Modeling method and device for Iwan model of bolt connection structure and electronic equipment

Abstract

The invention provides an Iwan model modeling method and device of a bolted connection structure and electronic equipment, and the method comprises the steps: constructing a dynamic pressure distribution function of the bolted connection structure based on a contact boundary of a contact surface in the bolted connection structure by applying a linear pressure distribution function; solving a density function based on the dynamic pressure distribution function and a friction theory to obtain a density function of yield displacement; and introducing the density function of the yield displacement into a general Iwan model to construct an Iwan model. According to the method provided by the invention, the dynamic pressure distribution function of the bolt connection structure is constructed by selecting the linear pressure distribution function and combining the contact boundary of the contact surface. And density function solving is carried out based on the dynamic pressure distribution function and the friction theory, and a density function of yield displacement is obtained. The density function of the yield displacement is introduced into the universal Iwan model, the Iwan model of the bolt connection structure is obtained, Iwan model construction with few parameters and good representation effect is achieved, and the calculation complexity of the Iwan model is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of data modeling, and in particular to an Iwan modeling method, device, and electronic equipment for a bolt connection structure. Background Art

[0002] Bolted connection structures play an important role in the field of complex equipment. How to ensure the safe and efficient performance of bolts under long-term external loads has become a major issue. Due to the friction between the thread and the nut, the contact objects will experience residual sticking, slipping, separation and other stages, which will have a huge impact on the structure. The contact state evolves between the bolt and the plate, and the contact pressure evolves between the upper and lower plates. However, the existing technology cannot monitor the contact evolution process in real time, so it is necessary to build a theoretical model to predict important processes such as tangential force and displacement, energy dissipation, stiffness degradation, and working state to improve the safety and reliability of the bolts during operation. Among them, the Iwan model is the focus of research, which can construct hysteresis curves, energy dissipation, and stiffness degradation curves, which can better characterize the physical properties of bolted connections.

[0003] However, the yield displacement density function in the currently constructed Iwan model has many unknown parameters, which greatly increases the complexity of the calculation. Summary of the invention

[0004] The present invention provides an Iwan model modeling method, device and electronic equipment for a bolt connection structure, which are used to solve the defect in the prior art that the yield displacement density function has many unknown parameters, which greatly increases the complexity of model calculation.

[0005] The present invention provides an Iwan model modeling method for a bolt connection structure, comprising: Based on the contact boundary of the contact surface in the bolt connection structure, a linear pressure distribution function is applied to construct a dynamic pressure distribution function of the bolt connection structure; Solving the density function based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement; The density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolt connection structure.

[0006] According to an Iwan model modeling method for a bolt connection structure provided by the present invention, the contact boundary of the contact surface in the bolt connection structure is applied based on a linear pressure distribution function to construct a dynamic pressure distribution function of the bolt connection structure, including: Based on the contact boundary of the contact surface, a linear pressure distribution function is applied to construct an initial dynamic pressure distribution function; Correcting the initial dynamic pressure distribution function to obtain a corrected dynamic pressure distribution function; Based on the preload correction parameter of the bolt connection structure, the corrected dynamic pressure distribution function is verified to obtain the dynamic pressure distribution function; The preload correction parameter is used to correct the deviation between the actual preload and the theoretical preload under the corrected dynamic pressure distribution function.

[0007] According to an Iwan model modeling method for a bolt connection structure provided by the present invention, the contact boundary based on the contact surface is applied with a linear pressure distribution function to construct an initial dynamic pressure distribution function, including: Based on the tangential force and the maximum pressure value, the linear pressure distribution function is longitudinally adjusted, and based on the tangential force and the maximum contact radius of the contact surface, the linear pressure distribution function is transversely adjusted to obtain an adjusted linear pressure distribution function; Based on the contact boundary of the contact surface, applying the adjusted linear pressure distribution function to obtain the initial dynamic pressure distribution function; The contact boundary is described based on an elliptic function.

[0008] According to an Iwan modeling method for a bolt connection structure provided by the present invention, the initial dynamic pressure distribution function is corrected to obtain a corrected dynamic pressure distribution function, including: When the pressure is zero, the maximum radius in the initial dynamic pressure distribution function is corrected based on the constraint method; Alternatively, the initial dynamic pressure distribution function is offset to obtain the modified dynamic pressure distribution function.

[0009] According to an Iwan model modeling method for a bolt connection structure provided by the present invention, the density function is solved based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement, including: Based on the dynamic pressure distribution function and the friction theory, friction shear stress is obtained; Based on the contact area of ​​the contact surface and the friction shear stress, the contact area is normalized to obtain a density function of the friction shear stress; Based on the mapping relationship between the friction shear stress and the yield force, and the density function of the friction shear stress, a density function of the yield force is obtained; Based on the linear relationship between the yield force and the yield displacement, and the density function of the yield force, a density function of the yield displacement is obtained.

