CN116090122A - Pipeline system dynamics modeling method considering clamp soft nonlinearity - Google Patents
Pipeline system dynamics modeling method considering clamp soft nonlinearity Download PDFInfo
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Abstract
The invention provides a pipeline system dynamics modeling method considering clamp soft nonlinearity, which comprises the following steps: based on a finite element method, establishing a nonlinear clamp-pipeline system dynamics model; performing model verification and nonlinear parameter identification on the established nonlinear clamp-pipeline system model; and further verifying the nonlinear clamp-pipeline system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designing vibration response characteristics. The invention provides a multi-degree-of-freedom nonlinear clamp-pipeline system model based on a genetic algorithm and a finite element method, which uses frequency errors and response amplitude errors between experiments and simulations as objective functions to identify nonlinear parameters, and verifies the modeled model through modal and vibration response experiments under different boundary conditions. The invention considers the soft nonlinear factor of the metal rubber clamp when predicting the vibration characteristic of the pipeline system, and has higher accuracy.
Description
Technical Field
The invention relates to the technical field of mechanical dynamics, in particular to a pipeline system dynamics modeling method considering clamp soft nonlinearity.
Background
The pipelines are used as important parts for connecting accessory devices such as an aircraft engine lubricating oil system, a fuel oil system, an adjusting system, a starting system and the like with other accessories, and are generally fixed on the casing through a clamp or connected with each other through the clamp to form a complex pipeline system. Various excitation forms of the aero-engine are transmitted to the pipeline system through the clamp, so that a dynamic model of the clamp is built, and understanding of vibration characteristics of the clamp-pipeline system has become a current research hot spot. While students have studied the dynamics of clamps, most have ignored their effects of nonlinearity in modeling, and the dynamics of piping systems containing clamp nonlinearities have not been sufficiently analyzed.
One of the functions of the clamp is to reduce vibrations of the pipe system. In the research of vibration characteristics of a pipeline system, a rigid constraint or flexible spring is generally adopted to equivalently model a clamp, but the clamp is of a split structure, and a gasket is made of a metal rubber material, so that the clamp is determined to have soft nonlinearity, and when the clamp is excited by the outside, friction occurs between metal wires in the metal rubber, so that nonlinear force is generated. Therefore, the linear model of the clamp can influence the accurate prediction of the vibration response of the pipeline, the nonlinear model of the metal rubber clamp is established and introduced into the pipeline model, and the research on the dynamics characteristics of the nonlinear clamp-pipeline system is significant.
In the clamp nonlinear modeling process, the determination of the nonlinear coefficient is very important. The reverse-push identification method is a method for identifying unknown parameters based on a test and a genetic algorithm, wherein a natural frequency error and a response amplitude error obtained by frequency sweeping are taken as target functions, a nonlinear coefficient is taken as an optimization variable, and the optimization variable corresponding to the minimum target function obtained by combining a pipeline system frequency response curve obtained by the test is taken as an identified clamp nonlinear coefficient. The identified nonlinear coefficient is introduced into a dynamics model to obtain an accurate nonlinear clamp-pipeline system dynamics model, and support can be provided for subsequent vibration analysis.
Disclosure of Invention
According to the technical problem, a pipeline system dynamics modeling method considering clamp soft nonlinearity is provided. The method has high solving efficiency, fills the blank of modeling research of the soft nonlinear clamp-pipeline system based on the finite element method, and provides support for subsequent pipeline vibration analysis.
The technical scheme adopted by the invention is as follows:
the invention provides a pipeline system dynamics modeling method considering clamp soft nonlinearity, which comprises the following steps:
based on a finite element method, establishing a nonlinear clamp-pipeline system dynamics model;
performing model verification and nonlinear parameter identification on the established nonlinear clamp-pipeline system model;
and further verifying the nonlinear clamp-pipeline system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designing vibration response characteristics.
Further, the method for establishing the nonlinear clamp-pipeline system dynamics model based on the finite element method specifically comprises the following steps: establishing a pipeline model;
introducing a nonlinear clamp;
and identifying the nonlinear coefficient.
