Aero-engine gear high-cycle fatigue reliability analysis method

Abstract

This invention discloses a method for high-cycle fatigue reliability analysis of aero-engine gears. Taking a gear transmission system of an aero-engine as the object, a finite element model of the gear is established using the ANSYS parametric design programming language. After acquiring experimental data, a proxy finite element model is obtained by actively learning the Kriging proxy model. Then, the proxy finite element model is corrected by the gradient deceleration particle swarm algorithm based on QMC to obtain a corrected high-precision finite element model. Considering the influence of uncertainties in size, material, and load on gear reliability, the S-N curve is fitted using gear contact fatigue test data. Next, the S-N curve is corrected and a life-based tooth surface contact fatigue limit state function is established. Finally, reliability analysis is performed using the corrected high-precision finite element model.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine reliability analysis, and specifically relates to a method for high-cycle fatigue reliability analysis of aero-engine gears. Background Technology

[0002] As the core power unit of an aircraft, the normal operation of an aero-engine directly affects the overall performance and safety of the aircraft. Without aero-engines, modern aviation would be impossible. The structural design and manufacturing process of aero-engines is extremely complex, involving multiple disciplines and high-precision processes, and imposing extremely stringent requirements on material selection, structural design, manufacturing processes, and performance verification.

[0003] In aero-engine systems, the accessory drive system plays a crucial role, especially the gear drive section. As a key link in power transmission, its main function is to efficiently and stably transmit the powerful force of the engine rotor to critical subsystems such as the fuel system, lubrication system, and aircraft accessories, ensuring that these systems work together to meet the diverse needs of flight. The gear drive system, as the core mechanical device for power transmission and speed matching, has a complex structure, including gear pairs, drive shafts, support bearings, housings, lubricants, prime movers, and loads.

[0004] However, despite the significant progress made in the aviation industry, numerous aircraft accidents throughout history, such as those in 1979, 1988, 2002, and up to 2021, have profoundly revealed the challenges and shortcomings in the reliability of aero engines. These accidents remind us that conducting comprehensive and in-depth reliability analysis and optimization design of aero engine transmission systems during the design and development phase is of immeasurable value for improving flight safety and extending engine lifespan.

[0005] Currently, as aero-engines develop towards higher power and higher speeds, aero-engine gear design faces unprecedented challenges. Gears operating under high loads are highly susceptible to fatigue damage, leading to decreased reliability and durability, and severely impacting the overall performance of the engine. Furthermore, aero-engine gear transmission systems and their accessories operate under extremely complex conditions, placing extremely stringent requirements on structural strength, machining accuracy, assembly quality, and the operating environment. Summary of the Invention

[0006] To address the aforementioned shortcomings in the existing technology, the high-cycle fatigue reliability analysis method for aero-engine gears provided by this invention solves the problems of the impact of uncertainties in size, material, and load on the high-cycle fatigue reliability of aero-engine gears.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: a method for high-cycle fatigue reliability analysis of aero-engine gears, comprising the following steps:

[0008] S1. Establish the finite element model of the gear transmission system of the aero-engine to be analyzed.

[0009] S2. Based on the gear finite element model, the corresponding proxy finite element model is constructed using the active learning Kriging proxy model, and then corrected to obtain the corrected high-precision finite element model.

[0010] S3. Based on the influence of uncertain factors on gear reliability, a gear contact fatigue test was conducted, and the SN curve was obtained by fitting the test data.

[0011] S4. Combining a high-precision finite element model and SN curves, a high-cycle fatigue reliability analysis of gears based on finite element simulation is conducted.

[0012] Further, step S1 specifically includes:

[0013] S11. Select the aero-engine gear transmission system to be analyzed and establish its corresponding 3D gear model;

[0014] S12. Mesh the established 3D gear model;

[0015] S13. Set the parameters for the 3D gear model after mesh generation, and perform finite element analysis of the gear to obtain the established gear finite element model.

