Aero-engine gear high-cycle fatigue reliability analysis method

Abstract

The invention discloses an aero-engine gear high-cycle fatigue reliability analysis method, which takes a certain aero-engine gear transmission system as an object, and establishes a gear finite element model by using an ANSYS parameterized design programming language; the method comprises the steps that after test data are obtained, an active learning Kriging proxy model is adopted to obtain a proxy finite element model, then the gear proxy finite element model is corrected through a QMC-based gradient deceleration particle swarm algorithm, and a corrected high-precision finite element model is obtained; in consideration of the influence of the uncertainty of the size, the material and the load on the reliability of the gear, fitting an S-N curve by adopting gear contact fatigue test data; then, correcting the S-N curve and establishing a life-based tooth surface contact fatigue limit state function; and finally, performing reliability analysis in combination with the corrected high-precision finite element model.

Description

Technical Field

[0001] The invention belongs to the field of aircraft engine reliability analysis, and in particular relates to an aircraft engine gear high cycle fatigue reliability analysis method. Background Art

[0002] As the core power unit of an aircraft, the normal operation of an aircraft engine is directly related to the overall performance and safety of the aircraft. Without aircraft engines, there would be no modern aviation. The structural design and manufacturing process of aircraft engines is extremely complex, involving multidisciplinary intersections and high-precision processes, and has extremely strict requirements on material selection, structural design, manufacturing processes, and performance verification.

[0003] In the aircraft engine system, the accessory transmission system occupies a pivotal position, especially the gear transmission part. As a key link in power transmission, its main function is to efficiently and stably transmit the powerful power of the engine rotor to the fuel system, lubrication system, aircraft accessories and other key subsystems to ensure that the various systems work together to meet the diverse needs during flight. The gear transmission system, as the core mechanical device for power transmission and speed matching, has a complex structure, including multiple key components such as gear pairs, transmission shafts, support bearings, housings, lubricants, prime movers and loads.

[0004] However, despite the remarkable progress made by the aviation industry, many aircraft crashes in history, such as those in 1979, 1988, 2002 and 2021, still deeply reveal the challenges and shortcomings of aircraft engine reliability. These accidents remind us that comprehensive and in-depth reliability analysis and optimization design of aircraft engine transmission systems during the design and development stage are of immeasurable value in improving flight safety and extending engine service life.

[0005] At present, as aircraft engines develop towards high power and high speed, aircraft gear design faces unprecedented challenges. Gears under high load operation are very prone to fatigue damage, resulting in reduced reliability and durability, seriously affecting the overall performance of the engine. In addition, aircraft engine gear transmission systems and their accessories work under extremely complex working conditions, which puts forward extremely stringent requirements on structural strength, processing accuracy, assembly quality and use environment. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the high-cycle fatigue reliability analysis method for aircraft engine gears provided by the present invention solves the problems such as the influence of uncertainty in size, material and load on the high-cycle fatigue reliability of aircraft engine gears.

[0007] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a method for high-cycle fatigue reliability analysis of aircraft engine gears, comprising the following steps:

[0008] S1. Establish a gear finite element model corresponding to the aircraft engine gear transmission system to be analyzed;

[0009] S2. Based on the gear finite element model, an active learning Kriging proxy model is used to construct a corresponding proxy finite element model, and the proxy finite element model is corrected to obtain a corrected high-precision finite element model;

[0010] S3. Conduct gear contact fatigue test based on the influence of uncertainty factors on gear reliability, and analyze the test data to obtain the SN curve;

[0011] S4. Combine the high-precision finite element model and SN curve to conduct high-cycle fatigue reliability analysis of gears based on finite element simulation.

[0012] Furthermore, the step S1 is specifically as follows:

[0013] S11, selecting an aircraft engine gear transmission system to be analyzed and establishing its corresponding 3D gear model;

[0014] S12, meshing the established 3D gear model;

[0015] S13. Setting parameters for the 3D gear model after meshing, and performing gear finite element analysis to obtain an established gear finite element model.

