Evaluation method and calculation device for high-cycle fatigue durability characteristic probability of engine rotor

Abstract

An engine rotor high-cycle fatigue durability characteristic probability evaluation method comprises the following steps: establishing a finite element model, and calculating a sensitivity matrix of design parameters and responses; establishing a probability distribution model of the response of the rotor part; calculating the mean value and variance of the design parameters according to the response of the rotor and the probability distribution relation of the design parameters, carrying out iterative calculation until the variance converges, and determining a calibration distribution function of the design parameters; and sampling according to the calibration distribution function to establish a sample set, calculating high-cycle fatigue performance data corresponding to the sample set by using a finite element model, and comparing the high-cycle fatigue performance data with Goodman curve calibration of the rotor part material. The invention further provides a computing device.

Description

Technical Field

[0001] This invention belongs to the field of aero-engines, specifically relating to a method and calculation device for probabilistic evaluation of the high-cycle fatigue durability characteristics of engine rotors. Background Technology

[0002] The fatigue performance of aero-engine rotors is a key factor in aero-engine safety assessment, and avoiding catastrophic consequences caused by vibration of components is a critical requirement in aero-engine design and manufacturing. During engine operation, high-speed airflow occurs in the inner and outer bypass ducts, and rotor components are subjected to random aerodynamic excitations, such as inlet airflow distortion, compressor bleed or surge, uneven combustion and oscillating combustion in the combustion chamber, and noise-induced excitations. When the excitation frequency approaches the rotor component's natural frequency, resonance can occur, causing a significant increase in vibration amplitude, increased stress on the structure, and increased deformation, leading to structural failure and the risk of irreversible damage. Therefore, engine design must ensure that engine components do not generate harmful resonances within the flight envelope and throughout the entire speed range. For specific components, the intersection of natural frequency and excitation is usually determined based on Campbell's diagram to avoid resonance zones in critical speed regions. It is generally believed that the cyclic stress generated by vibration is the HCF (high-cycle fatigue) stress borne by the rotor component. Due to the dense structure and complex flow field of engines, completely avoiding resonance at high frequencies is difficult to achieve in actual operating conditions. Therefore, examining whether HCF failure will occur in rotor components in critical resonance regions, thereby jeopardizing the integrity and safety of the engine, is highly necessary during engine design and certification. On the other hand, according to CCAR33.83, the engine must prove through testing that the vibration stress borne by components that may be excited by mechanical or aerodynamic forces (such as blades, bladed disks, etc.) is less than the material's endurance limit and retains a certain margin.

[0003] In the airworthiness certification process of aero-engines, the verification of vibration tests under CCAR 33.83 typically begins with analyzing the steady-state stress of components using the finite element method (FEM). This is followed by measuring the maximum dynamic stress of key components such as blades and bladed disks through whole-engine / core engine tests. Finally, the margin of the measured dynamic stress under the maximum steady-state stress is analyzed based on the Goodman curve of the material to determine if it meets the requirements under the allowable dynamic stress. However, due to factors such as boundary conditions, material properties, and simplified modeling, certain differences inevitably exist between the finite element model and the actual model, leading to errors in the analysis results. These errors include performance dispersion between blades due to dimensional deviations and material defects, dispersion in measurement results due to differences in strain gauge sensitivity, differences in the sensitivity of measured points to superimposed modes when multiple resonance points exist at the same rotational speed, and incomplete data due to test condition limitations. These uncertainties ultimately affect the accuracy of the evaluation. Therefore, providing a rotor HCF evaluation method that considers uncertainties is of positive significance for optimizing the engine design process and improving engine reliability. Summary of the Invention

[0004] The purpose of this invention is to provide a probabilistic evaluation method for the high-cycle fatigue durability characteristics of engine rotors, thereby improving the accuracy of HCF (High-Frequency Combustion) evaluation of engine rotors. This invention also provides a computing device.

[0005] According to one embodiment of the present invention, a method for probabilistic evaluation of high-cycle fatigue durability characteristics of an engine rotor is provided, the method comprising the following steps:

[0006] Step a): Establish the finite element model of the rotor component. The finite element model of the rotor component includes design parameters θ and response Y. The initial value of the design parameters is θ0. Calculate the sensitivity matrix S according to ΔY = SΔθ, where ΔY is the residual of Y and Δθ is the residual of θ.

