A Load Equivalent Method, System, Device and Medium for Evaluating Bolt Loosening

Abstract

The present invention provides a load equivalent method, system, device and medium for evaluating bolt loosening, which relates to the technical field of bolt evaluation. It includes solving the bending moment and lateral external load according to Castigliano's theorem, and establishing a first model as an equivalent model of bolt external load and screw rod load; establishing a second model according to the first model, and the second model is an equivalent relationship model between screw rod load and thread load; establishing a third model as an equivalent model of thread load and thread root stress; converting the load-time history of the bolt in the third model into the stress-time history of the thread root, and evaluating the loosening life of the bolt connection based on rainflow counting and Miner damage linear cumulative theory. The beneficial effect of the present invention provides technical support for the safe service of vehicle bolt connection equipment and the guarantee of driving safety, and has important scientific value and engineering significance for optimizing bolt connection parameters, preventing bolt loosening failure and ensuring the safe and stable operation of vehicles.

Description

Technical Field

[0001] The present invention relates to the technical field of bolt evaluation, and in particular, to a load equivalent method, system, device and medium for evaluating bolt loosening. Background Art

[0002] As an important connection method for transportation vehicles such as rail vehicles and automobiles, the reliability of bolt connections is a key factor affecting the safe operation of trains. With the continuous improvement of requirements such as the operating speed, lightweight, axle load, road network density, and train operation density of rail vehicles in China, the train operation environment has become increasingly complex and changeable. The bolt connections in various parts of the vehicle will bear greater and more complex alternating loads, and bolt loosening problems often occur. In the initial stage of bolt loosening, it may not affect the normal operation of the vehicle, but as the loosening further intensifies, it will cause the failure of the entire connection structure, seriously affecting the train operation safety.

[0003] Since the relationship between the external load characteristics of bolt connections and the load characteristics of the screw rod is an extremely complex equivalent relationship different from a single load transfer path, whether the external load that drives the bolt connection to loosen can be converted into a stress independent of the specific bolt structure is the key to establishing a general characteristic curve. However, currently, no bolt load equivalent method for evaluating bolt connection loosening has been found. Summary of the Invention

[0004] The purpose of the present invention is to provide a load equivalent method, system, device and medium for evaluating bolt loosening to improve the above problems. To achieve the above purpose, the technical solutions adopted by the present invention are as follows:

[0005] In the first aspect, the present application provides a load equivalent method for evaluating bolt loosening, including:

[0006] According to Castigliano's theorem, solve the bending moment and lateral external load, and establish a first model, where the first model is an equivalent model of bolt external load and screw rod load;

[0007] According to the first model, establish a second model, where the second model is an equivalent relationship model between screw rod load and thread load;

[0008] Based on the second model, calculate the thread root stress, and establish a third model, where the third model is an equivalent model of thread load and thread root stress;

[0009] Convert the load-time history of the bolt in the third model into a stress-time history of the thread root, and evaluate the loosening life of the bolt connection based on rainflow counting and Miner's linear cumulative damage theory

[0010] Preferably, according to Castigliano's theorem, solve for the bending moment and the lateral external load, and establish a first model, which includes:

[0011] Apply a lateral external load to the bolt connection in the pre-tightened state, and solve for the bending moment generated by the bending deformation of the screw rod. The calculation formula is as follows:

[0012]

[0013] In the formula, M is the bending moment, l1 is the clearance of the bolt hole, x3 is the distance from any position of the screw rod to the bolt head, I Z1 is the axial section moment of inertia of the bolt head, l2 is the clamping length, I Z2 is the transverse section moment of inertia of the screw rod, D is the lateral displacement, E b is the elastic modulus of the screw rod;

[0014] Establish a mechanical equivalent model, equivalent the lateral displacement of the bolt to the lateral external load, use Castigliano's theorem to calculate the bending moment equation of each section of the bolt connection, and solve for the lateral external load. The calculation formula is as follows:

[0015]

[0016] In the formula, F T is the lateral external load, I Z1 is the axial section moment of inertia of the bolt head, l2 is the clamping length, I Z2 is the transverse section moment of inertia of the screw rod, D is the lateral displacement, E b is the elastic modulus of the screw rod, l1 is the clearance of the bolt hole;

[0017] Establish a first model according to the bending moment and the lateral external load.

[0018] Preferably, establish a second model according to the first model. The second model is an equivalent relationship model between the load on the screw rod and the load on the screw threads, which includes:

[0019] Establish a force model of the screw threads. Select a micro-element on the screw thread surface, set the micro-element as an elastic body, and obtain the force on the screw threads under the lateral external load. The calculation formula is as follows:

[0020]

[0021] In the formula, α is the half angle of the thread profile, β is the lead angle of the thread, d2 is the pitch diameter of the bolt, z represents the distance from the screw thread to the top surface of the nut in the load direction, S A is the pre-tightening force F P and the sum of the forces S1 and S2 of the bending moment M on the micro-element, the direction is perpendicular to the screw thread inclined plane, S T is the force of the lateral external load F T on the micro-element, and is the same as FT in the same direction;

[0022] Based on the force of the thread, the load at the thread z is calculated using the preset boundary conditions, and its calculation formula is as follows:

[0023]

[0024] In the formula, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, and L is the height of the nut.

[0025] Based on the equivalent relationship between the load on the screw and the load on the thread, and by taking the derivative, the force on the thread microelement is obtained, and its calculation formula is as follows:

[0026]

[0027]

[0028]

[0029] In the formula, S1 is the force of the pre-tightening force F P acting on the microelement, S2 is the force of the bending moment M acting on the microelement, S T is the lateral external load of the pre-tightening force F T acting on the microelement, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, L is the height of the nut, d2 is the pitch diameter of the bolt, α is the half angle of the thread profile, and β is the lead angle of the thread.

[0030] Preferably, the stress at the root of the thread is calculated based on the second model, and a third model is established. The third model is an equivalent model of the thread load and the stress at the root of the thread, and it includes:

[0031] Based on the second model, a natural coordinate system is established on the microelement, and the forces S A and S T are converted into the principal stress perpendicular to the thread surface, the tangential stress along the radial direction, and the tangential stress along the tangential direction, and the transformation matrix is calculated;

[0032] When the friction force at the critical slip state of the thread surface is the maximum static friction force, taking the coordinate axes x, y, and z at the critical slip state as the equilibrium conditions, three-direction stresses on the thread microelement are obtained;

[0033] The nominal equivalent elastic stress of the thread is obtained from the stresses in three directions, and its calculation formula is as follows:

[0034]

[0035] In the formula, σ ns is the ratio of the nominal equivalent elastic stress, and σ1, σ2, and σ3 are the three principal stresses.

