Turbine disc low-cycle fatigue prediction method based on balance time scale method

Abstract

The invention discloses a turbine disc low-cycle fatigue prediction method based on a balance time scale method, relates to the technical field of turbine thermal protection, and is used for evaluating the low-cycle fatigue life of a recyclable rocket engine turbine disc. With the development of a reusable engine, the service time of a turbine disc is multiplied, which brings forward a significant demand for accurate prediction of the fatigue life of the turbine disc. The method comprises the following steps: constructing an engine turbine disc conjugate heat transfer calculation model; evaluating an acceleration factor by using a balance time scale method; performing conjugate heat transfer calculation on the turbine disc by using the acceleration factor; extracting gas heat data of the turbine disc; constructing a turbine disc finite element calculation model; clustering finite element models of conjugate heat transfer data; analyzing the structure of the turbine disc; and performing low-cycle fatigue prediction based on a local stress-strain method. According to the method, accurate prediction of the low-cycle fatigue of the turbine disc in the stable operation cycle under the engineering cost can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of thermal protection of aerospace engine turbines, and in particular relates to a method for predicting low-cycle fatigue of turbine disks based on a balanced time scale method, which is used for predicting fatigue life of turbine disks of reusable aerospace rocket engine turbines. Background Art

[0002] As a key component of an engine, the turbine disk operates in an environment of high temperature, high load, high speed, and high vibration. Disk damage due to strength and vibration issues is a common engine failure. The turbine disk has a complex overall structure and directly bears the brunt of the high temperature, high pressure, and high-speed airflow at the combustion chamber outlet. The environment in which it operates is extremely harsh. Due to thermal stress, localized areas may experience significant stress and strain, leading to various failures. Currently, turbine design is gradually moving toward high thrust-to-weight ratios and lightweight design. Failures caused by structural strength and fatigue life pose a serious threat to the reliability and safety of the engine. At the same time, to meet the design requirements of multiple starts and reused engines, an accurate quantitative analysis of the service life of the turbine disk is required.

[0003] To accurately assess the fatigue life of aerospace engine turbine disks, researchers have conducted a series of studies, among which the following two methods are widely used:

[0004] (1) CFD calculations were used to obtain the convective boundary conditions on the turbine disk surface, and then unsteady finite element calculations were performed to determine the temperature evolution within the turbine disk. However, since the effect of the solid domain temperature field evolution on the flow field was ignored, the uncertainty of the boundary conditions at the interface between the solid domain and the fluid domain significantly affected the prediction results.

[0005] (2) Carry out steady conjugate heat transfer calculations under rated operating conditions, and then perform structural fatigue analysis based on the analysis results of the steady-state flow field. However, this method cannot take into account the complex stress-strain history experienced by aerospace engines during stable operation, as well as the impact effects of mechanical, thermal, and centrifugal loads to a certain extent.

[0006] With the development of reusable engines, in-depth research on the fatigue life of turbine disks must be carried out. The core of this research is to obtain the time-varying data of aerodynamic forces, centrifugal forces and temperature loads during stable operation, and then analyze the impact on fatigue life.

[0007] Unsteady conjugate heat transfer simulations are considered to be more accurate than traditional heat conduction models in obtaining time-varying data on aerodynamic forces, centrifugal forces, and temperature loads because they eliminate the uncertainty of boundary conditions at the interface between the solid and fluid domains. However, the challenge with unsteady conjugate heat transfer calculations lies in the significant timescale difference between the solid domain (measured in seconds) and the fluid domain (measured in milliseconds or even microseconds). The long stable operating cycles of rocket engines (measured in minutes or even tens of minutes) make computational costs unacceptable. Summary of the Invention

[0008] To overcome the shortcomings of the prior art, the present invention aims to provide a method for predicting low-cycle fatigue of turbine disks based on the equilibrium time-scale method. This method effectively and efficiently predicts the time-varying data of aerodynamic, centrifugal, and thermal loads during the steady-state operation of aerospace engine turbines at an engineeringly acceptable computational cost. Furthermore, it achieves more accurate low-cycle fatigue life prediction for reusable aerospace engine turbine disks than traditional methods. This method is universally applicable and easy to use, making it more suitable for aerospace engine turbine designers.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is:

[0010] A method for predicting low-cycle fatigue of a turbine disk based on a balanced time scale method comprises the following steps:

[0011] Step 1, constructing a conjugate heat transfer calculation model for the turbine disk;

[0012] Step 2: Based on the operating conditions of the turbine disk during the stable operation phase, the time step and acceleration factor that can meet the requirements of engineering prediction accuracy and engineering calculation cost are evaluated using the balanced time scale method.