[0016] Furthermore, in step S2, the expression of the active learning Kriging proxy model is:

[0017]

[0018] In the formula, g K (X) represents the unknown Kriging surrogate model, f(X) = [f1(X), f2(X), L, f p (X)] T represents the basis function of the input variable X, β=[β1,β2,K,β p ] T represents the unknown coefficient of the corresponding regression function, z(X) represents the Gaussian process based on global simulation, and m is 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 MCSThe candidate sample points are formed into a sample point set S, and the initial sample points are 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 proxy model according to the expression of the active learning Kriging proxy model;

[0022] S21-3, use the initial proxy model to predict the response value of the candidate sample point set S0, and obtain the predicted mean μ g (x) and standard deviation σ g (x); where x comes from the prediction candidate sample point set S0;

[0023] S21-4. Using the learning function Find the best update sample point x * =argmin(U(x));

[0024] S21-5. Calculate the best updated sample point x * The response value is based on x * It updates the initial sample points;

[0025] S21-6, evaluate the current agent model;

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

[0027] S21-8, judging whether the model convergence condition is met according to the maximum error;

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

[0029] If not, the number of candidate sample points in the sample point set S is increased, and the process returns to step S21 - 4 .

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

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

[0032] Furthermore, the step S4 is specifically as follows:

[0033] S41. Combine the high-precision finite element model and the modified SN curve to establish the limit state function of tooth surface contact fatigue failure, and then calculate the failure probability;

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

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

[0036]

[0037] Failure probability P f It is expressed as:

[0038]

[0039] Where N f Indicates the critical stress cycle number when fatigue failure is reached, represents the total number of stress cycles required for design, f 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] Where m' represents the exponential proportional coefficient of the slope correction of the SN curve, N j Indicates the life value corresponding to the point in the SN curve, N0 indicates the initial life value when the correction starts, σ Hj represents the stress value corresponding to the point in the SN curve, σ H0 represents the initial stress value when correction starts, C' represents the product of the corrected stress value and the initial life value when correction starts, Indicates the corrected stress value.

[0043] The beneficial effects of the present invention are:

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

[0045] (2) In view of the inherent contradiction between accuracy and cost in traditional theoretical methods, the present invention innovatively introduces finite element model correction technology and integrates finite element analysis into the gear high-cycle fatigue reliability analysis process, in order to effectively reduce research costs while ensuring analysis accuracy, thus providing strong support for the progress in the field of aviation gear design. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1A flow chart of the high cycle fatigue reliability assessment method for aircraft engine gears provided by the present invention.

[0047] Figure 2 This is a 3D gear model diagram provided by the present invention.

[0048] Figure 3 This is a grid model diagram provided by the present invention.

[0049] Figure 4 This is a diagram of the finite element analysis results of the gear provided by the present invention.

[0050] Figure 5 This is a high cycle fatigue section diagram of the SN curve provided by the present invention.

[0051] Figure 6 This is the modified SN curve diagram provided by the present invention.

[0052] Figure 7 This is a failure probability convergence curve diagram provided by the present invention. DETAILED DESCRIPTION

[0053] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0054] The present application embodiment provides a method for analyzing the high cycle fatigue reliability of aircraft engine gears. Figure 1 As shown, the following steps are included:

[0055] S1. Establish a gear finite element model corresponding to the aircraft engine gear transmission system to be analyzed;

[0056] S2. Based on the gear finite element model, an active learning Kriging proxy model is used to construct a corresponding proxy finite element model, and the proxy finite element model is corrected to obtain a corrected high-precision finite element model;

[0057] S3. Conduct gear contact fatigue test based on the influence of uncertainty factors on gear reliability, and analyze the test data to obtain the SN curve;

[0058] S4. Combine the high-precision finite element model and SN curve to conduct high-cycle fatigue reliability analysis of gears based on finite element simulation.

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

[0060] S11, selecting an aircraft engine gear transmission system to be analyzed and establishing its corresponding 3D gear model;

[0061] S12, meshing the established 3D gear model;

[0062] Exemplarily, meshing of the established 3D gear model is performed by gear line, gear surface, and volume mesh stretching;

[0063] S13, setting parameters for the 3D gear model after meshing, and performing gear finite element analysis to obtain an established gear finite element model;

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

[0065] In one example of an embodiment of the present application, in the process of constructing a gear finite element model, a certain aircraft engine gear transmission system is taken as the object, and the ANSYS parametric design programming language is used to establish a gear finite element model whose material is 17CrNiMo6.

