Water turbine guide vane shaft-top cover rub-impact coupling system vibration characteristic analysis method

Abstract

The invention discloses a water turbine guide vane shaft-top cover rub-impact coupling system vibration characteristic analysis method which comprises the following steps: S1, establishing a reduction dynamic model of a guide vane shaft-top cover rub-impact coupling system by adopting a finite element method in combination with a fixed interface modal synthesis method; s2, analyzing an influence rule of a modal truncation number, a friction coefficient and a water flow surface load on first three orders of prestress modal characteristics of the guide vane shaft-top cover rub-impact coupling system based on a reduction kinetic model; s3, analyzing an influence rule of a near load end contact state, a near-far load end contact state and a friction coefficient on vibration response and spectral characteristics of the guide vane shaft-top cover rub-impact coupling system when the reduction kinetic model is subjected to harmonic excitation; and S4, evaluating whether the mixed-flow water turbine operates stably and safely based on the steps. By analyzing the vibration characteristics of the guide vane shaft-top cover rub-impact coupling system of the mixed-flow water turbine, the structural health state and fault of the mixed-flow water turbine are monitored and diagnosed.

Description

Technical Field

[0001] The invention relates to the technical field of rubbing fault analysis of a Francis turbine, and in particular to a vibration characteristic analysis method of a turbine guide vane shaft-top cover rubbing coupling system. Background Art

[0002] Francis turbine is an important component of the hydroelectric generator set and is subjected to water flow load for a long time. The guide vane shaft and the top cover are the core and key components of the Francis turbine. Under the action of water flow, the guide vane shaft and the top cover are prone to friction problems, which may cause abnormal vibration of the unit and affect normal use; in severe cases, it may cause damage to the equipment structure and cause major safety accidents. Therefore, it is necessary to carry out friction 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 the structural health monitoring of the Francis turbine.

[0003] Many scholars at home and abroad have conducted relevant research on the friction problem of key parts in Francis turbines. Zhang Reike et al. established a turbine rotor-bearing friction fault model 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 Dongming 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 turbine stator and rotor friction fault. Using the fourth-order Runge-Kutta method, Nie Sai et al. studied the influence of unbalanced magnetic pull, friction force and nonlinear oil film force on the vibration characteristics of turbine shaft system alone or in coupling. Based on the Jeffcott rotor model, Zhang et al. established a bending-torsion rotor-bearing coupling system with friction impact of a turbine unit, and analyzed the influence of excitation current, mass eccentricity and electromagnetic torque on the dynamic characteristics of the system. Xu Long et al. constructed a nonlinear dynamic model of parallel misalignment and rubbing coupling faults of the turbine rotor system, and discussed the influence of the unit speed, eccentricity and parallel misalignment on the nonlinear dynamic behavior of the system. Huang Zhiwei et al. proposed a rotor dynamic model of a turbine generator unit with misalignment and rubbing coupling faults, and used numerical methods to study the influence of misalignment, bearing stiffness and other parameter changes on the dynamic characteristics of the system. Zhang et al. constructed a coupled vibration model of the friction-impact system of the turbine unit, and analyzed the influence of friction-impact faults and electromagnetic excitation on the dynamic characteristics of the turbine rotor-bearing system. Wu et al. established a nonlinear dynamic model of the turbine shaft system under the action of elasticity and sealing force, and analyzed the nonlinear stability of the sealing system. The research results show that in the absence of external interference, the degree of friction between the runner and the sealing structure with nonlinear sealing force will not increase with the increase of speed. Liang Xing established a turbine rotor dynamic model under the multi-fault coupling mechanism, and analyzed the influence of factors such as mass eccentricity, rotor misalignment and speed on the dynamic characteristics of the system. The results show that the rotor of the hydropower unit is prone to periodic rubbing or chaotic motion when running at high speed. Wu et al. established a fault diagnosis model based on a one-dimensional convolutional neural network method, which can achieve timely and accurate rubbing fault detection by training with a turbine rotor vibration signal data set. Wu used a time-frequency method based on variational mode decomposition to analyze the rubbing fault of a turbine, and verified the effectiveness of the method by comparing it with experimental results.