[0010] According to an Iwan model modeling method for a bolt connection structure provided by the present invention, the density function of the yield displacement is introduced into a general Iwan model to construct the Iwan model of the bolt connection structure, comprising: Based on the density function of the yield displacement, the backbone curve of the general Iwan model is solved piecewise to obtain the backbone curve; Based on the backbone curve of the Iwan model, a hysteresis loop is obtained; Based on the backbone curve and the hysteresis loop, an Iwan model of the bolt connection structure is constructed.

[0011] The present invention also provides an Iwan model modeling device for a bolt connection structure, comprising: A linear pressure distribution unit, based on a contact boundary of a contact surface in a bolt connection structure, applies a linear pressure distribution function to construct a dynamic pressure distribution function of the bolt connection structure; A solving unit solves the density function based on the dynamic pressure distribution function and the friction theory to obtain the density function of the yield displacement; The modeling unit introduces the density function of the yield displacement into the general Iwan model to construct the Iwan model of the bolt connection structure.

[0012] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, an Iwan model modeling method for a bolt connection structure as described above is implemented.

[0013] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the Iwan model modeling method of the bolt connection structure as described in any one of the above is implemented.

[0014] The present invention also provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the Iwan model modeling method of the bolt connection structure as described above is implemented.

[0015] The Iwan model modeling method, device, and electronic device of the bolt connection structure provided by the present invention select a linear pressure distribution function with fewer parameters and better characterization effect, and combine the contact boundary of the contact surface in the bolt connection structure to construct a dynamic pressure distribution function of the bolt connection structure. Then, the density function is solved based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement. The density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolt connection structure, thereby realizing the construction of the Iwan model with fewer parameters and better characterization effect, and greatly reducing the calculation complexity of the constructed Iwan model. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 It is a flow chart of the Iwan model modeling method of the bolt connection structure provided by the present invention; Figure 2 Schematic diagram of three pressure distribution functions provided by the present invention; Figure 3 is a schematic diagram of contact boundary evolution provided by the present invention; Figure 4 is a schematic diagram of discretized pressure distribution provided by the present invention; Figure 5 is a schematic diagram of the prediction of the preload correction parameters provided by the present invention; Figure 6 is a schematic diagram of pressure distribution under the adjusted linear pressure distribution function provided by the present invention; Figure 7 It is a schematic diagram of backbone curve parameter identification provided by the present invention; Figure 8 It is a structural schematic diagram of an Iwan model modeling device of a bolt connection structure provided by the present invention; Fig. 9 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] In view of the above problems, the present invention provides an Iwan model modeling method for a bolted connection structure, which realizes a linear pressure distribution function with fewer parameters and better characterization effect, so as to construct a density function of the dynamic Iwan model, thereby reducing the computational complexity of the Iwan model of the bolted connection structure obtained based on the modeling. Figure 1 FIG. 1 is a flow chart of the Iwan model modeling method of the bolt connection structure provided by the present invention, such as Figure 1 As shown, the method includes: Step 110, based on the contact boundary of the contact surface in the bolt connection structure, applying the linear pressure distribution function, constructing the dynamic pressure distribution function of the bolt connection structure; Here, the contact surface in the bolt connection structure may include the lower surface of the bolt head, the contact between the upper surface of the nut and the plate, the contact between the thread and the nut, and the contact between the plates. In addition, it should be noted that under the action of the preload, the bolt connection structure causes the plate to generate pressure, and the application of a tangential external load causes the pressure to change. The pressure distribution law can be described based on the existing model function, and the real pressure distribution law can be characterized. Commonly used pressure distribution functions include: Fernlund pressure distribution, linear pressure distribution, and Hz pressure distribution. The embodiment of the present invention calculates the pressure distribution value between the plates through a high-precision finite element model, and simplifies the pressure distribution law through a linear pressure distribution function. The linear pressure distribution function here can be based on the causal relationship between pressure and radius, idealizes the distribution law, and establishes a univariate linear regression. The least squares method can be used to identify the parameters in the linear pressure distribution function, and the linear pressure distribution function can be expressed as: ; In the formula, represents the linear pressure distribution function; represents a constant; represents the slope; Indicates the radius.

[0020] Specifically, the contact boundary of the contact surface in the bolted connection structure can be described based on the elliptic function. Then, the pressure evolution law between the plates can be described by applying the linear pressure distribution function, and then the dynamic pressure distribution function of the bolted connection structure can be constructed.

[0021] It should be noted that a normal preload of 1000N-15000N is applied in the high-precision finite element model, and a tangential displacement load of 0.05mm is set to solve the pressure distribution law between the contact surfaces of the upper and lower plates. The edge diameter of the screw hole is taken as the origin, and the pressure values ​​in the tangential tensile direction are extracted respectively.

