A method for compiling a multi-parameter fatigue test spectrum based on the consistency of local load states

Abstract

The present invention discloses a method for compiling a multi-parameter fatigue test spectrum based on consistent local load states, comprising the following steps: converting a multi-parameter component load spectrum into a stress-strain history of a fatigue assessment point according to the finite element principle, and solving a linear equation of local stress-strain and component load; performing equivalent stress-strain calculation and calculation of the stress principal axis direction based on the discrete stress-strain time history to obtain an equivalent stress-strain time history and a stress principal axis time history; selecting a typical multi-axial load state cycle and determining the corresponding cumulative time; calculating the total cumulative damage of the original load spectrum, and performing an optimization search solution for the number of cycles corresponding to the multi-axial load state cycle selected in the above steps; randomly splicing each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the local load state and damage of the original load spectrum. The present invention realizes the damage consistency and local state consistency in the process of compiling a multi-parameter fatigue test load spectrum.

Description

Technical Field

[0001] The present invention belongs to the technical field of the compilation of multi-parameter fatigue test load spectra for aero-engines, and particularly relates to a method for compiling a fatigue test spectrum for aero-engine casing components under multi-parameter random loads. Background Art

[0002] Since the 1970s, great progress has been made in the research on single-parameter fatigue test load spectra, and they have also been widely applied in industrial fields such as aerospace, vehicles, and construction machinery. However, in engineering practice, most components are subjected to multiple random loads for a long time, and components are often prone to multi-axial fatigue damage and failure. Aero-engine casing components not only bear the gas force generated by gas flow but also bear the external force load generated by aircraft maneuvering flight. The changes in these two types of loads are often random, non-proportional, but have a certain correlation. When fatigue assessment is carried out on components subjected to such complex multi-parameter loads, the single-parameter fatigue test spectrum is no longer applicable. Therefore, in order to conduct a full and scientific life assessment of such components, a method for compiling a multi-parameter load fatigue test spectrum must be developed.

[0003] The domestic research on the multi-parameter fatigue test spectrum for aero-engine casing components started in the 1990s, and some methods for compiling the multi-parameter fatigue test spectrum for casings have also been developed. Zhang Yong et al. studied the matching of aero-engine aerodynamic loads and maneuvering loads, laying a foundation for reasonably determining the loads on components under multi-parameter loads. Shi Haiqiu et al. took the load-bearing casing of a certain type of engine as an example and proposed a method for compiling a fatigue test spectrum for aero-engine components based on load profile calculation.

[0004] However, the above methods cannot give a clear method for compiling a multi-parameter fatigue test spectrum for components, nor can they meet the requirements for spectrum compilation of fatigue damage consistency. Yang Yanhong, Zhao Yongming et al. respectively carried out the work of compiling a multi-parameter fatigue test spectrum from the perspective of multi-axial fatigue damage. However, in the process of spectrum compilation, in order to ensure damage consistency, parameters such as load amplitude and phase are optimized and searched for values, which results in a certain difference between the compiled fatigue test spectrum and the actual service load in terms of load characteristics and the local load state of the component.

[0005] In summary, the existing methods for compiling multi-parameter fatigue test spectra still have certain limitations. Under multi-parameter load conditions, compiling a fatigue test spectrum that is consistent with the local load state of the component under the actual load spectrum, has equivalent damage, and the same failure mode is still a key engineering problem that urgently needs to be solved, which also has important significance for the fatigue damage analysis and fatigue test research of aero-engine whole machines and casing components.

[0006] Therefore, it is necessary to develop a method for compiling a multi-parameter fatigue test spectrum that can consider the consistency of local load states and damage of aero-engine casing components, laying a foundation for the life determination of aero-engines and their components. Summary of the Invention

[0007] The object of the present invention is to provide a method for compiling a multi-parameter fatigue test spectrum based on the consistency of local load states, so as to achieve the damage consistency and local state consistency in the process of compiling the multi-parameter fatigue test load spectrum.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A method for compiling a multi-parameter fatigue test spectrum based on the consistency of local load states, comprising the following steps:

[0010] (1) Convert the multi-parameter component load spectrum into the stress-strain history of the fatigue assessment point according to the finite element principle, and solve the linear equation of the local stress-strain and the component load;

[0011] (2) Select the load time interval △t, discretely divide the load time history at equal time intervals, calculate the equivalent stress-strain and the calculation of the stress principal axis direction respectively according to the discrete stress-strain time history, and obtain the equivalent stress-strain time history and the stress principal axis time history;

[0012] (3) Discretely count the equivalent stress-strain history and the stress principal axis direction, select typical multi-axial load state cycles, and determine the corresponding cumulative time;

[0013] (4) Calculate the total cumulative damage of the original load spectrum according to the multi-axial fatigue damage model, and perform an optimization search and solution for the corresponding number of cycles of the multi-axial load state cycle selected in the above steps according to the principle of damage consistency;

[0014] (5) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the local load state and damage of the original load spectrum.

[0015] The specific content of step (1) is as follows:

[0016] (11) Calculate the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum through finite element software, including: material property and element type assignment, component modeling and mesh division, multi-load step solution, stress-strain data analysis;

[0017] (12) Solve the linear equation of the local stress-strain of the fatigue damage assessment point and the component load, and its expression is as follows:

[0018] σ(c,t) = K σ (c)·F(t)

[0019] ε(c,t) = K ε (c)·F(t)

[0020] Where c is the fatigue damage assessment point of the component, t is the load time, σ(c,t), ε(c,t), and F(t) are the stress, strain vector, and external load vector related to time at the fatigue damage assessment point of the component, respectively. The matrix expression forms of the above vectors are as follows:

[0021]

[0022] Where K σ (c), K ε (c) are the coefficient matrices of stress and strain with respect to the external load matrix, respectively, and they are constant over the load time history; σ xx (c,t), σ yy (c,t), σ zz (c,t), τ yz (c,t), τ xz (c,t), τ xy (c,t) represent the normal stress and shear stress in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; ε xx (c,t), ε yy (c,t), ε zz (c,t), γ yz (c,t), γ xz (c,t), γ xy (c,t) represent the normal strain and shear strain in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),...F num (t) represent the num paths of external loads borne by the component;

[0023] Perform a multiple linear equation calculation based on the stress-strain history obtained in step (11) to obtain the numerical solutions of the coefficient matrices K σ (c), K ε (c).

