A method for analyzing vibration characteristics of a guide vane shaft-top cover rubbing coupling system of a hydraulic turbine

Abstract

The application discloses a kind of vibration characteristics analysis methods of water turbine guide vane shaft-top cover rubbing coupling system, comprising the following steps: S1, using finite element method in combination with fixed interface modal synthesis method, the reduced dynamic model of guide vane shaft-top cover rubbing coupling system is established;S2, based on reduced dynamic model analysis mode truncation number, the influence law of friction coefficient and water flow surface load on the prestressed modal characteristics of guide vane shaft-top cover rubbing coupling system first 3 orders;S3, when reduced dynamic model is subjected to simple harmonic excitation, the influence law of near load end contact state, near-far load end contact state and friction coefficient on the vibration response and frequency spectrum characteristics of guide vane shaft-top cover rubbing coupling system;S4, based on the above steps, whether mixed-flow water turbine is stably and safely operated is evaluated.The application is analyzed by vibration characteristics of mixed-flow water turbine guide vane shaft-top cover rubbing coupling system, to monitor and diagnose the structural health state and failure of mixed-flow water turbine.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rub-impact fault analysis of Francis turbine, and particularly relates to a vibration characteristic analysis method of a Francis turbine guide vane shaft-top cover rub-impact coupling system. BACKGROUND

[0002] The Francis turbine is an important component of a hydroelectric generator set and is subjected to water flow load for a long time. The guide vane shaft and the top cover are core and key components of the Francis turbine and are prone to induce rub-impact between the guide vane shaft and the top cover under the action of water flow, which may cause abnormal vibration of the generator set and affect normal use, or even cause structural damage of the equipment and result in a major safety accident. Therefore, it is necessary to carry out rub-impact dynamics research on the guide vane shaft-top cover coupling system of the Francis turbine, so as to provide a theoretical and technical basis for structural health monitoring of the Francis turbine.

[0003] Many scholars have carried out relevant research on the key piece rub-impact problem in Francis turbine. Zhang et al. established a rub-impact fault model of water turbine rotor-bearing caused by unbalanced magnetic pull, and analyzed the influence of excitation current, rotor mass eccentricity and stator radial stiffness on the nonlinear vibration behavior of the system. Gou et al. studied the influence of electromagnetic stiffness, rotor mass eccentricity, damping and stator radial stiffness on the nonlinear dynamic characteristics of the rotor system based on the dynamic model of the rub-impact fault of water turbine stator and rotor. Nie et al. studied the influence of unbalanced magnetic pull, rub-impact force and nonlinear oil film force on the vibration characteristics of water turbine shaft system by using the fourth-order Runge-Kutta method. Zhang et al. established a bending-torsional rotor-bearing coupling system with friction impact of water turbine unit, and analyzed the influence of excitation current, mass eccentricity and electromagnetic torque on the dynamic characteristics of the system. Xu et al. constructed a nonlinear dynamic model of the rotor system of water turbine unit with parallel misalignment and rub-impact coupling faults, and discussed the influence of unit speed, eccentricity and parallel misalignment on the nonlinear dynamic behavior of the system. Huang et al. proposed a rotor dynamic model of water turbine generator unit with misalignment and rub-impact coupling faults, and studied the influence of misalignment, bearing stiffness and other parameters on the dynamic characteristics of the system by numerical method. Zhang et al. constructed a coupling vibration model of the friction-impact system of water turbine unit, and analyzed the influence of friction-impact fault and electromagnetic excitation on the dynamic characteristics of the rotor-bearing system of water turbine unit. Wu et al. established a nonlinear dynamic model of the shaft system of water turbine unit under the action of elasticity and sealing force, and analyzed the nonlinear stability of the sealing system. The results show that without external disturbance, the degree of rub-impact between the runner and the sealing structure with nonlinear sealing force will not increase with the increase of speed. Liang established a rotor dynamic model of water turbine under the coupling mechanism of multiple faults, and analyzed the influence of mass eccentricity, rotor misalignment and speed on the dynamic characteristics of the system. The results show that the rotor of water turbine unit is prone to periodic rub-impact or chaotic motion at high speed. Wu et al. established a fault diagnosis model based on one-dimensional convolutional neural network method, which can realize timely and accurate rub-impact fault detection through training of water turbine rotor vibration signal data set. Wu analyzed the rub-impact fault of water turbine by using time-frequency method based on variational mode decomposition, and verified the effectiveness of the method by comparing with experimental results.

[0004] In summary, many scholars have carried out in-depth and detailed research on the rub-impact coupling dynamics of rotor-stator system in water turbine, but less attention has been paid to the rub-impact problem of guide vane shaft-top cover coupling system induced by water flow in water turbine. SUMMARY

[0005] The application aims to provide a Francis turbine guide vane shaft-top cover rubbing coupling system vibration characteristic analysis method, a finite element reduced dynamics model of the Francis turbine guide vane shaft-top cover coupling system is established by using the fixed interface modal synthesis method, and a rubbing mechanical model of the guide vane shaft-top cover is established based on the contact dynamics theory, the rubbing problem of the guide vane shaft-top cover coupling system in the Francis turbine caused by water flow is analyzed, and the abnormal vibration and safety problems of the unit are reduced.