[0013] Step 3, modifying the full three-dimensional conjugate heat transfer solver based on the acceleration factor and calculating the conjugate heat transfer of the turbine disk;

[0014] Step 4: extract the aerodynamic and heat transfer data at the turbine disk grid nodes;

[0015] Step 5, constructing a finite element calculation model of the turbine disk;

[0016] Step 6: cluster the conjugate heat transfer calculation results into the turbine disk finite element calculation model using inverse distance weighted interpolation;

[0017] Step 7, analyzing the turbine disk structure based on the Von-Mises yield criterion;

[0018] Step 8: Predict low-cycle fatigue of turbine disk based on local stress-strain method.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] (1) This method fully considers the complex stress-strain history during the stable operation phase and the impact effects of mechanical, thermal, and centrifugal loads to a certain extent;

[0021] (2) This method breaks through the time scale matching technology of solid domain and fluid domain in unsteady conjugate heat transfer (CHT) calculation, and realizes the accurate prediction of low-cycle fatigue life of turbine disk at engineering calculation cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of a method for predicting low-cycle fatigue of a turbine disk based on the equilibrium time scale method of the present invention.

[0023] Figure 2 Schematic diagram of the inverse distance weighted clustering used in the present invention.

[0024] Figure 3 This is a comparison of temperature prediction results at different locations under different acceleration factors of a preferred embodiment of the present invention.

[0025] Figure 4 This is a diagram showing the predicted effect of solid domain temperature distribution under different acceleration factors in a preferred embodiment of the present invention.

[0026] Figure 5 This is a comparison of the total strain prediction results at different positions under different acceleration factors of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0027] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0028] The present invention provides a method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method. As a method for predicting low-cycle fatigue of turbine disks, this method effectively realizes the accurate prediction of time-varying data of aerodynamic force, centrifugal force and temperature load during the stable operation stage of aerospace engine turbine at an engineering acceptable calculation cost, and realizes the low-cycle fatigue life prediction of reusable aerospace engine turbine disks more accurately than traditional methods.

[0029] refer to Figure 1 As shown, it mainly includes the following steps:

[0030] Step 1: Construct a turbine disk conjugate heat transfer calculation model, which includes the turbine disk conjugate heat transfer calculation geometry and calculation grid.

[0031] This paper uses 3D modeling software to construct computational geometry, which includes the computational domains for the fluid flow through the engine turbine, the fluid computational domain for the engine turbine disk, and the solid computational domain for the engine turbine disk. It is important to note that engine turbine disks typically have pinholes for connecting other components. Their impact on flow and heat transfer is ignored, and the geometry at these pinholes is filled.

[0032] On this basis, the present invention uses three-dimensional computational grid generation software to mesh the conjugate heat transfer computational geometric model of the turbine disk to obtain the conjugate heat transfer computational grid of the turbine disk, wherein the computational grid generated by the fluid computational domain of the engine turbine disk and the computational grid generated by the solid computational domain of the engine turbine disk must ensure that the fluid-solid interface grid corresponds to each other. Boundary layers are arranged at the wall and fluid-solid interface of the fluid domain to meet the Yplus requirements of turbulence models such as SST k-omega. In the embodiment, the first layer of grid nodes is 0.0015 mm away from the wall, and the boundary layer grid expansion ratio is 1.5. An expansion layer is arranged at the fluid-solid interface of the solid domain to achieve a smooth transition with the boundary layer grid size of the fluid domain. In the embodiment, the first layer of grid nodes is 0.02 mm away from the wall, and the solid domain expansion layer expansion ratio is 1.4.

[0033] Step 2: Based on the operating conditions of the turbine disk during the stable operation phase, the balanced time scale method is used to evaluate the time step and acceleration factor that can meet the engineering prediction accuracy and engineering calculation cost.

[0034] This step uses the equilibrium time scale method to evaluate the time step and acceleration factor for the turbine disk's stable operating condition. Since this condition only considers low-cycle fatigue of the turbine disk, the frozen rotor method can be used to calculate the dynamic and static interface of the turbine disk. In this case, a time step of 0.01s satisfies the engineering prediction accuracy for the turbine disk's stable operation phase.