[0007] Step b): Provide vibration characteristic test data of the rotor component, including statistical data of the rotor component's natural modes and frequencies and mode shapes, and establish a probability distribution model of the rotor component's response;

[0008] Step c): Calculate the mean and variance function of the design parameters of the rotor component based on the probability distribution relationship between the rotor response and the design parameters of the rotor component, and substitute the mean and variance back into the probability distribution relationship for iterative calculation until the variance of the design parameters converges. The probability distribution function of the design parameters when the variance of the design parameters converges is used as the calibration distribution function.

[0009] Step d): Sampling is performed according to the calibration distribution function to establish a sample set;

[0010] Step e): Input the design parameters of the sample set into the finite element model of the rotor component, calculate the maximum steady-state stress, the maximum dynamic stress and location of the rotor component under the given working conditions, plot the calculation results as a scatter plot and compare them with the Goodman curve of the rotor component material to obtain the evaluation results of the high-cycle fatigue durability characteristics.

[0011] This method enables the evaluation of the probability distribution of HCF characteristics of aero-engine rotor components using a probabilistic approach, intuitively demonstrating the durability margin of the rotor components and providing analytical data support with uncertainties for cathode testing.

[0012] Furthermore, in some embodiments, the design parameters include the Young's modulus of the material and boundary conditions; the response includes natural frequencies and natural mode shapes; the finite element model includes a mass matrix and a stiffness matrix; and a first-order Taylor expansion of Y(θ) at θ0 is performed to obtain ΔY = SΔθ.

[0013] Furthermore, in some embodiments, in step b), the probability distribution relationship is a Gaussian distribution.

[0014] Furthermore, in some embodiments, in step c),

[0015]

[0016] Where θ is the design parameter of the rotor component, Y is the response of the rotor component, P(θ|Y) is the probability distribution of θ under condition Y, P(Y|θ) is the probability distribution of Y under condition θ, P(Y) is the probability distribution of Y, and P(θ) is the probability distribution of θ; S is the sensitivity matrix, ε Y Let ε be the error of Y. θ Let θ be the error, cov be the variance matrix, μ be the mean of θ0, and θ0 be the initial value of the design parameters.

[0017] Furthermore, in some embodiments, the mean value of the design parameter θ is θ*=θ0+(S T cov -1 (ε Y (YY(θ))+(θ-μ) T cov -1 (ε θ (θ-μ)).

[0018] Furthermore, in some embodiments, the variance cov(ε) corresponding to θ* θ* )=(1-(S T cov -1 (ε Y )S+cov -1(ε θ ))S T cov -1 (ε Y ))S)cov(ε θ ).

[0019] Furthermore, in some embodiments, in step d), the sampling method includes one or a combination of several of the following: uniform design, orthogonal design, central composite design, or Latin hypercube sampling design.

[0020] Furthermore, in some embodiments, in step d), the number of samples is at least 20.

[0021] Furthermore, in some embodiments, in step e), the given operating condition includes the three red line operating condition and / or the high-temperature takeoff operating condition.

[0022] According to another aspect of the present invention, a computing device is provided, the computing device including a memory and a processor, wherein the memory stores a computing program, and when the computing program is executed by the processor, it is able to implement the probabilistic evaluation method for high-cycle fatigue durability characteristics of engine rotors provided in any of the foregoing embodiments. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for probabilistic evaluation of the high-cycle fatigue durability characteristics of an engine rotor in one embodiment;

[0024] Figure 2 This is a schematic diagram comparing the data points of the sample set with the Goodman curve calibration in one embodiment.

[0025] The purpose of the above figures is to provide a detailed description of the invention so that those skilled in the art can understand the technical concept of the invention, and not to limit the invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0027] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment herein. The phrase appearing in various places in the specification does not necessarily refer to the same embodiment, nor is it limited to mutually exclusive, independent, or alternative embodiments. Those skilled in the art will understand that the embodiments herein can be combined with other embodiments without structural conflict. In the description herein, "a plurality of" means at least two.

[0028] In the process of airworthiness certification for aero engines, the verification of vibration tests according to CCAR33.83 firstly involves analyzing the steady-state stress of components using the finite element method; then, through whole-engine / core engine tests, the maximum dynamic stress of key components such as blades and disks is measured; finally, based on the Goodman curve of the material, the margin of the measured dynamic stress under the maximum steady-state stress is analyzed to see if it meets the requirements under the allowable dynamic stress.

