CN114036654A - Random multi-parameter fatigue test spectrum compiling method based on damage equivalence - Google Patents

Abstract

The invention discloses a multi-parameter fatigue test spectrum compiling method based on damage equivalence, which comprises the following steps of: obtaining a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics; converting the preprocessed multi-parameter component load spectrum into a stress-strain history of a fatigue examination point, and solving a linear equation of local stress strain and component load; carrying out time discretization on the stress-strain history of the fatigue examination point, and determining a critical plane by using a weight function based on damage time-varying parameters; calculating the total accumulated damage of the original load spectrum according to the multi-axial fatigue damage model; establishing a relation between an external load and multi-axis damage, and carrying out optimization search solving on an optimization parameter of a multi-parameter fatigue test spectrum model; and randomly splicing each level of load, and synthesizing a multi-parameter fatigue test spectrum with the same load characteristics and damage as the original load spectrum. The invention realizes the load characteristic consistency and the damage consistency in the multi-parameter fatigue test load spectrum compilation process.

Description

Random multi-parameter fatigue test spectrum compiling method based on damage equivalence

Technical Field

The invention belongs to the technical field of mechanical structure fatigue test load spectrum compilation, and particularly relates to a method for compiling a fatigue test spectrum of a complex mechanical component under a multi-parameter random load, which provides a load basis for multi-axial fatigue damage analysis and multi-axial fatigue test of the mechanical component under the random multi-parameter load and is an important step for life test evaluation of key parts of a engineering complex structure under a multi-parameter actual service load.

Background

At present, the research on fatigue test spectrums at home and abroad mostly focuses on compiling single-parameter fatigue test load spectrums and is widely applied to the industrial fields of aerospace, vehicles, engineering machinery and the like. However, in practical engineering applications, most mechanical components are subjected to random multi-parameter loads for a long time, and the components are often extremely prone to multi-axial fatigue damage and failure. Complex components such as aircraft engine case components, automotive gimbals and front suspensions are often subjected to typical random non-proportional multi-axis loads in actual service. Therefore, the single-parameter fatigue test spectrum is no longer suitable for performing fatigue examination on the components bearing complex multi-parameter loads, and a compiling method of the multi-parameter load fatigue test spectrum must be developed for performing sufficient and scientific service life examination on the components.

When the service life assessment test is carried out on the complex mechanical component, the loaded load spectrum of the complex mechanical component must reflect the actual working characteristics of the component to a certain extent. However, random load borne by the member is not easy to test and load, and a program fatigue test spectrum not only retains load characteristics to a certain extent, but also has simple form and strong operability, and is widely applied. The fighter plane fatigue test program spectrum is compiled by the high-town co-ordinators based on the two-dimensional probability statistics of the load average amplitude; the high cloud Kay also provides a program load spectrum compiling method for a vehicle body rack fatigue test based on the high cloud Kay. However, at present, there is no generally accepted compilation theory and method for a multi-parameter fatigue test program spectrum, only a few students research the multi-parameter fatigue test program spectrum to a certain extent, and people like Yangyong and Zhaoyuan nationality carry out compilation work of the multi-parameter fatigue test spectrum from the perspective of multi-axis fatigue damage, but the values of parameters such as load amplitude and phase have certain subjectivity, and the equivalent fatigue load method proposed and adopted by the mark Xuezilong company optimizes and searches the values to ensure damage consistency and ignores the distribution of the average amplitude of actual load, so that the compiled fatigue test spectrum and the actual service load have certain difference in load characteristics and multi-axis fatigue life expression.

In summary, the existing multi-parameter fatigue test spectrum compiling method has certain limitations, and a clear and generally accepted component multi-parameter fatigue test spectrum compiling method is not provided, so that the requirement of the fatigue damage consistency compiling spectrum is met to different degrees. Under the action of multi-parameter load, compiling a fatigue test spectrum which is consistent with the load characteristics, damage equivalence and failure mode of a component under an actual load spectrum is still a key engineering problem which needs to be solved urgently, and the method has important significance for fatigue damage analysis and fatigue test research of complex mechanical components in engineering practice.

Therefore, a multi-parameter fatigue test spectrum compiling method capable of considering the consistent load characteristics and damage of the engineering complex mechanical components is needed to be developed, and a foundation is laid for the life determination of the complex engineering machinery and parts thereof.