[0016] Further, in step S2, the expression for the actively learned Kriging agent model is:

[0017]

[0018] In the formula, g K (X) represents the unknown Kriging proxy model, f(X) = [f1(X), f2(X), ..., f p (X)] T Let β represent the basis functions of the input variable X, where β = [β1, β2, K, β...]. p ] T Let z(X) represent the unknown coefficients of the corresponding regression function, z(X) represent a Gaussian process based on global simulation, and m be the number of basis functions.

[0019] Furthermore, in step S2, the method for constructing the proxy finite element model is specifically as follows:

[0020] S21-1, Generate N MCSA set of candidate sample points is formed into a sample point set S, and an initial sample point is selected based on the experimental design to form a candidate sample point set S0, and its response value is calculated.

[0021] S21-2. Based on the initial sample points and their response values, construct the corresponding initial agent model according to the expression of the active learning Kriging agent model;

[0022] S21-3. Predict the response value of the candidate sample point set S0 using the initial surrogate model, and obtain the predicted mean μ. g (x) and standard deviation σ g (x); where x comes from the predicted candidate sample point set S0;

[0023] S21-4, Using Learning Functions Find the best update sample point x * =argmin(U(x));

[0024] S21-5. Calculate the optimal update sample point x. * The response value, and based on x * It updates the initial sample points;

[0025] S21-6. Evaluate the current agency model;

[0026] S21-7 Calculate the predicted response value obtained based on the current agent model. and the true value y i The error is taken as the maximum error;

[0027] S21-8. Based on the maximum error, determine whether the model convergence condition is met;

[0028] If so, the calculation is completed, and the constructed proxy finite element model is obtained;

[0029] If not, increase the number of candidate sample points in the sample point set S and return to steps S21-4.

[0030] Furthermore, in step S2, the constructed proxy finite element model is corrected using a gradient-decreasing particle swarm algorithm based on QMC.

[0031] Furthermore, in step S3, the uncertain influencing factors include size, material, and load.

[0032] Further, step S4 specifically includes:

[0033] S41. Combining the high-precision finite element model and the corrected SN curve, establish the limit state function for tooth surface contact fatigue failure, and then calculate the failure probability.

[0034] S42. Based on the calculated failure probability, AK-MCS is used to conduct high-cycle fatigue reliability analysis of gears using fused SN curves.

[0035] Furthermore, in step S41, the limit state function g(x) for tooth surface contact fatigue failure is expressed as:

[0036]

[0037] Failure probability P f Represented as:

[0038]

[0039] In the formula, N f This indicates the number of cycles required to reach the critical stress level before fatigue failure. f represents the total stress cycle number required by the design. X (x) represents the joint probability density function, and x represents the random variable that affects the structural response.

[0040] Furthermore, in step S41, the formula for correcting the SN curve is:

[0041]

[0042] In the formula, m' represents the exponential proportionality coefficient for correcting the slope of the SN curve, and N j This represents the lifetime value corresponding to the i-th point in the SN curve, where N0 represents the initial lifetime value when correction begins, and σ Hj σ represents the stress value corresponding to the i-th point in the SN curve. H0 C represents the initial stress value when correction begins, and C' represents the product of the corrected stress value and the initial lifetime value when correction begins. This indicates the corrected stress value.

[0043] The beneficial effects of this invention are as follows:

[0044] (1) This invention takes the gear transmission system of aero-engine as the research object, and explores in depth the uncertainty factors of gears in actual manufacturing process and service conditions. It aims to improve the reliability and durability of gear transmission system through advanced reliability analysis methods.

[0045] (2) In view of the inherent contradiction between accuracy and cost in traditional theoretical methods, this invention innovatively introduces finite element model correction technology and integrates finite element analysis into the high-cycle fatigue reliability analysis process of gears, so as to effectively reduce research costs while ensuring analysis accuracy and provide strong support for the advancement of aerospace gear design. Attached Figure Description

[0046] Figure 1The flowchart of the high-cycle fatigue reliability assessment method for aero-engine gears provided by the present invention is shown.