[0036] Based on the nominal equivalent elastic stress of the thread and the preset stress concentration coefficient at the root of the thread, the stress at the root of the thread is obtained, and an equivalent model of the thread load and the stress at the root of the thread is established. Its calculation formula is as follows:

[0037] σ t = K t σ ns

[0038] In the formula, σ t is the stress at the root of the thread, K t is the stress concentration coefficient at the root of the thread, that is, the ratio of the local maximum stress σ max of the material to the nominal equivalent elastic stress σ ns , and σ max can be obtained through finite element simulation.

[0039] In a second aspect, the present application also provides a load equivalent system for evaluating bolt loosening, including a first establishment module, a second establishment module, a third establishment module, and an evaluation module, where:

[0040] The first establishment module: is used to solve the bending moment and the lateral external load according to Castigliano's theorem and establish a first model, and the first model is an equivalent model of the bolt external load and the load on the screw rod;

[0041] The second establishment module: is used to establish a second model according to the first model, and the second model is an equivalent relationship model between the load on the screw rod and the thread load;

[0042] The third establishment module: is used to calculate the stress at the root of the thread based on the second model and establish a third model, and the third model is an equivalent model of the thread load and the stress at the root of the thread;

[0043] The evaluation module: is used to convert the load-time history of the bolt in the third model into the stress-time history at the root of the thread, and evaluate the loosening life of the bolt connection based on the rainflow counting and Miner's linear cumulative damage theory.

[0044] In a third aspect, the present application also provides a load equivalent device for evaluating bolt loosening, including:

[0045] A memory for storing a computer program;

[0046] A processor, which is configured to implement the steps of the load equivalent method for evaluating bolt loosening when executing the computer program.

[0047] In a fourth aspect, the present application further provides a readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned load equivalent method based on evaluating bolt loosening are implemented.

[0048] The beneficial effects of the present invention are as follows:

[0049] The present invention proposes a bolt load equivalent method for evaluating bolt connection loosening. By establishing an equivalent method between the external load of the bolt connection and the stress at the root of the thread, the load-time history of the bolt is equivalently converted into the stress-time history at the root of the thread. This method obtains the bolt load in real time through a load cell bolt and equivalently converts it into stress, overcoming the problems of difficult monitoring and acquisition of the lateral displacement of bolt connections in the actual service environment of vehicles, and difficult real-time evaluation of bolt loosening life. It has important scientific value and engineering significance for bolt connection safety assessment, structural optimization design, vehicle safety guarantee, etc.

[0050] The D-N curve of the bolt is obtained through the bolt loosening test. However, since it is difficult to monitor the lateral displacement of the bolt connection in the actual service environment of mechanical equipment, the bolt loosening life cannot be directly predicted through the D-N curve. Therefore, to solve this problem, the present invention will establish a bolt load equivalent model to equivalently convert the external load on the screw into the load on the screw and the stress at the root of the thread, so as to facilitate predicting the loosening life of the bolt.

[0051] Other features and advantages of the present invention will be described in the subsequent description. And, some of them will become obvious from the description, or can be understood by implementing the embodiments of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the written description, claims, and drawings. Description of the Drawings

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0053] Figure 1 It is a schematic flow chart of the load equivalent method for evaluating bolt loosening described in the embodiments of the present invention;

[0054] Figure 2Schematic structural diagram of the load equivalent system for evaluating bolt loosening according to an embodiment of the present invention;

[0055] Figure 3 Schematic structural diagram of the load equivalent device for evaluating bolt loosening according to an embodiment of the present invention;

[0056] Figure 4 Schematic diagram of the screw mechanical analysis model of the load equivalent method for evaluating bolt loosening according to an embodiment of the present invention;

[0057] Figure 5 Schematic diagram of the thread mechanical analysis model of the load equivalent method for evaluating bolt loosening according to an embodiment of the present invention;

[0058] Figure 6 Schematic diagram for comparing the finite element simulation bending moment with the theoretical calculated bending moment of the equivalent model of the bolt external load and the screw load in the load equivalent method for evaluating bolt loosening according to an embodiment of the present invention;

[0059] Figure 7 Schematic diagram for comparing the finite element simulation stress at the thread root with the theoretical calculated stress of the equivalent model of the screw load and the stress at the thread root in the load equivalent method for evaluating bolt loosening according to an embodiment of the present invention.

[0060] In the figure: 701, the first establishment module; 7011, the first solution unit; 7012, the second solution unit; 7013, the first establishment unit; 702, the second establishment module; 7021, the first calculation unit; 7022, the first acquisition unit; 7023, the second acquisition unit; 703, the third establishment module; 7031, the second calculation unit; 7032, the third acquisition unit; 7033, the fourth acquisition unit; 7034, the second establishment unit; 704, the evaluation module; 800, the load equivalent device for evaluating bolt loosening; 801, the processor; 802, the memory; 803, the multimedia component; 804, the I / O interface; 805, the communication component. Detailed implementation manners

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Components of the embodiments of the present invention described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0062] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used for descriptive distinction and cannot be construed as indicating or implying relative importance.

[0063] Embodiment 1:

[0064] Currently, the calculation methods for bolt loosening load conditions and load distribution are relatively mature, but the load equivalent method from the external load of the bolt connection to the stress at the root of the thread is lacking. A method for calculating the critical loosening load of a bolt considering thread flexibility disclosed in the invention patent application with the application (patent) number CN201910590358.7 establishes the load conditions for bolt connection loosening by considering the thread as a flexible body. This method is a concise and relatively accurate method for calculating the critical loosening load of a bolt connection, but it does not involve the calculation of load transfer and stress distribution in the bolt connection. Therefore, it is also impossible to evaluate the loosening life of the bolt based on the thread stress. A method for calculating the critical preloading margin of a bolt under an external load disclosed in the invention patent application with the application (patent) number CN202211681600.X obtains the minimum bolt preloading force required for the clamping parts not to separate by establishing a finite element model of the bolt connection under different contact states. This invention is a method for determining the preloading force of a bolt during assembly under working conditions and also does not involve the prediction of bolt loosening life. A method for calculating the load distribution of a composite material bolt connection considering the influence of clearance and friction disclosed in the invention patent application with the application (patent) number CN201610670979.2 calculates the load distribution of the bolt by establishing a structural node element model and a bolt connection model. This invention only provides a finite element simulation method for composite material bolt connections with high calculation efficiency and does not involve the load equivalence from the external load of the bolt connection to the stress at the root of the thread and the prediction of bolt loosening life.