Disclosure of Invention

The invention aims to provide a random multi-parameter fatigue test spectrum compilation method based on damage equivalence, and aims to solve the problem that multi-parameter load correlation consideration is lacked in fatigue test load spectrum compilation in the prior art.

In order to achieve the purpose, the invention adopts the following technical scheme:

a multi-parameter fatigue test spectrum compiling method based on damage equivalence comprises the following steps:

(1) carrying out peak-valley value detection and rain flow cycle counting aiming at a multi-parameter random load spectrum of a complex mechanical component to obtain respective load amplitude and mean value statistical results, carrying out grade division on the load amplitude by utilizing a load accumulation frequency curve, and correspondingly carrying out averaging value taking on the mean value to obtain a series of representative load cycles of each load, and carrying out multi-parameter load matching combination on a typical load cycle series to obtain a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics;

(2) converting the preprocessed multi-parameter component load spectrum into a stress-strain history of a fatigue examination point according to a finite element principle, and solving a linear equation of local stress strain and component load;

(3) carrying out time discretization on the stress-strain history of the fatigue examination point, and determining a critical plane by using a weight function based on damage time-varying parameters;

(4) calculating the total accumulated damage of the original load spectrum according to the multi-axial fatigue damage model;

(5) establishing a relation between external load and multi-axis damage based on a linear equation of a weight function critical plane, local stress strain and component load, determining a series of multi-axis fatigue damage values representing load cycle combination, and performing optimization search solution on the optimization parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency;

(6) and randomly splicing each level of load, and synthesizing a multi-parameter fatigue test spectrum with the same load characteristics and damage as the original load spectrum.

The specific steps of the step (1) are as follows:

(11) carrying out peak-valley value detection and rain flow circulation counting processing aiming at a multi-parameter random load spectrum of a complex mechanical component, wherein the peak-valley value detection is to judge the peak value or the valley value of each load time course, if so, retaining the peak value or the valley value, otherwise, removing the peak value or the valley value, and judging the data by a three-point method, namely reading three adjacent data points F (i-1), F (i) and F (i +1), and if the three adjacent data points are met:

[ F (i) -F (i-1) ] [ F (i +1) -F (i) ] is not less than 0 and F (i) -F (i-1) ≠ 0

Wherein, F (i) is the peak point or the valley point;

and the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of the material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following conditions: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely 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)|

therefore, the statistical result of the load full-cycle peak-valley value of each load is obtained, further the statistical information of the load full-cycle average amplitude value is obtained, and the calculation expression is as follows:

C_amp＝(F_peak-F_valley)/2

C_mean＝(F_peak+F_valley)/2

wherein, F_peak、F_valleyRespectively representing the peak value and the valley value of the rain flow counting cycle; c_amp、C_meanRespectively representing the amplitude and the valley of the rain flow counting cycle;

(12) based on the statistical information of the load full-cycle average amplitude in the step (11), a load accumulated frequency curve is drawn by taking the load amplitude as a vertical coordinate and the accumulated frequency as a horizontal coordinate, discrete grade division is carried out on a load amplitude interval according to the accumulated frequency curve by using an equal interval method or according to actual load distribution, and the load amplitude of each grade is determined, namely (A)_j,1,A_j,2,...,A_j,n) Determining the load frequency corresponding to each level of load by using the principle of equal damage interval, thereby averaging and taking the average value of each level of load to obtain the average value (M) of each level of step load_j,1,M_j,2,...,M_j,n) Thereby obtaining a series of representative load cycles for the jth load, i.e.

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)}

Wherein the content of the first and second substances,

is the number of cycles per load stage, j 1,2,.. the m, i 1,2,.. the n, m is the number of load channels, n is the number of stages per load division, and η is the number of stages per load division_j,iFor the normalized cycle count per load, the calculation expression is as follows:

(13) based on a series of representative load cycles determined by each load, traversing matching combination of multi-parameter load spectrums is carried out, and a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics is obtained, wherein the number of load matching combination is n^mI.e. generating n^mA plurality of multi-parameter load spectrum blocks, wherein each spectrum block parameter comprises 2M load average amplitude parameters (A, M) and phase parameters

M-1 in total and 1 cycle number of load combination, i.e.

