Methods for solving the dynamic characteristics of seal-rotor and seal-rotor bearing systems

Abstract

This invention belongs to the field of rotating machinery technology, specifically relating to a method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system. The method includes: 1. Obtaining four rotor dynamic coefficients at different speeds and whirl frequencies using steady-state or transient computational fluid dynamics methods; 2. Establishing a database of seal rotor dynamic coefficients based on two-dimensional cubic polynomial interpolation; 3. Setting the initial speed for the solution and specifying the initial operating condition; 4. Calculating the instantaneous whirl frequency of the rotor, finding the current seal rotor dynamic coefficients, and calculating the seal excitation force on the rotor; 5. Establishing the dimensionless dynamic model to be solved; 6. Substituting the seal excitation force obtained in step S4 into the dynamic equation established in step S5, performing numerical calculations, and determining whether the numerical solution converges. If not, returning to step S4; 7. Retaining the result when the calculation converges and determining whether the current speed is the upper limit of the desired speed.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery technology, specifically relating to a method for solving the dynamic characteristics of a seal-rotor and a seal-rotor bearing system. Background Technology

[0002] Rotating machinery systems are generally composed of core components such as rotors, disks, seals, and bearings. When calculating the dynamic characteristics of rotor systems, they are generally divided into sealed-rotor systems that only consider the excitation force of the seal and the unbalanced eccentricity of the disk, and sealed-rotor-bearing systems that consider both the excitation force of the seal and the nonlinear excitation force of the bearing oil film.

[0003] However, for the two systems mentioned above, in the process of model building and numerical solution, two sealing force models are generally used to describe the sealing excitation force: the Muszynska nonlinear sealing force model with analytical form and the Black-Childs sealing force model. The Muszynska nonlinear sealing force model can only describe labyrinth seals with circumferential continuity of the sealing cavity, while the Black-Childs sealing force model can only describe annular seals with circumferential continuity of the sealing cavity.

[0004] As can be seen from the above background introduction, the existing solutions for the dynamic characteristics of seal-rotor and seal-rotor bearing systems can only consider labyrinth seals and smooth annular seal structures with circumferentially continuous sealing cavities. They cannot calculate more damped sealing structures with circumferentially discontinuous structures (such as diaphragm labyrinth seals, honeycomb seals, perforated seals, bag seals, etc.) and perforated diaphragm labyrinth seal structures with circumferentially semi-continuous structures. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for calculating the dynamic characteristics of seals with circumferentially discontinuous and semi-continuous structures in seal-rotor and seal-rotor bearing systems. This method uses computational fluid dynamics to calculate the dynamic coefficients of the seal rotor at different rotational speeds and whirl frequencies, and expands the obtained database using interpolation functions. This database is then applied to the solution of the dynamic characteristics of the seal-rotor and seal-rotor bearing systems.

[0006] The technical solution adopted in this invention is: a method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system, the method comprising the following steps:

[0007] S1: Different rotational speeds are obtained by using steady-state or transient computational fluid dynamics methods. ω The four rotor dynamic coefficients of the sealing structure at the following values ​​(in r / min) and eddy frequency Ω (in Hz) are: direct stiffness coefficient K, cross-coupling stiffness coefficient K, and cross-coupling stiffness coefficient K.k Direct damping coefficient C and cross-coupling stiffness coefficient c .

[0008] S2: Establish a database of dynamic coefficients for sealed rotors based on two-dimensional cubic polynomial interpolation.

[0009] S3: Set the initial rotational speed for the solution, and specify the initial operating conditions of the seal-rotor system and the seal-rotor bearing system.

[0010] S4: Calculate the instantaneous whirl frequency of the rotor under this state based on the current system operating condition information, find the rotor dynamic coefficient of the current seal in the rotor dynamic coefficient interpolation database built in S2, and calculate the sealing excitation force on the rotor.

[0011] S5: Establish the dimensionless dynamic models of the seal-rotor system and the seal-rotor bearing system to be solved.

