Bolt connection strength simulation analysis method and system

Abstract

The invention provides a bolt connection strength simulation analysis method and system, and relates to the technical field of simulation analysis methods, and the method comprises the following steps: respectively calculating the axial rigidity of a bolt and the compression rigidity of a connected piece by adopting an axial elastic modulus method, constructing a parallel rigidity distribution model, and calculating the additional tension of the bolt; respectively calculating the axial tensile stress and the shear stress of the bolt by adopting an area uniform stress method, and calculating the equivalent stress of the bolt by adopting a shear strain energy equivalent method; and calculating the safety coefficient of the bolt by adopting an equivalent stress safety margin method, comparing the safety coefficient with a preset safety threshold value, and outputting a corresponding bolt strength grade. The additional pulling force is dynamically distributed through the rigidity of the bolt and the connected piece, and the force transmission characteristic in the actual bearing process is closer; by introducing the screw pitch to correct the nominal diameter, the actual stress distribution of the thread root is described more accurately; the equivalent stress is calculated through a shear strain energy equivalent method, and the yield criterion of the plastic material is better met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of simulation analysis method, in particular to a bolt connection strength simulation analysis method and system. BACKGROUND

[0002] Traditional bolt strength analysis methods are mostly based on single load assumption or simplified stiffness model, and the linear torque and pretightening force model ignores friction fluctuation and thread nonlinear deformation, resulting in large initial pretightening force error, and does not consider the parallel connection characteristics of the bolt and the connected member, and the distribution of the additional load depends on the empirical coefficient, which is difficult to adapt to complex working conditions, and the axial tension and transverse shear stress are often calculated independently, ignoring the coupling effect of the two, resulting in deviation of equivalent stress evaluation.

[0003] In the prior art, the method for analyzing the strength of the bolt and the bearing structure is disclosed in CN114757069A by dividing the three-dimensional model of the bearing structure matched with the bolt into a grid, generating a finite element model containing the bearing structure, and adding assembly boundary conditions. However, this method combines a linear torque model and a stiffness parallel distribution mechanism to improve the calculation accuracy of the initial pretightening force, does not quantify the additional tension based on the axial stiffness parallel model, accurately reflects the bolt-connection member cooperative stress characteristics, does not introduce the shear strain energy equivalent criterion, comprehensively considers the interaction of axial tension and transverse shear stress, does not dynamically associate the equivalent stress and material yield strength discrete interval, and generates a safety factor probability distribution, so there is an urgent need for a bolt connection strength simulation analysis method.

[0004] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The purpose of the present application is to provide a bolt connection strength simulation analysis method and system to solve the problems raised in the background.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical scheme: The bolt connection strength simulation analysis method comprises the following specific steps: S1: determining the effective cross-sectional area and transverse shear area of the thread on the bolt based on the basic parameters of the bolt to be analyzed; S2: obtaining the tightening torque applied to the bolt, constructing a linear pretightening force model to calculate the initial pretightening force of the bolt, obtaining the clamping length of the bolt, the effective contact area of the connected member and the bolt, and calculating the axial stiffness of the bolt and the compression stiffness of the connected member based on the effective cross-sectional area of the bolt using the axial elastic modulus method; S3: Obtain the external axial load of the bolt, construct a parallel stiffness distribution model based on the axial stiffness of the bolt and the compression stiffness of the connected member, and calculate the additional tension of the bolt, and obtain the total axial force of the bolt based on the initial pre-tightening force and the additional tension; S4: Obtain the transverse load of the bolt, calculate the axial tensile stress of the bolt and the shear stress of the bolt respectively by using the area uniform stress method based on the total axial force of the bolt thread, the effective cross-sectional area and the transverse shear area, and calculate the equivalent stress of the bolt by using the shear strain energy equivalent method based on the axial tensile stress of the bolt and the shear stress of the bolt; S5: Obtain the yield strength of the bolt material, calculate the safety factor of the bolt by using the equivalent stress safety margin method based on the equivalent stress, compare the safety factor with the preset safety threshold, and output the corresponding bolt strength grade.

[0007] Further, the effective cross-sectional area and the transverse shear area of the thread on the bolt are determined, and the specific steps are as follows: Obtain the pitch between adjacent threads and the nominal diameter of the bolt, wherein the nominal diameter of the bolt refers to the diameter of the bolt rod, that is, the outer diameter of the threaded part; the modified diameter value is obtained by subtracting the product of the pitch and a certain constant from the nominal diameter, the modified diameter is divided by 2 to obtain the radius value, and the square of the radius value is multiplied by the constant pi to obtain the effective cross-sectional area of the thread; When calculating the transverse shear area of the thread, the nominal diameter is divided by 2 to obtain the radius, and the square of the radius value is multiplied by the constant pi to obtain the transverse shear area of the thread.

[0008] Further, a linear pre-tightening force model is constructed to calculate the initial pre-tightening force of the bolt, and the specific steps are as follows: Obtain the assembly torque applied to the bolt, divide the assembly torque of the bolt by the product of the torque coefficient and the nominal diameter of the bolt, and the quotient obtained is the initial pre-tightening force formed by the bolt under the tightening condition.

