CN117131634B - Method, system, equipment and medium for constructing dynamics model of bolt connection structure - Google Patents
Method, system, equipment and medium for constructing dynamics model of bolt connection structure Download PDFInfo
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Abstract
The invention discloses a method, a system, equipment and a medium for constructing a dynamic model of a bolt connection structure, which relate to the field of mechanical engineering, and the method comprises the following steps: acquiring force-displacement curve experimental data of a bolt connection structure; obtaining a first derivative of displacement in the experimental data of the force-displacement curve to obtain experimental data of the rigidity-displacement curve of the bolt connection structure; modeling the connection rigidity of the bolt connection structure to obtain a rigidity reduction function; identifying parameters to be determined in the stiffness reduction function by utilizing stiffness-displacement curve experimental data; determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination; and constructing a rigidity-Iwan model of the bolt connection structure according to the density function. The invention can improve the calculation precision of equivalent modeling of the bolt connection structure.
Description
Technical Field
The invention relates to the field of mechanical engineering, in particular to a method, a system, equipment and a medium for constructing a dynamic model of a bolt connection structure.
Background
The bolted structure introduces nonlinear mechanical properties into the system, and when such structures are analyzed by common commercial finite element software, common methods are building detailed models, beam cell connection models, and rigid cell connection models. The beam unit and the rigid unit are connected with the model for quick calculation, but the calculation precision is lost, the calculation precision of the detailed model is higher, and the problem of overlong calculation time exists. The Iwan model can describe the contact nonlinear mechanical behavior of the bolted structure, but because of the limitation of the applicability of the density function used, the accuracy is limited by the mathematical model of the density function used in the identification of the contact nonlinear mechanical behavior of the bolted structure, so that the problem of calculation accuracy also exists.
Disclosure of Invention
Based on the above, the embodiment of the invention provides a method, a system, equipment and a medium for constructing a dynamic model of a bolt connection structure, so as to improve the calculation precision of equivalent modeling of the bolt connection structure.
In order to achieve the above object, the embodiment of the present invention provides the following solutions:
a method for constructing a dynamic model of a bolt connection structure comprises the following steps:
acquiring force-displacement curve experimental data of a bolt connection structure;
obtaining a first derivative of displacement in the force-displacement curve experimental data to obtain rigidity-displacement curve experimental data of the bolt connection structure;
modeling the connection rigidity of the bolt connection structure to obtain a rigidity reduction function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection;
identifying parameters to be determined in the stiffness reduction function by utilizing the stiffness-displacement curve experimental data;
determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination;
constructing a rigidity-Iwan model of the bolt connection structure according to the density function; the rigidity-Iwan model is used for representing the contact nonlinear mechanical property of the bolt connection structure; the stiffness-Iwan model includes: bone line equations and cyclic excitation equations.
Optionally, the expression of the stiffness decreasing function is:
wherein,a microscopic slippage starting point of the bolt connection structure; />A macroscopic slippage starting point of the bolt connection structure; k (K) 1 Initial rigidity before microscopic sliding occurs for the bolt connection structure; k (K) ∞ Residual rigidity after macroscopic sliding of the bolt connection structure; Δk is the amount of stiffness abrupt change of the bolted connection structure at the point where macroscopic slippage occurs; k (x) is a stiffness decreasing function; k (K) nol (x) As a function of the stiffness variation with respect to displacement x; />For micro-sliding starting point of bolt connection structure>The rigidity change function of the position takes a value; />For macroscopic sliding starting point of the bolt connection structure>The rigidity change function of the position takes a value; a, a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 And c 4 Are all distribution parameters; the parameters to be determined in the stiffness reduction function include:K 1 、K ∞ 、ΔK、a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 and c 4 。
Optionally, the expression of the density function is:
wherein ρ (x) is a density function with respect to displacement x; k (x) is a stiffness decreasing function; k (K) nol (x) As a function of displacement x;a microscopic slippage starting point of the bolt connection structure; />A macroscopic slippage starting point of the bolt connection structure; />A point which is infinitely far away after macroscopic sliding of the bolt connection structure; Δk is the amount of stiffness abrupt change of the bolted connection structure at the point where macroscopic slippage occurs; k (K) ∞ Residual rigidity after macroscopic sliding of the bolt connection structure; />For input of +.>Is a sea-going step function; />For input of +.>Is a sea-going step function; />For input of +.>Dirac impulse function; />For input of +.>Dirac impulse functions of (a).