......

And m parameters of k, h, and q are taken as values in {1,2, and so, n }, and each representative multi-parameter load cyclic spectrum block is represented, so that parameter expression of the multi-parameter fatigue test spectrum model is obtained.

The specific steps of the step (2) are as follows:

(21) determining the stress-strain history of the fatigue examination point of the component under the multi-parameter load spectrum, wherein the calculation of the stress-strain history of the fatigue examination point under the multi-parameter load spectrum is carried out by means of finite element software, and the calculation comprises the following steps: endowing material attributes and unit types, modeling and grid division of components, multi-load step solving and stress-strain data analysis;

(22) solving a linear equation of the local stress strain and the component load of the fatigue damage check point, wherein the expression is as follows:

σ(c,t)＝K_σ(c)·F(t)

ε(c,t)＝K_ε(c)·F(t)

wherein c is a component fatigue damage checking point, t is a load time, and σ (c, t), ε (c, t) and F (t) are respectively a stress vector, a strain vector and an external load vector of the component fatigue damage checking point, wherein the matrix expression form of the vectors is as follows:

wherein, K_σ(c)、K_ε(c) A matrix of coefficients of stress, strain, respectively, versus external load matrix, and which is constant over the time course of the load; sigma_xx(c,t)、σ_yy(c,t)、σ_zz(c,t)、τ_yz(c,t)、τ_xz(c,t)、τ_xy(c, t) respectively representing the normal stress and the shear stress under an xyz coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx(c,t)、ε_yy(c,t)、ε_zz(c,t)、γ_yz(c,t)、γ_xz(c,t)、γ_xy(c, t) respectively representing positive strain and shear strain under an xyz coordinate system, wherein subscripts of the positive strain and the shear strain correspond to the directions of the coordinate system; f₁(t)、F₂(t)、...F_m(t) represents the m external loads to which the member is subjected;

according to the reaction obtained in the above step (21)Performing multiple linear equation calculation on the force-strain process to obtain a coefficient matrix K_σ(c)、K_ε(c) The numerical solution of (c).

The specific steps of the step (3) are as follows:

(31) setting a discrete degree variable s, selecting a discrete time interval delta T of each load variable according to the sampling time delta T of the original load, wherein the relation among the variables is as follows:

△T＝s·△t

T＝N·△T

wherein T, N represents the total sampling time and total number of samples of the original load, so that the original load history σ (c, T), ε (c, T) with time interval of Δ T is refined into discrete data with time history of Δ T as load

(32) Discrete data of load time history according to step (31)

For the strain data of each discrete load point, determining the critical plane position (theta) of the discrete load time point by calculating the shear strain of any plane in space through coordinate rotation_cr(t_p),φ_cr(t_p) And then carrying out weight averaging on the critical plane position of the load process according to a weight function to obtain a weighted critical plane of the fatigue damage examination point, wherein the strain coordinate rotation calculation expression 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

wherein the content of the first and second substances,

wherein, the theta angle and the phi angle are coordinate rotation variables, the theta is an included angle between the projection of an X ' axis of a new coordinate system (X ' -Y ' -Z ') on an X-Y plane and the X axis, and the phi is an included angle between the X ' axis and the Z axis; sigma_xx、σ_yy、σ_zz、τ_yz、τ_xz、τ_xyRespectively representing normal stress and shear stress under an (X-Y-Z) coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx、ε_yy、ε_zz、γ_yz、γ_xz、γ_xyRespectively represent positive strain and shear strain, sigma 'in a (X-Y-Z) coordinate system'_xx、σ′_yy、σ′_zz、τ′_yz、τ′_xz、τ′_xyRespectively representing normal stress and shear stress under a (X ' -Y ' -Z ') coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon'_xx、ε′_yy、ε′_zz、γ′_yz、γ′_xz、γ′_xyRespectively representing positive strain and shear strain under a (X ' -Y ' -Z ') coordinate system; [ phi ] of_ε]、[Φ_σ]Representing a strain, stress rotation matrix;

the stress coordinate rotation calculation only needs to convert the corresponding strain into stress, i.e. sigma_x、σ_y、σ_zSubstitution of epsilon_x、ε_y、ε_z，τ_yz、τ_xz、τ_xyReplacement 1/2 gamma_yz、1/2γ_xz、1/2γ_xy(ii) a And the influence of the damage parameters on the critical plane based on each moment is the same, and the weight function is defined as:

wherein, tau_-1The range of variation is (0, 1) for shear fatigue limit, G is shear modulus, c is constant coefficient]，D(t_p) Is defined by the maximum shear strain gamma_max(t_p) The corresponding fatigue damage is calculated by the following expression:

D(t_p)＝1/N_p

wherein E is the elastic modulus of the material, N_pIs multiaxial fatigue life, σ'_f、b、ε′_fC represents a fatigue strength coefficient, a fatigue strength index, a fatigue ductility coefficient and a fatigue ductility index, respectively;

according to the critical plane (theta) at each moment in the load course_cr(t_p),φ_cr(t_p) Weight averaging is performed as follows:

wherein the content of the first and second substances,

for weighted critical plane locations, W is the sum of the weight coefficients.

The specific steps of the step (4) are as follows:

(41) converting the original multi-parameter random load history of the component check point into a stress-strain history on the critical plane based on the critical plane obtained in the step (3), wherein the calculation expression is as follows:

wherein the content of the first and second substances,

respectively representing the strain stress coordinate rotation matrixes determined by the weighted critical plane positions obtained in the step (32);

(42) converting the original multi-parameter random load history of the component into a series of stress and strain cycles by using a multi-axis cycle counting method, calculating the fatigue damage of each cycle by using a multi-axis fatigue damage model, and performing multi-axis damage accumulation of the whole original load spectrum to obtain the total damage D of the multi-axis fatigue of the original load spectrum_squenceExpressed as follows:

N_f＝f(σ_cr,ε_cr)

wherein N is_f、σ_cr、ε_crRepresenting the service life and the stress strain in the multi-axial fatigue damage model; n is_iRepresenting the number of cycles of the load cycle, N_iIndicating the multi-axial fatigue life of the load cycle.

The specific steps of the step (5) are as follows:

(51) establishing a relation between external load and multi-axis damage based on the critical plane direction of the weight function obtained in the step (3) and a linear equation of local stress strain and component load, and calculating damage of a series of typical load cycle combinations according to the damage calculation method in the step (4), wherein the relation between stress strain and external load cycle on the critical plane is as follows:

wherein, F₁(t)、F₂(t)、...、F_m(t) represents the external load to which the member is subjected; [ K ]_σ]、[K_ε]A matrix of coefficients of stress, strain versus external load matrix determined for step (22) { (A)_1,k,M_1,k),(A_2,h,M_2,h),...,(A_m,q,M_m,q) Determined by step (1), and phase information between the loads of the channels and the number of load cycles, i.e. the number of load cycles

The optimization selection is carried out by the following step (53), namely, the optimization vector is

(52) Carrying out optimization search solving on the optimized parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency, wherein the load combination cycle number meets the following proportional relation:

......

wherein the content of the first and second substances,

the number of cycles for each combination of loads is indicated,

the cycle number of the ith load and the jth load grade of the original load spectrum is represented;

(53) performing multivariate optimization search based on the multi-parameter fatigue test spectrum load parameter model, the average amplitude load grade information and the load cycle proportion equation, wherein the optimization target is that the total damage of each representative load cycle combined spectrum block after optimization is consistent with the total damage of the original load spectrum; the method for calculating the total damage of the optimized multi-parameter spectrum block is consistent with the step (41), and the optimization objective function is as follows:

wherein the content of the first and second substances,

(N_k,h,...,q)_{k,h,...,q∈{1,2,3,..,n}}e.N (natural number);

wherein D is_squenceTotal damage to multiaxial fatigue, D, representing the original load spectrum_block,jRepresenting the total damage of the multi-axial fatigue of each load combination cycle spectrum block;

N_k,h,...,q(k, h,., q ∈ {1,2, 3., n }) represents the phase and cycle number, respectively, of each load combination cyclic spectrum block;

therefore, the load average amplitude, the phase difference and the load combined cycle number information of the component multi-parameter fatigue test load spectrum block which is consistent with the original load spectrum damage are obtained.

