A method for compiling a random multi-parameter fatigue test spectrum based on damage equivalence

Abstract

The present invention discloses a method for compiling a multi-parameter fatigue test spectrum based on damage equivalence, comprising the following steps: obtaining a multi-parameter fatigue test spectrum model that fully encompasses the characteristics of actual multi-parameter loads; converting the pre-processed multi-parameter component load spectrum into the stress-strain history of the fatigue assessment point and solving the linear equation of the local stress-strain and the component load; discretizing the stress-strain history of the fatigue assessment point in time and determining the critical plane using the weight function based on the time-varying damage parameter; calculating the total cumulative damage of the original load spectrum according to the multi-axial fatigue damage model; establishing the relationship between the external load and the multi-axial damage, and performing an optimization search and solution for the optimization parameters of the multi-parameter fatigue test spectrum model; randomly splicing each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the load characteristics and damage of the original load spectrum. The present invention realizes the consistency of load characteristics and damage in the process of compiling the multi-parameter fatigue test load spectrum.

Description

Technical Field

[0001] The present invention belongs to the technical field of the compilation of fatigue test load spectra for mechanical structures, and particularly relates to a method for compiling fatigue test spectra of complex mechanical components under multi-parameter random loads, providing a load basis for multi-axial fatigue damage analysis and multi-axial fatigue tests of mechanical components under random multi-parameter loads, and being an important step in the life test assessment of key components of engineering complex structures under actual multi-parameter service loads. Background Art

[0002] At present, the research on fatigue test spectra at home and abroad mostly focuses on the compilation of single-parameter fatigue test load spectra, and it has also been widely applied in industrial fields such as aerospace, vehicles, and construction machinery. However, in actual engineering applications, most mechanical components are under the action of random multi-parameter loads for a long time, and the components are often prone to multi-axial fatigue damage and then failure. For example, complex components such as aero-engine casings, automotive universal joints, and front suspensions often bear typical random non-proportional multi-axial loads during actual service. Therefore, single-parameter fatigue test spectra are no longer applicable to fatigue assessment of such components under complex multi-parameter loads. To conduct a full and scientific life assessment of such components, a method for compiling multi-parameter load fatigue test spectra must be developed.

[0003] When conducting a life assessment test on complex mechanical components, the load spectrum applied must reflect the actual working characteristics of the components to a certain extent. However, the random loads borne by the components are not easy to test and apply. The program fatigue test spectrum not only retains the load characteristics to a certain extent but also has a simple form and strong operability, and has been widely used. Academician Gao Zhentong compiled a fatigue test program spectrum for fighter jets based on the two-dimensional probability statistics of load mean amplitudes; Gao Yunkai also proposed a method for compiling a program load spectrum for vehicle body bench fatigue tests based on this. However, there is currently no generally recognized compilation theory and method for multi-parameter fatigue test program spectra, and only a small number of scholars have conducted some research on it. Yang Yanhong, Zhao Yongming, etc. respectively carried out the compilation work of multi-parameter fatigue test spectra from the perspective of multi-axial fatigue damage, but the values of parameters such as load amplitudes and phases are somewhat subjective. The equivalent fatigue load method proposed and adopted by PSA Peugeot Citroën optimizes and searches for values to ensure consistent damage while ignoring the actual load mean amplitude distribution, which results in a certain difference between the compiled fatigue test spectrum and the actual service load in terms of load characteristics and multi-axial fatigue life performance.

[0004] In summary, the existing methods for compiling multi-parameter fatigue test spectra still have certain limitations. There is no clear and generally recognized method for compiling multi-parameter fatigue test spectra for components, and the requirements for compiling spectra with consistent fatigue damage are satisfied to varying degrees. Under the action of multi-parameter loads, it is still a key engineering problem that urgently needs to be solved to compile a fatigue test spectrum that is consistent with the load characteristics of components under the actual load spectrum, has equivalent damage, and the same failure mode. This is also of great significance for the fatigue damage analysis and fatigue test research of complex mechanical components in engineering practice.

[0005] Therefore, it is necessary to develop a method for compiling multi-parameter fatigue test spectra that can consider the consistent load characteristics and damage of complex mechanical components in engineering, laying a foundation for the life determination of complex construction machinery and its components. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for compiling a random multi-parameter fatigue test spectrum based on damage equivalence to solve the problem that the compilation of fatigue test load spectra in the prior art lacks consideration of the correlation relationship of multi-parameter loads.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for compiling a multi-parameter fatigue test spectrum based on damage equivalence includes the following steps:

[0009] (1) Detect the peak and valley values and perform rain-flow cycle counting on the multi-parameter random load spectrum of the complex mechanical component to obtain the statistical results of the load amplitude and mean value of each load. Use the load cumulative frequency curve to divide the load amplitude into grades, and the mean value is correspondingly averaged to obtain a series of representative load cycles for each load path. The typical load cycle series is used for the matching combination of multi-parameter loads to obtain a multi-parameter fatigue test spectrum model that fully contains the actual multi-parameter load characteristics;

[0010] (2) According to the finite element principle, convert the preprocessed 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;

[0011] (3) Discretize the stress-strain history of the fatigue assessment point in time, and use the weight function based on the damage time-varying parameter to determine the critical plane;

[0012] (4) Calculate the total cumulative damage of the original load spectrum according to the multi-axial fatigue damage model;

[0013] (5) Based on the linear equations of the critical plane with weight function, local stress-strain and component load, establish the relationship between external load and multiaxial damage, determine the multiaxial fatigue damage values representing a series of load cycle combinations, and perform an optimization search and solution for the optimization parameters of the multi-parameter fatigue test spectrum model established in step (1) above according to the principle of damage consistency;

[0014] (6) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the load characteristics and damage of the original load spectrum.

[0015] The specific steps of step (1) are as follows:

[0016] (11) Conduct peak-valley value detection and rain-flow cycle counting processing on the multi-parameter random load spectrum of complex mechanical components. Among them, peak-valley value detection is to judge the peak or valley points for each load time history. If so, retain them; otherwise, remove them. Perform a three-point method judgment on the data, that is, read three adjacent data points F(i - 1), F(i), F(i + 1). If the following conditions are met:

[0017] [F(i) - F(i - 1)][F(i + 1) - F(i)] ≥ 0 and F(i) - F(i - 1) ≠ 0

[0018] where F(i) is the peak point or valley point;

[0019] Rain-flow cycle counting is to extract the full load cycles of the load history based on the principle of the material stress-strain hysteresis loop. Continuously read four points in the load history, that is, two peak values and two valley values. The selection basis for the full cycle is that the absolute value of the difference between the middle two points is less than the sum of the absolute values of the differences between the previous two points and the next two points, that is, the following conditions are met:

[0020] |F(i + 2) - F(i + 1)| ≤ |F(i + 1) - F(i)|

[0021] |F(i + 2) - F(i + 1)| ≤ |F(i + 3) - F(i + 2)|

[0022] From this, the statistical results of the peak-valley values of the full load cycles of each load path are obtained, and then the statistical information of the average amplitude of the full load cycles is obtained. Its calculation expression is as follows:

[0023] C amp =(F peak -F valley ) / 2

[0024] C mean =(F peak +F valley ) / 2

[0025] where, F peak 、Fvalley respectively represent the peak and valley values of the rainflow counting cycle; C amp , C mean respectively represent the amplitude and mean value of the rainflow counting cycle;