Optionally, the equation of bone line has the expression:
wherein F (x) is the force experienced at displacement x;for +.>Is a function of density of (a).
Optionally, the cyclic excitation equation includes: a force-displacement relationship integral expression of the compression stroke and a force-displacement relationship integral expression of the tension stroke;
the force-displacement relationship integral expression of the compression stroke is:
wherein F is C (x) Representing the force experienced at displacement x in the compression stroke; a represents the amplitude of the input periodic cyclical stimulus;
the force-displacement relationship integral expression of the stretching stroke is as follows:
wherein F is T (x) Representing the force experienced at displacement x during the stretching stroke.
Optionally, determining the density function of the bolting structure according to the stiffness decreasing function after the parameter determination specifically includes:
and (3) solving a first derivative of the displacement in the rigidity decreasing function after the parameter determination and taking the opposite number to obtain a density function of the bolt connection structure.
Optionally, acquiring force-displacement curve experimental data of the bolting structure specifically includes:
and carrying out a quasi-static experiment of unidirectional stretching or unidirectional compression on the bolt connection structure from the static balance position to obtain experimental data of a force-displacement curve.
The invention also provides a system for constructing the dynamics model of the bolt connection structure, which comprises the following steps:
the first data acquisition module is used for acquiring force-displacement curve experimental data of the bolt connection structure;
the second data calculation module is used for obtaining a first derivative of the displacement in the force-displacement curve experimental data to obtain the rigidity-displacement curve experimental data of the bolt connection structure;
the rigidity descending function construction module is used for modeling the connection rigidity of the bolt connection structure to obtain a rigidity descending function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection;
the parameter identification module is used for identifying parameters to be determined in the rigidity descending function by utilizing the rigidity-displacement curve experimental data;
the density function determining module is used for determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination;
the rigidity-Iwan model construction module is used for constructing a rigidity-Iwan model of the bolt connection structure according to the density function; the rigidity-Iwan model is used for representing the contact nonlinear mechanical property of the bolt connection structure; the stiffness-Iwan model includes: bone line equations and cyclic excitation equations.
The invention also provides electronic equipment, which comprises a memory and a processor, wherein the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic equipment to execute the method for constructing the dynamic model of the bolt connection structure.
The invention also provides a computer readable storage medium storing a computer program which when executed by a processor implements the above method for constructing a dynamic model of a bolting structure.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the embodiment of the invention, the Stiffness-Iwan Model (S-Iwan Model) is constructed by utilizing the Stiffness-decreasing Function (S-D Function) to describe the contact nonlinear mechanical behavior of the bolt connection structure, so that the dynamic characteristic equivalence of the specific bolt connection structure is realized, the nonlinear dynamic performance of the bolt connection structure is reflected better on the premise of not consuming a large amount of calculation resources and calculation cost, and the calculation precision of the equivalent modeling of the bolt connection structure is improved. Compared with a specific bolt structure model, the calculation time is shortened; compared with the traditional Iwan model, the calculation accuracy is improved; for a dynamic calculation scene containing a bolt connection structure, the dynamic calculation efficiency is effectively improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for constructing a dynamic model of a bolting structure according to an embodiment of the present invention;
FIG. 2 is a schematic view of a single bolt connection plate structure according to an embodiment of the present invention;
FIG. 3 is a schematic view of the dimensions of a first single bolt connection plate according to an embodiment of the present invention;
FIG. 4 is a schematic illustration of dimensions of a second single bolt web applied in accordance with an embodiment of the present invention;
FIG. 5 is a schematic diagram of experimental data of displacement excitation 1 according to an embodiment of the present invention;
FIG. 6 is a graph illustrating a density function provided by an embodiment of the present invention;
FIG. 7 is a schematic diagram of experimental data and an S-Iwan model bone line curve provided by an embodiment of the present invention;
FIG. 8 is a schematic diagram of experimental data and a hysteresis curve of an S-Iwan model provided by an embodiment of the present invention;
FIG. 9 is a graph showing experimental data and S-Iwan model bone line curve errors provided by an embodiment of the present invention;
FIG. 10 is a graph showing experimental data and S-Iwan model stiffness provided in an embodiment of the present invention;
fig. 11 is a block diagram of a dynamic model construction system for a bolting structure according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described below with reference to the accompanying drawings in the embodiments of the present invention.