[0012] S6: Substitute the sealing excitation force obtained from S4 into the dynamic equations of the sealing-rotor system and the sealing-rotor bearing system established in S5, perform numerical calculations, and determine whether the numerical solution converges. If it does not converge, return to S4.

[0013] S7: Retain the result when the calculation converges, and determine whether the current speed is the upper limit of the required speed. If the upper limit of the required speed has not been reached, set the speed to the current speed plus one speed step, and return to S4 to continue the calculation. If the upper limit of the required speed is reached, it means that the solution of the dynamic characteristics of the seal-rotor system and the seal-rotor bearing system has been completed.

[0014] Furthermore, in S2, a two-dimensional cubic polynomial interpolation formula is used to interpolate the four rotor dynamic coefficients calculated in S1, obtaining a rotor dynamic coefficient interpolation database within the desired speed and whirl frequency range. The two-dimensional cubic polynomial interpolation formula is as follows:

[0015] In the formula, a , b , c , d , e , f , g , h , i , j The coefficients of the interpolation equation are derived from the rotational speed and eddy frequency ( ω The dynamic coefficients are obtained by fitting every 4 adjacent sets of dynamic coefficients within the -Ω) space. P For K, k C cAny rotor dynamics coefficient in the database; the obtained rotor dynamics coefficient interpolation database is based on... ω With Ω as the independent variable, P , which is a series of two-dimensional coefficient surfaces for the dependent variable.

[0016] Furthermore, the initial operating condition in S3 is a set of displacements or velocities for a given rotor that are initially non-zero.

[0017] Furthermore, the method for calculating the instantaneous eddy frequency of the rotor in S4 is as follows:

[0018]

[0019] In the formula, Let be the velocity of the rotor in the x-direction at any given moment. Y The displacement of the rotor in the y-direction at the same moment is obtained from the rotor dynamics coefficient interpolation database. That is, the current sealing excitation force on the rotor is obtained by using the current rotational speed and whirl frequency as parameters, and selecting the corresponding value from a series of two-dimensional coefficient surfaces in S2 as the current sealing rotor dynamic coefficient.

[0020] Furthermore, in S5, a dynamic approach is used to establish the rotor centroid. O D Displacement in mutually perpendicular directions within the rotor cross section xoy ( X and Y ),speed( and ), acceleration ( and The dynamic equations relating the forces acting on the rotor are as follows: The force acting on the rotor is its weight. M D g in M D For the mass of the rotor, g The acceleration is due to gravity; the rotor's center of mass... O G The periodic excitation force caused by the offset r relative to the centroid and Where t is the time parameter; the sealing excitation force exerted by the sealing structure on the rotor system F x and F y The dimensionless dynamic models of the sealed rotor system and the sealed rotor bearing system are calculated from the dynamic models of the sealed rotor system and the sealed rotor bearing system, using dimensionless displacement (…). x = X / c r， y =Y / c r ) and dimensionless time ( The dimensionless form is obtained by performing dimensionless transformation.

[0021] Furthermore, the numerical methods in S6 are fourth-order Runge-Kutta methods, Newmark-beta methods, and other numerical iterative methods. The method to determine whether the numerical solution has converged is to calculate whether the relative error of the dimensionless displacement of the rotor before and after the numerical solution is greater than 1e-6 and whether the absolute error is greater than 1e-8. If it is greater than the above values, the numerical solution has not yet converged; otherwise, it has converged.

[0022] Furthermore, S7 retains the results at the time of calculation convergence, that is, it saves the rotor displacement and speed values ​​calculated in the current state. The upper limit of the speed and the speed step size are defined as the maximum value of the speed range to be calculated, and the speed step size is a value that is divisible by the difference between the maximum and minimum values ​​of the speed range within the speed range.