[0026] (12) Based on the statistical information of the average amplitude of the full load cycle in step (11), draw a load cumulative frequency curve with the load amplitude as the vertical coordinate and the cumulative frequency as the horizontal coordinate. Discretely divide the load amplitude interval into levels using the equal interval method or according to the actual load distribution, and determine the load amplitudes of each level of stepped load, that is, (A j,1 , A j,2 ,..., A j,n ). Using the principle of equal damage interval, determine the load frequencies corresponding to each level of load, and then average the mean values of each level of load to obtain the mean values of each level of stepped load, that is, (M j,1 , M j,2 ,..., M j,n ). Thus, a series of representative load cycles for the j-th load path are obtained, that is,

[0027]

[0028] or {(A j,1 , M j,1 , η j,1 ), (A j,2 , M j,2 , η j,2 ),...,(A j,n , M j,n , η j,n )}

[0029] Among them, is the number of cycles of each level of load, j = 1, 2,..., m, i = 1, 2,..., n, m is the number of load channels, n is the number of levels divided for each load path, and η j,i is the proportion of the normalized number of cycles of each level of load, and its calculation expression is as follows:

[0030]

[0031] (13) Based on the series of representative load cycles determined for each load path, perform traversal matching combinations of multi-parameter load spectra, and then obtain a multi-parameter fatigue test spectrum model that fully contains the characteristics of the actual multi-parameter load. The number of load matching combinations is n m , that is, n m multi-parameter load spectrum blocks are generated. Each spectrum block parameter includes a total of 2m average amplitude parameters (A, M) for each load path, m - 1 phase parameters in total, and 1 load combination cycle number, that is,

[0032] ......

[0034]

[0035] Among them, the m parameters k, h,..., q take values from {1, 2,..., n}, representing each representative multi-parameter load cycle spectrum block, from which the parameter expression of the multi-parameter fatigue test spectrum model is obtained.

[0036] The specific steps of the said step (2) are as follows:

[0037] (21) Determine the stress-strain history of the fatigue assessment point of the component under the multi-parameter load spectrum. The calculation of the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum is carried out with the aid of finite element software, including: ① Assigning material properties and element types, ② Component modeling and mesh generation, ③ Solving for multiple load steps, ④ Stress-strain data analysis;

[0038] (22) 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:

[0039] σ(c, t) = K σ (c)·F(t)

[0040] ?ε(c, t) = K ε (c)·F(t)

[0041] 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 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:

[0042]

[0043] 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 directions; ε xx (c, t), ε yy (c, t), ε zz (c, t), γ yz (c, t), γxz (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 directions of the coordinate system; F1(t), F2(t), ...F m (t) represents the m-way external load borne by the component;

[0044] According to the stress-strain history obtained in the above step (21), the multivariate linear equation calculation is performed to obtain the coefficient matrix K σ (c), K ε Numerical solution of (c).

[0045] The specific steps of step (3) are:

[0046] (31) Let the discrete degree variable s be the discrete time interval Δt of each load history selected according to the sampling time ΔT of the original load. The relationship between the variables is as follows:

[0047] ΔT=s·Δt

[0048] T=N·ΔT

[0049] Among them, T and N are the total sampling time and total number of samples of the original load, thereby refining the original load history σ(c,t) and ε(c,t) with ΔT as the time interval into discrete data with Δt as the load time history

[0050] (32) The load time history discrete data according to step (31) For the strain data of each discrete load point, the shear strain of any plane in space is calculated by coordinate rotation to determine the critical plane position (θ cr (t p ),φ cr (t p )), and then perform weighted averaging on the critical plane positions of the load history according to the weight function to obtain the weighted critical plane of the fatigue damage assessment point, where the strain coordinate rotation calculation expression is as follows:

[0051] {ε′ xx ε′ yy ε′ zz γ′ yz γ′ xz γ′ xy} T =[Φ ε ]{ε xx ε yy ε zz γ yz γ xz γ xy} T

[0052] {σ′ xx σ′ yy σ′ zz τ′ yz τ′ xz τ′ xy} T =[Φ σ {σ xx σ yy σ zz τ yz τ xz τ xy} T

[0053] where

[0054] where the angles θ and φ are coordinate rotation variables, θ is the angle between the projection of the X'-axis of the new coordinate system (X'-Y'-Z') on the X-Y plane and the X-axis, and φ is the angle between the X'-axis and the Z-axis; σ xx 、σ yy 、σ zz 、τ yz 、τ xz 、τ xy respectively represent the normal stress and shear stress in the (X-Y-Z) coordinate system, and their subscripts correspond to the coordinate system directions; ε xx 、ε yy 、ε zz 、γ yz 、γ xz 、γ xy respectively represent the normal strain and shear strain in the (X-Y-Z) coordinate system, σ′ xx 、σ′ yy 、σ′ zz 、τ′ yz 、τ′ xz 、τ′ xy respectively represent the normal stress and shear stress in the (X'-Y'-Z') coordinate system, and their subscripts correspond to the coordinate system directions; ε′ xx 、ε′ yy 、ε′ zz 、γ′ yz 、γ′ xz 、γ′ xy respectively represent the normal strain and shear strain in the (X'-Y'-Z') coordinate system; [Φ ε 、[Φ σ represent the strain and stress rotation matrices;

[0055] The stress coordinate rotation calculation only needs to transform the corresponding strain into stress, that is, σ x 、σ y 、σz Replace ε x 、ε y 、ε z ,τ yz 、τ xz 、τ xy Replace 1 / 2γ yz 、1 / 2γ xz 、1 / 2γ xy ; And based on the assumption that the influence of the damage parameter at each moment on the critical plane is the same, the weight function is defined as:

[0056]

[0057] Where τ -1 is the shear fatigue limit, G is the shear modulus, c is a constant coefficient, and its range of variation is (0, 1], D(t p ) is the fatigue damage corresponding to the maximum shear strain γ max (t p ), and its calculation expression is:

[0058]

[0059] D(t p ) = 1 / N p

[0060] Where E is the elastic modulus of the material, N p is the multiaxial fatigue life, σ′ f 、b、ε′ f 、c respectively represent the fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient, and fatigue ductility index;

[0061] According to the critical plane (θ cr (t p ), φ cr (t p )) at each moment in the load history, perform weighted averaging as follows:

[0062]

[0063] Where is the weighted critical plane position, and W is the sum of the weight coefficients.

[0064] The specific steps of step (4) are as follows:

[0065] (41) Based on the critical plane obtained in step (3), convert the original multi-parameter random load history of the component assessment point into the stress-strain history on the critical plane, and its calculation expression is as follows:

[0066]

[0067] Among them, respectively represent the strain-stress coordinate rotation matrix determined by the weighted critical plane position obtained in step (32);

[0068] (42) 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, thereby using 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, thereby obtaining the total multiaxial fatigue damage D of the original load spectrum squence , which is expressed as follows:

[0069] N f = f(σ cr , ε cr )

[0070]

[0071] Among them, N f , σ cr , ε cr represent the life, stress and strain in the multiaxial fatigue damage model; n i represents the number of cycles of the load cycle, and N i represents the multiaxial fatigue life of the load cycle.

