Liquid-filled rotor stability analysis and transient calculation method based on multi-frequency vortex decomposition

Abstract

The invention discloses a liquid-filled rotor stability analysis and transient calculation method based on multi-frequency vortex decomposition, and the method comprises the implementation steps: 1) building a dual-rotor finite element model, obtaining an uncoupled fluid cross stiffness state space, and calculating a characteristic value corresponding to each order mode of a system; 2) on the basis of a multi-frequency vortex hypothesis, calculating the fluid cross stiffness under the characteristic value corresponding to each order modal of the system step by step, coupling the fluid cross stiffness into a system state space equation, and carrying out iterative calculation to obtain the characteristic value of each order convergence of the system under the influence of the liquid-solid coupling effect; 3) calculating the liquid exciting force of each order mode based on the convergent system characteristic value, and decomposing the total displacement response of the system into each order mode of the system based on a mode superposition principle; and 4) carrying out transient dynamic solution analysis on the rotor dynamic model after liquid-solid coupling in combination with an explicit-implicit separation solution frame order-by-order mode. The method solves the problem that in a traditional liquid-solid coupling rotor stability analysis method, a traditional concentrated mass model can only process single vortex motion frequency.

Description

Technical Field

[0001] The invention relates to the field of finite element simulation of computer-aided calculation of liquid-solid coupled rotor dynamics, and in particular to a stability analysis and transient calculation method of a liquid-filled rotor based on multi-frequency vortex decomposition. Background Art

[0002] A centrifuge is a typical liquid-filled rotor device that mainly uses liquid as the working medium. When it is partially filled with liquid, the liquid-solid coupling between the liquid and the rotor will cause the rotor to have an unstable region in the speed range near the first-order critical point. In this region, the liquid-filled rotor will vibrate asynchronously to a large extent due to the influence of liquid excitation, thereby affecting its operating stability and even causing production accidents, further delaying the research and development progress of large centrifuges in my country.

[0003] The traditional research method of liquid-filled rotors is to consider the entire rotor as a concentrated mass model. However, the low-degree-of-freedom model is difficult to accurately characterize the dynamic characteristics of the increasingly complex structure of the centrifuge liquid-filled rotor, and it is also impossible to consider the influence of the system's high-order modes. In order to clarify the instability mechanism of the liquid-filled rotor under liquid-solid coupling and the stability change law of the high-order modes, the centrifuge liquid-filled rotor can be accurately modeled based on the finite element method. However, the existing fluid force model can only consider the single-frequency vortex of the rotor. The introduction of the finite element method means that it is necessary to solve the contradiction between the multi-frequency vortex and the only single-frequency vortex fluid force model. To this end, based on the principle of modal superposition, the multi-frequency vortex of the rotor can be regarded as the sum of multiple single-frequency vortices, the displacement can be decomposed into each order mode, and the stability range of the liquid-filled rotor can be analyzed and calculated step by step. Then, based on the converged system eigenvalues, the linear-nonlinear explicit and implicit separation solution method is combined to efficiently solve the transient response of the liquid-filled rotor under liquid-solid coupling. Summary of the invention

[0004] The stability analysis and transient calculation method of a liquid-filled rotor based on multi-frequency eddy decomposition provided by the present invention can solve the problems that the concentrated mass model is difficult to accurately characterize the overall dynamic characteristics of the rotor system and cannot analyze the stability interval changes of the system's high-order modes when analyzing the liquid-solid coupling dynamic characteristics of the liquid-filled rotor in the traditional way. The present invention also combines the principle of modal superposition to solve the problem that the existing single-frequency eddy fluid force model cannot meet the multi-frequency eddy assumption brought by the finite element method. In order to improve the transient calculation efficiency of the liquid-filled rotor under the multi-modal liquid-solid coupling, the present invention also adopts a linear-nonlinear explicit and 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 ability to suppress high-frequency modal oscillation responses, and finally solves the nonlinear transient dynamic response of the system quickly, stably and accurately.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] 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;

[0007] 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;

[0008] S3. Based on the principle of modal superposition, the external force and total displacement of the rotor are decomposed into each mode, and the fluid excitation force is calculated step by step. Combined with the linear-nonlinear explicit and implicit separation method, the displacement response of each modal after convergence of the liquid-filled rotor system is solved step by step by iterative step.