[0009] Further, the clamping length of the bolt refers to the thickness of the connected member between the bolt head contact surface and the nut contact surface, and the axial stiffness of the bolt and the compression stiffness of the connected member are calculated by using the axial elastic modulus method based on the effective cross-sectional area of the bolt, and the specific steps are as follows: Multiply the effective cross-sectional area of the thread by the elastic modulus of the bolt material, and then divide the product by the clamping length to obtain the axial stiffness representing the ability of the bolt to resist axial tensile deformation; Determine the effective cross-sectional area of the connected member, which is calculated by calculating the tangent value of the pressure diffusion angle of the bolt head and the connected member, multiplying the tangent value by the clamping length, adding the contact radius of the bolt head and the connected member to the product, and then taking the square value, and multiplying the square value by the constant pi to obtain the effective cross-sectional area of the connected member.​ The effective contact area of the connected member is multiplied by the elastic modulus of the connected member material, and the obtained product is divided by the clamping length, so as to obtain the compression stiffness representing the compression deformation resistance of the connected member.

[0010] Further, the total axial force of the bolt is obtained, and the specific steps are as follows: A parallel stiffness distribution model is constructed, specifically, the bolt and the connected member are equivalent to a parallel system, according to Hooke's law, the load borne by each component is proportional to its own stiffness, the additional tension actually borne by the bolt is equal to the external axial load multiplied by a distribution coefficient, the distribution coefficient is the ratio of the axial stiffness of the bolt to the sum of the axial stiffness of the bolt and the compression stiffness of the connected member; The additional tension of the bolt is equal to the external axial load multiplied by the axial stiffness of the bolt, and then divided by the sum of the axial stiffness of the bolt and the compression stiffness of the connected member, and the total axial force finally borne by the bolt is obtained by directly adding the initial pretightening force and the additional tension.

[0011] Further, the equivalent stress of the bolt is calculated by using the shear strain energy equivalent method, and the specific steps are as follows: The transverse load of the bolt is obtained, based on the total axial force of the bolt thread, the effective cross-sectional area and the transverse shear area, the axial tensile stress of the bolt and the shear stress of the bolt are calculated by using the area uniform stress method, specifically, the total axial tension borne by the bolt is uniformly distributed to the effective cross-sectional area of the thread, and the total axial force is divided by the effective cross-sectional area, so as to calculate the axial tensile stress; The transverse shear load borne by the bolt is uniformly distributed to the transverse shear area of the bolt, and the transverse load is divided by the transverse shear area, so as to calculate the shear stress; Based on the axial tensile stress of the bolt and the shear stress of the bolt, the equivalent stress of the bolt is calculated by using the shear strain energy equivalent method, and the square root of the sum of the square of the axial tensile stress and three times the square of the shear stress is calculated, so as to obtain the equivalent stress of the bolt.

[0012] Further, the safety factor of any grid center point is compared with the set safety threshold value, if the safety factor exceeds the safety threshold value, the grid position is regarded as a risk area, and the specific steps are as follows When is greater than or equal to 0.8, it indicates that the grid center point is in a safe state; when is greater than or equal to 0.5 and less than 0.8, it indicates that the grid center point is in a warning state; when is less than 0.5, it indicates that the grid center point is in a high-risk state.

[0013] Further, the corresponding bolt strength grade is output, and the specific steps are as follows: The yield strength of the bolt material is acquired, the safety factor of the bolt is calculated based on the equivalent stress by using the equivalent stress safety margin method, specifically, the yield strength of the bolt material is compared with the equivalent stress of the bolt, the ratio of the two is calculated, and the obtained safety factor represents the safety margin of the bolt relative to the material yield limit under the current load state; The safety factor is compared with the preset safety threshold value, when the safety factor is greater than 2, it indicates that it is relatively reliable, when the safety factor is greater than or equal to 1.5 and less than 2, it indicates that it is slightly deformed, and when the safety factor is less than 1.5, it indicates that it is in a relatively dangerous state.

[0014] The application further provides a bolt connection strength simulation analysis system, which is used for executing the above-mentioned analysis method and comprises: A data acquisition module is configured to determine the effective cross-sectional area and the transverse shear area of the thread on the bolt based on the basic parameters of the bolt to be analyzed; A stiffness acquisition module is configured to acquire the tightening torque applied to the bolt, construct a linear pre-tightening force model to calculate the initial pre-tightening force of the bolt, acquire the clamping length of the bolt and the effective contact area between the connected parts and the bolt, and calculate the axial stiffness of the bolt and the compression stiffness of the connected parts respectively based on the effective cross-sectional area of the bolt by using the axial elastic modulus method; A force acquisition module is configured to acquire the external axial load of the bolt, construct a parallel stiffness distribution model based on the axial stiffness of the bolt and the compression stiffness of the connected parts, and calculate the additional tension of the bolt, and acquire the total axial force of the bolt based on the initial pre-tightening force and the additional tension; An equivalent stress acquisition module is configured to acquire the transverse load of the bolt, calculate the axial tensile stress of the bolt and the shear stress of the bolt respectively by using the area uniform stress method based on the total axial force of the bolt thread, the effective cross-sectional area and the transverse shear area, and calculate the equivalent stress of the bolt by using the shear strain energy equivalent method based on the axial tensile stress of the bolt and the shear stress of the bolt; A threshold comparison module is configured to acquire the yield strength of the bolt material, calculate the safety factor of the bolt based on the equivalent stress by using the equivalent stress safety margin method, compare the safety factor with the preset safety threshold value, and output the corresponding bolt strength grade.

