A Stability Analysis and Transient Calculation Method of Liquid-Filled Rotors Based on Multi-Frequency Vortex Decomposition

Abstract

The present invention discloses a method for analyzing the stability and transient calculation of a liquid-filled rotor based on multi-frequency whirling decomposition. The implementation steps of the method include: 1) establishing a "dual-rotor" finite element model, obtaining the uncoupled fluid cross-stiffness state space, and calculating the eigenvalues corresponding to each order of the system modes; 2) based on the multi-frequency whirling hypothesis, calculating the fluid cross-stiffness corresponding to the eigenvalues of each order of the system modes one by one, coupling it into the system state space equation, and iteratively calculating to obtain the converged eigenvalues of each order of the system under the influence of the liquid-solid coupling effect; 3) calculating the liquid exciting force of each order of the mode based on the converged system eigenvalues, and decomposing the total displacement response of the system into each order of the system modes based on the mode superposition principle; 4) performing transient dynamics solution analysis on the rotor dynamics model after liquid-solid coupling for each order of the mode in combination with the explicit-implicit separation solution framework. This method solves the problem that the traditional lumped mass model in the traditional liquid-solid coupling rotor stability analysis method can only handle a single whirling frequency.

Description

Technical Field

[0001] The present invention relates to the field of finite element simulation for computer-aided calculation of rotor dynamics with liquid-solid coupling, and particularly to a method for analyzing the stability and transient calculation of a liquid-filled rotor based on multi-frequency whirling decomposition. Background Art

[0002] A centrifuge is a typical liquid-filled rotor device mainly using liquid as the working medium. When it is in the condition of partial liquid filling, the liquid-solid coupling effect between the liquid and the rotor will cause the rotor to generate an unstable region in the rotational speed range near the first critical speed. In this region, the liquid-filled rotor will undergo extremely large-amplitude non-synchronous vibration due to the influence of liquid excitation, which will affect its operation stability and even cause production accidents, and further delay the R & D process of large-scale centrifuges in our country.

[0003] The traditional research method for liquid-filled rotors is to consider the entire rotor as a lumped mass model. However, a low-degree-of-freedom model is difficult to accurately characterize the increasingly complex dynamic characteristics of the liquid-filled rotor of a centrifuge, and it is also impossible to consider the influence of the high-order modes of the system. To clarify the instability mechanism of the liquid-filled rotor under the liquid-solid coupling effect and the stability change law of the high-order modes, an accurate model of the liquid-filled rotor of a centrifuge can be established based on the finite element method. However, the existing fluid force model can only consider the single-frequency whirling of the rotor. Introducing the finite element method means that it is necessary to solve the contradiction between multi-frequency whirling and the only single-frequency whirling fluid force model. Therefore, the multi-frequency whirling of the rotor can be regarded as the sum of multiple single-frequency whirlings based on the modal superposition principle, and the displacement is decomposed into each order of mode and the stability interval of the liquid-filled rotor is analyzed and calculated step by step. Then, based on the converged system eigenvalues, the transient response of the liquid-filled rotor under the liquid-solid coupling effect is efficiently solved by combining the linear-nonlinear explicit-implicit separation solution method. Summary of the Invention

[0004] The method for analyzing the stability and transient calculation of a liquid-filled rotor based on multi-frequency whirling decomposition provided by the present invention can solve problems such as that the lumped mass model is difficult to accurately characterize the overall dynamic characteristics of the rotor system and cannot analyze the stability interval change of the high-order modes of the system when analyzing the liquid-solid coupling dynamic characteristics of the liquid-filled rotor traditionally. The present invention also combines the modal superposition principle to solve the problem that the existing single-frequency whirling fluid force model cannot meet the multi-frequency whirling assumption brought by the finite element method. To improve the transient calculation efficiency under the multi-modal liquid-solid coupling of the liquid-filled rotor, the present invention also adopts a linear-nonlinear explicit-implicit separation transient calculation method based on the G-α numerical calculation method, which overcomes the problem that the conventional Newmark-β method has no suppression ability for the high-frequency modal oscillation response, and finally quickly, stably and accurately solves the nonlinear transient dynamic response of the system.