[0047] Figure 2 The 3D gear model diagram provided for this invention.

[0048] Figure 3 The mesh model diagram provided for this invention.

[0049] Figure 4 The image shows the finite element analysis results of the gear provided by this invention.

[0050] Figure 5 The high-cycle fatigue segment diagram of the SN curve provided by this invention.

[0051] Figure 6 The modified SN curve provided for this invention.

[0052] Figure 7 The failure probability convergence curve provided for this invention. Detailed Implementation

[0053] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0054] This application provides a method for high-cycle fatigue reliability analysis of aero-engine gears, such as... Figure 1 As shown, it includes the following steps:

[0055] S1. Establish the finite element model of the gear transmission system of the aero-engine to be analyzed.

[0056] S2. Based on the gear finite element model, the corresponding proxy finite element model is constructed using the active learning Kriging proxy model, and then corrected to obtain the corrected high-precision finite element model.

[0057] S3. Based on the influence of uncertain factors on gear reliability, a gear contact fatigue test was conducted, and the SN curve was obtained by fitting the test data.

[0058] S4. Combining a high-precision finite element model and SN curves, a high-cycle fatigue reliability analysis of gears based on finite element simulation is conducted.

[0059] Step S1 in this embodiment of the application is specifically as follows:

[0060] S11. Select the aero-engine gear transmission system to be analyzed and establish its corresponding 3D gear model;

[0061] S12. Mesh the established 3D gear model;

[0062] For example, the established 3D gear model is meshed by gear lines, gear surfaces, and volume mesh extrusion;

[0063] S13. Set the parameters for the 3D gear model after mesh generation, and perform finite element analysis on the gear to obtain the established finite element model of the gear.

[0064] For example, the ANSYS parameter design language (APDL) is used to complete the settings of materials, contact and rotating pairs, working loads, etc., and to perform gear finite element analysis.

[0065] In one example of the embodiments of this application, in the process of constructing the gear finite element model, a gear transmission system of an aero-engine is taken as the object, and the ANSYS parametric design programming language is used to establish a gear finite element model with 17CrNiMo6 material.

[0066] For example, a modified gear made of 17CrNiMo6 is modeled, and its 3D model is as follows: Figure 2 As shown.

[0067] Specifically, in the modeling process, the single-tooth model was first divided into six regions, and the mesh quantity was set for each line. The plane42 element was used for mesh generation, and a three-tooth model was created by copying. Finally, the solid185 3D element was used for volume mesh extrusion to obtain the mesh model, which was then saved as follows: Figure 3 As shown.

[0068] During the finite element analysis, APDL was used to read the cdb and iges format files of the gear model, and the three important parts of the gear were selected based on their positional relationships, as shown in Table 1.

[0069] Table 1

[0070]

[0071] The three important gear surfaces are named by creating node groups. The gear pair assembly begins by rotating the first gear by a certain angle and then translating it to a position that won't affect the node group settings of the second gear. After setting the position of the first gear, import the second gear and set the node groups and rotation / translation positional relationships in the same way to ensure precise assembly of the two gears. Since the gear pair is made of the same material, the contact is a flexible surface-to-surface contact. Because the mesh density of the two gears is similar and they are made of the same material, based on the selection principle for concave and convex surfaces, the pinion tooth surface is defined as the target surface, and the gear tooth surface as the contact surface. The element for the target surface is selected as TARGE170, and the element for the contact surface is selected as CONTA174. When defining the contact pair properties, the friction coefficient of the contact surface is set to 0.05. During gear pair transmission, the gear shaft is fixed. To establish this revolute pair, two MPC184 elements are first created at the center of the shaft hole, and the inner diameter of the shaft hole and the nodes on both sides are constrained to these two elements through multi-point constraints, enabling the application of constraints and loads. Finally, the load was set. Since the large gear is the driving gear, it was fixed with a zero rotational speed. The small gear is the driven gear, and a torque was applied to it. Finite element analysis was then performed, and the results are as follows: Figure 4 As shown in the figure. The finite element analysis results of the gear show that the maximum stress value is located at the meshing point.