The invention aims to provide a method, a system, equipment and a medium for constructing a dynamic model of a bolt connection structure, wherein a rigidity-Iwan model is constructed through a rigidity reduction function to describe the contact nonlinear mechanical behavior of the bolt connection structure, so that the calculation precision of equivalent modeling of the bolt connection structure is improved.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The bolt connection structure has strong nonlinear mechanical characteristics, and the connection rigidity of the bolt connection structure shows nonlinear change in the sliding process of each friction surface influenced by tangential force, so that the force-displacement relationship is also nonlinear relation change. Fractal contact theory is the basis of many contact and friction theories, and is characterized in that the contact condition is assumed to be that a rigid surface and a rough surface are contacted, and the heights of microprotrusions with the same curvature radius in the rough surface are assumed to meet Gaussian distribution.
Fractal contact theory attempts to analyze from a microscopic perspective, while there are also many theories and models such as Iwan models, which model analysis from macroscopic effects. According to the embodiment, the rigidity reduction function is established, the novel rigidity-Iwan model is obtained through deduction and used for describing the contact nonlinear mechanical behavior of the bolt connection structure, and compared with the traditional Iwan model, the calculation accuracy is improved. The following describes each embodiment in detail.
Example 1
Referring to fig. 1, the method for constructing a dynamic model of a bolting structure according to the present embodiment includes:
step 101: and acquiring experimental data of a force-displacement curve of the bolt connection structure.
The method specifically comprises the following steps: and carrying out a quasi-static experiment of unidirectional stretching or unidirectional compression on the bolt connection structure from the static balance position to obtain experimental data of a force-displacement curve.
Step 102: and (3) obtaining a first derivative of the displacement in the force-displacement curve experimental data to obtain the rigidity-displacement curve experimental data of the bolt connection structure.
Step 103: modeling the connection rigidity of the bolt connection structure to obtain a rigidity reduction function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection.
The method comprises the steps of carrying out mathematical modeling on the connection rigidity of a bolt connection structure by adopting four Gaussian distribution functions based on an Iwan model, constructing a rigidity reduction function, converting the rigidity reduction function into a density function through a conversion relation with the density function after the rigidity reduction function is established, and establishing a rigidity-Iwan model based on the density function.
The expression of the rigidity decreasing function is a segmented expression, specifically:
wherein,a microscopic slippage starting point of the bolt connection structure; />A macroscopic slippage starting point of the bolt connection structure; k (K) 1 Initial rigidity before microscopic sliding occurs for the bolt connection structure; k (K) ∞ Residual rigidity after macroscopic sliding of the bolt connection structure; Δk is the amount of stiffness abrupt change of the bolted connection structure at the point where macroscopic slippage occurs; k (K) nol (x) Defined as a stiffness variation function with respect to displacement x; from constant stiffness K 1 、K ∞ And a stiffness variation function K with respect to displacement x nol (x) The rigidity decreasing function K (x) is formed together, and the K (x) describes the decreasing change condition of the rigidity of the whole process of the bolt connection structure from the time before micro sliding to the time after macro sliding; />For micro-sliding starting point of bolt connection structure>The stiffness change function of the location takes a value, and the stiffness decrease function K (x) of the location is continuous; />For macroscopic sliding starting point of the bolt connection structure>Rigidity of the locationThe change function takes the value, and the rigidity decreasing function K (x) at the position has mutation, namely is discontinuous; a, a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 And c 4 Are all distribution parameters; the parameters to be determined in the stiffness reduction function include: />K 1 、K ∞ 、ΔK、a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 And c 4 ；/>The expression "defined as".