[0023] The beneficial effects of this invention are as follows: It provides a method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system. This method uses computational fluid dynamics to calculate the dynamic coefficients of the seal rotor at different rotational speeds and whirl frequencies, and expands the obtained database using interpolation functions. This database is then applied to solving the dynamic characteristics of the seal-rotor and seal-rotor bearing system. Because the results obtained from computational fluid dynamics are used as the basic data in the database during the solution process, the types of sealing structures considered are not limited. This allows for the solution of the dynamic characteristics of circumferentially discontinuous and semi-continuous seal structures in the seal-rotor and seal-rotor bearing system, providing a new approach for the dynamic behavior analysis of rotating machinery seal-rotor and seal-rotor bearing systems. Attached Figure Description

[0024] Figure 1 This is a flowchart of the method for solving the dynamic characteristics of the seal-rotor and seal-rotor bearing systems;

[0025] Figure 2 This is a schematic diagram of the main structure of the sealing-rotor system in Embodiment 2;

[0026] Figure 3 This is a side view of the sealing-rotor system in Embodiment 2.

[0027] Figure 4 This is a schematic diagram of the database construction method in Example 2;

[0028] Figure 5 This is a schematic diagram of the traditional labyrinth seal structure considered in calculation (1) of Example 2;

[0029] Figure 6 This is a comparison diagram of the bifurcation results obtained by using the traditional Muszynska nonlinear force model and the dynamic property solution method in the calculation of Example 2 (1);

[0030] Figure 7 This is a comparison chart of the dimensionless maximum amplitude results obtained by using the traditional Muszynska nonlinear force model and the dynamic characteristic solution method in the calculation of Example 2 (1);

[0031] Figure 8 The calculation (2) in Example 2 and the structural schematic diagram of the circumferential discontinuous seal-partition labyrinth seal considered in Example 3 are shown below.

[0032] Figure 9 This is a schematic diagram of the circumferential semi-continuous seal-perforated diaphragm labyrinth seal structure considered in calculation (2) of Example 2;

[0033] Figure 10 The diagram of the sealing-rotor system bifurcation obtained by solving the diaphragm labyrinth seal in the calculation of Example 2 (2) is shown.

[0034] Figure 11 The diagram of the sealing-rotor system bifurcation obtained by solving the perforated diaphragm labyrinth seal in the calculation of Example 2 (2) is shown.

[0035] Figure 12 This is a schematic diagram of the sealed-rotor bearing system structure in Embodiment 3;

[0036] Figure 13 This is a bifurcation diagram of the seal-rotor bearing system obtained by solving the diaphragm labyrinth seal in Example 3. Detailed Implementation

[0037] Example

[0038] like Figure 1 As shown, the method for solving the dynamic characteristics of the seal-rotor and seal-rotor bearing system includes the following steps:

[0039] S1: Different rotational speeds are obtained by using steady-state or transient computational fluid dynamics methods. ω The four rotor dynamic coefficients of the sealing structure at the following values ​​(in r / min) and eddy frequency Ω (in Hz) are: direct stiffness coefficient K, cross-coupling stiffness coefficient K, and cross-coupling stiffness coefficient K. k Direct damping coefficient C and cross-coupling stiffness coefficient c .

[0040] S2: Establish a database of sealed rotor dynamic coefficients based on two-dimensional cubic polynomial interpolation; use the two-dimensional cubic polynomial interpolation formula to interpolate the four rotor dynamic coefficients calculated in S1 to obtain a database of rotor dynamic coefficient interpolation within the required speed and whirl frequency range. The two-dimensional cubic polynomial interpolation formula is:

[0041] In the formula, a , b , c , d , e , f , g , h , i , j The coefficients of the interpolation equation are derived from the rotational speed and eddy frequency ( ω The dynamic coefficients are obtained by fitting every 4 adjacent sets of dynamic coefficients within the -Ω) space. P For K, k C c Any rotor dynamics coefficient in the database; the obtained rotor dynamics coefficient interpolation database is based on... ω With Ω as the independent variable, P , which is a series of two-dimensional coefficient surfaces for the dependent variable.

[0042] S3: Set the initial rotational speed for the solution, and give the initial operating conditions of the seal-rotor system and the seal-rotor bearing system. The initial operating conditions are a set of displacements or velocities of the given rotor that are not initially zero.

