A Dynamic Modeling Method for a Fluid Delivery Pipeline with a Connecting Hose

Abstract

The present invention provides a method for dynamic modeling of a fluid transportation pipeline with a connecting hose, including: establishing a dynamic model of a fluid transportation pipeline system with a connecting hose based on the finite element method; validating the established dynamic model of the fluid transportation pipeline system with a connecting hose; conducting modal tests under different fluid pressures based on the validated model to obtain the influence law of fluid parameters on the natural frequency of the fluid transportation pipeline with a connecting hose. The present invention can provide a more accurate and comprehensive dynamic model for the analysis of the natural characteristics and vibration response of a fluid transportation pipeline system under fluid excitation. Based on the finite element method, the model of the present invention has better flexibility and higher solution efficiency when evaluating the natural characteristics of a fluid transportation pipeline system. Based on the proposed model, numerical and experimental methods are respectively used to study the influence law of fluid parameters of a fluid transportation pipeline system on its natural characteristics. The present invention can provide a premise for the vibration analysis of fluid transportation pipelines in subsequent projects.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical dynamics, and in particular to a method for dynamics modeling of a fluid delivery pipeline with a connecting hose. Background Art

[0002] The function of the aero-engine fluid delivery pipeline is to deliver fluid media to the engine and various parts of the aircraft. During the delivery process, the pump source is often connected to the pipeline system through a hose. Since fluid pulsation will cause pipeline vibration, it will cause pipeline system failure for a long time and thus affect the safe operation of the aero-engine. Therefore, understanding the dynamic characteristics of the pipeline system when delivering fluid has become a current research hotspot. The basis for studying this problem is to establish an accurate model of the fluid delivery pipeline with a connecting hose.

[0003] The inherent characteristic analysis reveals the natural frequency and vibration modal characteristics of the system. The support stiffness and boundary stiffness of the system have a significant impact on its inherent characteristics. The boundary stiffness and its inverse identification method is a method for identifying stiffness based on experiments and genetic algorithms. The error of the natural frequency is used as the objective function, and the stiffness is used as the optimization variable. The optimization variable corresponding to the minimized objective function is obtained by combining the frequency response function of the pipeline system obtained from the experiment, which is the identified boundary stiffness. It is introduced into the model to obtain a more accurate dynamic model of the fluid delivery pipeline system, providing support for subsequent vibration analysis.

[0004] In the past few decades, rich results have been achieved in the dynamic analysis of fluid pipelines. In order to better analyze the impact of fluid-structure interaction (FSI) on the inherent characteristics of fluid pipelines, scholars have used transfer matrix method, semi-analytical method and finite element method to establish pipeline system models. The transfer matrix method is suitable for chain pipeline structures and has a wide range of applications, but it often has the disadvantage of numerical instability. The semi-analytical method is often used to deal with nonlinear vibration problems of fluid pipelines, but its disadvantage is that it is only applicable to single pipes and is difficult to apply to complex pipeline systems. The finite element method is more flexible and efficient in dealing with the structural vibration of pipelines. Although some scholars have studied the inherent characteristics of fluid pipelines, most studies have ignored the influence of connecting hoses, etc., and the dynamic analysis of fluid pipeline systems containing connecting hoses is not sufficient. Summary of the invention

[0005] According to the technical problems raised above, a method for dynamic modeling of a fluid delivery pipeline with a connecting hose is provided. The invention takes into account the influence of the connecting hose, has a high solution efficiency while ensuring the calculation accuracy, fills the gap in the research of connecting hose modeling, and provides support for the subsequent vibration analysis of the fluid delivery pipeline.

[0006] The technical means adopted by the present invention are as follows:

[0007] A dynamic modeling method for an infusion pipeline with a connecting hose, comprising:

[0008] Based on the finite element method, establish a dynamic model of the infusion pipeline system with a connecting hose;

[0009] Verify the dynamic model of the infusion pipeline system with a connecting hose;

[0010] Based on the verified model, conduct modal tests under different fluid pressures to obtain the influence law of fluid parameters on the natural frequency of the infusion pipeline with a connecting hose.