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

[0067] Specifically, in the modeling process, the single tooth model is first divided into six regions, and the number of grids is set for each line. Plane42 is used as a 2D unit for grid division, and a three-tooth model is established by copying. Finally, the 3D unit solid185 is used for volume grid stretching to obtain the grid model and save it as follows: Figure 3 shown.

[0068] During the finite element analysis process, APDL is used to read the cdb and iges format files of the gear model, and the three important parts of the gear are selected according to the position relationship as shown in Table 1.

[0069] Table 1

[0070]

[0071] Name the three important gear surfaces by establishing node groups. Start assembling the gear pair, rotate the first gear by a certain angle, and then translate it to a position that will not affect the setting of the second gear node group. After setting the position of the first gear, import the second gear, and set the node group and the position relationship of rotation and translation in the same way to accurately assemble the two gears. The materials of the gear pair are the same, so the contact is a surface-to-surface contact of the flexible body. Since the mesh density of the two gears is similar and they are both made of the same material, according to the selection principle of concave and convex surfaces, the small gear tooth surface is defined as the target surface and the large gear tooth surface is defined as the contact surface. And the unit of the target surface is selected as TARGE170, and the unit of the contact surface is selected as CONTA174. When defining the contact pair properties, set the friction coefficient of the contact surface to 0.05. When the gear pair is transmitting, the gear shaft is fixed. In order to establish this revolving pair, first establish two MPC184 units at the center of the shaft hole, and constrain the inner diameter of the shaft hole and the nodes on both sides to these two units through multi-point constraints, which can realize the application of constraints and loads. Finally, the load is set. Since the large gear is the driving wheel, the large gear is fixedly constrained, that is, its rotation speed is zero. The small gear is the driven wheel, and torque is applied to the small gear. Finite element analysis is performed, and the results of the finite element analysis are as follows: Figure 4 As shown in Figure 2. From the finite element analysis results of the gear, it can be seen that the maximum stress value point is located at the meshing point.

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

[0073] Table 3

[0074]

[0075] As can be seen from Table 3, the three proxy models have good results in terms of relative values ​​of proxy effect, with R2 exceeding 0.95, but the effects of Kriging and GP are significantly better than RSM, reaching above 0.99. For the absolute value of the proxy effect, since the maximum stress of the gear tooth surface within the limited working condition range is higher than 1000MPa, it can be calculated that the root mean square error of Kriging and GP is 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, according to the comparison between the test data and the finite element analysis data, its average error is already lower than 3%. In order to reduce the accuracy drop after the proxy finite element and further improve the model accuracy, therefore, the active learning Kriging proxy model is used in the embodiment of the present application to construct a higher accuracy proxy finite element model.

[0077] In an example of an embodiment of the present application, the active learning Kriging proxy model in step S2 regards the limit state function as a realization of a random process, which is divided into two parts: a global linear regression model and a random process model, which respectively model the global trend and local variability; based on this, the expression of the active learning Kriging proxy model is:

[0078]

[0079] In the formula, g K (X) represents the unknown Kriging surrogate model, f(X) = [f1(X), f2(X), L, f p (X)] T represents the basis function of the input variable X, β=[β1,β2,K,β p ] T represents the unknown coefficient of the corresponding regression function, m is the number of basis functions, z(X) represents 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 the Gaussian distribution.

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

[0081] S21-1. Generate N MCS The candidate sample points are formed into a sample point set S, and the initial sample points are 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 proxy model according to the expression of the active learning Kriging proxy model;

[0083] S21-3, use the initial proxy model to predict the response value of the candidate sample point set S0, and obtain the predicted mean μ g (x) and standard deviation σ g (x); where x comes from the prediction candidate sample point set S0;

[0084] S21-4. Using the learning function Find the best update sample point x* =argmin(U(x));

[0085] S21-5. Calculate the best updated sample point x * The response value is based on x * It updates the initial sample points;

[0086] S21-6, evaluate the current agent model;

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

[0088] S21-8, judging whether the model convergence condition is met according to the maximum error;

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

[0090] If not, the number of candidate sample points in the sample point set S is increased, and the process returns to step S21 - 4 .