[0072] In one example of the embodiments of this application, in order to select a proxy model with better proxy effect when constructing the proxy finite element model, three typical proxy models, namely response surface method (RSM), Kriging, and Gaussian process (GP), were used to build a finite element model based on the proxy model. After running in ANSYS, the three proxy models were constructed respectively, and the proxy effect evaluation of different proxy models is shown in Table 3.

[0073] Table 3

[0074]

[0075] As shown in Table 3, all three surrogate models perform well in terms of relative surrogate effectiveness, with R² exceeding 0.95. However, Kriging and GP are significantly better than RSM, reaching over 0.99. Regarding the absolute value of the surrogate effectiveness, since the maximum stress on the gear tooth surface is higher than 1000 MPa within the limited operating conditions, the root mean square error of Kriging and GP can be calculated to be less than 2% of the stress.

[0076] Since the purpose of the proxy gear finite element model is to obtain an implicit function that can replace the finite element analysis, the average error of the proxy finite element model is already less than 3% based on the comparison between experimental data and finite element analysis data. In order to reduce the decrease in accuracy after proxying the finite element model and further improve the model accuracy, the active learning Kriging proxy model is used to construct a higher accuracy proxy finite element model in this embodiment of the application.

[0077] In one example of an embodiment of this application, the active learning Kriging surrogate model in step S2 treats the limit state function as an implementation of a stochastic process, consisting of two parts: a global linear regression model and a stochastic process model, which respectively model the global trend and local variability; based on this, the expression of the active learning Kriging surrogate model is:

[0078]

[0079] In the formula, g K (X) represents the unknown Kriging proxy model, f(X) = [f1(X), f2(X), ..., f p (X)] T Let β represent the basis functions of the input variable X, where β = [β1, β2, K, β...]. p ] T Let represent the unknown coefficients of the corresponding regression function, m be the number of basis functions, and z(X) represent a Gaussian process based on global simulation with an expectation of 0 and a variance of . For any unknown x, g K (x) all conform to a Gaussian distribution.

[0080] In one example of an embodiment of this application, the method for constructing the proxy finite element model in step S2 is specifically as follows:

[0081] S21-1, Generate N MCS A set of candidate sample points is formed into a sample point set S, and an initial sample point is selected based on the experimental design to form a candidate sample point set S0, and its response value is calculated.

[0082] S21-2. Based on the initial sample points and their response values, construct the corresponding initial agent model according to the expression of the active learning Kriging agent model;

[0083] S21-3. Predict the response value of the candidate sample point set S0 using the initial surrogate model, and obtain the predicted mean μ. g (x) and standard deviation σ g (x); where x comes from the predicted candidate sample point set S0;

[0084] S21-4, Using Learning Functions Find the best update sample point x* =argmin(U(x));

[0085] S21-5. Calculate the optimal update sample point x. * The response value, and based on x * It updates the initial sample points;

[0086] S21-6. Evaluate the current agency model;

[0087] S21-7 Calculate the predicted response value obtained based on the current agent model. and the true value y i The error is taken as the maximum error;

[0088] S21-8. Based on the maximum error, determine whether the model convergence condition is met;

[0089] If so, the calculation is completed, and the constructed proxy finite element model is obtained;

[0090] If not, increase the number of candidate sample points in the sample point set S and return to steps S21-4.

[0091] For example, in steps S21-6, the surrogate model is evaluated using the correlation coefficient and the root mean square error (RMSE), where the correlation index R... 2 Represented as:

[0092]

[0093] The root mean square error (RMSE) is expressed as:

[0094]

[0095] In the formula, m is the number of samples; y i Indicates a genuine response; Indicates the predicted response; It is the mean of the function's true response.

[0096] In one embodiment of this application, in step S2, the constructed proxy finite element model is corrected using a gradient descent particle swarm algorithm based on QMC.