[0024] The specific content of step (2) is as follows:

[0025] (21) Set the dispersion variable n, and select the discrete time interval △t for each load range according to the sampling time △T of the original load. The relationship between the variables is as follows:

[0026] △T = n·△t

[0027] T = N·△T

[0028] Among them, T and N are the total sampling time and the total number of samples of the original load. Thus, the original load histories σ(c,t) and ε(c,t) with a time interval of ΔT are refined into discrete data of the load time history with a time interval of Δt.

[0029] (22) According to the discrete data of the load time history in step (21) Calculate the equivalent stress-strain and the direction cosines of the stress principal axis for each discrete load point to obtain the discrete time history of the local load state at the fatigue damage assessment point of the component. The calculation expression of the equivalent stress-strain is as follows:

[0030]

[0031]

[0032] Among them, σ eq , ε eq respectively represent the equivalent stress and the equivalent strain; σ xx , σ yy , σ zz , τ yz , τ xz , τ xy respectively represent the normal stress and the shear stress in the xyz coordinate system, and their subscripts correspond to the coordinate directions; ε xx , ε yy , ε zz , γ yz , γ xz , γ xy respectively represent the normal strain and the shear strain in the xyz coordinate system, and their subscripts correspond to the coordinate directions; Thus, the discrete time histories of the equivalent stress-strain σ eq (c,t), ε eq (c,t) can be obtained;

[0033] The calculation of the direction cosines of the stress principal axis requires solving the eigenvalues and eigenvectors of the stress matrix at the current load time point. The solution equation is as follows:

[0034]

[0035] Among them, σ xx (c,t), σ yy (c,t), σ zz (c,t), τ yz (c,t), τ xz (c,t), τ xy (c,t) respectively represent the discrete data of the load time history in the xyz coordinate system The normal stress and shear stress, with their subscripts corresponding to the coordinate system directions, where σ(c,t), l, m, and n are the principal stresses to be solved and their direction cosine values.

[0036] Solve the above characteristic equation for σ(c,t) to obtain the three principal stresses at the fatigue damage assessment point, namely σ1(c,t), σ2(c,t), and σ3(c,t), where σ1(c,t) > σ2(c,t) > σ3(c,t), as well as the direction cosines l1(c,t), m1(c,t) of the stress principal axis corresponding to the maximum principal stress σ1(c,t) and the direction cosines l2(c,t) of the stress principal axis corresponding to the secondary principal stress σ2(c,t).

[0037] Calculate the equivalent stress and strain for each load time interval respectively. Equivalent principal stress σ 1,i 、σ 2,i and the direction cosines l 1,i 、m 1,i 、n 2,i , where the equivalent stress and strain and the equivalent principal stress variables take the maximum values within each load time interval [t i , t i +Δt], while the direction cosines of the equivalent stress principal axis take the average values within each load time interval [t i , t i +Δt]. Their calculation expressions are as follows:

[0038]

[0039]

[0040] σ 1,i =max{σ1(c,t)|t∈[t i , t i +Δt]}

[0041] σ 2,i =max{σ2(c,t)|t∈[t i , t i +Δt]}

[0042] l 1,i =(max{l1(c,t)|t∈[t i , t i +Δt]}+min{l1(c,t)|t∈[t i , t i +Δt]}) / 2

[0043] m 1,i =(max{m1(c,t)|t∈[t i , ti +Δt]} + min{m1(c, t)|t ∈ [t i , t i +Δt]}) / 2

[0044] l 2,i =(max{l2(c, t)|t ∈ [t i , t i +Δt]} + min{l2(c, t)|t ∈ [t i , t i +Δt]}) / 2

[0045] wherein, the max{} and min{} functions respectively represent the maximum and minimum values of the current variable in the interval;

[0046] Thus, the discrete time history of the local load state of the component fatigue damage assessment point is obtained.

[0047] The specific content of step (3) is as follows:

[0048] (31) Based on the equivalent stress - strain time history and the stress principal axis time history obtained in step (2), taking the equivalent equivalent stress and the direction cosines l 1,i , m 1,i of the two equivalent stress principal axes as the main statistical variables, perform statistical analysis of three - dimensional variables. Additionally, σ 1,i , σ 2,i , l 2,i are used as auxiliary statistical variables;

[0049] (32) According to the three - dimensional variable statistical analysis in step (31), perform three - dimensional K - Means clustering analysis. Classify according to the proximity of the local load state values. According to the clustering results, divide the discrete load states, that is, the equivalent equivalent stress and the direction cosines of the two equivalent stress principal axes, into m categories, and take the centroid value of each category as the typical load state cycle of each category Obtain a series of typical load state cycles that can reflect the actual local load state of the component Back - solve the stress, strain vectors, and external load vectors according to the typical load state cycle. The calculation expressions are as follows:

[0050]

[0051]

[0052] wherein, is the equivalent equivalent stress of the typical load state cycle, and are both the weighted average values within the typical state cycle class, is the third principal stress of the typical load state cycle to be solved; represents the three principal stresses of the m-th type of typical load state cycle, l i,j , m i,j and n i,j represent the direction cosine values corresponding to the three principal stresses of the m-th type of typical load state cycle; σ xx,j , σ yy,j , σ zz,j , τ yz,j , τ xz,j , τ xy,j respectively represent the normal stress and shear stress of the m-th type of typical load state cycle in the xyz coordinate system, and their subscripts correspond to the coordinate system directions;

[0053] Thus, the stress-strain vector of the typical load state cycle is obtained by reverse load solution from the linear equation of local stress-strain and component load in step (1). A series of typical external load cycles {F 1,j (t)F 2,j (t)... F n,j (t)} j＝1,2,3,...,m ;

[0054] (33) Calculate the total cumulative time of each typical load state cycle obtained by clustering according to step (32). The calculation expression is as follows:

[0055]

[0056] where, t total,j represents the total time of the j-th type of typical load state cycle, represents the j-th type of typical load state cycle, △t i respectively represent the discrete load states and their time intervals obtained in step (22).