[0006] To achieve the above-mentioned purpose, the application provides the following technical scheme.

[0007] A Francis turbine guide vane shaft-top cover rubbing coupling system vibration characteristic analysis method, comprising the following steps:

[0008] S1, a reduced dynamics model of the guide vane shaft-top cover rubbing coupling system is established by using the finite element method combined with the fixed interface modal synthesis method;

[0009] S2, the influence law of the modal truncation number, the friction coefficient and the water flow surface load on the first three prestressed modal characteristics of the guide vane shaft-top cover rubbing coupling system is analyzed based on the reduced dynamics model;

[0010] S3, the influence law of the near load end contact state, the near-far load end contact state and the friction coefficient on the vibration response and frequency spectrum characteristics of the guide vane shaft-top cover rubbing coupling system is analyzed when the reduced dynamics model is subjected to a simple harmonic excitation;

[0011] S4, the vibration characteristics of the guide vane shaft-top cover rubbing coupling system are analyzed based on steps S2 and S3, so as to evaluate whether the Francis turbine is stably and safely operated.

[0012] In some embodiments, in S1, the following steps are included:

[0013] S11, a dynamics model of the guide vane shaft-top cover rubbing coupling system is established by intercepting 1 / 16 sector structure of the guide vane shaft-top cover rubbing coupling system; the guide vane shaft-top cover rubbing coupling system comprises a guide vane shaft, a top cover and a contact area;

[0014] S12, the reduced dynamics equations of the guide vane shaft substructure and the top cover substructure are respectively established based on the fixed interface modal synthesis method.

[0015] In some embodiments, the guide vane shaft substructure retains the nodes attached to the guide vane shaft contact surface and the section center nodes N1 and N2 as master nodes, the top cover substructure retains the nodes attached to the top cover contact surface as master nodes, and the remaining nodes are slave nodes; neither the guide vane shaft substructure nor the top cover substructure includes the guide vane shaft contact area surface elements (including thin layer elements and target elements) and the top cover contact area surface elements (including thin layer elements and contact elements).

[0016] In some embodiments, the reduced order dynamic equation is:

[0017]

[0018] wherein,

[0019]

[0020] In the formula, M i , C i , K i , and F i are the mass matrix, damping matrix, stiffness matrix, and external load vector of the substructure i, respectively; i = 1 or 2, which are the guide vane shaft substructure and the top cover substructure, respectively; u i，m is the physical degree of freedom corresponding to the retained master node; y rj is the generalized degree of freedom when the modal truncation number is r i ; m is the master degree of freedom; s is the slave degree of freedom; T i is the transformation matrix; G i，sm is the static constraint mode; Φ i is the master mode; I i is the unit matrix; 0 i is the zero matrix; K i，ss is the stiffness matrix corresponding to the slave node; K i，sm is the coupling stiffness matrix corresponding to the slave node and the master node; u i，s is the physical degree of freedom corresponding to the slave node.

[0021] In some embodiments, S2 comprises the following steps:

[0022] S21, respectively analyze the influence of the guide vane shaft truncation number and the top cover truncation number on the natural frequency of the guide vane shaft-top cover rubbing coupling system;

[0023] S22, analyze the influence of the water flow surface load p and the friction coefficient μ on the first three order natural frequencies of the guide vane shaft-top cover rubbing coupling system.

[0024] In some embodiments, the convergence deviation of the first three order natural frequencies of the reduced dynamic model is:

[0025]

[0026] In the formula, r1 is the guide vane shaft truncation number; r2 is the top cover truncation number; j = 1, 2, 3; f j is the first three order natural frequencies of the reduced dynamic model, j = 1, 2, 3.

[0027] A vibration characteristic analysis system of a guide vane shaft-top cover rubbing coupling system of a hydraulic turbine, comprising:

[0028] The generating module is used for generating the reduced dynamic model of the guide vane shaft-top cover rubbing coupling system by using the finite element method in combination with the fixed interface modal synthesis method.

[0029] The first analysis module is used for analyzing the influence law of the modal truncation number, the friction coefficient and the water flow surface load on the prestress modal characteristics of the first three orders of the guide vane shaft-top cover rubbing coupling system based on the reduced dynamic model generated by the generating module.

[0030] The second analysis module is used for analyzing the influence law of the near load end contact state, the near-far load end contact state and the friction coefficient on the vibration response and the frequency spectrum characteristics of the guide vane shaft-top cover rubbing coupling system when the reduced dynamic model is subjected to the harmonic excitation.

[0031] The output evaluation module is used for evaluating the vibration characteristics of the guide vane shaft-top cover rubbing coupling system based on the analysis results of the first analysis module and the second analysis module, thereby evaluating whether the mixed-flow hydraulic turbine is stably and safely operated, and outputting the evaluation result.

[0032] Compared with the prior art, the present application has the following beneficial effects:

[0033] The fixed interface modal synthesis method is applied to the vibration analysis of the guide vane shaft-top cover rubbing coupling system of the mixed-flow hydraulic turbine, a reduced model of the guide vane shaft-top cover coupling system with high precision is constructed, and the calculation efficiency is improved. By studying the action mechanism of the water flow load and the friction coefficient on the rubbing fault of the guide vane shaft-top cover coupling system, the influence of different contact faults on the first three orders of the natural frequency of the system is analyzed, and the influence law of the contact state and the friction coefficient on the vibration response of the system under the water flow excitation is analyzed, so as to monitor and diagnose the structural health state and the fault of the mixed-flow hydraulic turbine. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 It is a cross-sectional structure schematic diagram of the mixed-flow hydraulic turbine unit of the embodiment 1 of the present application.