[0004] In summary, many scholars have conducted in-depth and detailed research on the friction coupling dynamic behavior of the rotor-stator system in the turbine, but less attention has been paid to the friction problem induced by the water flow in the guide vane shaft-top cover coupling system of the turbine. Summary of the invention

[0005] The purpose of the present invention is to provide a method for analyzing the vibration characteristics of a turbine guide vane shaft-top cover rubbing coupling system. A finite element reduced dynamic model of a mixed flow turbine guide vane shaft-top cover coupling system is established by using a fixed interface modal synthesis method. At the same time, a guide vane shaft-top cover rubbing characterization mechanical model is established based on contact dynamics theory. By analyzing the rubbing problem induced by water flow in the guide vane shaft-top cover coupling system in the turbine, abnormal vibration and safety problems of the unit are reduced.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system comprises the following steps:

[0008] S1. The reduced dynamics model of the guide vane shaft-top cover friction coupling system is established by combining the finite element method with the fixed interface modal synthesis method.

[0009] S2. Analyze the influence of modal cutoff number, friction coefficient and water surface load on the first three-order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system based on the reduced dynamics model;

[0010] S3. Analyze the influence of the near-load contact state, near-distal load contact state and friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system when the reduced dynamics model is subjected to simple harmonic excitation;

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

[0012] In some embodiments, S1 includes the following steps:

[0013] S11, intercepting a 1 / 16 sector structure of the guide vane shaft-top cover friction coupling system to establish a dynamic model of the guide vane shaft-top cover friction coupling system; the guide vane shaft-top cover friction coupling system includes a guide vane shaft, a top cover and a contact area;

[0014] S12. Based on the fixed interface modal synthesis method, the reduced-order dynamic equations of the guide vane shaft substructure and the top cover structure are established respectively.

[0015] In some embodiments, the guide vane shaft substructure retains the nodes to which the guide vane shaft contact surface is attached and the cross-sectional center nodes N1 and N2 as master nodes, and the top cover structure retains the nodes to which the top cover contact surface is attached as master nodes, and the remaining nodes are slave nodes; the guide vane shaft substructure and the top cover structure do not include the surface units of the guide vane shaft contact area (including thin layer units and target units) and the surface units of the top cover contact area (including thin layer units and contact units).

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

[0017]

[0018] in,

[0019]

[0020] Where M i , C i , K i 、F i are the mass matrix, damping matrix, stiffness matrix and external load vector of substructure i respectively; i = 1 or 2, respectively, the guide vane shaft substructure and the top cover structure; u i，m The physical degrees of freedom corresponding to the reserved master node; y rj The modal cutoff number is r i The generalized degree of freedom when T is ; m is the main degree of freedom; s is the secondary degree of freedom; i is the transformation matrix; G i，sm is the static constraint mode; Φ i Main mode; I i is the identity matrix; 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.

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

[0022] S21. 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 friction coupling system respectively;

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

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

[0025]

[0026] Where r1 is the number of cut-offs of the guide vane shaft; r2 is the number of cut-offs of the top cover; j = 1, 2, 3; f j To reduce the first three natural frequencies of the dynamic model, j = 1, 2, 3.

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

[0028] Generation module: The finite element method combined with the fixed interface modal synthesis method is used to generate the reduced dynamics model of the guide vane shaft-top cover friction coupling system;

[0029] The first analysis module: Based on the reduced dynamics model generated by the generation module, it is used to analyze the influence of the modal cutoff number, friction coefficient and water surface load on the first three-order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system;

[0030] The second analysis module is used to analyze the influence of the near-load contact state, near-distal load contact state and friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system when the reduced dynamics model is subjected to simple harmonic excitation;

[0031] Output evaluation module: Based on the analysis results of the first analysis module and the second analysis module, it is used to evaluate the vibration characteristics of the guide vane shaft-top cover friction coupling system, so as to evaluate whether the Francis turbine is operating stably and safely, and output the evaluation results.

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

[0033] The present invention applies the fixed interface modal synthesis method to the vibration analysis of the guide vane shaft-top cover friction coupling system of the Francis turbine, constructs a reduced model of the guide vane shaft-top cover coupling system with high accuracy, and improves the calculation efficiency. By studying the mechanism of water flow load and friction coefficient on the friction failure of the guide vane shaft-top cover coupling system, the influence of different contact failures on the first three natural frequencies of the system, and the influence of contact state and friction coefficient on the vibration response of the system under water flow excitation are analyzed, so as to monitor and diagnose the structural health status and failure of the Francis turbine. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a schematic diagram of the cross-sectional structure of a mixed flow turbine unit according to Example 1 of the present invention.