[0065] At present, the bolt loosening monitoring method based on vibro-acoustic modulation and the method for evaluating bolt loosening based on the lateral displacement-loosening life curve in the laboratory environment are relatively mature, but their limitations are similar. Both evaluate bolt loosening by obtaining the displacement of the bolt connection. However, in the actual multi-axis random vibration service environment, the bolt connection of mechanical equipment is a non-linear and strongly coupled closed system. The formation and evolution mechanism of bolt loosening is complex, with many influencing factors, and it is difficult to accurately obtain the lateral displacement. This makes these bolt loosening evaluation methods still face many challenges in practical engineering applications.

[0066] This embodiment provides a load equivalent method for evaluating bolt loosening.

[0067] See Figure 1 , which shows that this method includes step S100, step S200, step S300 and step S400.

[0068] S100. According to Castigliano's theorem, solve the bending moment and the lateral external load, and establish a first model, where the first model is an equivalent model of the bolt external load and the load on the screw rod.

[0069] It can be understood that in this step S100, it includes S101, S102 and S103, where:

[0070] S101. Apply a lateral external load to the bolt connection in the pre-tightened state, and solve the bending moment generated by the bending deformation of the screw rod. The calculation formula is as follows:

[0071]

[0072] In the formula, M is the bending moment, l1 is the clearance of the bolt hole fit, x3 is the distance from any position of the screw rod to the bolt head, I Z1 is the axial section moment of inertia of the bolt head, l2 is the clamping length, I Z2 is the lateral section moment of inertia of the screw rod, D is the lateral displacement, E b is the elastic modulus of the screw rod;

[0073] It should be noted that when a lateral external load is applied to the bolt connection in the pre-tightened state, the screw rod will be subjected to an axial force and a bending moment. Figure 4 (a) As shown, when the bolt connection is only subjected to the pre-tightening force E P , no slip occurs on each contact surface, and it is in the clamped state at this time. If a lateral displacement external load is applied to the upper plate, the contact surface between the upper plate and the bolt head will be subjected to the frictional force F f , forcing the bolt head to also move laterally. Due to the relative constraint of the thread pair of the nut, this causes the screw rod to be subjected to the bending moment M and generate bending deformation.

[0074] In order to solve the bending moment M, establish Figure 4(b) The mechanical equivalent model shown, this mechanical model belongs to the problem of secondary static indeterminacy. The lateral displacement D is equivalent to the lateral external load F T , and by using Castigliano's theorem in mechanics of materials, the bending moment equations for each section of the bolt connection are as follows:

[0075]

[0076] In the formula, l1 is the fit clearance of the bolt hole, F C1 and F C2 are the support forces borne when the bolt head contacts the upper plate, x1 and x2 are the distances from any position of the fit gap to the support point, and x3 is the distance from any position of the screw rod to the bolt head.

[0077] It can be seen from the above formula that the key to obtaining M lies in solving F C1 and F C2 , because the actual vertical displacements at points A and C are 0. Based on Castigliano's second theorem, by removing the reaction forces at these points, we can obtain:

[0078]

[0079] In the formula, I Z1 is the axial section moment of inertia of the bolt head; I Z2 is the lateral section moment of inertia of the screw rod; E b is the elastic modulus of the screw rod, and l2 is the clamping length.

[0080] Substituting equation (1) into equation (2), the support forces at points A and C can be obtained as:

[0081]

[0082] The bending moment of the B–E section is:

[0083]

[0084] Based on Castigliano's second theorem, the equivalent relationship between the lateral displacement D and the lateral external load F T is:

[0085]

[0086] S102. Establish a mechanical equivalent model, equivalent the lateral displacement of the bolt to the lateral external load, use Castigliano's theorem to calculate the bending moment equations for each section of the bolt connection, and solve the lateral external load. From equation (5), its calculation formula is as follows:

[0087]

[0088] In the formula, F T is the lateral external load, I Z1 is the axial section moment of inertia of the bolt head, l2 is the clamping length, IZ2 is the moment of inertia of the screw's transverse section, D is the transverse displacement, and E b is the elastic modulus of the screw, and l1 is the clearance between the bolt hole and the mating part;

[0089] It should be noted that substituting Equation (6) into Equation (4) gives the bending moment of the screw as:

[0090]

[0091] S103. Establish a first model based on the bending moment and the transverse external load.

[0092] S200. Establish a second model based on the first model. The second model is an equivalent relationship model between the load on the screw and the load on the thread teeth.

[0093] It should be noted that based on the above, an equivalent model between the external load on the bolt and the load on the screw has been established. In order to establish a complete equivalent model of the bolt load, in this section, the equivalent relationship between the load on the screw and the load on the thread teeth will be derived and established.

[0094] It can be understood that in this step S200, it includes S201, S202, and S203, where:

[0095] S201. Establish a force model for the thread teeth. Select a micro-element on the thread tooth surface, set the micro-element as an elastic body, and obtain the force on the thread teeth under the transverse external load. The calculation formula is as follows:

[0096]

[0097] In the formula, α is the half angle of the thread profile, β is the lead angle of the thread, d2 is the pitch diameter of the bolt, z represents the distance from the thread tooth to the top surface of the nut in the load direction, and S A is the pre-tightening force F P and the sum of the forces S1 and S2 of the bending moment M on the micro-element, and the direction is perpendicular to the thread tooth inclined plane. S T is the force of the transverse external load F T on the micro-element, and the direction is the same as that of F T ;

[0098] It should be noted that when the screw undergoes bending deformation, the contact relationship of the thread pair is relatively complex, and the stress states at different positions of the thread teeth are different. It is found that the normal stress and radial stress on the thread tooth surface in the load direction are both the largest. Therefore, the present invention has established a thread tooth force model as shown in Figure 5 . Take a micro-element on the thread tooth surface, and consider the micro-element as an elastic body to derive the force on the thread teeth under the transverse external load. S A is the pre-tightening force F P and the sum of the forces S1 and S2 of the bending moment M on the micro-element, and the direction is perpendicular to the thread tooth inclined plane. S Tis the lateral external load F T acting on the infinitesimal element, in the same direction as F T Taking the O point of the contact surface between the nut and the lower plate as the origin, the force acting on each infinitesimal element of the meshing thread turns along the nut thickness direction is calculated as follows:

[0099]

[0100] In the formula, α is the half angle of the thread profile, β is the lead angle of the thread, d2 is the pitch diameter of the bolt, and z represents the distance from the thread to the top surface of the nut in the load direction.

