Strength simulation analysis method and system for bolt connection

Abstract

The application provides a bolt connection strength simulation analysis method and system, relates to the technical field of simulation analysis methods, and comprises the following steps: respectively calculating the axial stiffness of a bolt and the compression stiffness of a connected part by adopting an axial elastic modulus method, constructing a parallel stiffness distribution model, and calculating additional tension of the bolt; respectively calculating axial tensile stress of the bolt and shear stress of the bolt by adopting an area uniform stress method; and calculating equivalent stress of the bolt by adopting a shear strain energy equivalent method; calculating a safety factor of the bolt by adopting an equivalent stress safety margin method, comparing the safety factor with a preset safety threshold, and outputting a corresponding bolt strength grade. Additional tension is dynamically distributed according to the stiffness of the bolt and the connected part, so that the force transmission characteristics are closer to actual bearing; the pitch correction nominal diameter is introduced, so that the actual stress distribution of the thread root is more accurately described; and the equivalent stress is calculated by the shear strain energy equivalent method, so that the yield criterion of the plastic material is more in line with the yield criterion.

Description

Technical Field

[0001] This invention relates to the field of simulation analysis methods, specifically to a strength simulation analysis method and system for bolted connections. Background Technology

[0002] Traditional bolt strength analysis methods are mostly based on a single load assumption or a simplified stiffness model. Their linear torque and preload models ignore friction fluctuations and nonlinear deformation of the thread, resulting in a large error in the initial preload. Furthermore, they do not consider the parallel stiffness characteristics of the bolt and the connected parts, and the distribution of additional loads depends on empirical coefficients, making it difficult to adapt to complex working conditions. Axial tension and transverse shear stress are often calculated independently, ignoring their coupling effect, which leads to deviations in equivalent stress assessment.

[0003] In the prior art, CN114757069A discloses a method for analyzing the strength of the load-bearing structure and bolts by meshing a three-dimensional model of the load-bearing structure that mates with the bolts, generating a finite element model containing the load-bearing structure, and adding assembly boundary conditions. However, while this method combines a linear torque model with a stiffness parallel distribution mechanism to improve the accuracy of the initial preload calculation, it does not quantify the additional tensile force based on the axial stiffness parallel model, accurately reflect the cooperative stress characteristics of the bolt and the connected parts, introduce an equivalent shear strain energy criterion, comprehensively consider the interaction between axial tension and transverse shear stress, and dynamically correlate the discrete range of equivalent stress and material yield strength to generate a probability distribution of the safety factor. Therefore, a strength simulation analysis method for bolted connections is urgently needed.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for strength simulation analysis of bolted connections to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The strength simulation analysis method for bolted connections includes the following steps:

[0008] 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;

[0009] S2: Obtain the tightening 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.

[0010] 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.

[0011] 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.

[0012] 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.

[0013] Further, the effective cross-sectional area and transverse shear area of ​​the bolt thread are determined, and the specific steps are as follows:

[0014] 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.

[0015] 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.

[0016] Furthermore, a linear preload model is constructed to calculate the initial preload of the bolt. The specific steps are as follows:

[0017] 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.

[0018] Furthermore, 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 modulus of elasticity method, specifically:

[0019] 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.

[0020] 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.

[0021] 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.

[0022] Further, the total axial force of the bolt is obtained through the following steps:

[0023] 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.

[0024] 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.

[0025] Furthermore, the equivalent stress of the bolt is calculated using the shear strain energy equivalent method. The specific steps are as follows:

[0026] 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.

[0027] 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.

[0028] 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.

[0029] Furthermore, the safety factor of any grid center point is compared with a set safety threshold. If it exceeds the safety threshold, the grid location is considered a risk area. The specific steps are as follows:

[0030] when A value greater than or equal to 0.8 indicates the grid center point. In a safe state; when A value greater than or equal to 0.5 but less than 0.8 indicates the center point of the grid. In a state of alert; when When it is less than 0.5, it indicates the center point of the grid. They are in a high-risk state.