[0035] In this step, the stable operation stage of the turbine disk is a typical convection heating / cooling process, and its progress can be characterized by the following simplified formula:

[0036]

[0037] Where c p,S represents the specific heat capacity of solid at constant pressure, with subscripts S and F representing solid and fluid respectively, i.e., ρ S represents the solid density, V S A represents the volume of the solid. S represents the solid surface area, T S and T F represents the solid temperature and fluid temperature, t represents time, and α represents the heat transfer coefficient.

[0038] Its evolution process is expressed as follows:

[0039]

[0040] Where, T S,0 is the initial solid temperature, T F is the fluid temperature;

[0041] The acceleration factor SF is defined based on the constant pressure specific heat capacity of the turbine disk solid material:

[0042]

[0043] In the formula is the corrected constant-pressure specific heat capacity; at this time, the time scale of the solid domain temperature response t * for:

[0044]

[0045] It should be noted that in order to ensure the consistency of the calculation results before and after the acceleration factor is applied, the rationality of the acceleration factor needs to be evaluated using the Fourier number and the Biewt number. The Biewt number and the Fourier number before and after the acceleration factor are ensured to be within the preset error range to meet the requirements of engineering accuracy. The evaluation formula is as follows:

[0046]

[0047] Where Bi and Fo are the Bivolt number and Fourier number evaluated according to the calculation conditions and time step before the acceleration factor is applied, respectively. * and Fo * are the Bivouac number and Fourier number evaluated according to the calculation conditions and time step after using the acceleration factor, L is the characteristic length of the turbine disk, λ S is the thermal conductivity of the solid domain material.

[0048] This step adjusts the time scale by adjusting the acceleration factor SF. Since the time scale is reduced, the required computation time is shortened while the time step remains unchanged, thus reducing the computation cost.

[0049] After evaluation, setting SF to 100 was found to be the optimal value for balancing computational cost and accuracy. In this example, the effectiveness of this method was quantitatively demonstrated by comparing prediction results with SF set to 10 and 100. Setting SF to 10 and 100 represents a 10x and 100x speedup, respectively, compared to the baseline, meaning the computational cost is reduced to 1 / 10 and 1 / 100.

[0050] Step 3: Modify the turbine disk conjugate heat transfer solver based on the acceleration factor and perform turbine disk conjugate heat transfer calculation.

[0051] Use the turbine disk conjugate heat transfer calculation grid established in step 1 to import the full 3D conjugate heat transfer solver. Set it up according to the structure of the turbine disk calculation model, where the dynamic and static rotor method can be used for the dynamic and static interface.

[0052] According to the time step (0.01s) and acceleration factors (10, 100) evaluated in step 2, the calculation parameters (such as time step and physical parameters) of the full three-dimensional conjugate heat transfer calculation are set, and then the transient calculation of the full three-dimensional conjugate heat transfer of the turbine disk is carried out. The transient calculation results of the full three-dimensional conjugate heat transfer of the turbine disk at each time step are saved to form a calculation time series data set.

[0053] Step 4: Extract the aerodynamic and heat transfer data at the turbine disk grid nodes.

[0054] Data extraction is performed on the time series data set obtained from the full 3D conjugate heat transfer calculation of the turbine disk in Step 3. Specifically, the temperature at the grid nodes in the solid domain of the turbine disk and the pressure at the grid nodes at the fluid-solid interface in the solid domain of the turbine disk are extracted at each time. The calculated time series data is corrected to obtain the accelerated turbine disk temperature field and surface pressure field data.

[0055] Taking SF = 10 as an example, in this example, step 3 yields a computational time series data set saved and constructed with a time step of 0.01 seconds. Due to the balanced time stepping method, the temperature evolution within the turbine disk is accelerated, evolving the temperature field with a time step of 0.1 seconds. After time series correction, physical time series data for the turbine disk temperature field and surface pressure field are obtained.

[0056] Figure 3 A comparison of temperature prediction results at different locations under different acceleration factors is shown. Figure 4 The temperature distribution prediction results of the solid domain under different acceleration factors are shown. The temperature prediction results shown demonstrate the consistency of temperature prediction under this method.

[0057] Step 5: Construct a turbine disk finite element calculation model, which includes the turbine disk finite element calculation geometry and calculation mesh.