[0057] Specifically, step (4) is as follows:

[0058] (41) Use the multiaxial cycle counting method to convert the original multi-parameter random load history of the component into a series of stress and strain cycles, and obtain the maximum shear strain increment and the maximum normal strain increment on the maximum shear strain plane within each cycle. Then, use the multiaxial fatigue damage model to calculate the fatigue damage of each cycle and perform the multiaxial damage accumulation of the entire original load spectrum. Thus, the total multiaxial fatigue damage of the original load spectrum is obtained, as shown below:

[0059]

[0060] where, ni Denotes the number of cycles of the load cycle, N i Denotes the multiaxial fatigue life of the load cycle;

[0061] (42) Determine the ratio of the number of cycles between each state cycle according to the total cumulative time corresponding to each typical load state cycle counted in step (3), and its expression is as follows:

[0062]

[0063] Where m is the total number of typical load state cycles selected in step (3); n1, n2,..., n m Denotes the number of cycles of each typical load state cycle, t total,1 、t total,2 、...、t total,m Denotes the total cumulative time corresponding to each typical load state cycle;

[0064] (43) Since n1, n2,..., n m Are proportional and can perform univariate optimization search. The optimization goal is that the total damage of each typical state cycle spectrum block after optimization is consistent with the total damage of the original load spectrum. The calculation method of the total damage of the multi-parameter spectrum block after optimization is the same as that in step (41), and its optimization objective function is as follows:

[0065]

[0066] Where D squence Denotes the total multiaxial fatigue damage of the original load spectrum, D block,j Denotes the total multiaxial fatigue damage of each typical load state cycle spectrum block;

[0067] Thus, the load amplitude and cycle number information (σ j (c, t), n j ) of the multi-parameter load spectrum block consistent with the damage of the original load spectrum are obtained. Furthermore, the external load spectrum block information (F j (t), n j ) of the component is obtained, j = 1, 2,..., m, that is

[0068]

[0069] Beneficial effects: The present invention adopts the idea of consistent local load states of components and selects a series of typical state cycles based on this, so as to compile a multi-parameter fatigue test spectrum with damage consistency as the optimization goal. Compared with the existing method for compiling the multi-parameter fatigue test spectrum of aero-engines, it has the following advantages:

[0070] (1) Simple and intuitive, with clear steps and precise description;

[0071] Analyze the local load time history of the fatigue damage assessment points of components, select the equivalent stress and the cosine of the maximum principal stress direction as the main state parameters, and use the maximum principal stress, the secondary principal stress and their direction cosines as auxiliary parameters to conduct load state parameter statistics. Based on the statistical results, select typical load cycles, and thus optimize the compilation of damage consistency. This is more reasonable and has stronger versatility than the multi-parameter load spectrum compilation method that only takes damage consistency as the main means.

[0072] (2) It has broad engineering application value;

[0073] The multi-parameter fatigue test spectrum compilation method proposed by the present invention is simple and has strong versatility. Therefore, under the existing technical conditions, the present invention can be used to reasonably compile a multi-parameter fatigue test spectrum with consistent damage under complex mechanical components and actual load conditions, and has broad engineering application value.

[0074] (3) Research new multi-axial damage models and multi-axial fatigue life analysis methods;

[0075] The multi-parameter fatigue test spectrum compilation method compiled by the present invention can reflect the actual local load state of components, provide a load basis for researching multi-axial damage and multi-axial fatigue life analysis methods for a certain mechanical component under actual service conditions, and can preliminarily conduct multi-axial fatigue tests at the material level according to the multi-parameter fatigue test spectrum compiled by the present invention to reduce the design and R & D costs and time.

[0076] In summary, the present invention provides a basis for the multi-axial fatigue damage analysis of aero-engine casing components under random multi-parameter loads, and provides a basis for the multi-parameter fatigue test assessment of such complex mechanical components. Description of the Drawings

[0077] Figure 1 is the finite element model of the hollow thin-walled and open-hole component;

[0078] Figure 2 is the external load time history curve of the component in the example of the present invention;

[0079] Figure 3 is the stress time history of the fatigue assessment point of the component;

[0080] Figure 4 is the strain time history of the fatigue assessment point of the component;

[0081] Figure 5 is the equivalent stress time history of the fatigue damage assessment point of the component;

[0082] Figure 6 is the time history of the cosine of the stress principal axis direction corresponding to the maximum principal stress;

[0083] Figure 7 is the equivalent stress time interval history of the fatigue damage assessment point of the component;

[0084] Figure 8 is the stress principal axis direction cosine time interval history of the fatigue damage assessment point of the component;

[0085] Figure 9 is the distribution and clustering result of the local load state points of the fatigue damage assessment point of the component;

[0086] Figure 10 is the total cumulative time distribution of the typical load state cycles;

[0087] Figure 11 is the statistical chart of the total cumulative time of the load state cycle and the optimized number of cycles;

[0088] Figure 12 is the multi-parameter fatigue test spectrum. Detailed implementation manners

[0089] The following further explains the present invention with reference to the accompanying drawings.

[0090] A method for compiling a multi-parameter fatigue test spectrum based on consistent local load states according to the present invention uses the multi-parameter measured component load spectrum as the basic spectrum compilation data, calculates the stress-strain time history of the multi-axial fatigue damage assessment point of the component according to the finite element principle, and determines the local load state time history of the assessment point based on this, that is, the equivalent stress-strain history and the time history information of the multi-axial stress principal axis direction, divides the load parameters at equal time intervals and conducts statistical analysis on them, selects typical multi-axial state cycles, and determines the number of load cycles with consistent damage according to such load cycles, so as to randomly connect the determined multi-parameter load spectrum blocks to obtain a multi-parameter fatigue test spectrum with consistent local load states and consistent damage of the component. The specific steps are as follows:

[0091] (1) Convert the multi-parameter component load spectrum into the stress-strain history of the fatigue assessment point according to the finite element principle, and solve the linear equation of the local stress-strain and the component load; specifically:

[0092] (11) Calculate the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum through finite element software, including: assigning material properties and element types, component modeling and mesh division, multi-load step solution, and stress-strain data analysis;

[0093] (12) Solve the linear equation of the local stress-strain of the fatigue damage assessment point and the component load, and its expression is as follows:

[0094] σ(c,t) = K σ (c)·F(t)

[0095] ε(c,t) = Kε (c)·F(t)

[0096] Among them, c is the fatigue damage assessment point of the component, t is the load time, σ(c,t), ε(c,t), and F(t) are the stress, strain vector, and external load vector related to time at the fatigue damage assessment point of the component, respectively. The matrix expression forms of the above vectors are as follows:

[0097]

[0098] Among them, K σ (c), K ε (c) are the coefficient matrices of stress and strain with respect to the external load matrix, respectively, and they are constant over the load time history; σ xx (c,t), σ yy (c,t), σ zz (c,t), τ yz (c,t), τ xz (c,t), τ xy (c,t) represent the normal stress and shear stress in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; ε xx (c,t), ε yy (c,t), ε zz (c,t), γ yz (c,t), γ xz (c,t), γ xy (c,t) represent the normal strain and shear strain in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),...F num (t) represent the num paths of external loads borne by the component;

[0099] Perform a multiple linear equation calculation based on the stress-strain history obtained in step (11) to obtain the numerical solutions of the coefficient matrices K σ (c), K ε (c).