[0015] Compared with the prior art, the application has the following beneficial effects: By accurately calculating the effective cross-sectional area of the thread and the transverse shear area, avoiding the stress underestimation caused by the cross-sectional area simplification of the traditional method, normalizing the axial stiffness and compression stiffness with the clamping length, constructing the core parameters of the stiffness parallel model, ensuring the theoretical rigor of the load distribution calculation; based on the deformation compatibility condition, the external load is distributed in proportion to the stiffness, the total axial force of the bolt is accurately quantified, the shear strain energy equivalence criterion is introduced, the interaction of axial tension and transverse shear stress is comprehensively considered, the consistency of equivalent stress prediction and measurement is improved, the safety factor probability distribution is generated by dynamically correlating the equivalent stress and the discrete interval of material yield strength, and the balance of high reliability and lightweight demand is adapted. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 It is the overall method flowchart of the present application; Figure 2 It is the change relationship diagram between the axial tensile stress of the bolt and the corresponding equivalent stress; Figure 3 It is the change relationship diagram between the shear stress of the bolt and the corresponding equivalent stress; Figure 4 It is the overall system schematic diagram of the present application. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the usual meaning understood by those skilled in the art to which the present application belongs. The "first", "second" and similar words used in the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent the relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] EMBODIMENT: Please refer to Figures 1-3 The present application provides a technical scheme: The strength simulation analysis method of bolt connection, the specific steps include: S1: determining the effective cross-sectional area of the thread and the transverse shear area of the bolt based on the basic parameters of the bolt to be analyzed; The effective cross-sectional area and the transverse shear area of the thread on the bolt are determined, and the specific steps are as follows: The pitch between adjacent threads and the nominal diameter of the bolt are obtained, wherein the nominal diameter of the bolt refers to the diameter of the bolt rod, that is, the outer diameter of the threaded portion; the modified diameter value is obtained by subtracting the product of the pitch and a specific constant from the nominal diameter, the modified diameter is divided by 2 to obtain the radius value, and the square of the radius value is multiplied by the constant pi to obtain the effective cross-sectional area of the thread; When calculating the transverse shear area of the thread, the nominal diameter is divided by 2 to obtain the radius, and the square of the radius value is multiplied by the constant pi to obtain the transverse shear area of the thread.

[0020] The formula on which the above process is based is as follows: Among them, represents the nominal diameter of the bolt; represents the pitch between threads; represents the effective cross-sectional area of the thread; The transverse shear area of the thread is calculated by the nominal cross-sectional method: Among them, represents the transverse shear area of the thread.

[0021] In the above process, the minimum cross-sectional area of the thread root, that is, the effective cross-sectional area, is calculated by introducing the pitch parameter and a specific correction coefficient, which accurately reflects the real bearing area of the bolt when subjected to axial tension, and lays a foundation for subsequent accurate calculation of tensile stress. At the same time, the complete cross-sectional area of the rod, that is, the transverse shear area, is calculated directly according to the nominal diameter of the bolt, which represents the main bearing cross section of the bolt resisting transverse shear force. The calculation of these two areas is the starting point for subsequent evaluation of the tensile and shear resistance of the bolt, and the accuracy directly determines the reliability of the entire strength simulation analysis result.

[0022] The effective cross-sectional area of the thread is the equivalent geometric area of the actual bearing stress of the bolt under axial tensile load, reflecting the reduction of the bearing capacity of the thread root due to geometric weakening such as thread tooth groove, and the calculation can avoid the underestimation of axial stress caused by ignoring the geometric correction of thread tooth groove in the traditional method, thereby improving the accuracy of the evaluation of the tensile strength of the bolt; the transverse shear area is the nominal geometric area of the shear stress of the bolt under transverse load such as shear or torsion, and the calculation simplifies the modeling difficulty of complex thread root shear stress distribution; In the calculation of the effective area of the thread, the constant term ​, derived from the thread geometry correction factor, corresponding to the ratio of thread height to pitch, for standard unified threads, thread height is , correction factor , including thread root radius compensation, ensuring that the effective cross-sectional area matches the true load-carrying capacity, and the nominal diameter present a positive correlation, Significant increase in effective cross-sectional area, and the pitch present an inverse correlation, Increasing the correction term decreases; in calculating the transverse shear area, only with positive correlation, The increase will increase the square .

[0023] S2: Obtain the tightening torque applied to the bolt, construct a linear pretension force model to calculate the initial pretension force of the bolt, obtain the clamping length of the bolt, the effective contact area of the connected parts and the bolt, based on the effective cross-sectional area of the bolt, respectively calculate the axial stiffness of the bolt and the compression stiffness of the connected parts by using the axial elastic modulus method; The specific steps for constructing a linear pretension force model to calculate the initial pretension force of the bolt are as follows: Obtain the assembly torque applied to the bolt, divide the assembly torque of the bolt by the product of the torque coefficient and the nominal diameter of the bolt, and the quotient obtained is the initial pretension force of the bolt under the tightening condition.

[0024] The formula used in the above process is: Where, Torque coefficient; Assembly torque; Nominal diameter of the bolt; Initial pretension force of the bolt.