[0101] In the formula and are solved through the deformation compatibility equation of strain and deformation in elasticity mechanics, as shown in the following formula:

[0102]

[0103] The strains ε1, ε2, and ε3 generated at z of the bolt and nut under the action of axial force, bending moment, and lateral force are respectively:

[0104]

[0105]

[0106]

[0107] In the formula, A b and A n , E b and E n , I by and I ny , f b and f n , G b and G n are respectively the cross-sectional areas, elastic moduli, moments of inertia about the y-axis, shear shape factors, and shear moduli of the bolt and nut.

[0108] S202. Based on the force acting on the thread, the load at z of the thread is calculated using the preset boundary conditions, and its calculation formula is as follows:

[0109]

[0110] In the formula, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient for the pre-tightening force term, λ2 is the correction coefficient for the bending moment term, λ3 is the correction coefficient for the lateral external load term, e is the natural constant, and L is the nut height.

[0111] S203. Based on the equivalent relationship between the load on the screw and the load on the thread, and by taking the derivative, the force on the thread element is obtained. Its calculation formula is as follows:

[0112]

[0113]

[0114]

[0115] In the formula, S1 is the pre-tightening force F P the force on the element, S2 is the force on the element caused by the bending moment M, S T is the lateral external load of the pre-tightening force F T the force on the element, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, L is the nut height, d2 is the bolt pitch diameter, α is the half thread angle, and β is the lead angle.

[0116] It should be noted that in order to solve the deformation of the thread, Yamamoto proposed that the deformation of the thread with unit width under force is caused by five situations: bending, shear force, root tilt, root shear, and radial component force, as shown in Eqs. (13)-(15).

[0117] External thread:

[0118]

[0119] In the formula, δ 1b is the deformation of the external thread caused by bending, δ 2b is the deformation of the external thread caused by shear, δ 3b is the deformation of the external thread caused by root tilt, δ 4b is the deformation of the external thread caused by root shear, δ 5b is the deformation of the external thread caused by the radial component force; v b is the Poisson's ratio of the bolt, w is the unit force, E b is the elastic modulus of the bolt, and α is the half thread angle.

[0120] Internal thread:

[0121]

[0122] In the formula, δ 1b is the deformation of the internal thread caused by bending, δ 2b is the deformation of the internal thread caused by shear, δ 3b is the deformation of the internal thread caused by root tilt, δ 4bFor the internal thread deformation caused by root shear, δ 5b For the internal thread deformation caused by the radial component force; v n For the Poisson's ratio of the nut, w is the unit acting force, E b For the elastic modulus of the nut, α is the half angle of the thread profile.

[0123]

[0124] In the formula, δ 1b , δ 2b , δ 3b , δ 4b and δ 5b are the external thread deformations caused by bending, shear force, root tilt, root shear and radial component force respectively; δ 1n , δ 2n , δ 3n , δ 4n and δ 5n are the internal thread deformations caused by bending, shear force, root tilt, root shear and radial component force respectively; k b and k n are the Poisson's ratio and elastic deformation coefficient of the bolt and nut respectively, w is the unit acting force. k b , k n can be obtained by substituting Equation (13 - 14) into Equation (15).

[0125] Substituting Equation (8) into Equations (13)–(15), the deformation amounts generated by the bolt and nut at z under the action of axial force, bending moment and transverse force are:

[0126]

[0127]

[0128]

[0129] In the formula, δ b1 , δ b2 and δ b3 are the deformation amounts generated by the bolt at z under the action of axial force, bending moment and transverse force respectively, δ n1 , δ n2 and δ n3 are the deformation amounts generated by the nut at z under the action of axial force, bending moment and transverse force respectively, respectively represent the radial deformation coefficients of the bolt and nut, and their expressions are:

[0130]

[0131] In the formula, D0 is the diameter of the circle with the pitch diameter d2 as the inner diameter and equal to the hexagonal area of the nut, P is the pitch.

[0132] Let v b = v n = v. Substituting Eqs. (10)-(18) into Eq. (11) gives:

[0133]

[0134] Wherein, A b and A n , E b and E n , I by and I ny , f b and f n are the cross-sectional areas, elastic moduli, moments of inertia about the y-axis, and shear shape factors of the bolt and nut respectively, k b and k n are the Poisson's ratios and elastic deformation coefficients of the bolt and nut respectively, β is the lead angle, d2 is the pitch diameter of the bolt, ν is the Poisson's ratio, and represent the radial deformation coefficients of the bolt and nut respectively.

[0135] The above differential equation is a second-order linear differential equation with boundary conditions. Since the nut height is L, the boundary conditions of the differential equation can be set as:

[0136]

[0137] Wherein, F P is the pre-tightening force and L is the nut height.

[0138]

[0139] Wherein, M is the bending moment and L is the nut height.

[0140]

[0141] T is the lateral external load and L is the nut height.

[0142] Substituting the boundary conditions into Eq. (20), the load at the thread z can be obtained as:

[0143]

[0144] Wherein, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient for the pre-tightening force term, λ2 is the correction coefficient for the bending moment term, λ3 is the correction coefficient for the lateral external load term, e is the natural constant, and L is the nut height.

[0145]

[0146] In the formula, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the transverse external load term, A b and A n , E b and E n , I by and I ny , f b and f n are respectively the cross-sectional areas, elastic moduli, moments of inertia about the y-axis, and shear shape coefficients of the bolt and the nut, k b and k n are respectively the Poisson's ratios and elastic deformation coefficients of the bolt and the nut, β is the lead angle, d2 is the pitch diameter of the bolt, ν is the Poisson's ratio, and respectively represent the radial deformation coefficients of the bolt and the nut. Equation (24) has revealed the equivalent relationship between the load on the screw and the load on the thread teeth. To derive the force on the microelement, taking the derivative of it gives:

[0147]

[0148] Substituting Equation (26) into Equation (8), the force on the thread tooth microelement can be obtained as:

[0149]

[0150] S300. Calculate the stress at the root of the thread tooth based on the second model, and establish a third model, which is an equivalent model of the thread tooth load and the stress at the root of the thread tooth.