[0097] For example, the implementation steps of the above-mentioned gradient descent particle swarm optimization algorithm based on QMC are as follows:

[0098] S22-1. Generate two different Sobol sequences respectively;

[0099] S22-2. Set the intervals for the initial position and initial velocity, and generate the initial position and initial velocity using sequences respectively;

[0100] S22-3, Calculate the response of the initial particle swarm;

[0101] S22-4. Find the individual optimal value for each particle;

[0102] S22-5. Find the global optimum for the entire population;

[0103] S22-6. Update velocity and position based on the optimal values ​​of the group and individuals, where the velocity calculation formula is:

[0104]

[0105] In the formula, k is the weight value, which is related to the relative difference between the current point and the optimal value point.

[0106] S22-7 Calculate the updated particle swarm response;

[0107] S22-8. Determine whether the algebra settings are met. If not, return to step S224; if so, end the correction.

[0108] In one example of an embodiment of this application, the uncertain influencing factors in step S3 include size, material, and load.

[0109] For example, to assess the fatigue life or fatigue strength of a gear, it is necessary to establish the relationship between load and life. Fatigue failure of materials or structures operating at room temperature depends on the magnitude of the external load. Microscopically, the initiation of fatigue cracks is related to local microscopic plasticity, but macroscopically, at low cyclic stress levels, elastic strain plays a dominant role, resulting in a longer fatigue life, known as stress fatigue or high-cycle fatigue (HCF). At high cyclic stress levels, plastic strain plays a dominant role, resulting in a shorter fatigue life, known as strain fatigue or low-cycle fatigue (LCF). If the cyclic stress level is very low, the material or structure is macroscopically in an elastic state, resulting in a very long fatigue life; this condition is called very high-cycle fatigue (VHCF).

[0110] Analysis of contact fatigue test data revealed the high-cycle fatigue segment of the contact fatigue curve (SN) at 50% reliability within the finite life range of the tested gears, as shown below. Figure 5 As shown, the gear contact fatigue limit stress is calculated to be 1444 MPa based on the fitted SN curve.

[0111] In one example of an embodiment of this application, step S4 specifically involves:

[0112] S41. Combining the high-precision finite element model and the corrected SN curve, establish the limit state function for tooth surface contact fatigue failure, and then calculate the failure probability.

[0113] S42. Based on the calculated failure probability, AK-MCS is used to conduct high-cycle fatigue reliability analysis of gears using fused SN curves.

[0114] In one example of an embodiment of this application, in step S41, given an n-dimensional input X = [X1, X2, K, X...] n ] T The gear. Assume that gear failure depends solely on the number of cycles N required to reach the critical stress level at fatigue failure. f Total stress cycles required by design Related to the total stress cycle count required by the design. Less than the actual total number of stress cycles N that has been borne f The gear system will be determined to be in a state of failure at this point. Therefore, the limit state function g(x) for tooth surface contact fatigue failure is expressed as:

[0115]

[0116] Failure probability P f Represented as:

[0117]

[0118] In the formula, N f This indicates the number of cycles required to reach the critical stress level before fatigue failure. f represents the total stress cycle number required by the design. X (x) represents the joint probability density function, where x represents the random variable affecting the structural response; specifically, f X (x) represents the joint probability density function of random variables such as size, material, and load parameters. Random variables that affect the structural response include size, material, and load.

[0119] Specifically, when obtaining the critical stress cycle number, the tooth surface contact stress response is obtained through finite element analysis, and the critical stress cycle number at which fatigue failure occurs under this response is obtained using the modified SN curve; the formula for correcting the slope of the SN curve is as follows:

[0120]

[0121] In the formula, m' represents the exponential proportionality coefficient for correcting the slope of the SN curve, and N j This represents the lifetime value corresponding to the i-th point in the SN curve, where N0 represents the initial lifetime value when correction begins, and σ Hj σ represents the stress value corresponding to the i-th point in the SN curve. H0 C represents the initial stress value when correction begins, and C' represents the product of the corrected stress value and the initial lifetime value when correction begins. This indicates the corrected stress value.

