Unsteady aerodynamic force analysis method and system considering blade mistuning

Abstract

The invention relates to the technical field of aero-engines, and discloses an unsteady aerodynamic force analysis method and system considering blade mistuning, and the method comprises the steps: constructing a multi-channel grid model comprising two adjacent rotor blades and a flow channel between the two adjacent rotor blades, and obtaining a dangerous mode and a dangerous pitch diameter of the rotor blades through an influence coefficient method; under the condition of considering the detuning amount of the rotor blade, based on a dynamic grid mapping method, an unsteady flow field of the rotor blade under a dangerous pitch diameter of a dangerous mode is calculated, based on a dynamic mode decomposition method, an agent model between unsteady aerodynamic force and vibration displacement of the blade is constructed, and through carrying out structural dynamics simulation analysis on the rotor blade, a dynamic model is established. According to the method, the unsteady aerodynamic force and vibration displacement information of the rotor blade are obtained, the blade unsteady aerodynamic force change caused by frequency detuning of the rotor blade of the gas compressor can be accurately simulated, and accurate unsteady aerodynamic force is provided for multi-physical field solution of the rotor blade.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of aero-engines and discloses an analysis method and system for unsteady aerodynamic force considering blade mistuning. BACKGROUND

[0002] With the design of high thrust ratio of an aero-engine, the single-stage aerodynamic load of a compression system is increasingly high, and the temperature load and unsteady aerodynamic force borne by a compressor blade are continuously increased. In order to further reduce the weight of the engine, a large number of new lightweight materials are used in manufacturing, and the blade profile presents more complex three-dimensional bending and twisting characteristics. These design trends make the unsteady aerodynamic force generated by the unstable flow in the compressor increase, the airflow excitation frequency presents a wideband multi-modal characteristic, and the rotor blade is at a higher dynamic stress level, which often induces the high-cycle fatigue problem of the compressor blade of the aero-engine.

[0003] The flow-induced vibration problem of the compressor blade is essentially a typical flow, solid and heat multi-physical field coupling problem. In the design stage, how to evaluate the unsteady aerodynamic force of the compressor rotor blade is directly related to the reliability of the blade operation. The compressor blade is usually machined by a five-axis numerical control machine tool, and the profile degree of the profile is extremely high. Due to the natural limitation of mechanical machining, there is a certain deviation in each blade profile, that is, the natural frequency of the circumferential blade is mistuned. The mistuning of the blade is reflected in the blade vibration, which is that the amplitude of part of the blade is increased, and the blade vibration frequency is distributed in a certain region. Taking the machining of the integral blade disc by the current five-axis numerical control machine tool as an example, the mechanical machining usually causes the mistuning of the blade frequency of about 5%. Due to the existence of circumferential unevenness, the traditional unsteady numerical simulation method must use the full-circumferential method to calculate the unsteady aerodynamic force of the blade, so that the numerical calculation amount is too large, and the simulation time is difficult to meet the requirements of engineering application. SUMMARY

[0004] The purpose of the application is to provide an analysis method and system for unsteady aerodynamic force considering blade mistuning, which can accurately simulate the change of the unsteady aerodynamic force of the compressor rotor blade caused by the frequency mistuning and provide accurate unsteady aerodynamic force for the multi-physical field solution of the rotor blade.

[0005] In order to achieve the above technical effects, the technical scheme adopted by the application is:

[0006] An analysis method for unsteady aerodynamic force considering blade mistuning comprises the following steps: Taking two adjacent rotor blades of a compression component and the flow passage therebetween as a single channel, a plurality of continuously distributed single channels on the whole ring of the rotor of the compression component are selected to construct a multi-channel grid model; Carrying out steady calculation of the multi-channel grid model by using CFD software to obtain steady flow field and surface pressure and surface temperature of each rotor blade under the multi-channel grid model; Taking corresponding surface pressure and surface temperature of the rotor blade and rotor speed as prestress input of modal analysis, simulating to obtain natural frequency and modal vector of the rotor blade under the examination mode; Applying unsteady calculation boundary condition on the multi-channel grid model, setting the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain and the remaining rotor blades as rigid state, and according to the natural frequency and modal vector under the examination mode, analyzing to obtain modal work of each pitch under the examination mode of the rotor blade by using time-marching based influence coefficient method; Defining the pitch of the rotor blade under the examination mode with minimum modal work as a dangerous pitch, setting the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain and the remaining rotor blades as rigid state, carrying out multi-channel unsteady calculation under the preset mistuning condition of the rotor blade at the dangerous pitch, and outputting pressure, grid point displacement, grid point velocity and corresponding blade surface normal vector of each grid point of the rotor blade at each time step; According to the pressure, grid point displacement, grid point velocity and corresponding blade surface normal vector of each grid point of the rotor blade at each time step, establishing a proxy model between unsteady aerodynamic force and vibration displacement of the blade at the dangerous pitch based on dynamic modal decomposition method, and carrying out structural dynamics simulation analysis of the rotor blade by using fluid-solid coupling method to obtain unsteady aerodynamic force and vibration displacement information of the blade at different times.