[0035] Figure 2 It is a dynamic modeling process schematic diagram of the guide vane shaft-top cover coupling system of the mixed-flow hydraulic turbine based on the embodiment 1 of the present application; wherein figure (a) is a mechanical model, and figure (b) is a reduced dimension reduction model of the mechanical model of figure (a).

[0036] Figure 3 It is a prestress modal analysis process schematic diagram of the embodiment 1 of the present application.

[0037] Figure 4Figure is the influence diagram of the truncated number r1 of the guide vane shaft and the truncated number r2 of the top cover on the first three order natural frequencies of the reduced model (p=100 MPa, μ=0.3) of the embodiment 1 of the application, wherein figure (a) is the variation law of the first order natural frequency with the truncated number r1 of the guide vane shaft and the truncated number r2 of the top cover, figure (b) is the variation law of the second order natural frequency with the truncated number r1 of the guide vane shaft and the truncated number r2 of the top cover, figure (c) is the variation law of the third order natural frequency with the truncated number r1 of the guide vane shaft and the truncated number r2 of the top cover, and figure (d) is the variation law of the convergence deviation of the first three order natural frequencies with the truncated number r1 of the guide vane shaft and the truncated number r2 of the top cover.

[0038] Figure 5 Figure is the comparison diagram of the first three order modes of the full model and the reduced model (p=100 MPa, μ=0.3) of the embodiment 1 of the application, wherein figure (a) is the first three order modes of the full model, and figure (b) is the first three order modes of the reduced model (after reconstruction).

[0039] Figure 6 Figure is the influence diagram of the water flow surface load p and the friction coefficient μ on the contact degree of the system of the embodiment 1 of the application, wherein figure (a) is the variation law of the contact area of the near load end and the far load end with the water flow surface load p and the friction coefficient μ, and figure (b) is the variation law of the contact area of the near load end and the far load end with the water flow surface load p and the friction coefficient μ.

[0040] Figure 7 Figure is the contact state and the contact stress distribution diagram of the rub-impact surface under the given conditions of the statics analysis of the embodiment 1 of the application, wherein figure (a) is the contact state and the contact stress of the near load end and the far load end when the working condition is p=10 MPa, μ=0.02, figure (b) is the contact state and the contact stress of the near load end and the far load end when the working condition is p=10 MPa, μ=0.5, figure (c) is the contact state and the contact stress of the near load end and the far load end when the working condition is p=100 MPa, μ=0.02, and figure (d) is the contact state and the contact stress of the near load end and the far load end when the working condition is p=100 MPa, μ=0.5.

[0041] Figure 8 Figure is the influence diagram of the water flow surface load p and the friction coefficient μ on the natural frequency of the system of the embodiment 1 of the application, wherein figure (a) is the variation law of the first three order natural frequencies of the full model with the water flow surface load p and the friction coefficient μ, figure (b) is the variation law of the first three order natural frequencies of the reduced model with the water flow surface load p and the friction coefficient μ, and figure (c) is the variation law of the error of the first three order natural frequencies of the reduced model and the full model with p and the friction coefficient μ.

[0042] Figure 9Figure is a schematic diagram of the combined deformation beam model of the guide vane shaft of the embodiment 1 of the present application; wherein figure (a) is the load and boundary condition of the guide vane shaft, figure (b) is the deformation of the combined beam, and figure (c) is the deflection variation law of the contact at the far load end.

[0043] Figure 10 Figure is a schematic diagram of the amplitude-frequency response curve comparison of the full model and the reduced model of the embodiment 1 of the present application (p0=10MPa, μ=0.5).

[0044] Figure 11 Figure is a schematic diagram of the natural frequency distribution of the top cover, the guide vane shaft and the guide vane shaft-top cover coupling system of the embodiment 1 of the present application (p0=10MPa, μ=0.5).

[0045] Figure 12 Figure is a schematic diagram of the vibration response comparison of the full model and the reduced model of the embodiment 1 of the present application (p0=10MPa); wherein figure (a) is the vibration response comparison of the full model and the reduced model under the working condition of p0=10MPa, μ=0.02, and figure (b) is the vibration response comparison of the full model and the reduced model under the working condition of p0=10MPa, μ=0.5.

[0046] Figure 13 Figure is a schematic diagram of the amplitude-frequency response curve comparison of the full model and the reduced model of the embodiment 1 of the present application (p0=100MPa, μ=0.5).

[0047] Figure 14 Figure is a schematic diagram of the natural frequency distribution of the top cover, the guide vane shaft and the guide vane shaft-top cover coupling system of the embodiment 1 of the present application (p0=100MPa, μ=0.5).

[0048] Figure 15 Figure is a schematic diagram of the vibration response comparison of the full model and the reduced model of the embodiment 1 of the present application (p0=100MPa); wherein figure (a) is the vibration response comparison of the full model and the reduced model under the working condition of p0=100MPa, μ=0.02, and figure (b) is the vibration response comparison of the full model and the reduced model under the working condition of p0=100MPa, μ=0.5.