Further, the building of the pipeline model specifically includes:
according to the finite element method, the iron-wood sinkoff beam units are adopted to discrete the whole pipeline, each beam unit is provided with two nodes, each node is provided with four degrees of freedom, and the displacement vectors of the unit nodes are defined as:
q e ＝[v i ,w i ,θ yi ,θ zi ,v j ,w j ,θ yj ,θ zj ] T
representing any node displacement vector within a cell as:
wherein N (x) is a unit shape function, and its expression is as follows:
obtaining a partial differential equation of a pipeline according to the Hamiltonian principle and the minimum potential energy principle, substituting a unit displacement vector into the equation to obtain a stiffness matrix and a mass matrix of a unit under a local coordinate system, wherein a damping matrix adopts a Rayleigh damping form:
wherein ρ is p 、l k And A p Respectively representing the density, length and cross-sectional area of the kth piping unit; i y And I z Representing the moment of section inertia with respect to oy and oz, respectively; v and w represent translational displacement of either cross-section along the y and z axes; θ y And theta z Respectively represents the angular displacement of any section around the y and z directions, E and G respectively represent Young modulus and shear modulus, and kappa y And kappa (kappa) z Respectively representing the shearing coefficients about y and z axes, wherein the value of the thin-wall cylindrical part is 0.5; the variable superscript strap prime (') indicates taking the first derivative, f, with respect to coordinate x 1 、f 2 Is the first two-order natural frequency, ζ 1 ＝ξ 2 =0.02 is the first two-order modal damping ratio;
further, the introduction of the nonlinear clamp specifically comprises:
considering the influence of clamp width, the metal felt single clamp is equally dispersed into two linear springs and two nonlinear springs along the axial direction, wherein the actual measurement rigidity of the linear springs introduced into the clamp is obtained by multiple test measurement: k (k) cy ＝1×10 7 N/m，k cz ＝8×10 6 N/m，k cθy ＝70Nm/rad，k cθz =30 Nm/rad, each linear spring rate being 1/2 of the measured stiffness in that direction;
when external excitation exists, nonlinear restoring force is generated between the metal wires, and the nonlinear restoring force f is assumed ni And displacement x i The relation of (2) is:
f ni ＝k ni x i 3 ,i＝v,w,θ y ,θ z
wherein k is ni Is unknown non-linear rigidity coefficient of the clamp, x i For displacement of the clips in this direction, when k ni When=0, the supporting rigidity is formed by nonlinear springThe spring degenerates into a linear spring; in order to solve the problem that the nonlinear term is difficult to solve in the stiffness matrix, the nonlinear stiffness term is moved to the right into the force vector, so that a dynamics equation of the nonlinear clamp-pipeline system is obtained as follows:
wherein M is p 、C p And K p Respectively a mass matrix, a damping matrix and a rigidity matrix of the pipeline; c (C) c Is a damping matrix of the clamp; k (K) c A linear stiffness matrix of the clamp; q is the generalized displacement vector of the system; f is an external force vector; f (F) n Is a nonlinear force vector:
to simplify the calculation, assume the nonlinear stiffness coefficients k in four directions ni Equal, then the vibration response test is needed to be applied to k ni And (5) carrying out identification.
The equivalent viscous damping coefficient of the metal rubber clamp is determined through analysis of a hysteresis loop of the metal rubber clamp, and the energy dissipated by the clamp is expressed as:
ΔW＝πPa＝πxT
maxnmaxn
wherein a is n And T n Respectively the intercept of the elliptic loop on the coordinate axis, P max For restoring force at maximum deformation, the elastic potential energy possessed by the system is expressed as:
thus, the damping loss factor is expressed as:
the equation for an ellipse is expressed as:
for viscous damping systems, let c c For equivalent viscous damping coefficient, the restoring force in the dry friction system is:
when x=0, the restoring force of the system is:
P(x) x＝0 ＝c c x max ω
according to the equivalent principle, the restoring force in the dry friction hysteresis system is equal to the equivalent viscous damping force in the equivalent viscous system, and then the following are:
thus:
wherein k is the measured rigidity of the clamp, eta is the damping loss factor, omega is the excitation frequency, and the damping changes along with the increase of the excitation amplitude due to the nonlinearity of the metal rubber material, so as to correct the equivalent viscous damping coefficient c c Introducing a modified nonlinear damping coefficient c n The corrected nonlinear damping coefficient is c n c c ；
Further, the identifying the nonlinear coefficient specifically includes:
to determine an unknown nonlinear stiffness coefficient k in a nonlinear clamp-system dynamics equation n And nonlinear damping coefficient c n Parameter identification is carried out according to the input excitation and output response results of the test;
constructing an objective function by using the frequency error and the response amplitude error of the test, and performing reverse identification by a genetic algorithm; at the resonance frequency omega 0 Two sides of (1) take two frequency points omega m And omega n And omega m ＞ω n The corresponding response amplitudes of the two points are equal, namely A mop ＝A nop Respectively calculating test and simulation in omega n And omega 0 And (3) carrying out iterative solution on the response amplitude error by adopting a genetic algorithm and a Newmark-beta method, and finally obtaining the identified nonlinear coefficient.