[0005] To solve the above technical problems, the present invention provides the following technical solutions:

[0006] S1. Establish a finite element model of the liquid-filled rotor system and perform modal analysis on the finite element model of the liquid-filled rotor system;

[0007] S2. Obtain the cross stiffness of the fluid acting on the liquid-solid coupling system in each order of mode, and iterate with the modal analysis to obtain the converged system eigenvalues;

[0008] S3. Based on the modal superposition principle, decompose the external force and total displacement of the rotor into each order of mode, calculate the fluid excitation force step by step, and combine the linear-nonlinear explicit-implicit separation method to iteratively solve the displacement response of each order of mode after convergence for the liquid-filled rotor system.

[0009] S1 includes the steps:

[0010] S1.1 Measure the actual size of the rotor, divide the nodes, where the centrifuge sleeve is regarded as the outer rotor with a rotational speed of 0, and the rotating shaft is regarded as the inner rotor, and construct a rotor finite element model based on the Timoshenko beam theory and the finite element method;

[0011] S1.2 Convert the rotor dynamics equation into the state space form and perform modal analysis to calculate the eigenvalues and eigenvectors of each order of mode without the fluid-structure coupling effect;

[0012] S2 includes the steps:

[0013] S2.1 According to the fluid cross stiffness formula under single-frequency whirling, calculate the fluid cross stiffness corresponding to the two sets of conjugate eigenvalues of each order of mode one by one, couple the cross stiffness into the state space in S1, and iteratively solve the eigenvalues of each order of mode until stable convergence;

[0014] S2.2 For the two sets of conjugate eigenvalues of each order of mode, select the eigenvalue with the largest real part as the stability criterion of the liquid-solid coupling liquid-filled rotor system at the rotational speed at this moment.

[0015] S2.3 Perform stability analysis on each order of mode, and the rotational speed range where the real part of the eigenvalue is greater than 0 is the instability interval under the liquid-solid coupling action of the liquid-filled rotor.

[0016] S3 includes the steps:

[0017] S3.1 Decompose the external excitation and displacement response of the rotor into each order of mode, where the displacement at the initial moment is simplified to the displacement response without fluid excitation;

[0018] S3.2 Calculate the fluid excitation force corresponding to each order of mode step by step based on the converged system eigenvalues;

[0019] S3.2 Based on the transient calculation method of explicit-implicit separation, separate the linear and nonlinear nodes of the rotor, and use the G-α numerical calculation method to obtain the integral formula of the rotor motion equation;

[0020] In S3.3, the Newton-Raphson iteration formula is used to solve the nonlinear node responses at each order step by step, and then the displacements, velocities, and accelerations of all nodes at each order are deduced inversely.

[0021] In S3.4, based on the modal superposition principle, the displacements of each order are superimposed to obtain the total response of the liquid-filled rotor under the liquid-solid coupling effect.

[0022] The present invention has the following advantages:

[0023] The method for analyzing the stability and transient calculation of a liquid-filled rotor based on multi-frequency whirling decomposition provided by the present invention regards the multi-frequency whirling of the liquid-filled rotor as the sum of multiple single-frequency whirlings by introducing the finite element modeling method and combining the modal superposition principle. It realizes the accurate modeling of the centrifuge rotor under complex elastic support conditions, making the transient simulation results of the liquid-filled rotor under the liquid-solid coupling effect closer to the actual working conditions compared with the traditional lumped mass model. By introducing the linear-nonlinear explicit-implicit separation algorithm, the present invention extracts the nonlinear nodes of the rotor, realizes the iterative calculation dimension of the high-dimensional finite element model of the rotor, and greatly reduces the time for calculating the transient response. By combining the G-α numerical calculation method with the explicit trapezoidal method to calculate the transient response of the system order by order, the problem that the traditional Newmark-β numerical calculation method lacks the ability to suppress the high-order modes of the system is avoided. Description of the Drawings

[0024] Figure 1 It is the finite element model of the liquid-filled rotor established in the embodiment of the present invention.

