Structure multi-axial fatigue life prediction method under random vibration load

Abstract

The invention provides a method for predicting the multi-axial fatigue life of a structure under a random vibration load, and the method comprises the steps: decomposing a power spectrum density function of a non-Gaussian random vibration load into three-order Gaussian components through a Gaussian mixture model, and loading each-order component into a structure model as a load, a stress component power spectral density function is extracted from the dangerous position, the maximum variance value of the equivalent stress power spectral density function of the space plane is calculated based on the multi-axis fatigue criterion and the maximum variance method, and the critical plane position is determined. And processing the dangerous point multi-axis power spectral density function into a single-axis equivalent power spectral density function based on a critical plane frequency domain method, calculating a third-order non-Gaussian mixture probability density function of the equivalent stress power spectral density function according to a Dirlik method, and predicting fatigue damage and life of the structure. According to the method, the influence of the multi-axial stress state on the fatigue life of the structure is considered, so that the problem of predicting the fatigue life of the structure better conforms to a fatigue damage mechanism, and the method is simple and has better universality.

Description

Technical Field

[0001] The invention belongs to the technical field of structural fatigue life prediction, and relates to a method for predicting fatigue life of a structure under a random vibration load and in a multi-axial stress state. Background Art

[0002] The strategic position of high-end equipment such as modern aero engines, hypersonic vehicles, and high-precision missiles has become prominent, and the problem of equipment structure fatigue life prediction has become one of the most active and challenging directions in the field of mechanical strength today. Many structures are subjected to various loads such as internal and external pressure difference, high and low temperature, vibration and impact during service. Under the combined effect of these complex working conditions, stress concentration is very likely to occur in weak parts, which is also one of the reasons for fatigue failure of the structure.

[0003] Harsh service environment is an important factor leading to fatigue failure of structures. Under random vibration loads, the stress state of local parts of the structure is complex, which is prone to fatigue failure. Most of the random vibration loads encountered in engineering are non-Gaussian random loads. However, in practice, most of the treatment of such loads is assumed to be Gaussian random loads for calculation and analysis. This leads to the use of Gaussian assumptions for random vibration fatigue life analysis, which often results in large deviations, posing huge safety hazards to the service or use of equipment. As a result, some key structures still suffer unexpected fatigue failures during use under harsh conditions in the field after passing the Gaussian random vibration test, and fail to meet the expected life and reliability indicators. Therefore, researchers hope to find a method that can accurately and reliably predict structural fatigue damage and life under non-Gaussian random vibration loads.

[0004] Frequency domain and time domain methods are the two main ways to deal with this type of problem. Although the time domain method has good calculation accuracy, it has a large amount of calculation and is not suitable for the analysis of actual engineering problems. For the frequency domain method, since the current frequency domain method is proposed for Gaussian random loads, directly using the frequency domain method to calculate the damage under non-Gaussian random vibration loads will result in large errors. In addition, since the structure is in a multi-axial stress state under random vibration loads, the current research on frequency domain problems under multi-axial states is still insufficient.

[0005] Therefore, how to effectively reduce the fatigue life prediction error of the structure under the multi-axial stress state of random vibration load is an urgent problem to be solved by technical personnel in this field. Summary of the invention

[0006] In view of this, the present invention proposes a method for predicting the multi-axial fatigue life of structures under random vibration loads, which solves the problem of large errors in fatigue life prediction of multi-axial stress states of structures under non-Gaussian random vibration loads based on a frequency domain method.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] The present invention discloses a method for predicting multi-axial fatigue life of a structure under random vibration load, comprising the following steps:

[0009] S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectral density function frequency domain load through Fourier transform;

[0010] S2: Calculate the high-order spectral moment parameters of the frequency domain load of the power spectral density function, and decompose the frequency domain load of the power spectral density function into third-order Gaussian component loads using a Gaussian mixture model based on the high-order spectral moment parameters;