[0049] Figure 16 Figure is a schematic diagram of the structure of the embodiment 2 of the present application.

[0050] In the figure:

[0051] 11, guide vane shaft-top cover contact area, 12, top cover, 13, guide vane crank, 14, control ring, 15, servomotor connecting rod, 16, guide vane shaft, 17, movable guide vane, 18, bottom ring, 19, runner. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application; based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort fall within the protection scope of the present application.

[0053] Embodiment 1

[0054] A vibration characteristic analysis method of a guide vane shaft-top cover rubbing coupling system of a hydraulic turbine, comprising the following steps:

[0055] S1, a reduced dynamics model of the guide vane shaft-top cover rubbing coupling system is established by using a finite element method in combination with a fixed interface modal synthesis method.

[0056] As shown in Figure 1 , key components of the Francis turbine unit include a guide vane shaft-top cover contact area, a control ring 14, a servomotor push-pull plate 15, a guide vane crank arm 13, a guide vane shaft 16, a movable guide vane 17, a top cover 12, a bottom ring 18, a runner 19 and the like structure. Water enters the runner 19 radially, forms a central circulation through the movable guide vane 17, and is discharged axially after rotating the runner 19 to do work.

[0057] As shown in Figure 2 , the periodic symmetry of the structure is considered in the embodiment, and a 1 / 16 sector structure of the guide vane shaft-top cover rubbing coupling system is intercepted to establish a dynamics model of the guide vane shaft-top cover rubbing coupling system, and the model is reduced by using the fixed interface modal synthesis method.

[0058] The guide vane shaft-top cover rubbing coupling system includes a guide vane shaft (including 5797 solid elements, obtained by using ANSYS software), a top cover (including 17984 solid elements) and a contact area (including 242 thin layer elements and 242 target elements of the guide vane shaft contact area surface, and 288 thin layer elements and 288 contact elements of the top cover contact area surface) and the like three parts. The parameter settings of the materials of all components of the guide vane shaft-top cover rubbing coupling system are as follows: Young's modulus E = 200 GPa, Poisson's ratio v = 0.3, density p = 7850 kg / m 3 . In addition, according to the service environment of the guide vane shaft-top cover coupling system, the relevant displacement boundary conditions are set as follows: the top cover upper flange (such as face 4 in Figure 2 (a)) and the two end cylindrical surfaces of the guide vane shaft (such as faces 2 and 3 in Figure 2 (a)) are set as fixed constraints. The action of water flow on the movable guide vane is regarded as a uniformly distributed surface load p acting on the movable guide vane (such as face 1 in Figure 2 (a)).

[0059] Based on the fixed interface modal synthesis method, the substructures of the guide vane shaft and the top cover are established respectively. The guide vane shaft substructure retains the nodes attached to the guide vane shaft contact surface and the cross-section center nodes N1 and N2 as the main nodes (such as Figure 2 (a)), the top cover structure retains the nodes attached to the top cover contact surface as the main nodes (see Figure 2 (b)), and the remaining nodes are used as slave nodes. It should be noted that the surface elements of the guide vane shaft contact area (including thin layer elements and target elements) and the surface elements of the top cover contact area (including thin layer elements and contact elements) are not included in the substructure. The motion equation of each substructure i (i = 1 and 2 represent the guide vane shaft substructure and the top cover structure respectively) is:

[0060]

[0061] Where M i 、C i , K i 、F i are the mass matrix, damping matrix, stiffness matrix and external load vector (including water flow load and friction load) of substructure i respectively; and u i are the acceleration vector, velocity vector and displacement vector of substructure i respectively.

[0062] The calculation expression is:

[0063]

[0064] Wherein, f1 and f2 are the first-order and second-order natural frequencies of the guide vane shaft and top cover friction coupling system in different contact states, respectively; ξ1 and ξ2 are the damping ratios corresponding to f1 and f2, respectively. In this embodiment, ξ1 = ξ2 = 0.02; when the system is in near-load-end contact, f1 = 57.52 Hz and f2 = 108.84 Hz; when the system is in near-far-load-end contact, f1 = 111.15 Hz and f2 = 154.69 Hz.

[0065] The matrix equation of formula (1) is divided into the master degree of freedom "m" and the slave degree of freedom "s", and the related matrices and vectors are expressed as follows:

[0066]

[0067]

[0068] in,

[0069]

[0070] Where u i，m The physical degree of freedom corresponding to the reserved master node; y i，rThe modal cutoff number is r i The generalized degrees of freedom when T i is the transformation matrix, and the calculation expression is:

[0071]

[0072] Where G i,sm is the static constraint mode, I i is the unit matrix; Φ i Main mode; 0 i is a zero matrix; K i,ss is the stiffness matrix corresponding to the slave node; K i,sm is the coupling stiffness matrix corresponding to the slave node and the master node; u i，s is the physical degree of freedom corresponding to the slave node.