[0043] S4: Calculate the instantaneous whirl frequency of the rotor under this state based on the current system operating condition information. Find the rotor dynamic coefficient of the current seal in the rotor dynamic coefficient interpolation database established in S2, and calculate the sealing excitation force on the rotor. The method for calculating the instantaneous whirl frequency of the rotor is as follows:

[0044]

[0045] In the formula, Let be the velocity of the rotor in the x-direction at any given moment. Y The displacement of the rotor in the y-direction at the same moment is obtained from the rotor dynamics coefficient interpolation database. That is, the current sealing excitation force on the rotor is obtained by using the current rotational speed and whirl frequency as parameters, and selecting the corresponding value from a series of two-dimensional coefficient surfaces in S2 as the current sealing rotor dynamic coefficient.

[0046] S5: Establish dimensionless dynamic models of the seal-rotor system and the seal-rotor bearing system to be solved; use dynamic methods to establish the rotor centroid. O DDisplacement in mutually perpendicular directions within the rotor cross section xoy ( X and Y ),speed( and ), acceleration ( and The dynamic equations relating the forces acting on the rotor; the forces acting on the rotor are the rotor's weight. M D g in M D For the mass of the rotor, g The acceleration is due to gravity; the rotor's center of mass... O G The periodic excitation force caused by the offset r relative to the centroid and Where t is the time parameter; the sealing excitation force exerted by the sealing structure on the rotor system F x and F y The dimensionless dynamic models of the sealed rotor system and the sealed rotor bearing system are obtained from the dynamic models of the sealed rotor system and the sealed rotor bearing system, which select dimensionless displacements. x = X / c r， y = Y / c r ) and dimensionless time ( The dimensionless form is obtained by performing dimensionless transformation.

[0047] S6: Substitute the sealing excitation force obtained from S4 into the dynamic equations of the sealing-rotor system and the sealing-rotor bearing system established in S5, and use numerical methods to calculate and determine whether the numerical solution converges. If it does not converge, return to S4. The numerical methods are fourth-order Runge-Kutta methods, Newmark-beta methods, and other numerical iterative methods. The method to determine whether the numerical solution converges is: calculate whether the relative error of the dimensionless displacement of the rotor before and after the numerical solution is greater than 1e-6 and whether the absolute error is greater than 1e-8. If it is greater than the above values, the numerical solution has not yet converged. If it is less than the above values, it has converged.

[0048] S7: Retain the results at the convergence point of the calculation and determine whether the current rotational speed is the upper limit of the required rotational speed. If the upper limit of the required rotational speed has not yet been reached, set the rotational speed to the current rotational speed plus one rotational speed step and return to S4 to continue the calculation. If the upper limit of the required rotational speed has been reached, it means that the solution of the dynamic characteristics of the seal-rotor system and the seal-rotor bearing system has been completed. Retain the results at the convergence point of the calculation, that is, save the rotor displacement and velocity values ​​calculated in the current state. The upper limit of the rotational speed and the rotational speed step are the maximum values ​​of the rotational speed range to be calculated. The rotational speed step is a value that is divisible by the difference between the maximum and minimum values ​​of the rotational speed range within the rotational speed range. Example

[0049] like Figure 2 and Figure 3 The diagram shows a sealed-rotor system, wherein the rotor shaft length is... l 0 =1m, axis radius R Sh =0.015m, wheel length l D =0.05m, roulette radius R D =0.03m, the Young's modulus of the rotor is 206 GPa, and the rotor density is 7850 kg / m³. 3 Equivalent unbalanced eccentricity of the roulette wheel r =0.00001m. Considering the equivalent unbalanced eccentricity of the disk in the sealed-rotor system and the received gravity, the dynamic equation of the system can be obtained:

[0050]

[0051] In the formula:

[0052] X, Y These are the rotor displacements (m, m);

[0053] D d 、K D These are the rotor's structural damping (N·s / m) and structural stiffness (N / m), respectively.