[0011] S3: Load the structural model with the third-order Gaussian component load three times, each time loading the structural model with the same-order Gaussian component load in the three axes X, Y, and Z directions, and perform random vibration analysis on each loading operation, calculate the root mean square of the Von Mises stress at each node, and determine the node position where the maximum value of the root mean square of the Von Mises stress is located as the dangerous point position of the structure;

[0012] S4: extracting the power spectrum density function of the stress component at the dangerous point position, calculating the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multi-axial fatigue criterion and the maximum variance method, and determining the orientation coefficient of the critical plane;

[0013] S5: Based on the orientation coefficient of the critical plane, a power spectrum density matrix in the random process is introduced, and the multi-axial stress power spectrum density function is equivalently treated as a uniaxial stress power spectrum density function;

[0014] S6: Calculate the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method, combine the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function, and predict the fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function.

[0015] Preferably, S2 includes:

[0016] S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameter of the zero-mean Gaussian process is expressed as a function of the standard deviation:

[0017]

[0018] In the formula, m j is the j-th order spectral moment parameter, α i (i=1,2,3) is the weight coefficient of the third-order Gaussian component, σ i(i=1,2,3) is the standard deviation of the third-order Gaussian component stress;

[0019] S22: According to the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α 1 , α 2 , α 3 , σ 1 , σ 2 , σ 3 ;

[0020] S23: Determine the third-order power spectral density function component with Gaussian characteristics (G 1 (f), G 2 (f), G 3 (f)) value:

[0021] G 1 (f) = η 1 G(f),G 2 (f) = η 2 G(f),G 3 (f) = η 3 G(f);

[0022] Where G(f) is the frequency domain load of the power spectral density function, η 1 , η 2 and η 3 is the proportionality constant, is the variance of a non-Gaussian random process:

[0023]

[0024] Preferably, in S3: calculate the root mean square δ of the Von Mises stress of each node eq :

[0025]

[0026] In the formula, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz They are the shear stresses in the three axes of X, Y and Z.

[0027] Preferably, S4 includes:

[0028] S41: Extract the power spectrum density function of stress components for nodes at dangerous locations (G xx ,G yy ,G zz ,G xy ,G xz ,Gyz );

[0029] S42: Determine the maximum stress variance value expression based on the power spectrum density function of the stress component:

[0030]

[0031] In the formula, the stress variance μ kl for:

[0032]

[0033] When k=1, G kl (f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross power spectral density function;

[0034] a k 、a l =[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ] is the row vector of the orientation coefficient determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated by the cosines of the principal stress directions represented by the three Euler angles;

[0035] S43: The three Euler angles are rotated incrementally at every unit angle, the maximum variance value of the equivalent stress of the plane obtained by all angle combinations in the space is calculated, the orientation coefficient and the stress variance of the equivalent power spectrum density function at the maximum variance value are calculated, and the critical plane position is determined.

[0036] Preferably, in S5: the equivalent stress power spectrum density function G eq (f) is:

[0037] In the formula, G kk (f) is the auto-power spectral density function, a k is the critical plane orientation coefficient determined when the variance of equivalent stress is maximum.

[0038] Preferably, the step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 comprises:

[0039]

[0040] In the formula,

[0041] D 3 =1-D1 -D 2 ,

[0042] In the formula, m 0 ,m 1 ,m 2 ,m 4 are the four moments of inertia of the power spectral density function, and their expressions are:

[0043]

[0044] Preferably, the step of combining the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function in S6 includes:

[0045] f GMM (s) = α 1 p 1 (s 1 )+α 2 p 2 (s 2 )+α 3 p 3 (s 3 );

[0046] In the formula, f GMM (s) is the stress amplitude probability density function of the Gaussian mixture model, p 1 (s),p 2 (s),p 3 (s) are the probability density functions of the three stress amplitudes of the Gaussian component, α i is the weight coefficient of the Gaussian component.