[0022] Figure 2 is a schematic diagram of three pressure distribution functions provided by the present invention, such as Figure 2 As shown in the figure, under the condition of small preload, the three pressure distribution functions are well characterized. Under the condition of large preload, the three pressure distribution functions all have deviations at the edge of the screw hole, and the linear pressure and Fernlund pressure distributions have deviations at the farthest point of the screw hole. However, the Hz pressure distribution has a large deviation, which does not conform to the contact pressure distribution law of the plate in the finite element. Under different initial preloads, it can be seen from the deviation area that the fitting accuracy of the two is similar, and both can characterize the pressure distribution of the bolt connection contact surface. The Fernlund pressure distribution function is a quartic function, which contains 5 unknown parameters, while the linear pressure distribution has only 2 unknown parameters, which can simplify the calculation. Therefore, a linear function with fewer parameters, better characterization effect and simple structure is selected as the pressure distribution function to derive the density function expression of the Iwan model that can characterize the contact mechanism, thereby greatly reducing the complexity required for the calculation.

[0023] Step 120, solving the density function based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement; Specifically, the friction shear stress expression can be derived from the plate contact surface pressure through the Coulomb friction theory, and then the density function expression of the yield force and yield displacement can be derived. In detail, based on the contact area of ​​the contact surface and the friction shear stress, the contact area can be normalized to obtain the density function of the friction shear stress. Based on the mapping relationship between the friction shear stress and the yield force, and the density function of the friction shear stress, the density function of the yield force is obtained. Finally, based on the linear relationship between the yield force and the yield displacement, and the density function of the yield force, the density function of the yield displacement is derived.

[0024] Step 130: introducing the density function of the yield displacement into a general Iwan model to construct an Iwan model of the bolt connection structure.

[0025] Here, the general Iwan model is given by The ideal elastic-plastic Jenkins unit consists of a single sliding damper and a stiffness of The linear springs form an elastic-plastic Jenkins unit, and its maximum yield stress is Among them, the yield displacement Yield The relationship can be expressed as In the initial loading stage, the sliding damper is subjected to tangential tension T , the resulting displacement is x In addition, in the initial loading stage, the total tangential force of the bolted connection structure consists of two parts, namely the force generated by the yielded member and the force generated by the unyielded member.

[0026] Specifically, by introducing the density function of the yield displacement into the general Iwan model with residual stiffness, the dynamic backbone curve and hysteresis loop can be obtained, and the relationship between the dynamic linear pressure of the joint surface of the bolted connection structure and the dynamic characteristics can be established, that is, the Iwan model of the bolted connection structure is constructed.

[0027] The method provided by the embodiment of the present invention selects a linear pressure distribution function with fewer parameters and better characterization effect, and combines the contact boundary of the contact surface in the bolt connection structure to construct a dynamic pressure distribution function of the bolt connection structure. Then, the density function is solved based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement. The density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolt connection structure, which realizes the construction of the Iwan model with fewer parameters and better characterization effect, and greatly reduces the computational complexity of the constructed Iwan model.

[0028] Based on any of the above embodiments, step 110 includes: Based on the contact boundary of the contact surface, a linear pressure distribution function is applied to construct an initial dynamic pressure distribution function; Correcting the initial dynamic pressure distribution function to obtain a corrected dynamic pressure distribution function; Based on the preload correction parameter of the bolt connection structure, the corrected dynamic pressure distribution function is verified to obtain the dynamic pressure distribution function; The preload correction parameter is used to correct the deviation between the actual preload and the theoretical preload under the corrected dynamic pressure distribution function.

[0029] Here, when studying the evolution law of the contact boundary of the contact surface, Figure 3 is a schematic diagram of the contact boundary evolution provided by the present invention, such as Figure 3 As shown, a 1000N preload and a 0.04-0.30mm tangential displacement load are applied. T When the contact shape is ≤261N, the area around the screw hole shows a circular sticky state when there is no tangential force. With the application of tangential force, the sticky area gradually decreases, and the contact shape gradually evolves from a circle to an ellipse. T When the contact force is ≥261N, the contact area gradually transitions from a sticky state to a slipping state, and the slipping area continuously extends from the outside to the inside.x The directional slip length is shortened. y As the slip length increases, the contact area exceeds the plate boundary, and the plate "cuts off" the contact area. Under no tangential load conditions, the contact area is circular. Under tangential force, the contact area between the plates can be approximated as an ellipse. The tangential tension direction is defined as x , the vertical direction is y Therefore, the contact boundary shape can be approximated as an ellipse. The contact boundary can be expressed by the following formula: ; With the increase of tangential displacement load, the contact ellipse boundary changes gradually, the minor semi-axis shortens, the major semi-axis increases, and exceeds the maximum width of the plate. , Evolution value; the short semi-axis value decreases with the increase of tangential load, and the long semi-axis value increases with the increase of tangential load. The short semi-axis function conforms to exponential change, and the long semi-axis function conforms to linear change. The general formula is: ; ; In the formula, , , , , These are parameters to be identified. is the maximum value of the major semi-axis. According to the established finite element model, the parameters of the minor semi-axis and the major semi-axis are: , , , , , , the unit is mm.

[0030] Therefore, the contact area can be obtained by calculating the ellipse area based on the above formula: for: ; In the formula, Indicates the radius of the screw hole.

[0031] According to the major axis change formula, when When , the contact area gradually evolves and does not reach the maximum semi-major axis. When , a truncation area appears on the joint surface of the flat plates, and the elliptical contact area calculated by the above formula is too small.