[0031] Further, output the corresponding bolt strength grade. The specific steps are as follows:

[0032] 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.

[0033] 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.

[0034] The present invention also provides a strength simulation analysis system for bolted connections, the analysis system being used to perform the above-described analysis method, comprising:

[0035] 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.

[0036] 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.

[0037] 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.

[0038] 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.

[0039] 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.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] By accurately calculating the effective cross-sectional area and transverse shear area of ​​the thread, the stress underestimation caused by the simplification of the cross-sectional area in traditional methods is avoided. The axial stiffness and compressive stiffness are normalized with clamping length to construct the core parameters of the stiffness parallel model, ensuring the theoretical rigor of the additional load distribution calculation. Based on the deformation compatibility condition, the external load is distributed according to the stiffness ratio, the total axial force of the bolt is accurately quantified, and the shear strain energy equivalent criterion is introduced. The interaction between axial tension and transverse shear stress is integrated to improve the consistency between the equivalent stress prediction and the measured value. By dynamically correlating the discrete interval of equivalent stress and material yield strength, a safety factor probability distribution is generated to adapt to the balance between high reliability and lightweight requirements. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0043] Figure 2 This is a graph showing the relationship between the axial tensile stress and the corresponding equivalent stress of the bolt.

[0044] Figure 3 This is a graph showing the relationship between the shear stress and the corresponding equivalent stress of the bolt.

[0045] Figure 4 This is a schematic diagram of the overall system of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0047] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0048] Example:

[0049] Please see Figures 1-3 The present invention provides a technical solution:

[0050] The strength simulation analysis method for bolted connections includes the following steps:

[0051] 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;

[0052] The specific steps to determine the effective cross-sectional area and transverse shear area of ​​the bolt thread are as follows:

[0053] 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.

[0054] 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.

[0055] The formula upon which the above process is based is:

[0056]

[0057] in, Indicates the nominal diameter of the bolt; Indicates the pitch between threads; Indicates the effective cross-sectional area of ​​the thread;

[0058] The transverse shear area of ​​the thread is calculated using the nominal section method:

[0059]

[0060] in, This indicates the transverse shear area of ​​the thread.

[0061] In the above process, by introducing pitch parameters and specific correction coefficients, the minimum cross-sectional area at the thread root, i.e., the effective cross-sectional area, is calculated. This accurately reflects the weakest true load-bearing area of ​​the bolt under axial tensile force, laying the foundation for subsequent accurate calculation of tensile stress. Simultaneously, the complete cross-sectional area of ​​the shank, i.e., the transverse shear area, is calculated directly from the bolt's nominal diameter. This area represents the main load-bearing section of the bolt resisting transverse shear force. The calculation of these two areas is the starting point for subsequent evaluations of the bolt's tensile and shear capabilities, and their accuracy directly determines the reliability of the entire strength simulation analysis results.

[0062] The effective cross-sectional area of ​​a thread is the equivalent geometric area of ​​the actual stress borne by the bolt under axial tensile load. It reflects the reduction in load-bearing capacity at the thread root due to geometric weakening, such as thread grooves. (Calculation...) This avoids the underestimation of axial stress caused by neglecting thread groove geometry correction in traditional methods, thus improving the accuracy of bolt tensile strength assessment. The transverse shear area is the nominal geometric area of ​​the bolt subjected to shear stress under transverse loads such as shear or torsion, calculated using the nominal section method. This simplifies the modeling difficulty of shear stress distribution at the root of complex threads;

[0063] In calculating the effective area of ​​the thread, the constant term Derived from the thread profile geometry correction factor, it corresponds to the ratio of thread height to pitch. For standard unified threads, the thread height is... Correction factor This includes compensation for the root fillet radius to ensure that the effective cross-sectional area matches the actual load-bearing capacity. With nominal diameter Showing a positive correlation, Increasing the effective cross-sectional area significantly improves With pitch Showing an inverse correlation, Increasing the correction term Reduce; in calculating the transverse shear area, Only with Positive correlation Increasing will increase quadratically .