[0007] Further, at least 7 continuously distributed single channels are selected to construct the multi-channel grid model, and the number of continuously distributed single channels is odd.

[0008] Further, the modal work of each pitch under the examination mode of the rotor blade is analyzed by using is the number of single channels in the multi-channel grid model, , is the vibration period of the rotor blade under the examination mode, is the vibration frequency of the rotor blade under the examination mode, is the phase angle of the rotor blade under the examination mode, is the numerical simulation time, , represents integrating the closed surface of the modal force of the rotor blade, is the blade surface pressure, is the modal vector of the rotor blade under the examination mode, is the rotor blade surface normal vector,​​ for rotor blade surface area, is a differential symbol.

[0009] Further, the preset mistuning condition is that the maximum mistuning amount of the blade frequency is , and the sweep frequency setting of the rotor blade vibration is , wherein is the natural frequency under the test vibration mode, is the numerical simulation time.

[0010] To achieve the above technical effects, the application further provides an analysis system considering blade mistuning of unsteady aerodynamic force, comprising: A network model construction module is configured to select multiple continuously distributed single channels on a whole ring of the compressor rotor to construct a multi-channel grid model by taking the adjacent two rotor blades and the flow passage therebetween of the compression component as a single channel; A first analysis module is configured to perform steady calculation of the multi-channel grid model by using CFD software to obtain the steady flow field and the surface pressure P and surface temperature T of each rotor blade under the multi-channel grid model; A second analysis module is configured to take the surface pressure and surface temperature of the corresponding rotor blade and the rotor speed as the prestress input of modal analysis to simulate and obtain the natural frequency and modal vector of the rotor blade under the test vibration mode; A third analysis module is configured to apply unsteady calculation boundary conditions on the multi-channel grid model, set the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain, and set the remaining rotor blades as rigid state, and according to the natural frequency and modal vector under the test vibration mode, analyze and obtain the modal work of each pitch under the test vibration mode by using the influence coefficient method based on time advancement; A fourth analysis module is configured to define the pitch with the minimum modal work of the rotor blade under the test vibration mode as a dangerous pitch, set the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain, and set the remaining rotor blades as rigid state, perform multi-channel unsteady calculation considering the preset mistuning condition of the rotor blade at the dangerous pitch, and output the pressure, grid point displacement, grid point velocity of the rotor blade surface grid point at each time step, and the blade surface normal vector corresponding to each grid point; A fifth analysis module is configured to establish a proxy model between the unsteady aerodynamic force and the vibration displacement of the blade at the dangerous pitch based on the dynamic modal decomposition method according to the pressure, grid point displacement, grid point velocity of the rotor blade surface grid point at each time step, and the blade surface normal vector corresponding to each grid point, and perform structural dynamics simulation analysis of the rotor blade by using the fluid-solid coupling method to obtain the unsteady aerodynamic force and vibration displacement information of the blade at different times.

[0011] Further, in the network model construction module, at least 7 single channels in continuous distribution are selected to construct a multi-channel grid model, and the number of single channels in continuous distribution is an odd number.

[0012] Further, in the third analysis module, the preset frequency is used to calculate the modal frequency of the rotor blade under the examination vibration mode. The modal power of the rotor blade under the examination vibration mode is obtained by analysis. Wherein, is the number of single channels in the multi-channel grid model, , is the vibration period of the rotor blade under the examination vibration mode, is the vibration frequency of the rotor blade under the examination vibration mode, is the phase angle of the rotor blade under the examination vibration mode, is the numerical simulation time, , represents the integral of the rotor blade modal force closed surface, is the blade surface pressure, is the modal vector of the rotor blade under the examination vibration mode, is the rotor blade surface normal vector, is the rotor blade surface area, is the differential symbol.