[0054] F x 、F y Let (N, N) be the component of the sealing force perpendicular to the cross-section, given by K. k C c Calculated;

[0055] M D The mass of the wheel (kg);

[0056] g The acceleration due to gravity ( g = 9.8m / s 2 );

[0057] ω Rotor speed (display unit: r / min, calculation unit: rad / s);

[0058] t r For real time (s).

[0059] The structural damping of the rotor is calculated using Rayleigh damping, i.e.

[0060]

[0061] in, k 1 and k 2 There are two Rayleigh factors. According to Rayleigh's method, the Rayleigh factor... k 1 and k 2 This can be expanded to:

[0062] ;

[0063] In the formula:

[0064] ω n1 ω n2 These are the first and second natural frequencies of the rotor, respectively.

[0065] ξ 1、 ξ2 is the damping ratio of the first two modes, with values ​​of ξ1=0.02 and ξ2=0.04.

[0066] Select dimensionless displacement x = X / c r， y = Y / c r and dimensionless time To simplify the calculation process, a fourth-order Runge-Kutta numerical algorithm is used to solve the dimensionless state equations.

[0067] like Figure 4 As shown, the cross-coupling stiffness coefficient of the labyrinth seal is... kFor example, this paper demonstrates the process of expanding the initial data (6 x 7, 42 sets) obtained from computational fluid dynamics into a database of 101 x 30001 sets (3030101 sets). In the application of this solution method, for each type of seal, it is necessary to separately adjust K, k C c The four sets of data were broadened and then applied to subsequent calculation processes.

[0068] Example 2 involves comparing two sets of calculations to verify the results.

[0069] By applying the Muszynska nonlinear force model and the solution method for the dynamic characteristics of the seal-rotor and seal-rotor bearing systems (hereinafter referred to as the "solution method") to the seal-rotor system using a traditional labyrinth seal, the solution is obtained. Figure 2 The bifurcation diagram of the sealed-rotor system in the speed range of 1000 r / min to 10000 r / min is shown to verify the accuracy of the solution method.

[0070] in, Figure 5 The structural parameters of a traditional labyrinth seal are shown, where the rotor radius is 30 mm and the sealing gap is c. r The sealing cavity height h is 3.5 mm, the sealing tooth gap l1 is 3.8 mm, the sealing tooth width t is 0.25 mm, and the cavity width l2 is 2.3 mm.

[0071] Figure 6 This demonstrates the use of the Muszynska nonlinear force model and the solution method for this dynamic property, respectively. Figure 2 The diagram shows the bifurcation of the sealed-rotor system after dynamic calculation. The diagram reveals that the proposed dynamic characteristic solution method achieves the same level of capability as the traditional Muszynska nonlinear force model in solving the dynamic characteristics of the sealed-rotor system at different speeds. Within the speed range of 100–1100 r / min, the description of the dynamic behavior of the sealed-rotor system by this proposed method is clearer than that using the traditional Muszynska nonlinear force model.

[0072] Figure 7 The figure shows the dimensionless maximum amplitude obtained by using the Muszynska nonlinear force model and the solution method of this dynamic characteristic. It can be seen from the figure that the rotational speed at which the maximum amplitude of the sealed-rotor system is obtained by the solution method of this dynamic characteristic is consistent with that obtained by using the traditional Muszynska nonlinear force model, with only a slight difference in the value of the dimensionless maximum amplitude.

[0073] comprehensive Figure 6 and Figure 7The comparison results show that the solution method for the dynamic characteristics of the sealed-rotor and sealed-rotor bearing systems has sufficient accuracy for solving the dynamic characteristics of the sealed-rotor system.

[0074] By solving the dynamic characteristics of the seal-rotor system using different types of seals, including traditional labyrinth seals (circumferential continuous seals), diaphragm labyrinth seals (circumferential discontinuous seals), and perforated diaphragm labyrinth seals (circumferential semi-continuous seals), the research object of the seal-rotor system dynamics is transformed from circumferential continuous seals to circumferential discontinuous seals and circumferential semi-continuous seals, thereby verifying the innovation and technical effect of the dynamic characteristic solving method.