[0122] The corrected SN curve is as follows Figure 6 As shown.

[0123] In one example of an embodiment of this application, in step S42, AK-MCS is used to conduct high-cycle fatigue reliability analysis of gears based on fused SN curves; specifically, it includes the following steps:

[0124] S42-1, Generate N MCS A set of candidate sample points is formed into a point set S, and an initial set of sample points is extracted based on the experimental design to form a point set S0, and the response value is calculated.

[0125] S42-2. Based on the initial sample points and their response values, construct the initial Kriging model according to the expression of the active learning Kriging surrogate model.

[0126] S42-3. Predict the response values ​​of the candidate sample point set S using the initial Kriging model, and obtain the predicted mean μ. g (x) and standard deviation σ g (x), where x comes from the predicted candidate sample point set S0;

[0127] S42-4. Find the optimal update iteration sample point x using the point addition criterion expressions of four learning functions: EI, EFF, U, and H. * ;

[0128] S42-5. Determine the convergence condition (whether the maximum error is less than 10 MPa; where the maximum error is the predicted response value). and the true value y i (The maximum value of the error.) Does it satisfy the following?

[0129] If yes, proceed to step S42-7; otherwise, proceed to step S42-6.

[0130] S42-6. Calculate and update sample point x * The response value, and based on x * Update the initial sample points and return to step S42-2;

[0131] S42-7, Using the correlation coefficient R 2 The root mean square error (RMSE) is used to evaluate agent performance.

[0132] S42-8. Calculate the coefficient of variation of the failure probability. The coefficient of variation can be expressed as:

[0133]

[0134] S42-9. Determine whether the convergence condition (coefficient of variation is less than 0.05) is met;

[0135] If yes, then end the calculation process; otherwise, increase the number of candidate sample points S and return to step S42-3.

[0136] Specifically, in the above steps, let Φ(·) be the cumulative distribution function operator of the standard normal distribution variable. For a standard normally distributed variable, the probability density function operator is used.

[0137] Specifically, the learning functions involved in step S42-4 include the expected improvement (EI) learning function, the learning function EFF, the learning function U, and the learning function H. These four learning functions will subsequently be combined with AK-MCS for high-cycle fatigue reliability analysis, and the optimal update iteration sample point x in step S42-4 will be used... * The criteria for adding points are determined by the expression of each learning function.

[0138] The expected improvement (EI) learning function iteratively searches for new sample points until it finds the global optimum. Its approach involves adding the point with the highest EI value to the sample point set and iterating again to find the optimal solution. The formula for calculating the learning function EI is as follows:

[0139]

[0140] In the formula, f min (x)=(y1,y2,K,y n ) represents the existing optimal value; Φ(·), These represent the cumulative function and density function of the standard distribution, respectively; It is an estimate of s(x), derived from the sample points x. i The observed value y(x) i This allows us to obtain the set of observed values ​​Y(x) and the estimated values. Where y(x) i This can be represented as:

[0141] y(x i )=μ+ε(x i ), (i = 1, K, n)

[0142] In the formula, μ represents a stochastic process; ε(x) i ) follows a variance of σ 2 It follows a standard normal distribution.

[0143] The criteria for adding points are as follows:

[0144] x* =argmax(EIF(X))

[0145] Its stopping criteria are:

[0146] max(EI(x))≤C

[0147] In the formula, C takes a value according to the needs of the proxy model, and is usually 0.01.

[0148] The basic idea of ​​the learning function EFF is to determine whether a test sample point has the potential to cross the ultimate failure boundary based on the weighted distance between the test sample point and the ultimate failure boundary. The formula for calculating the learning function EFF is as follows:

[0149]

[0150] In the formula, μ g (x) represents the predicted value of the sample point; σ g (x) represents the standard deviation of the predicted value; f(·) represents the probability density function of the failure mode function; The failure boundary is defined by ε(x); ε(x) represents the acceptable error range from the boundary of the limit state function. Let be the distance between the test sample point and the acceptable boundary of the limit state function. τ + (x)=(g + (x)-μ g (x)) / σ g (x).