[0011] Further, the establishment of the dynamic model of the infusion pipeline system with a connecting hose based on the finite element method includes:

[0012] Establish an infusion pipeline model to obtain the stiffness matrix, mass matrix, and damping matrix of the pipeline;

[0013] Introduce the measured stiffness, discretize the clamp equivalently as a spring to obtain the clamp stiffness matrix;

[0014] Model the pipe joint with beam elements to obtain the stiffness matrix and mass matrix of the pipe joint;

[0015] Introduce the fluid term to obtain the stiffness matrix, mass matrix, and damping matrix of the fluid;

[0016] Equivalent the connecting hose as a spring, and use the backstepping identification method to obtain the equivalent boundary stiffness matrix of the hose based on the genetic algorithm and the measured frequency response function;

[0017] Perform coordinate transformation, and finally obtain the mass matrix and stiffness matrix of the pipeline system through element assembly, and further obtain the dynamic equation of the infusion pipeline system with a connecting hose.

[0018] Further, the establishment of the infusion pipeline model to obtain the stiffness matrix, mass matrix, and damping matrix of the pipeline specifically includes:

[0019] According to the finite element method, discretize the entire pipeline using Timoshenko beam elements. Each beam element has two nodes. Assuming each node has four degrees of freedom, define the node displacement vector as:

[0020] q e =[v i ,w i ,θ yi ,θ zi ,v j ,w j ,θ yj ,θ zj T

[0021] ​The element displacement vector can be expressed as:

[0022]

[0023] where N(x) is the element shape function, and its expression is as follows:

[0024]

[0025] N v =[N v1 (x) 0 0 N v2 (x) N v3 (x) 0 0 N v4 (x)]

[0026] N w =[0 N w1 (x) N w2 (x) 0 0 N w3 (x) N w4 (x) 0]

[0027]

[0028]

[0029] According to Hamilton's principle and the principle of minimum potential energy, the partial differential equation of the pipeline can be obtained. Substituting the element displacement vector into the equation, the stiffness matrix K p , mass matrix M p and damping matrix C p of the element in the local coordinate system can be obtained, where the damping matrix C p adopts the Rayleigh damping form:

[0030]

[0031]

[0032]

[0033] In the above formula, ρ p , l k and A p respectively refer to the density, length and cross-sectional area of the k-th pipeline element; I y and I z respectively represent the cross-sectional moments of inertia about oy and oz; v and w are the translational displacements of any cross-section along the y and z axes; θ y and θ z respectively represent the rotational displacements of any cross-section about the y and z directions, E and G respectively represent Young's modulus and shear modulus, κ y and κ zThey represent the shear coefficients with respect to the y and z axes respectively, and the value for thin-walled cylindrical parts is 0.5; the prime (′) in the superscript of the variable indicates the first-order derivative with respect to the coordinate x, f1 and f2 are the first two natural frequencies, and ξ1 = ξ2 = 0.02 are the first two modal damping ratios.

[0034] Furthermore, by introducing the measured stiffness and equivalently discretizing the clamp into springs, the stiffness matrix K of the clamp is obtained c , specifically including:

[0035] Considering the influence of the clamp width, the single-connected metal felt clamp is equivalently discretized into two transverse springs and two angular springs, and the stiffness of each spring is 1 / 2 of the measured stiffness in that direction, where the measured stiffness of the clamp is obtained through multiple tests.

[0036] Furthermore, by introducing the fluid terms, the stiffness matrix, mass matrix, and damping matrix of the fluid are obtained, specifically including:

[0037] When considering the steady fluid flow in the pipe, the Coriolis force and centrifugal force related to the fluid velocity will affect the pipeline vibration, where the Coriolis force term is The centrifugal force term due to the pipeline bending is According to the virtual work generated by the fluid force, the stiffness matrix K f , mass matrix M f and damping matrix C f of the fluid element in the local coordinate system are obtained:

[0038]

[0039]

[0040]

[0041] In the formula, m f is the mass of the fluid in the pipeline, ρ f and A f respectively refer to the density and cross-sectional area of the fluid element, p is the fluid pressure, v is the fluid velocity, and μ is the Poisson's ratio of the pipeline.

[0042] Furthermore, by equivalently discretizing the connecting hose into springs and using the backstepping identification method, based on the genetic algorithm and the measured frequency response function, the equivalent boundary stiffness matrix of the hose is obtained, specifically including:

[0043] The connecting hose is mainly composed of a rigid pipe in the metal part and a rubber hose. The rigid pipe is equivalently discretized into a beam element model, and the rubber hose is equivalently discretized into a transverse spring and an angular spring. Since the stiffness of the hose cannot be directly measured, a target function is constructed based on the measured frequency response function, and the backstepping identification is obtained through the genetic algorithm;

[0044] Assuming that the axial and torsional directions of the hose are fixed, it is necessary to identify the equivalent stiffness of the hose in the vertical y and horizontal z directions. Therefore, K y and K z For the optimization variable, its constraints (value range) are:

[0045]

[0046] The objective function established is:

[0047]

[0048] Where n = 4, Fre op is the natural frequency calculated by the current optimal individual simulation, Fre ex is the natural frequency measured by the test.