Further, the model verification and nonlinear parameter identification are carried out on the established nonlinear clamp-pipeline system model, and the model verification and nonlinear parameter identification specifically comprise the mode verification and vibration response verification of a clamp-pipeline system hammering test.
Further, the test instruments required for modal verification of the clamp-pipe system hammer test include a three-way acceleration sensor, a force hammer and a 12-channel LMS system; in order to ensure the accuracy of test results, the natural frequency of the clamp-pipeline system is obtained through multiple hammering tests; and carrying out dynamic modeling by adopting a finite element method, obtaining the natural frequency and the vibration mode of the pipeline by solving the eigenvalue and the eigenvector, and comparing the simulation and test frequency and the vibration mode result to verify the model.
Further, the vibration response verification of the clamp-pipe system hammer test specifically comprises: adopting an electromagnetic vibration table to carry out simple harmonic excitation under different excitation amplitudes of 0.5g, 1g, 2g and 3g on a clamp-pipeline system, setting a frequency sweeping bandwidth according to a hammering test result, wherein the time length of each frequency sweeping test is 2.5min, and processing an acceleration signal of a target position by a LMS SCADAS mobile front end and transmitting the acceleration signal to an LMS mobile workstation; and identifying the nonlinear coefficient of the clamp by adopting a genetic algorithm and a test frequency response curve, identifying the natural frequency of the pipeline by the frequency corresponding to the formants in the frequency response under the sweep frequency excitation after the clamp is brought back to the model, and verifying the model by comparing the frequency and the response amplitude of the simulation and the test under the sweep frequency excitation.
Further, the method further verifies the nonlinear clamp-pipe system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designs vibration response characteristics, wherein the different boundary conditions specifically comprise:
and identifying nonlinear coefficients of the clamp by adopting a genetic algorithm and a test frequency response curve, respectively bringing the identified nonlinear coefficients back to clamp-pipeline of the solid support-bullet support boundary and clamp-pipeline system of the bullet support-bullet support boundary, respectively identifying natural frequencies of the pipeline by frequencies corresponding to formants in frequency response under sweep frequency excitation, and finally, further verifying the model by comparing simulated and tested frequencies and response amplitudes.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the pipeline system dynamics modeling method considering the clamp soft nonlinearity, which is provided by the invention, the soft nonlinearity of the metal rubber clamp is considered, so that the calculation accuracy of the model is improved.
2. According to the pipeline system dynamics modeling method considering clamp soft nonlinearity, firstly, a dynamics model of a pipeline system comprising a clamp is deduced according to the Hamiltonian principle and the minimum potential energy principle, the clamp actual measurement linear support rigidity and nonlinear rigidity are introduced, and the accuracy of the model is verified through a hammering test of a pipeline; and secondly, identifying a nonlinear coefficient through a frequency response curve obtained by a sweep frequency test, and carrying out test verification. And finally substituting the identified nonlinear coefficients into nonlinear clamp-pipeline models under different boundary conditions, and respectively performing test verification.
3. The pipeline system dynamics modeling method considering the clamp soft nonlinearity fills the blank of pipeline system dynamics modeling considering the clamp soft nonlinearity, and provides support for subsequent pipeline system vibration response analysis.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of a pipeline dynamics modeling method that accounts for clamp soft nonlinearity in accordance with the present invention;
FIG. 2 is a schematic diagram of a piping system according to the present invention, in which clamp soft nonlinearity is considered;
FIG. 3 is a flowchart of an optimization iteration of the clamp nonlinear coefficients of the present invention;
FIG. 4 is a graph showing simulation and experimental comparison of the frequency response function of the nonlinear clamp-pipe system of the present invention;
FIG. 5 is a diagram showing the vibration mode simulation and test comparison of the nonlinear clamp-pipe system of the present invention;
FIG. 6 is a graph of test results of vibration response of the piping system at different excitation amplitudes of the present invention;
FIG. 7 is a diagram of an iterative process for optimizing the nonlinear coefficients of the clamp of the present invention;
FIG. 8 is a graph of results of vibration response simulation and test comparison of a nonlinear clamp-line system of the present invention;
FIG. 9 is a graph showing the frequency response function simulation and test comparison of the nonlinear clamp-pipe system under two boundary conditions of the present invention;
FIG. 10 is a graph of simulated and experimental comparison of the vibrational response of a nonlinear clamp-line system under the clamped-clamped boundary of the present invention;
fig. 11 is a graph of vibration response simulation versus test for a nonlinear clamp-line system under a spring-spring boundary of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The invention will be described in detail below with reference to the drawings in connection with embodiments.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise. Meanwhile, it should be clear that the dimensions of the respective parts shown in the drawings are not drawn in actual scale for convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail, but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
In the description of the present invention, it should be understood that the azimuth or positional relationships indicated by the azimuth terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal", and "top, bottom", etc., are generally based on the azimuth or positional relationships shown in the drawings, merely to facilitate description of the present invention and simplify the description, and these azimuth terms do not indicate and imply that the apparatus or elements referred to must have a specific azimuth or be constructed and operated in a specific azimuth, and thus should not be construed as limiting the scope of protection of the present invention: the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition, the terms "first", "second", etc. are used to define the components, and are only for convenience of distinguishing the corresponding components, and the terms have no special meaning unless otherwise stated, and therefore should not be construed as limiting the scope of the present invention.