[0025] Figure 2 It is the flow chart of the stability analysis method under the action of multi-frequency whirling in the embodiment of the present invention.

[0026] Figure 3 It is the first four-order stability curve diagram of the liquid-filled rotor system under different fluid viscosity conditions in the embodiment of the present invention.

[0027] Figure 4 It is the device for analyzing the stability and dynamic calculation of the liquid-filled rotor based on multi-frequency whirling decomposition in the embodiment of the present invention.

[0028] Figure 5 It is the decomposition result of the unbalance response of each order of the rotor in the liquid-filled system in the embodiment of the present invention.

[0029] Figure 6 It is the spectrum waterfall diagram of the simulation transient response of the liquid-filled rotor system in the embodiment of the present invention.

[0030] Figure 7 It is the spectrum waterfall diagram of the experimental vibration response of the liquid-filled rotor system in the embodiment of the present invention. Detailed Embodiments

[0031] As Figure 1 shown, a method and device for transient calculation of the dynamic characteristics of the whole machine rotor based on the flexible foundation transfer function implemented by the present invention are as follows:

[0032] Based on the modal decomposition principle, this example regards the multi-frequency whirling of the liquid-filled rotor as the sum of multiple single-frequency whirlings, conducts a stability analysis on each order of the modal of the liquid-filled rotor system one by one, analyzes the stability interval of each order of the modal, and combines the linear-nonlinear explicit-implicit separation algorithm to conduct a transient response analysis of the rotor. The specific calculation steps are as follows:

[0033] The protection scope of the present invention is not limited to the description of this implementation method.

[0034] In the first step, establish a finite element model of the liquid-filled system and conduct a modal analysis on the liquid-filled system;

[0035] 1) Split the liquid-filled rotor system into beam elements, disk elements, and bearing elements. Based on the Timoshenko beam theory, model the rotating shaft, regard the disk element as a concentrated mass element, and regard the bearing element as a support element to provide a reaction force for the rotor system. Finally, establish the dynamic equation of the rotor system as follows:

[0036]

[0037] In the formula, M, C, G, and K are the overall mass, damping, gyroscopic effect, and stiffness matrices of the liquid-filled rotor system after being assembled completely, and q are the acceleration, velocity, and displacement vectors of the liquid-filled rotor system respectively, Ω is the rotational speed of the liquid-filled rotor system, F is the external excitation force received by the liquid-filled rotor system, including the unbalance force F u , the support force F b , and the fluid excitation force F l , that is:

[0038] F = F u + F b + F l

[0039] 2) Convert the dynamic equation of the rotor system into the state space form:

[0040]

[0041] In the formula, A and B are the coefficient matrices in the process of converting the rotor dynamic equation into the state space, z is the state variable, and Q is the state space force vector:

[0042]

[0043] Solve the eigenvalues of the state space equation to obtain the eigenvalues λ corresponding to each order of the modal of the liquid-filled systemm and the modal matrix ψ, where:

[0044] λ mn , λ m(n+1) = σ m ±jw m , m = 1, 2, 3...., n = 1, 3

[0045] The subscript m represents the corresponding modal order during solution, and n represents the eigenvalue sequence number corresponding to this modal order. Since each modal order corresponds to two sets of conjugate roots, that is, 4 eigenvalues, so n ∈ {1, 2, 3, 4}. Among them, the real part σ m is the stability criterion for the m-th order mode of the liquid-filled rotor system, and the imaginary part w m is the natural frequency of the m-th order of the liquid-filled rotor system, and j is the imaginary unit.