[0072] The specific steps of the said step (5) are as follows:

[0073] (51) Based on the critical plane direction of the weight function obtained in step (3), and the linear equation of the local stress and strain and the component load, establish the relationship between the external load and the multiaxial damage, and calculate the damage of a series of typical load cycle combinations according to the damage calculation method in step (4), where the stress and strain on the critical plane and the external load cycle relationship formula is as follows:

[0074]

[0075] Among them, F1(t), F2(t),..., F m (t) represents the external load borne by the component; [K σ , [K ε are the coefficient matrices of stress and strain for the external load matrix determined in step (22), {(A 1,k , M 1,k ), (A 2,h , M 2,h ),..., (A m,q , M m,q )} is determined by step (1), and the phase information between the loads of each channel and the number of load cycles, that is is optimally selected by the following step (53), that is, the optimization vector is

[0076] (52) Optimize and search for the optimized parameters of the multi-parameter fatigue test spectrum model established in step (1) according to the principle of damage consistency, where the load combination cycle numbers satisfy the following proportional relationship:

[0077] ......

[0079]

[0080] where, represents the cycle number of each load combination, represents the cycle number of the i-th load of the original load spectrum at the j-th load level;

[0081] (53) Based on the above multi-parameter fatigue test spectrum load parameter model, the mean amplitude load level information, and the load cycle ratio equation, perform a multi-variable optimization search. The optimization objective is that the total damage of each representative load cycle combination 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 (42), and its optimization objective function is as follows:

[0082]

[0083] where,

[0084] (N k,h,...,q ) k,h,...,q∈{1,2,3,..,n} ∈N (natural number);

[0085] where, D squence represents the multi-axial fatigue total damage of the original load spectrum, and D block,j represents the multi-axial fatigue total damage of each load combination cycle spectrum block; N k,h,...,q (k, h,..., q ∈ {1, 2, 3,.., n}) respectively represent the phase and cycle number of each load combination cycle spectrum block;

[0086] Thus, the load mean amplitude, phase difference, and load combination cycle number information of the multi-parameter fatigue test load spectrum block of the component that is consistent with the damage of the original load spectrum are obtained.

[0087] Beneficial effects: Based on the compilation idea of the single-parameter fatigue test spectrum, the present invention selects typical load cycle series, performs matching combinations of multi-parameters by typical load cycles, and thus compiles a multi-parameter fatigue test spectrum with damage consistency as the optimization objective. Compared with the existing multi-parameter fatigue test spectrum compilation methods, it has the following beneficial effects:

[0088] (1) Simple and intuitive, with clear steps and accurate descriptions;

[0089] Taking the random multi-parameter component load spectrum as the basic spectrum compilation data, perform the mean amplitude statistics based on rainflow counting for each load data path and divide the series of typical load cycles. Conduct the matching combination of multi-parameter loads from the typical load cycles, use the weight function method to determine the critical plane of the component fatigue assessment point, and calculate the cumulative total damage of the original load spectrum using the multiaxial cycle counting and multiaxial damage model; establish the relationship between the external load and the multiaxial damage based on the weight function critical plane, and thus optimize and search for the block cycle number and load phase of the multi-parameter load spectrum based on the damage consistency objective. Randomly arrange and connect the load spectrum blocks to generate the multi-parameter fatigue test spectrum, which is more reasonable and has stronger versatility compared to the method of subjectively selecting several load parameters to compile the multi-parameter load spectrum.

[0090] (2) It has broad engineering application value;

[0091] The method for compiling the multi-parameter fatigue test spectrum 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 that is consistent with the load characteristics and damage of complex mechanical components under actual load conditions, and has broad engineering application value.

[0092] (3) Research new multiaxial damage models and multiaxial fatigue life analysis methods;

[0093] The method for compiling the multi-parameter fatigue test spectrum of the present invention can reflect the actual load characteristics and damage characteristics of the component, and can provide a basis for compiling the load spectrum for researching multiaxial damage and multiaxial fatigue life analysis methods under the actual service conditions of specific mechanical components. Moreover, the multi-parameter fatigue test spectrum compiled according to the present invention can be used to preliminarily conduct multiaxial fatigue tests at the material level to reduce the design and R & D costs and time.

[0094] In summary, the present invention provides a basis for the multiaxial fatigue damage analysis of complex mechanical components in engineering practice 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

[0095] Figure 1 It is the time history curve diagram of the external load of the component in the embodiment of the present invention;

[0096] Figure 2 It is the peak-valley value detection curve diagram of the external load time history of the component in the embodiment of the present invention;

[0097] Figure 3 It is the rainflow statistical histogram of the mean amplitude of the random external load borne by the component;

[0098] Figure 4 It is the cumulative frequency curve diagram of the random external load of the component;

[0099] Figure 5 It is the result of component load level classification and representative load cycle information;

[0100] Figure 6 It is the traversal matching combination schematic diagram of the multi-parameter load spectrum of the component;

[0101] Figure 7 It is the stress time history of the fatigue assessment point of the component;

[0102] Figure 8 It is the strain time history of the fatigue assessment point of the component;

[0103] Figure 9 It is the schematic diagram of three-dimensional coordinate rotation and strain on an arbitrary plane;

[0104] Figure 10 It is the optimization information of the multi-parameter fatigue test load spectrum block with consistent damage;

[0105] Figure 11 It is the multi-parameter fatigue test load spectrum (sorting one) based on damage equivalence;

[0106] Figure 12 It is the multi-parameter fatigue test load spectrum (sorting two) based on damage equivalence. Detailed implementation mode

[0107] The present invention will be further described below in conjunction with examples.

[0108] A method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to the present invention uses a random multi-parameter component load spectrum as the basic spectrum compilation data, respectively performs the mean amplitude statistics based on rainflow counting on each load data path and divides a series of typical load cycles; performs the matching combination of multi-parameter loads from the typical load cycles, and establishes a multi-parameter fatigue test spectrum parameter model including the actual multi-parameter load characteristics; uses the weight function method to determine the critical plane of the fatigue assessment point of the component, and calculates the cumulative total damage of the original load spectrum using multi-axis cycle counting and multi-axis damage models; establishes the relationship between the external load and multi-axis damage based on the weight function critical plane, and determines the multi-axis fatigue damage value of the representative load combination cycle; performs an optimization search and solution for parameters such as the number of cycles and the phase between loads of the multi-parameter load parameter model according to the principle of damage consistency, and generates a multi-parameter fatigue test spectrum with the same load characteristics and damage as the original load spectrum by randomly arranging and connecting the optimized multi-parameter load spectrum blocks. The specific steps are as follows:

[0109] (1) Detect the peak and valley values and perform rainflow cycle counting on the multi-parameter random load spectra of complex mechanical components to obtain the statistical results of the load amplitude and mean value for each. Use the load cumulative frequency curve to classify the load amplitudes, and average the mean values accordingly. Thus, a series of representative load cycles for each load path are obtained. Match and combine the multi-parameter loads from these typical load cycle series to obtain a multi-parameter fatigue test spectrum model that fully encompasses the characteristics of the actual multi-parameter loads. The specific steps are as follows:

[0110] (11) Detect the peak and valley values and perform rainflow cycle counting on the multi-parameter random load spectra of complex mechanical components. Among them, peak and valley value detection is to judge the peak or valley points for each load time history. If it is, retain it; otherwise, remove it. Use the three-point method to judge the data, that is, read three adjacent data points F(i - 1), F(i), F(i + 1). If the following conditions are met:

[0111] [F(i) - F(i - 1)][F(i + 1) - F(i)] ≥ 0 and F(i) - F(i - 1) ≠ 0

[0112] where F(i) is the peak or valley point;

[0113] Rainflow cycle counting is to extract the full load cycles of the load history based on the principle of the material stress-strain hysteresis loop. Continuously read four points in the load history, namely two peaks and two valleys. The basis for selecting the full cycle is that the absolute value of the difference between the middle two points is less than the sum of the absolute values of the differences between the previous two points and the following two points, that is, the following conditions are met:

[0114] |F(i + 2) - F(i + 1)| ≤ |F(i + 1) - F(i)|

[0115] |F(i + 2) - F(i + 1)| ≤ |F(i + 3) - F(i + 2)|

[0116] Thus, the statistical results of the peak and valley values of the full load cycles of each load path are obtained, and further the statistical information of the average amplitude of the full load cycles is obtained. Its calculation expression is as follows:

[0117] C amp =(F peak -F valley ) / 2

[0118] C mean =(F peak +F valley ) / 2

[0119] where F peak 、F valley represent the peak and valley values of the rainflow counting cycle respectively; C amp 、C meanrespectively represent the amplitude and mean value of the rainflow counting cycle;

[0120] (12) Based on the statistical information of the full-cycle average amplitude of the load in step (11), draw a load cumulative frequency curve with the load amplitude as the vertical coordinate and the cumulative frequency as the horizontal coordinate. Discretely divide the load amplitude interval into levels using the equal interval method or according to the actual load distribution, and determine the stepped load amplitudes at all levels, that is, (A j,1 , A j,2 ,..., A j,n ). Using the principle of equal damage intervals, determine the load frequencies corresponding to each level of load, and then average the mean values of each level of load to obtain the stepped load means at all levels, that is, (M j,1 , M j,2 ,..., M j,n ). Thus, a series of representative load cycles for the j-th load path are obtained, that is

[0121]

[0122] or {(A j,1 , M j,1 , η j,1 ), (A j,2 , M j,2 , η j,2 ),...,(A j,n , M j,n , η j,n )}

[0123] where is the number of cycles of each level of load, j = 1, 2,..., m, i = 1, 2,..., n, m is the number of load channels, n is the number of levels divided for each load path, and η j,i is the proportion of the normalized cycle number of each level of load, and its calculation expression is as follows:

[0124]

[0125] (13) Based on the series of representative load cycles determined for each load path, perform traversal matching combinations of multi-parameter load spectra to obtain a multi-parameter fatigue test spectrum model that fully contains the characteristics of actual multi-parameter loads. The number of load matching combinations is n m , that is, n m multi-parameter load spectrum blocks are generated. Each spectrum block parameter includes a total of 2m average amplitude parameters (A, M) for each load path, m - 1 phase parameters in total, and 1 load combination cycle number, that is

[0126] ......

[0128]

[0129] Among them, the m parameters k, h,..., q take values from {1, 2,..., n}, representing each representative multi-parameter load cycle spectrum block, from which the parameter expression of the multi-parameter fatigue test spectrum model is obtained. Among them, the average load amplitude parameter is obtained from the statistical measurement of the load, and the phase parameter and the load combination cycle number are optimized according to the following step (53) based on the principle of consistent damage.

[0130] (2) According to the finite element principle, convert the preprocessed 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; the specific steps are as follows:

[0131] (21) Determine the stress-strain history of the fatigue assessment point of the component under the multi-parameter load spectrum. The calculation of the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum is carried out with the help of finite element software, including: ① Assigning material properties and element types, ② Component modeling and mesh generation, ③ Solving multiple load steps, ④ Stress-strain data analysis;

[0132] (22) 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:

[0133] σ(c,t) = K σ (c)·F(t)

[0134] ε(c,t) = K ε (c)·F(t)

[0135] 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 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:

[0136]

[0137] 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 in 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 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, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),... F m (t) represents the m-way external load borne by the component;

[0138] Perform a multiple linear equation calculation based on the stress-strain history obtained in the above step (21) to obtain the coefficient matrix K σ (c), K ε (c) numerical solution.

[0139] (3) Discretize the stress-strain history of the fatigue assessment point in time, and determine the critical plane using the weight function based on the time-varying damage parameter; the specific steps are as follows:

[0140] ((31) Set the discretization variable s, and select the discrete time interval Δt for each load history according to the sampling time ΔT of the original load. The relationship between the variables is as follows:

[0141] ΔT = s·Δt

[0142] T = N·ΔT

[0143] where T and N are the total sampling time and total number of samples of the original load. Thus, the original load history σ(c,t), ε(c,t) with a time interval of ΔT is refined into discrete data of the load time history with a time interval of Δt

[0144] ((32) According to the discrete data of the load time history obtained in step (31) For the strain data at each discrete load point, determine the position of the critical plane (θ cr (t p ), φ cr (t p )) of the spatial arbitrary plane by calculating the shear strain through coordinate rotation, and then perform a weighted average of the critical plane positions of the load history according to the weight function to obtain the weighted critical plane of the fatigue damage assessment point. The expression for the strain coordinate rotation calculation is as follows:

[0145] {ε′ xx ε′ yy ε′ zz γ′ yz γ′ xz γ′ xy} T =[Φ ε {ε xxε yy ε zz γ yz γ xz γ xy} T

[0146] {σ′ xx σ′ yy σ′ zz τ′ yz τ′ xz τ′ xy} T =[Φ σ {σ xx σ yy σ zz τ yz τ xz τ xy} T

[0147] Among them,

[0148] Among them, the θ angle and the φ angle are coordinate rotation variables. θ is the angle between the projection of the X'-axis of the new coordinate system (X'-Y'-Z') on the X-Y plane and the X-axis, and φ is the angle between the X'-axis and the Z-axis; σ xx 、σ yy 、σ zz 、τ yz 、τ xz 、τ xy respectively represent the normal stress and shear stress in the (X-Y-Z) coordinate system, and their subscripts correspond to the coordinate system directions; ε xx 、ε yy 、ε zz 、γ yz 、γ xz 、γ xy respectively represent the normal strain and shear strain in the (X-Y-Z) coordinate system, σ′ xx 、σ′ yy 、σ′ zz 、τ′ yz 、τ′ xz 、τ′ xy respectively represent the normal stress and shear stress in the (X'-Y'-Z') coordinate system, and their subscripts correspond to the coordinate system directions; ε′ xx 、ε′ yy 、ε′ zz 、γ′ yz 、γ′ xz 、γ′ xy respectively represent the normal strain and shear strain in the (X'-Y'-Z') coordinate system; [Φ ε 、[Φ σ] represents the strain and stress rotation matrix;

[0149] The stress coordinate rotation calculation only needs to transform the corresponding response into stress, that is, σ x , σ y , σ z Replace ε x , ε y , ε z , τ yz , τ xz , τ xy Replace 1 / 2γ yz , 1 / 2γ xz , 1 / 2γ xy ; Based on the assumption that the damage parameters at each moment have the same influence on the critical plane, the weight function is defined as:

[0150]

[0151] Among them, τ -1 is the shear fatigue limit, G is the shear modulus, c is a constant coefficient, and its range is (0,1], D(t p ) is the maximum shear strain γ max (t p ) The corresponding fatigue damage is calculated as follows:

[0152]

[0153] D(t p )=1 / N p

[0154] Where E is the elastic modulus of the material, N p is the multiaxial fatigue life, σ′ f , b, ε′ f , c represent fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient and fatigue ductility index respectively;

[0155] According to the critical plane (θ cr (t p ),φ cr (t p )), perform weighted averaging as follows:

[0156]

[0157] in, is the weighted critical plane position, and W is the sum of weight coefficients.