[0049] Furthermore, the coordinate transformation can finally obtain the mass matrix and stiffness matrix of the pipeline system through the unit grouping, and further obtain the dynamic equation of the fluid delivery pipeline system with the connecting hose, which specifically includes:

[0050] All Timoshenko beam unit matrices are obtained in the local coordinate system oxyz, and they must be converted to the global coordinate system OXYZ during the unit assembly process, and finally the discrete dynamic model of the flow pipeline is established in this coordinate system;

[0051] The node displacement vector in the global coordinate system can be expressed as:

[0052]

[0053] The node displacement vector in the local coordinate system can be expressed as

[0054]

[0055] The relationship between the node displacement of the beam element in the local coordinate system of the beam element and the global coordinate system of the system:

[0056]

[0057] Among them, T is the coordinate transformation matrix, T1 is the node transformation matrix,

[0058] Element stiffness matrix in the global coordinate system and the mass matrix The expression is:

[0059]

[0060] Finally, the mass matrix and stiffness matrix of the pipeline system can be obtained through the unit set, and further the dynamic equation can be obtained as follows:

[0061]

[0062] In the formula, M p is the pipeline element mass matrix; M f is the fluid element mass matrix; M j is the mass matrix of the pipe joint; C p is the pipeline element damping matrix; C f is the fluid element damping matrix; K p is the pipeline element stiffness matrix, K f is the fluid element stiffness matrix; K c is the stiffness matrix of the clamp; K j is the stiffness matrix of the pipe joint; K s is the equivalent stiffness matrix of the hose part; u is the generalized displacement vector of the system; F is the external load vector.

[0063] Furthermore, the model verification of the established dynamic model of the fluid-conveying pipeline system with connecting hoses includes:

[0064] Modal verification based on the empty pipe hammering experiment with connecting hoses and verification of the influence of fluid parameters based on the fluid-conveying pipeline hammering experiment with connecting hoses;

[0065] The test instruments required for the empty pipe hammering experiment with connecting hoses include a three-axis acceleration sensor, a force hammer, and a 12-channel LMS system; to ensure the accuracy of the test results, through multiple hammering tests, the natural frequencies of the fluid-conveying pipeline system with connecting hoses are obtained; using the finite element method, the equivalent boundary stiffness of the connecting hoses is identified through the genetic algorithm and the experimental frequency response function, and finally the natural frequencies of the fluid-conveying pipeline are obtained; the model is verified by comparing the frequency results of the two;

[0066] The verification of the influence of fluid parameters based on the fluid-conveying pipeline hammering experiment with connecting hoses includes: using a gear pump as the pump source to apply fluid excitation to the fluid-conveying pipeline, and applying pump source excitations of 3 MPa, 6 MPa, 9 MPa, 12 MPa, and 15 MPa respectively; conducting multiple hammering tests again to obtain the natural frequencies of the fluid-conveying pipeline system under different fluid pressures; the model is further verified by comparing the natural frequencies obtained from simulation and experiment.

[0067] Furthermore, the modal test under different fluid pressures is carried out based on the verified model to obtain the influence law of fluid parameters on the natural frequencies of the fluid-conveying pipeline with connecting hoses, including:

[0068] According to the natural frequency change rate curve, the natural frequency drop rate under different fluid pressures is calculated, where the calculation formula of the natural frequency change rate is as follows:

[0069]

[0070] Compared with the prior art, the present invention has the following advantages:

[0071] 1. The method for dynamic modeling of a fluid delivery pipeline with a connecting hose provided by the present invention takes into account the influence of the connecting hose and has a high solution efficiency while ensuring calculation accuracy.

[0072] 2. The dynamic modeling method of the fluid delivery pipeline with a connecting hose provided by the present invention firstly derives the dynamic model of the fluid delivery pipeline system including the pipe joint according to the Hamilton principle and the principle of minimum potential energy, introduces the measured support stiffness of the clamp and the equivalent boundary stiffness of the connecting hose, and verifies the accuracy of the model through a pipeline hammer test with a connecting hose. Then, a gear pump is used to excite the fluid under different pressures in the fluid delivery pipeline, and numerical and experimental analyses are performed to determine the influence of fluid pressure on the inherent characteristics of the pipeline.

[0073] 3. The dynamic modeling method of the fluid delivery pipeline with a connecting hose provided by the present invention fills the gap in the study of the inherent characteristics of the fluid delivery pipeline with a connecting hose and provides support for the subsequent vibration analysis of the fluid delivery pipeline.