[0075] in, Figure 8 This paper presents a structure for a circumferentially discontinuous seal—a diaphragm labyrinth seal. Φ The dimensions of the sealed labyrinth section of the partition labyrinth are... Figure 5 The traditional maze shown is sealed in the same way, with the four additional sets of partitions using circumferential angles. θ Let represent , with a value of 2°.

[0076] Figure 9 This paper presents a structure of a circumferential semi-continuous seal—a perforated diaphragm labyrinth seal, wherein the basic dimensions of the perforated diaphragm labyrinth seal are similar to those of... Figure 8 The labyrinth seal shown is consistent, and the four additional sets of circumferential perforations use the same aperture. Φ Let represent , with a value of 1 mm.

[0077] Using this dynamic characteristic solution method, calculations are performed separately for diaphragm labyrinth seals and perforated diaphragm labyrinth seals. Figure 2 The diagram shows the bifurcation of the sealed-rotor system within the speed range of 1000 r / min to 10000 r / min. The result is as follows: Figure 10 The diagram shown is a bifurcation diagram of a seal-rotor system using a diaphragm labyrinth seal, similar to... Figure 11 The diagram shows a bifurcation of a seal-rotor system using a perforated septum labyrinth seal. The dynamic characteristics of the seal-rotor system at a specific speed are indicated in the figure.

[0078] pass Figure 10 , Figure 11 The results confirm that this dynamic characteristic solution method can solve the dynamic problems of circumferential discontinuous seals and circumferential semi-continuous seals in the seal-rotor system. Example

[0079] Figure 12The diagram illustrates a sealed-rotor bearing system. The numbers in the diagram represent shaft segment numbers, where segments 4, 6, 8, and 10 are equivalent compressor disks, and segments 12 and 14 are equivalent turbine disks. Bearing oil film force acts on segments 2 and 16. This embodiment uses the Capone oil film force model. The sealing excitation force acts on all six disks mentioned above. The seal type is selected... Figure 8 The diagram shows a partition labyrinth sealing structure.

[0080] The dynamic characteristics of the above-mentioned sealed-rotor bearing system were calculated using this dynamic characteristic solution method, and the results are as follows: Figure 13 The diagram shows the bifurcation of the sealed-rotor bearing system as a function of rotational speed. The types of dynamic behavior of the system at different rotational speeds are marked in the figure. The Poincaré mapping results of the system in partial motion states are shown on the right.

[0081] This disclosure describes various aspects of the present technical solution with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of the technical solution are not necessarily intended to include all aspects of the present technical solution. It should be understood that the various concepts and embodiments described above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed in this technical solution are not limited to any particular implementation. Furthermore, some aspects of this technical solution can be used alone or in any suitable combination with other aspects disclosed in this technical solution.

[0082] Although the present technical solution has been disclosed above with reference to preferred embodiments, it is not intended to limit the present technical solution. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the present technical solution. Therefore, the scope of protection of the present technical solution shall be determined by the claims.