[0100] (2) Select the load time interval △t, discretely divide the load time history at equal time intervals, and perform equivalent stress-strain calculation and stress principal axis direction calculation according to the discrete stress-strain time history, respectively, to obtain the equivalent stress-strain time history and the stress principal axis time history; specifically:

[0101] (21) Set the discretization variable n, and select the discrete time interval △t for each load range according to the sampling time △T of the original load. The relationship between the variables is as follows:

[0102] △T = n·△t

[0103] T = N·△T

[0104] Among them, T and N are the total sampling time and the total number of samples of the original load. Thus, the original load histories σ(c,t) and ε(c,t) with a time interval of ΔT are refined into discrete data of the load time history with a time interval of Δt.

[0105] (22) According to the discrete data of the load time history in step (21) Calculate the equivalent stress-strain and the direction cosines of the stress principal axis for each discrete load point to obtain the discrete time history of the local load state at the fatigue damage assessment point of the component. The calculation expression of the equivalent stress-strain is as follows:

[0106]

[0107]

[0108] Among them, σ eq and ε eq respectively represent the equivalent stress and the equivalent strain; σ xx , σ yy , σ zz , τ yz , τ xz , τ xy respectively represent the normal stress and the shear stress in the xyz coordinate system, and their subscripts correspond to the coordinate directions; ε xx , ε yy , ε zz , γ yz , γ xz , γ xy respectively represent the normal strain and the shear strain in the xyz coordinate system, and their subscripts correspond to the coordinate directions; Thus, the discrete time histories of the equivalent stress-strain σ eq (c,t) and ε eq (c,t) can be obtained;

[0109] The calculation of the direction cosines of the stress principal axis requires solving the eigenvalues and eigenvectors of the stress matrix at the current load time point. The solution equation is as follows:

[0110]

[0111] Among them, σ xx (c,t), σ yy (c,t), σ zz (c,t), τ yz (c,t), τ xz (c,t), τ xy (c,t) respectively represent the discrete data of the load time history in the xyz coordinate system The normal stress and shear stress, with their subscripts corresponding to the coordinate system directions, where σ(c,t), l, m, and n are the principal stresses to be solved and their direction cosine values;

[0112] Solve the above characteristic equation for σ(c,t) to obtain the three principal stresses at the fatigue damage assessment point, namely σ1(c,t), σ2(c,t), and σ3(c,t), where σ1(c,t) > σ2(c,t) > σ3(c,t), as well as the direction cosines l1(c,t), m1(c,t) of the stress principal axis corresponding to the maximum principal stress σ1(c,t) and the direction cosines l2(c,t) of the stress principal axis corresponding to the secondary principal stress σ2(c,t);

[0113] Calculate the equivalent stress and strain for each load time interval Equivalent principal stress σ 1,i 、σ 2,i and the direction cosines l 1,i 、m 1,i 、l 2,i , where the equivalent stress and strain and the equivalent principal stress variables take the maximum values within each load time interval [t i ,t i +△t], while the direction cosines of the equivalent stress principal axis take the mean values within each load time interval [t i ,t i +△t]. Their calculation expressions are as follows:

[0114]

[0115]

[0116] σ 1,i =max{σ1(c,t)|t∈[t i ,t i +△t]}

[0117] σ 2,i =max{σ2(c,t)|t∈[t i ,t i +△t]}

[0118] l 1,i =(max{l1(c,t)|t∈[t i ,t i +△t]}+min{l1(c,t)|t∈[t i ,t i +△t]}) / 2

[0119] m 1,i =(max{m1(c,t)|t∈[t i ,ti +Δt]} + min{m1(c, t)|t ∈ [t i , t i +Δt]}) / 2

[0120] l 2,i =(max{l2(c, t)|t ∈ [t i , t i +Δt]} + min{l2(c, t)|t ∈ [t i , t i +Δt]}) / 2

[0151] Figure 1 where the max{} and min{} functions represent the maximum and minimum values of the current variable in the interval, respectively; Figure 2 Figure 3 Thus, the discrete time history of the local load state of the component fatigue damage assessment point is obtained. Figure 4 (3) Discretely statistically analyze the equivalent stress-strain history and the stress principal axis direction, select typical multiaxial load state cycles, and determine the corresponding cumulative time; specifically:

[0152] (31) Based on the equivalent stress-strain time history and the stress principal axis time history obtained in step (2), where the equivalent equivalent stress

[0153] and the two equivalent stress principal axis direction cosines l 1,i , m 1,i are the main statistical variables, perform a three-dimensional variable statistical analysis, and there are also σ 1,i , σ 2,i , l 2,i as auxiliary statistical variables;

[0154] (32) According to the three-dimensional variable statistical analysis in step (31), perform a three-dimensional K-Means clustering analysis, where the classification is performed according to the proximity of the local load state values. According to the clustering results, the discrete load states, that is, the equivalent equivalent stress and the two equivalent stress principal axis direction cosines, are divided into m classes, and the centroid value of each class is taken as the typical load state cycle of each class A series of typical load state cycles that can reflect the actual local load state of the component are obtained

[0155] Reverse solve the stress, strain vectors, and external load vectors according to the typical load state cycle, and the calculation expressions are as follows:

[0156]

[0157]

[0158] where,

[0159] is the equivalent equivalent stress of the typical load state cycle, and are both weighted averages within the typical state cycle class, is the third principal stress of the typical load state cycle to be solved; represents the three - dimensional principal stresses of the m - type typical load state cycle, where l i,j , m i,j and n i,j represent the direction cosine values corresponding to the three - dimensional principal stresses of the m - type typical load state cycle; σ xx,j , σ yy,j , σ zz,j , τ yz,j , τ xz,j , τ xy,j respectively represent the normal stress and shear stress of the m - type typical load state cycle in the xyz coordinate system, and their subscripts correspond to the coordinate system directions;

[0129] Thus, the stress - strain vector of the typical load state cycle is obtained by reverse - solving the load from the linear equation of local stress - strain and component load in step (1), and a series of typical external load cycles {F 1,j (t)F 2,j (t)...F n,j (t)} j＝1,2,3,...,m ;

[0130] (33) Calculate the total cumulative time of each typical load state cycle obtained by clustering according to step (32). The calculation expression is as follows:

[0131]

[0132] where t total,j represents the total time of the j - th type of typical load state cycle, represents the j - th type of typical load state cycle, △t i respectively represent the discrete load states and their time intervals obtained in step (22).