[0074] Based on the above reasons, the present invention can be widely promoted in the fields of mechanical dynamics and the like. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0076] Figure 1 The present invention is a flow chart of a method for analyzing inherent characteristics of a fluid delivery pipeline with a connecting hose.

[0077] Figure 2 It is a schematic diagram of a fluid delivery pipeline model with a connecting hose according to the present invention.

[0078] Figure 3 It is a schematic diagram of the modal test results of the fluid delivery pipeline with a connecting hose of the present invention.

[0079] Figure 4 This is a diagram of the iterative process of optimizing the equivalent boundary stiffness of the hose of the present invention.

[0080] Figure 5 Schematic diagram of the comparison results between the numerical and experimental frequency response functions of the fluid delivery pipeline system with a connecting hose according to the present invention.

[0081] Figure 6 Schematic diagram of the comparison results between the numerical and experimental modal vibration modes of the fluid delivery pipeline system with a connecting hose according to the present invention.

[0082] Figure 7 Schematic diagram of the comparison results between the numerical and experimental frequency response functions of the fluid delivery pipeline system with a connecting hose under 15 MPa pressure according to the present invention.

[0083] Figure 8 Schematic diagram of the test results and simulation results of the change curves of the natural frequencies of each order of the pipeline under different fluid pressures according to the present invention. Specific implementation manners

[0084] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0085] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. The description of at least one exemplary embodiment below is actually only illustrative and in no way limits the present invention and its application or use. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0086] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0087] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such technologies, methods, and devices should be regarded as part of the authorized specification. In all the examples shown and discussed here, any specific values should be construed as merely exemplary and not as a limitation. Therefore, 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 drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0088] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by orientation words such as "front, rear, upper, lower, left, right", "lateral, vertical, perpendicular, horizontal", and "top, bottom", etc. are generally based on the orientation or positional relationships shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description. Without contrary instructions, these orientation words do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it should not be construed as limiting the scope of protection of the present invention: the orientation words "inner, outer" refer to the inside and outside relative to the contour of each component itself.

[0089] For ease of description, spatial relative terms such as "above...", "over...", "on the upper surface of...", "above", etc. can be used here to describe the spatial positional relationships of one device or feature shown in the drawings with other devices or features. It should be understood that the spatial relative terms are intended to encompass different orientations in use or operation in addition to the orientation described in the drawings for the device. For example, if the device in the drawing is inverted, the device described as "above other devices or structures" or "over other devices or structures" will then be positioned "below other devices or structures" or "beneath other devices or structures". Thus, the exemplary term "above..." can include both the orientations of "above..." and "below...". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations should be made for the spatial relative descriptions used here.

[0090] In addition, it should be noted that the use of words such as "first", "second", etc. to define components is only for the convenience of differentiating the corresponding components. Without otherwise stating, the above words have no special meaning. Therefore, it should not be construed as limiting the scope of protection of the present invention.

[0091] Such as Figure 1 、2 As shown in 2 , the present invention provides a method for dynamic modeling of an infusion pipeline with a connecting hose, including:

[0092] S1. Based on the finite element method, establish a dynamic model of the infusion pipeline system with a connecting hose;

[0093] Specifically, as a preferred embodiment of the present invention, in step S1, based on the finite element method, establishing a dynamic model of the infusion pipeline system with a connecting hose includes:

[0094] S11. Establish an infusion pipeline model to obtain the stiffness matrix, mass matrix, and damping matrix of the pipeline;

[0095] According to the finite element method, the entire pipeline is discretized using Timoshenko beam elements. Each beam element has two nodes. Assuming that each node has four degrees of freedom, the node displacement vector is defined as:

[0096] q e =[v i ,w i ,θ yi ,θ zi ,v j ,w j ,θ yj ,θ zj T

[0097] The element displacement vector can be expressed as:

[0098]

[0099] where N(x) is the element shape function, and its expression is as follows:

[0100]

[0101] N v =[N v1 (x) 0 0 N v2 (x) N v3 (x) 0 0 N v4 (x)]

[0102] N w =[0 N w1 (x) N w2 (x) 0 0 N w3 (x) N w4 (x) 0]

[0103]

[0104] ​

[0105] Based on Hamilton's principle and the principle of minimum potential energy, the partial differential equations of the pipeline can be obtained. Substituting the element displacement vector into the equations, the stiffness matrix K of the element in the local coordinate system is obtained p , mass matrix M p and damping matrix C p , where the damping matrix C p adopts the Rayleigh damping form:

[0106]

[0107]

[0108]

[0109] In the above formula, ρ p , l k and A p respectively refer to the density, length and cross-sectional area of the k-th pipeline element; I y and I z respectively represent the cross-sectional moments of inertia about oy and oz; v and w are the translational displacements of any cross-section along the y and z axes; θ y and θ z respectively represent the rotational displacement of any cross-section about the y and z directions, E and G respectively represent Young's modulus and shear modulus, κ y and κ z respectively represent the shear coefficients about the y and z axes, and the value for thin-walled cylindrical parts is 0.5; the variable superscript with a prime (′) represents the first derivative with respect to the coordinate x, f1 and f2 are the first two natural frequencies, and ξ1 = ξ2 = 0.02 are the first two modal damping ratios.

[0110] S12. Introduce the measured stiffness, discretize the clamp equivalently as a spring, and obtain the stiffness matrix of the clamp;

[0111] Considering the influence of the clamp width, the single-connected metal felt clamp is equivalently discretized into two transverse springs and two angular springs, and the stiffness of each spring is 1 / 2 of the measured stiffness in that direction, where the measured stiffness of the clamp is obtained through multiple tests.

[0112] S13. Model the pipe joint with beam elements to obtain the stiffness matrix and mass matrix of the pipe joint;

[0113] Model the pipe joint part with Timoshenko beam elements. The specific method is the same as the pipeline modeling method, so it will not be elaborated here. Obtain the stiffness and mass matrices of the pipe joint element, and then assemble them with the stiffness and mass matrices of the pipe element.

[0114] S14. Introduce the fluid terms to obtain the stiffness matrix, mass matrix and damping matrix of the fluid;

[0115] When considering the steady fluid flow in a pipe, the Coriolis force and centrifugal force related to the fluid velocity will affect the pipeline vibration. The Coriolis force term is The centrifugal force term due to the pipeline bending is According to the virtual work generated by the fluid force, the stiffness matrix K of the fluid element in the local coordinate system is obtained f , the mass matrix M f and the damping matrix C f :

[0116]

[0117]

[0118]

[0119] In the formula, m f is the mass of the fluid in the pipeline, ρ f and A f respectively refer to the density and cross-sectional area of the fluid element, p is the fluid pressure, v is the fluid velocity, and μ is the Poisson's ratio of the pipeline.

[0120] S15. The connecting hose is equivalent to a spring. By using the backstepping identification method and based on the genetic algorithm and the measured frequency response function, the equivalent boundary stiffness matrix of the hose is obtained;

[0121] The connecting hose is mainly composed of a hard pipe in the metal part and a rubber hose. The hard pipe is equivalently discretized into a beam element model, and the rubber hose is equivalently discretized into a transverse spring and an angular spring. Since the stiffness of the hose cannot be directly measured, a target function is constructed based on the measured frequency response function, and the backstepping identification is obtained through the genetic algorithm;

[0122] Assume that the axial and torsional directions of the hose are fixed. Then, the equivalent stiffness in the vertical y and horizontal z directions of the hose needs to be identified. Therefore, let K y and K z be the optimization variables, and their constraint conditions (value ranges) are:

[0123]

[0124] The established target function is:

[0125]

[0126] In the formula, n = 4, Fre op is the natural frequency calculated by the simulation of the current optimal individual, and Fre ex is the natural frequency measured in the experiment.

[0127] S16. Perform coordinate transformation. Through element assembly, the mass matrix and stiffness matrix of the pipeline system can be finally obtained, and further the dynamic equation of the fluid-conveying pipeline system with connecting hoses can be obtained.

[0128] All Timoshenko beam element matrices are obtained in the local coordinate system oxyz. During the element assembly process, they need to be transformed into the global coordinate system OXYZ, and finally the discrete dynamic model of the fluid-conveying pipeline is established in this coordinate system.

[0129] The nodal displacement vector in the global coordinate system can be expressed as:

[0130]

[0131] The nodal displacement vector in the local coordinate system can be expressed as

[0132]

[0133] The relationship between the nodal displacements of the beam element in the local coordinate system of the beam element and the global coordinate system of the system:

[0134]

[0135] where T is the coordinate transformation matrix and T1 is the nodal transformation matrix.