[0013] Further, in the fourth analysis module, the preset mistuning condition is that the maximum mistuning amount of the blade frequency is , and the sweep frequency setting of the rotor blade vibration is , Wherein, is the natural frequency under the examination vibration mode, is the numerical simulation time.

[0014] Compared with the prior art, the present application has the beneficial effects that the present application comprehensively considers the influence of the blade mistuning on the blade aerodynamic force change on the rotor blade structure dynamics, so as to accurately simulate the blade unsteady aerodynamic force change of the compressor rotor blade due to the frequency mistuning, improve the accuracy of numerical simulation, and meet the actual engineering application, and provide accurate unsteady aerodynamic force for the multi-physical field solution of the rotor blade. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is the flowchart of the analysis method of the unsteady aerodynamic force considering the blade mistuning in the embodiment. DETAILED DESCRIPTION

[0016] The present application will be further described in detail below in combination with the embodiments and drawings. However, it should not be understood that the above-mentioned subject matter of the present application is limited to the following embodiments only, and any technology realized based on the content of the present application belongs to the scope of the present application.

[0017] Embodiment 1 Referring to Figure 1 An analysis method of unsteady aerodynamic force considering blade mistuning, comprising: Taking two adjacent rotor blades of a compression component and a flow passage between the two rotor blades as a single channel, a plurality of single channels distributed continuously on a whole ring of the rotor of the compression component are selected to construct a multi-channel grid model; A steady calculation of the multi-channel grid model is carried out by using a CFD software to obtain a steady flow field under the multi-channel grid model and surface pressure P and surface temperature T of each rotor blade; Surface pressure, surface temperature and rotor speed corresponding to each rotor blade are taken as prestress input of modal analysis, and simulation is carried out to obtain natural frequency and modal vector of each rotor blade under a test mode; Unsteady calculation boundary conditions are applied to the multi-channel grid model, and the rotor blades in the middle of the multi-channel grid model are set as dynamic grid domains, and the remaining rotor blades are set as rigid states, and modal work of each pitch under a test mode is obtained by using a time-based influence coefficient method according to natural frequency and modal vector under the test mode; The pitch of the rotor blade under the test mode with minimum modal work is defined as a dangerous pitch, the rotor blades in the middle of the multi-channel grid model are set as dynamic grid domains, and the remaining rotor blades are set as rigid states, and multi-channel unsteady calculation under a preset mistuned condition of the rotor blade is carried out at the dangerous pitch, and pressure, grid point displacement, grid point velocity and blade surface normal vector corresponding to each grid point of the rotor blade at each time step are output; According to the pressure, grid point displacement, grid point velocity and blade surface normal vector corresponding to each grid point of the rotor blade at each time step, a proxy model between unsteady aerodynamic force and vibration displacement of the blade at the dangerous pitch is established based on a dynamic modal decomposition method, and fluid-structure coupling method is used to carry out structural dynamics simulation analysis of the rotor blade to obtain unsteady aerodynamic force and vibration displacement information of the blade at different times.

[0018] In the embodiment, by constructing a multi-channel grid model comprising two adjacent rotor blades and the flow passage therebetween, steady calculation is carried out by using CFD software, the pressure and temperature distribution on the blade surface are obtained, accurate prestress input is provided for subsequent modal analysis, the dangerous mode of the rotor blade and the dangerous pitch diameter are obtained by using the influence coefficient method; under the condition of considering the mistuning amount of the rotor blade, the unsteady flow field of the rotor blade under the dangerous mode and the dangerous pitch diameter is calculated based on the dynamic grid mapping method, the proxy model between the unsteady aerodynamic force of the blade and the vibration displacement is constructed based on the dynamic modal decomposition method, and the unsteady aerodynamic force and the vibration displacement information of the rotor blade are obtained by carrying out structural dynamics simulation analysis of the rotor blade. The unsteady aerodynamic force calculation method considering the mistuning of the blade provided in the application considers the influence of the aerodynamic force change of the blade caused by the mistuning of the blade on the structural dynamics of the rotor blade, so that the unsteady aerodynamic force change of the compressor rotor blade caused by the frequency mistuning can be accurately simulated, the accuracy of numerical simulation is improved, and the accurate unsteady aerodynamic force for solving the multi-physical field of the rotor blade is provided.