[0151] It should be noted that based on the above steps, for the convenience of calculating the stress at the root of the thread tooth, as Figure 5 shown, a natural coordinate system (b, τ, n) is established on the microelement, and S A and S T are converted into the principal stress S n perpendicular to the thread tooth surface, the shear stress S τ along the radial direction, and the shear stress S b along the tangential direction.

[0152] It can be understood that in this step S300, it includes S301, S302, S303, and S304, where:

[0153] S301. Based on the second model, a natural coordinate is established on the microelement, and the acting forces S A and S T are converted into the principal stress perpendicular to the thread tooth surface, the shear stress along the radial direction, and the shear stress along the tangential direction, and the transformation matrix is calculated;

[0154] It should be noted that by rotating the global coordinate system by α about the y-axis and then by β about the x-axis, it is transformed into the natural coordinate system (b, τ, n), and the transformation matrix between the two coordinate systems is:

[0155]

[0156] where,

[0157] T = T1T2 (29)

[0158]

[0159]

[0160] Then:

[0161]

[0162] Substituting Equation (32) into Equation (28), the transformation matrix can be obtained as:

[0163]

[0164] S302. When the friction force on the thread surface is at the critical slip state, it is the maximum static friction force. Taking the x, y, and z axes of the coordinate system in the critical slip state as the equilibrium conditions, three-direction stresses on the thread microelement are obtained;

[0165] It should be noted that when the friction force on the thread surface is at the critical slip state, it is the maximum static friction force. Under this state, from the equilibrium conditions of the x, y, and z axes of the coordinate system, the three-direction stresses on the thread microelement are:

[0166]

[0167] In the formula, μ is the static friction coefficient.

[0168] To find the magnitudes of the principal stresses on the microelement, as Figure 5 shown, a six-sided microelement is taken on the thread, where σ 11 = S n , τ 12 = S τ , τ 13 = S b . Since the forces on the left and right of the microelement are basically symmetric, σ 22 = σ 33 = τ 23 = 0 can be taken. According to the theorem of shear stress reciprocity, τ 12 = τ 21 , τ 13 = τ 31 , τ 23 = τ 32。

[0169] The stress tensor of the infinitesimal element is:

[0170]

[0171] The characteristic equation is:

[0172]

[0173] Wherein, I1, I2, and I3 are:

[0174]

[0175] Since I1, I2, and I3 are the first, second, and third invariants of the stress tensor respectively, they can be expressed as:

[0176]

[0177] Wherein, σ1, σ2, and σ3 are the three principal stresses.

[0178] S303. Obtain the nominal equivalent elastic stress of the thread according to the stresses in three directions, and its calculation formula is as follows:

[0179]

[0180] Wherein, σ ns is the ratio of the nominal equivalent elastic stress, and σ1, σ2, and σ3 are the three principal stresses.

[0181] S304. Based on the nominal equivalent elastic stress of the thread and the preset stress concentration coefficient at the root of the thread, obtain the stress at the root of the thread and establish an equivalent model of the thread load and the stress at the root of the thread, and its calculation formula is as follows:

[0182] σ t = K t σ ns

[0183] Wherein, σ t is the stress at the root of the thread, K t is the stress concentration coefficient at the root of the thread, that is, the ratio of the local maximum stress σ max to the nominal equivalent elastic stress σ ns and σ max can be obtained through finite element simulation.

[0184] It should be noted that, for the convenience of separately obtaining the loads on the screw rod and the thread tooth loads, two modeling methods are adopted for the bolt. Model Ⅰ is used to simulate the load-bearing state of the screw rod under external loads. This model simplifies the thread pair structure and treats the bolt and nut as a whole. This is because the screw rod is the main research object for the load-bearing analysis of the bolt and has little relation with the thread pair. Simplifying the thread can greatly improve the calculation efficiency. Model Ⅱ is used to simulate the load-bearing state of the thread teeth. Since the contact relationship between the thread pairs is relatively complex during the lateral vibration process, a refined model with threads needs to be established strictly according to the structural parameters to ensure the accuracy of the simulation results. Lateral displacements are applied to the upper plate for both models to simulate the load-bearing process of the bolt, and the bending moment of the screw rod or the thread tooth stress is output as the simulation result.

[0185] Verification of the equivalent model of bolt external load and screw rod load: The accuracy of the equivalent model of bolt external load and load-bearing is verified by comparing the screw rod load simulated by Model Ⅰ with the theoretically calculated load. Taking the bottom surface of the bolt head as the origin, five transverse sections at distances of 0 mm, 12.5 mm, 25 mm, 37.5 mm, and 50 mm from the origin are respectively defined as the integral output sections a, b, c, d, and e, and the bending moment values of the sections are output. The finite element simulation results are compared with the theoretically calculated results of the equivalent model of bolt external load and screw rod load as Figure 6 shown. It can be seen that the degree of coincidence between the theory and the simulation results is relatively high, which verifies the accuracy of the equivalent model of bolt external load and screw rod load and its universality for bolts of different diameters.

[0186] It should be noted that the verification of the equivalent model of screw rod load and the stress at the root of the thread tooth is to verify the accuracy of the equivalent model of screw rod load and thread tooth load by comparing the thread tooth stress simulated by Model Ⅱ with the theoretically calculated stress. First, the maximum stress at the root of the first working thread tooth of the M10 bolt is obtained through the above finite element simulation method; then, the nominal equivalent elastic stress is calculated using the equivalent model of screw rod load and thread tooth load, and the ratio of the two is the stress concentration coefficient at the root of the thread tooth. The average value of the stress concentration coefficient at the root of the thread tooth is 2.76. Substituting it into the equivalent model of screw rod load and thread tooth load can obtain the maximum stress at the root of the theoretically calculated thread tooth. The comparison between the simulated thread tooth stress and the theoretically calculated stress is as Figure 7 (the relative deviation is taken as the absolute value). It can be seen that the errors between the theoretical values obtained based on the bolt load equivalent model and the finite element simulation results for the three bolt diameters are all very small, and the maximum deviation is only 4.85%, verifying the accuracy of the equivalent model of screw rod load and thread tooth load.

[0187] S400. Convert the load-time history of the bolt in the third model into the stress-time history at the root of the thread tooth, and evaluate the loosening life of the bolt connection based on the rainflow counting and Miner damage linear cumulative theory.

[0188] It is understandable that in this step, first, the load-time history of the vehicle bolts is obtained in real time through the load-measuring bolts; then, based on the above bolt load equivalent models (the equivalent model of bolt external load and screw rod load, the equivalent model of screw rod load and thread load, and the equivalent model of thread load and thread root stress), the load-time history of the bolts is converted into the stress-time history of the thread roots, and the loosening life of the bolt connection is evaluated based on the rain flow counting and Miner damage linear cumulative theory.