[0046] Second step, obtain the cross stiffness of the fluid acting on the liquid-solid coupling system in each order of mode, and iterate with the modal analysis to obtain the converged system eigenvalues;

[0047] 1) Based on the fluid N-S equation, establish the hydrodynamic equation, and combine the finite difference method to solve the differential equation to derive that the fluid cross stiffness of the m-th order mode of the system under the fluid-solid coupling action is:

[0048]

[0049] In the formula, S m is the equivalent cross stiffness of the m-th order of the liquid-filled rotor system, and k XX , k XY , k YX and k YY are the equivalent stiffness coefficients of the fluid under the fluid-solid coupling action, and their forms are:

[0050]

[0051] m l is the liquid mass when the drum is filled with liquid, v is the dynamic viscosity of the fluid, and r o is the inner wall radius of the drum, and are the auxiliary variables constructed when solving the N-S hydrodynamic equation respectively, aiming to decouple the equation in two perturbation directions. The superscripts ''' and '' respectively represent the third derivative and the second derivative of the corresponding function.

[0052] 2) Couple the cross stiffness of the m-th order mode fluid with the state space expression of the rotor system, and calculate the n-th eigenvalue λ mn of the m-th order mode of the new liquid-filled rotor system under the fluid-solid coupling action. When λ mnWhen the iterative convergence condition is met (when the 2-norm of the eigenvalues calculated in two consecutive times satisfies the convergence accuracy of 1e-4), it is considered that the calculation of the nth eigenvalue of the mth order mode of the rotor system is completed; otherwise, the fluid cross stiffness in (1) is recalculated and the solution is redone until the convergence requirement is satisfied. Figure 2 It is the flow chart of the stability analysis method under the action of multi-frequency whirling.

[0053] 3) Select the eigenvalue with the largest real part from the two sets of eigenvalues obtained in the solution of the mth order as the stability criterion for the mth order. If the largest real part σ m ≥0 of the mth order, it is considered that the mth order of the rotor system is unstable; otherwise, it is considered that the mth order of the system is stable. Figure 3 It is the curve diagram of the first four order stability types of the liquid-filled rotor system under different fluid viscosity conditions.

[0054] The third step: Based on the modal superposition principle, decompose the external forces and total displacements acting on the rotor into each order of mode, calculate the fluid excitation force order by order, and combine the linear-nonlinear explicit-implicit separation method to iteratively solve the displacement response of each order of mode of the liquid-filled rotor system after convergence.

[0055] 1) To calculate the system response of each order of mode step by step, it is necessary to decompose the unbalanced force, bearing force, etc. acting on the rotor system into the corresponding modes. According to the rotor dynamics equation, the physical space coordinates are transformed into modal space coordinates through the modal matrix:

[0056] z = Ψg

[0057] where z is the state variable of the liquid-filled rotor system in the physical space, g is the state variable of the liquid-filled rotor system in the modal space, Ψ is the complex modal matrix of the liquid-filled rotor, and ψ i is the modal column vector of the i-th column of the liquid-filled rotor system:

[0058] Ψ = [ψ 1 ψ 2 … ψ 2n

[0059] Substitute it into the state space expression to get:

[0060]

[0061] Then the mth order and nth modal coordinate of the acting force in the modal space is:

[0062]

[0063] In the formula is the mth order and nth component in the modal space. Since there are two sets of a total of 4 eigenvalues in the mth order mode, the external acting force on the system in the mth order mode in the physical space is:

[0064]

[0065] In the formula, is the m-th external force other than the fluid force in the physical space, and Ψ 4(m-1)+n is the eigenvector corresponding to the n-th eigenvalue of the m-th order in the complex modal matrix of the liquid-filled rotor system. Since it is a non-square matrix, the generalized inverse should be used for calculation when inverting it. Figure 4 is the decomposition result of the external force other than the fluid force of the system.

[0066] 2) According to the formula above, the m-th order fluid force of the system is solved as:

[0067]

[0068] In the formula, is the m-th order liquid excitation force of the liquid-filled rotor system, and the m-th order displacement q of the liquid-filled rotor system m is:

[0069]

[0070] Figure 5 is the decomposition result of the unbalance response of each order of the liquid-filled rotor system. Then the external excitation force and F received by the m-th order of the rotor system m is:

[0071]

[0072] 3) Perform linear-nonlinear explicit-implicit separated transient dynamics solution on the system. Based on the explicit-implicit separated transient calculation method, separate the linear and nonlinear nodes of the rotor system. Since this patent is based on the finite element method for rotor dynamics modeling, there must be high-order modes in the system. The traditional Newmark-β method has no ability to suppress the oscillation response of high-frequency modes, while the G-α method can introduce numerical damping to suppress the low-damping numerical oscillation effect caused by high-order modes. Therefore, the G-α calculation method is used to obtain the integral formula of the rotor motion equation.