[0032] Specifically, the contact boundary of the contact surface can be described based on the elliptic function, and the linear pressure distribution function can be applied to construct the initial dynamic pressure distribution function. =0, the maximum radius of the pressure distribution function is 12.33607mm. However, through the finite element identification of the contact edge function, it can be seen that the maximum pressure radius is 11.19226. Therefore, it is necessary to correct the maximum radius when the pressure is zero. Therefore, in order to improve the accuracy of the initial dynamic pressure distribution function, the initial dynamic pressure distribution function can be corrected by the constraint method or the offset method to obtain the corrected dynamic pressure distribution function.

[0033] Furthermore, in order to further improve the accuracy of the dynamic pressure distribution function, the modified dynamic pressure distribution function may be verified to obtain the final dynamic pressure distribution function. Figure 4 is a schematic diagram of the discretized pressure distribution provided by the present invention, such as Figure 4 As shown in the figure, in the sticking stage, the initial contact state is circular, and then under the action of static friction, the contact state gradually evolves into an ellipse. In the sliding stage, the initial contact state is an ellipse. Under the interaction of static friction and dynamic friction, as the tangential load increases, the radius (semi-short axis) reaching zero pressure gradually decreases, the semi-semi-long axis continues to increase, and finally cuts off at the maximum half-width of the plate. In this process, the slope of the ellipse gradually decreases, the pressure around the screw hole is the maximum value, and the maximum contact boundary pressure is zero. Discrete analysis of the linear pressure distribution is performed, and the contact area is divided into discrete ellipse. When , the discretized area can be approximated as the area of ​​the entire region. Therefore, by discretizing the contact area and correcting the linear pressure distribution, the error between the preload force after pressure correction and the theoretical preload force can be verified, and the accuracy of the corrected dynamic pressure distribution function can be verified.

[0034] In detail, assuming that the length of the minor axis of the ellipse keeps increasing equidistantly, and the major axis changes with the curvature and the minor axis, then The ellipticity gradually increases, that is, from 1 to Gradually increases. Therefore, the minor semi-axis, major semi-axis, and ellipticity of the i-th ellipse are: ; Therefore, the area of ​​the i-th ellipse is Discrete preload They are: ; ; Preload correction parameters It can be expressed as a dynamic equation that changes with the tangential external force: ; In the formula, is the theoretical preload value, which can be obtained through finite element software.

[0035] Then, the modified dynamic pressure distribution function is verified by the preload correction parameter of the bolt connection structure. Then, the modified dynamic pressure distribution function can be optimized based on the optimization algorithm to obtain a final accurate dynamic pressure distribution function with good characterization effect. In one embodiment, the preload value under the modified dynamic pressure distribution function can be calculated using Matlab software and compared with the theoretical preload. Analysis of different tangential forces , Discrete order The influence on the dynamic pressure distribution function. Based on the discrete 1000th order, the correction parameters are studied. Following tangential force of the changing relationship. Figure 5 is a schematic diagram of the prediction of the preload correction parameters provided by the present invention, such as Figure 5 As shown, areas A and C are The correction parameters of the B and D areas are The correction parameters obtained by the offset method are greater than those obtained by the correction method. When the calculated preload is greater than the theoretical preload, the pressure distribution function has a better characterization effect. Then, based on the Levenberg-Marquardt optimization algorithm, a nonlinear exponential decay fitting function is used. The modified parameter curve is iteratively calculated, the optimal solution of the function is taken, and multiple parameters of the exponential function are obtained. The formula is: ; In the formula, , , All of them are parameters, and the optimal solution can be obtained through algorithm iteration. Table 1 shows the fitting parameters of the nonlinear exponential function, as shown in the following table:

[0036] It should be noted that is the fitting accuracy. The closer its value is to 1, the better the fitting effect is. The fitting accuracy of the constraint method and the offset method is high, indicating that the fitting effect through the nonlinear exponential decay function is better. Introducing the linear pressure distribution function can make up for the contact area lost in the elliptical area formula. Therefore, the final dynamic pressure distribution function It can be expressed as: ; In the formula, is the constraint method or offset method, = 0, the pressure distribution function, the function of the longitudinal tangential force , function of the transverse tangential force . The formula can be simplified to: ; Compared with the assumption that the pressure curve needs to be corrected in the prior art, the method provided by the embodiment of the present invention has certain limitations. By verifying the corrected dynamic pressure distribution function based on the preload correction parameter of the bolt connection structure, the dynamic pressure distribution function is obtained, which greatly improves the accuracy of the dynamic pressure distribution function.

[0037] Based on any of the above embodiments, the contact boundary based on the contact surface is applied with a linear pressure distribution function to construct an initial dynamic pressure distribution function, including: Based on the tangential force and the maximum pressure value, the linear pressure distribution function is longitudinally adjusted, and based on the tangential force and the maximum contact radius of the contact surface, the linear pressure distribution function is transversely adjusted to obtain an adjusted linear pressure distribution function; Based on the contact boundary of the contact surface, applying the adjusted linear pressure distribution function to obtain the initial dynamic pressure distribution function; The contact boundary is described based on an elliptic function.