The segmented expression of the stiffness reduction function can be equivalently reconstructed into an equation through a Haifenesin step function H (x), and the reconstructed expression is as follows:
a point which is infinitely far away after macroscopic sliding of the bolt connection structure; h (x) is a Haifenesin step function;for input of +.>Is a sea-going step function; />For input of +.>Is a sea-going step function; />For input of +.>Is a sea-going step function of (c).
One of the main characteristics of the rigidity decreasing function is that the nonlinear phase of the rigidity change of the bolt connection structure is expressed by a Gaussian distribution form; the second main characteristic is that aiming at the diversity of the concrete structure of the bolt connection, the adaptability of the rigidity decreasing function is enhanced, and the function expression of the four groups of Gaussian distribution sub-components to the nonlinear stage is adopted; the third main characteristic is that the rigidity decreasing function has continuous rigidity change at the microscopic sliding point, discontinuous rigidity change at the macroscopic sliding point, and abrupt quantity.
Step 104: and identifying parameters to be determined in the stiffness reduction function by using the stiffness-displacement curve experimental data.
Step 105: and determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination.
Specifically, the first derivative of the displacement in the stiffness decreasing function after the parameter determination is calculated and the opposite number is obtained, so that the density function of the bolt connection structure is obtained. The density function is a function of the density of the stiffness-Iwan model. The expression of the density function is:
wherein ρ (x) is a density function with respect to displacement x; delta (x) is a dirac impulse function;is input asDirac impulse function; />For input of +.>Dirac impulse functions of (a).
Step 106: and constructing a rigidity-Iwan model of the bolt connection structure according to the density function.
The stiffness-Iwan model is used to characterize the contact nonlinear mechanical properties of the bolted joint. The stiffness-Iwan model includes: bone line equations and cyclic excitation equations. The cyclic excitation equation includes: a force-displacement relationship integral expression of the compression stroke and a force-displacement relationship integral expression of the tension stroke.
The expression of the bone line equation is:
wherein F (x) is the force experienced at displacement x;for +.>Is a function of density of (a).
The bone line equation reflects the dynamics of the bolt connection structure under the action of tangential directional unidirectional excitation from an initial state, and the quality of the curve fitting precision of the bone line equation directly reflects whether the stiffness-Iwan model (namely an equivalent model) is effective or not and influences the fitting precision of the tangential directional periodic cyclic excitation.
If the input excitation is a periodic excitation and the amplitude is A, the compression stroke is represented by a subscript C, and the tension stroke is represented by a subscript T. The force-displacement relationship integral expression of the compression stroke is:
wherein F is C (x) Representing the force experienced at displacement x in the compression stroke; a represents the amplitude of the input periodic cyclical stimulus.
The compression stroke equation and the tension stroke equation of the stiffness-Iwan model satisfy the map assumption: f (F) C (x)＝-F T (-x)。
The force-displacement relationship integral expression for the stretch stroke is:
F T (x) Representing the force experienced at displacement x during the stretching stroke.
The force-displacement curve of the bolt connection structure can form a hysteresis loop under periodic cyclic excitation, and the area surrounded by the hysteresis loop represents the energy loss of the structure under periodic excitation, so that the fitting precision of the hysteresis loop directly reflects the calculation precision of the energy loss.