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

[0036] Figure 3 It is a schematic diagram of the prestressed modal analysis process of Example 1 of the present invention.

[0037] Figure 4Schematic diagram of the influence of the guide vane shaft truncation number r1 and the top cover truncation number r2 on the first three natural frequencies of the reduced model in Example 1 of the present invention (p = 100MPa, μ = 0.3); wherein Figure (a) shows the variation law of the first-order natural frequency with the guide vane shaft truncation number r1 and the top cover truncation number r2, Figure (b) shows the variation law of the second-order natural frequency with the guide vane shaft truncation number r1 and the top cover truncation number r2, Figure (c) shows the variation law of the third-order natural frequency with the guide vane shaft truncation number r1 and the top cover truncation number r2, and Figure (d) shows the variation law of the convergence deviation of the first three-order natural frequencies with the guide vane shaft truncation number r1 and the top cover truncation number r2.

[0038] Figure 5 Schematic diagram of the comparison of the first three modes of the full model and the reduced model of Example 1 of the present invention (p=100MPa, μ=0.3); wherein Figure (a) is the first three modes of the full model, and Figure (b) is the first three modes of the reduced model (after reconstruction).

[0039] Figure 6 Schematic diagram of the influence of the water surface load p and the friction coefficient μ on the contact degree of the system in Example 1 of the present invention; Figure (a) shows the change law of the contact area of ​​the near-load end and the far-load end of the full model with the water surface load p and the friction coefficient μ, and Figure (b) shows the change law of the contact area of ​​the near-load end and the far-load end of the reduced model with the water surface load p and the friction coefficient μ.

[0040] Figure 7 Schematic diagram of the contact state and contact stress distribution of the friction surface under given conditions of the static analysis of Example 1 of the present invention; wherein Figure (a) shows the contact state and contact stress of the near load end and the far load end when the working condition is p = 10MPa, μ = 0.02, Figure (b) shows the contact state and contact stress of the near load end and the far load end when the working condition is p = 10MPa, μ = 0.5, Figure (c) shows the contact state and contact stress of the near load end and the far load end when the working condition is p = 100MPa, μ = 0.02, and Figure (d) shows the contact state and contact stress of the near load end and the far load end when the working condition is p = 100MPa, μ = 0.5.

[0041] Figure 8 Schematic diagram of the influence of the water surface load p and the friction coefficient μ on the natural frequency of the system in Example 1 of the present invention; wherein Figure (a) shows the variation law of the first three natural frequencies of the full model with the water surface load p and the friction coefficient μ, Figure (b) shows the variation law of the first three natural frequencies of the reduced model with the water surface load p and the friction coefficient μ, and Figure (c) shows the variation law of the errors of the first three natural frequencies of the reduced model and the full model with p and the friction coefficient μ.

[0042] Fig. 9This is a schematic diagram of a combined deformation beam model in which the guide vane shaft of Example 1 of the present invention is simplified; wherein Figure (a) shows the load and boundary conditions on the guide vane shaft, Figure (b) shows the deformation of the combined beam, and Figure (c) shows the variation law of the deflection at the contact point of the far load end.

[0043] Fig.10 Schematic diagram of comparison of amplitude-frequency response curves of the full model and the reduced model of Example 1 of the present invention (p0=10MPa, μ=0.5).

[0044] Fig.11 It is a schematic diagram of the distribution diagram of each order of natural frequencies (p0=10MPa, μ=0.5) of the top cover, the guide vane shaft and the guide vane shaft-top cover coupling system in Example 1 of the present invention.

[0045] Fig.12 Schematic diagram of vibration response comparison (p0=10MPa) of the full model and the reduced model of Example 1 of the present invention; wherein Figure (a) is a vibration response comparison of the full model and the reduced model when p0=10MPa, μ=0.02, and Figure (b) is a vibration response comparison of the full model and the reduced model when p0=10MPa, μ=0.5.

[0046] Fig.13 Schematic diagram of comparison of amplitude-frequency response curves of the full model and the reduced model of Example 1 of the present invention (p0=100MPa, μ=0.5).

[0047] Fig.14 Schematic diagram of the distribution of natural frequencies of each order (p0=100MPa, μ=0.5) of the top cover, the guide vane shaft and the guide vane shaft-top cover coupling system in Example 1 of the present invention.