[0038] It should be noted that the linear pressure distribution function can describe the evolution law of pressure between plates, and the change of tangential force will lead to the change of maximum pressure value and maximum pressure radius. The pressure in the positive direction of the axis is analyzed by finite element evolution. r = 0, the pressure reaches its peak value, and as the pressure radius increases, the pressure value gradually decreases linearly to 0. The pressure peak area increases linearly with the tangential tension, and the radius reaching the zero pressure value decreases linearly with the tangential tension. Therefore, it is necessary to adjust the linear pressure distribution function in the lateral and longitudinal directions to compensate for the pressure changes caused by the tangential external load.

[0039] Specifically, in order to establish the dynamic change distribution function under different tangential tension conditions, it is necessary to add the longitudinal evolution coefficient of the linear pressure function. There is a linear relationship between the peak pressure and the tangential tension, so the pressure distribution function can be The formula for geometric doubling is: ; In the formula, the value calculated by the embodiment of the present invention is =2.41×10 -3 , is the tangential tension, is the peak pressure at T=0.

[0040] As the tangential external force increases, the radius when the pressure value reaches zero decreases linearly. The distance of the maximum radius is extracted by finite element analysis, and the pressure distribution function is adjusted laterally according to the linear function. The ratio of the lateral radius length is: ; In the formula, =9.22×10 -3 , for =0 when the maximum contact radius.

[0041] Therefore, the adjusted linear pressure distribution function with tangential load is: ; Further, based on the contact boundary of the contact surface, an adjusted linear pressure distribution function is applied to obtain an initial dynamic pressure distribution function.

[0042] It should be noted that the pressure distribution curve under tangential tension of T = 180N and 554N can be constructed based on adjusting the linear pressure distribution function and the finite element model. Figure 6 is a schematic diagram of pressure distribution under the adjusted linear pressure distribution function provided by the present invention, such as Figure 6 As shown, when the pressure is at the peak value, the optimized adjusted linear pressure distribution function has a high degree of overlap with the fitting function of the original dynamic pressure. When the pressure is zero, the radius of the optimized adjusted linear pressure distribution function is larger than the fitting curve of the original function, and the radii are: 10.77675mm, 10.02866mm and 7.5789mm, 6.7168mm respectively. There is a certain deviation between the two curves when the pressure is zero, but the overall fitting effect is good. Therefore, the accuracy of the adjusted linear pressure distribution function after adjustment in the embodiment of the present invention is proved.

[0043] exist =0, the maximum radius of the pressure distribution function is 12.33607mm. However, through the finite element identification results of the contact boundary function, it can be seen that the maximum pressure radius is 11.19226. Therefore, it is necessary to correct the maximum radius when the pressure is zero. Based on any of the above embodiments, the initial dynamic pressure distribution function is corrected to obtain a corrected dynamic pressure distribution function, including: When the pressure is zero, the maximum radius in the initial dynamic pressure distribution function is corrected based on the constraint method; Alternatively, the initial dynamic pressure distribution function is offset to obtain the modified dynamic pressure distribution function.

[0044] Specifically, it can be based on the constraint method, which = 0, so that the zero pressure value is located at the maximum value of the contact boundary. Alternatively, the linear function can be offset downward based on the offset method so that the pressure result is consistent with the contact boundary function. Based on any of the two correction methods, the initial dynamic pressure distribution function is corrected to obtain a corrected dynamic pressure distribution function.

[0045] In detail, based on the constraint method, =0, the dynamic pressure distribution function is expressed as: ; Based on the offset method, =0, the dynamic pressure distribution function is expressed as: ; Therefore, the two correction methods can be used to correct

[0046] The dynamic pressure distribution function is substituted into the above-mentioned adjusted dynamic pressure distribution function to obtain the modified dynamic pressure distribution function under different tangential forces: ; ; The method provided in an embodiment of the present invention corrects the maximum radius in the initial dynamic pressure distribution function based on the constraint method when the pressure is zero; or, offsets the initial dynamic pressure distribution function, thereby obtaining a more accurate corrected dynamic pressure distribution function.

[0047] Based on any of the above embodiments, the density function is solved based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement, including: Based on the dynamic pressure distribution function and the friction theory, friction shear stress is obtained; Based on the contact area of ​​the contact surface and the friction shear stress, the contact area is normalized to obtain a density function of the friction shear stress; Based on the mapping relationship between the friction shear stress and the yield force, and the density function of the friction shear stress, a density function of the yield force is obtained; Based on the linear relationship between the yield force and the yield displacement, and the density function of the yield force, a density function of the yield displacement is obtained.

[0048] Specifically, through Coulomb friction theory, the friction shear stress can be derived from the pressure on the contact surface of the flat plate. The expression is: ; In the formula, Represents the friction coefficient.