[0073] Substituting formula (4) into formula (1), the reduced-order dynamic equation of the substructure is obtained as follows:

[0074]

[0075] Where,

[0076] S2. Based on the reduced model of the guide vane shaft-top cover coupling system, the influence of the modal truncation number, friction coefficient and water static load on the first three order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system is analyzed. This embodiment mainly conducts prestressed modal analysis of the guide vane shaft-top cover coupling system based on the prestressed modal analysis framework of the linear perturbation method. The specific process is as follows: Figure 3 As shown, the following steps are included:

[0077] Basic analysis: Perform static analysis to solve the node displacement solution and contact state of the system in equilibrium under specific water flow static load and constant friction coefficient between the guide vane shaft and the top cover;

[0078] The first stage of linear perturbation: restart from the basic analysis, update the K matrix based on the node displacement solution and the guide vane shaft-top cover contact state in the static analysis, and delete the external load;

[0079] The second stage of linear perturbation: Generate M matrix and perform modal analysis.

[0080] S21. Analysis of the influence of modal cutoff number.

[0081] The guide vane shaft-top cover coupling system includes a guide vane shaft substructure and a top cover structure, and the effects of the guide vane shaft truncation number and the top cover truncation number on the natural frequency of the guide vane shaft-top cover friction coupling system are analyzed respectively.

[0082] like Figure 4When the water flow surface load p = 100 MPa and the friction coefficient μ = 0.3, the convergence deviation of the first three order natural frequencies of the reduced model is:

[0083]

[0084] In the formula, r1 is the guide vane shaft truncation number; and r2 is the top cover truncation number.

[0085] As Figure 4 (a) and (c) show that when the guide vane shaft truncation number is constant, the first three order natural frequencies f j (j = 1, 2, 3) of the reduced dynamic model gradually converge and tend to be stable with the increase of the top cover truncation number, and it can be seen from Figure 4 (d) that the top cover truncation number has a relatively small influence on f1, and has a relatively large influence on f2 and f3; when the top cover truncation number is constant, the first three order natural frequencies f j (j = 1, 2, 3) of the reduced dynamic model are almost not affected by the guide vane shaft truncation number. This is mainly because the mass of the top cover is much larger than that of the guide vane shaft, and the hollow shell structure of the top cover makes its stiffness smaller than that of the guide vane shaft, so that the mode of the guide vane shaft-top cover coupling system is dominated by the top cover mode. Figure 4 (d) shows that when r1 ≥ 1 and r2 ≥ 12 (such as Figure 4 A1, A2 and A3 in (c)), the convergence deviation Et j (j = 1, 2, 3) are all less than 1%. In this embodiment, r1 = 1 and r2 = 12 are taken for the model reduction.

[0086] When the water flow surface load p = 100 MPa and the friction coefficient μ = 0.3, the first three order prestressed modes of the full model and the reduced model are as shown in Figure 5 The maximum error of the natural frequency is 0.13%, thereby verifying the effectiveness of the reduced model.

[0087] S22, load and friction coefficient influence.

[0088] As Figure 6 (a) and Figure 6 (b) show that when the friction coefficient μ is constant, the near load end contact area A N increases with the increase of the flow surface load p, and the far load end contact area A N slowly decreases with the increase of the friction coefficient μ, but the change degree is small; when the friction coefficient μ is constant, the near load end contact area A F increases with the increase of the flow surface load p, and there is a phenomenon of obvious transition from no contact to contact; and when the flow surface load p is constant, the far load end contact area A F decreases with the increase of the friction coefficient μ. Figure 7The contact state and contact stress of the contact region after static analysis under four given conditions are shown. When p = 10 MPa, μ = 0.02 or μ = 0.5, there is only contact at the near load end between the guide vane shaft and the top cover; when p = 100 MPa, μ = 0.02 or μ = 0.5, there is contact at both the near load end and the far load end, the contact area at the near load end is much larger than that at the far load end, and the stress distribution is also more concentrated at the near load end

[0089] As shown in Figure 8 (a) and Figure 8 (b), when the friction coefficient μ is constant, f1 increases with the increase of the water surface load p, and there is an obvious step increase in the process of the increase of f1, which is mainly because the contact state between the guide vane shaft and the top cover changes from the near load end contact to the near-far load end contact, the mutation of the contact state will cause the step increase of the overall stiffness of the system, so that f1 mutates, as can be seen from the mutation regions B1 and B2, with the increase of the friction coefficient μ, the water surface load p corresponding to the mutation of f1 also increases, in regions B3 and B4, the guide vane shaft and the top cover maintain the near-far load end contact state, when the water surface load p is constant, f1 increases with the increase of the friction coefficient μ; when the friction coefficient μ is constant, f2 increases with the increase of the water surface load p, in regions B5 and B6, when the water surface load p is constant, f2 decreases to a certain extent with the increase of the friction coefficient μ, in regions B7 and B8, f2 increases with the increase of the friction coefficient μ; the overall change range of f3 is relatively small, when the friction coefficient μ is constant, f3 increases with the increase of the water surface load p, when the water surface load p is constant, f3 basically increases with the increase of the friction coefficient μ, only in regions B9 and B 10 , f3 decreases to a certain extent.

[0090] Figure 8 (c) compares the error Es j (j = 1, 2, 3) between the reduced model and the full model with the variation law of the water surface load p and the friction coefficient μ, wherein Es j is defined as follows:

[0091]

[0092] In the formula, f j Redu (p, μ), f j Ful (p, μ) are the jth (j = 1, 2, 3) order natural frequency of the reduced model and the full model based on the given water surface load p and friction coefficient μ, respectively.