[0073] After separating and reordering the linear and nonlinear nodes of the rotor system, the motion equation can be written as:

[0074]

[0075] In the formula, m represents the m-th order mode, the subscript i represents the linear node, s represents the nonlinear node, M ii , M is , M si and M ss are respectively the mass sub-matrices re-divided after the linear-nonlinear separation of the liquid-filled rotor system. The same applies to the damping matrix C and the stiffness matrix K. and are the external forces such as the mth-order unbalance forces of the linear nodes and non-linear nodes of the liquid-filled rotor system, respectively, is the mth-order non-linear hydrodynamic force of the liquid-filled rotor system, and are the acceleration response, velocity response and displacement response of the linear nodes of the liquid-filled rotor system, respectively, and are the acceleration response, velocity response and displacement response of the mth-order of the non-linear nodes of the liquid-filled rotor system, respectively, w m is the natural frequency of the mth-order of the liquid-filled rotor system.

[0076] Based on the recurrence formula of the G-α numerical integration method, the velocity and acceleration formulas of the liquid-filled rotor system can be obtained by the following formula:

[0077]

[0078] where, and are the acceleration response, velocity response and displacement response of the mth-order of the corresponding nodes of the liquid-filled rotor system at the time t+Δt, respectively, is the (r-2)th derivative of the displacement response of the corresponding nodes of the liquid-filled rotor system at the time t. When r takes 2, 3 and 4 respectively, they represent the displacement response, velocity response and acceleration response of the liquid-filled rotor system. α r and β r are the rth coefficients corresponding to the G-α numerical algorithm used to solve the liquid-filled rotor system, and their forms are as follows:

[0079]

[0080] where, α m , α f and γ are the parameters introduced in the G-α numerical calculation process, and ρ i is the numerical damping introduced by the G-α numerical calculation method. The larger ρ i is, the greater the numerical damping of the algorithm, and the more obvious the suppression effect on the high-frequency mode oscillation response. Further, the integral relation satisfied by the non-linear nodes is deduced as:

[0081]

[0082] where, H and f 0 m are the coefficient matrices deduced in the process of solving the displacement response of the mth-order non-linear nodes of the liquid-filled rotor system, and their specific forms are as follows:

[0083]

[0084] Π pq =α 1M pq +β 1 C pq +K pq , p, q = i, s

[0085] 4) To solve for the nonlinear nodal displacements, a function needs to be constructed Calculating the displacements of the nonlinear nodes using the Newton - Raphson method essentially involves solving the solution of, and the nonlinear nodes at time t + Δt The iterative form is expressed as follows:

[0086]

[0087] In the formula, n is the number of iteration steps, and are the displacement responses of the m - th order of the nonlinear nodes of the liquid - filled rotor system at the (n + 1)-th and n - th steps respectively in the iterative process, is the function to be solved The corresponding Jacobian matrix, and the expression of the Jacobian matrix J is:

[0088]

[0089] After several iterations, the displacement response of the nonlinear nodes of the liquid - filled rotor system can be obtained. To iteratively solve for the m - th order displacement response of the linear nodes of the liquid - filled rotor system at time t + Δt Transforming the rotor motion equation after linear - nonlinear separation gives:

[0090]

[0091] In the formula, is the force vector of the m - th order of the liquid - filled rotor system at time t under the action of linear and nonlinear nodes, and its specific form is:

[0092]

[0093] Substituting the m - th order nonlinear nodal displacement of the liquid - filled rotor system into the above formula, the linear nodal displacement of the liquid - filled rotor system is calculated Substituting it into the G - α recurrence formula, the linear nodal velocity of the liquid - filled rotor system can be solved and acceleration After completing the rotor dynamics transient calculations for all modes step - by - step and then superimposing them, the transient response calculation of the liquid - filled rotor system under the influence of multi - frequency whirling is completed as:

[0094]

[0095] In the formula, qk It is the sum of the total displacement responses under the influence of each order mode of the linear or non - linear nodes of the liquid - filled rotor system. is the m - th order displacement response of the linear or non - linear nodes of the liquid - filled rotor system, and x is the modal order required in the process of solving the transient response of the liquid - filled rotor system.