[0189] Embodiment 2:

[0190] As Figure 2 shown, this embodiment provides a load equivalent system for evaluating bolt loosening. Refer to Figure 2 The system includes a first establishment module 701, a second establishment module 702, a third establishment module 703, and an evaluation module 704, where:

[0191] The first establishment module 701: is used to solve the bending moment and the lateral external load according to Castigliano's theorem and establish a first model, and the first model is the equivalent model of bolt external load and screw rod load;

[0192] The second establishment module 702: is used to establish a second model according to the first model, and the second model is the equivalent relationship model between the screw rod load and the thread load;

[0193] The third establishment module 703: is used to calculate the thread root stress based on the second model and establish a third model, and the third model is the equivalent model of thread load and thread root stress;

[0194] The evaluation module 704: is used to convert the load-time history of the bolts in the third model into the stress-time history of the thread roots, and evaluate the loosening life of the bolt connection based on the rain flow counting and Miner damage linear cumulative theory.

[0195] Specifically, the first establishment module includes a first solution unit, a second solution unit, and a first establishment unit, where:

[0196] The first solution unit 7011: is used to apply a lateral external load to the bolt connection in the pre-tightened state and solve the bending moment generated by the bending deformation of the screw rod. Its calculation formula is as follows:

[0197]

[0198] In the formula, M is the bending moment, l1 is the clearance of the bolt hole fit, x3 is the distance from any position of the screw rod to the bolt head, I Z1 is the axial section moment of inertia of the bolt head, l2 is the clamping length, I Z2 is the lateral section moment of inertia of the screw rod, D is the lateral displacement, E bis the elastic modulus of the screw;

[0199] The second solution unit 7012: used to establish a mechanical equivalent model, equivalent the lateral displacement of the bolt to a lateral external load, calculate the bending moment equations of each section of the bolt connection by using Castigliano's theorem, and solve the lateral external load. Its calculation formula is as follows:

[0200]

[0201] In the formula, F T is the lateral external load, I Z1 is the axial sectional moment of inertia of the bolt head, l2 is the clamping length, I Z2 is the lateral sectional moment of inertia of the screw, D is the lateral displacement, E b is the elastic modulus of the screw, l1 is the fit clearance of the bolt hole;

[0202] The first establishment unit 7013: used to establish a first model according to the bending moment and the lateral external load.

[0203] Specifically, the second establishment module includes a first calculation unit, a first acquisition unit and a second acquisition unit, where:

[0204] The first calculation unit 7021: used to establish a thread force model, select an infinitesimal on the thread surface, set the infinitesimal as an elastic body, and obtain the acting force of the thread under the lateral external load. Its calculation formula is as follows:

[0205]

[0206] In the formula, α is the half thread angle, β is the lead angle, d2 is the pitch diameter of the bolt, z represents the distance from the thread to the top surface of the nut in the load direction, S A is the pre-tightening force F P and the sum of the acting forces S1 and S2 of the bending moment M on the infinitesimal, the direction is perpendicular to the thread slope, S T is the lateral external load F T acting on the infinitesimal, and the direction is the same as that of F T ;

[0207] The first acquisition unit 7022: used to calculate the load at the thread z based on the acting force of the thread by using the preset boundary conditions. Its calculation formula is as follows:

[0208]

[0209] In the formula, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the pre-tightening force term correction coefficient, λ2 is the bending moment term correction coefficient, λ3 is the lateral external load term correction coefficient, e is the natural constant, and L is the nut height.

[0210] The second obtaining unit 7023: For obtaining the acting force on the thread microelement based on the equivalent relationship between the load on the screw and the load on the thread teeth and performing differentiation, and its calculation formula is as follows:

[0211]

[0212]

[0213]

[0214] In the formula, S1 is the pre-tightening force F P The acting force on the microelement, S2 is the acting force of the bending moment M on the microelement, S T Is the lateral external load of the pre-tightening force F T The acting force on the microelement, F P Is the pre-tightening force, M is the bending moment, F T Is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, L is the nut height, d2 is the bolt pitch diameter, α is the thread profile half angle, and β is the lead angle.

[0215] Specifically, the third establishing module 703 includes a second calculation unit 7031, a third obtaining unit 7032, a fourth obtaining unit 7033, and a second establishing unit 7034, where:

[0216] The second calculation unit 7031: For establishing a natural coordinate on the microelement based on the second model, and converting the acting forces S A And S T Into the principal stress perpendicular to the thread surface, the tangential stress along the radial direction, and the tangential stress along the tangential direction, and calculating to obtain the transformation matrix;

[0217] The third obtaining unit 7032: For when the friction force at the critical slip state of the thread surface is the maximum static friction force, using the coordinate axes x, y, and z in the critical slip state as the equilibrium conditions to obtain the three-direction stresses on the thread microelement;

[0218] The fourth obtaining unit 7033: For obtaining the nominal equivalent elastic stress of the thread based on the three-direction stresses, and its calculation formula is as follows:

[0219]

[0220] In the formula, σ ns Is the ratio of the nominal equivalent elastic stress, and σ1, σ2, and σ3 are the three principal stresses.

[0221] Second establishment unit 7034: For obtaining the stress at the root of the thread based on the nominal equivalent elastic stress of the thread and the preset stress concentration coefficient at the root of the thread, and establishing an equivalent model of the thread load and the stress at the root of the thread, and its calculation formula is as follows:

[0222] σ t =K t σ ns

[0223] In the formula, σ t is the stress at the root of the thread, and K t is the stress concentration coefficient at the root of the thread, that is, the ratio of the local maximum stress σ max of the material to the nominal equivalent elastic stress σ ns , and σ max can be obtained through finite element simulation.

[0224] It should be noted that regarding the system in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0225] Embodiment 3:

[0226] Corresponding to the above method embodiment, in this embodiment, a load equivalent device for evaluating bolt loosening is further provided. A load equivalent device for evaluating bolt loosening described below and a load equivalent method for evaluating bolt loosening described above can be referred to each other correspondingly.