[0136] The element stiffness matrix and mass matrix in the global coordinate system are expressed as:

[0137]

[0138] Through element assembly, the mass matrix and stiffness matrix of the pipeline system can be finally obtained, and further the dynamic equation can be obtained as:

[0139]

[0140] In the formula, M p is the pipeline element mass matrix; M f is the fluid element mass matrix; M j is the mass matrix of the pipe joint; C p is the pipeline element damping matrix; C f is the fluid element damping matrix; K p is the pipeline element stiffness matrix, K f is the fluid element stiffness matrix; K c is the stiffness matrix of the clamp; K j is the stiffness matrix of the pipe joint; K sis the equivalent stiffness matrix of the hose part; u is the generalized displacement vector of the system; F is the external load vector.

[0141] S2. Verify the model of the fluid-conveying pipeline system with connecting hoses established;

[0142] Specifically, as a preferred implementation manner of the present invention, the verification of the model of the fluid-conveying pipeline system with connecting hoses established includes:

[0143] Modal verification based on the empty-pipe hammering experiment of the connecting hose and verification of the influence of fluid parameters based on the hammering experiment of the fluid-conveying pipeline with connecting hoses; specifically:

[0144] For the model established in the present invention, first, the empty-pipe modal verification of the connecting hose is carried out. The parameters of the fluid-conveying pipeline system are shown in Table 1. The lengths of each pipe section (see Figure 2 ) are shown in Table 2. The test instruments required for the modal experiment include a three-axis acceleration sensor (PCB 356A01), a force hammer (PCB 086C01), and a 12-channel LMS system (SC-XS12-A). The clamp is composed of two hoop bands and metal rubber. Using a self-designed fixture, the stiffness of the clamp, K y = 7.3×10 6 N / m, K z = 1.4×10 7 N / m, K θy = 35.0 Nm / rad, K θz = 78.9 Nm / rad.

[0145] To ensure the accuracy of the test results, through multiple hammering tests, the frequency response function of the pipeline system with connecting hoses under the constrained mode is obtained, as Figure 3 shown. There are 4 natural frequencies in the range of 0 - 1000 Hz. The natural frequencies of the pipeline are identified through the peaks of the frequency response function, as shown in Table 3.

[0146] Table 1 Parameters of the fluid-conveying pipeline system.

[0147]

[0148] Table 2 Lengths of each pipe section of the fluid-conveying pipeline.

[0149]

[0150] The hose parts at both ends have a great influence on the natural frequency of the pipeline and cannot be ignored. However, it is impossible to directly determine the hose stiffness through experimental testing. Therefore, a method of combining the genetic algorithm with the experimental frequency response function is considered to inversely identify and obtain the equivalent boundary stiffness of the hose part. Assuming that the axial and torsional directions of the hose are fixed, it is necessary to identify the equivalent stiffness K y and K z in the vertical y and horizontal z directions of the hose.

[0151] The initial population size is set to 40; the maximum number of iterations is set to 60; the crossover probability is 0.8; the mutation probability is 0.01. Figure 4 is the iteration process diagram of the genetic algorithm. After 60 iterations, the objective function finally converges to 0.275, and the optimal values of the corresponding optimization variables are: K y = 2.7×10 6 N / m, K z = 1.9×10 6 N / m.

[0152] After identifying and obtaining the equivalent stiffness of the hose, it is brought back into the finite element model for verification. The comparison of the frequency response functions between the simulation and the experiment is as Figure 5 shown. The comparison results of the natural frequencies of each order within 1000 Hz are shown in Table 3. It can be seen that the error does not exceed 3%. Figure 6 The comparison results of the modal shapes of each order between the experiment and the simulation in the vertical y direction are also given, indicating that the experiment and the simulation are in good agreement, and verifying the effectiveness of the equivalent model of the hose.

[0153] Table 3 Comparison of the natural frequencies of each order of the pipeline with hoses under the constraint conditions

[0154]

[0155] Based on the above dynamic model, a gear pump is used to simulate the pump source excitation. The pressure of the pump source fluid pulsation excitation is adjusted to 0 MPa, 3 MPa, 6 MPa, 9 MPa, 12 MPa, and 15 MPa respectively. Impact tests are carried out on the pipeline system with connecting hoses under fluid excitation to obtain the frequency response function. Taking 15 MPa as an example, Figure 7 is the frequency response function of the fluid conveying pipeline system with connecting hoses under 15 MPa fluid excitation, where f fluid is the fluid excitation frequency. By identifying the natural frequency of the pipeline through the peak value of the measured frequency response function, the simulation results are compared with the experimental results. The natural frequency results within 1000 Hz are shown in Table 4. Compared with the experimental results, the maximum error of the model proposed in the present invention is 2.7%, and the frequency calculation results of the two are in good agreement, verifying the correctness of the established model.