[0091] Exemplarily, in step S21-6, the correlation coefficient and root mean square error RMSE are used to evaluate the proxy model, where the correlation index R 2 It is expressed as:

[0092]

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

[0094]

[0095] Where m is the number of samples; y i Indicates a true response; represents the predicted response; is the mean of the true response of the function.

[0096] In an example of an embodiment of the present application, in step S2, a QMC-based gradient reduction particle swarm algorithm is used to correct the constructed proxy finite element model.

[0097] Exemplarily, the implementation steps of the QMC-based gradient-reduction particle swarm algorithm are as follows:

[0098] S22-1, generate two different Sobol sequences respectively;

[0099] S22-2, setting the interval of the initial position and the initial speed, and using the sequence to generate the initial position and the initial speed respectively;

[0100] S22-3, calculating the response of the initial particle group;

[0101] S22-4, find the individual optimum of each particle;

[0102] S22-5, find the global optimal value of the entire group;

[0103] S22-6. Update the speed and position according to the optimal values ​​of the group and the individual, where the speed 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, calculating the updated particle swarm response;

[0107] S22-8, determine whether the algebraic setting is satisfied, if not, return to step S224; if satisfied, end the correction.

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

[0109] For example, in order to evaluate the fatigue life or fatigue strength of gears, it is necessary to establish the relationship between load and life. The fatigue failure of materials or structures working at room temperature depends on the size of the external load. From a microscopic point of view, the initiation of fatigue cracks is related to local microplasticity, but from a macroscopic point of view, when the cyclic stress level is low, elastic strain plays a dominant role, and the fatigue life is longer at this time, which is called stress fatigue or high cycle fatigue (HCF). When the cyclic stress level is high, plastic strain plays a dominant role, and the fatigue life is shorter at this time, which is called strain fatigue or low cycle fatigue (LCF). If the cyclic stress level is very low, the material or structure is in an elastic state macroscopically, and the fatigue life is very long at this time. This situation is called very high cycle fatigue (VHCF).

[0110] By analyzing the contact fatigue test data, the high cycle fatigue section of the SN curve at 50% reliability within the limited life range of the test gear is as follows Figure 5 As shown in the figure, the gear contact fatigue limit stress calculated by fitting the SN curve is 1444MPa.

[0111] In an example of an embodiment of the present application, step S4 is specifically as follows:

[0112] S41. Combine the high-precision finite element model and the modified SN curve to establish the limit state function of tooth surface contact fatigue failure, and then calculate the failure probability;

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

[0114] In an example of the embodiment of the present application, in step S41, given an n-dimensional input X=[X1, X2, K, X n ] T Assume that whether the gear fails depends only on the critical stress cycle number N when fatigue failure is reached. f Total number of stress cycles required by design When the total number of stress cycles required by the design Less than the total number of stress cycles N actually experienced f When the gear system is judged to be in failure state, the limit state function g(x) of tooth surface contact fatigue failure is expressed as:

[0115]

[0116] Failure probability P f It is expressed as:

[0117]

[0118] Where N f Indicates the critical stress cycle number when fatigue failure is reached, represents the total number of stress cycles required for design, f X (x) represents the joint probability density function, 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. The 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 when fatigue failure is reached under this response is obtained by using the modified SN curve; wherein, the calculation formula for correcting the slope of the SN curve is:

[0120]

[0121] Where m' represents the exponential proportional coefficient of the slope correction of the SN curve, N j Indicates the life value corresponding to the point in the SN curve, N0 indicates the initial life value when the correction starts, σ Hj represents the stress value corresponding to the point in the SN curve, σ H0 represents the initial stress value when correction starts, C' represents the product of the corrected stress value and the initial life value when correction starts, Indicates the corrected stress value.