[0158] (4) Calculate the total cumulative damage of the original load spectrum based on the multiaxial fatigue damage model; the specific steps are:

[0159] (41) Based on the critical plane obtained in step (3), the original multi-parameter random load history of the component assessment point is transformed into the stress-strain history on the critical plane, and its calculation expression is as follows:

[0160]

[0161] Among them, respectively represent the strain-stress coordinate rotation matrix determined by the weighted critical plane position obtained in step (32);

[0162] (42) Using the multi-axial cyclic counting method, the original multi-parameter random load history of the component is transformed into a series of stress and strain cycles. Then, the fatigue damage of each cycle is calculated using the multi-axial fatigue damage model, and the multi-axial damage accumulation of the entire original load spectrum is carried out. Thus, the total multi-axial fatigue damage D of the original load spectrum is obtained squence , as shown below:

[0163] N f =f(σ cr ,ε cr )

[0164]

[0165] Among them, N f 、σ cr 、ε cr represent the life, stress and strain in the multi-axial fatigue damage model; n i represents the number of cycles of the load cycle, and N i represents the multi-axial fatigue life of the load cycle.

[0166] (5) Based on the linear equations of the weight function critical plane, local stress-strain and component load, establish the relationship between external load and multi-axial damage, determine the multi-axial fatigue damage values of a series of representative load cycle combinations, and optimize and search for solutions for the optimization parameters of the multi-parameter fatigue test spectrum model established in step (1) above according to the principle of damage consistency; the specific steps are as follows:

[0167] (51) Based on the direction of the weight function critical plane obtained in step (3), and the linear equations of local stress-strain and component load, establish the relationship between external load and multi-axial damage, and calculate the damage of a series of typical load cycle combinations according to the damage calculation method in step (4). Among them, the stress-strain and external load cycle relationship formula on the critical plane is as follows:

[0168]

[0169] Among them, F1(t), F2(t),..., F m (t) represent the external loads borne by the component; [K σ , [Kε is the coefficient matrix of the stress and strain determined in step (22) with respect to the external load matrix, {(A 1,k , M 1,k ), (A 2,h , M 2,h ),..., (A m,q , M m,q )} is determined by step (1), and the phase information and load cycle number among the loads of each channel, that is, are optimally selected by the following step (53), that is, the optimization vector is

[0170] (52) Optimize and search for the solution of the optimization parameters of the multi-parameter fatigue test spectrum model established in step (1) according to the principle of damage consistency, where the load combination cycle number satisfies the following proportional relationship:

[0171] ......

[0173]

[0174] where, represents the cycle number of each load combination, represents the cycle number of the i-th load and the j-th load level of the original load spectrum;

[0175] (53) Based on the above multi-parameter fatigue test spectrum load parameter model, the average amplitude load level information, and the load cycle ratio equation, perform multi-variable optimization search. The optimization goal is that the total damage of each representative load cycle combination 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 (42), and its optimization objective function is as follows:

[0176]

[0177] where, (N k,h,...,q ) k,h,...,q∈{1,2,3,..,n} ∈ N (natural number);

[0178] where, D squence represents the multi-axial fatigue total damage of the original load spectrum, and D block,j represents the multi-axial fatigue total damage of each load combination cycle spectrum block; respectively represent the phase and cycle number of each load combination cycle spectrum block;

[0179] Thus, the load average amplitude, phase difference, and load combination cycle number information of the component multi-parameter fatigue test load spectrum block consistent with the damage of the original load spectrum are obtained.

[0180] (6) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the load characteristics and damage of the original load spectrum.

[0181] The present invention will be further described below in conjunction with embodiments and the accompanying drawings.

[0182] Embodiment

[0183] An example analysis of the present invention is carried out with the random tensile-torsional load spectrum of a hollow thin-walled open cylindrical member.

[0184] The specific steps of step (1) are as follows:

[0185] (11) Perform peak-valley value detection and rain-flow cycle counting processing on the multi-parameter random load spectrum of complex mechanical components (such as Figure 1 ). Among them, peak-valley value detection is to judge the peak or valley points of each load time history. If so, retain them; otherwise, remove them. The data is judged by the three-point method, that is, read three adjacent data points F(i - 1), F(i), F(i + 1). If the following conditions are met:

[0186] [F(i) - F(i - 1)][F(i + 1) - F(i)] ≥ 0 and F(i) - F(i - 1) ≠ 0

[0187] Then F(i) is a peak point or a valley point. For example, Figure 2 is the external load time history curve of the component after removing non-peak-valley data points. Among them, the tensile load is reduced from 500 load data points to 350 data points, and the torsional load is reduced from 500 data points to 331 data points.

[0188] Rain-flow cycle counting is to extract the full load cycle of the load history based on the principle of the material stress-strain hysteresis loop. Continuously read four points in the load history, that is, two peaks and two valleys. The basis for selecting the full cycle is: the absolute value of the difference between the middle two points is less than the sum of the absolute values of the differences between the previous two points and the differences between the following two points, that is, the following conditions are met:

[0189] |F(i + 2) - F(i + 1)| ≤ |F(i + 1) - F(i)|

[0190] |F(i + 2) - F(i + 1)| ≤ |F(i + 3) - F(i + 2)|

[0191] From this, the statistical results of the peak-valley values of the full load cycle of each load path can be obtained. Further, the statistical information of the average amplitude of the full load cycle can be obtained. Its calculation expression is as follows:

[0192] C amp =(F peak -F valley ) / 2

[0193] C mean = (F peak + F valley ) / 2

[0194] wherein, F peak and F valley respectively represent the peak value and the valley value of the rainflow counting cycle; C amp and C mean respectively represent the amplitude value and the valley value of the rainflow counting cycle. As Figure 3 is the three-dimensional frequency histogram of the average amplitude of the random tensile load and torsional load borne by the component in this example after rainflow statistics.

[0195] (12) Based on the statistical information of the average amplitude of the full cycle of the load in the above step (11), draw a load cumulative frequency curve with the load amplitude as the vertical coordinate and the cumulative frequency as the horizontal coordinate (as Figure 4 ), and further, discretely divide the load amplitude interval into discrete levels by using the equal interval method or according to the actual load distribution based on the cumulative frequency curve, determine the load amplitudes of each level of stepped load. In this example, a three-level equal interval division method is adopted, and the tensile load amplitudes (A 1,1 , A 1,2 , A 1,3 ) and torsional load amplitudes (A 2,1 , A 2,2 , A 2,3 ) can be obtained. As shown by the horizontal dotted line in Figure 5 , use the principle of equal damage interval to determine the load frequencies corresponding to each level of load, and thus average the mean values of each level of load to obtain the mean values of each level of stepped load (M 1,1 , M 1,2 , M 1,3 ) and (M 2,1 , M 2,2 , M 2,3 ). From this, a series of representative load cycles of each channel load can be obtained, that is

[0196] Tensile load:

[0197] And torsional load:

[0198] where is the number of cycles of each level of load, j = 1, 2, i = 1, 2, 3. As shown in Figure 5 are the results of level division and the information of representative load cycles.