[0019] Based on the same inventive concept, the embodiment also provides an unsteady aerodynamic force analysis system considering the mistuning of the blade, comprising: A network model construction module is configured to select a plurality of continuously distributed single channels on the whole ring of the compressor rotor, and construct a multi-channel grid model by taking the adjacent two rotor blades and the flow passage therebetween as a single channel. A first analysis module is configured to carry out steady calculation of the multi-channel grid model by using CFD software, and obtain the steady flow field and the surface pressure P and surface temperature T of each rotor blade under the multi-channel grid model. A second analysis module is configured to take the surface pressure and surface temperature of the corresponding rotor blade and the rotor speed as the prestress input of modal analysis, and simulate to obtain the natural frequency and modal vector of the rotor blade under the examination mode. A third analysis module is configured to apply unsteady calculation boundary conditions on the multi-channel grid model, set the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain, and set the remaining rotor blades as a rigid state, analyze the modal work of each pitch diameter of the rotor blade under the examination mode by using the influence coefficient method based on time advancement according to the natural frequency and modal vector under the examination mode. A fourth analysis module is configured to define the pitch diameter with the minimum modal work of the rotor blade under the examination mode as the dangerous pitch diameter, set the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain, and set the remaining rotor blades as a rigid state, carry out multi-channel unsteady calculation under the dangerous pitch diameter considering the preset mistuning condition of the rotor blade, and output the pressure, grid point displacement, grid point velocity and blade surface normal vector corresponding to each grid point of the rotor blade surface at each time step. The fifth analysis module is configured to establish a proxy model between the unsteady aerodynamic force and the vibration displacement of the blade at the dangerous pitch diameter based on a dynamic modal decomposition method according to the pressure, the grid point displacement, the grid point velocity and the blade surface normal vector corresponding to each grid point of the rotor blade surface grid point at each time step, and to perform a rotor blade structural dynamics simulation analysis by using a fluid-structure coupling method to obtain the unsteady aerodynamic force and the vibration displacement information of the blade at different times.

[0020] Embodiment 2 See Figure 1 In this embodiment, the analysis method and process of the unsteady aerodynamic force of the blade considered in the present application are described in detail by taking a 7-channel grid model formed by 7 single channels of a certain compressor as an example. The analysis process is as follows: Step 1: Taking the adjacent two rotor blades and the flow passage therebetween of the compression component as a single channel, a plurality of continuously distributed single channels are selected on the rotor whole ring of the compression component to construct a multi-channel grid model. In this embodiment, a 7-channel grid model of the compressor rotor blade is established.

[0021] It should be noted that in some other embodiments, the number of single channels in the multi-channel grid model can also be selected as needed, such as 9, 11, etc. The selection principle followed is that at least 7 continuously distributed single channels are used to construct a multi-channel grid model, and the number of continuously distributed single channels is odd.

[0022] Step 2: The steady calculation of the multi-channel grid model is performed by using the CFD software to obtain the steady flow field and the surface pressure P and the surface temperature T of each rotor blade under the multi-channel grid model. In this embodiment, the steady calculation of the 7-channel grid model of the compressor is performed by using the commercial CFD software to obtain the steady flow field and the surface pressure P and the surface temperature T of the rotor blade under the 7-channel model.

[0023] Step 3: The surface pressure, the surface temperature and the rotor speed of the corresponding rotor blade are taken as the prestress input of the modal analysis, and the natural frequency and the modal vector of the rotor blade under the test vibration mode are simulated and obtained. In this embodiment, the modal analysis of the rotor blade including the prestress is performed by establishing a finite element model of the rotor blade, wherein the prestress includes the centrifugal force of the rotor caused by the rotor speed, the aerodynamic force caused by the surface pressure of the rotor blade and the thermal stress caused by the temperature, and the natural frequency and the modal vector of the rotor blade under the test vibration mode are extracted.