The bolted connection may introduce nonlinear mechanical properties into the system, and a dynamic model of the bolted connection is typically introduced when analyzing or designing the system containing the bolted connection. According to the embodiment of the invention, from the perspective of constructing the rigidity descending function, a density function with stronger applicability to the contact nonlinear mechanical behavior of the bolt connection structure is deduced, and a rigidity-Iwan model with higher precision is constructed by using the density function, so that a system with the bolt connection structure can be analyzed or designed more accurately.
In practical application, for a specific bolt connecting piece, one implementation process of the method for constructing the dynamic model of the bolt connecting structure is as follows: for a certain bolt connecting piece, an equivalent model of the bolt connecting structure can be built by constructing an S-Iwan model only by obtaining a group of force-displacement curve data through experiments. Specific:
s1, carrying out unidirectional stretching or unidirectional compression quasi-static experiments on the bolt connecting piece to obtain experimental data of a force-displacement curve.
The method comprises the steps of carrying out unidirectional stretching or unidirectional compression quasi-static experiments on the bolt connecting piece from a static balance position, wherein one end is used as a fixed constraint end, the other end is used as a load input end, and recording experimental data of force-displacement curves from the moment of applying excitation until a period of macroscopic slippage occurs.
S2, the first derivative of the obtained force-displacement curve experimental data on the displacement x is obtained, and the stiffness-displacement curve experimental data are obtained.
And S3, carrying out parameter identification on the S-D function by utilizing stiffness-displacement curve experimental data.
Among the parameters to be determinedK 1 、K ∞ The delta K can be determined according to the force-displacement curve and the rigidity-displacement curve, and the Gaussian item distribution parameter a 1 ～c 4 The determination can be performed by means of a numerical calculation tool such as commercial software Matlab and the like in a curve parameter fitting mode.
S4, obtaining a density function according to the conversion relation between the S-D function and the density function.
And according to the definition of the density function, solving a first order derivative of the S-D function on the displacement x and taking the opposite number to obtain the density function of the S-Iwan model.
S5, constructing an S-Iwan model according to the obtained density function.
After the density function is obtained, a bone line equation and a cyclic excitation equation of the S-Iwan model can be obtained based on the density function, and specific expressions of the equations are not described herein.
The S-Iwan model can better calculate the force-displacement curve and energy loss under the unidirectional load working condition and the cyclic load working condition.
In order to verify the effectiveness of the above method, a case based on a virtual experiment is given below, and the result of the case shows that the S-Iwan model for the bolting structure has higher calculation accuracy, specifically as follows:
taking a finite element model of a single-bolt connection plate structure as an example, the method of the above embodiment of the present invention is described. Fig. 2 is a schematic view of a structure of a single bolt connection plate, wherein the single bolt connection plate for fixing end is a first single bolt connection plate, the size of which is shown in fig. 3, and the single bolt connection plate for applying load end is a second single bolt connection plate, the size of which is shown in fig. 4.
The three parts (a), (b) and (c) in fig. 3 are respectively a front view, a side view and a top view of the first single bolt connecting plate, and referring to fig. 3, the total length of the first single bolt connecting plate is 155mm, the total width is 40mm and the total thickness is 8mm; the length direction is divided into three sections of 50mm, 52mm and 53mm, and the thicknesses of the corresponding plates are 8mm, 4mm and 3.5mm respectively; the diameter of the through hole is 11mm, and the through hole is positioned at a position 20mm away from the long side and 25mm away from the short side.
The three parts (a), (b) and (c) in fig. 4 are respectively a front view, a side view and a top view of the second single bolt connecting plate, and referring to fig. 4, the total length of the second single bolt connecting plate is 155mm, the total width is 40mm and the total thickness is 8mm; the length direction is divided into three sections of 50mm, 52mm and 53mm, and the thicknesses of the corresponding plates are 8mm, 3mm and 2.5mm respectively; the diameter of the through hole is 11mm, and the through hole is positioned at a position 20mm away from the long side and 25mm away from the short side.