[0009] S1 includes the steps:

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

[0011] S1.2 Convert the rotor dynamics equation into state space form, perform modal analysis, and calculate the eigenvalues ​​and eigenvectors of each modal order before being affected by fluid-solid coupling;

[0012] S2 includes the steps:

[0013] 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;

[0014] 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.

[0015] 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.

[0016] S3 includes the following steps:

[0017] 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;

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

[0019] S3.2 is a transient calculation method based on explicit and implicit separation, which separates the linear and nonlinear nodes of the rotor and uses the G-α numerical calculation method to obtain the integral formula of the rotor motion equation;

[0020] S3.3 uses the Newton-Raphson iterative formula to solve the nonlinear node response under each mode step by step, and then inverts the displacement, velocity and acceleration response of all nodes under each mode.

[0021] 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.

[0022] The present invention has the following advantages:

[0023] The stability analysis and transient calculation method of the liquid-filled rotor based on multi-frequency vortex decomposition provided by the present invention regards the multi-frequency vortex of the liquid-filled rotor as the sum of multiple single-frequency vortices by introducing the finite element modeling method and combining the modal superposition principle. Accurate modeling of the centrifuge rotor under complex elastic support conditions is achieved, so that compared with the traditional concentrated mass model, the transient simulation results of the liquid-filled rotor under liquid-solid coupling are closer to the actual working conditions. The present invention introduces a linear-nonlinear explicit and implicit separation algorithm to extract the nonlinear nodes of the rotor, realize the iterative calculation dimension of the high-dimensional rotor finite element model, and greatly reduce the time for calculating the transient response. By combining the G-α numerical calculation method with the display trapezoidal method to calculate the transient response of the system step by step, the problem of the traditional Newmark-β numerical calculation method's lack of suppression ability for the system's high-order modes is avoided. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0026] Figure 3 This is a graph showing the first four stable curves of the liquid-filled rotor system under different fluid viscosity conditions in an embodiment of the present invention.

[0027] Figure 4 It is a device for analyzing the stability and calculating the dynamics of a liquid-filled rotor based on multi-frequency vortex decomposition in an embodiment of the present invention.

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

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

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

[0031] like Figure 1 As shown, a method and device for transient calculation of rotor dynamics of a whole machine based on flexible basic transfer function implemented by the present invention:

[0032] Based on the modal decomposition principle, this example regards the multi-frequency vortex of the liquid-filled rotor as the sum of multiple single-frequency vortices, performs stability analysis on each mode of the liquid-filled rotor system, analyzes the stability range of each mode, and combines the linear-nonlinear explicit and implicit separation algorithm to perform rotor transient response analysis. 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] The first step is to establish a finite element model of the liquid filling system and perform modal analysis on the liquid filling system;

[0035] 1) The liquid-filled rotor system is divided into beam units, disk units and bearing units. The shaft is modeled based on the Timoshenko beam theory. The disk unit is regarded as a concentrated mass unit, and the bearing unit is regarded as a support unit to provide a support reaction force for the rotor system. The dynamic equation of the rotor system is finally established as follows:

[0036]

[0037] Where M, C, G and K are the total mass, damping, gyroscopic effect and stiffness matrix of the liquid-filled rotor system after assembly. and q are the acceleration, velocity and displacement vector of the liquid-filled rotor system, Ω is the rotation speed of the liquid-filled rotor system, and F is the external excitation force on the liquid-filled rotor system, including the unbalanced force F u , Support force F b and fluid excitation force F l ,Right now:

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

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

[0040]

[0041] Where A and B are coefficient matrices in the process of converting the rotor dynamics equations into the state space, z is the state variable, and Q is the state space force vector:

[0042]

[0043] Solve the eigenvalue of the state space formula to obtain the eigenvalue λ corresponding to each mode 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 when solving, and n represents the eigenvalue number corresponding to the modal order. Since each mode corresponds to two sets of conjugate roots, that is, 4 eigenvalues, n∈{1,2,3,4}. m is the mth-order modal stability criterion of the liquid-filled rotor system, and the imaginary part w m is the mth order natural frequency of the liquid-filled rotor system, and j is the imaginary unit.