[0025] In the above process, by establishing a simplified linear pretension force model, direct and rapid mapping from tightening torque to initial pretension force of the bolt is realized. This method integrates various factors such as thread friction and end face friction involved in the tightening process into a torque coefficient that is easy to use, thereby avoiding tedious test calibration and significantly improving the efficiency of engineering design and assembly control. By clearly defining the quantitative influence of torque, torque coefficient and bolt diameter on pretension force, this model can guide actual operation and help accurately control the clamping force in the assembly process, ensuring that the connection pair has sufficient initial locking force to resist loosening and separation, and providing a reliable calculation starting point for subsequent load distribution analysis and strength checking. It is the key input basis for the entire bolt connection strength simulation.

[0026] The assembly torque is mainly dependent on the preset and control of the tightening tool. The operator uses a calibrated torque wrench, electric or hydraulic tightening machine to tighten according to the specific torque value specified in the design drawing, process document or relevant standard. During the tightening process, the tool will accurately output the preset torque value. When the value is reached, the tool will usually give a prompt or automatically stop to ensure that the applied rotational torque is consistent with the design requirements.

[0027] The initial preload is the axial tension applied by the torque during the tightening process, which is used to form a clamping force between the bolt and the connected part to prevent the connected part from loosening or separating. By linear model, the tightening torque is directly mapped to the quantifiable preload, simplifying the traditional test calibration process and realizing the rapid calculation and control of the preload, represents the externally applied rotational torque, i.e. assembly torque, which directly drives the bolt to produce axial elongation deformation, and is the energy input source of the preload, and are in a positive proportional relationship, increasing directly improves the preload; and are in an inverse proportional relationship. The increase of the friction coefficient, i.e. , leads to more torque energy dissipated as friction heat, reducing the preload conversion efficiency, and are in an inverse proportional relationship, which reflects that larger diameter bolts require larger torque to achieve the same preload; The clamping length of the bolt refers to the thickness of the connected part between the bolt head contact surface and the nut contact surface. Based on the effective cross-sectional area of the bolt, the axial stiffness of the bolt and the compression stiffness of the connected part are calculated by the axial elastic modulus method, specifically: The effective cross-sectional area of the thread is multiplied by the elastic modulus of the bolt material, and then the product is divided by the clamping length, to obtain the axial stiffness representing the bolt's resistance to axial tensile deformation; The effective cross-sectional area of the connected part is determined by calculating the tangent value of the pressure diffusion angle of the bolt head and the connected part, multiplying the clamping length, adding the contact radius of the bolt head and the connected part, taking the square value, and multiplying the square value by pi to obtain the effective cross-sectional area of the connected part; The effective contact area of the connected part calculated is multiplied by the elastic modulus of the connected part material, and then the product is divided by the clamping length, to obtain the compression stiffness representing the resistance of the connected part to compression deformation.

[0028] The formula used in the above process is: wherein, represents the axial stiffness of the bolt; represents the clamping length of the bolt; represents the elastic modulus of the bolt; represents the effective cross-sectional area of the thread; wherein, represents the compression stiffness of the connected piece; represents the elastic modulus of the connected piece; represents the effective contact area of the connected piece; represents the contact radius of the bolt head and the connected piece; represents the pressure diffusion angle of the bolt head and the connected piece.

[0029] In the above process, represents the ability of the bolt to resist deformation under axial tensile load, defined as the tensile force required to produce unit axial deformation, through the effective cross-sectional area and the elastic modulus cooperating, accurately quantifying the stiffness of the bolt, avoiding the overestimation of stiffness caused by ignoring the thread root weakening effect of traditional empirical formula, represents the ability of the connected piece to resist compression deformation under the action of bolt pre-tightening force, defined as the pressure required to produce unit compression deformation, based on the pressure diffusion angle correcting the effective contact area , reflecting the three-dimensional diffusion effect of clamping force in the connected piece, through the cooperative calculation of elastic modulus and diffusion area, avoiding the risk of plastic deformation of the connected piece caused by local stress concentration.

[0030] wherein, directly determines the equivalent area of the bearing cross-section of the bolt material, increases, linearly improves , represents the inherent property of the material, increases, linearly enhances the stiffness, represents the length of the force-bearing section of the bolt, increases, resulting in an increase in axial deformation, thereby reducing stiffness; and and present a positive correlation, and the increase of material stiffness or contact area enhances the compression resistance, increases directly expands the initial contact area, represents the diffusion angle of the clamping force in the connected piece, increases significantly improves the diffusion area, With The longer the clamping length, the greater the compression deformation under the same pressure, and the lower the stiffness; The calculation process scientifically simulates the three-dimensional diffusion effect of the bolt pretightening force in the actual connecting piece. The model assumes that the pretightening force diffuses outward along a conical surface at an angle to the axis of the connected piece, i.e. the pressure diffusion angle With the increase of the clamping length , the pressure acting surface expands outward with a radial increment of , thereby forming an equivalent bearing area much larger than the initial contact surface.

[0031] S3: Obtain the external axial load of the bolt, construct a parallel stiffness distribution model based on the axial stiffness of the bolt and the compression stiffness of the connected piece, and calculate the additional tension of the bolt, and obtain the total axial force of the bolt based on the initial pretightening force and the additional tension; The specific steps for obtaining the total axial force of the bolt are as follows: Construct a parallel stiffness distribution model, specifically: equivalent the bolt and the connected piece into a parallel system, according to Hooke's law, the load shared by each component is proportional to its own stiffness, the additional tension actually borne by the bolt is equal to the external axial load multiplied by a distribution coefficient, the distribution coefficient is the ratio of the axial stiffness of the bolt to the sum of the axial stiffness of the bolt and the compression stiffness of the connected piece; The additional tension of the bolt is equal to the external axial load multiplied by the axial stiffness of the bolt, and then divided by the sum of the axial stiffness of the bolt and the compression stiffness of the connected piece. The total axial force finally borne by the bolt is obtained by directly adding the initial pretightening force and the additional tension.