[0047] Preferably, the step of predicting fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function in S6 includes:

[0048] Find the fatigue damage of the structural model under non-Gaussian loading:

[0049]

[0050] Where, ν P is the frequency at which the stress amplitude crosses zero; k, C are power function forms NS k = SN curve parameter of C; T 0 is the total loading time;

[0051] The fatigue life T of the structural model is:

[0052]

[0053] It can be seen from the above technical solution that, compared with the prior art, the beneficial effects of the present invention include:

[0054] (1) The present invention establishes a prediction method for estimating the multiaxial fatigue life of structures under non-Gaussian random vibration loads, solves the problem of using frequency domain methods to predict the multiaxial fatigue life of structures under non-Gaussian random vibration loads, and the third-order Gaussian mixture model improves the accuracy of the calculation results;

[0055] (2) The present invention uses the maximum variance method to find the critical plane at the dangerous point of the structure, and calculates the equivalent stress power spectrum density function on the critical plane of the dangerous position based on the multi-axis frequency domain method of the maximum shear stress criterion. The calculation process is relatively simple and the effect is good;

[0056] (3) The present invention combines the accurate results of the time domain method and the simple calculation of the frequency domain method. Based on the damage equivalence principle, the equivalent power spectral density function is converted into a time domain result through an inverse Fourier transform, and a hybrid frequency-time domain process is established. Compared with the frequency domain method based on the critical plane, the amount of calculation is greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on the provided drawings without creative work.

[0058] Figure 1 A flow chart of a method for predicting multi-axial fatigue life of a structure under random vibration loads provided by an embodiment of the present invention;

[0059] FIG. 2( a ) is a front view of a structural model provided by an embodiment of the present invention;

[0060] FIG2( b ) is a top view of a structural model provided by an embodiment of the present invention;

[0061] FIG3( a ) is a schematic diagram of a random vibration load in the time domain according to an embodiment of the present invention;

[0062] FIG3( b ) is a schematic diagram of a frequency domain form of a random vibration load provided by an embodiment of the present invention;

[0063] FIG4( a ) is a schematic diagram of the auto-power spectrum density function of the stress component at the dangerous point provided by an embodiment of the present invention;

[0064] FIG4( b ) is a schematic diagram of a power spectrum density function of equivalent stress at a dangerous point provided by an embodiment of the present invention;

[0065] Figure 5A schematic diagram comparing the life prediction results using the frequency domain and time domain processing methods provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting multi-axial fatigue life of a structure under a random vibration load, comprising the following steps:

[0068] S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectral density function frequency domain load through Fourier transform;

[0069] S2: Calculate the high-order spectral moment parameters of the power spectral density function frequency domain load, and decompose the power spectral density function frequency domain load into the third-order Gaussian component load using the Gaussian mixture model based on the high-order spectral moment parameters;

[0070] S3: Load the structural model with the third-order Gaussian component load three times, each time loading the structural model with the same-order Gaussian component load in the three axes X, Y, and Z directions, and perform random vibration analysis on each loading operation, calculate the root mean square of the Von Mises stress at each node, and determine the node position where the maximum value of the root mean square of the Von Mises stress is located as the dangerous point position of the structure;

[0071] S4: extract the power spectrum density function of the stress component at the dangerous point, calculate the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multiaxial fatigue criterion and the maximum variance method, and determine the orientation coefficient of the critical plane;

[0072] S5: Based on the orientation coefficient of the critical plane, the power spectrum density matrix in the random process is introduced, and the multiaxial stress power spectrum density function is equivalent to the uniaxial stress power spectrum density function;

[0073] S6: The stress amplitude probability density function of the uniaxial stress power spectrum density function is calculated according to the frequency domain Dirlik method. The three stress amplitude probability density functions are combined with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function. The fatigue damage and life of the structural model under non-Gaussian load are predicted based on the third-order non-Gaussian mixture probability density function.