[0029] However, due to factors such as boundary conditions, material properties, and simplified modeling, there are differences between the finite element model and the actual model, which leads to certain errors between the analysis results of conventional methods and actual measurements. For example, due to factors such as material manufacturing deviations and material defects, there is a certain degree of dispersion between blades; due to differences in strain gauge sensitivity, there is also dispersion in the measurements of different strain gauges at the same location; there may be multiple resonance points at the same rotational speed, and when identifying superimposed modes, the sensitivity of the measured points to the measurements of different modes also varies; the measured points may be damaged or abnormal, and the survival rate of strain gauges during the test is not high enough, resulting in incomplete data; and the number of whole-machine test runs is limited by labor, cost, and cycle constraints; due to the limitation of the patch position, the measured point may not be the point of maximum strain, and the data of the maximum strain position needs to be inverted through strain distribution, which also leads to errors.

[0030] In whole-engine / core dynamic stress measurement tests, the measured points are affected by factors such as differences in finite element models, blade dispersion, strain gauge dispersion, identification accuracy, and analysis accuracy. Current technical solutions can only conservatively estimate whether the HCF durability margin of the same batch of rotor components meets requirements through coefficient correction and margin guarantees, without quantitatively determining the HCF characteristics of that batch of blades. These multiple uncertainties ultimately lead to insufficiently conservative HCF durability margins calculated based on measured dynamic stress, affecting the indication of airworthiness compliance.

[0031] To address the aforementioned problems, one embodiment of the present invention provides a probabilistic evaluation method for the high-cycle fatigue durability characteristics of an engine rotor.

[0032] like Figure 1 As shown, the method includes the following steps:

[0033] Step a): Establish a finite element model of the engine rotor component to be analyzed. In different embodiments, the engine rotor component can be a blade, a bladed disk, or other rotating parts of an aero-engine. Design parameters are used as inputs to the finite element model. In a preferred embodiment, the design parameters include the Young's modulus of the material and boundary conditions. The response is the finite element output characteristic quantity of the component. In a preferred embodiment, the response includes the natural frequency and the natural mode shape.

[0034] For ease of calculation, it is assumed that the structural response can be constructed as a function of the design parameters with respect to the mass and stiffness matrices:

[0035] θ = [θ1, θ2, θ3…θ n ] T ,

[0036] Y(θ) = f(K(θ), M(θ)),

[0037] Where θ is the design parameter of the engine rotor component that needs to be corrected and evaluated, which is an n-dimensional vector; Y is the response; K is the stiffness matrix; and M is the mass matrix.

[0038] Under normal circumstances, the response Y exhibits a nonlinear relationship with the design parameters θ. Given a set of initial design parameters θ0 for the finite element model, performing a first-order Taylor expansion on Y(θ), and assuming the order of the response Y is m, we can obtain the following after conversion:

[0039]

[0040] Furthermore, the relationship between the residuals of the response Y and the residuals of the design parameter θ can be obtained through conversion:

[0041] ΔY = SΔθ.

[0042] Where ΔY is the residual of the response Y, Δθ is the residual of the design parameter θ, and S is the sensitivity matrix. In different embodiments, the sensitivity matrix can be solved using the Nelson method, the bisection method, or the calculation module of a general-purpose finite element analysis software.

[0043] Step b): Provide vibration characteristic test data of the rotor components (Bench test data accumulation). This test data is obtained through vibration tests of rotor components with a certain sample size. In the preferred embodiment, the sample size is at least 30. Measure the natural modes of the rotor components and perform cumulative statistical analysis on the frequency and mode shape data to obtain a probability distribution model of the rotor component response.

[0044] In a preferred embodiment, it is assumed that the error follows a Gaussian distribution:

[0045] Y = +ε Y ,

[0046] ε Y ~N(0,cov(ε) Y )).

[0047] Similarly, design parameters may also be affected by environmental or human factors and exhibit a probability distribution trend. Based on engineering experience and accumulated engineering data in the database, it is assumed that the errors of the design parameter θ also conform to a certain Gaussian distribution:

[0048] Y(θ)= +SΔθ,

[0049] θ~N(θ*,cov(ε θ )),

[0050] cov(ε θ ,ε Y ) = 0.