[0032] The formula on which the above process is based is: Wherein, represents the additional tension of the bolt; represents the external axial load of the bolt; In the above process, by establishing a parallel stiffness distribution model, the distribution law of the external axial load between the bolt and the connected piece in the bolt connection system is scientifically revealed. This method gets rid of the roughness of traditional empirical estimation methods such as the simple assumption that the bolt bears all or part of the load, but makes accurate calculation according to the actual proportion of the stiffness of the two, so as to more truly simulate the actual stress increment of the bolt under external load.

[0033] ​The external axial load borne by the bolt is obtained by overall force analysis of the connecting structure, and the load is derived from the working load borne by the connecting components. When determining the load, the load acting on the bolt in the axial direction, i.e. along the bolt axis, is obtained through theoretical calculation according to the load working condition such as normal working, starting, stopping or abnormal state and the force transmission path.

[0034] is the external load When the external load is applied to the bolt, the additional axial tension component actually borne by the bolt reflects the load distribution relationship between the bolt and the connected components in the parallel stiffness model. The external load is accurately distributed by the stiffness ratio, avoiding the overestimation or underestimation risk caused by the traditional experience method such as uniform distribution assumption; determines the distribution ratio of the external load, when is much larger than , is approximately equal to , the bolt bears the entire external load, and when is much smaller than , is approximately 0, and the external load is mainly borne by the connected components; the greater the bolt stiffness, the higher the proportion of the external load borne by the bolt, and the external load increases directly and linearly to increase the additional tension; the greater the stiffness of the connected components, the higher the proportion of the external load borne by the connected components, and the bolt additional tension decreases; The total axial force of the bolt is obtained by adding the initial pretightening force and the additional tension: wherein, represents the total axial force of the bolt; represents the initial pretightening force of the bolt.

[0035] In the above process, the total axial force of the bolt is calculated by adding the initial pretightening force and the additional tension, because this way completely reflects the load superposition principle of the bolt in the entire stress process. Before the external axial load is applied, the bolt has established the initial pretightening force through tightening, which is the basic clamping force of the connecting system; when the external load acts, part of the system according to the stiffness distribution relationship, i.e. the additional tension, is superimposed on the bolt, and the other part offsets the residual compression force between the connected components, therefore, the total force actually borne by the bolt is the algebraic sum of the initial force in the pretightening state and the incremental force caused by the external load.

[0036] S4: Obtain the lateral load of the bolt, based on the total axial force of the bolt thread, the effective cross-sectional area and the lateral shear area, respectively calculate the axial tensile stress of the bolt and the shear stress of the bolt by using the area uniform stress method, based on the axial tensile stress of the bolt and the shear stress of the bolt, calculate the equivalent stress of the bolt by using the shear strain energy equivalent method; The equivalent stress of the bolt is calculated by using the shear strain energy equivalent method, and the specific steps are as follows: The transverse load of the bolt is obtained, and based on the total axial force of the bolt thread, the effective cross-sectional area and the transverse shear area, the axial tensile stress of the bolt and the shear stress of the bolt are calculated by using the area uniform stress method respectively, specifically: the total axial tension of the bolt is uniformly distributed to the effective cross-sectional area of the thread, and the total axial force is divided by the effective cross-sectional area, so as to calculate the axial tensile stress; The transverse shear load of the bolt is uniformly distributed to the transverse shear area of the bolt, and the transverse load is divided by the transverse shear area, so as to calculate the shear stress; The formula on which the above process is based is as follows: Among them, represents the axial tensile stress of the bolt; Among them, represents the shear stress of the bolt; represents the transverse load of the bolt; represents the transverse shear area of the thread; In the above process, by using the area uniform stress method, the complex load such as the total axial tension and the transverse shear force borne by the bolt is respectively converted into the uniform stress acting on the corresponding dangerous cross section, realizing the clear quantification and decoupling analysis of the key stress state of the bolt; The method uses the accurately calculated effective cross-sectional area and transverse shear area as the reference to calculate the axial tensile stress representing the tensile strength of the material and the shear stress representing the shear capacity, which avoids the calculation deviation caused by stress coupling or unclear cross section definition, so that the safety state of the bolt under the two main failure modes of tension and shear can be respectively reviewed and accurately checked; Reflects the tensile stress generated on the unit effective cross-sectional area of the bolt under the action of the total axial force , represents the stress intensity of the bolt material under the axial load, and the effective cross-sectional area accurately quantifies the actual stress distribution of the dangerous cross section of the bolt, avoiding the risk of underestimation caused by the traditional simplified formula such as ignoring the thread stress concentration coefficient; The greater the total axial force is, the greater the tensile stress is, and the equivalent tensile area of the thread dangerous cross section increases, which can share the stress and reduce , the greater the total axial force is, the more significant the tensile stress is; Reflects the shear stress generated on the unit shear area of the bolt under the action of the transverse load , represents the ability of the bolt to resist transverse deformation or slip, and is based on the transverse shear area , the shear stress component of the bolt under the coupling of multi-directional load is accurately calculated; lateral shear force caused by insufficient friction or vibration, increasing causes increasing, the effective area of the bolt shank or thread participating in shear increasing can reduce shear stress; Based on the axial tensile stress of the bolt and the shear stress of the bolt, the equivalent stress of the bolt is calculated by using the shear strain energy equivalent method, that is, the square root of the sum of the square of the axial tensile stress and three times the square of the shear stress is calculated to obtain the equivalent stress of the bolt.