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

[0123] In an example of an embodiment of the present application, in step S42, AK-MCS is used to carry out gear high cycle fatigue reliability analysis integrating SN curves; specifically, the following steps are included:

[0124] S42-1. Generate N MCS The candidate sample points form a point set S, and based on the experimental design, the initial sample points are extracted 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 an initial Kriging model according to the active learning Kriging surrogate model expression;

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

[0127] S42-4, respectively use the four learning functions, namely, the EI learning function, the learning function EFF, the learning function U and the learning function H, to find the best update iteration sample point x * ;

[0128] S42-5, determine the convergence condition (whether the maximum error is less than 10MPa; where the maximum error is the predicted response value and the true value y i The maximum value of the error. ) is satisfied;

[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 is based on x * Update the initial sample point and return to step S42-2;

[0131] S42-7. Using the correlation coefficient R 2 and root mean square error RMSE to evaluate the agent effect;

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

[0133]

[0134] S42-9, judging whether the convergence condition (whether the coefficient of variation is less than 0.05) is satisfied;

[0135] If so, the calculation process ends; otherwise, the number of candidate sample points S is increased and the process returns to step S42-3.

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

[0137] Specifically, the learning functions involved in step S42-4 include expected improvement (EI) learning function, learning function EFF, learning function U and learning function H. These four learning functions will be combined with AK-MCS to perform high cycle fatigue reliability analysis, and the optimal update iteration sample point x in the above step S42-4 is * It is determined by the point addition criterion expression of each learning function.

[0138] Among them, the expected improvement (EI) learning function gradually searches for new sample points until the global optimal point is found. The idea of ​​adding points is to add the point with the largest EI value to the sample point set and iterate again to find the optimal solution. The calculation formula of the learning function EI is as follows:

[0139]

[0140] In the formula, f min (x)=(y1,y2,K,y n ) represents the current optimal value; Φ(·), Represent the cumulative function and density function of the standard distribution respectively; is the estimated value of s(x), which is obtained from the sample point x i The observed value y(x i ), we can get the observed value set Y(x) and the estimated value Among them, y(x i ) can be expressed as:

[0141] y(x i )=μ+ε(x i ), (i=1,K,n)

[0142] In the formula, μ represents a random process; ε(x i ) is subject to variance σ 2 The standard normal distribution of .

[0143] Among them, the points adding criteria are:

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

[0145] The stopping criteria are:

[0146] max(EI(x))≤C

[0147] Where C is determined according to the requirements of the proxy model and is usually 0.01.

[0148] The basic idea of ​​the learning function EFF is to determine whether the test sample point has the possibility of crossing the limit failure boundary based on the weighted distance between the test sample point and the limit failure boundary. The calculation formula of the learning function EFF is as follows:

[0149]

[0150] In the formula, μ g (x) is the predicted value of the sample point; σ g (x) is the standard deviation of the predicted value; f(·) is the probability density function of the failure mode function; is the failure boundary; ε(x) represents the acceptable error range from the boundary of the limit state function; is 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 points adding criteria are:

[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 is usually taken as 0.001.

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

[0157]

[0158] The points adding criteria are:

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

[0160] The corresponding termination criterion is:

[0161] min(U(x))≥n

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

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

[0164]

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

[0166] The points adding criteria are:

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

[0168] The 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 0.5.

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

[0172] S42-01, Generate quantity N through Sobol sequence t The initial training sample set S0 is transferred to the parameterized finite element model of ANSYS in the form of a text file through MATLAB.

[0173] ANSYS performs finite element analysis and returns the stress responses 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 build the initial Kriging proxy model.

[0174] S42-02, Use the same Sobol sequence to generate a number of N MCS The training sample set S MCS , and by constructing a proxy model with a learning function Prediction training sample set S MCSIf the stop condition of the learning function is met, the Kriging proxy model converges and step S42-03 is executed; otherwise, the samples selected by the learning function are calculated through the high-cycle fatigue reliability analysis model and added to the training sample set to reconstruct the Kriging proxy model and step S42-02 is executed;

[0175] S42-03, through 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 ) does not reach the convergence criterion, the number of Monte Carlo samples is increased and step S4202 is executed; otherwise, the Kriging proxy model based on convergence Calculate the failure probability P of gear high cycle fatigue life f .

[0176] Considering the high cost of finite element analysis and the difficulty in obtaining failure probability through MCS, the classic AK-MCS+U is used as the benchmark method for failure probability calculation. This method continuously adds samples until CV(P f )<0.01, the number of added points is 1765, and the failure probability curve changes with the number of added points as shown in Figure 7 shown.