[0133] (4) Calculate the total cumulative damage of the original load spectrum according to the multiaxial fatigue damage model, and perform an optimization search and solution for the corresponding number of cycles of the multiaxial load state cycle selected in the above steps; specifically:

[0134] (41) The original multi-parameter random load history of the component is transformed into a series of stress and strain cycles by using the multi-axis cyclic counting method, and the maximum shear strain increment and the maximum normal strain increment on the maximum shear strain plane within each cycle are obtained. Then, the fatigue damage of each cycle is calculated by using the multi-axis fatigue damage model, and the multi-axis damage accumulation of the entire original load spectrum is carried out. Thus, the total multi-axis fatigue damage of the original load spectrum is obtained, which is expressed as follows:

[0135]

[0136] where n i represents the number of cycles of the load cycle, and N i represents the multi-axis fatigue life of the load cycle;

[0137] (42) According to the total cumulative time corresponding to each typical load state cycle counted in step (3), the ratio of the number of cycles between each state cycle is determined, and its expression is as follows:

[0138]

[0139] where m is the total number of typical load state cycles selected in step (3); n1, n2,..., n m represent the number of cycles of each typical load state cycle, and t total,1 , t total,2 ,..., t total,m represent the total cumulative time corresponding to each typical load state cycle;

[0140] (43) Since n1, n2,..., n m are proportional, a single-variable optimization search can be carried out. The optimization goal is that the total damage of each typical state cycle spectrum block after optimization is consistent with the total damage of the original load spectrum. The calculation method of the total damage of the multi-parameter spectrum block after optimization is the same as that in step (41), and its optimization objective function is as follows:

[0141]

[0142] where D squence represents the total multi-axis fatigue damage of the original load spectrum, and D block,j represents the total multi-axis fatigue damage of each typical load state cycle spectrum block;

[0143] Thus, the load amplitude and cycle number information (σ j (c, t), n j ) of the multi-parameter load spectrum block consistent with the damage of the original load spectrum are obtained, j = 1, 2,..., m. Furthermore, the external load spectrum block information (F j (t), n j ) of the component is obtained, j = 1, 2,..., m, that is

[0144]

[0145] (5) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the local load state and damage of the original load spectrum.

[0146] The present invention will be further described below in conjunction with embodiments and drawings.

[0147] Embodiment

[0148] An example analysis of the present invention is now carried out on a hollow thin-walled open-ended cylindrical member subjected to random tensile-torsional loads at both ends.

[0149] (1) According to the finite element principle, convert the multi-parameter component load spectrum into the stress-strain history of the fatigue assessment point, and solve the linear equation of the local stress-strain and the component load;

[0150] (11) Determine the stress-strain history of the fatigue assessment point of the component under the multi-parameter load spectrum.

[0151] The calculation of the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum is mainly carried out with the aid of finite element software, including: ① Assigning material properties and element types, ② Modeling and meshing the component, such as Figure 1 , ③ Solving with multiple load steps, the time history of the external load of the component is as Figure 2 , ④ Analyzing stress and strain data, the stress and strain time history curves of the fatigue damage assessment point are as Figure 3 , Figure 4 .

[0152] (12) Solve the linear equation of the local stress-strain of the fatigue damage assessment point and the component load, and its expression is as follows:

[0153] σ(c,t) = K σ (c)·F(t)

[0154] ε(c,t) = K ε (c)·F(t)

[0155] Where c is the fatigue damage assessment point of the component, t is the load time, σ(c,t), ε(c,t), and F(t) are the stress, strain vector related to time, and external load vector of the fatigue damage assessment point of the component respectively. The matrix expression forms of the above vectors are as follows:

[0156]

[0157] K σ K ε (c) are the coefficient matrices of stress and strain with respect to the external load matrix respectively, and they are constant over the load time history; σxx (c, t), σ yy (c, t), σ zz (c, t), τ yz (c, t), τ xz (c, t), τ xy (c, t) represent the normal stress and shear stress in the xyz coordinate system respectively, and their subscripts correspond to the coordinate system directions; ε xx (c, t), ε yy (c, t), ε zz (c, t), γ yz (c, t), γ xz (c, t), γ xy (c, t) represent the normal strain and shear strain in the xyz coordinate system respectively, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),... F num (t) represents the num - path external load borne by the component.

[0158] Performing a multiple - linear equation calculation based on the stress - strain history obtained in step (11), the coefficient matrix K σ (c), K ε The numerical solution of (c) is calculated for this example as follows:

[0159]

[0160]

[0161] (2) Select the load time interval Δt, perform an equally - spaced time - interval discretization of the load time history, and calculate the equivalent stress - strain and the direction of the stress principal axis respectively according to the discrete stress - strain time history, obtaining the equivalent stress - strain time history and the stress principal axis time history;

[0162] (21) Let the discretization variable be n, select the discrete time interval Δt for each load range according to the sampling time ΔT of the original load, and the relational expression between the variables is as follows:

[0163] ΔT = n·Δt; T = N·ΔT

[0164] Among them, T and N are the total sampling time and the total number of samples of the original load. Thus, the original load history σ(c, t), ε(c, t) with ΔT as the time interval is refined into discrete data of the load time history with Δt as the interval

[0165] (22); According to the discrete data of the load time history performed in step (21) Calculate the equivalent stress, strain, and the direction angle of the stress principal axis at each discrete load point to obtain the discrete time history of the local load state at the fatigue damage assessment point of the component. The calculation expression for the equivalent stress and strain is as follows:

[0166]

[0167]

[0168] Among them, σ eq and ε eq respectively represent the equivalent stress and equivalent strain; σ xx , σ yy , σ zz , τ yz , τ xz , τ xy respectively represent the normal stress and shear stress in the xyz coordinate system, and their subscripts correspond to the coordinate directions; ε xx , ε yy , ε zz , γ yz , γ xz , γ xy respectively represent the normal strain and shear strain in the xyz coordinate system, and their subscripts correspond to the coordinate directions; From this, the discrete time history of the equivalent stress and strain σ eq (c, t), ε eq (c, t) can be obtained.