[0093] Figure 8(c) as shown, when p ∈ [5, 100] MPa (Δp = 5 MPa), μ ∈ [0, 0.5] (Δμ = 0.02), the error value of the first order natural frequency of the reduced model and the full model is not more than 0.06%, the error value of the second order natural frequency is not more than 0.18%, and the error value of the third order natural frequency is not more than 0.04%, thereby verifying the effectiveness of the guide vane shaft-top cover coupling system constructed based on the reduced method.

[0094] In order to further illustrate the first three order natural frequencies f j (j = 1, 2, 3) of the reduced dynamics model from the mechanism, the phenomenon that the water flow surface load p increases with the increase of the friction coefficient μ when the mutation occurs, as shown in Figure 9 , the guide vane shaft is simplified to an equal cross-section simply supported beam model from the perspective of material mechanics. The size parameters of the simply supported beam are set as follows: l = 2753.7 mm, a = 617 mm, b = 1433 mm, c = 191.7 mm, d = 501.7 mm, the cross-sectional moment of inertia O = 4.533 × 108 mm 4 . Here, the water flow surface load borne by the movable guide vane is equivalent to a concentrated load p·A, and the load acting area A = 335930 mm 2 (as shown in the movable guide vane surface 1 in Figure 2 (a)).

[0095] Due to the deformation of the movable guide vane caused by the water flow surface load p, the guide vane shaft and the top cover first contact at the near load end, and the top cover generates a contact force F N and a friction force F S (as shown in Figure 9 (a)) on the guide vane shaft. The gap value δ = 1 mm of the guide vane shaft and the top cover at the far load end contact area, and when the deflection w of the guide vane shaft at the far load end contact is ≥1 mm, the guide vane shaft and the top cover are in contact. Based on the deflection linear superposition principle under multiple loads in material mechanics, the deflection w of the far load end contact can be regarded as the linear superposition of the deflections w N , produced by the concentrated load p·A, the contact force F S at the near load end contact, and the friction force F p , and the expression is as follows:

[0096]

[0097] In the formula, w p is the deflection produced by the concentrated load p·A; is the deflection produced by the contact force F N at the near load end contact; is the deflection produced by the friction force F S at the near load end contact.

[0098] like Figure 9 As shown in (c), in region C1, when p<9.68MPa, the friction coefficient μ is constant, and the deflection w at the far-end contact increases with the increase of the water surface load p. When the water surface load p is constant, the deflection w at the far-end contact does not change with the change of the friction coefficient μ. This is mainly because there is no contact between the guide vane shaft and the top cover, so the change of the friction coefficient μ has no effect on the deflection w at the far-end contact. In region C2, when p≥9.68MPa, contact occurs at the near-load end, and the friction coefficient μ is constant. The deflection w at the far-load end contact increases with the increase of the water surface load p. When the water surface load p is constant, the deflection w at the far-load end contact decreases with the increase of the friction coefficient μ, resulting in a larger water surface load p being required when the guide vane shaft-top cover coupling system transitions from near-load end contact to near-far-load end contact. This reveals from the perspective of the structural deformation mechanism why the increase in the friction coefficient μ causes the water surface load p to increase when the guide vane shaft-top cover coupling system switches from near-load end contact to near-far-load end contact.

[0099] S3. Vibration response analysis.

[0100] By comparing the reduced model and the full model of the friction coupling system between the guide vane shaft and the top cover, the movable guide vane surface 1 is subjected to simple harmonic excitation p=p0·sin(2π·f e ·t) is applied, and the influence of the near-load end contact and the near-distal load end contact as well as the friction coefficient μ on the vibration response and spectrum characteristics of the guide vane shaft-top cover coupling system is analyzed. Figure 2 As shown in (a), p0 is the amplitude of the uniformly distributed water flow surface load on the movable guide vane surface 1, f e is the excitation frequency of the uniform water flow load, and t is the time for the uniform water flow surface load to act. In this embodiment, the solution time t = 60 / f e , time integration step Δt=1 / (128·f e ), with vibration response data acquired from the center point N1 of the rubbing region near the guide vane shaft. The influence of the near-load contact state, the near-distal load contact state, and the friction coefficient on the vibration response and spectral characteristics of the guide vane shaft-top cover rubbing coupling system under simple harmonic excitation in the reduced dynamics model was analyzed.

[0101] S31. Analysis of system vibration response under rubbing near the load end only;

[0102] Depend on Figure 7 (a) and Figure 7 (b) It can be seen that when p0 = 10 MPa, there is friction between the guide vane shaft and the top cover only near the load end. Therefore, based on p0 = 10 MPa and μ = 0.5, the system is calculated at f e ∈[20, 120]Hz X-axis amplitude-frequency response curve, such as Figure 10 As shown.Figure 10 It can be seen that there are the first-order resonance point D1 (57 Hz, 0.2589 mm) and the second-order resonance point D2 (108 Hz, 0.2612 mm) in the studied excitation frequency range. This is mainly because they are close to the first-order and second-order natural frequencies of the guide vane shaft-top cover coupling system, respectively. Figure 11 As shown, the amplitude amplification phenomenon occurs. In addition, in order to further identify the dominant mode of the guide vane shaft-top cover coupling system at the resonance, Figure 11 The distribution diagrams of the natural frequencies of the guide vane shaft, top cover and guide vane shaft-top cover coupling system at p = 10 MPa and μ = 0.5 are drawn. Figure 11 It can be seen that the coupled system is dominated by the first-order and second-order vibration modes of the top cover at D1 and D2, respectively.