[0227] Figure 3 is a block diagram of a load equivalent device 800 for evaluating bolt loosening shown according to an exemplary embodiment. As Figure 3 shown, the load equivalent device 800 for evaluating bolt loosening includes: a processor 801 and a memory 802. The load equivalent device 800 for evaluating bolt loosening further includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0228] Among them, the processor 801 is used to control the overall operation of the load equivalent device 800 for evaluating bolt loosening, so as to complete all or part of the steps in the above-mentioned load equivalent method for evaluating bolt loosening. The memory 802 is used to store various types of data to support the operation of the load equivalent device 800 for evaluating bolt loosening. These data may include, for example, instructions for any application or method operating on the load equivalent device 800 for evaluating bolt loosening, as well as application-related data, such as contact data, sent and received messages, pictures, audio, video, and so on. The memory 802 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic memory, flash memory, magnetic disk or optical disc. The multimedia component 803 may include a screen and an audio component. Among them, the screen may be a touch screen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone, and the microphone is used to receive external audio signals. The received audio signals may be further stored in the memory 802 or sent through the communication component 805. The audio component also includes at least one speaker for outputting audio signals. The I / O interface 804 provides an interface between the processor 801 and other interface modules, and the above-mentioned other interface modules may be a keyboard, a mouse or buttons, etc. These buttons may be virtual buttons or physical buttons. The communication component 805 is used for wired or wireless communication between the load equivalent device 800 for evaluating bolt loosening and other devices. Wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G or 4G, or a combination of one or more of them. Therefore, the corresponding communication component 805 may include: a Wi-Fi module, a Bluetooth module or an NFC module.

[0229] In an exemplary embodiment, the load equivalent device 800 for evaluating bolt loosening can be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components, and is used to execute the above-mentioned load equivalent method for evaluating bolt loosening.

[0230] In another exemplary embodiment, a computer-readable storage medium including program instructions is further provided. When the program instructions are executed by a processor, the steps of the above-mentioned load equivalent method for evaluating bolt loosening are implemented. For example, the computer-readable storage medium can be the above-mentioned memory 802 including program instructions, and the above program instructions can be executed by the processor 801 of the load equivalent device 800 for evaluating bolt loosening to complete the above-mentioned load equivalent method for evaluating bolt loosening.

[0231] Embodiment 4:

[0232] Corresponding to the above method embodiment, in this embodiment, a readable storage medium is further provided. A readable storage medium described below can be correspondingly referred to with a load equivalent method for evaluating bolt loosening described above.

[0233] A computer program is stored on the readable storage medium. When the computer program is executed by a processor, the steps of the load equivalent method for evaluating bolt loosening in the above method embodiment are implemented.

[0234] The readable storage medium can specifically be various readable storage media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc that can store program codes.

[0235] In summary, the present invention establishes an equivalent model of bolt load, equivalently converts the load-time history of the bolt into the stress-time history at the root of the thread, and then evaluates the loosening life of the bolt connection based on the rainflow counting and Miner's linear cumulative damage theory. This method can obtain the bolt load in real time through a load cell bolt and equivalently convert it into stress, overcoming the problems of difficult monitoring and acquisition of the lateral displacement of bolt connections in the actual service environment of vehicles and difficult real-time evaluation of the bolt loosening life. It provides theoretical guidance and technical support for the safe service of vehicle bolt connection equipment and the guarantee of driving safety, and has important scientific value and engineering significance for optimizing bolt connection parameters, preventing sudden loosening failure of bolts, and ensuring the safe and stable operation of vehicles.

[0236] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0237] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present invention, and all of them should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A load equivalent method for evaluating bolt loosening, characterized in that Including: According to Castigliano's theorem, solve the bending moment and lateral external load, and establish a first model, where the first model is an equivalent model of bolt external load and screw rod load; Establish a second model based on the first model, where the second model is an equivalent relationship model between screw rod load and thread load; Calculate the stress at the root of the thread based on the second model, and establish a third model, where the third model is an equivalent model of thread load and stress at the root of the thread; Convert the load-time history of the bolt in the third model into a stress-time history at the root of the thread, and evaluate the loosening life of the bolt connection based on rainflow counting and Miner's linear cumulative damage theory; Among them, establishing the second model based on the first model, where the second model is an equivalent relationship model between screw rod load and thread load, including: Establish a thread force model, select an infinitesimal on the thread surface, set the infinitesimal as an elastic body, and obtain the force of the thread under the lateral external load. The calculation formula is as follows: Where α is the half angle of the thread profile, β is the lead angle of the thread, d2 is the pitch diameter of the bolt, z represents the distance from the thread to the top surface of the nut in the load direction, and S A is the pre-tightening force F P and the sum of the acting forces S1 and S2 of the bending moment M on the microelement, with the direction perpendicular to the thread inclined plane. S T is the lateral external load F T acting on the microelement, and is in the same direction as F T ; Based on the force of the thread, calculate the load at the z position of the thread using the preset boundary conditions. The calculation formula is as follows: where F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, and L is the nut height; Based on the equivalent relationship between screw rod load and thread load, and perform differentiation to obtain the force on the thread infinitesimal. The calculation formula is as follows: Wherein, S1 is the pre-tightening force F P acting on the micro-element, S2 is the force of the bending moment M acting on the micro-element, S T is the lateral external load of the pre-tightening force F T acting on the micro-element, F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, L is the nut height, d2 is the bolt pitch diameter, α is the half thread angle, β is the lead angle; Among them, calculating the stress at the root of the thread based on the second model, and establishing a third model, where the third model is an equivalent model of thread load and stress at the root of the thread, including: Based on the second model, natural coordinates are established on the infinitesimal element, and the acting forces S A and S T are converted into the principal stress perpendicular to the thread surface, the tangential stress along the radial direction, and the tangential stress along the tangential direction, and the transformation matrix is calculated; When the friction force on the thread surface is at the critical slip state, it is the maximum static friction force. Take the coordinate axes x, y, and z at the critical slip state as the equilibrium conditions to obtain the three-direction stresses on the thread infinitesimal; Obtain the nominal equivalent elastic stress of the thread according to the three-direction stresses. The calculation formula is as follows: where σ ns is the ratio of the nominal equivalent elastic stress, and σ1, σ2, and σ3 are the three principal stresses; Based on the nominal equivalent elastic stress of the thread and the preset stress concentration coefficient at the root of the thread, obtain the stress at the root of the thread, and establish an equivalent model of thread load and stress at the root of the thread. The calculation formula is as follows: σ t = K t σ ns Where, σ t is the stress at the root of the thread, K t is the stress concentration factor at the root of the thread, i.e., the ratio of the local maximum stress σ max to the nominal equivalent elastic stress σ ns , and σ max can be obtained through finite element simulation.