[0051] Where θ* is the mean of θ, and cov(ε) θ ,ε Y Let θ be the covariance of Y, and cov(ε) be the covariance of θ and Y. θ ,ε Y =0 means that the two are considered to be unrelated.

[0052] Step c): Using Bayes' theorem (Bayes method), the prior probabilities of the relevant probability distributions are corrected to estimate the design parameters θ, resulting in:

[0053]

[0054] Where P(θ|Y) represents the probability of θ under Y, i.e., the posterior probability, which is the probability distribution of the design parameter θ affected by the error in response to Y; P(Y|θ) represents the probability of Y under θ, i.e., the probability distribution of the response Y under a certain probability distribution of the design parameter θ; P(θ) represents the subjective judgment of the probability of θ, i.e., the prior probability, which is the probability distribution of the design parameter based on the subjective judgment; and P(Y) represents the probability of Y occurring, i.e., the likelihood function, which is the objective probability distribution of the response. Integrating the probability distribution function can reduce it to a constant, i.e.:

[0055] P(θ|Y)∝P(Y|θ)·P(θ).

[0056] From the above equation, we can see that: given the prior probability of the design parameter θ and the probability distribution of the response Y, the posterior probability of the design parameter θ can be obtained by calculating the joint probability minimum density of the error. The posterior probability distribution of the design parameter θ and the prior probability distribution are of the same type, called conjugate distributions. Assuming that both P(Y|θ) and P(θ) follow a certain Gaussian distribution, then P(θ|Y) also follows a Gaussian distribution.

[0057]

[0058] Where μ is the mean of the initial value θ0 of the design parameter θ.

[0059] Therefore, the estimated value of the design parameter θ can be determined by the minimum value of the joint probability density:

[0060] J(θ)=min[(YY(θ)) T cov-1 (ε Y (YY(θ))+(θ-μ) T cov -1 (ε θ (θ-μ)],

[0061] Taking the derivative with respect to θ, we obtain the mean value θ* of the new design parameters after calculation:

[0062] θ*=θ0+(S T cov -1 (ε Y )S+cov -1 (ε θ )S T cov -1 (ε Y ))(Y*-Y0), where Y* is the mean of the response Y.

[0063] The variance corresponding to θ* can be calculated as follows:

[0064] cov(ε θ* )=(1-(S T cov -1 (ε Y )S+cov -1 (ε θ ))S T cov -1 (ε Y ))S)cov(ε θ ).

[0065] The mean θ* and variance cov(ε) of the new design parameters obtained after calculation are used. θ* Substitute back into P(θ|Y) and repeat the above calculation process (i.e., replace μ and cov(ε) in the original expression). θ )), until cov(ε θ* When the coordinates converge, the probability distribution function of θ is the calibration distribution function.

[0066] θ~N(θ*,cov(ε θ* )).

[0067] Step d): Sampling is performed according to the calibration distribution function to establish a sample set. In different embodiments, sampling can be implemented based on one or a combination of methods such as uniform design, orthogonal design, central composite design, or Latin hypercube sampling design. The sampling yields a sample set θ1-θ1 consisting of k response surface fitting samples. k In a preferred embodiment, k is not less than 20.

[0068] Step e): Based on the sample set, establish a finite element model and perform maximum steady-state stress analysis on the rotor component under a given specific operating condition. Simultaneously, analyze the maximum dynamic stress and its location on the rotor component within a given resonant speed region. In a preferred embodiment, the given operating conditions include the three-red-line exposure or high-temperature takeoff conditions. Plot the calculated data as a scatter plot and compare it with the Goodman curve calibration of the rotor component material to obtain the evaluation results of the high-cycle fatigue characteristics of the component considering the influence of uncertain factors.

[0069] In a preferred embodiment, the results of performing 30 samplings using the above method and comparing them with Goodman curve calibration are as follows: Figure 2 As shown, the distance between the scatter points and the Goodman curve represents the margin of the rotor component considering uncertainties. Figure 2 The scatter plots show that, under the corresponding design parameter θ, the margin is approximately 30%.