The upper and lower faces of the first single bolt-connecting plate are fixedly restrained, the reference numeral 1 in fig. 2 indicates the fixed restraint, and the linear displacement excitation is applied to the second single bolt-connecting plate:
displacement excitation 1: unidirectional excitation, wherein the amplitude A is 0.1mm;
displacement excitation 2: the amplitude A of the cyclic excitation is 0.1mm;
the bolt pretightening force 6000N is applied, the pretightening force direction is shown as F1 in fig. 2, and the direction of applying linear displacement excitation to the second single bolt connecting plate is shown as F2 in fig. 2. The contact surfaces of the nut and the screw are in binding contact, all other contact surfaces are in friction contact, and the friction coefficient is set to be 0.2.
The first step: the single bolt connection plate structure is just an application case of the present invention, and the actual bolt connection structure can be different. Boundary condition settings are performed on the model as described in fig. 2, and force-displacement data are analyzed and recorded by finite element software. If a physical test mode is adopted, the corresponding force and displacement are recorded by using a sensor and a corresponding sensing signal acquisition system, and the data processing method and effect of the subsequent steps are not affected.
And a second step of: and extracting action reaction force data of the fixed end or any one end of the input end from the input virtual experimental data with the type of displacement excitation 1, forming a force-displacement curve with the input displacement load, and obtaining a first order derivative of displacement to obtain a stiffness-displacement curve, as shown in figure 5.
And a third step of: the undetermined parameters of the S-D function are determined by an experimental force-displacement curve and an experimental rigidity-displacement curve, wherein the undetermined parameters can be conveniently obtained by two curvesK 1 、K ∞ Δk, see table 1 below; gaussian term distribution parameter a 1 ～c 4 The determination can be performed by means of a numerical calculation tool such as commercial software Matlab by means of curve parameter fitting, see table 2 below, with subscript i=1, 2,3,4 in table 2.
TABLE 1 Curve identification parameters
TABLE 2 Gaussian distribution parameter identification
From fig. 5, it can be analyzed that: the rigidity value of the rigidity curve is easy to know to decline from the beginning, and the rigidity value can be identified according to definition0mm; the linear property can be restored from non-linear property through the force-displacement curve and the rigidity curveIt is known that the bolted connection turns from micro-slip to macro-slip, identifiable by definition +.>0.060756mm; determine->Then according to definition, K can be obtained 1 106880N/mm; the integral residual rigidity K after macroscopic sliding is obtained through a rigidity curve ∞ Tending to 0N/mm; determine->After that, by definition, a ΔK of 500N/mm can be obtained.
Fourth step: the stiffness reduction function of the parameters is used for obtaining the density function of the S-Iwan model according to the stiffness reduction function determined by the parameters, as shown in figure 6.
Fifth step: substituting the density function into the expressions of the bone line equation and the cyclic excitation equation can obtain the bone line force-displacement curve and the cyclic excitation force-displacement curve of the S-Iwan model, and the virtual experimental data pair is shown in fig. 7 and 8. The specific expressions of the S-Iwan model bone line force-displacement equation and the cyclic excitation force-displacement equation are as follows:
to reduce the formula repetition writing and simplify the formulas, the following functions are custom:
wherein a is i 、b i 、c i (i=1, 2,3, 4) is the stiffness reduction function K (x)Is defined. Here S 1 、S 2 、S 3 All are artificially constructed functions, and the purpose is to reduce the repetition amount in the subsequent formula without specific significance; i. and l and u are values representing corresponding positions in the right-end formula of the equation, so that the function of conveniently and simply replacing writing is achieved, and no specific meaning is provided. Using the custom function, the S-Iwan model bone line force-displacement equation can be expressed as (the solution of the definite integral at the right end of the equation is omitted):
S-Iwan model cyclic excitation force-displacement curve compression travel equation:
according to the map assumption, the stretch travel equation is:
F C (x)＝-F T (-x)。
the error of the S-Iwan model is compared with the error of experimental data, the error of each point of the bone line curve is shown in figure 9, the absolute error amount is not more than 5N, and the relative error amount is not more than 1%; the cyclic displacement excitation curve is also called a hysteresis loop, the enclosed area represents the energy loss in each excitation period, and the S-Iwan model is compared with an experiment, and the relative error of the energy loss is also lower than 3 percent.