[0103] like Figure 10 As shown, it shows that the X-axis amplitude-frequency response curves of the full model and the reduced model are in good agreement, which further proves the effectiveness of the reduced modeling method of the present invention. Figure 12 We further compare the full model and the reduced model at D1 in terms of f e =57Hz, p0=10MPa, μ=0.02 and 0.5.

[0104] like Figure 12 As shown in , the time history response curves of the reduced model and the full model in the X direction are in good agreement. Take the X-direction and Y-direction vibration responses within t∈[500,1000]ms, as shown in Figure 12 The corresponding spectrum curves are obtained by fast Fourier transform for regions E1 and E2. It can be seen from the spectrum curve that the spectrum components of the vibration response are mainly reflected in the multiples of the excitation frequency, such as Figure 12 2f in e , 3f e , 4f e ,···, and at odd multiples of 3f e 、5f e and 7f e The amplitude amplification phenomenon occurs at 3f. e 、5f e and 7f e They are respectively close to the system's 3rd-order natural frequency (184.24Hz), 6th-order natural frequency (281.43Hz), and 9th-order natural frequency (396.9Hz), resulting in amplitude amplification.

[0105] In addition, the solution time of the full model and the reduced model when p = 10 MPa, μ = 0.02 and μ = 0.5 are shown in Table 1.

[0106] Table 1 Comparison of solution time of full model and reduced model (p0 = 10 MPa)

[0107]

[0108] The reduced model reduces the calculation time by 48.67% compared with the full model under low friction coefficient (μ=0.02), and reduces the calculation time by 49.17% compared with the full model under high friction coefficient (μ=0.5).

[0109] S32, near-far load end rubbing system vibration response analysis;

[0110] As shown in Figure 7 (c) and Figure 7 (d), when the load p0=100MPa is applied to the active guide vane surface 1 (as shown in Figure 2 (a)), both near load end rubbing and far load end rubbing exist between the guide vane shaft and the top cover. As shown in Figure 13 , the X-direction amplitude-frequency response curves of the full model and the reduced model are in good agreement. There is a first-order resonance point D3 (155Hz, 1.042mm) in the range of the excitation frequency studied, which is mainly due to the fact that it is close to the second-order natural frequency of the guide vane shaft-top cover coupling system, as shown in Figure 14 , which further causes amplitude amplification, and as can be seen from Figure 14 , the vibration mode of the coupling system at the resonance point is dominated by the top cover vibration mode.

[0111] Figure 15 The X-direction time history responses of the reduced model and the full model at D3 are compared respectively at f e =155Hz, μ=0.02 and μ=0.5, as well as the corresponding frequency spectrum characteristics. It can be seen that the X-direction time history response curves of the reduced model and the full model are in good agreement. The X-direction time history responses in the time interval t∈[150,300]ms (as shown in the areas E3 and E4 in Figure 15 ) are analyzed by frequency spectrum. The system frequency spectrum appears amplitude amplification at odd multiple frequencies (3f e , 5f e and 7f e ), which is mainly due to the fact that 3f e , 5f e and 7f e are close to the 11th order natural frequency (448.68Hz), the 25th order natural frequency (765.3Hz) and the 33rd order natural frequency (1075.16Hz) of the system respectively, so that amplitude amplification occurs.

[0112] The solving time of the full model and the reduced model under p0=100MPa, μ=0.02 and μ=0.5 is compared in Table 2.

[0113] Table 2 Comparison of solving time of full model and reduced model (p0=100MPa)

[0114]

[0115] The reduced model reduces the calculation time by 39.36% compared with the full model under a low friction coefficient (μ=0.02), and reduces the calculation time by 47.92% compared with the full model under a high friction coefficient (μ=0.5).

[0116] S4, analyzing the vibration characteristics of the guide vane shaft-top cover rubbing coupling system based on steps S2 and S3, so as to evaluate whether the mixed-flow hydraulic turbine is stably and safely operated.

[0117] The application applies the fixed interface modal synthesis method to vibration analysis of the guide vane shaft-top cover rubbing coupling system of the mixed-flow hydraulic turbine, constructs a reduced model of the guide vane shaft-top cover coupling system with high precision, and improves the calculation efficiency. The action mechanism of the water flow load and the friction coefficient on the rubbing fault of the guide vane shaft-top cover coupling system is researched, the influence of different contact faults on the first three order natural frequencies of the system is analyzed, and the influence law of the contact state and the friction coefficient on the vibration response of the system under water flow excitation is explored, so as to monitor and diagnose the structural health state and fault of the mixed-flow hydraulic turbine.