[0064] S2: Obtain the tightening 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.

[0065] The specific steps for constructing a linear preload model to calculate the initial preload of the bolt are as follows:

[0066] 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.

[0067] The formula used in the above process is:

[0068]

[0069] in, Indicates the torque coefficient; Indicates assembly torque; Indicates the nominal diameter of the bolt; This indicates the initial preload of the bolt.

[0070] In the above process, a simplified linear preload model was established, achieving a direct and rapid mapping from tightening torque to bolt initial preload. This method integrates multiple factors involved in the complex tightening process, such as thread friction and end-face friction, into an easy-to-use torque coefficient, thereby avoiding cumbersome experimental calibration and significantly improving the efficiency of engineering design and assembly control. By clarifying the quantitative influence relationship between torque, torque coefficient, and bolt diameter on preload, this model can guide actual operation and help accurately control the clamping force during assembly. It ensures that the connection pair has sufficient initial locking force to resist loosening and separation, and provides a reliable calculation starting point for subsequent load distribution analysis and strength verification. It is the key input foundation for the entire bolt connection strength simulation.

[0071] Obtaining the assembly torque mainly depends on the preset and control of the fastening tools. The operator uses a calibrated torque wrench, electric tightening machine or hydraulic tool to tighten according to the specific torque value specified in the design drawings, process documents or relevant standards. During the tightening process, the tool will accurately output the preset torque value. When the value is reached, the tool will usually issue a prompt or stop automatically to ensure that the applied rotational torque is consistent with the design requirements.

[0072] Initial preload is the axial tensile force applied by torque during bolt tightening. It is used to create a clamping force between the bolt and the connected parts, preventing loosening or separation. A linear model is used to calculate the tightening torque. It directly maps to quantifiable preload, simplifying the traditional test calibration process and enabling rapid calculation and control of preload. This refers to the externally applied rotational torque, also known as the assembly torque, which directly drives the bolt to produce axial elongation deformation and is the energy input source of the preload. and They exhibit a direct proportional relationship. Increase the direct preload; and The relationship is inversely proportional; as the coefficient of friction increases, that is... Increasing the torque leads to more torque energy being dissipated as frictional heat, reducing the preload conversion efficiency. and The inverse proportional relationship demonstrates that larger diameter bolts require greater torque to achieve the same preload.

[0073] 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:

[0074] 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.

[0075] 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.

[0076] 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.

[0077] The formula used in the above process is:

[0078]

[0079] in, Indicates the axial stiffness of the bolt; Indicates the clamping length of the bolt; This indicates the elastic modulus of the bolt. Indicates the effective cross-sectional area of ​​the thread;

[0080]

[0081] in,

[0082]

[0083] Indicates the compressive stiffness of the connected components; Indicates the elastic modulus of the connected components; Indicates the effective contact area of ​​the connected components; Indicates the contact radius between the bolt head and the connected parts; This indicates the pressure diffusion angle between the bolt head and the connected parts.

[0084] In the above process, This represents the ability of a bolt to resist deformation under axial tensile load, defined as the tensile force required to produce a unit axial deformation, expressed through the effective cross-sectional area. With elastic modulus The synergistic effect of these factors accurately quantifies bolt stiffness, avoiding the overestimation of stiffness caused by neglecting the weakening effect at the thread root in traditional empirical formulas. Characterizing the ability of connected components to resist compressive deformation under bolt preload, it is defined as the pressure required to produce a unit compressive deformation, based on the pressure diffusion angle. Correcting the effective contact area This reflects the three-dimensional diffusion effect of clamping force in the connector, through the elastic modulus. The calculation of the diffusion area helps avoid the risk of plastic deformation of the connectors caused by local stress concentration.