As shown in FIG. 10, the stiffness-displacement curve of the S-Iwan model is observed, and the fitting degree of the S-Iwan model and the experimental stiffness-displacement curve is higher, so that the S-D function provided by the embodiment of the invention has better adaptability and higher calculation precision on the nonlinear change of the connection stiffness of the bolt connection structure, and the calculation precision on the nonlinear mechanical property of the bolt connection structure of the S-Iwan model derived from the S-D function is improved.
Example two
In order to perform a corresponding method of the above embodiment to achieve the corresponding functions and technical effects, a system for constructing a dynamic model of a bolting structure is provided below.
Referring to fig. 11, the system includes:
the first data acquisition module 201 is configured to acquire experimental data of a force-displacement curve of the bolting structure.
And the second data calculation module 202 is configured to obtain the stiffness-displacement curve experimental data of the bolting structure by obtaining a first derivative of the displacement in the force-displacement curve experimental data.
The rigidity-decreasing function construction module 203 is configured to model the connection rigidity of the bolt connection structure, so as to obtain a rigidity-decreasing function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection.
And the parameter identification module 204 is used for identifying parameters to be determined in the stiffness reduction function by using the stiffness-displacement curve experimental data.
The density function determining module 205 is configured to determine a density function of the bolting structure according to the stiffness decreasing function after the parameter determination.
A stiffness-Iwan model construction module 206 for constructing a stiffness-Iwan model of the bolted joint structure according to the density function; the rigidity-Iwan model is used for representing the contact nonlinear mechanical property of the bolt connection structure; the stiffness-Iwan model includes: bone line equations and cyclic excitation equations.
Example III
The embodiment provides an electronic device, including a memory and a processor, where the memory is configured to store a computer program, and the processor is configured to run the computer program to cause the electronic device to execute the method for constructing a dynamic model of a bolting structure according to the first embodiment.
Alternatively, the electronic device may be a server.
In addition, the embodiment of the invention also provides a computer readable storage medium, which stores a computer program, and the computer program realizes the method for constructing the dynamic model of the bolt connection structure in the first embodiment when being executed by a processor.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. The method for constructing the dynamic model of the bolt connection structure is characterized by comprising the following steps of:
acquiring force-displacement curve experimental data of a bolt connection structure;
obtaining a first derivative of displacement in the force-displacement curve experimental data to obtain rigidity-displacement curve experimental data of the bolt connection structure;
modeling the connection rigidity of the bolt connection structure to obtain a rigidity reduction function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection;
identifying parameters to be determined in the stiffness reduction function by utilizing the stiffness-displacement curve experimental data;
determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination;
constructing a rigidity-Iwan model of the bolt connection structure according to the density function; the rigidity-Iwan model is used for representing the contact nonlinear mechanical property of the bolt connection structure; the stiffness-Iwan model includes: bone line equations and cyclic excitation equations.