[0024] ​Step four, applying unsteady calculation boundary conditions on the multi-channel grid model, and setting the rotor blade in the middle of the multi-channel grid model as a dynamic grid domain, and setting the remaining rotor blades as rigid state, and obtaining the modal work of each pitch under the examination mode shape of the rotor blade according to the natural frequency, modal vector under the examination mode shape, and using the influence coefficient method based on time promotion to analyze and obtain the modal work of each pitch under the examination mode shape of the rotor blade In this embodiment, on the basis of the seven-channel grid model of the compressor rotor blade 7 constructed in step one, unsteady calculation boundary conditions are applied, the rotor blade in the middle of the seven-channel grid model is set as a dynamic grid domain, and the remaining six rotor blades are set as rigid state. The influence coefficient method based on time promotion is used to calculate the modal work of each pitch of the rotor blade under the examination mode shape , wherein is the number of single channels in the multi-channel grid model, , is the vibration period of the rotor blade under the examination mode shape, is the vibration frequency of the rotor blade under the examination mode shape, is the phase angle of the rotor blade under the examination mode shape, is the numerical simulation time, , represents the integral of the rotor blade modal force closed surface, is the blade surface pressure, is the modal vector of the rotor blade under the examination mode shape, is the rotor blade surface normal vector, is the rotor blade surface area, is the differential symbol.

[0025] Step five, the pitch of the rotor blade under the examination mode shape with the minimum modal work is defined as the dangerous pitch, the rotor blade in the middle of the multi-channel grid model is set as a dynamic grid domain, and the remaining rotor blades are set as rigid state, and the multi-channel unsteady calculation considering the preset mistuning condition of the rotor blade is carried out at the dangerous pitch, and the pressure, grid point displacement, grid point velocity of the rotor blade surface grid point at each time step, and the blade surface normal vector corresponding to each grid point are output. In this embodiment, the preset mistuning condition is that the maximum mistuning amount of the blade frequency is , and the sweep frequency of the rotor blade vibration is set to , , wherein is the natural frequency under the examination mode shape, is the numerical simulation time. The unsteady calculation result outputs the pressure, coordinates, grid displacement, grid velocity and blade surface normal vector of the rotor blade surface grid point at each time step.

[0026] Step six, according to the pressure of each time step rotor blade surface grid point, grid point displacement, grid point velocity and each grid point corresponding blade surface normal vector, based on dynamic modal decomposition method, the proxy model between the dangerous pitch under the blade unsteady aerodynamic force and vibration displacement is established, the fluid-solid coupling method is used to carry out the rotor blade structure dynamics simulation analysis, and the unsteady aerodynamic force and vibration displacement information of the blade at different times are obtained.

[0027] The above is only the preferred embodiment of the present application, and is not used to limit the present application, any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. An analytical method for unsteady aerodynamic forces considering blade mistuning, characterized in that, include: Using the flow channel between two adjacent rotor blades of the compression component as a single channel, a multi-channel mesh model is constructed by selecting multiple continuously distributed single channels on the entire rotor ring of the compression component. Steady-state calculations of the multi-channel mesh model were performed using CFD software to obtain the steady flow field and the surface pressure and surface temperature of each rotor blade under the multi-channel mesh model. Using the surface pressure, surface temperature, and rotor speed of the corresponding rotor blades as the prestress input for modal analysis, the natural frequencies and modal vectors of the rotor blades under the test mode shape are obtained through simulation. Unsteady computational boundary conditions are applied to the multi-channel mesh model, and the rotor blades in the middle of the multi-channel mesh model are set as dynamic mesh domains, while the remaining rotor blades are set as rigid states. Based on the natural frequencies and modal vectors under the test mode shape, the modal work of each node diameter of the rotor blades under the test mode shape is obtained by analyzing the influence coefficient method based on time progression. The pitch diameter with the minimum modal work of the rotor blade under the test mode shape is defined as the critical pitch diameter. The rotor blade in the middle of the multi-channel mesh model is set as the moving mesh domain, and the other rotor blades are set as rigid. Multi-channel unsteady calculation is carried out under the critical pitch diameter considering the preset detuning conditions of the rotor blade. The pressure, displacement, velocity and blade surface normal vector of each mesh point on the rotor blade surface are output at each time step. Based on the pressure, displacement, velocity, and blade surface normal vector of each grid point on the rotor blade surface at each time step, a proxy model between the unsteady aerodynamic forces and vibration displacements of the blade under the critical nodal diameter is established using the dynamic mode decomposition method. The rotor blade structure dynamics simulation analysis is carried out using the fluid-structure interaction method to obtain the unsteady aerodynamic forces and vibration displacement information of the blade at different times.