[0049] Under the action of tangential load, the contact surface of the plate changes from a sticky state to a sliding state. It gradually slides from the outer edge of the contact to the screw hole position and finally covers the entire contact surface. The area of ​​the sliding area can be expressed as the area of ​​the contact boundary ellipse and the The area of ​​the contact boundary ellipse here is s(r) It can be expressed as: ; Therefore, based on the contact area Frictional shear stress The contact area is normalized to obtain the area of ​​the slip region. s( ) :

[0050] Then, the density function of the friction shear stress can be obtained by differentiating the area of ​​the slip region. The density function of the friction shear stress is It can be expressed as:

[0051] Furthermore, based on the mapping relationship between friction shear stress and yield force, the mapping relationship can be expressed as: Among them, the mapping parameters and maximum pressure The mapping parameters can be derived from Following tangential force The dynamic relationship is: ; Therefore, the density function of yield force can be expressed as: ; In the formula, Yield The density function of .

[0052] Finally, based on the linear relationship between the density distribution function of yield force and yield displacement, and the density function of yield force, the density function of yield displacement can be derived. Here, the linear relationship between the density distribution function of yield force and yield displacement can be expressed as: ; ; Therefore, the density function of the yield displacement here can be derived as: ; In the formula, Yield displacement The density function of .

[0053] It should be noted that under the same yield displacement conditions, the greater the tangential force, the greater the density function. Before the macro slippage, as the yield displacement increases, the density function gradually decreases, and its rate gradually tends to be flat. When the function reaches 0, the greater the tangential force, the greater the yield displacement value.

[0054] Based on any of the above embodiments, the density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolted connection structure, including: Based on the density function of the yield displacement, the backbone curve of the general Iwan model is solved piecewise to obtain the backbone curve; Based on the backbone curve of the Iwan model, a hysteresis loop is obtained; Based on the backbone curve and the hysteresis loop, an Iwan model of the bolt connection structure is constructed.

[0055] Specifically, the density function of the yield displacement can be substituted into the formula to solve the backbone curve of the general Iwan model in sections. Matlab software can be used to perform complex integration on the backbone curve of the Iwan model of the linear spring. The adaptive quadrature method is used to calculate the value of the integral in an iterative form. The backbone curve and hysteresis loop of the Iwan model are calculated with minimum error. Here, the backbone curve expression of the Iwan model of the linear spring is introduced as: ; In the formula, T(x) express stage, i.e. the backbone curve of the micro-slip nonlinear stage; represents the residual stiffness.

[0056] Since Coulomb friction theory cannot be applied to the sticking stage, the sticking stage shows a linear change, which is proportional to the initial stiffness. The macro-slip stage also shows a linear change, which is proportional to the residual stiffness. Therefore, the backbone curve solution expression of the sticking stage is: ; The backbone curve solution expression in the macro-sliding stage is: ; Figure 7 is a schematic diagram of backbone curve parameter identification provided by the present invention, such as Figure 7 As shown, the backbone curves corresponding to the sticking stage, micro-slip stage and macro-slip stage are represented respectively.

[0057] Furthermore, the hysteresis loop of the model can be derived from the backbone curve according to the Masing criterion. Here, the expressions of the hysteresis loops in the loading and unloading stages can be: ; In order to facilitate the direct application of the hysteresis loop in the existing model, the criterion is replaced by mathematics, and the hysteresis loop in the loading and unloading stages can be expressed as: ; It should be noted that the dynamic Iwan model based on linear pressure distribution has a total of 10 parameters: stiffness , function of the transverse tangential force g(T) , the function of the longitudinal tangential force f(T) ,constant , slope , Preload correction parameters , friction coefficient , Screw hole radius , Macro sliding displacement point and cyclic displacement A Parameter identification can be performed by finite element software or experimental methods to construct the backbone curve and hysteresis loop of the Iwan model.

[0058] The method proposed in the embodiment of the present invention can more accurately simulate the interaction between bolts and plates when they are subjected to stress. The contact surface between the plates is circular when no stress is applied, and gradually evolves into an elliptical shape when subjected to tangential force. When there is no tangential force, the area around the screw hole shows a circular sticky state. With the application of tangential force, the sticky area gradually decreases, and the contact shape gradually evolves from a circle to an ellipse, and does not reach the maximum major semi-axis. When the contact area gradually transitions from a sticky state to a slipping state, the slipping area continues to extend from the outside to the inside. The directional slip length is shortened. As the slip length increases, the contact area exceeds the plate boundary, and the plate "cuts off" the contact area. Among various pressure distribution functions, linear pressure distribution has the advantages of simple structure and fewer parameters, which can characterize the pressure distribution law of the bonding surface. , Vertical The pressure was corrected by the constraint method and the offset method, and the corrected preload was verified. Through the evolution process under different tangential forces, the dynamic pressure distribution function was constructed, providing a theoretical basis for the establishment of the Iwan model density function.