[0085] in, It directly determines the equivalent area of ​​the load-bearing cross section of the bolt material. Increase, linearly improve , Indicates the inherent properties of a material. Increase, linearly enhance stiffness, Indicates the length of the bolt's stressed section. Increasing the axial deformation leads to a decrease in stiffness. and and There is a positive correlation; both increased material stiffness and increased contact area enhance compressive strength. Increase the initial contact area directly. This indicates the angle at which the clamping force spreads within the connected components. Increase significantly improve diffusion area and There is an inverse correlation: the longer the clamping length, the greater the compressive deformation under the same pressure, and the lower the stiffness.

[0086] The calculation process scientifically simulates the three-dimensional diffusion effect of bolt preload in actual fasteners. This model assumes that the preload originates from the bolt head or nut contact surface, i.e., at a radius of... Starting from a point at a certain angle to the axis of the connected component, i.e., the pressure diffusion angle. The conical surface spreads outwards, with increasing clamping length. With the increase, the pressure surface is The radial increment extends outward, thus forming an equivalent bearing area that is much larger than the initial contact surface.

[0087] 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.

[0088] The specific steps for obtaining the total axial force of the bolt are as follows:

[0089] 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.

[0090] 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.

[0091] The formula upon which the above process is based is:

[0092]

[0093] in, Indicates the additional tensile force on the bolt; Indicates the external axial load on the bolt;

[0094] In the above process, by establishing a parallel stiffness distribution model, the distribution law of external axial load between the bolt and the connected parts in the bolted connection system is scientifically revealed. This method gets rid of the roughness of traditional empirical estimation methods such as simply assuming that the bolt bears all or part of the load. Instead, it performs accurate calculations based on the actual ratio of the stiffness of the two, so as to more realistically simulate the actual force increment of the bolt under external load.

[0095] The external axial load borne by the bolt is obtained through the overall force analysis of the connection structure. This load comes from the working load borne by the connecting parts. When determining it, it is necessary to obtain the load component acting on the bolt axially, i.e. along the bolt axis, through theoretical calculation based on the load conditions such as normal operation, start-up, shutdown or abnormal state and the force transmission path.

[0096] External load When applied to the bolt, the additional axial tensile force component actually borne by the bolt reflects the load distribution relationship between the bolt and the connected parts in the parallel stiffness model. The external load is accurately distributed through the stiffness ratio, avoiding the risk of overestimation or underestimation caused by traditional empirical methods such as the assumption of uniform distribution. Determine the distribution ratio of external loads, when Much larger hour, Approximately equal to The bolts bear all external loads when much smaller hour, Approximately 0, the external load is mainly borne by the connected parts; the greater the stiffness of the bolt, the higher the proportion of the external load it shares, and the increase in external load directly and linearly increases the additional tensile force; the greater the stiffness of the connected parts, the higher the proportion of the external load it shares, and the lower the additional tensile force of the bolt.

[0097] The total axial force of the bolt is obtained by adding the initial preload and the additional tensile force:

[0098]

[0099] in, This indicates the total axial force on the bolt; This indicates the initial preload of the bolt.

[0100] In the above process, the total axial force of the bolt is calculated as the sum of the initial preload and the additional tensile force because this method fully reflects the principle of load superposition during the entire stress process. Before the external axial load is applied, the bolt has already established an initial preload through tightening, which is the basic clamping force of the connection system. When the external load is applied, according to the stiffness distribution relationship, part of the additional tensile force will be superimposed on the bolt, while the other part will offset the residual clamping force between the connected parts. Therefore, the total force actually borne by the bolt is the algebraic sum of the initial force under preload and the incremental force caused by the external load.

[0101] 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.

[0102] The equivalent stress of the bolt is calculated using the shear strain energy equivalent method. The specific steps are as follows:

[0103] 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.

[0104] 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.