[0048] Fig.15 Schematic diagram of the vibration response comparison (p0=100 MPa) of the full model and the reduced model of Example 1 of the present invention; wherein Figure (a) is the vibration response comparison of the full model and the reduced model when p0=100 MPa, μ=0.02, and Figure (b) is the vibration response comparison of the full model and the reduced model when p0=100 MPa, μ=0.5.

[0049] Fig.16 This is a schematic diagram of the structure of Example 2 of the present invention.

[0050] As shown in the figure:

[0051] 11. Guide vane shaft-top cover contact area, 12. Top cover, 13. Guide vane crank arm, 14. Control ring, 15. Relay 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 invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0053] Example 1

[0054] A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system comprises the following steps:

[0055] S1. The reduced dynamics model of the guide vane shaft-top cover friction coupling system is established by combining the finite element method with the fixed interface modal synthesis method.

[0056] like Figure 1 As shown in FIG. 1 , the key components of the Francis turbine unit include the guide vane shaft-top cover contact area, the control ring 14, the relay push-pull plate 15, the guide vane arm 13, the guide vane shaft 16, the movable guide vane 17, the top cover 12, the bottom ring 18, the runner 19 and other structures. Water enters the runner 19 from the radial direction, forms a central circulation through the movable guide vane 17, drives the runner 19 to rotate and do work, and then is discharged along the axial direction.

[0057] like Figure 2 As shown, this embodiment takes into account the periodic symmetry of the structure, intercepts the 1 / 16 sector structure of the guide vane shaft-top cover friction coupling system to establish the dynamic model of the guide vane shaft-top cover friction coupling system, and reduces the system model through the fixed interface mode synthesis method.

[0058] The guide vane shaft-top cover friction coupling system consists of three parts: the guide vane shaft (including 5797 solid units, obtained by ANSYS software), the top cover (including 17984 solid units) and the contact area (including 242 thin layer units on the surface of the guide vane shaft contact area, 242 target units and 288 thin layer units and 288 contact units on the surface of the top cover contact area). The parameters of all component materials of the guide vane shaft-top cover friction coupling system are set as follows: Young's modulus E = 200GPa, Poisson's ratio v = 0.3, density ρ = 7850kg / 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 flange surface on the top cover (such as Figure 2 (a) Middle surface 4) and the cylindrical surfaces at both ends of the guide vane shaft (such as Figure 2 (a) The fixed support constraints are set on the middle surface 2 and surface 3. The effect of water flow on the movable guide vane is regarded as a uniform surface load p acting on the movable guide vane (such as Figure 2 (a) Middle surface 1).

[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 contact surface of the guide vane shaft and the cross-section center nodes N1 and N2 as the main nodes (such as Figure 2 (a)), the top cover structure retains the node attached to the top cover contact surface as the main node (see Figure 2 (b)), and the remaining nodes are used as slave nodes. It should be noted that the surface units of the guide vane shaft contact area (including thin layer units and target units) and the surface units of the top cover contact area (including thin layer units and contact units) 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 friction coupling system between the guide vane shaft and the top cover under 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=57.52Hz, f2=108.84Hz; when the system is in near-far-load-end contact, f1=111.15Hz, f2=154.69Hz.

[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] In the formula, u i，m The physical degrees 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] In the formula, G i,sm is the statically constrained 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] In the formula,

[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 flow 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 when the system is in equilibrium state under the action of specific water flow static load and the constant friction coefficient between the guide vane shaft and the top cover;

[0078] Linear perturbation stage 1: restart from the basic analysis, update the K matrix based on the node displacement solution in the static analysis and the guide vane shaft-top cover contact state, 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 comprises a guide vane shaft substructure and a top cover structure, and 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 friction coupling system is analyzed respectively.

[0082] like Figure 4As shown in the figure, when the water surface load p = 100 MPa and the friction coefficient μ = 0.3, the convergence deviation of the first three natural frequencies of the reduced model is:

[0083]

[0084] Where r1 is the number of cut-offs of the guide vane shaft; r2 is the number of cut-offs of the top cover.

[0085] like Figure 4 It can be seen from Figures (a) to (c) that when the number of guide vane shaft cuts is constant, the first three natural frequencies f of the reduced dynamic model are j (j=1, 2, 3) gradually converges and stabilizes with the increase of the number of top cover cutoffs. Figure 4 (d) It can be seen that the top cover truncation number has a relatively small effect on f1, but a relatively large effect on f2 and f3; when the top cover truncation number is constant, the first three natural frequencies f of the reduced dynamic model j (j=1,2,3) is almost unaffected by the number of guide vane shaft cutoffs. This is mainly because the mass of the top cover is much greater 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, r2≥12 (e.g. Figure 4 A1, A2, A3), convergence deviation Et j (j=1, 2, 3) are all less than 1%. In this embodiment, r1=1 and r2=12 are used to reduce the model.