[0059] Through Coulomb friction theory, the friction shear stress expression is derived. And through the normalized contact area and dynamic mapping parameters, the density distribution function of the yield displacement is derived, which is the core of the Iwan model. The specific parameters in the model are identified by the finite element method, and the parameter identification under four preload conditions is carried out. In addition, the accuracy of the Iwan model prediction is verified by not considering the contact evolution and the dynamic change contact evolution. The linear change is adopted in the viscous stage, and the density function of the yield displacement is combined in the micro-slip stage. The restoring force-displacement curve is constructed by the iterative integration of the Iwan model. The macro-slip stage is also a linear stage, and its change slope is the residual stiffness. The average value of the Pearson product difference correlation coefficient of the stiffness degradation model can reach 0.95995, while the correlation coefficient of the Iwan model established in the prior art is 0.774, and the Iwan model established in the embodiment of the present invention is improved by 19.4%. The average correlation coefficient of the backbone curve reaches 0.96058, and the degree of agreement is high. The accuracy of the Iwan model constructed in the embodiment of the present invention is proved, and the connection between the dynamic linear pressure of the joint surface of the bolt structure and the dynamic characteristics is established.

[0060] Based on any of the above embodiments, Figure 8 : is a structural schematic diagram of the Iwan model modeling device of the bolt connection structure provided by the present invention, such as Figure 8 As shown, the device comprises: A linear pressure distribution unit 810, based on a contact boundary of a contact surface in a bolt connection structure, applies a linear pressure distribution function to construct a dynamic pressure distribution function of the bolt connection structure; A solving unit 820 solves the density function based on the dynamic pressure distribution function and the friction theory to obtain the density function of the yield displacement; The modeling unit 830 introduces the density function of the yield displacement into the general Iwan model to construct the Iwan model of the bolt connection structure.

[0061] The device provided by the embodiment of the present invention selects a linear pressure distribution function with fewer parameters and better characterization effect, and combines the contact boundary of the contact surface in the bolt connection structure to construct a dynamic pressure distribution function of the bolt connection structure. Then, the density function is solved based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement. The density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolt connection structure, which realizes the construction of the Iwan model with fewer parameters and better characterization effect, and greatly reduces the computational complexity of the constructed Iwan model.

[0062] Based on any of the above embodiments, the linear pressure distribution unit is specifically used for: Based on the contact boundary of the contact surface, a linear pressure distribution function is applied to construct an initial dynamic pressure distribution function; Correcting the initial dynamic pressure distribution function to obtain a corrected dynamic pressure distribution function; Based on the preload correction parameter of the bolt connection structure, the corrected dynamic pressure distribution function is verified to obtain the dynamic pressure distribution function; The preload correction parameter is used to correct the deviation between the actual preload and the theoretical preload under the corrected dynamic pressure distribution function.

[0063] Based on any of the above embodiments, the linear pressure distribution unit is further specifically used for: Based on the tangential force and the maximum pressure value, the linear pressure distribution function is longitudinally adjusted, and based on the tangential force and the maximum contact radius of the contact surface, the linear pressure distribution function is transversely adjusted to obtain an adjusted linear pressure distribution function; Based on the contact boundary of the contact surface, applying the adjusted linear pressure distribution function to obtain the initial dynamic pressure distribution function; The contact boundary is described based on an elliptic function.

[0064] Based on any of the above embodiments, the linear pressure distribution unit is further specifically used for: When the pressure is zero, the maximum radius in the initial dynamic pressure distribution function is corrected based on the constraint method; Alternatively, the initial dynamic pressure distribution function is offset to obtain the modified dynamic pressure distribution function.

[0065] Based on any of the above embodiments, the solving unit is specifically used for: Based on the dynamic pressure distribution function and the friction theory, friction shear stress is obtained; Based on the contact area of ​​the contact surface and the friction shear stress, the contact area is normalized to obtain a density function of the friction shear stress; Based on the mapping relationship between the friction shear stress and the yield force, and the density function of the friction shear stress, a density function of the yield force is obtained; Based on the linear relationship between the yield force and the yield displacement, and the density function of the yield force, a density function of the yield displacement is obtained.

[0066] Based on any of the above embodiments, the modeling unit is specifically used for: Based on the density function of the yield displacement, the backbone curve of the general Iwan model is solved piecewise to obtain the backbone curve; Based on the backbone curve of the Iwan model, a hysteresis loop is obtained; Based on the backbone curve and the hysteresis loop, an Iwan model of the bolt connection structure is constructed.

[0067] Fig. 9 An example of a physical structure diagram of an electronic device is shown in FIG. Fig. 9 As shown, the electronic device may include: a processor 910, a communication interface 920, a memory 930 and a communication bus 940, wherein the processor 910, the communication interface 920 and the memory 930 communicate with each other through the communication bus 940. The processor 910 may call the logic instructions in the memory 930 to execute the Iwan model modeling method of the bolt connection structure, the method comprising: based on the contact boundary of the contact surface in the bolt connection structure, applying the linear pressure distribution function, constructing the dynamic pressure distribution function of the bolt connection structure; solving the density function based on the dynamic pressure distribution function and the friction theory to obtain the density function of the yield displacement; introducing the density function of the yield displacement into the general Iwan model to construct the Iwan model of the bolt connection structure.