[0199] (13) Further, based on the series of representative load cycles determined for each load path, perform as Figure 6By traversing and matching the combinations of the multi-parameter load spectra shown, a multi-parameter fatigue test spectrum model that fully encompasses the characteristics of the actual multi-parameter loads can be obtained. Among them, the number of load matching combinations is 9, that is, 9 multi-parameter load spectrum blocks are generated. Each spectrum block parameter includes 4 average amplitude parameters for each load path, 1 phase parameter, and 1 load combination cycle number, that is

[0200]

[0201] Among them, each represents a representative multi-parameter load cycle combination spectrum block. Thus, the parameter expression of the multi-parameter fatigue test spectrum model can be obtained. The average amplitude parameter of the load can be obtained from the statistics of the measured load, such as Figure 5 shown, while the phase parameter and the load combination cycle number are optimized based on the damage consistency principle in the following step (53).

[0202] The specific steps of the said step (2) are as follows:

[0203] (21) Determine the stress-strain history of the fatigue assessment point of the component under the multi-parameter load spectrum,

[0204] 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 Component modeling and mesh generation, ③ Solving with multiple load steps, ④ Stress-strain data analysis. The stress and strain time history curves of the fatigue damage assessment point are as Figure 7 、 Figure 8 .

[0205] (22) 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:

[0206] σ(c,t) = K σ (c)·F(t)

[0207] ε(c,t) = K ε (c)·F(t)

[0208] 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 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:

[0209]

[0210] 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 in 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 m (t) represents the m - way external load borne by the component.

[0211] According to the stress - strain history obtained in step (21), perform a multiple linear equation calculation to obtain the coefficient matrix K σ (c), K ε (c) numerical solution, for this example, the calculation is as follows:

[0212]

[0213] The specific steps of the said step (3) are as follows:

[0214] (31) Let the dispersion variable s = 10, select the discrete time interval Δt = 0.1 for each load history according to the sampling time ΔT = 1 of the original load. The relationship between variables is as follows:

[0215] ΔT = s·Δt

[0216] T = N·ΔT

[0217] where T and N are the total sampling time and total number of samples of the original load. Based on the above - mentioned dispersion variable, discretize the stress - strain history of the fatigue assessment point in time, and thus refine the original load history σ(c, t), ε(c, t) with ΔT as the time interval into discrete data of the load - time history with Δt as the load time interval

[0218] (32) According to the discrete data of the load - time history obtained in step (31), for the strain data of each discrete load point, determine the critical plane position (θ cr (t p ), φ cr (t p )) of the space arbitrary plane by coordinate rotation calculation for the shear strain at this discrete load time point, as Figure 9It is a schematic diagram of three-dimensional coordinate rotation and strain on an arbitrary plane. Then, according to the weight function, the critical plane positions of the load history are weighted and averaged to obtain the weighted critical plane of this fatigue damage assessment point. The calculation expression for strain coordinate rotation is as follows:

[0219] {ε′ xx ε′ yy ε′ zz γ′ yz γ′ xz γ′ xy} T =[Φ ε {ε xx ε yy ε zz γ yz γ xz γ xy} T

[0220] {σ′ xx σ′ yy σ′ zz τ′ yz τ′ xz τ′ xy} T =[Φ σ {σ xx σ yy σ zz τ yz τ xz τ xy} T

[0221] Where, where the angles θ and φ are coordinate rotation variables. θ is the angle between the projection of the X'-axis of the new coordinate system (X'-Y'-Z') on the X-Y plane and the X-axis, and φ is the angle between the X'-axis and the Z-axis; σ xx 、σ yy 、σ zz 、τ yz 、τ xz 、τ xy respectively represent the normal stress and shear stress in the (X-Y-Z) coordinate system, and their subscripts correspond to the coordinate system directions; ε xx 、ε yy 、ε zz 、γ yz 、γ xz 、γ xy respectively represent the normal strain and shear strain in the (X-Y-Z) coordinate system, σ′ xx 、σ′ yy 、σ′ zz 、τ′ yz 、τ′xz , τ′ xy respectively represent the normal stress and shear stress in the (X′-Y′-Z′) coordinate system, and their subscripts correspond to the coordinate system directions; ε′ xx , ε′ yy , ε′ zz , γ′ yz , γ′ xz , γ′ xy respectively represent the normal strain and shear strain in the (X′-Y′-Z′) coordinate system; [Φ ε , [Φ σ represent the strain and stress rotation matrices.

[0222] For stress coordinate rotation calculation, only the corresponding strain needs to be transformed into stress, that is, σ x , σ y , σ z replace ε x , ε y , ε z , τ yz , τ xz , τ xy replace 1 / 2γ yz , 1 / 2γ xz , 1 / 2γ xy . Based on the assumption that the influence of the damage parameter at each moment on the critical plane is the same, the weight function is defined as:

[0223]

[0224] where τ -1 is the shear fatigue limit, G is the shear modulus, c is a constant coefficient, and its variation range is (0, 1], D(t p ) is the fatigue damage corresponding to the maximum shear strain γ max (t p ), and its calculation expression is:

[0225]

[0226] D(t p ) = 1 / N p

[0227] where E is the elastic modulus of the material, N p is the multiaxial fatigue life, σ′ f , b, ε′ f , c respectively represent the fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient, and fatigue ductility index.

[0228] Furthermore, according to the critical plane (θ cr (t p ), φcr (t p )) is weighted averaged, and its general form is as follows:

[0229]

[0230] Wherein, is the weighted critical plane position, and W is the total weight coefficient.

[0231] The specific steps of the said step (4) are as follows:

[0232] (41) Based on the critical plane obtained in the above step (3), the original multi-parameter random load history of the component assessment point is transformed into the stress and strain history on the critical plane, and its calculation expression is as follows:

[0233]

[0234] Wherein, respectively represent the strain-stress coordinate rotation matrix determined by the weighted critical plane position obtained in step (32).

[0235] (42) In this example, the multi-axial cyclic counting method proposed by Wang-Brown 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 amplitude γ max 、the maximum positive strain increment δε n and the mean normal stress σ n,mean in each cycle are obtained, and its calculation expression is as follows:

[0236]

[0237] Wherein, v is the total number of discrete load steps in the load cycle, and r, s are the discrete load step numbers.