[0058] Considering the differences in the constitutive equation mechanisms between finite element analysis and conjugate heat transfer calculations, conjugate heat transfer calculations require a fine mesh to resolve flow evolution and to meet the requirements of the YPlus fluid boundary layer mesh and solid expansion layer mesh to resolve large gradients in physical properties at the fluid-solid interface. In contrast, finite element analysis utilizes precise conjugate heat transfer calculation results, eliminating the need for a fine solid domain mesh to capture heat transfer evolution and requiring only the computational accuracy required for finite element analysis. Therefore, the solid computational domain of the engine turbine disk constructed using 3D modeling software in step 1 is used as the computational geometry for the turbine disk finite element model. The finite element analysis computational mesh does not require fine meshing at the boundaries, and the mesh size can be significantly larger than that of the solid computational domain. The finite element analysis computational mesh for the turbine disk has a significantly smaller number of nodes than the solid computational domain mesh for the engine turbine disk, saving computational cost while maintaining accuracy. It is important to note that the pin holes in the solid computational domain of the engine turbine disk are ignored in the conjugate heat transfer calculation model. The spatial location of the pin holes in the turbine disk finite element calculation model must be annotated to apply constraints in subsequent structural analysis.

[0059] Step 6: Use inverse distance weighted interpolation to cluster the conjugate heat transfer calculation results into the turbine disk finite element calculation model.

[0060] Because the grid nodes of the computational grid of the turbine disk finite element calculation model are different from the computational grid of the engine turbine disk solid computational domain. In order to ensure that the conjugate heat transfer calculation results of the turbine disk are successfully loaded onto the turbine disk finite element analysis computational grid, the inverse distance weighted clustering method is introduced. Specifically, for each grid node of the computational grid of the turbine disk finite element calculation model, the kd tree algorithm is used to search for the three nearest computational grid nodes in the engine turbine disk solid computational domain computational grid, and the temperature and pressure values of the above three computational grid nodes are clustered according to the distance weight to obtain the node temperature and pressure of the turbine disk finite element analysis computational grid. The schematic diagram is shown as follows: Figure 2 As shown:

[0061] The weighted formula is as follows:

[0062]

[0063] Where w i The weight of the i-th grid in the solid computational domain of the engine turbine disk; d i is the distance from the grid to the location to be clustered, T and P are the temperature and pressure values of the conjugate calculation results respectively, is the temperature at the location to be clustered, T(X i ,Y i) is the temperature value of the conjugate calculation result of the i-th grid, is the pressure at the location to be clustered, P(X i ,Y i ) is the pressure value at the position to be clustered, n=3, and the position to be clustered is the calculation grid of the turbine disk finite element calculation model.

[0064] Step 7: Analysis of turbine disk structure based on Von-Mises yield criterion.

[0065] Considering the harsh operating conditions of turbine disks in engines (typically rocket engines), significant thermal stresses can occur in the structure, causing them to exceed the material's yield limit in some areas. Therefore, considering the disk's structural characteristics and service environment, and the elastic-plastic properties of the material, a structural analysis based on the Von-Mises yield criterion was performed. The elastic region follows the generalized Hooke's law, while the plastic region follows the flow law. Based on the structural analysis results, the total strain amplitude in key areas (blade root, blade tip, and areas with large temperature gradients) was extracted.

[0066] Specifically, the structural strain increment is expressed as:

[0067] dε=dε e +dε p

[0068] Where: dε e is the elastic strain increment; dε p is the plastic strain increment.

[0069] When the equivalent stress reaches the new yield limit, the material will enter the yield state again. The Mises criterion for isotropic hardening material is:

[0070]

[0071] In the formula is the equivalent stress; is the total amount of plastic equivalent strain; T is the temperature; S is the relationship function.

[0072] The relationship between stress increment and strain increment in the elastic region is:

[0073] dσ=D e dε e

[0074] Where: dσ is the stress increment; D e is the elastic matrix.

[0075] In the plastic region, the normal flow law is followed:

[0076]

[0077] Then there is a relationship between stress increment and strain increment:

[0078] dσ=(D e -D p )dε=D ep dε

[0079] Where D p is the plasticity matrix; D ep is the elastic-plastic matrix.

[0080] According to the incremental elastic-plastic stress-strain relationship and the virtual displacement principle, the finite element equation of the thermal elastic-plastic problem can be derived:

[0081]

[0082] Where P f is the volume load vector; P T is the surface load vector; is the temperature strain load vector; K ep is the elastoplastic stiffness matrix:

[0083] K ep =∫ V B T D ep BdV

[0084] Where B is the strain matrix.

[0085] Step 8: Prediction of low-cycle fatigue of turbine disk based on local stress-strain method.