Claims

1. A method for solving the dynamic characteristics of a seal-rotor and a seal-rotor bearing system, characterized in that, The method for solving dynamic characteristics includes the following steps: S1: Different rotational speeds are obtained by using steady-state or transient computational fluid dynamics methods. ω The four rotor dynamic coefficients of the sealing structure at the eddy frequency Ω are: direct stiffness coefficient K, cross-coupling stiffness coefficient K, and cross-coupling stiffness coefficient K. k Direct damping coefficient C and cross-coupled damping coefficient c ; S2: Establish a database of dynamic coefficients for sealed rotors based on two-dimensional cubic polynomial interpolation; S3: Set the initial rotational speed for the solution, and specify the initial operating conditions of the seal-rotor system and the seal-rotor bearing system; S4: Calculate the instantaneous eddy frequency of the rotor under this state based on the current system operating condition information, find the rotor dynamic coefficient of the current seal in the rotor dynamic coefficient interpolation database built in S2, and calculate the sealing excitation force on the rotor. S5: Establish the dimensionless dynamic models of the seal-rotor system and the seal-rotor bearing system to be solved; S6: Substitute the sealing excitation force obtained from S4 into the dynamic equations of the sealing-rotor system and the sealing-rotor bearing system established in S5, perform the calculation using numerical methods, and determine whether the numerical solution converges. If it does not converge, return to S4. S7: Retain the result when the calculation converges, and determine whether the current speed is the upper limit of the required speed. If the upper limit of the required speed has not been reached, set the speed to the current speed plus one speed step, and return to S4 to continue the calculation. If the upper limit of the required speed is reached, it means that the solution of the dynamic characteristics of the seal-rotor system and the seal-rotor bearing system has been completed.

2. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, In step S2, a two-dimensional cubic polynomial interpolation formula is used to interpolate the four rotor dynamic coefficients calculated in S1, thereby obtaining a rotor dynamic coefficient interpolation database within the desired speed and whirl frequency range. The two-dimensional cubic polynomial interpolation formula is as follows: In the formula, a , b , c , d , e , f , g , h , i , j The interpolation equation coefficients are obtained by fitting every four adjacent sets of dynamic coefficients in the rotational speed-whirl frequency space. P For K, k C c Any one of the rotor dynamics coefficients in the equation; The obtained rotor dynamics coefficient interpolation database is based on ω With Ω as the independent variable, P , which is a series of two-dimensional coefficient surfaces for the dependent variable.

3. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, The initial operating condition in S3 is a set of displacements or velocities of a given rotor that are not initially zero.

4. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, The method for calculating the instantaneous eddy frequency of the rotor in S4 is as follows: In the formula, Let be the velocity of the rotor in the x-direction at any given moment. Y This represents the rotor's displacement in the y-direction at the same moment; The sealing excitation force currently experienced by the rotor is found in the rotor dynamics coefficient interpolation database. That is, the current rotational speed and whirl frequency are used as parameters, and the corresponding values ​​are selected from a series of two-dimensional coefficient surfaces in S2 as the current sealing rotor dynamics coefficients.

5. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, In step S5, a dynamic approach is used to establish the rotor centroid. O D The dynamic equations relating displacement, velocity, acceleration, and force in mutually perpendicular directions within the rotor cross section xoy; The force acting on the rotor in the dynamic equation is the weight of the rotor. M D g ,in M D For the mass of the rotor, g The acceleration is due to gravity; the rotor's center of mass... O G The periodic excitation force caused by the offset r relative to the centroid and Where t is the time parameter; the sealing excitation force exerted by the sealing structure on the rotor system F x and F y It is calculated from the sealed rotor dynamics coefficient; The dimensionless dynamic models of the sealed-rotor system and the sealed-rotor bearing system are obtained by selecting dimensionless displacement and dimensionless time from the dynamic models of the sealed-rotor system and the sealed-rotor bearing system and then making them dimensionless.

6. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, The numerical methods in S6 are the fourth-order Runge-Kutta and Newmark-beta numerical iterative methods; The method to determine whether the numerical solution has converged is as follows: calculate whether the relative error of the dimensionless displacement of the rotor before and after the numerical solution is greater than 1e-6 and whether the absolute error is greater than 1e-8. If it is greater than the above values, the numerical solution has not yet converged. If it is less than the above values, then it has converged.

7. The method for solving the dynamic characteristics of a seal-rotor and seal-rotor bearing system according to claim 1, characterized in that, In S7, the results of the calculation convergence are retained, that is, the rotor displacement and speed values ​​calculated in the current state are saved; the upper limit of the speed and the speed step size are retained, that is, the maximum value of the speed range to be calculated, and the speed step size is a value that is divisible by the difference between the maximum and minimum values ​​of the speed range within the speed range.

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