[0046] The second step is to 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;

[0047] 1) Based on the fluid NS equation, the fluid dynamics equation is established, and the finite difference method is used to solve the differential equation to derive the fluid cross stiffness of the mth mode of the system under the action of fluid-solid coupling:

[0048]

[0049] In the formula, S m is the mth-order equivalent cross stiffness of the liquid-filled rotor system, k XX , k XY , k YX and k YY is the equivalent stiffness coefficient of the fluid under liquid-solid coupling, and its form is:

[0050]

[0051] m l is the mass of liquid when the drum is full of liquid, v is the dynamic viscosity of the fluid, r o is the inner wall radius of the drum, and are auxiliary variables constructed when solving the NS fluid dynamics equations. The purpose is to decouple the equations in two disturbance directions. The superscripts "' and " represent the third-order derivative and second-order derivative of the corresponding functions, respectively.

[0052] 2) Couple the m-th modal fluid cross stiffness with the rotor system state space expression to calculate the n-th eigenvalue λ of the m-th mode of the new liquid-filled rotor system under liquid-solid coupling mn , when λ mnWhen the iterative convergence condition is met (when the two norms of the eigenvalues ​​calculated twice meet the convergence accuracy of 1e-4), it is considered that the nth eigenvalue of the mth mode of the rotor system has been calculated. Otherwise, the fluid cross stiffness in 1) is recalculated and re-solved until the convergence requirement is met. Figure 2 This is a flow chart of the stability analysis method under the action of multi-frequency vortex.

[0053] 3) Select the eigenvalue with the largest real part among the two sets of eigenvalues ​​solved for the mth order as the mth order stability criterion. If the mth order maximum real part σ m If ≥0, the rotor system is considered to be m-th order unstable, otherwise, the system is considered to be m-th order stable. Figure 3 These are the first four-order stability curves of the liquid-filled rotor system under different fluid viscosity conditions.

[0054] The third step: Based on the principle of modal superposition, the external force and total displacement of the rotor are decomposed into each mode, and the fluid excitation force is calculated step by step. Combined with the linear-nonlinear explicit and implicit separation method, the displacement response of each modal after convergence of the liquid-filled rotor system is solved step by step by iterative solution.

[0055] 1) In order to calculate the system response under each mode step by step, the unbalanced force and support force of the rotor system need to be decomposed into the corresponding mode. According to the rotor dynamics equation, the physical space coordinates are transformed into modal space coordinates through the modal matrix:

[0056] z=Ψg

[0057] Among them, 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, ψ i is the i-th mode column vector of the liquid-filled rotor system:

[0058] Ψ=[ψ1 ψ2 … ψ 2n ]

[0059] Put it into the state space and express it as:

[0060]

[0061] Then the mth order nth modal coordinates of the force in the modal space are:

[0062]

[0063] In the formula is the nth component of the mth order in the modal space. Since there are two groups of 4 eigenvalues ​​in the mth order mode, the external force of the system in the mth order mode in the physical space is:

[0064]

[0065] In the formula, is the mth-order external force in physical space except fluid force, Ψ 4(m-1)+n is the eigenvector corresponding to the nth eigenvalue of the mth 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 It is the decomposition result of the external forces of the system except the fluid force.

[0066] 2) According to the previous formula, solve the m-th order fluid force of the system and get:

[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 m for:

[0069]

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

[0071]

[0072] 3) Solve the transient dynamics of the system with explicit and implicit separation of linear and nonlinear. Based on the transient calculation method of explicit and implicit separation, 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 of the system, and the traditional Newmark-β method has no ability to suppress high-frequency modal oscillation response, 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 equation of motion can be written as:

[0074]

[0075] Where m represents the mth order mode, the subscript i represents a linear node, s represents a nonlinear node, and M ii 、M is 、M si With M ss They are the mass sub-matrices of the liquid-filled rotor system re-divided after linear-nonlinear separation, and the damping matrix C and stiffness matrix K are the same. and They are the external forces such as the mth order unbalanced force at the linear nodes and nonlinear nodes of the liquid-filled rotor system, is the mth-order nonlinear fluid force of the liquid-filled rotor system, and They are respectively the linear node acceleration response, velocity response and displacement response of the liquid-filled rotor system. and are respectively the acceleration response, velocity response and displacement response of the mth order of the nonlinear node of the liquid-filled rotor system, w m is the mth order natural frequency of the liquid-filled rotor system.