[0070] Another embodiment of the present invention provides a computing device including a memory and a processor. The memory stores a computing program, which, when executed by the processor, can implement the probabilistic evaluation method for high-cycle fatigue durability characteristics of engine rotors provided in any of the above embodiments. In different embodiments, the computing device can be configured as a general-purpose computer, a specially built computing device such as a microcontroller, or a cloud computing device or virtual machine.

[0071] The purpose of the above embodiments is to provide a further detailed description of the present invention in conjunction with the accompanying drawings, so that those skilled in the art can understand the technical concept of the present invention. Within the scope of the present invention, optimization or equivalent substitution of the method steps involved, as well as combination of implementations in different embodiments without causing structural or principle conflicts, all fall within the protection scope of the present invention.

Claims

1. A method for probabilistic evaluation of high-cycle fatigue durability characteristics of an engine rotor, characterized in that, Includes the following steps: Step a): Establish the finite element model of the rotor component. The finite element model of the rotor component includes design parameters θ and response Y. The initial value of the design parameters is θ0. Calculate the sensitivity matrix S according to ΔY = SΔθ, where ΔY is the residual of Y and Δθ is the residual of θ. Step b): Provide vibration characteristic test data of the rotor component, including statistical data of the rotor component's natural modes and frequencies and mode shapes, and establish a probability distribution model of the rotor component's response; Step c): Calculate the mean and variance function of the design parameters of the rotor component based on the probability distribution relationship between the rotor response and the design parameters of the rotor component, and substitute the mean and variance back into the probability distribution relationship for iterative calculation until the variance of the design parameters converges. The probability distribution function of the design parameters when the variance of the design parameters converges is used as the calibration distribution function. Step d): Sampling is performed according to the calibration distribution function to establish a sample set; Step e): Input the design parameters of the sample set into the finite element model of the rotor component, calculate the maximum steady-state stress, the maximum dynamic stress and location of the rotor component under the given working conditions, plot the calculation results as a scatter plot and compare them with the Goodman curve of the rotor component material to obtain the evaluation results of the high-cycle fatigue durability characteristics.

2. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1, characterized in that, The design parameters include the Young's modulus of the material and boundary conditions. The response includes the natural frequency and natural mode shape. The finite element model includes the mass matrix and stiffness matrix. A first-order Taylor expansion of Y(θ) at θ0 yields ΔY = SΔθ.

3. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1 or 2, characterized in that, In step b), the probability distribution relationship is a Gaussian distribution.

4. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1 or 2, characterized in that, In step c), Where θ is the design parameter of the rotor component, Y is the response of the rotor component, P(θ|Y) is the probability distribution of θ under condition Y, P(Y|θ) is the probability distribution of Y under condition θ, P(Y) is the probability distribution of Y, and P(θ) is the probability distribution of θ; S is the sensitivity matrix, ε Y Let ε be the error of Y. θ Let θ be the error, cov be the variance matrix, μ be the mean of θ0, and θ0 be the initial value of the design parameters.

5. The probabilistic evaluation method for high-cycle fatigue durability characteristics of engine rotors according to claim 4, characterized in that, The mean value of the design parameter θ is θ* = θ0 + (S T cov -1 (ε Y (YY(θ))+(θ-μ) T cov -1 (ε θ (θ-μ)).

6. The probabilistic evaluation method for high-cycle fatigue durability characteristics of engine rotors according to claim 5, characterized in that, The variance cov(ε corresponding to θ* θ* ) = (1 - (S T cov -1 (ε Y )S + cov -1 (ε θ ))S T cov -1 (ε Y ))S)cov(ε θ ).

7. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1 or 2, characterized in that, In step d), the sampling method includes one or a combination of several of the following: uniform design, orthogonal design, central composite design, or Latin hypercube sampling design.

8. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1 or 2, characterized in that, In step d), the number of samples is at least 20.

9. The method for probabilistic evaluation of high-cycle fatigue durability characteristics of engine rotors according to claim 1 or 2, characterized in that, In step e), the given operating conditions include the three red line operating conditions and / or the high temperature takeoff operating conditions.

10. A computing device, comprising a memory and a processor, characterized in that, The memory stores a calculation program, which, when executed by the processor, enables the implementation of the probabilistic evaluation method for high-cycle fatigue durability characteristics of engine rotors as described in any one of claims 1 to 9.

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