As shown in fig. 1 and 2, the invention provides a pipeline system dynamics modeling method considering clamp soft nonlinearity, which specifically comprises the following steps:
s1, establishing a nonlinear clamp-pipeline system dynamics model based on a finite element method;
s2, performing model verification and nonlinear parameter identification on the established nonlinear clamp-pipeline system model;
and S3, further verifying the nonlinear clamp-pipeline system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designing vibration response characteristics.
In specific implementation, as a preferred embodiment of the present invention, the specific process of step S1 is as follows:
s11, establishing a pipeline model;
the whole pipeline is discretized by adopting the Tie-Szechwan koch beam units, each beam unit is provided with two nodes, each node is provided with four degrees of freedom, and the unit node displacement vector can be defined as:
q e ＝[v i ,w i ,θ yi ,θ zi ,v j ,w j ,θ yj ,θ zj ] T (1)
any node displacement vector within a cell can be expressed as:
wherein N (x) is a unit shape function, and its expression is as follows:
according to the Hamiltonian principle and the minimum potential energy principle, a partial differential equation of a pipeline can be obtained, a unit displacement vector is substituted into the equation, a stiffness matrix and a mass matrix of a unit under a local coordinate system can be obtained, and a damping matrix adopts a Rayleigh damping form:
wherein ρ is p 、l k And A p Respectively the density, length and cross-sectional area of the kth piping unit. I y And I z Representing the moment of inertia in cross section with respect to oy and oz, respectively; v and w are translational displacements of either cross section along the y and z axes; θ y And theta z Respectively represents the angular displacement of any section around the y and z directions, E and G respectively represent Young modulus and shear modulus, and kappa y And kappa (kappa) z The shear coefficients about the y and z axes are represented, respectively, with a thin-walled cylinder having a value of 0.5. The variable superscript strap prime (') indicates taking the first derivative, f, with respect to coordinate x 1 、f 2 Is the first two-order natural frequency, ζ 1 ＝ξ 2 =0.02 is the first two-order modal damping ratio.
S12, introducing a nonlinear clamp;
considering the influence of clamp width, the metal felt single clamp is equally dispersed into two linear springs and two nonlinear springs along the axial direction, wherein the actual measurement rigidity of the linear springs which can be introduced into the clamp is obtained through multiple test measurements: k (k) cy ＝1×10 7 N/m，k cz ＝8×10 6 N/m，k cθy ＝70Nm/rad，k cθz =30 Nm/rad, each linear spring rate is 1/2 of the measured rate in that direction.
In the previous experiments, the natural frequency of the clamp-pipe system often shows dependence on the excitation amplitude, mainly because the elastic restoring force of the metal rubber material has strong soft nonlinearity, and therefore, a high-order nonlinear model is generally adopted for characterization. The amplitude-frequency characteristic of a dry friction system composed of metal rubber is mainly determined by nonlinear factors of displacement three times, so that nonlinear restoring force is generated among metal wires when external excitation exists, and the nonlinear restoring force f is assumed ni And displacement x i The relation of (2) is:
f ni ＝k ni x i 3 , i＝v,w,θ y ,θ z (7)
wherein k is ni Is unknown non-linearRigidity coefficient, x i For displacement of the clips in this direction, when k ni When=0, the support stiffness is degraded by the nonlinear spring to a linear spring. In order to solve the problem that the nonlinear term is difficult to solve in the stiffness matrix, the nonlinear stiffness term is moved to the right into the force vector, so that a dynamics equation of the nonlinear clamp-pipeline system can be obtained as follows:
wherein M is p 、C p And K p Respectively a mass matrix, a damping matrix and a rigidity matrix of the pipeline; c (C) c Is a damping matrix of the clamp; k (K) c A linear stiffness matrix of the clamp; q is the generalized displacement vector of the system; f is an external force vector; f (F) n Is a nonlinear force vector.