[0074] The structural model used in this embodiment is shown in Figure 2, where Figure (a) is the front view of the structural model and Figure (b) is the top view of the structural model, with the unit in mm. In the figure, L is the length of the sample, W is the width, H is the height, b4 is the notch width, and θ is the notch opening angle. The dimensional parameters of the structural model are: L = 180mm, W = 16mm, H = 1.8mm, b1 = 45mm, b2 = 1.8mm, b3 = 20mm, b4 = 7mm, θ = 60°, through hole for

[0075] In the embodiment, random vibration analysis is performed on the aluminum alloy test piece under non-Gaussian random vibration load. In the analysis, the left end of the aluminum alloy test piece is fixedly constrained.

[0076] The material used for the structural model in the embodiment may be aluminum alloy 6061-T6 material, wherein the test piece is tested at room temperature.

[0077] In one embodiment, in S1, the non-Gaussian random vibration time domain load x(t) with a certain kurtosis and skewness is converted into the corresponding power spectrum density function frequency domain load G(f) by Fourier transform, wherein the kurtosis value of the non-Gaussian random vibration load is taken as 5 and the skewness value is taken as 0.01. 3 and skewness γ 4 The calculation expression is:

[0078]

[0079] Where E[·] is the expected value operator, μ x and δ x are the mean and standard deviation of x(t), respectively. Skewness γ 3 Represents the degree to which the amplitude distribution of the random process is asymmetric, kurtosis γ 4 Characterizes the sharpness of the peak and the width of the tail of the probability density function curve of the random process amplitude. As shown in Figure 3, it is a non-Gaussian random vibration load and its power spectrum density function.

[0080] In one embodiment, S2 includes:

[0081] S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameters of the zero-mean Gaussian process are expressed as a function of the standard deviation:

[0082]

[0083] In the formula, m j is the j-th order spectral moment parameter, α i (i=1,2,3) is the weight coefficient of the third-order Gaussian component, σ i (i=1,2,3) is the standard deviation of the third-order Gaussian component stress;

[0084] S22: According to the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α 1 , α 2 , α 3 , σ 1 , σ 2 , σ 3 ;

[0085] S23: Determine the third-order power spectral density function component with Gaussian characteristics (G 1 (f), G 2 (f), G 3 (f)) value:

[0086] G 1 (f) = η 1 G(f),G 2 (f) = η 2 G(f),G 3 (f) = η 3 G(f);

[0087] Where G(f) is the frequency domain load of the power spectral density function, η 1 , η 2 and η 3 is the proportionality constant, is the variance of a non-Gaussian random process:

[0088]

[0089] In this embodiment, the specific execution steps for calculating the high-order spectral moment parameters of the non-Gaussian load are:

[0090] Since the non-Gaussian power spectrum load needs to be decomposed into the third-order Gaussian component power spectrum density function, it is necessary to calculate the 2nd, 4th, 6th, 8th, and 10th (m 2 ,m 4 ,m 6 ,m 8 ,m 10 )-order high-order spectral moment parameters. The calculation formula of high-order spectral moment parameters is:

[0091]

[0092] The specific steps for calculating the weight coefficient of the Gaussian component in combination with the Gaussian mixture model are:

[0093] The power spectral density function of the non-Gaussian load is decomposed into three-order power spectral density function components with Gaussian characteristics (G 1 (f), G 2 (f), G 3 (f)).

[0094] According to the Gaussian mixture model formula, the higher-order moments of the zero-mean Gaussian process can be expressed as a function of the standard deviation, so:

[0095]

[0096] In the formula, α i (i=1,2,3) is the Gaussian component coefficient, σ i (i=1,2,3) is the standard deviation of Gaussian component stress. Since the Gaussian component coefficient has the following relationship:

[0097] α 1 +α 2 +α 3 =1

[0098] According to the above equations, the unknown parameter α can be solved 1 , α 2 , α 3 , σ 1 , σ 2 , σ 3 .