[0169] The calculation of the direction cosine of the stress principal axis requires solving the eigenvalues and eigenvectors of the stress matrix at the current load time point. The solution equation is as follows:

[0170]

[0171] Among them, σ xx (c, t), σ yy (c, t), σ zz (c, t), τ yz (c, t), τ xz (c, t), τ xy (c, t) respectively represent the discrete data of the load time history in the xyz coordinate system of the normal stress and shear stress, and their subscripts correspond to the coordinate directions. σ(c, t), l, m, and n are the principal stress and its direction cosine values to be solved.

[0172] Solving the above characteristic equation for σ(c,t), the principal stresses at the fatigue damage assessment point can be obtained, namely σ1(c,t), σ2(c,t), σ3(c,t), where σ1(c,t) > σ2(c,t) > σ3(c,t), and the direction cosines l1(c,t), m1(c,t) of the stress principal axis corresponding to the maximum principal stress σ1(c,t) and the direction cosines l2(c,t) of the stress principal axis corresponding to the secondary principal stress σ2(c,t).

[0173] Thus, by performing calculations for this example, the time history of the local load state at the fatigue damage assessment point of the component can be obtained. The time history of the equivalent stress at the fatigue damage assessment point of the component is as Figure 5 , and the time history of the direction cosines l1(c,t), m1(c,t) of the stress principal axis corresponding to the maximum principal stress σ1(c,t) is as Figure 6 .

[0174] Furthermore, calculate the equivalent equivalent stress strain in each load time interval equivalent principal stress σ 1,i , σ 2,i and the direction cosines l 1,i , m 1,i , l 2,i , where the equivalent equivalent stress strain and the equivalent principal stress variable take the maximum value within each load time interval [t i , t i +△t], and the direction cosines of the equivalent stress principal axis take the average value within each load time interval [t i , t i +△t]. Their calculation expressions are as follows:

[0175]

[0176]

[0177] σ 1,i =max{σ1(c,t)|t∈[t i , t i +△t]}

[0178] σ 2,i =max{σ2(c,t)|t∈[t i , t i +△t]}

[0179] l 1,i =(max{l1(c,t)|t∈[t i , t i +△t]}+min{l1(c,t)|t∈[t i , t i+△t]}) / 2

[0180] m 1,i =(max{m1(c,t)|t∈[t i ,t i +△t]}+min{m1(c,t)|t∈[t i ,t i +△t]}) / 2

[0181] l 2,i =(max{l2(c,t)|t∈[t i ,t i +△t]}+min{l2(c,t)|t∈[t i ,t i +△t]}) / 2

[0182] where the max{} and min{} functions represent the maximum and minimum values of the current variable in the interval, respectively.

[0183] Thus, for this example, the value information of the time interval of the local load state at the fatigue damage assessment point of the component can be obtained through calculation. The time interval history of the equivalent stress at the fatigue damage assessment point of the component is as Figure 7 , and the time history of the cosines l1, m1 of the stress principal axis direction corresponding to the maximum principal stress σ1(c,t) is as Figure 8 .

[0184] (3) Discretely statistically analyze the equivalent stress-strain history and the stress principal axis direction, select typical multiaxial load state cycles, and determine the corresponding cumulative time;

[0185] (31) Based on the discretized equivalent equivalent stress-strain history and the discretized equivalent stress principal axis direction cosine time history obtained in the above step (2), where the equivalent equivalent stress and the two equivalent stress principal axis direction cosines l 1,i , m 1,i are the main statistical variables, further perform statistical analysis of three-dimensional variables. Additionally, σ 1,i , σ 2,i , l 2,i are auxiliary statistical variables;

[0186] (32) According to the three-dimensional variable statistical analysis in the above step (31), perform three-dimensional K-Means clustering analysis, where the classification is based on the proximity of the local load state values. According to the clustering results, the discrete load states, i.e., the equivalent equivalent stress and the two equivalent stress principal axis direction cosines, can be divided into m categories, and the maximum equivalent stress cycle state of each category is taken as the typical load state cycle of each category Further, a series of typical load state cycles that can reflect the actual local load state of the component are obtained. Still further, the stress, strain vectors, and external load vectors are solved backward according to the typical load state cycles. The calculation expressions are as follows:

[0187]

[0188]

[0189] Among them, is the equivalent stress of the typical load state cycle, and are both weighted average values within the typical state cycle class, is the third principal stress of the typical load state cycle to be solved; represents the three principal stresses of the mth type of typical load state cycle, l i,j , m i,j and n i,j represent the direction cosine values corresponding to the three principal stresses of the mth type of typical load state cycle; σ xx,j , σ yy,j , σ zz,j , τ yz,j , τ xz,j , τ xy,j respectively represent the normal stresses and shear stresses of the mth type of typical load state cycle in the xyz coordinate system, and their subscripts correspond to the coordinate system directions.

[0190] Thus, the stress-strain vector of the typical load state cycle can be obtained. Further, from the linear equation of local stress-strain and component load in step (1), by performing backward load solution, a series of typical external load cycles {F 1,j (t) F 2,j (t)... F n,j (t)} j＝1,2,3,...,m can be obtained.

[0191] (33) According to the series of typical load state cycles obtained in the above step (32) , calculate the total cumulative time of each typical load state cycle respectively. The calculation expression is as follows:

[0192]

[0193] Among them, t total,j represents the total time of the jth type of typical load state cycle, represents the jth type of typical load state cycle, △t iRespectively represent the discrete load states obtained in step (22) and their time intervals.

[0194] Thus, for this example, calculations can be performed to obtain the distribution of local load state points and the clustering results of the component fatigue damage assessment points as Figure 9 . The total cumulative time distribution of each typical load state cycle is as Figure 10 .