To simplify the calculation, assume the nonlinear stiffness coefficients k in four directions ni Equal, then the vibration response test is needed to be applied to k ni And (5) carrying out identification.
Because structural damping and viscous damping exist in the metal rubber material damping element, the concept of equivalent viscous damping coefficient is introduced, the equivalent damping is used for replacing a complex damping mechanism, and the equivalent viscous damping coefficient is determined through analysis of a hysteresis loop of the metal rubber clamp. The energy dissipated by the clip can be expressed as:
ΔW＝πP max a n ＝πx max T n (10)
wherein a is n And T n Respectively the intercept of the elliptic loop on the coordinate axis, P max Is the restoring force at maximum deformation. The elastic potential energy of the system can be expressed as:
the damping loss factor can thus be expressed as:
the equation for an ellipse can be expressed as:
for viscous damping systems, let c c For equivalent viscous damping coefficient, the restoring force in the dry friction system is:
when x=0, the restoring force of the system is:
P(x) x＝0 ＝c c x max ω (15)
according to the equivalent principle, the restoring force in the dry friction hysteresis system is equal to the equivalent viscous damping force in the equivalent viscous system, and then the following are:
thus:
wherein k is the measured rigidity of the clamp, eta is the damping loss factor, and omega is the excitation frequency. Due to the material nonlinearity of the metal rubber, the damping changes with increasing excitation amplitude. Therefore, in order to correct the equivalent viscous damping coefficient c c Introducing a modified nonlinear damping coefficient c n The corrected nonlinear damping coefficient is c n c c 。
S13, identifying nonlinear coefficients;
to determine an unknown nonlinear stiffness coefficient k in a nonlinear clamp-system dynamics equation n And nonlinear damping coefficient c n Parameter identification is required based on the input (stimulus) and output (response) results of the test.
The frequency error and response amplitude error of the test are used to construct an objective function, which is identified by a genetic algorithm in a reverse way, as shown in fig. 3. The error for the response amplitude is mainly obtained according to the improved half-power bandwidth method at the resonance frequency omega 0 Two sides of (1) take two frequency points omega m And omega n (ω m ＞ω n ) The corresponding response amplitudes of these two points are equal (A mop ＝A nop ) Respectively calculating test and simulation in omega n And omega 0 And (3) carrying out iterative solution on the response amplitude error by adopting a genetic algorithm and a Newmark-beta method, and finally obtaining the identified nonlinear coefficient.
In the specific implementation, as a preferred embodiment of the present invention, in the step S2, model verification and nonlinear parameter identification are performed on the established nonlinear clamp-pipe system model, which specifically includes mode verification and vibration response verification of a clamp-pipe system hammering test.
For the model established by the invention, the mode verification is firstly carried out. The parameters of the piping system are shown in table 1. The test instruments required for the modal experiments included a three-way acceleration sensor (PCB 356A 01), a force hammer (PCB 086C 01), and a 12-channel LMS system (SC-XS 12-A). The clamp is composed of two bands and metal rubber, the tightening torque is 8N.m, and the rigidity, k of the clamp is obtained through multiple measurements by utilizing a self-designed clamp cy ＝1×10 7 N/m，k cz ＝8×10 6 N/m，k cθy ＝70Nm/rad，k cθz ＝30Nm/rad。
In order to ensure the accuracy of the test result, the frequency response function and the vibration mode of the pipeline system under the constraint mode are obtained through multiple hammering tests, and the natural frequency of the pipeline is identified through the peak value of the frequency response function, as shown in table 2. The frequency response function comparison chart of the simulation and the test is shown in fig. 4, and the vibration mode pair is shown in fig. 5, so that the test is better matched with the simulation, and the effectiveness of the clamp-pipeline model is preliminarily verified.