[0096] Figure 6 It is the displacement spectrum waterfall diagram of the transient solution response of the liquid - filled rotor system based on the multi - frequency whirling decomposition principle.

[0097] This application also discloses a device for analyzing the stability and performing dynamic calculations of a liquid - filled rotor based on multi - frequency whirling decomposition. For specific components, refer to:

[0098] Decomposition module: Configured to perform the decomposition of the system response and excitation force based on the modal superposition theory.

[0099] Analysis module: Configured to perform the modal analysis of the "dual - rotor" model. Among them, the modal characteristics of the rotor model are reflected in the eigenvalues and eigenvectors of each order of the system. The system stability is reflected by the eigenvalues, providing the system modal information for the fluid module, and iterating with the fluid module until the calculation results converge.

[0100] Fluid module: Configured to perform the method for solving the hydrodynamic equations based on the finite - difference method to obtain the part of the excitation force of the fluid on the rotor wall, and feedback the fluid cross - stiffness under the fluid - solid coupling to the analysis module, and iterating with the analysis module until the calculation results converge.

[0101] Coupling module: Configured to perform coupling the fluid equivalent cross - stiffness to the state - space equation of the "dual - rotor" model and updating the rotor dynamic model under the liquid - solid coupling of the system.

[0102] Calculation module: Configured to perform the linear - non - linear decoupling calculation method based on the G - α numerical solution method to solve the coupled dynamic model order by order.

[0103] To verify the rationality of this algorithm, a transient simulation of the liquid - filled rotor system was carried out based on the method of this patent and compared with the experimental phenomena for verification:

[0104] In this example, the rotor finite - element model is as Figure 1 shown. The intermediate bearings are at nodes 11 and 19, the electromagnetic bearing is at node 27, where electromagnetic excitation force can be applied to control the rotor vibration. An unbalance of 3.5 g·mm∠0° is applied at node 25, and the fluid force is applied at node 36 (liquid disk). To reflect the vibration response characteristics of the entire liquid - filled rotor system under the fluid - solid coupling, the rotor is set to accelerate from 0 rpm to 3000 rpm with an acceleration of 4π rad / s 2 and the spectrum waterfall diagram of the vibration signal is plotted, asFigure 6 as shown

[0105] Figure 7 It is the experimental result of the liquid-filled rotor system at a rotational speed of 1200 rpm. It can be seen that a non-synchronous vibration frequency affected by fluid excitation appears near the main frequency, while in the simulation result Figure 6 near the main frequency, the vibration components under the action of fluid excitation also obviously appear. This verifies the effectiveness of the transient solution method for the liquid-filled rotor proposed in this patent based on multi-frequency whirling decomposition, solves the problem that the traditional lumped mass model in the traditional liquid-solid coupled rotor stability analysis method can only handle a single whirling frequency, and realizes the efficient solution of multiple-order modes of complex finite element models.

[0106] The above is the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art of this technology can make appropriate adjustments without departing from the principle of the present invention, and these adjustments should be included in the protection scope of the present invention.