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

[0087] S22, influence of load and friction coefficient.

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

[0089] like Figure 8 (a) and Figure 8 As shown in (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 phenomenon in the process of f1 increasing. This 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-distal load end contact. The sudden change in the contact state will cause a step increase in the overall stiffness of the system, thereby causing f1 to mutate. It can be seen from the mutation areas B1 and B2 that with the increase of the friction coefficient μ, the water surface load p corresponding to the mutation of f1 also increases. In areas B3 and B4, the guide vane shaft and the top cover remain in near-distal load end contact. state, when the water flow 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 flow surface load p. In areas B5 and B6, when the water flow surface load p is constant, f2 decreases to a certain extent with the increase of the friction coefficient μ. In areas B7 and B8, f2 increases with the increase of the friction coefficient μ. The overall change range of f3 is small. When the friction coefficient μ is constant, f3 increases with the increase of the water flow surface load p. When the water flow surface load p is constant, f3 basically increases with the increase of the friction coefficient μ. Only in areas B9 and B 10 There was a certain degree of decline.

[0090] Figure 8 (c) Comparison of the error Es between the first three natural frequencies of the reduced model and the full model j (j=1,2,3) changes with the flow surface load p and friction coefficient μ, where 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 frequencies obtained by the reduced model and the full model based on the given water surface load p and friction coefficient μ, respectively.

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

[0094] In order to further explain the mechanism of the first three natural frequencies f of the reduced dynamics model, j (j=1,2,3), when a sudden change occurs, the water surface load p increases with the increase of the friction coefficient μ, such as Fig. 9 As shown, in this embodiment, the guide vane shaft is simplified into a simple supported beam model of uniform cross section from the perspective of material mechanics. The dimension parameters of the simple supported beam are set as follows: l = 2753.7 mm, a = 617 mm, b = 1433 mm, c = 191.7 mm, d = 501.7 mm, and the section inertia moment O = 4.533 × 108 mm 4 Here, the water surface load on the movable guide vane is equivalent to a concentrated load p·A, and the load action area A=335930mm 2 (like Figure 2 (a) shows the movable guide vane surface 1). The Young's modulus of the simply supported beam is E = 200 GPa.

[0095] As the movable guide vane is deformed by the water surface load p, the guide vane shaft and the top cover first come into contact at the near-load end, and at the same time, the top cover generates a contact force F on the guide vane shaft. N and friction F S (like Fig. 9 (a)). The gap value between the guide vane shaft and the top cover in the contact area at the far load end is δ = 1mm. When the deflection w of the guide vane shaft at the far load end contact is ≥ 1mm, the guide vane shaft and the top cover come into contact. Based on the principle of linear superposition of deflections under multiple loads in material mechanics, the deflection w at the far load end contact can be regarded as a concentrated load p·A, and the contact force F at the near load end contact N and friction F S The deflection w generated p , The linear superposition of is expressed as follows:

[0096]

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

[0098] like Fig. 9 As shown in (c), in area 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 flow surface load p. When the water flow 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 contact at the far-load end increases with the increase of the water surface load p. When the water surface load p is constant, the deflection w at the contact at the far-load end decreases with the increase of the friction coefficient μ, resulting in a larger water surface load p required for the guide vane shaft-top cover coupling system to transition from the near-load end contact to the near-far-load end contact. This reveals from the perspective of the structural deformation mechanism why the increase in the friction coefficient μ will increase the water surface load p when the guide vane shaft-top cover coupling system switches from the near-load end contact to the 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 active guide vane surface 1 is subjected to simple harmonic excitation p = p0·sin(2π·f e ·t), 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 ), the vibration response data is obtained from the center point N1 of the friction area near the guide vane shaft. When the reduced dynamics model is subjected to simple harmonic excitation, the influence of the contact state near the load end, the contact state near-distal load end and the friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system is 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 at 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 Fig.10 As shown. Fig.10 It can be seen that there are 1st-order resonance point D1 (57 Hz, 0.2589 mm) and 2nd-order resonance point D2 (108 Hz, 0.2612 mm) in the studied excitation frequency range. This is mainly because they are close to the 1st-order and 2nd-order natural frequencies of the guide vane shaft-top cover coupling system, respectively. Fig.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, Fig.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 = 10MPa and μ = 0.5 are plotted. Fig.11 It can be seen that the coupled system is dominated by the 1st and 2nd order vibration modes of the top cover at D1 and D2, respectively.