Table 1 parameters of the piping system
Table 2 natural frequency contrast for piping system under constraint
Based on the dynamics model, the electromagnetic vibration table is adopted to simulate basic excitation, the frequency sweep range is set to be 360Hz-400 Hz according to the hammering test, the frequency sweep tests with excitation amplitudes of 0.5g, 1g, 2g and 3g are respectively carried out, the vibration response result of the system can be obtained, the response peak value is identified, and the inherent frequencies of each order corresponding to different frequency sweep excitation amplitudes can be accurately obtained. The transmissibility is an important index for measuring the vibration isolation of the clamping band, and the dynamic transmissibility can be defined as:
wherein a is out For system output acceleration amplitude, a in The dynamic transfer curves for different excitation amplitudes are shown in fig. 6 for the system input acceleration amplitude. Along with the increase of the excitation amplitude, the natural frequency of the system is reduced, and the transmissibility of the clamp is gradually reduced, so that the clamp has soft nonlinearity, and when the excitation amplitude is increased, the clamp can effectively restrain severe vibration, and the vibration reduction effect is obvious.
And based on a Newmark-beta method and a genetic algorithm, reversely pushing and identifying nonlinear coefficients of the clamp under different excitation amplitudes, and optimizing an iteration result chart as shown in figure 7. After the nonlinear coefficient is obtained, as shown in table 3, the nonlinear coefficient is substituted into a nonlinear clamp-pipeline system, and finally a comparison result of the simulation and test frequency response curve is obtained, as shown in fig. 8. The trend of the visible curve is basically consistent, the error is within the allowable range of engineering, and the correctness of the built model and the validity of parameter identification are verified. As the excitation increases, the first order modal frequencies of the system will shift to the left, due to the soft nonlinear nature of the band, again validating the model.
TABLE 3 test results at different excitation amplitudes
In specific implementation, in the step S3, the nonlinear clamp-pipe system model under different boundary conditions is further verified by using the model verified in the step S2 and the identified nonlinear parameters, and the vibration response characteristics of the nonlinear clamp-pipe system model are studied.
In order to further verify the established nonlinear clamp-pipe model, two pipe system dynamics tests under boundary conditions are respectively carried out: the left end supports the pipeline system supported by the right end clamping hoop and the two ends are both pipeline systems supported by the clamping hoops. The length of the tube in the test is 400mm, the diameter is 8mm, and the natural frequency and the frequency response function of the tube can be obtained by respectively performing hammering tests. And respectively establishing corresponding finite element models, wherein the obtained natural frequency comparison results of simulation and test are shown in table 4, and the frequency response function pairs are shown in fig. 9. The fundamental trend of the visible curves has good consistency, indicating that the modeled model is relatively accurate.
TABLE 4 simulation and experimental comparison results of natural frequencies under different boundary conditions
And (3) carrying out vibration response test on the nonlinear clamp-pipeline system under the clamped-sprung boundary condition, setting the frequency sweep range to 300-320Hz according to the result of the hammering test, and carrying out frequency sweep test under different excitation amplitudes (0.5 g, 1g, 2g and 3 g), so that the vibration response result of the system can be obtained, the response peak value can be identified, and the natural frequency corresponding to different frequency sweep excitation amplitudes can be accurately obtained. Substituting the identified nonlinear coefficient into the pipeline model again can obtain the vibration response comparison result of simulation and test as shown in fig. 10, and the natural frequency and acceleration response amplitude are shown in table 5. The trend of the curve is basically consistent, the errors of the natural frequency and the acceleration vibration response amplitude are small, the error can be controlled within 6%, the identification result is universal, and the accuracy of the nonlinear clamp-pipeline system model is high.
TABLE 5 simulation and test results of non-linear clamp-pipeline under solid-spring support
And (3) carrying out vibration response test on the nonlinear clamp-pipeline system under the condition of the spring support-spring support boundary, setting the frequency sweep range to 260-280Hz according to the result of the hammering test, and carrying out frequency sweep test under different excitation amplitudes (0.5 g, 1g, 2g and 3 g), so that the vibration response result of the system can be obtained, the response peak value is identified, and the natural frequency corresponding to different frequency sweep excitation amplitudes can be accurately obtained. Substituting the identified nonlinear coefficient into the pipeline model again can obtain the vibration response comparison result of simulation and test as shown in fig. 11, and the natural frequency and acceleration response amplitude are shown in table 6. The graph information shows that the frequency response curve trends of the simulation and test are basically consistent, the errors of the natural frequency and the acceleration vibration response amplitude are smaller, the errors can be controlled within 2%, the identification result is universal, and the established nonlinear clamp-pipeline system model is higher in accuracy.
TABLE 6 simulation and test results of non-linear clamp-pipeline under spring-spring
The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the design of the present invention.