[0118] Embodiment 2

[0119] A vibration characteristic analysis system of a guide vane shaft-top cover rubbing coupling system of a hydraulic turbine, comprising:

[0120] A generation module: a finite element method combined with a fixed interface modal synthesis method is used to generate a reduced dynamic model of the guide vane shaft-top cover rubbing coupling system;

[0121] A first analysis module: based on the reduced dynamic model generated by the generation module, the influence law of the modal truncation number, the friction coefficient and the water flow surface load on the first three order pre-stressed modal characteristics of the guide vane shaft-top cover rubbing coupling system is analyzed;

[0122] A second analysis module: used to analyze the influence law of the near load end contact state, the near-far load end contact state and the friction coefficient on the vibration response and frequency spectrum characteristics of the guide vane shaft-top cover rubbing coupling system when the reduced dynamic model is subjected to harmonic excitation;

[0123] An output evaluation module: based on the analysis results of the first analysis module and the second analysis module, the vibration characteristics of the guide vane shaft-top cover rubbing coupling system are evaluated, so as to evaluate whether the mixed-flow hydraulic turbine is stably and safely operated.

[0124] The vibration characteristic analysis system of the turbine guide vane shaft-top cover friction coupling system of the present invention can be installed in a computer device. The computer device includes a processor, a memory, and a computer program stored in the memory and runnable on the processor, such as a program for generating vibration characteristic analysis of the turbine guide vane shaft-top cover friction coupling system. The memory includes at least one type of readable storage medium, and the readable storage medium includes a flash memory, a mobile hard disk, a multimedia card, a card-type memory (for example, SD or DX memory, etc.), a magnetic memory, a magnetic disk, an optical disk, etc. The processor is the control core of the electronic device, and uses various interfaces and lines to connect the various components of the entire computer device. By running or executing the programs or modules stored in the memory, and calling the data stored in the memory, the processor performs various functions of the computer device and processes data.

[0125] The module described in the present invention refers to a series of computer program segments that can be executed by a processor of a computer device and can complete fixed functions, and is stored in a memory of the computer device.

[0126] The technical features of the above embodiments can be combined arbitrarily (as long as there is no contradiction in the combination of these technical features). In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described; these embodiments that are not explicitly written should also be considered to be within the scope of this specification.

Claims

1. A method for analyzing the vibration characteristics of a guide vane shaft-top cover rubbing coupling system of a hydraulic turbine, characterized in that, The method comprises the following steps: S1, using finite element method combined with fixed interface modal synthesis method, a reduced dynamic model of the guide vane shaft-top cover rubbing coupling system is established; the method comprises the following steps: S11, a 1 / 16 sector structure of the guide vane shaft-top cover rubbing coupling system is intercepted to establish a dynamic model of the guide vane shaft-top cover rubbing coupling system; the guide vane shaft-top cover rubbing coupling system comprises a guide vane shaft, a top cover and a contact area; S12, a reduced dynamic equation of the guide vane shaft substructure and the top cover substructure is respectively established; S2, based on the reduced dynamic model, the influence law of modal truncation number, friction coefficient and water flow surface load on the prestressed modal characteristics of the first three orders of the guide vane shaft-top cover rubbing coupling system is analyzed; the method comprises the following steps: S21, the influence of the guide vane shaft truncation number and the top cover truncation number on the natural frequency of the guide vane shaft-top cover rubbing coupling system is analyzed respectively; S22, analyze water flow surface load p and friction coefficient μ The influence of the guide vane shaft-top cover rubbing coupling system on the first three order natural frequencies S3, the influence law of the near load end contact state, the near-far load end contact state and the friction coefficient on the vibration response and frequency spectrum characteristics of the guide vane shaft-top cover rubbing coupling system under the action of the reduced dynamic model under the action of the harmonic excitation is analyzed; S4, based on steps S2 and S3, the vibration characteristics of the guide vane shaft-top cover rubbing coupling system are analyzed, so as to evaluate whether the mixed-flow water turbine is stably and safely operated.

2. The method according to claim 1, wherein The guide vane shaft substructure retains the nodes attached to the guide vane shaft contact surface and the section center nodes N1 and N2 as master nodes, and the top cover substructure retains the nodes attached to the top cover contact surface as master nodes, and the remaining nodes as slave nodes; neither the guide vane shaft substructure nor the top cover substructure includes guide vane shaft contact area surface elements and top cover contact area surface elements.

3. The method of claim 2, wherein the method further comprises: The reduced dynamic equation is: ； Wherein, ； ； ； ； ； ； ; In the formula, , , , are the mass matrix, the damping matrix, the stiffness matrix and the external load vector of the substructure respectively; are the guide vane shaft substructure and the top cover substructure respectively; is the physical degree of freedom corresponding to the reserved master node; is the generalized degree of freedom when the modal truncation number is ; is the master degree of freedom; is the slave degree of freedom; is the transformation matrix; is the static constraint mode; is the master mode; is the unit matrix; is the zero matrix; is the stiffness matrix corresponding to the slave node; is the coupling stiffness matrix corresponding to the slave node and the master node; is the physical degree of freedom corresponding to the slave node.

4. The method of claim 3, wherein the method further comprises: The convergence deviation of the first three orders of the reduced dynamic model is: wherein is the number of blade axis truncations; is the number of top cover truncations; ; is the first three natural frequencies of the reduced dynamics model, .

5. A water turbine guide vane shaft-top cover rubbing coupling system vibration characteristic analysis system, which applies the water turbine guide vane shaft-top cover rubbing coupling system vibration characteristic analysis method of any one of claims 1-4.

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