[0156] Table 4 Natural frequencies of each order of the pipeline under fluid excitation at different pressures

[0157]

[0158] S3. Based on the verified model, perform modal tests under different fluid pressures to obtain the influence law of fluid parameters on the natural frequency of the fluid conveying pipeline with a connecting hose.

[0159] In specific implementation, as a preferred implementation manner of the present invention, in order to study the influence law of fluid pressure on the natural frequency of the fluid conveying pipeline with a connecting hose, the natural frequencies under six pressure conditions are plotted together, as Figure 8 shown. Generally speaking, the natural frequencies of each order decrease with the increase of pressure. The decline amplitudes of the first two orders of frequencies (actually two directions of the first-order frequency) are relatively large, while the decline speeds of the third-order and fourth-order frequencies (actually two directions of the first-order frequency) are slower. According to the natural frequency change rate curve, the natural frequency decline rate of the fluid pressure from 0 MPa to 15 MPa can be calculated. The comparison results between the present invention and the experimental decline rate are shown in Table 5. The decline rate decreases with the increase of the modal order, further verifying the effectiveness of the model of the present invention.

[0160] Table 5 Comparison of the decline rate of natural frequency with pressure

[0161]

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic modeling method for an infusion pipeline with a connecting hose, characterized in that, Including: Based on the finite element method, establish the dynamic model of the fluid conveying pipeline system with a connecting hose, including: Establish the fluid conveying pipeline model to obtain the stiffness matrix, mass matrix and damping matrix of the pipeline; Introduce the measured stiffness, discretize the clamp equivalently as a spring to obtain the clamp stiffness matrix; Model the pipe joint with beam elements to obtain the stiffness matrix and mass matrix of the pipe joint; Introduce the fluid term to obtain the stiffness matrix, mass matrix and damping matrix of the fluid; Equivalently regard the connecting hose as a spring, and adopt the backstepping identification method. Based on the genetic algorithm and the measured frequency response function, obtain the equivalent boundary stiffness matrix of the hose; Perform coordinate transformation. Through element assembly, the mass matrix and stiffness matrix of the pipeline system can be finally obtained, and further obtain the dynamic equation of the fluid conveying pipeline system with a connecting hose, specifically including: All Timoshenko beam element matrices are obtained in the local coordinate system oxyz. During the element assembly process, they need to be transformed into the global coordinate system OXYZ. Finally, establish the discrete dynamic model of the fluid conveying pipeline in this coordinate system; The node displacement vector in the global coordinate system is expressed as: Q i = [V i , W i , θ Yi , θ Zi T ​ The node displacement vector in the local coordinate system is expressed as The relationship between the node displacements of the beam element in the local coordinate system of the beam element and the global coordinate system of the system: where T is the coordinate transformation matrix and T1 is the node transformation matrix, the element stiffness matrix and the mass matrix are expressed as: Through element assembly, the mass matrix and stiffness matrix of the pipeline system can be finally obtained, and the further obtained dynamic equation is: where, M p is the mass matrix of the pipeline element; M f is the mass matrix of the fluid element; M j is the mass matrix of the pipe joint; C p is the damping matrix of the pipeline element; C f is the damping matrix of the fluid element; K p is the stiffness matrix of the pipeline element, K f is the stiffness matrix of the fluid element; K c is the stiffness matrix of the clamp; K j is the stiffness matrix of the pipe joint; K s is the equivalent stiffness matrix of the hose part; u is the generalized displacement vector of the system; F is the external load vector; Verify the dynamic model of the fluid conveying pipeline system with a connecting hose established; Based on the verified model, conduct modal tests under different fluid pressures to obtain the influence law of fluid parameters on the natural frequency of the fluid conveying pipeline with a connecting hose.

2. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, characterized in that The establishment of the fluid conveying pipeline model to obtain the stiffness matrix, mass matrix and damping matrix of the pipeline specifically includes: According to the finite element method, use Timoshenko beam elements to discretize the entire pipeline. Each beam element has two nodes. Assuming that each node has four degrees of freedom, define the node displacement vector as: q e = [v i , w i , θ yi , θ zi , v j , w j , θ yj , θ zj T ​ The element displacement vector is expressed as: Among them, N(x) is the element shape function, and its expression is as follows: The partial differential equation of the pipeline is obtained based on Hamilton's principle and the principle of minimum potential energy. Substituting the element displacement vector into the equation, the stiffness matrix K of the element in the local coordinate system is obtained. p , the mass matrix M p and the damping matrix C p , where the damping matrix C p adopts the Rayleigh damping form: In the above formula, ρ p , l k and A p respectively refer to the density, length, and cross-sectional area of the k-th pipeline unit; I y and I z respectively represent the cross-sectional moments of inertia about oy and oz; v and w are the translational displacements of any cross-section along the y and z axes; θ y and θ z respectively represent the angular displacement of any cross-section about the y and z directions. E and G respectively represent Young's modulus and shear modulus, κ y and κ z respectively represent the shear coefficients about the y and z axes, and the value for thin-walled cylindrical parts is 0.5; the variable superscript with a prime (′) represents the first derivative with respect to the coordinate x, f1 and f2 are the first two natural frequencies, and ξ1 = ξ2 = 0.02 are the first two modal damping ratios.

3. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, wherein Introduce the measured stiffness, discretize the clamp equivalently into a spring, and obtain the clamp stiffness matrix K c , which specifically includes: Considering the influence of the clamp width, equivalently discretize the single-connected metal felt clamp into two transverse springs and two angular springs. The stiffness of each spring is 1 / 2 of the measured stiffness in that direction. The measured stiffness of the clamp is obtained through multiple tests.

4. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, characterized in that, The introduction of the fluid term to obtain the stiffness matrix, mass matrix and damping matrix of the fluid specifically includes: When considering the steady fluid flow in a pipe, the Coriolis force and centrifugal force related to the fluid velocity will affect the pipeline vibration, where the Coriolis force term is The centrifugal force term due to the pipeline bending is According to the virtual work generated by the action of fluid forces, the stiffness matrix K of the fluid element in the local coordinate system is obtained f , the mass matrix M f and the damping matrix C f : where m f is the mass of the fluid in the pipeline, ρ f and A f respectively refer to the density and cross-sectional area of the fluid element, p is the fluid pressure, v is the fluid velocity, and μ is the Poisson's ratio of the pipeline.

5. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, characterized in that, The equivalent of the connecting hose as a spring and the use of the backstepping identification method to obtain the equivalent boundary stiffness matrix of the hose based on the genetic algorithm and the measured frequency response function specifically include: The connecting hose is mainly composed of a hard pipe in the metal part and a rubber hose. Equivalently discretize the hard pipe into a beam element model, and equivalently discretize the rubber hose into a transverse spring and an angular spring. Since the stiffness of the hose cannot be directly measured, a target function is constructed based on the measured frequency response function, and the backstepping identification is obtained through the genetic algorithm; Assume that the axial and torsional directions of the hose are fixed. Then, it is necessary to identify the equivalent stiffness in the vertical y and horizontal z directions of the hose. Therefore, let K y and K z be the optimization variables, and their constraint conditions are: The established target function is: where n = 4, Fre op is the natural frequency calculated by simulating the current optimal individual, and Fre ex is the natural frequency measured by the experiment.

6. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, wherein The verification of the dynamic model of the fluid conveying pipeline system with a connecting hose established includes: Modal verification based on the impact experiment of an empty pipe with a connecting hose and verification of the influence of fluid parameters based on the impact experiment of a fluid-conveying pipeline with a connecting hose; The test instruments required for the impact experiment of an empty pipe with a connecting hose include a three-axis acceleration sensor, a force hammer, and a 12-channel LMS system; to ensure the accuracy of the test results, the natural frequency of the fluid-conveying pipeline system with a connecting hose is obtained through multiple impact experiments; the finite element method is used to identify the equivalent boundary stiffness of the connecting hose through the genetic algorithm and the experimental frequency response function, and finally the natural frequency of the fluid-conveying pipeline is obtained; the model is verified by comparing the frequency results of the two; The verification of the influence of fluid parameters based on the impact experiment of a fluid-conveying pipeline with a connecting hose includes: using a gear pump as the pump source to apply fluid excitation to the fluid-conveying pipeline, and applying pump source excitations of 3 MPa, 6 MPa, 9 MPa, 12 MPa, and 15 MPa respectively; multiple impact experiments are carried out again to obtain the natural frequencies of the fluid-conveying pipeline system under different fluid pressures; the model is further verified by comparing the natural frequencies obtained from simulation and experiment.

7. The dynamic modeling method of the fluid delivery pipeline with a connecting hose according to claim 1, characterized in that, The modal experiment under different fluid pressures is carried out based on the verified model to obtain the influence law of fluid parameters on the natural frequency of the fluid-conveying pipeline with a connecting hose, including: According to the natural frequency change rate curve, calculate the natural frequency decrease rate under different fluid pressures, where the calculation formula of the natural frequency change rate is as follows:

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