[0105] The formula upon which the above process is based is:

[0106]

[0107] in, This indicates the axial tensile stress of the bolt;

[0108]

[0109] in, This represents the shear stress of the bolt; Indicates the lateral load on the bolt; This indicates the transverse shear area of ​​the thread;

[0110] In the above process, by adopting the area uniform stress method, the complex loads borne by the bolt, such as the total axial tensile force and the transverse shear force, are transformed into uniform stresses acting on the corresponding critical sections, realizing clear quantification and decoupled analysis of the key stress state of the bolt. This method uses the accurately calculated effective cross-sectional area and transverse shear area as benchmarks to calculate the axial tensile stress characterizing the tensile strength of the material and the shear stress characterizing the shear capacity, respectively. This avoids calculation deviations caused by stress coupling or unclear section definition, and enables the safety status of the bolt under the two main failure modes of tension and shear to be examined and accurately verified separately.

[0111] Reflects the total axial force of the bolt The tensile stress generated per unit effective cross-sectional area under axial load characterizes the strength of the bolt material under axial load. This is determined by the effective cross-sectional area. It accurately quantifies the actual stress distribution at the critical section of the bolt, avoiding the underestimation of risk caused by traditional simplified formulas such as ignoring the thread stress concentration factor; The larger the value, the linearly increasing tensile stress, and the equivalent tensile area of ​​the thread's critical section. Increasing the stress can distribute it and reduce the stress. The greater the total axial force, the more significant the tensile stress.

[0112] Reflects the bolt under lateral load Under the action of shear stress, the shear stress generated per unit shear area characterizes the bolt's ability to resist lateral deformation or slippage, based on the lateral shear area. Accurately calculate the shear stress components of bolts under multi-directional load coupling; Transverse shear force caused by insufficient friction or vibration Enlargement leads to Increase the effective area of ​​the bolt shank or thread that participates in shear resistance. Increasing the value can reduce shear stress;

[0113] 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.

[0114] The formula upon which the above process is based is:

[0115]

[0116] in, This represents the equivalent stress of the bolt.

[0117] In the above process, calculation It is based on the shear strain energy strength theory, also known as the Mises criterion. Its core is to convert the two different stress components, axial tensile stress and transverse shear stress, that the bolt is simultaneously subjected to into a single, equivalent tensile stress.

[0118] The Mises criterion states that the yielding of a material under multiaxial stress primarily depends on its internally accumulated shear strain energy. The sum of squares in the formula reflects the coupled contribution of the two stresses to the material's deformation energy. The shear stress term, multiplied by a coefficient of 3, reflects the specific weight of the shear strain energy on the material's yielding. The equivalent stress calculated in this way can comprehensively and quantitatively characterize the overall stress severity of a bolt under combined tensile and shear stress, thus allowing direct comparison with the uniaxial tensile yield strength of the material. This provides a unified and scientific criterion for determining whether a bolt has yielded or undergone plastic deformation.

[0119] Based on the Mises criterion, the stress on a bolt under combined stress conditions (tension and shear) is uniformly converted into an equivalent uniaxial tensile stress. This characterizes the comprehensive yield risk of the bolt material under multiaxial loads and accurately quantifies the additional damage to the material caused by shear deformation through shear strain energy weighting. It directly affects the equivalent effect in the form of a squared term, and its growth has an impact on... The contribution is nonlinearly accelerated. The equivalent stress is affected by a term of 3 times the square, and its weight is significantly higher than that of tensile stress of the same magnitude. The increase in axial tensile stress directly leads to an increase in equivalent stress, and the rate of increase accelerates with the increase in stress level. The increase in shear stress has a higher weight, i.e., a coefficient of 3, which increases the equivalent stress.

[0120] In the above embodiments, 20 sets of data on the axial tensile stress of the bolt and the corresponding equivalent stress are given to reflect the change of equivalent stress with the change of the axial tensile stress of the bolt, as shown in Table 1:

[0121] Table 1: Relationship between axial tensile stress and corresponding equivalent stress of bolts

[0122]

[0123] As can be seen from Table 1 above, In this case, The effect of the equivalent force is directly influenced by the square term, and its growth has an impact on... The contribution exhibits a nonlinear acceleration characteristic.