[0037] The formula on which the above process is based is: Among them, represents the equivalent stress of the bolt.

[0038] In the above process, the calculation is based on the shear strain energy strength theory, also known as the Mises criterion, which is to convert the two different stress components, the axial tensile stress and the lateral shear stress, which the bolt bears simultaneously, into a single equivalent tensile stress.

[0039] The principle of the Mises criterion is that the theory believes that the yield of the material under multi-directional stress state mainly depends on the shear strain energy accumulated inside. The square sum relationship in the formula reflects the coupling contribution of the two stresses to the material deformation energy, and the shear stress term multiplied by the coefficient 3 reflects the special influence weight of shear deformation energy on material yield. The equivalent stress calculated in this way can comprehensively and quantitatively represent the overall stress severity of the bolt under the combined stress state of tension and shear, so it can be directly compared with the uniaxial tensile yield strength of the material, providing a unified and scientific criterion for judging whether the bolt has yielded or deformed plastically.

[0040] is based on the Mises criterion to convert the stress of the bolt under the combined stress state of tension and shear into equivalent uniaxial tensile stress, representing the comprehensive yield risk of the bolt material under multi-directional load, and accurately quantifying the additional damage of shear deformation to the material through shear strain energy weighting, in the form of a square term directly affects the equivalent stress, and its growth contributes to nonlinear acceleration, in the form of a 3 times square term, its weight is significantly higher than that of the same order of magnitude of tensile stress, the increase of axial tensile stress directly leads to the increase of equivalent stress, and the increase rate accelerates with the increase of stress level, and the increase of shear stress increases the equivalent stress with a higher weight, i.e. with a coefficient of 3.

[0041] In the above embodiment, 20 sets of data of the axial tensile stress of the bolt and the corresponding equivalent stress are given to reflect the change of the equivalent stress with the change of the axial tensile stress of the bolt, as shown in Table 1: Table 1: Change relationship table between the axial tensile stress of the bolt and the corresponding equivalent stress As can be seen from the above Table 1, In the case of The square term directly affects the equivalent stress, and the growth contributes to the non-linear acceleration of .

[0042] In the above embodiment, 20 sets of data of the shear stress of the bolt and the corresponding equivalent stress are given to reflect the change of the equivalent stress with the change of the shear stress of the bolt, as shown in Table 2: Table 2: Change relationship table between the shear stress of the bolt and the corresponding equivalent stress As can be seen from the above Table 2, In the case of The equivalent stress is affected by the 3 times square term, and the weight is significantly higher than that of the tensile stress of the same order of magnitude. The increase of the axial tensile stress directly leads to the increase of the equivalent stress.

[0043] S5: Obtain the yield strength of the bolt material, calculate the safety factor of the bolt based on the equivalent stress by using the equivalent stress safety margin method, compare the safety factor with the preset safety threshold, and output the corresponding bolt strength grade.

[0044] Obtain the yield strength of the bolt material, calculate the safety factor of the bolt based on the equivalent stress by using the equivalent stress safety margin method, specifically, compare the yield strength of the bolt material with the equivalent stress of the bolt, calculate the ratio of the two, and obtain the safety factor. The safety factor represents the safety margin of the bolt relative to the material yield limit under the current load state; The formula on which the above process is based is: Among them, represents the yield strength of the bolt material; represents the safety factor of the bolt; Compare the safety factor with the preset safety threshold. When the safety factor is greater than 2, it means that it is relatively reliable; when the safety factor is greater than or equal to 1.5 and less than 2, it means slight deformation; and when the safety factor is less than 1.5, it means a relatively dangerous state.

[0045] In the above process, by directly comparing the comprehensive stress level of the bolt under complex tensile-shear composite stress state, i.e. equivalent stress, with the inherent yield strength of its material, a clear quantitative safety factor is calculated, thereby transforming the strength analysis from abstract stress calculation to intuitive safety performance evaluation.

[0046] By directly comparing the strength limit of the bolt under multi-stress load With the comprehensive stress level Establish a unified quantitative criterion, The higher the material strength, the greater the safety margin; The reverse inhibitory factor of safety factor, the increase of external load or the lack of structural stiffness leads to The linear decay of safety margin; When the safety factor is greater than 2, it means that the actual working stress of the bolt is much lower than the yield strength of the material, and there is sufficient safety reserve to cope with load fluctuations, stress concentration and material performance degradation caused by long-term service. It is considered as a safe ideal state. Secondly, when the safety factor is between 1.5 and 2, it means that the working stress has approached but has not reached the yield limit. In some extreme or non-uniform load conditions, the material may enter a small amount of plastic deformation stage locally, but the overall connection can still maintain its function. This state indicates that the design is close to the limit and needs to be paid attention to. Finally, when the safety factor is less than 1.5, it means that the working stress is very close to or even reaches the yield strength of the material, and the bolt may have significant plastic deformation or yield. The pretightening force of the connection pair will be lost quickly, and there is a high risk of loosening or failure, so design modification or strengthening must be carried out. Among them, the safety factor 2 is a reliable threshold, which is widely used in traditional specifications such as mechanical design and pressure vessels. It provides a general safety margin that can better cover load fluctuations, calculation model uncertainties, material performance dispersions and manufacturing errors, and is considered as a benchmark line that takes into account safety and conservatism in static strength design. 1.5 is often considered as the bottom line of elastic design or the critical point of entering plastic design. Below this value means that the stress has approached the yield limit too much and is prone to uncontrollable yield under accidental overload or stress concentration. These two dividing points come from the quantitative risk grading scale that has been widely verified and accepted in repeated practice and failure analysis, as well as the expert scoring.