[0099] In this step, a Gaussian mixture model is used to decompose the non-Gaussian process into Gaussian processes with different weight coefficients. The weight coefficients represent the probability of the three Gaussian components appearing in the time domain.

[0100] The non-Gaussian power spectral density function is further decomposed into three power spectral density functions of Gaussian components of different magnitudes using high-order statistics, and the Gaussian decomposition characteristics are introduced into the frequency domain. The specific execution steps are as follows:

[0101] Variance of a non-Gaussian random process It can be expressed as:

[0102]

[0103] To derive the Gaussian component power spectral density function based on frequency domain data, it is necessary to determine G 1 (f), G 2 (f) and G 3 (f). Assuming that it is proportional along the frequency axis, that is:

[0104] G 1 (f) = η 1 G(f),G 2 (f) = η 2 G(f),G 3 (f) = η 3 G(f);

[0105] Where η 1 , η 2 and η3 is the proportional constant, and the calculation formula is:

[0106]

[0107] In one embodiment, the structural model in S3 is loaded with the same first-order Gaussian component load in the three directions XYZ each time, and a finite element analysis is performed each time until the loading analysis of the three-order Gaussian component loads is completed, that is, a total of three finite element analyses are performed: the root mean square δ of the Von Mises stress at each node is calculated eq :

[0108]

[0109] In the formula, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz They are the shear stresses in the three axes of X, Y and Z.

[0110] In this embodiment, the material parameters of the aluminum alloy 6061-T6 used in the specimen model are detailed in Table 1.

[0111] Table 1 Material parameters of aluminum alloy 6061-T6

[0112] parameter value Young's modulus 68.9GPa density 2849Kg / m3 Poisson's ratio 0.33 Yield Strength 275MPa Ultimate tensile strength 310MPa

[0113] In one embodiment, S4 includes:

[0114] S41: Extract the power spectrum density function of stress components for nodes at dangerous locations (G xx ,G yy ,G zz ,G xy ,G xz ,G yz ), the maximum variance value of stress is calculated based on the power spectrum density function. Figure 4(a) shows the corresponding auto-power spectrum density function of the stress component.

[0115] S42: Determine the maximum stress variance value expression based on the power spectrum density function of the stress component:

[0116]

[0117] In the formula, the stress variance μ kl for:

[0118]

[0119] When k=1, G kl(f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross power spectral density function;

[0120] a k 、a l =[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ] is the row vector of the orientation coefficient determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated by the cosines of the principal stress directions represented by the three Euler angles;

[0121] S43: The three Euler angles are rotated incrementally at every unit angle, such as a unit angle of 0.5°, and the maximum variance value of the equivalent stress of the plane obtained by all angle combinations in the space is calculated. The orientation coefficient and stress variance of the equivalent power spectrum density function at the maximum variance value are calculated to complete the determination of the critical plane position.

[0122] In this embodiment, S42 includes the following specific execution steps:

[0123] Azimuth coefficient a k 、a l =[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ] can be expressed as:

[0124]

[0125] a 4 =2(l 1 m 1 -l 3 m 3 ),a 5 =2(l 1 n 1 -l 3 n 3 ),a 6 =2(n 1 m 1 -n 3 m 3 );

[0126] In the formula, l i ,m i ,n i are the direction cosines of the principal stresses, which can be represented by the three Euler angles φ, θ, ψ:

[0127] l1 =cosψcosφ-cosθcosψsinφ,m 1 =sinψcosφ+cosθcosψsinφ,

[0128] n 1 = sinθsinφ,l 2 =-cosψcosφ-cosθcosψcosφ,

[0129] m 2 =-sinψcosφ+cosθcosψcosφ,n 2 = sinθcosφ,

[0130] l 3 = sinθsinψ,m 3 = -sinθcosψ,n 3 = cosθ

[0131] In the formula, (0≤θ<π, 0≤ψ<π, 0≤φ<2π).