[0124] In the above embodiments, 20 sets of data on the shear stress of the bolt and the corresponding equivalent stress are given to reflect the change of equivalent stress with the shear stress of the bolt, as shown in Table 2:

[0125] Table 2: Relationship between shear stress and corresponding equivalent stress of bolts

[0126]

[0127] As can be seen from Table 2 above, In this case, The equivalent stress is affected by a term that is 3 times the square, and its weight is significantly higher than that of tensile stress of the same magnitude. The increase in axial tensile stress directly leads to an increase in equivalent stress.

[0128] 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.

[0129] 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.

[0130] The formula upon which the above process is based is:

[0131]

[0132] in, Indicates the yield strength of the bolt material; Indicates the safety factor of the bolt;

[0133] 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.

[0134] In the above process, by directly comparing the comprehensive stress level of the bolt under complex tensile-shear combined stress state, i.e., the equivalent stress, with the inherent yield strength of its material, a clearly quantified safety factor is calculated, thereby transforming the strength analysis from abstract stress calculation into an intuitive safety performance assessment.

[0135] By measuring the ultimate strength of bolts under multiple stress loads With overall stress level Direct comparison to establish unified quantitative criteria. It is a positive driving factor for the safety factor; the higher the material strength, the greater the safety margin. It is a reverse inhibition factor of the safety factor, caused by increased external load or insufficient structural stiffness. As the margin increases, the safety margin decreases linearly.

[0136] When the safety factor is greater than 2, it means that the actual working stress of the bolt is far below the material's yield strength, providing ample safety margin and reliably handling load fluctuations, stress concentration, and potential material performance degradation from long-term service. This is considered an ideal and safe state. Secondly, when the safety factor is between 1.5 and 2, it means that the working stress is close to but has not yet reached the yield strength. Under certain extreme or non-uniform load conditions, the material may locally enter a stage of slight plastic deformation, but the overall connection can still maintain its function. This state indicates that the design is approaching its limit and requires attention. Finally, when the safety factor is less than 1.5, it indicates that the working stress is very close to or even reaches the material's yield strength. The bolt is likely to undergo significant plastic deformation or yielding, and the preload of the connection will be rapidly lost, posing a high risk of loosening or failure. Design modifications or reinforcements are necessary.

[0137] Among them, the safety factor of 2, as a reliable threshold, is widely used in traditional specifications such as mechanical design and pressure vessels. It provides a general safety margin that can well cover load fluctuations, calculation model uncertainties, material property dispersion, and manufacturing errors, and is regarded as a baseline that balances safety and conservatism in static strength design. On the other hand, 1.5 is often regarded as the bottom line of elastic design or the critical point for entering plastic design. Below this value, it means that the stress is too close to the yield limit, and uncontrollable yielding is very likely to occur under accidental overload or stress concentration. These two dividing points are derived from a combination of a widely verified and accepted quantitative risk classification scale formed through repeated practice and failure analysis, and expert scoring.

[0138] Please see Figure 4 The present invention also provides a strength simulation analysis system for bolted connections, the analysis system being used to perform the above-described analysis method, including:

[0139] 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.

[0140] 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.

[0141] 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.

[0142] 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.

[0143] 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.

[0144] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0145] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0146] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0147] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method of simulating the strength of a bolted connection, characterized by the steps of Comprise: S1: 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; S2: the assembly torque applied to the bolt is obtained, a linear pre-tightening force model is constructed to calculate the initial pre-tightening force of the bolt, the clamping length of the bolt, the effective contact area of the connected member and the bolt are obtained, based on the effective cross-sectional area of the bolt, the axial stiffness of the bolt and the compression stiffness of the connected member are calculated by using the axial elastic modulus method; S3: the external axial load of the bolt is obtained, based on the axial stiffness of the bolt and the compression stiffness of the connected member, a parallel stiffness distribution model is constructed, and the additional tension of the bolt is calculated, based on the initial pre-tightening force and the additional tension, the total axial force of the bolt is obtained; S4: 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 respectively, 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; S5: the yield strength of the bolt material is obtained, based on the equivalent stress, the safety factor of the bolt is calculated by using the equivalent stress safety margin method, the safety factor is compared with the preset safety threshold, and the corresponding bolt strength grade is output; The total axial force of the bolt is obtained, and the specific steps are: A parallel stiffness distribution model is constructed, which is equivalent to a system in parallel with the bolt and the connected member, 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, which 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, the total axial force finally borne by the bolt is obtained by directly adding the initial pre-tightening force and the additional tension; The equivalent stress of the bolt is calculated by using the shear strain energy equivalent method, and the specific steps are: 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 respectively, which is: 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, which 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, and the equivalent stress of the bolt is obtained.