[0238] Furthermore, the fatigue damage of each cycle is calculated by using the Wang-Brown multi-axial fatigue damage model, and the multi-axial damage accumulation of the entire original load spectrum is carried out. Thus, the multi-axial fatigue total damage D squence of the original load spectrum can be obtained, which is expressed as follows:

[0239]

[0240]

[0241] Wherein, γ max 、δε n 、σ n,mean respectively represent the maximum shear strain, the maximum positive strain increment and the mean normal stress on the critical plane; υ′, E are the equivalent Poisson's ratio and elastic modulus of the material, S is the material constant; N f is the multi-axial fatigue life, σ′f , b, ε′ f , c represent the fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, and fatigue ductility exponent respectively; n i represents the number of cycles of the load cycle, N i represents the multiaxial fatigue life of the load cycle.

[0242] The specific steps of step (5) are as follows:

[0243] (51) Based on the critical plane direction of the weight function obtained in the above step (3) and the linear equation of the local stress-strain and the component load, establish the relationship between the external load and the multiaxial damage. Calculate the damage of a series of typical load cycle combinations according to the damage calculation method in the above step (4). The stress-strain and external load cycle relationship on the critical plane is as follows:

[0244]

[0245] Among them, F1(t), F2(t),..., F m (t) represents the external load borne by the component; [K σ , [K ε are the coefficient matrices of the stress and strain with respect to the external load matrix determined in step (22). {(A 1,k , M 1,k ), (A 2,q , M 2,q )} are determined by the above step (1), and the phase information between the loads of each channel and the number of load cycles, that is, is optimized and selected by the following step (53), that is, the optimization vector is

[0246] (52) Optimize and search for the solution of the optimization parameters of the multi-parameter fatigue test spectrum model established in the above step according to the principle of damage consistency. The number of cycles of the load combination satisfies the following proportional relationship:

[0247]

[0248] Among them, N k,h (k, h ∈ {1, 2, 3}) represents the number of cycles of each load combination, represents the number of cycles of the i-th load of the original load spectrum at the j-th load level.

[0249] (53) Further, based on the above multi-parameter fatigue test spectrum load parameter model, the average amplitude load level information, and the load cycle ratio equation, multi-variable optimization search can be performed. The optimization objective is that the total damage of each representative load cycle combination 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 (42) above, and its optimization objective function is as follows:

[0250]

[0251] Wherein, (N k,q ) k,q∈{1,2,3} ∈ N (natural numbers).

[0252] Thus, the load average amplitude, phase difference, and load combination cycle number information of the multi-parameter fatigue test load spectrum block consistent with the damage of the original load spectrum can be obtained. Thus, according to this example, optimization search is performed, Figure 10 which is the optimization information of the multi-parameter fatigue test load spectrum block consistent with the damage of the component.

[0253] The specific steps of step (6) are as follows:

[0254] Randomly splice each multi-parameter load combination spectrum block, and a multi-parameter fatigue test spectrum consistent with the load characteristics and damage of the original load spectrum can be obtained, such as Figure 11 、 Figure 12 the multi-parameter program fatigue test spectra with different spectrum block orderings shown.

[0255] The above is only a specific implementation manner of the present invention, and the purpose, technical solution, and beneficial effects of the present invention have been further described in detail. Finally, it should be noted that the above is only the preferred embodiment of the present invention and does not impose any formal restrictions on the present invention. For those engaged in research and technology in this technical field, without departing from the scope of the technical solution of the present invention, non-innovative refinements, changes, and modifications made to the technical solution of the present invention using the above content shall 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 damage equivalence, characterized in that: Including the following steps: (1) Conduct peak-valley value detection and rain-flow cycle counting on the multi-parameter random load spectrum of complex mechanical components to obtain the statistical results of the load amplitude and mean value for each load. Use the load cumulative frequency curve to classify the load amplitude levels, and average the mean values accordingly. Thus, a series of representative load cycles for each load path are obtained. Then, match and combine the multi-parameter loads from the typical load cycle series to obtain a multi-parameter fatigue test spectrum model that fully contains the characteristics of the actual multi-parameter loads; The specific steps of step (1) are as follows: (11) Conduct peak-valley value detection and rain-flow cycle counting on the multi-parameter random load spectrum of complex mechanical components. Among them, peak-valley value detection is to judge the peak or valley points for each load time history. If it is, it is retained; otherwise, it is removed. The data is judged by the three-point method, that is, read three adjacent data points F(i - 1), F(i), F(i + 1). If the following conditions are met: [F(i) - F(i - 1)][F(i + 1) - F(i)] ≥ 0 and F(i) - F(i - 1) ≠ 0 where F(i) is the peak point or valley point; Rain-flow cycle counting is to extract the full load cycles of the load history based on the principle of the material stress-strain hysteresis loop. Continuously read four points in the load history, that is, two peaks and two valleys. The basis for selecting the full cycle is that the absolute value of the difference between the middle two points is less than the sum of the absolute values of the differences between the previous two points and the differences between the latter two points, that is, the following conditions are met: |F(i + 2) - F(i + 1)| ≤ |F(i + 1) - F(i)| |F(i + 2) - F(i + 1)| ≤ |F(i + 3) - F(i + 2)| Thus, the statistical results of the peak-valley values of the full load cycles of each load path are obtained, and then the statistical information of the average amplitude of the full load cycles is obtained. Its calculation expression is as follows: C amp = (F peak - F valley ) / 2 C mean = (F peak + F valley ) / 2 Among them, F peak and F valley respectively represent the peak value and the valley value of the rainflow counting cycle; C amp and C mean respectively represent the amplitude and the mean value of the rainflow counting cycle. (12) Based on the statistical information of the average amplitude of the full load cycle in step (11), a load cumulative frequency curve is plotted with the load amplitude as the vertical coordinate and the cumulative frequency as the horizontal coordinate. According to the cumulative frequency curve, the load amplitude interval is discretely graded using the equal interval method or according to the actual load distribution to determine the load amplitudes of each level of step loads, that is, (A j,1 , A j,2 ,..., A j,n ). Using the principle of equal damage intervals, the load frequencies corresponding to each level of load are determined, and then the average value of each level of load mean is obtained, that is, the load means of each level of step loads (M j,1 , M j,2 ,..., M j,n ). Thus, a series of representative load cycles of the j-th load path are obtained, that is, or {(A j,1 , M j,1 , η j,1 ), (A j,2 , M j,2 , η j,2 ),..., (A j,n , M j,n , η j,n )} Among them, is the number of cycles of each level of load, j = 1, 2,..., m, i = 1, 2,..., n, m is the number of load channels, n is the number of levels into which each load is divided, and η j,i is the proportion of the normalized number of cycles of each level of load, and its calculation expression is as follows: (13) Based on the series of representative load cycles determined for each load path, traverse and match the combinations of multi-parameter load spectra, and a multi-parameter fatigue test spectrum model that fully encompasses the actual multi-parameter load characteristics can be obtained. The number of load matching combinations is n m , that is, n m multi-parameter load spectrum blocks are generated. The parameters of each spectrum block include a total of 2m average amplitude parameters (A, M) for each load path, a total of m - 1 phase parameters, and 1 load combination cycle number, that is ...... where the m parameters k, h,..., q take values from {1, 2,..., n}, representing each representative multi-parameter load cycle spectrum block, and thus the parameter expression of the multi-parameter fatigue test spectrum model is obtained; (2) According to the finite element principle, convert the preprocessed 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; (3) Discretize the stress-strain history of the fatigue assessment point in time, and determine the critical plane using the weight function based on the time-varying damage parameter; (4) Calculate the total cumulative damage of the original load spectrum according to the multiaxial fatigue damage model; (5) Based on the critical plane of the weight function and the linear equation of the local stress-strain and the component load, establish the relationship between the external load and the multiaxial damage, determine the multiaxial fatigue damage values of the series of representative load cycle combinations, and optimize and search for solutions for the optimization parameters of the multi-parameter fatigue test spectrum model established in step (1) above according to the principle of damage consistency; (6) Randomly splice each level of load to synthesize a multi-parameter fatigue test spectrum that is consistent with the load characteristics and damage of the original load spectrum; 2. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 1, wherein: The specific steps of step (2) are as follows: (21) Determine the stress-strain history of the fatigue assessment point of the component under the multi-parameter load spectrum. The calculation of the stress-strain history of the fatigue assessment point under the multi-parameter load spectrum is carried out with the aid of finite element software, including: ① Assigning material properties and element types; ② Modeling the component and meshing; ③ Solving with multiple load steps; ④ Analyzing stress and strain data. (22) Solve the linear equation of the local stress and 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 respectively the coefficient matrices of stress and strain with respect to the external load matrix, 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) respectively represent the normal stress and shear stress in the xyz coordinate system, 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) respectively represent the normal strain and shear strain in the xyz coordinate system, and their subscripts correspond to the coordinate system directions; F1(t), F2(t),... F m (t) represents the m - path external load borne by the component; Perform a multiple linear equation calculation based on the stress-strain history obtained in the above step (21) to obtain the coefficient matrix K σ (c), K ε (c) numerical solution.