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

[0077]

[0078] In the formula, and are respectively the acceleration response, velocity response and displacement response of the corresponding node of the liquid-filled rotor system at the mth order at time t+Δt, is the r-2nd order derivative of the displacement response of the corresponding node of the liquid-filled rotor system at time t. When r is 2, 3, and 4, it represents the displacement response, velocity response, and acceleration response of the liquid-filled rotor system, respectively. r With 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] In the formula, α m , α f and γ are the parameters introduced in the numerical calculation process of G-α, ρ i is the numerical damping introduced by the G-α numerical calculation method, ρ i The larger the value, the greater the numerical damping of the algorithm, and the more obvious the suppression effect on high-frequency modal oscillation response. It is further deduced that the integral relationship satisfied by the nonlinear node is:

[0081]

[0082] Among them, H and f0 m They are the coefficient matrices derived in the process of solving the m-th order nonlinear node displacement response of the liquid-filled rotor system, and their specific forms are as follows:

[0083]

[0084] Π pq =α1M pq +β1Cpq +K pq ,p,q=i,s

[0085] 4) To solve the nonlinear node displacement, a constructor is required The Newton-Raphson method is essentially used to calculate the displacement of nonlinear nodes. The solution, nonlinear node 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 n+1th and nth steps in the mth order iteration process of the nonlinear node of the liquid-filled rotor system, The function to be solved is constructed The corresponding Jacobian matrix, the Jacobian matrix J expression is:

[0088]

[0089] After several iterations, the displacement response of the nonlinear nodes of the liquid-filled rotor system can be obtained, which is 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 can be obtained:

[0090]

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

[0092]

[0093] Displace the mth-order nonlinear node of the liquid-filled rotor system Substituting the above formula, the linear node displacement of the liquid-filled rotor system is calculated as Substituting it into the G-α recursive formula, the linear node velocity of the liquid-filled rotor system can be solved With acceleration After completing the transient calculation of rotor dynamics of all modes step by step and superimposing them, the transient response calculation of the liquid-filled rotor system under the influence of multi-frequency vortex can be completed as follows:

[0094]

[0095] In the formula, q kis the sum of the total displacement responses of the liquid-filled rotor system under the influence of each mode of the linear or nonlinear nodes, is the mth-order displacement response of the linear or nonlinear node of the liquid-filled rotor system, and x is the modal order required to solve the transient response of the liquid-filled rotor system.

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

[0097] The present application also discloses a liquid-filled rotor stability analysis and dynamics calculation device based on multi-frequency vortex decomposition, the specific composition of which is as follows:

[0098] Decomposition module: configured to perform system response and excitation force decomposition based on modal superposition theory;

[0099] 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 system modal information to the fluid module and iterate with the fluid module until the calculation results converge;

[0100] 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;

[0101] 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;

[0102] The calculation module is configured to execute a linear-nonlinear decoupling calculation method based on a G-α numerical solution method to solve the coupled dynamic model step by step.

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

[0104] In this example, the rotor finite element model is as follows: Figure 1 As shown in the figure, the intermediate bearings are at nodes 11 and 19, and the electromagnetic bearing is at node 27. 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 (at the liquid plate). In order to reflect the vibration response characteristics of the entire liquid-filled rotor system under the action of fluid-solid coupling, the rotor is set to rotate at 4πrad / s 2 The acceleration is accelerated from 0rpm to 3000rpm, and the spectrum waterfall diagram of the vibration signal is drawn, such as Figure 6 shown.

[0105] Figure 7 The experimental results of the liquid-filled rotor system at 1200 rpm show that there is an asynchronous vibration frequency near the main frequency due to fluid excitation, while in the simulation results Figure 6 The vibration component under fluid excitation also appears clearly near the main frequency. This verifies the effectiveness of the transient solution method of the liquid-filled rotor based on multi-frequency vortex decomposition proposed in this patent, solves the problem that the traditional concentrated mass model in the traditional liquid-solid coupling rotor stability analysis method can only handle a single vortex frequency, and realizes the efficient solution of multi-order modes of complex finite element models.

[0106] The above is a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art can make appropriate adjustments without departing from the principles 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 mode, and the fluid excitation force is calculated step by step. Combined with the linear-nonlinear explicit and implicit separation method, the displacement response of each modal after convergence of the liquid-filled rotor system is solved step by step by iterative step.

2. The method for stability analysis and transient calculation of a liquid-filled rotor 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, S2 comprises the steps of: 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.

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, 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 a transient calculation method based on explicit and implicit separation, which separates the linear and nonlinear nodes of the rotor and uses the 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.

5. According to the method for analyzing the stability of a liquid-filled rotor and calculating the transient state based on multi-frequency eddy motion 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; The calculation module is configured to execute a linear-nonlinear decoupling calculation method based on a G-α numerical solution method to solve the coupled dynamic model step by step.

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