal surface pressure per unit area of ​​the bolt joint surface is related to the normal load borne by the bolt joint surface, and the unit is MPa; The excitation frequency is expressed in units of 1000 ppm. ; and These represent the normal and tangential dynamic displacement amplitudes of the bolt joint surface, respectively, in units of... ; This represents the dynamic stiffness coefficient of the bonding surface normal. This represents the tangential dynamic stiffness coefficient of the bonding surface. Indicates the normal damping coefficient of the bonding surface. Indicates the tangential damping coefficient of the mating surface; This represents the surface pressure coefficient of the normal dynamic stiffness of the bonding surface. This represents the surface pressure coefficient, which indicates the tangential dynamic stiffness of the bonding surface. This represents the normal damping surface pressure coefficient of the bonding surface. Indicates the tangential damping surface pressure coefficient of the joint surface; This represents the dynamic stiffness frequency coefficient of the combined surface normal. This represents the dynamic stiffness frequency coefficient of the combined surface normal. This represents the normal damping frequency coefficient of the bonding surface. Indicates the tangential damping frequency coefficient of the mating surface; This represents the dynamic displacement amplitude coefficient of the combined surface normal dynamic stiffness. This represents the dynamic displacement amplitude coefficient of the tangential dynamic stiffness of the bonding surface. This represents the coefficient of dynamic displacement amplitude of the normal damping at the interface. This represents the dynamic displacement amplitude coefficient of the tangential damping at the interface; the above parameters were obtained experimentally. Step 3: Construct a virtual material layer for the bolt joint. This virtual material layer is a medium with uniform thickness and properties equivalent to the micro-protrusions of the joint, located between the two contact surfaces. This material layer employs a transversely isotropic constitutive model. Specifically, the Z-direction elastic modulus E... z The normal contact stiffness of the equivalent mating surface is used; the X-direction elastic modulus Ex is used; the tangential contact stiffness of the equivalent mating surface is used; the in-plane shear modulus G xz The tangential friction stiffness used for the equivalent mating surface is determined based on the friction coefficient and normal pressure; the distribution range of the virtual material layer is an annular region centered on the bolt hole and bounded by the preload pressure cone. Based on the analytical parameters of the virtual material layer of the bolt joint, a constitutive model of the stress-strain relationship is constructed. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows: （5）， Step 4: Solve for the analytical parameters of the virtual material layer, i.e., the elastic modulus. Elastic modulus shear modulus Poisson's ratio Compared to Poisson They are as follows: （11）， （13）， （17）， （18）， （19）； In the formula, The nominal contact area of ​​the mating surfaces. This represents the actual contact area. The composite elastic modulus of the material. For the specimen thickness, along the joint The strain in the axial direction is ,along The strain in the axial direction is Along the joint The strain in the axial direction is Virtual materials in In-plane edge Poisson's ratio for axial tension and compression is ,exist In-plane edge Poisson's ratio for axial tension and compression is ; Step 5: Based on the virtual material layer of the bolt joint, solve for its equivalent thickness and equivalent density, as follows: The equivalent thickness of the virtual material layer is expressed by equation (21): （21）， The equivalent density of the virtual material layer is expressed as Equation (22); （22）。 2. A nonlinear parameter equivalent modeling system for bolted joints based on virtual materials, characterized in that, include: The bolt joint experimental data acquisition module is used to acquire normal and tangential experimental data of bolt joints per unit area; The fitting module is used to fit the acquired experimental data to obtain the normal and tangential dynamic stiffness and damping of the bolt joint surface per unit area. The specific formulas are as follows. （1）， （2）， （3）， （4）， The virtual material layer construction module for bolted joints is used to construct a virtual material layer for bolted joints. Based on the analytical parameters of the virtual material layer, a constitutive model of the stress-strain relationship is constructed. The analytical parameters of the virtual material layer include those along... elastic modulus of shaft ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane ,as follows: （5）， The virtual material layer analytical parameter solving module is used to solve for the analytical parameters of the virtual material layer, namely the elastic modulus. ,along elastic modulus of shaft ,exist Shear modulus of a plane ,exist Poisson's ratio in a plane and in Poisson's ratio in a plane They are as follows: （11）， （13）， （17）， （18）， （19）； The equivalent thickness and equivalent density calculation module is used to calculate the equivalent thickness and equivalent density of the virtual material layer at the bolt joint, as follows: The equivalent thickness of the virtual material layer is expressed by equation (21): （21）， The equivalent density of the virtual material layer is expressed as Equation (22); （22）。

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