[0103] like Fig.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. Fig.12 The full model and the reduced model at D1 are further compared in f e =57Hz, p0=10MPa, X-axis displacement time history response and its spectral characteristics when μ=0.02 and 0.5.

[0104] like Fig.12 As shown in Figure 2, 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 2 Fig.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 Fig.12 2f 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 (184.24 Hz), 6th-order natural frequency (281.43 Hz), and 9th-order natural frequency (396.9 Hz), 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 is 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 at low friction coefficient (μ=0.02) reduces the computational time by 48.67% compared to the full model, while the reduced model at high friction coefficient (μ=0.5) reduces the computational time by 49.17% compared to the full model.

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

[0110] like Figure 7 (c) and Figure 7 As shown in (d), when the movable guide vane surface 1 (such as Figure 2 (a) shows that when the load p0 = 100 MPa, there is friction at the near-load end and the far-load end between the guide vane shaft and the top cover. Fig.13 As shown in the figure, the X-axis amplitude-frequency response curves of the full model and the reduced model are in good agreement. There is a first-order resonance point D3 (155 Hz, 1.042 mm) in the studied excitation frequency range, which is mainly due to its proximity to the second-order natural frequency of the guide vane shaft-top cover coupling system, as shown in Fig.14 As shown, the amplitude amplification phenomenon occurs, and from Fig.14 It can be seen that the vibration mode of the coupling system at this resonance point is dominated by the top cover vibration mode.

[0111] Fig.15 The reduced model at D3 and the full model at f are compared. e =155Hz, μ = 0.02 and μ = 0.5, and the corresponding spectral 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. Take the X-direction time-history response within t∈[150,300]ms (such as Fig.15 The spectrum of the system is analyzed in the odd-order multiples (3f e , 5f e and 7f e ) appears to be amplified, which is mainly due to the 3f e , 5f e and 7f e They are respectively close to the 11th-order natural frequency (448.68 Hz), 25th-order natural frequency (765.3 Hz), and 33rd-order natural frequency (1075.16 Hz) of the system, resulting in amplitude amplification.

[0112] The comparison of solution time of the full model and the reduced model when p0 = 100 MPa, μ = 0.02 and μ = 0.5 is shown in Table 2.

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

[0114]

[0115] When the friction coefficient is low (μ=0.02), the reduced model reduces the computational time by 39.36% compared to the full model. When the friction coefficient is high (μ=0.5), the reduced model reduces the computational time by 47.92% compared to the full model.

[0116] S4. Analyze the vibration characteristics of the guide vane shaft-top cover friction coupling system based on steps S2 and S3, so as to evaluate whether the Francis turbine operates stably and safely.

[0117] The present invention applies the fixed interface modal synthesis method to the vibration analysis of the guide vane shaft-top cover friction coupling system of the Francis turbine, constructs a reduced model of the guide vane shaft-top cover coupling system with high accuracy, and improves the calculation efficiency. The mechanism of the water flow load and friction coefficient on the friction failure of the guide vane shaft-top cover coupling system is studied, the influence of different contact failures on the first three natural frequencies of the system is analyzed, and the influence of the contact state and friction coefficient on the vibration response of the system under water flow excitation is explored, so as to monitor and diagnose the structural health status and failure of the Francis turbine.

[0118] Example 2

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

[0120] Generation module: The finite element method combined with the fixed interface modal synthesis method is used to generate the reduced dynamics model of the guide vane shaft-top cover friction coupling system;

[0121] The first analysis module: Based on the reduced dynamics model generated by the generation module, it is used to analyze the influence of the modal cutoff number, friction coefficient and water surface load on the first three-order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system;

[0122] The second analysis module is used to analyze the influence of the near-load contact state, near-distal load contact state and friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system when the reduced dynamics model is subjected to simple harmonic excitation;

[0123] Output evaluation module: Based on the analysis results of the first analysis module and the second analysis module, it is used to evaluate the vibration characteristics of the guide vane shaft-top cover friction coupling system, so as to evaluate whether the Francis turbine is operating stably and safely.