[0132] In one embodiment, in S5: the expression of the equivalent power spectrum density function is:

[0133]

[0134] In the formula, G kk (f) represents the auto-power spectral density function, G kl (f) represents the cross-power spectral density function, a k 、a l The critical plane orientation coefficient determined when the equivalent stress has the maximum variance.

[0135] When using the frequency domain critical surface method for analysis, the influence of the cross-spectral power spectrum density on the fatigue life results can be ignored. Therefore, the equivalent stress power spectrum density function can be simplified to:

[0136]

[0137] In the formula, G kk (f) is the auto-power spectral density function, a k is the critical plane orientation coefficient determined when the variance of equivalent stress is the largest. Figure 4(b) shows the power spectrum density function of equivalent stress.

[0138] It should be noted that, in this embodiment, S5 obtains three different uniaxial stress power spectrum density functions after three finite element analyses. Each uniaxial power spectrum density function is obtained by extracting the stress power spectrum density functions (G xx ,G yy,G zz ,G xy ,G xz ,G yz ) are equivalent, and the expression forms of the three uniaxial stress power spectrum density functions are the same. The specific calculation results are different due to the differences in the stress power spectrum density functions in the six directions of each uniaxial stress power spectrum density function.

[0139] In one embodiment, the step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 includes:

[0140]

[0141] In the formula,

[0142] D 3 =1-D 1 -D 2 ,

[0143] In the formula, m 0 ,m 1 ,m 2 ,m 4 are the four moments of inertia of the power spectral density function, and their expressions are:

[0144]

[0145] In one embodiment, the step of combining the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function in S6 includes:

[0146] f GMM (s) = α 1 p 1 (s 1 )+α 2 p 2 (s 2 )+α 3 p 3 (s 3 );

[0147] In the formula, f GMM (s) is the stress amplitude probability density function of the Gaussian mixture model, p 1 (s),p 2 (s),p 3 (s) are the probability density functions of the three stress amplitudes of the Gaussian component, α i is the weight coefficient of the Gaussian component.

[0148] In one embodiment, the step of predicting fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function in S6 includes:

[0149] Find the fatigue damage of the structural model under non-Gaussian loading:

[0150]

[0151] Where, ν P Indicates the frequency at which the stress amplitude crosses the zero value; k, C are power function forms NS k = SN curve parameter of C; T 0 Indicates the total loading time;

[0152] The fatigue life T of the structural model is:

[0153]

[0154] Based on the damage equivalence principle, the equivalent power spectral density function in S5 is converted into time domain results through inverse Fourier transform, and a hybrid frequency-time domain process is established. The fatigue damage and life of the structure are calculated according to the Miner cumulative damage criterion and the rain flow counting method, and compared with the results of S6. Figure 5 It is a comparison chart between the frequency domain results and the time domain results according to the method of the invention. Among them, the frequency domain results are the results analyzed and calculated in step S6 of the present invention; the time domain results are the results calculated by the equivalent power spectrum converted into the time domain process in step S5 of the present invention. The life values ​​of the frequency domain results and the time domain results are within a 2-fold error band. Comparison explanation: By decomposing the power spectrum of non-Gaussian loads into multiple Gaussian components, the classical frequency domain method can be used to solve the non-Gaussian vibration problem. The prediction results combined with the multi-axis stress power spectrum equivalent criterion are close to the time domain results, which illustrates the rationality and effectiveness of the multi-axis fatigue life prediction method of structures under random vibration random vibration loads.

[0155] The above is a detailed introduction to the method for predicting the multi-axial fatigue life of structures under random vibration loads provided by the present invention. In this embodiment, specific examples are used 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 general technical personnel in this field, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0156] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined in the present embodiments may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown in the present embodiment, but will conform to the widest range consistent with the principles and novel features disclosed in the present embodiment.