Claims

1. A method for stability analysis and transient calculation of a liquid-filled rotor based on multi-frequency eddy decomposition, characterized in that: The implementation steps of this method include the following: S1. Establish a finite element model of a liquid-filled rotor system and perform modal analysis on the finite element model of the liquid-filled rotor system; S2, obtain the cross stiffness of the fluid acting on the liquid-solid coupling system in each mode, and iterate with the modal analysis to obtain the converged system eigenvalues; S3. Based on the principle of modal superposition, the external force and total displacement of the rotor are decomposed into each order mode, and the fluid excitation force is calculated step by step. In combination with the linear-nonlinear explicit and implicit separation method, the displacement response of each order of the liquid-filled rotor system is solved step by step after convergence. S2 includes the steps: S2.1 calculates the fluid cross stiffness corresponding to two groups of conjugate eigenvalues ​​of each mode one by one according to the fluid cross stiffness formula under the single-frequency vortex, couples the cross stiffness into the state space in S1, and iteratively solves the eigenvalues ​​of each mode until stable convergence; S2.2 corresponds to two sets of conjugate eigenvalues ​​for each mode, and the eigenvalue with the largest real part is selected as the stability criterion of the liquid-solid coupled liquid-filled rotor system at the speed at that moment; S2.3 performs stability analysis on each mode, and the speed range where the real part of the eigenvalue is greater than 0 is the instability range of the liquid-solid coupling of the liquid-filled rotor.

2. The method for analyzing the stability of a liquid-filled rotor and calculating the transient state based on multi-frequency eddy decomposition according to claim 1, characterized in that: In S1: S1.1 Measure the actual size of the rotor and divide the nodes. Consider the centrifuge sleeve as the outer rotor with a speed of 0 and the shaft as the inner rotor. Construct a rotor finite element model based on Timoshenko beam theory and finite element method, and establish the dynamic equation of the liquid-filled rotor. S1.2 Convert the rotor dynamics equations into state space form and perform modal analysis to calculate the eigenvalues ​​and eigenvectors of each modal order before being affected by fluid-solid coupling.

3. According to the method for analyzing the stability of a liquid-filled rotor and calculating the transient state based on multi-frequency eddy decomposition according to claim 1, S3 comprises the steps of: S3.1 Decompose the external excitation and displacement response of the rotor into various modes, where the displacement at the initial moment is simplified to the displacement response without fluid excitation; S3.2 Calculate the fluid excitation force corresponding to each mode step by step based on the converged system eigenvalue calculation; S3.2 is based on the transient calculation method of explicit and implicit separation, which separates the linear and nonlinear nodes of the rotor and adopts G- α Numerical calculation method, to obtain the integral formula of the rotor motion equation; S3.3 uses the Newton-Raphson iterative formula to solve the nonlinear node response of each mode step by step, and then inversely derives the displacement, velocity and acceleration response of all nodes of each mode; S3.4 Based on the principle of modal superposition, the displacements of each modal order are superimposed to obtain the total response of the liquid-filled rotor under liquid-solid coupling.

4. According to the method for analyzing the stability of a liquid-filled rotor and calculating the transient state based on multi-frequency eddy decomposition according to claim 1, the system for implementing the method comprises: Decomposition module, analysis module, fluid module, coupling module and calculation module; The decomposition module is connected to the analysis module, the analysis module inputs the system modal information to the fluid module, the fluid module is connected to the coupling module, the coupling module is connected to the analysis module and the calculation module respectively, and the calculation module is connected to the decomposition module through the next order calculation; Decomposition module: configured to perform system response and excitation force decomposition based on modal superposition theory; Analysis module: It is configured to perform modal analysis of the "dual rotor" model. The modal characteristics of the rotor model are reflected in the eigenvalues ​​and eigenvectors of each order of the system. The system stability is reflected by the eigenvalues, which provide the system modal information to the fluid module and iterate with the fluid module until the calculation results converge. Fluid module: It is configured to execute the solution method of fluid dynamics equation based on finite difference method to obtain the exciting force of fluid on rotor wall, feed back the cross stiffness of fluid under fluid-solid coupling to the analysis module, and iterate with the analysis module until the calculation results converge; Coupling module: It is configured to execute the coupling of the fluid equivalent cross stiffness to the state space equations of the "dual rotor" model, and update the rotor dynamics model under the liquid-solid coupling of the system; Compute module: is configured to perform G-based α The linear-nonlinear decoupling calculation method of the numerical solution method solves the coupled dynamic model step by step.

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