2. The method for constructing a dynamic model of a bolted structure according to claim 1, wherein the expression of the stiffness reduction function is:
wherein,a microscopic slippage starting point of the bolt connection structure; />A macroscopic slippage starting point of the bolt connection structure; k (K) 1 Initial rigidity before microscopic sliding occurs for the bolt connection structure; k (K) ∞ Residual rigidity after macroscopic sliding of the bolt connection structure; Δk is the amount of stiffness abrupt change of the bolted connection structure at the point where macroscopic slippage occurs; k (x) is a stiffness decreasing function; k (K) nol (x) As a function of the stiffness variation with respect to displacement x; />For micro-sliding starting point of bolt connection structure>The rigidity change function of the position takes a value;for macroscopic sliding starting point of the bolt connection structure>The rigidity change function of the position takes a value; a, a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 And c 4 Are all distribution parameters; the parameters to be determined in the stiffness reduction function include: />K 1 、K ∞ 、ΔK、a 1 、a 2 、a 3 、a 4 、b 1 、b 2 、b 3 、b 4 、c 1 、c 2 、c 3 And c 4 。
3. The method for constructing a dynamic model of a bolted structure according to claim 1, wherein the density function is expressed as:
wherein ρ (x) is a density function with respect to displacement x; k (x) is a stiffness decreasing function; k (K) nol (x) As a function of the stiffness variation with respect to displacement x;a microscopic slippage starting point of the bolt connection structure; />A macroscopic slippage starting point of the bolt connection structure; />A point which is infinitely far away after macroscopic sliding of the bolt connection structure; Δk is the amount of stiffness abrupt change of the bolted connection structure at the point where macroscopic slippage occurs; k (K) ∞ Residual rigidity after macroscopic sliding of the bolt connection structure; />For input of +.>Is a sea-going step function; />For input of +.>Is a sea-going step function; />For input of +.>Dirac impulse function; />For input of +.>Dirac impulse functions of (a).
4. The method for constructing a dynamic model of a bolted structure according to claim 1, wherein the equation of the bone line is expressed as:
wherein F (x) is the force experienced at displacement x;for +.>Is a function of density of (a).
5. The method of claim 4, wherein the cyclic excitation equation comprises: a force-displacement relationship integral expression of the compression stroke and a force-displacement relationship integral expression of the tension stroke;
the force-displacement relationship integral expression of the compression stroke is:
wherein F is C (x) Representing the force experienced at displacement x in the compression stroke; a represents the amplitude of the input periodic cyclical stimulus;
the force-displacement relationship integral expression of the stretching stroke is as follows:
wherein F is T (x) Representing the force experienced at displacement x during the stretching stroke.
6. The method for constructing a dynamic model of a bolted structure according to claim 1, wherein determining a density function of the bolted structure according to the stiffness-decreasing function after the parameter determination comprises:
and (3) solving a first derivative of the displacement in the rigidity decreasing function after the parameter determination and taking the opposite number to obtain a density function of the bolt connection structure.
7. The method for constructing a dynamic model of a bolted structure according to claim 1, wherein obtaining experimental data of a force-displacement curve of the bolted structure comprises:
and carrying out a quasi-static experiment of unidirectional stretching or unidirectional compression on the bolt connection structure from the static balance position to obtain experimental data of a force-displacement curve.
8. A system for constructing a dynamic model of a bolted structure, comprising:
the first data acquisition module is used for acquiring force-displacement curve experimental data of the bolt connection structure;
the second data calculation module is used for obtaining a first derivative of the displacement in the force-displacement curve experimental data to obtain the rigidity-displacement curve experimental data of the bolt connection structure;
the rigidity descending function construction module is used for modeling the connection rigidity of the bolt connection structure to obtain a rigidity descending function; the stiffness reduction function represents a relationship between displacement and stiffness of the bolted connection;
the parameter identification module is used for identifying parameters to be determined in the rigidity descending function by utilizing the rigidity-displacement curve experimental data;
the density function determining module is used for determining a density function of the bolt connection structure according to the rigidity decreasing function after the parameter determination;
the rigidity-Iwan model construction module is used for constructing a rigidity-Iwan model of the bolt connection structure according to the density function; the rigidity-Iwan model is used for representing the contact nonlinear mechanical property of the bolt connection structure; the stiffness-Iwan model includes: bone line equations and cyclic excitation equations.
9. An electronic device comprising a memory for storing a computer program and a processor that runs the computer program to cause the electronic device to perform the bolting dynamics model construction method according to any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that it stores a computer program which, when executed by a processor, implements the bolting structure dynamics model construction method according to any one of claims 1 to 7.
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