[0047] Please refer to Figure 4 The application further provides a strength simulation analysis system for bolt connection, which is used to execute the above-mentioned analysis method, comprising: A data acquisition module is used to determine the effective cross-sectional area and transverse shear area of the thread on the bolt based on the basic parameters of the bolt to be analyzed. The rigidity acquisition module is configured to acquire a tightening torque applied to the bolt, construct a linear pre-tightening force model to calculate an initial pre-tightening force of the bolt, acquire a clamping length of the bolt, and an effective contact area of the connected member and the bolt, calculate an axial rigidity of the bolt and a compression rigidity of the connected member based on the effective cross-sectional area of the bolt by using an axial elastic modulus method, respectively. The force acquisition module is configured to acquire an external axial load of the bolt, construct a parallel rigidity distribution model based on the axial rigidity of the bolt and the compression rigidity of the connected member, and calculate an additional tension of the bolt, acquire a total axial force of the bolt based on the initial pre-tightening force and the additional tension. The equivalent stress acquisition module is configured to acquire a transverse load of the bolt, calculate an axial tensile stress of the bolt and a shear stress of the bolt based on the total axial force of the bolt thread, the effective cross-sectional area, and the transverse shear area by using an area uniform stress method, respectively, and calculate an equivalent stress of the bolt based on the axial tensile stress of the bolt and the shear stress of the bolt by using a shear strain energy equivalent method. The threshold comparison module is configured to acquire a yield strength of the bolt material, calculate a safety factor of the bolt based on the equivalent stress by using an equivalent stress safety margin method, compare the safety factor with a preset safety threshold, and output a corresponding bolt strength grade.

[0048] The above formulas are all dimensionless values, and the formulas are obtained by collecting a large amount of data to simulate a formula of the nearest real situation, and the preset parameters in the formulas are set by a person skilled in the art according to actual conditions.

[0049] The above embodiments can be realized wholly or partially by software, hardware, firmware, or any combination thereof. When realized by software, the above embodiments can be realized in the form of a computer program product wholly or partially. Those skilled in the art can realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0050] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, and can be located in one place or distributed on multiple network units. Part or all of the units can be selected to achieve the purpose of the embodiments.

[0051] The above is merely specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for strength simulation analysis of bolted connections, characterized by the following steps: include: S1: Determine the effective cross-sectional area and transverse shear area of ​​the bolt thread based on the basic parameters of the bolt to be analyzed; S2: Obtain the assembly torque applied to the bolt, construct a linear preload model to calculate the initial preload of the bolt, obtain the clamping length of the bolt and the effective contact area between the bolt and the connected parts, and calculate the axial stiffness of the bolt and the compressive stiffness of the connected parts based on the effective cross-sectional area of ​​the bolt using the axial elastic modulus method. S3: Obtain the external axial load of the bolt, construct a parallel stiffness distribution model based on the axial stiffness of the bolt and the compressive stiffness of the connected parts, and calculate the additional tensile force of the bolt. Based on the initial preload and the additional tensile force, obtain the total axial force of the bolt. S4: Obtain the transverse load of the bolt. Based on the total axial force, effective cross-sectional area and transverse shear area of ​​the bolt thread, calculate the axial tensile stress and shear stress of the bolt using the area uniform stress method. Based on the axial tensile stress and shear stress of the bolt, calculate the equivalent stress of the bolt using the shear strain energy equivalent method. S5: Obtain the yield strength of the bolt material, calculate the bolt safety factor based on the equivalent stress safety margin method, compare the safety factor with the preset safety threshold, and output the corresponding bolt strength grade.

2. The strength simulation analysis method for bolted connections according to claim 1, characterized in that, The specific steps to determine the effective cross-sectional area and transverse shear area of ​​the bolt thread are as follows: To obtain the pitch between adjacent threads and the nominal diameter of the bolt, where the nominal diameter refers to the diameter of the bolt shank, i.e., the outer diameter of the threaded portion; this is achieved by subtracting the pitch from the nominal diameter by a specific constant. The product of the two is used to obtain the corrected diameter value. The corrected diameter is divided by 2 to obtain the radius value. The square of the radius value is multiplied by pi to obtain the effective cross-sectional area of ​​the thread. To calculate the transverse shear area of ​​a thread, divide the nominal diameter by 2 to obtain the radius, and then multiply the square of the radius by pi to get the transverse shear area of ​​the thread.

3. The strength simulation analysis method for bolted connections according to claim 1, characterized in that, The specific steps for constructing a linear preload model to calculate the initial preload of the bolt are as follows: Obtain the assembly torque applied to the bolt, divide the bolt assembly torque by the product of the torque coefficient and the nominal diameter of the bolt, and the quotient is the initial preload formed by the bolt under the tightening condition.