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

[0178] Table 5

[0179]

[0180] It can be seen from Table 5 that for gears made of 17CrNiMo6, there is no obvious difference in the coefficient of variation of the failure probability of the four methods. However, the use of learning function U and learning function H can reduce the calculation error of the failure probability to less than 1% after convergence. Among them, the cost of learning function U is lower, and the cost of learning function EI is lower than that of the other three methods, but the failure probability error is slightly higher.

[0181] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0182] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for high cycle fatigue reliability analysis of aircraft engine gears, characterized in that: The following steps are involved: S1. Establish a gear finite element model corresponding to the aircraft engine gear transmission system to be analyzed; S2. Based on the gear finite element model, the active learning Kriging proxy model is used to construct the corresponding proxy finite element model, and the proxy finite element model is corrected to obtain a corrected high-precision finite element model; S3. Conduct gear contact fatigue test based on the influence of uncertainty factors on gear reliability, and analyze the test data to obtain the SN curve; S4. Combine the high-precision finite element model and SN curve to conduct high-cycle fatigue reliability analysis of gears based on finite element simulation.

2. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 1, characterized in that: The step S1 is specifically as follows: S11, selecting an aircraft engine gear transmission system to be analyzed and establishing its corresponding 3D gear model; S12, meshing the established 3D gear model; S13. Setting parameters for the 3D gear model after meshing, and performing gear finite element analysis to obtain an established gear finite element model.

3. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 1, characterized in that: In step S2, the expression of the active learning Kriging proxy model is: In the formula, g K (X) represents the unknown Kriging surrogate model, f(X) = [f1(X), f2(X), L, f p (X)] T represents the basis function of the input variable X, β=[β1,β2,K,β p ] T represents the unknown coefficient of the corresponding regression function, z(X) represents the Gaussian process based on global simulation, and m is the number of basis functions.

4. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 3, characterized in that: In step S2, the method for constructing the proxy finite element model is specifically as follows: S21-1. Generate N MCS The candidate sample points are formed into a sample point set S, and the initial sample points are selected based on the experimental design to form a candidate sample point set S0, and its response value is calculated; S21-2, based on the initial sample points and their response values, construct the corresponding initial proxy model according to the expression of the active learning Kriging proxy model; S21-3, use the initial proxy model to predict the response value of the candidate sample point set S0, and obtain the predicted mean μ g (x) and standard deviation σ g (x); where x comes from the prediction candidate sample point set S0; S21-4. Using the learning function Find the best update sample point x * =argmin(U(x)); S21-5. Calculate the best updated sample point x * The response value is based on x * It updates the initial sample points; S21-6, evaluate the current agent model; S21-7. Calculate the predicted response value obtained based on the current proxy model and the true value y i The error is taken as the maximum error; S21-8, judging whether the model convergence condition is met according to the maximum error; If so, the calculation is completed and the constructed proxy finite element model is obtained; If not, the number of candidate sample points in the sample point set S is increased, and the process returns to step S21 - 4 .

5. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 1, characterized in that: In the step S2, the constructed proxy finite element model is corrected using a QMC-based gradient reduction particle swarm algorithm.

6. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 1, characterized in that: In step S3, the uncertain influencing factors include size, material and load.

7. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 1, characterized in that: The step S4 is specifically as follows: S41. Combine the high-precision finite element model and the modified SN curve to establish the limit state function of tooth surface contact fatigue failure, and then calculate the failure probability; S42. Based on the calculated failure probability, AK-MCS is used to carry out high-cycle fatigue reliability analysis of gears integrating SN curves.

8. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 7, characterized in that: In step S41, the limit state function g(x) of tooth surface contact fatigue failure is expressed as: Failure probability P f It is expressed as: Where N f Indicates the critical stress cycle number when fatigue failure is reached, represents the total number of stress cycles required by the design, f X (x) represents the joint probability density function, and x represents the random variable that affects the structural response.

9. The method for high cycle fatigue reliability analysis of aircraft engine gears according to claim 7, characterized in that: In step S41, the formula for correcting the SN curve is: Where m' represents the exponential proportional coefficient of the slope correction of the SN curve, N j Indicates the life value corresponding to the point in the SN curve, N0 indicates the initial life value when the correction starts, σ Hj represents the stress value corresponding to the point in the SN curve, σ H0 represents the initial stress value when correction starts, C' represents the product of the corrected stress value and the initial life value when correction starts, Indicates the corrected stress value.

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