3. The multi-parameter fatigue test spectrum compilation method based on damage equivalence according to claim 1, characterized in that: The specific steps of step (3) are as follows: (31) Set the dispersion variable s, and select the discrete time interval Δt of each load history according to the sampling time ΔT of the original load. The relational expression between the variables is as follows: ΔT = s·Δt T = N·ΔT 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. (32) Discrete data of the load time history according to step (31) For the strain data at each discrete load point, the critical plane position (θ cr (t p ), φ cr (t p )) of any plane in space is determined by calculating the shear strain through coordinate rotation at this discrete load time point. Then, the weighted average of the critical plane positions of the load history is performed according to the weight function to obtain the weighted critical plane of this fatigue damage assessment point. The expression for the strain coordinate rotation calculation is as follows: {ε′ xx ε′ yy ε′ zz γ′ yz γ′ xz γ′ xy} T =[Φ ε {ε xx ε yy ε zz γ yz γ xz γ xy} T {σ′ xx σ′ yy σ′ zz τ′ yz τ′ xz τ′ xy} T =[Φ σ {σ xx σ yy σ zz τ yz τ xz τ xy} T Among them, Among them, the θ angle and the φ angle are coordinate rotation variables. θ is the angle between the projection of the X'-axis of the new coordinate system (X'-Y'-Z') on the X-Y plane and the X-axis, and φ is the angle between the X'-axis and the Z-axis; σ xx 、σ yy 、σ zz 、τ yz 、τ xz 、τ xy respectively represent the normal stress and shear stress in the (X-Y-Z) 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 (X-Y-Z) coordinate system, σ' xx 、σ' yy 、σ' zz 、τ' yz 、τ' xz 、τ' xy respectively represent the normal stress and shear stress in the (X'-Y'-Z') 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 (X'-Y'-Z') coordinate system; [Φ ε 、[Φ σ represent the strain and stress rotation matrices; The stress coordinate rotation calculation only needs to transform the corresponding strain into stress, that is, σ x , σ y , σ z replace ε x , ε y , ε z , τ yz , τ xz , τ xy replace 1 / 2γ yz , 1 / 2γ xz , 1 / 2γ xy ; and based on the assumption that the influence of the damage parameter at each moment on the critical plane is the same, the weight function is defined as: Among them, τ -1 is the shear fatigue limit, G is the shear modulus, c is a constant coefficient, and its variation range is (0, 1], D(t p ) is the fatigue damage corresponding to the maximum shear strain γ max (t p ), and its calculation expression is: D(t p ) = 1 / N p where E is the elastic modulus of the material, N p is the multiaxial fatigue life, and σ′ f , b, ε′ f , and c represent the fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, and fatigue ductility exponent, respectively; According to the critical plane (θ cr (t p ), φ cr (t p )) at each moment in the load history, weighted averaging is performed as follows: Among them, is the weighted critical plane position, and W is the total weight coefficient.

4. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 3, wherein: The specific steps of step (4) are as follows: (41) Based on the critical plane obtained in step (3), convert the original multi-parameter random load history of the component assessment point into the stress-strain history on the critical plane, and its calculation expression is as follows: Among them, respectively represent the strain-stress coordinate rotation matrix determined by the weighted critical plane position obtained in step (32); (42) The original multi-parameter random load history of the component is converted into a series of stress and strain cycles by using the multi-axis cyclic counting method. 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, so as to obtain the total multi-axis fatigue damage D of the original load spectrum squence , which is shown as follows: N f = f(σ cr , ε cr ) Among them, N f , σ cr , ε cr represent the life, stress and strain in the multiaxial fatigue damage model; n i represents the number of cycles of the load cycle, and N i represents the multiaxial fatigue life of the load cycle.

5. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 4, wherein: The specific steps of step (5) are as follows: (51) Based on the critical plane direction of the weight function obtained in step (3) and the linear equation of the local stress and strain and the component load, establish the relationship between the external load and the multiaxial damage, and calculate the damage of a series of typical load cycle combinations according to the damage calculation method in step (4). The relational expression between the stress and strain on the critical plane and the external load cycle is as follows: Among them, F1(t), F2(t),..., F m (t) represents the external loads borne by the component; [K σ , [K ε are the coefficient matrices of stress and strain determined in step (22) with respect to the external load matrix, {(A 1,k , M 1,k ), (A 2,h , M 2,h ),..., (A m,q , M m,q )} is determined in step (1), and the phase information between the loads of each channel and the number of load cycles, that is is optimally selected by the following step (53), that is, the optimization vector is (52) Optimize and search for the optimization parameters of the multi-parameter fatigue test spectrum model established in step (1) according to the principle of damage consistency. The number of load combination cycles satisfies the following proportional relational expression: ...... Among them, represents the number of cycles of each load combination, (i ∈ {1, 2, 3,.., m}, j ∈ {1, 2, 3,.., n}) represents the number of cycles of the i-th load path and the j-th load level of the original load spectrum; (53) Based on the above multi-parameter fatigue test spectrum load parameter model, the average amplitude load level information, and the load cycle ratio equation, conduct a multi-variable optimization search. The optimization goal is that the total damage of each representative load cycle combination 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 (42), and its optimization objective function is as follows: Among them, (N k,h,...,q ) k,h,...,q∈{1,2,3,..,n} ∈ N (natural numbers); 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 load combination cyclic spectrum block; (i ∈ {1, 2, 3,.., m}), N k,h,...,q (k, h,..., q ∈ {1, 2, 3,.., n}) respectively represent the phase and the number of cycles of each load combination cyclic spectrum block; Thus, the load average amplitude, phase difference, and load combination cycle number information of the multi-parameter fatigue test load spectrum block of the component that is consistent with the damage of the original load spectrum are obtained.

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