4. The strength simulation analysis method for bolted connections according to claim 1, characterized in that, The clamping length of the bolt refers to the thickness of the connected parts from the bolt head contact surface to the nut contact surface. Based on the effective cross-sectional area of ​​the bolt, the axial stiffness of the bolt and the compressive stiffness of the connected parts are calculated using the axial elastic modulus method, specifically: Multiply the effective cross-sectional area of ​​the thread by the elastic modulus of the bolt material, and then divide the resulting product by the clamping length to obtain the axial stiffness, which characterizes the bolt's ability to resist axial tensile deformation. To determine the effective cross-sectional area of ​​the connected parts, specifically: calculate the tangent of the pressure diffusion angle between the bolt head and the connected parts, multiply it by the clamping length, add the contact radius between the bolt head and the connected parts to the product, take the square value, and multiply the square value by pi to obtain the effective cross-sectional area of ​​the connected parts. Multiply the calculated effective contact area of ​​the connected parts by the elastic modulus of the connected parts material, and then divide the resulting product by the clamping length to obtain the compressive stiffness, which characterizes the ability of the connected parts to resist compressive deformation.

5. The strength simulation analysis method for bolted connections according to claim 4, characterized in that, The specific steps for obtaining the total axial force of the bolt are as follows: Construct a parallel stiffness distribution model, specifically: treat the bolt and the connected parts as a parallel system. According to Hooke's Law, the load borne by each component is proportional to its own stiffness. The additional tensile force actually borne by the bolt is equal to the external axial load multiplied by a distribution coefficient, which is the ratio of the bolt's own axial stiffness to the sum of the bolt's axial stiffness and the compressive stiffness of the connected parts. The additional tensile force of a bolt is equal to the external axial load multiplied by the bolt's axial stiffness, and then divided by the sum of the bolt's axial stiffness and the compressive stiffness of the connected parts. The total axial force ultimately borne by the bolt is obtained by directly adding the initial preload and the additional tensile force.

6. The strength simulation analysis method for bolted connections according to claim 5, characterized in that, The specific steps for calculating the equivalent stress of the bolt using the shear strain energy equivalent method are as follows: To obtain the transverse load of the bolt, based on the total axial force, effective cross-sectional area, and transverse shear area of ​​the bolt thread, the axial tensile stress and shear stress of the bolt are calculated using the area uniform stress method. Specifically, the total axial tensile force borne by the bolt is evenly distributed on the effective cross-sectional area of ​​the thread, and the total axial force is divided by the effective cross-sectional area to calculate the axial tensile stress. The transverse shear load borne by the bolt is evenly distributed over the transverse shear area of ​​the bolt, and the shear stress is calculated by dividing the transverse load by the transverse shear area. Based on the axial tensile stress and shear stress of the bolt, the equivalent stress of the bolt is calculated using the shear strain energy equivalent method. Specifically, the equivalent stress of the bolt is obtained by calculating the square root of the sum of the square of the axial tensile stress and the square of three times the shear stress.

7. The strength simulation analysis method for bolted connections according to claim 6, characterized in that, The specific steps for determining the bolt strength grade corresponding to the output are as follows: The yield strength of the bolt material is obtained. Based on the equivalent stress, the safety factor of the bolt is calculated using the equivalent stress safety margin method. Specifically, the yield strength of the bolt material is compared with the equivalent stress of the bolt, and the ratio of the two is calculated. The resulting safety factor characterizes the safety margin of the bolt relative to the yield limit of the material under the current load condition. The safety factor is compared with the preset safety threshold. When the safety factor is greater than 2, it indicates that the system is relatively reliable. When the safety factor is greater than or equal to 1.5 and less than 2, it indicates that the system is slightly deformed. When the safety factor is less than 1.5, it indicates that the system is relatively dangerous.

8. A strength simulation analysis system for bolted connections, characterized in that: The analysis system is used to execute the analysis method according to any one of claims 1-7, including: The data acquisition module is used to determine the effective cross-sectional area and transverse shear area of ​​the threads on the bolt based on the basic parameters of the bolt to be analyzed. The stiffness acquisition module is used to acquire the tightening torque applied to the bolt, construct a linear preload model to calculate the initial preload of the bolt, acquire the clamping length of the bolt and the effective contact area between the bolt and the connected parts, and calculate the axial stiffness of the bolt and the compressive stiffness of the connected parts based on the effective cross-sectional area of ​​the bolt using the axial elastic modulus method. The force acquisition module is used to acquire the external axial load of the bolt, construct a parallel stiffness distribution model based on the axial stiffness of the bolt and the compressive stiffness of the connected parts, and calculate the additional tensile force of the bolt. Based on the initial preload and the additional tensile force, the total axial force of the bolt is acquired. The equivalent stress acquisition module is used to acquire the transverse load of the bolt. Based on the total axial force, effective cross-sectional area and transverse shear area of ​​the bolt thread, the axial tensile stress and shear stress of the bolt are calculated by the area uniform stress method, respectively. Based on the axial tensile stress and shear stress of the bolt, the equivalent stress of the bolt is calculated by the shear strain energy equivalent method. The threshold comparison module is used to obtain the yield strength of the bolt material, calculate the safety factor of the bolt based on the equivalent stress safety margin method, compare the safety factor with the preset safety threshold, and output the corresponding bolt strength grade.

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