[0068] In addition, the logic instructions in the above-mentioned memory 930 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0069] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the Iwan model modeling method of the bolted connection structure provided by the above methods. The method includes: based on the contact boundary of the contact surface in the bolted connection structure, applying a linear pressure distribution function to construct a dynamic pressure distribution function of the bolted connection structure; solving the density function based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement; introducing the density function of the yield displacement into a general Iwan model to construct the Iwan model of the bolted connection structure.

[0070] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it is implemented to execute the Iwan model modeling method of the bolted connection structure provided by the above-mentioned methods. The method includes: based on the contact boundary of the contact surface in the bolted connection structure, applying a linear pressure distribution function to construct a dynamic pressure distribution function of the bolted connection structure; solving the density function based on the dynamic pressure distribution function and friction theory to obtain a density function of the yield displacement; introducing the density function of the yield displacement into a general Iwan model to construct the Iwan model of the bolted connection structure.

[0071] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0072] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An Iwan model modeling method for a bolt connection structure, characterized in that: include: Based on the contact boundary of the contact surface in the bolt connection structure, a linear pressure distribution function is applied to construct a dynamic pressure distribution function of the bolt connection structure; Solving the density function based on the dynamic pressure distribution function and friction theory to obtain the density function of the yield displacement; The density function of the yield displacement is introduced into the general Iwan model to construct the Iwan model of the bolt connection structure.

2. The Iwan model modeling method of the bolt connection structure according to claim 1, characterized in that: The method of applying a linear pressure distribution function based on a contact boundary of a contact surface in a bolt connection structure to construct a dynamic pressure distribution function of the bolt connection structure includes: Based on the contact boundary of the contact surface, a linear pressure distribution function is applied to construct an initial dynamic pressure distribution function; Correcting the initial dynamic pressure distribution function to obtain a corrected dynamic pressure distribution function; Based on the preload correction parameter of the bolt connection structure, the corrected dynamic pressure distribution function is verified to obtain the dynamic pressure distribution function; The preload correction parameter is used to correct the deviation between the actual preload and the theoretical preload under the corrected dynamic pressure distribution function.

3. The Iwan model modeling method of the bolt connection structure according to claim 2, characterized in that: The contact boundary based on the contact surface is applied with a linear pressure distribution function to construct an initial dynamic pressure distribution function, including: Based on the tangential force and the maximum pressure value, the linear pressure distribution function is longitudinally adjusted, and based on the tangential force and the maximum contact radius of the contact surface, the linear pressure distribution function is transversely adjusted to obtain an adjusted linear pressure distribution function; Based on the contact boundary of the contact surface, applying the adjusted linear pressure distribution function to obtain the initial dynamic pressure distribution function; The contact boundary is described based on an elliptic function.

4. The Iwan model modeling method of the bolt connection structure according to claim 2, characterized in that: The correcting the initial dynamic pressure distribution function to obtain a corrected dynamic pressure distribution function includes: When the pressure is zero, the maximum radius in the initial dynamic pressure distribution function is corrected based on the constraint method; Alternatively, the initial dynamic pressure distribution function is offset to obtain the modified dynamic pressure distribution function.

5. The Iwan model modeling method for a bolt connection structure according to any one of claims 1 to 4, characterized in that: The density function is solved based on the dynamic pressure distribution function and the friction theory to obtain the density function of the yield displacement, including: Based on the dynamic pressure distribution function and the friction theory, friction shear stress is obtained; Based on the contact area of ​​the contact surface and the friction shear stress, the contact area is normalized to obtain a density function of the friction shear stress; Based on the mapping relationship between the friction shear stress and the yield force, and the density function of the friction shear stress, a density function of the yield force is obtained; Based on the linear relationship between the yield force and the yield displacement, and the density function of the yield force, a density function of the yield displacement is obtained.

6. The Iwan model modeling method for a bolt connection structure according to any one of claims 1 to 4, characterized in that: The step of introducing the density function of the yield displacement into a general Iwan model to construct the Iwan model of the bolt connection structure comprises: Based on the density function of the yield displacement, the backbone curve of the general Iwan model is solved piecewise to obtain the backbone curve; Based on the backbone curve of the Iwan model, a hysteresis loop is obtained; Based on the backbone curve and the hysteresis loop, an Iwan model of the bolt connection structure is constructed.

7. An Iwan model modeling device for a bolt connection structure, characterized in that: include: A linear pressure distribution unit, based on a contact boundary of a contact surface in a bolt connection structure, applies a linear pressure distribution function to construct a dynamic pressure distribution function of the bolt connection structure; A solving unit solves the density function based on the dynamic pressure distribution function and the friction theory to obtain the density function of the yield displacement; The modeling unit introduces the density function of the yield displacement into the general Iwan model to construct the Iwan model of the bolt connection structure.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the Iwan model modeling method of the bolt connection structure according to any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the Iwan model modeling method for the bolt connection structure according to any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the Iwan model modeling method for the bolt connection structure according to any one of claims 1 to 6 is implemented.

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