2. The analytical method according to claim 1, characterized in that, Select at least 7 consecutively distributed single channels to construct a multi-channel mesh model, and the number of consecutively distributed single channels must be odd.

3. The analytical method according to claim 1, characterized in that, use Analysis yields modal work of the rotor blades at each pitch diameter under the tested vibration mode. ,in This refers to the number of single channels in a multi-channel mesh model. , To assess the vibration period of the rotor blades under different vibration modes, To assess the vibration frequency of the rotor blades under the specified mode shape, To assess the phase angle of the rotor blades under the mode shape, For numerical simulation time, , This represents the integration over the closed surface of the modal forces of the rotor blades. The pressure on the blade surface. To evaluate the modal vectors of the rotor blades under different vibration modes, The normal vector of the rotor blade surface. The surface area of ​​the rotor blades. This is the differential symbol.

4. The analytical method according to claim 1, characterized in that, The preset detuning condition is: the maximum detuning amount of the blade frequency is... The sweep frequency of rotor blade vibration is set to , ,in To assess the natural frequencies under different vibration modes, This represents the numerical simulation time.

5. An analytical system for unsteady aerodynamic forces considering blade mistuning, characterized in that, include: The network model building module is used to construct a multi-channel mesh model by selecting multiple continuously distributed single channels on the entire rotor ring of the compression component, taking two adjacent rotor blades of the compression component and the flow channel between them as single channels. The first analysis module is used to perform steady-state calculations on the multi-channel mesh model using CFD software, and to obtain the steady flow field and the surface pressure P and surface temperature T of each rotor blade under the multi-channel mesh model. The second analysis module is used to simulate and obtain the natural frequencies and modal vectors of the rotor blades under the test mode shape by taking the surface pressure, surface temperature and rotor speed of the corresponding rotor blades as the prestress input for modal analysis. The third analysis module is used to apply unsteady computational boundary conditions to the multi-channel mesh model, and set the rotor blades in the middle of the multi-channel mesh model as the moving mesh domain, and set the remaining rotor blades as the rigid state. Based on the natural frequency and modal vector under the test mode, the modal work of each node diameter of the rotor blade under the test mode is obtained by using the influence coefficient method based on time progression. The fourth analysis module defines the critical pitch diameter as the pitch diameter with the minimum modal work of the rotor blade under the test mode shape. The rotor blade in the middle of the multi-channel mesh model is set as a moving mesh domain, and the other rotor blades are set as rigid. Multi-channel unsteady calculations are carried out under the critical pitch diameter considering the preset detuning conditions of the rotor blade. The module outputs the pressure, displacement, velocity of the mesh points on the rotor blade surface and the blade surface normal vector corresponding to each mesh point at each time step. The fifth analysis module is used to establish a proxy model between the unsteady aerodynamic forces and vibration displacements of the blade under the critical nodal diameter based on the pressure, displacement, velocity of the grid points on the rotor blade surface at each time step, as well as the blade surface normal vector corresponding to each grid point. It then uses the fluid-structure interaction method to carry out the dynamic simulation analysis of the rotor blade structure and obtain the unsteady aerodynamic forces and vibration displacement information of the blade at different times.

6. The analysis system according to claim 5, characterized in that, In the network model construction module, at least 7 continuously distributed single channels are selected to construct a multi-channel mesh model, and the number of continuously distributed single channels is odd.

7. The analysis system according to claim 5, characterized in that, In the third analysis module, using Analysis yields modal work of the rotor blades at each pitch diameter under the tested vibration mode. ,in This refers to the number of single channels in a multi-channel mesh model. , To assess the vibration period of the rotor blades under different vibration modes, To assess the vibration frequency of the rotor blades under the specified mode shape, To assess the phase angle of the rotor blades under the mode shape, For numerical simulation time, , This represents the integration over the closed surface of the modal forces of the rotor blades. The pressure on the blade surface. To evaluate the modal vectors of the rotor blades under different vibration modes, The normal vector of the rotor blade surface. The surface area of ​​the rotor blades. This is the differential symbol.

8. The analysis system according to claim 5, characterized in that, In the fourth analysis module, the preset detuning condition is: the maximum detuning amount of the blade frequency is The sweep frequency of rotor blade vibration is set to , ,in To assess the natural frequencies under different vibration modes, This represents the numerical simulation time.

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