[0151] The criteria for adding points are as follows:

[0152] x * =argmax(EFF(X))

[0153] Its termination criterion is defined as:

[0154] max(EFF(x))≤d

[0155] In the formula, the value of d affects the accuracy of the proxy model, and it is usually taken as 0.001.

[0156] The basic idea of ​​the learning function U is the distance between the surrogate model's predicted value and the failure surface, as well as the standard deviation of the estimated value. Its calculation formula is as follows:

[0157]

[0158] The criteria for adding points are as follows:

[0159] x * =argmin(U(x))

[0160] The corresponding termination criteria are:

[0161] min(U(x))≥n

[0162] In the formula, the value of n determines the accuracy of the active learning model, and it is usually taken as 2.

[0163] The learning function H is a new addition criterion proposed based on the principle of information entropy. The formula for calculating the learning function H is as follows:

[0164]

[0165] In the formula, g + (x) and g - (x) represent the allowable boundary values ​​of the limit state function, and g represents the limit state function. + (x)=ε(x), g - (x)=ε(x), ε(x)=2σ g (x).

[0166] The criteria for adding points are as follows:

[0167] x * =argmax(H(x))

[0168] Its termination criteria are:

[0169] max(H(x))≤h

[0170] In the formula, the corresponding h value can be selected according to the accuracy requirements of different models, and the value is usually taken as 0.5.

[0171] In one example of an embodiment of this application, the specific process of solving the high-cycle fatigue reliability of gears based on MATLAB-ANSYS simulation is given as follows:

[0172] S42-01, Generate N quantities using Sobol sequences. t The initial training sample set S0 is transferred to the parametric finite element model of ANSYS as a text file via MATLAB.

[0173] ANSYS performs finite element analysis and returns the stress response of these samples. MATLAB calculates the corresponding fatigue life based on the SN curves and these responses, and then uses the initial samples and responses to establish an initial Kriging surrogate model.

[0174] S42-02, Using the same Sobol sequence, the number of generated quantities is N. MCS training sample set S MCS And by constructing a proxy model with a learning function. Predict the training sample set S MCSThe response. If the stopping condition of the learning function is met, the Kriging surrogate model converges, and step S42-03 is executed; otherwise, the sample selected by the learning function is calculated through the high-cycle fatigue reliability analysis model and added to the training sample set, the Kriging surrogate model is reconstructed, and step S42-02 is executed;

[0175] S42-03, Using the training sample set S MCS Calculate the failure probability P f and its coefficient of variation CV(P) f If the coefficient of variation CV(P) f If the convergence criterion is not met, increase the number of Monte Carlo samples and proceed to step S4202; otherwise, use the convergent Kriging surrogate model. Calculate the high-cycle fatigue life failure probability P of gears f .

[0176] Considering the high cost of finite element analysis and the difficulty in obtaining failure probability through MCS, the classic AK-MCS+U method is adopted as the benchmark method for calculating failure probability. This method continuously adds samples until CV(P) is obtained. f When the value is less than 0.01, the number of points added is 1765. The curve showing the change in failure probability with the number of points added is as follows. Figure 7 As shown.

[0177] High-cycle fatigue reliability analysis was performed using AK-MCS combined with four learning functions. The results of the baseline method and the other four methods are shown in Table 5. The number of finite element analysis calls, N... call It is represented by the number of initial points plus the number of points added to the learning function. P f CV(P) represents the failure probability predicted by the Kriging surrogate model. f ) represents the coefficient of variation of the failure probability.

[0178] Table 5

[0179]

[0180] As shown in Table 5, for gears made of 17CrNiMo6, there is no significant difference in the coefficient of variation of failure probability among the four methods. However, the learning functions U and H can reduce the calculation error of failure probability to below 1% after convergence. Among them, the cost of learning function U is lower, and the cost of learning function EI is lower than the other three, but the failure probability error is slightly higher.