2. The load equivalent method for evaluating bolt loosening according to claim 1, wherein According to Castigliano's theorem, solve the bending moment and lateral external load, and establish the first model, including: Apply a lateral external load to the bolt connection in the pre-tightened state, and solve the bending moment generated by the bending deformation of the screw rod. The calculation formula is as follows: Wherein, M is the bending moment, l1 is the fit clearance of the bolt hole, x3 is the distance from any position of the screw rod to the bolt head, I Z1 is the moment of inertia of the bolt head in the axial section, l2 is the clamping length, I Z2 is the moment of inertia of the screw rod in the transverse section, D is the lateral displacement, E b is the elastic modulus of the screw rod; Establish a mechanical equivalent model, equivalent the lateral displacement of the bolt to the lateral external load, use Castigliano's theorem to calculate the bending moment equation of each section of the bolt connection, and solve the lateral external load. The calculation formula is as follows: Where, F T is the lateral external load, I Z1 is the moment of inertia of the axial section of the bolt head, l2 is the clamping length, I Z2 is the moment of inertia of the lateral section of the screw rod, D is the lateral displacement, E b is the elastic modulus of the screw rod, and l1 is the fit clearance of the bolt hole; Establish a first model according to the bending moment and the lateral external load.

3. A load equivalent system for evaluating bolt loosening, characterized in that, Including: The first establishment module: used to solve the bending moment and lateral external load according to Castigliano's theorem, and establish a first model, where the first model is an equivalent model of bolt external load and screw rod load; The second establishment module: used to establish a second model based on the first model, where the second model is an equivalent relationship model between screw rod load and thread load; The third establishment module: used to calculate the stress at the root of the thread based on the second model, and establish a third model, where the third model is an equivalent model of thread load and stress at the root of the thread; Evaluation module: used to convert the load-time history of the bolt in the third model into the stress-time history at the root of the thread, and evaluate the loosening life of the bolt connection based on rainflow counting and Miner's linear cumulative damage theory; Among them, the second establishment module includes: The first calculation unit: used to establish a thread force model, select a microelement on the thread surface, set the microelement as an elastic body, and obtain the acting force of the thread under the lateral external load. The calculation formula is as follows: Where α is the half angle of the thread profile, β is the lead angle of the thread, d2 is the pitch diameter of the bolt, z represents the distance from the thread to the top surface of the nut in the load direction, and S A is the pre-tightening force F P and the sum of the forces S1 and S2 exerted by the bending moment M on the microelement, with the direction perpendicular to the thread inclined plane. S T is the lateral external load F T exerted on the microelement, in the same direction as F T ; The first acquisition unit: used to calculate the load at the thread z based on the acting force of the thread using the preset boundary conditions. The calculation formula is as follows: where F P is the pre-tightening force, M is the bending moment, F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, and L is the nut height; The second acquisition unit: used to obtain the acting force on the thread microelement based on the equivalent relationship between the load on the screw and the thread load and by taking the derivative. The calculation formula is as follows: Wherein, S1 is the pre-tightening force F P acting on the infinitesimal element, S2 is the force exerted by the bending moment M on the infinitesimal element, and S T is the lateral external load F of the pre-tightening force T acting on the infinitesimal element, F P is the pre-tightening force, M is the bending moment, and F T is the lateral external load, λ1 is the correction coefficient of the pre-tightening force term, λ2 is the correction coefficient of the bending moment term, λ3 is the correction coefficient of the lateral external load term, e is the natural constant, L is the nut height, d2 is the pitch diameter of the bolt, α is the half angle of the thread profile, and β is the lead angle of the thread; Among them, the third establishment module includes: The second calculation unit: used to establish natural coordinates on the micro-elements based on the second model, and convert the acting forces S A and S T into the principal stress perpendicular to the thread surface, the tangential stress along the radial direction, and the tangential stress along the tangential direction, and calculate the transformation matrix; The third acquisition unit: when the friction force on the thread surface is the maximum static friction force in the critical slip state, use the coordinate axes x, y, and z in the critical slip state as the equilibrium conditions to obtain the three-direction stresses on the thread microelement; The fourth acquisition unit: used to obtain the nominal equivalent elastic stress of the thread based on the three-direction stresses. The calculation formula is as follows: where, σ ns is the ratio of the nominal equivalent elastic stress, and σ1, σ2 and σ3 are the three principal stresses; The second establishment unit: used to obtain the thread root stress based on the nominal equivalent elastic stress of the thread and the preset stress concentration coefficient at the thread root, and establish an equivalent model between the thread load and the thread root stress. The calculation formula is as follows: σ t = K t σ ns Where, σ t is the stress at the root of the thread, K t is the stress concentration factor at the root of the thread, i.e., the ratio of the local maximum stress σ max to the nominal equivalent elastic stress σ ns , and σ max can be obtained through finite element simulation.

4. The load equivalent system for evaluating bolt loosening according to claim 3, characterized in that The first establishment module includes: The first solution unit: used to apply a lateral external load to the bolt connection in the pre-tightened state, and solve the bending moment generated by the bending deformation of the screw. The calculation formula is as follows: Wherein, M is the bending moment, l1 is the fit clearance of the bolt hole, x3 is the distance from any position of the screw rod to the bolt head, I Z1 is the moment of inertia of the bolt head in the axial section, l2 is the clamping length, I Z2 is the moment of inertia of the screw rod in the transverse section, D is the lateral displacement, E b is the elastic modulus of the screw rod; The second solution unit: used to establish a mechanical equivalent model, equivalent the lateral displacement of the bolt to the lateral external load, calculate the bending moment equation of each section of the bolt connection using Castigliano's theorem, and solve the lateral external load. The calculation formula is as follows: Where, F T is the lateral external load, I Z1 is the moment of inertia of the axial section of the bolt head, l2 is the clamping length, I Z2 is the moment of inertia of the lateral section of the screw rod, D is the lateral displacement, E b is the elastic modulus of the screw rod, and l1 is the fit clearance of the bolt hole; The first establishment unit: used to establish a first model based on the bending moment and the lateral external load.

5. A load equivalent device for evaluating bolt loosening, characterized in that, Including: A memory, used to store computer programs; A processor, used to implement the load equivalent method for evaluating bolt loosening as described in any one of claims 1 to 2 when executing the computer program.

6. A readable storage medium, characterized in that: A computer program is stored on the readable storage medium, and when the computer program is executed by the processor, it implements the load equivalent method for evaluating bolt loosening as described in any one of claims 1 to 2.

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