Claims

1. A method for predicting multiaxial fatigue life of a structure under random vibration load, characterized in that: The steps include: S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectral density function frequency domain load through Fourier transform; S2: Calculate the high-order spectral moment parameters of the frequency domain load of the power spectral density function, and decompose the frequency domain load of the power spectral density function into third-order Gaussian component loads using a Gaussian mixture model based on the high-order spectral moment parameters; S3: Load the structural model with the third-order Gaussian component load three times, each time loading the structural model with the same-order Gaussian component load in the three axes X, Y, and Z directions, and perform random vibration analysis on each loading operation, calculate the root mean square of the Von Mises stress at each node, and determine the node position where the maximum value of the root mean square of the Von Mises stress is located as the dangerous point position of the structure; S4: extracting the power spectrum density function of the stress component at the dangerous point position, calculating the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multi-axial fatigue criterion and the maximum variance method, and determining the orientation coefficient of the critical plane; S5: Based on the orientation coefficient of the critical plane, a power spectrum density matrix in the random process is introduced, and the multi-axial stress power spectrum density function is equivalently treated as a uniaxial stress power spectrum density function; S6: Calculate the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method, combine the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function, and predict the fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function.

2. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The S2 includes: S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameter of the zero-mean Gaussian process is expressed as a function of the standard deviation: In the formula, m j is the j-th order spectral moment parameter, α i (i=1,2,3) is the weight coefficient of the third-order Gaussian component, σ i (i=1,2,3) is the standard deviation of the third-order Gaussian component stress; S22: According to the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α1, α2, α3, σ1, σ2, σ3; S23: Determine the value of the third-order power spectral density function components (G1(f), G2(f), G3(f)) with Gaussian characteristics: G1(f)=eta1G(f), G2(f)=eta2G(f), G3(f)=eta3G(f); Where G(f) is the frequency domain load of the power spectrum density function, η1, η2 and η3 are proportional constants, is the variance of a non-Gaussian random process:

3. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: In S3: Calculate the root mean square δ of Von Mises stress at each node eq : In the formula, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz They are the shear stresses in the three axes of X, Y and Z.

4. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The S4 includes: S41: Extract the power spectrum density function of stress components for nodes at dangerous locations (G xx ,G yy ,G zz ,G xy ,G xz ,G yz ); S42: Determine the maximum stress variance value expression based on the power spectrum density function of the stress component: In the formula, the stress variance μ kl for: When k=1, G kl (f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross power spectral density function; a k 、a l =[a1,a2,a3,a4,a5,a6] is the row vector of orientation coefficients determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated using the cosines of the principal stress directions represented by the three Euler angles; S43: The three Euler angles are rotated incrementally at every unit angle, the maximum variance value of the equivalent stress of the plane obtained by all angle combinations in the space is calculated, the orientation coefficient and the stress variance of the equivalent power spectrum density function at the maximum variance value are calculated, and the critical plane position is determined.

5. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: In S5: equivalent stress power spectrum density function G eq (f) is: In the formula, G kk (f) is the auto-power spectral density function, a k is the critical plane orientation coefficient determined when the variance of equivalent stress is maximum.

6. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 includes: In the formula, Where m0, m1, m2, and m4 are the four moments of inertia of the power spectral density function, and their expressions are:

7. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 6, characterized in that: The step of combining the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function in S6 includes: f GMM (s)=α1p1(s1)+α2p2(s2)+α3p3(s3); In the formula, f GMM (s) is the stress amplitude probability density function of the Gaussian mixture model, p1(s), p2(s), p3(s) are the three stress amplitude probability density functions of the Gaussian components, α i is the weight coefficient of the Gaussian component.

8. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 7, characterized in that: The step of predicting fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function in S6 includes: Find the fatigue damage of the structural model under non-Gaussian loading: Where, ν P is the frequency at which the stress amplitude crosses zero; k, C are power function forms NS k = SN curve parameter of C; T0 is the total loading time; The fatigue life T of the structural model is:

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