[0086] The local stress-strain method is used to predict the low-cycle fatigue life. Considering that the load borne by the structure is asymmetric, the influence of the average load is considered and the Morrow elastic stress linear correction method is used. The Manson-Coffin formula after the average stress correction is:

[0087]

[0088] Where: σ′ f and ε′ f is the fatigue strength coefficient and fatigue ductility coefficient; E is the elastic modulus; N f is the fatigue life of the structure; b and c are the fatigue strength index and fatigue ductility index.

[0089] Since the material fatigue performance test data is based on uniaxial stress or strain tests, multiaxial stress correction is required. The Von-Mises stress correction method and the Manson-McKnight multiaxial stress method are used to correct the stress. Assuming that the material is isotropic, the average stress and stress amplitude in the three orthogonal directions of x, y, and z are:

[0090]

[0091] Where σ x,m , σ y,m , σ z,m represents the average stress in three orthogonal directions, σ x,a , σ y,a , σ z,a Represents the stress amplitude in three orthogonal directions. The subscripts x, y, and z represent the orthogonal directions. The subscripts max and min represent the maximum and minimum values of the relevant physical quantities, respectively.

[0092] The corresponding shear stress is

[0093]

[0094] Where τ xy,m , τ yz,m , τ xz,m They represent the average shear stress acting along the second coordinate axis on the plane with the normal direction as the first coordinate axis, τ xy,a , τ yz,a , τ xz,a They respectively represent the shear stress amplitude acting along the second coordinate axis on the plane whose normal direction is the first coordinate axis.

[0095] The equivalent uniaxial stress state under the multiaxial stress state is:

[0096]

[0097] Where σ1 and σ2 represent the first and third principal stresses, σ m , σ a are the equivalent uniaxial mean stress and stress amplitude under the multiaxial stress state.

[0098] The most vulnerable areas for turbine blade failure are the blade tip, blade root, and high temperature gradient areas on the disk belly. The total strain at these locations is extracted to assess the low-cycle fatigue of the turbine disk. Figure 5 The total strain at the leading and trailing blade roots of turbine disk blades at different time scales is shown. The results show that the total strain predictions for turbine disks are consistent across different time scales. This demonstrates that the present invention can accurately predict low-cycle fatigue of turbine disks while significantly reducing computational costs.

Claims

1. A method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method, characterized in that: The following steps are involved: Step 1, constructing a conjugate heat transfer calculation model for the turbine disk; Step 2: Based on the operating conditions of the turbine disk during the stable operation phase, the time step and acceleration factor that can meet the requirements of engineering prediction accuracy and engineering calculation cost are evaluated using the balanced time scale method. Step 3, modifying the full three-dimensional conjugate heat transfer solver based on the acceleration factor and calculating the conjugate heat transfer of the turbine disk; Step 4: extract the aerodynamic and heat transfer data at the turbine disk grid nodes; Step 5, constructing a finite element calculation model of the turbine disk; Step 6: cluster the conjugate heat transfer calculation results into the turbine disk finite element calculation model using inverse distance weighted interpolation; Step 7, analyzing the turbine disk structure based on the Von-Mises yield criterion; Step 8: Predict low-cycle fatigue of turbine disk based on local stress-strain method.

2. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 1, characterized in that: The turbine disk conjugate heat transfer calculation model includes computational geometry and computational grid; The computational geometry is constructed using 3D modeling software, which includes the computational domain of the engine turbine flow fluid, the computational domain of the engine turbine disk fluid, and the computational domain of the engine turbine disk solid. The computational geometry is meshed using three-dimensional computational grid generation software to obtain the computational grid. The computational grid generated by the fluid computational domain of the engine turbine disk and the computational grid generated by the solid computational domain of the engine turbine disk must ensure that the fluid-solid interface grid corresponds to each other. Boundary layers are arranged at the wall and fluid-solid interface of the fluid domain to meet the yplus requirements of the turbulence model. An expansion layer is arranged at the fluid-solid interface of the solid domain to achieve a smooth transition with the boundary layer grid size of the fluid domain.

3. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 1, characterized in that: The process of the turbine disk stable operation stage in step 2 is characterized by the following formula: Where c p,S represents the specific heat capacity of solid at constant pressure, ρ S represents the solid density, V S A represents the volume of the solid. S represents the solid surface area, T S and T F represents solid temperature and fluid temperature, t represents time, and α represents heat transfer coefficient; The evolution process is shown as follows: Where, T S,0 is the initial solid temperature, T F is the fluid temperature; The acceleration factor SF is defined based on the specific heat capacity at constant pressure: In the formula is the corrected constant-pressure specific heat capacity; at this time, the time scale of the solid domain temperature response t * for: The time scale can be adjusted by adjusting the acceleration factor SF.

4. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 3 is characterized in that: The Biwalt number and Fourier number before and after the acceleration factor are applied are both within the preset error range to meet the requirements of engineering accuracy. The evaluation formula is as follows: Where Bi and Fo are the Bivolt number and Fourier number evaluated according to the calculation conditions and time step before the acceleration factor is applied, respectively. * and Fo * are the Bivouac number and Fourier number evaluated according to the calculation conditions and time step after using the acceleration factor, L is the characteristic length of the turbine disk, λ S is the thermal conductivity of the solid domain material.

5. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 1, characterized in that: In step 3, the computational grid of the turbine disk conjugate heat transfer calculation model is used to import the full 3D conjugate heat transfer solver. The computational parameters of the full 3D conjugate heat transfer calculation are set according to the time step and acceleration factor evaluated in step 2. Then, the full 3D conjugate heat transfer transient calculation of the turbine disk is performed, and the transient calculation results of the full 3D conjugate heat transfer of the turbine disk at each time step are saved to form a time series data set. In step 4, the temperature at the grid nodes of the solid domain of the turbine disk and the pressure at the grid nodes at the fluid-solid interface of the solid domain of the turbine disk are extracted from the time series data set at each moment.

6. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 1, characterized in that: The turbine disk finite element calculation model includes computational geometry and computational mesh; the solid computational domain of the engine turbine disk constructed by three-dimensional modeling software in step 1 is used as the computational geometry of the turbine disk finite element calculation model, and the turbine disk finite element calculation model is meshed using three-dimensional computational mesh generation software to obtain a computational mesh.

7. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 6, characterized in that: In step 6, for each grid node of the turbine disk finite element calculation model calculation grid, the kd tree algorithm is used to search for the three closest calculation grid nodes in the engine turbine disk solid calculation domain calculation grid, and the temperature and pressure values of the above three calculation grid nodes are clustered according to the distance weight to obtain the node temperature and pressure of the turbine disk finite element analysis calculation grid: The weighted formula is as follows: Where w i Calculate the weight of the i-th grid in the solid computational domain of the engine turbine disk; d i is the distance from the grid to the location to be clustered, T and P are the temperature and pressure values of the conjugate calculation results respectively, is the temperature at the location to be clustered, T(X i ,Y i ) is the temperature value of the conjugate calculation result of the i-th grid, is the pressure at the location to be clustered, P(X i ,Y i ) is the pressure value at the position to be clustered, n=3, and the position to be clustered is the calculation grid of the turbine disk finite element calculation model.

8. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 5, characterized in that: In step 7, based on the structural characteristics and service environment of the turbine disk and taking into account elastic-plastic factors, a structural analysis is performed based on the Von-Mises yield criterion, wherein the elastic area follows the generalized Hooke's law and the plastic area follows the flow law. The total strain amplitude of the key areas is extracted based on the structural analysis results. The key areas are the blade root, blade tip and large temperature gradient area.

9. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 1, characterized in that: In step 8, the Morrow elastic stress linear correction method is used, and the Manson-Coffin formula after mean stress correction is: Where: σ′ f and ε′ f is the fatigue strength coefficient and fatigue ductility coefficient; E is the elastic modulus; N f is the fatigue life of the structure; b and c are the fatigue strength index and fatigue ductility index.

10. The method for predicting low-cycle fatigue of turbine disks based on the equilibrium time scale method according to claim 9, characterized in that: The stress is corrected using the Von-Mises stress correction method and the Manson-McKnight multiaxial stress method. Assuming that the material is isotropic, the average stress and stress amplitude in the three orthogonal directions of x, y, and z are: Where σ x,m , σ y,m , σ z,m represents the average stress in three orthogonal directions, σ x,a , σ y,a , σ z,a represents the stress amplitude in three orthogonal directions, the subscripts x, y, and z represent the orthogonal directions, and the subscripts max and min represent the maximum and minimum values of the relevant physical quantities, respectively; The corresponding shear stress is Where τ xy,m , τ yz,m , τ xz,m They represent the average shear stress acting along the second coordinate axis on the plane with the normal direction as the first coordinate axis, τ xy,a , τ yz,a , τ xz,a They represent the shear stress amplitude acting along the second coordinate axis on the plane whose normal direction is the first coordinate axis; The equivalent uniaxial stress state under the multiaxial stress state is: Where σ1 and σ2 represent the first and third principal stresses, σ m , σ a are the equivalent uniaxial mean stress and stress amplitude under the multiaxial stress state.

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