2. The bolt-connection strength simulation analysis method according to claim 1, characterized by, The effective cross-sectional area and the transverse shear area of the thread on the bolt are determined, and the specific steps are: acquiring 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 shank, i.e. the outer diameter of the threaded portion; obtaining a corrected diameter value by subtracting the product of the pitch and the diameter of the bolt from the nominal diameter and dividing the corrected diameter value by 2, obtaining a radius value, and multiplying the square of the radius value by 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, the square of the radius value is multiplied by the circular constant to obtain the transverse shear area of the thread.

3. The bolt-connection strength simulation analysis method according to claim 1, characterized by, The bolt initial pretightening force is calculated by constructing a linear pretightening force model, and the specific steps are as follows: The bolt assembly torque is obtained, and the bolt assembly torque is divided by the product of the torque coefficient and the bolt nominal diameter, and the quotient is the initial pretightening force formed by the bolt.

4. The bolt-connection strength simulation analysis method according to claim 1, characterized by, The bolt clamping length refers to the thickness of the connected member between the bolt head contact surface and the nut contact surface, and based on the effective cross-sectional area of the bolt, the axial elastic modulus method is used to calculate the axial stiffness of the bolt and the compression stiffness of the connected member, 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 of the bolt resisting axial tensile deformation; The effective cross-sectional area of the connected member is determined, specifically: the tangent value of the pressure diffusion angle of the bolt head and the connected member is calculated, and then multiplied by the clamping length, and the product is added to the contact radius of the bolt head and the connected member, and then squared, and then multiplied by the result of the square value. The effective cross-sectional area of the connected member is obtained. The effective contact area of the connected member calculated is multiplied by the elastic modulus of the connected member material, and then the product is divided by the clamping length, to obtain the compression stiffness of the connected member resisting compression deformation.

5. The bolt-connection strength simulation analysis method according to claim 1, characterized by, The corresponding bolt strength grade is output, and the specific steps are as follows: The yield strength of the bolt material is obtained, and based on the equivalent stress, the safety factor of the bolt is calculated by 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, and the safety factor obtained 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, when the safety factor is greater than 2, it means more reliable; when the safety factor is greater than or equal to 1.5 and less than 2, it means slight deformation; when the safety factor is less than 1.5, it means a more dangerous state.

6. A bolt connection strength simulation analysis system characterized by: The analysis system is used to execute the analysis method of any one of claims 1-5, comprising: 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 obtain the tightening torque applied to the bolt, construct a linear pretightening force model to calculate the initial pretightening force of the bolt, obtain the clamping length of the bolt and the effective contact area of the connected member and the bolt, and calculate the axial stiffness of the bolt and the compression stiffness of the connected member based on the effective cross-sectional area of the bolt. An acting force acquisition module is configured to 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 based on the initial pretightening force and the additional tension. An equivalent stress acquisition module is configured to obtain the transverse load of the bolt, calculate the axial tensile stress of the bolt and the shear stress of the bolt based on the total axial force, the effective cross-sectional area and the transverse shear area of the bolt thread by using the area uniform stress method, and calculate the equivalent stress of the bolt based on the axial tensile stress of the bolt and the shear stress of the bolt by using the shear strain energy equivalent method. The threshold comparison module is configured to acquire the yield strength of the bolt material, calculate the safety factor of the bolt by using an equivalent stress safety margin method based on the equivalent stress, compare the safety factor with a preset safety threshold, and output a corresponding bolt strength grade.

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