[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 run on the processor, such as a turbine guide vane shaft-top cover friction coupling system vibration characteristic analysis generation program. Wherein, 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 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, and executes various functions of the computer device and processes data by running or executing programs or modules stored in the memory, and calling data stored in the memory.

[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 may be arbitrarily combined (as long as there is no contradiction in the combination of these technical features). 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 vibration characteristics of a turbine guide vane shaft-top cover friction coupling system, characterized in that: The following steps are involved: S1. The reduced dynamics model of the guide vane shaft-top cover friction coupling system is established by combining the finite element method with the fixed interface modal synthesis method. S2. Analyze the influence of modal cutoff number, friction coefficient and water surface load on the first three-order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system based on the reduced dynamics model; S3. Analyze the influence of the near-load contact state, near-distal load contact state and friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system when the reduced dynamics model is subjected to simple harmonic excitation; S4. Analyze the vibration characteristics of the guide vane shaft-top cover friction coupling system based on steps S2 and S3, so as to evaluate whether the Francis turbine operates stably and safely.

2. A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system according to claim 1, characterized in that: S1 includes the following steps: S11, intercepting a 1 / 16 sector structure of the guide vane shaft-top cover friction coupling system to establish a dynamic model of the guide vane shaft-top cover friction coupling system; the guide vane shaft-top cover friction coupling system includes a guide vane shaft, a top cover and a contact area; S12. Establish the reduced-order dynamic equations of the guide vane shaft substructure and the top cover structure respectively.

3. A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system according to claim 2, characterized in that: The guide vane shaft substructure retains the nodes to which the guide vane shaft contact surface is attached and the cross-sectional center nodes N1 and N2 as the main nodes, and the top cover structure retains the nodes to which the top cover contact surface is attached as the main nodes, and the remaining nodes are used as slave nodes; the guide vane shaft substructure and the top cover structure do not include the surface units of the guide vane shaft contact area and the surface units of the top cover contact area.

4. A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system according to claim 3, characterized in that: The reduced-order kinetic equation is: in, Where M i , C i , K i 、F i are the mass matrix, damping matrix, stiffness matrix and external load vector of substructure i respectively; i = 1 or 2, respectively, the guide vane shaft substructure and the top cover structure; u i,m The physical degrees of freedom corresponding to the reserved master nodes; The modal cutoff number is r o The generalized degree of freedom when T is ; m is the main degree of freedom; s is the secondary degree of freedom; i is the transformation matrix; G i,sm is the static constraint mode; Φ i Main mode; I i is the identity matrix; 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.

5. The vibration characteristic analysis method of a turbine guide vane shaft-top cover friction coupling system according to claim 1, characterized in that: S2 includes the following steps: S21. 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 friction coupling system respectively; S22. Analyze the influence of the water surface load p and the friction coefficient μ on the first three natural frequencies of the guide vane shaft-top cover friction coupling system.

6. A method for analyzing vibration characteristics of a turbine guide vane shaft-top cover friction coupling system according to claim 5, characterized in that: The convergence deviation of the first three natural frequencies of the reduced dynamics model is: Where r1 is the number of cuts on the guide vane shaft; r2 is the number of cuts on the top cover; j = 1, 2, 3; f j To reduce the first three natural frequencies of the dynamic model, j = 1, 2, 3.

7. A vibration characteristic analysis system for a turbine guide vane shaft-top cover friction coupling system, using the vibration characteristic analysis method for a turbine guide vane shaft-top cover friction coupling system as claimed in any one of claims 1 to 6, characterized in that: include: Generation module: The finite element method combined with the fixed interface modal synthesis method is used to generate the reduced dynamics model of the guide vane shaft-top cover friction coupling system; The first analysis module: Based on the reduced dynamics model generated by the generation module, it is used to analyze the influence of the modal cutoff number, friction coefficient and water surface load on the first three-order prestressed modal characteristics of the guide vane shaft-top cover friction coupling system; The second analysis module is used to analyze the influence of the near-load contact state, near-distal load contact state and friction coefficient on the vibration response and spectrum characteristics of the guide vane shaft-top cover friction coupling system when the reduced dynamics model is subjected to simple harmonic excitation; Output evaluation module: Based on the analysis results of the first analysis module and the second analysis module, it is used to evaluate the vibration characteristics of the guide vane shaft-top cover friction coupling system, thereby evaluating whether the Francis turbine is operating stably and safely, and outputting the evaluation results.

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