[0195] (4) Calculate the total cumulative damage of the original load spectrum according to the multiaxial fatigue damage model, and perform an optimized search and solution for the number of cycles corresponding to the multiaxial load state cycles selected in the above steps according to the principle of damage consistency;

[0196] (41) In this example, the Wang-Brown multiaxial cycle counting method is used to transform the original multi-parameter random load history of the component into a series of stress and strain cycles, and the maximum shear strain increment and the maximum normal strain increment on the maximum shear strain plane within each cycle are obtained. Furthermore, the fatigue damage of each cycle is calculated using the Wang-Brown multiaxial fatigue damage model, and the multiaxial damage accumulation of the entire original load spectrum is performed. Thus, the total multiaxial fatigue damage D of the original load spectrum can be obtained squence , as shown below:

[0197]

[0198]

[0199] Among them, γ max , δε n , σ n,mean respectively represent the maximum shear strain, the normal strain increment, and the mean normal stress on the critical plane; υ′ and E are the equivalent Poisson's ratio and elastic modulus of the material, and S is a material constant; N f is the multiaxial fatigue life, σ′ f , b, ε′ f , and c respectively represent the fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, and fatigue ductility exponent; n i represents the number of cycles of the load cycle, and N i represents the multiaxial fatigue life of the load cycle.

[0200] (42) Determine the ratio of the number of cycles between each state cycle according to the total cumulative time corresponding to each typical load state cycle counted in the above step (3). The expression is as follows:

[0201]

[0202] Among them, m is the total number of typical load state cycles selected in the above step (3); n1, n2,..., n mRepresents the number of cycles for each typical load state cycle, t total,1 、t total,2 、...、t total,m Represents the total cumulative time corresponding to each typical load state cycle.

[0203] (43) Since n1, n2,..., n m are proportional, a single-variable optimization search can be carried out. The optimization objective is that the total damage of each typical state cycle spectrum block after optimization is the same as the total damage of the original load spectrum. The calculation method of the total damage of the multi-parameter spectrum block after optimization is the same as that in step (41) above, and its optimization objective function is as follows:

[0204]

[0205] Among them, D squence represents the total multiaxial fatigue damage of the original load spectrum, and D block,j represents the total multiaxial fatigue damage of each typical load state cycle spectrum block.

[0206] Thus, the load amplitude and cycle number information (σ j (c, t), n j ) of the multi-parameter load spectrum block that is the same as the damage of the original load spectrum can be obtained, j = 1, 2,..., m. Further, the external load spectrum block information (F j (t), n j ) of the component can be obtained, j = 1, 2,..., m, that is

[0207]

[0208] Thus, according to this example, an optimization search is carried out, Figure 11 is a statistical chart of the total cumulative time and the number of cycles after optimization for each load state cycle.

[0209] (5) Randomly splice each multi-parameter load spectrum block, and a multi-parameter fatigue test spectrum that is the same as the local load state and damage of the original load spectrum can be obtained, as Figure 12 shown.

[0210] The above is only a specific implementation manner of the present invention, and the purpose, technical solution and beneficial effects of the present invention are further described in detail. Finally, it should be noted that: the above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. For those in the technical field of research and technology, without departing from the scope of the technical solution of the present invention, non-innovative retouches, changes and modifications made to the technical solution of the present invention using the above content should also be regarded as within the protection scope of the present invention.

Claims

1. A method for compiling a multi-parameter fatigue test spectrum based on the consistency of local load states, characterized in that: It includes the following steps: (1) Convert the multi-parameter component load spectrum into the stress-strain history of the fatigue assessment point according to the finite element principle, and solve the linear equation of the local stress-strain and the component load; (2) Select the load time interval △t, discretize the load time history at equal time intervals, calculate the equivalent stress-strain and the direction of the stress principal axis respectively according to the discrete stress-strain time history, and obtain the equivalent stress-strain time history and the stress principal axis time history; (3) Discretely statistically analyze the equivalent stress-strain history and the direction of the stress principal axis, select typical multi-axial load state cycles, and determine the corresponding cumulative time; (4) Calculate the total cumulative damage of the original load spectrum according to the multi-axial fatigue damage model, and perform an optimization search and solution for the number of cycles corresponding to the multi-axial load state cycles selected in the above steps according to the principle of damage consistency; The specific content of step (4) is as follows: (41) Use the multi-axial cycle counting method to convert the original multi-parameter random load history of the component into a series of stress and strain cycles, and obtain the maximum shear strain increment and the maximum positive strain increment on the maximum shear strain plane within each cycle. Then, use the multi-axial fatigue damage model to calculate the fatigue damage of each cycle and perform the multi-axial damage accumulation of the entire original load spectrum, so as to obtain the multi-axial fatigue total damage of the original load spectrum, which is expressed as follows: Among them, n i represents the number of cycles of the load cycle, and N i represents the multiaxial fatigue life of the load cycle; (42) Determine the ratio of the number of cycles between each state cycle according to the total cumulative time corresponding to each typical load state cycle statistically analyzed in step (3), and its expression is as follows: Among them, m is the total number of cycles of the typical load state selected in step (3); n1, n2,..., n m represents the number of cycles of each typical load state cycle, t total,1 , t total,2 ,... t total,m represents the total cumulative time corresponding to each typical load state cycle; (43) Since n1, n2,..., n m are proportional, univariate optimization search can be carried out. The optimization goal is that the total damage of each typical state cyclic spectrum block after optimization is consistent with the total damage of the original load spectrum. The calculation method and steps of the total damage of the multi-parameter spectrum block after optimization are the same as those in (41). The optimization objective function is as follows: Among them, D squence represents the total multiaxial fatigue damage of the original load spectrum, and D block,j represents the total multiaxial fatigue damage of each cyclic spectrum block of the typical load state; Thus, the load amplitude and cycle number information (σ j (c,t),n j ) of the multi-parameter load spectrum block consistent with the original load spectrum damage are obtained, where j = 1, 2, ..., m. Furthermore, the external load spectrum block information (F j (t),n j ) of the component is obtained, where j = 1, 2, ..., m, that is (5) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the local load state and damage of the original load spectrum.

2. The multi-parameter fatigue test spectrum compilation method based on consistent local load states according to claim 1, characterized in that: The specific content of step (1) is as follows: (11) Calculate the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum through finite element software, including: assigning material properties and element types, component modeling and mesh generation, multi-load step solution, and stress-strain data analysis; (12) Solve the linear equation of the local stress-strain of the fatigue damage assessment point and the component load, and its expression is as follows: σ(c,t) = K σ (c)·F(t) ε(c,t) = K ε (c)·F(t) Where c is the fatigue damage assessment point of the component, t is the load time, σ(c,t), ε(c,t), and F(t) are the stress, strain vector, and external load vector related to time at the fatigue damage assessment point of the component respectively. The matrix expression forms of the above vectors are as follows: Among them, K σ (c), K ε (c) are the coefficient matrices of stress and strain with respect to the external load matrix, respectively, and they are constant over the load time history; σ xx (c, t), σ yy (c, t), σ zz (c, t), τ yz (c, t), τ xz (c, t), τ xy (c, t) represent the normal stress and shear stress in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; ε xx (c, t), ε yy (c, t), ε zz (c, t), γ yz (c, t), γ xz (c, t), γ xy (c, t) represent the normal strain and shear strain in the xyz coordinate system, respectively, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),... F num (t) represents the num paths of external loads borne by the component; Perform a multiple linear equation calculation based on the stress-strain history obtained in step (11) to obtain the coefficient matrix K σ (c), K ε (c) numerical solution.