Claims (9)
1. A method of modeling pipeline system dynamics that accounts for clamp soft nonlinearity, comprising:
based on a finite element method, establishing a nonlinear clamp-pipeline system dynamics model;
performing model verification and nonlinear parameter identification on the established nonlinear clamp-pipeline system model;
and further verifying the nonlinear clamp-pipeline system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designing vibration response characteristics.
2. The method for modeling dynamics of a pipe system in consideration of soft nonlinearity of a clamp according to claim 1, wherein the establishing a dynamics model of a nonlinear clamp-pipe system based on a finite element method specifically comprises:
establishing a pipeline model;
introducing a nonlinear clamp;
and identifying the nonlinear coefficient.
3. The method for modeling pipeline system dynamics taking into account clamp soft nonlinearity according to claim 2, wherein the building the pipeline model specifically comprises:
according to the finite element method, the iron-wood sinkoff beam units are adopted to discrete the whole pipeline, each beam unit is provided with two nodes, each node is provided with four degrees of freedom, and the displacement vectors of the unit nodes are defined as:
q e ＝[v i ,w i ,θ yi ,θ zi ,v j ,w j ,θ yj ,θ zj ] T
representing any node displacement vector within a cell as:
wherein N (x) is a unit shape function, and its expression is as follows:
N v ＝[N v1 (x)0 0N v2 (x)N v3 (x)0 0N v4 (x)]
N w ＝[0N w1 (x)N w2 (x)0 0N w3 (x)N w4 (x)0]
obtaining a partial differential equation of a pipeline according to the Hamiltonian principle and the minimum potential energy principle, substituting a unit displacement vector into the equation to obtain a stiffness matrix and a mass matrix of a unit under a local coordinate system, wherein a damping matrix adopts a Rayleigh damping form:
wherein ρ is p 、l k And A p Respectively representing the density, length and cross-sectional area of the kth piping unit; i y And I z Representing the moment of section inertia with respect to oy and oz, respectively; v and w represent translational displacement of either cross-section along the y and z axes; θ y And theta z Respectively represents the angular displacement of any section around the y and z directions, E and G respectively represent Young modulus and shear modulus, and kappa y And kappa (kappa) z Respectively representing the shearing coefficients about y and z axes, wherein the value of the thin-wall cylindrical part is 0.5; the variable superscript strap prime (') indicates taking the first derivative, f, with respect to coordinate x 1 、f 2 Is the first two-order natural frequency, ζ 1 ＝ξ 2 =0.02 is the first two-order modal damping ratio.
4. The method for modeling dynamics of a piping system in consideration of soft nonlinearity of a band according to claim 2, wherein the introducing of the nonlinear band specifically comprises:
considering the influence of clamp width, the metal felt single clamp is equally dispersed into two linear springs and two nonlinear springs along the axial direction, wherein the actual measurement rigidity of the linear springs introduced into the clamp is obtained by multiple test measurement: k (k) cy ＝1×10 7 N/m，k cz ＝8×10 6 N/m，k cθy ＝70Nm/rad，k cθz =30 Nm/rad, each linear spring rate being 1/2 of the measured stiffness in that direction;
when external excitation exists, nonlinear restoring force is generated between the metal wires, and the nonlinear restoring force f is assumed ni And displacement x i The relation of (2) is:
f ni ＝k ni x i 3 ,i＝v,w,θ y ,θ z
wherein k is ni Is unknown of clampLinear stiffness coefficient, x i For displacement of the clips in this direction, when k ni When=0, the support stiffness is degraded from a nonlinear spring to a linear spring; in order to solve the problem that the nonlinear term is difficult to solve in the stiffness matrix, the nonlinear stiffness term is moved to the right into the force vector, so that a dynamics equation of the nonlinear clamp-pipeline system is obtained as follows:
wherein M is p 、C p And K p Respectively a mass matrix, a damping matrix and a rigidity matrix of the pipeline; c (C) c Is a damping matrix of the clamp; k (K) c A linear stiffness matrix of the clamp; q is the generalized displacement vector of the system; f is an external force vector; f (F) n Is a nonlinear force vector:
to simplify the calculation, assume the nonlinear stiffness coefficients k in four directions ni Equal, then the vibration response test is needed to be applied to k ni Identifying;
the equivalent viscous damping coefficient of the metal rubber clamp is determined through analysis of a hysteresis loop of the metal rubber clamp, and the energy dissipated by the clamp is expressed as:
ΔW＝πPa＝πx T
max n max n
wherein a is n And T n Respectively the intercept of the elliptic loop on the coordinate axis, P max For restoring force at maximum deformation, the elastic potential energy possessed by the system is expressed as:
thus, the damping loss factor is expressed as:
the equation for an ellipse is expressed as:
for viscous damping systems, let c c For equivalent viscous damping coefficient, the restoring force in the dry friction system is:
when x=0, the restoring force of the system is:
P(x)| x＝0 ＝c c x max ω
according to the equivalent principle, the restoring force in the dry friction hysteresis system is equal to the equivalent viscous damping force in the equivalent viscous system, and then the following are:
thus:
wherein k is the measured rigidity of the clamp, eta is the damping loss factor, omega is the excitation frequency, and the damping changes along with the increase of the excitation amplitude due to the nonlinearity of the metal rubber material, so as to correct the equivalent viscous damping coefficient c c Introducing a modified nonlinear damping coefficient c n The corrected nonlinear damping coefficient is c n c c 。
5. The method for modeling dynamics of a pipe system in consideration of soft nonlinearity of a band as claimed in claim 2, wherein the identifying the nonlinearity coefficient comprises:
to determine an unknown nonlinear stiffness coefficient k in a nonlinear clamp-system dynamics equation n And nonlinear damping coefficient c n Parameter identification is carried out according to the input excitation and output response results of the test;
constructing an objective function by using the frequency error and the response amplitude error of the test, and performing reverse identification by a genetic algorithm; at the resonance frequency omega 0 Two sides of (1) take two frequency points omega m And omega n And omega m ＞ω n The corresponding response amplitudes of the two points are equal, namely A mop ＝A nop Respectively calculating test and simulation in omega n And omega 0 And (3) carrying out iterative solution on the response amplitude error by adopting a genetic algorithm and a Newmark-beta method, and finally obtaining the identified nonlinear coefficient.
6. The method for modeling dynamics of a piping system in consideration of soft nonlinearity of a band clamp according to claim 1, wherein the model verification and nonlinear parameter identification are performed on the established nonlinear band clamp-piping system model, and specifically include mode verification and vibration response verification of a hammering test of the band clamp-piping system.
7. The method for modeling pipeline system dynamics taking into account soft nonlinearity of band clamp according to claim 6, wherein: the test instrument required by the modal verification of the hammering test of the clamp-pipeline system comprises a three-way acceleration sensor, a force hammer and a 12-channel LMS system; in order to ensure the accuracy of test results, the natural frequency of the clamp-pipeline system is obtained through multiple hammering tests; and carrying out dynamic modeling by adopting a finite element method, obtaining the natural frequency and the vibration mode of the pipeline by solving the eigenvalue and the eigenvector, and comparing the simulation and test frequency and the vibration mode result to verify the model.
8. The method for modeling pipeline system dynamics taking into account soft nonlinearity of band clamp according to claim 6, wherein: the vibration response verification of the clamp-pipe system hammering test specifically comprises the following steps: adopting an electromagnetic vibration table to carry out simple harmonic excitation under different excitation amplitudes of 0.5g, 1g, 2g and 3g on a clamp-pipeline system, setting a frequency sweeping bandwidth according to a hammering test result, wherein the time length of each frequency sweeping test is 2.5min, and processing an acceleration signal of a target position by a LMS SCADAS mobile front end and transmitting the acceleration signal to an LMS mobile workstation; and identifying the nonlinear coefficient of the clamp by adopting a genetic algorithm and a test frequency response curve, identifying the natural frequency of the pipeline by the frequency corresponding to the formants in the frequency response under the sweep frequency excitation after the clamp is brought back to the model, and verifying the model by comparing the frequency and the response amplitude of the simulation and the test under the sweep frequency excitation.
9. The method for modeling pipeline system dynamics taking into account clamp soft nonlinearity according to claim 1, wherein: the method further verifies the nonlinear clamp-pipe system model under different boundary conditions by using the verified model and the identified nonlinear parameters, and designs vibration response characteristics, wherein the different boundary conditions specifically comprise:
and identifying nonlinear coefficients of the clamp by adopting a genetic algorithm and a test frequency response curve, respectively bringing the identified nonlinear coefficients back to clamp-pipeline of the solid support-bullet support boundary and clamp-pipeline system of the bullet support-bullet support boundary, respectively identifying natural frequencies of the pipeline by frequencies corresponding to formants in frequency response under sweep frequency excitation, and finally, further verifying the model by comparing simulated and tested frequencies and response amplitudes.
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| CN116702381B (en) * | 2023-08-10 | 2023-11-03 | 航天科工火箭技术有限公司 | Equivalent and vibration response calculation method for non-linearity of bolt connection |
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