[0181] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0182] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for analyzing high-cycle fatigue reliability of aeroengine gears, characterized in that, Includes the following steps: S1. Establish the finite element model of the gear transmission system of the aero-engine to be analyzed. S2. Based on the gear finite element model, the corresponding proxy finite element model is constructed using the active learning Kriging proxy model, and then corrected to obtain the corrected high-precision finite element model. S3. Based on the influence of uncertain factors on gear reliability, a gear contact fatigue test was conducted, and the SN curve was obtained by fitting the test data. S4. Combining the high-precision finite element model and SN curve, perform high-cycle fatigue reliability analysis of gears based on finite element simulation. Step S4 specifically involves: S41. Combining the high-precision finite element model and the corrected SN curve, establish the limit state function for tooth surface contact fatigue failure, and then calculate the failure probability. S42. Based on the calculated failure probability, use AK-MCS to conduct high-cycle fatigue reliability analysis of gears using fused SN curves. In the step S41, the limit state function of the tooth surface contact fatigue failure is represented as: is represented as: Failure probability is represented as: In the formula, This indicates the number of cycles required to reach the critical stress level before fatigue failure. This represents the total number of stress cycles required by the design. Denotes the joint probability density function. Represents random variables that affect the structural response; In step S41, the formula for correcting the SN curve is: In the formula, This represents the exponential scaling factor used to correct the slope of the SN curve. This represents the lifetime value corresponding to the j-th point in the SN curve. This indicates the initial lifetime value when the correction begins. This represents the stress value corresponding to the j-th point in the SN curve. This indicates the initial stress value when the correction begins. This represents the product of the corrected stress value and the initial lifetime value at the start of the correction. This indicates the corrected stress value.

2. The aeroengine gear high-cycle fatigue reliability analysis method of claim 1, wherein, Step S1 specifically involves: S11. Select the aero-engine gear transmission system to be analyzed and establish its corresponding 3D gear model; S12. Mesh the established 3D gear model; S13. Set the parameters for the 3D gear model after mesh generation, and perform finite element analysis of the gear to obtain the established gear finite element model.

3. The method of claim 1, wherein, In step S2, the expression for the actively learned Kriging proxy model is: In the formula, Represents an unknown Kriging proxy model. Indicates input variables basis functions, This represents the unknown coefficients of the corresponding regression function. This represents a Gaussian process based on global simulation. The number of basis functions.

4. The aeroengine gear high-cycle fatigue reliability analysis method of claim 3, wherein, In step S2, the method for constructing the proxy finite element model is as follows: S21-1, Generation A set of candidate sample points is formed. Based on the experimental design, initial sample points were selected to form a candidate sample point set. Calculate its response value; S21-2. Based on the initial sample points and their response values, construct the corresponding initial agent model according to the expression of the active learning Kriging agent model; S21-3. Predicting candidate sample point sets using an initial surrogate model. The response value is used to obtain the predicted mean. and standard deviation ;in, From the predicted candidate sample point set ; S21-4, utilizing a learning function Finding optimal update sample points ; S21-5, calculating the optimal update sample point response value, and updating the initial sample point based on the initial sample point; S21-6. Evaluate the current agency model; S21-7 Calculate the predicted response value obtained based on the current agent model. and the true value The error is taken as the maximum error; S21-8. Based on the maximum error, determine whether the model convergence condition is met; If so, the calculation is completed, and the constructed proxy finite element model is obtained; If not, increase the sample point set. Count the number of candidate sample points and return to step S21-4.

5. The method of claim 1, wherein, In step S2, the constructed proxy finite element model is corrected using a gradient descent particle swarm algorithm based on QMC.

6. The aeroengine gear high-cycle fatigue reliability analysis method of claim 1, wherein, In step S3, the uncertain influencing factors include size, material, and load.

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