3. The method for compiling a multi-parameter fatigue test spectrum based on consistent local load states according to claim 1, wherein: The specific content of step (2) is as follows: (21) Set the discretization variable n, and select the discrete time interval △t for each load range according to the sampling time △T of the original load. The relationship between the variables is as follows: △T = n·△t T = N·△T Among them, T and N are the total sampling time and the total number of samples of the original load; thus, the original load histories σ(c,t) and ε(c,t) with a time interval of △T are refined into discrete data of the load time history with a time interval of △t (22) According to the discrete data of the load time history in step (21) Calculate the equivalent stress-strain and the direction cosine of the stress principal axis for each discrete load point, and obtain the discrete time history of the local load state at the fatigue damage assessment point of the component. The calculation expression of the equivalent stress-strain is as follows: Among them, σ eq and ε eq represent the equivalent stress and equivalent strain respectively; σ xx , σ yy , σ zz , τ yz , τ xz , τ xy represent the normal stress and shear stress in the xyz coordinate system respectively, and their subscripts correspond to the coordinate system directions; ε xx , ε yy , ε zz , γ yz , γ xz , γ xy represent the normal strain and shear strain in the xyz coordinate system respectively, and their subscripts correspond to the coordinate system directions; Thus, the discrete time histories of the equivalent stress and strain, σ eq (c, t) and ε eq (c, t), can be obtained; The calculation of the stress principal axis direction cosine needs to solve the eigenvalues and eigenvectors of the stress matrix at the current load time point, and its solution equation is as follows: Among them, σ xx (c, t), σ yy (c, t), σ zz (c, t), τ yz (c, t), τ xz (c, t), τ xy (c, t) respectively represent the discrete data of the load time history in the xyz coordinate system of the normal stress and shear stress, and their subscripts correspond to the coordinate system directions. σ(c, t), l, m, n are the principal stresses to be solved and their direction cosine values; Solve the above characteristic equation for σ(c,t) to obtain the three principal stresses at the fatigue damage assessment point, namely σ1(c,t), σ2(c,t), and σ3(c,t), where σ1(c,t) > σ2(c,t) > σ3(c,t), as well as the direction cosines l1(c,t), m1(c,t) of the stress principal axis corresponding to the maximum principal stress σ1(c,t) and the direction cosines l2(c,t) of the stress principal axis corresponding to the secondary principal stress σ2(c,t); Calculate the equivalent equivalent stress and strain for each load time interval respectively Equivalent principal stress σ 1,i , σ 2,i and the direction cosines l 1,i , m 1,i , l 2,i , where the equivalent equivalent stress and strain and the equivalent principal stress variable take the maximum value within each load time interval [t i , t i +Δt], and the direction cosines of the equivalent stress principal axis take the mean value within each load time interval [t i , t i +Δt]. The calculation expressions are as follows: σ 1,i = max{σ1(c,t)|t ∈ [t i , t i + Δt]} σ 2,i = max{σ2(c,t) | t ∈ [t i , t i + Δt]} l 1,i = (max{l1(c, t)|t ∈ [t i , t i + Δt]} + min{l1(c, t)|t ∈ [t i , t i + Δt]}) / 2 m 1,i = (max{m1(c, t) | t ∈ [t i , t i + Δt]} + min{m1(c, t) | t ∈ [t i , t i + Δt]}) / 2 l 2,i = (max{l2(c, t) | t ∈ [t i , t i + Δt]} + min{l2(c, t) | t ∈ [t i , t i + Δt]}) / 2 where the max{} and min{} functions represent the maximum and minimum values of the current variable in the interval, respectively; Thus, the discrete time history of the local load state at the fatigue damage assessment point of the component is obtained.

4. The multi-parameter fatigue test spectrum compilation method based on consistent local load states according to claim 1, characterized in that: The specific content of step (3) is as follows: (31) Based on the equivalent stress-strain time history and stress principal axis time history obtained in step (2), taking the equivalent equivalent stress and the direction cosines l of the two equivalent stress principal axes 1,i , m 1,i as the main statistical variables, perform statistical analysis of three-dimensional variables. Additionally, σ 1,i , σ 2,i , l 2,i are auxiliary statistical variables; (32)Based on the three-dimensional variable statistical analysis in step (31), three-dimensional K-Means clustering analysis is performed, in which classification is carried out according to the proximity of local load state values. According to the clustering results, the discrete load states, i.e., equivalent von Mises stress and the direction cosines of the two equivalent stress principal axes, are divided into m categories, and the centroid values of each category are taken as the typical load state cycles of each category. A series of typical load state cycles that can reflect the actual local load state of the component are obtained. The stress, strain vectors, and external load vectors are solved backward according to the typical load state cycles, and the calculation expressions are as follows: Among them, is the equivalent stress of the typical load state cycle, and are both the weighted average values within the typical state cycle class, is the third principal stress of the typical load state cycle to be solved; represents the three principal stresses of the m - type typical load state cycle, where l i,j , m i,j and n i,j represent the direction cosine values corresponding to the three principal stresses of the m - type typical load state cycle; σ xx,j , σ yy,j , σ zz,j , τ yz,j , τ xz,j , τ xy,j respectively represent the normal stresses and shear stresses of the m - type typical load state cycle in the xyz coordinate system, and their subscripts correspond to the coordinate system directions; The typical load state cycle is thus obtained of the stress-strain vector, which is obtained by solving the reverse load from the linear equation of the local stress-strain and the component load in step (1). The series of typical external load cycles {F 1,j (t)F 2,j (t)...F n,j (t)} j＝1,2,3,...,m ; (33)A series of typical load state cycles obtained by clustering according to step (32) Calculate the total cumulative time of each typical load state cycle respectively, and its calculation expression is as follows: where t total,j represents the total time of the j-th typical load state cycle, represents the j-th typical load state cycle, △t i respectively represent the discrete load states and their time intervals obtained in step (22).

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