Has the advantages that: the typical load cycle series is selected based on the compiling idea of the single-parameter fatigue test spectrum, and the typical load cycle is used for matching and combining the multi-parameter loads, so that the multi-parameter fatigue test spectrum is compiled by taking damage consistency as an optimization target, and compared with the traditional multi-parameter fatigue test spectrum compiling method, the method has the following beneficial effects:

(1) the method is simple and intuitive, and has clear steps and accurate description;

taking a random multi-parameter component load spectrum as basic spectrum data, respectively carrying out average amplitude statistics based on rain flow counting on each path of load data and dividing a series of typical load cycles, carrying out matching combination of multi-parameter loads by the typical load cycles, determining a critical plane of a component fatigue checking point by using a weight function method, and calculating the cumulative total damage of the original load spectrum by using multi-axis cycle counting and a multi-axis damage model; the relation between the external load and the multi-axis damage is established based on the weight function critical plane, so that the optimization searching and determination based on the damage consistency target are carried out on the cycle number and the load phase of the multi-parameter load spectrum block, the multi-parameter fatigue test spectrum is generated by randomly arranging and connecting the load spectrum blocks, and compared with the compiling method for subjectively selecting a plurality of load parameters to carry out the multi-parameter load spectrum, the compiling method is more reasonable and has stronger universality.

(2) Has wide engineering application value;

the multi-parameter fatigue test spectrum provided by the invention is simple in compiling method and strong in universality, so that under the existing technical condition, the multi-parameter fatigue test spectrum with consistent load characteristics and damage under the conditions of a complex mechanical component and an actual load can be reasonably compiled by using the method, and the method has wide engineering application value.

(3) Researching a new multi-axis damage model and a multi-axis fatigue life analysis method;

the multi-parameter fatigue test spectrum compiling method compiled by the invention can reflect the actual load characteristics and damage characteristics of the component, can provide a load spectrum compiling basis for researching the multi-axial damage and multi-axial fatigue life analysis method under the actual service working condition of the specific mechanical component, and can preliminarily carry out the multi-axial fatigue test of the material level according to the multi-parameter fatigue test spectrum compiled by the invention so as to reduce the design research and development cost and time.

In conclusion, the method provides a basis for multi-axial fatigue damage analysis of the actual complex mechanical component under random multi-parameter load, and provides a basis for multi-parameter fatigue test evaluation of the complex mechanical component.

Drawings

FIG. 1 is a graph of external load time history for an exemplary component of the present invention;

FIG. 2 is a graph of peak to valley detection of the time history of an external load of an exemplary component of the present invention;

FIG. 3 is a statistical histogram of random external load-mean-amplitude rain flows experienced by a component;

FIG. 4 is a graph of the frequency of random external load accumulation for a component;

FIG. 5 is a component load ranking result and representative load cycle information;

FIG. 6 is a schematic diagram of a traversal matching combination of a multi-parameter load spectrum of a component;

FIG. 7 is a stress time history for a fatigue checkpoint for a component;

FIG. 8 is a time history of strain at a component fatigue-checking point;

FIG. 9 is a schematic diagram of three-dimensional coordinate rotation and strain in an arbitrary plane;

FIG. 10 is a graph of damage-consistent multi-parameter fatigue test load spectrum block optimization information;

FIG. 11 is a multi-parameter fatigue test load spectrum (rank one) based on damage equivalence;

fig. 12 is a multi-parameter fatigue test load spectrum based on damage equivalence (rank two).

Detailed Description

The present invention will be further described with reference to examples.

The invention relates to a multi-parameter fatigue test spectrum compiling method based on damage equivalence, which takes a random multi-parameter component load spectrum as basic compiling spectrum data, respectively carries out average amplitude value statistics based on rain flow counting on each path of load data and divides a series of typical load cycles; matching and combining multi-parameter loads by a typical load cycle, and establishing a multi-parameter fatigue test spectrum parameter model containing actual multi-parameter load characteristics; determining a critical plane of a component fatigue checking point by using a weight function method, and calculating the accumulated total damage of an original load spectrum by using multi-axis cycle counting and a multi-axis damage model; establishing a relation between external load and multi-axis damage based on a weight function critical plane, and determining a multi-axis fatigue damage value of a representative load combined cycle; and performing optimization search solving on the parameters such as the cycle number, the phase between loads and the like on the multi-parameter load parameter model according to the principle of damage consistency, and randomly arranging and connecting the optimized multi-parameter load spectrum blocks to generate a multi-parameter fatigue test spectrum with the same load characteristics and damage as the original load spectrum. The method comprises the following specific steps:

(1) carrying out peak-valley value detection and rain flow cycle counting aiming at a multi-parameter random load spectrum of a complex mechanical component to obtain respective load amplitude and mean value statistical results, carrying out grade division on the load amplitude by utilizing a load accumulation frequency curve, and correspondingly carrying out averaging value taking on the mean value to obtain a series of representative load cycles of each load, and carrying out multi-parameter load matching combination on a typical load cycle series to obtain a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics; the method comprises the following specific steps:

(11) carrying out peak-valley value detection and rain flow circulation counting processing aiming at a multi-parameter random load spectrum of a complex mechanical component, wherein the peak-valley value detection is to judge the peak value or the valley value of each load time course, if so, retaining the peak value or the valley value, otherwise, removing the peak value or the valley value, and judging the data by a three-point method, namely reading three adjacent data points F (i-1), F (i) and F (i +1), and if the three adjacent data points are met:

[ F (i) -F (i-1) ] [ F (i +1) -F (i) ] is not less than 0 and F (i) -F (i-1) ≠ 0

Wherein, F (i) is the peak point or the valley point;

and the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of the material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following conditions: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely 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)|

therefore, the statistical result of the load full-cycle peak-valley value of each load is obtained, further the statistical information of the load full-cycle average amplitude value is obtained, and the calculation expression is as follows:

C_amp＝(F_peak-F_valley)/2

C_mean＝(F_peak+F_valley)/2

wherein, F_peak、F_valleyRespectively representing the peak value and the valley value of the rain flow counting cycle; c_amp、C_meanRespectively representing the amplitude and the valley of the rain flow counting cycle;

(12) based on the statistical information of the load full-cycle average amplitude in the step (11), a load accumulated frequency curve is drawn by taking the load amplitude as a vertical coordinate and the accumulated frequency as a horizontal coordinate, discrete grade division is carried out on a load amplitude interval according to the accumulated frequency curve by using an equal interval method or according to actual load distribution, and the load amplitude of each grade is determined, namely (A)_j,1,A_j,2,...,A_j,n) Determining the load frequency corresponding to each level of load by using the principle of equal damage interval, thereby averaging and taking the average value of each level of load to obtain the average value (M) of each level of step load_j,1,M_j,2,...,M_j,n) Thereby obtaining a series of representative load cycles for the jth load, i.e.

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)}

Wherein the content of the first and second substances,

is the number of cycles per load stage, j 1,2,.. the m, i 1,2,.. the n, m is the number of load channels, n is the number of stages per load division, and η is the number of stages per load division_j,iFor the normalized cycle count per load, the calculation expression is as follows:

(13) based on a series of representative load cycles determined by each load, traversing matching combination of multi-parameter load spectrums is carried out, and a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics is obtained, wherein the number of load matching combination is n^mI.e. generating n^mA plurality of multi-parameter load spectrum blocks, wherein each spectrum block parameter comprises 2M load average amplitude parameters (A, M) and phase parameters

M-1 in total and 1 cycle number of load combination, i.e.

......

And m parameters of k, h, and q are taken as values in {1,2, and so, n }, and each representative multi-parameter load cycle spectrum block is represented, so that parameter expression of the multi-parameter fatigue test spectrum model is obtained, wherein the load average amplitude parameter is obtained by actual measurement load statistics, and the phase parameter and the load combination cycle number are optimized and taken by the following step (53) based on a damage consistency principle.

(2) Converting the preprocessed multi-parameter component load spectrum into a stress-strain history of a fatigue examination point according to a finite element principle, and solving a linear equation of local stress strain and component load; the method comprises the following specific steps:

(21) determining the stress-strain history of the fatigue examination point of the component under the multi-parameter load spectrum, wherein the calculation of the stress-strain history of the fatigue examination point under the multi-parameter load spectrum is carried out by means of finite element software, and the calculation comprises the following steps: endowing material attributes and unit types, modeling and grid division of components, multi-load step solving and stress-strain data analysis;

(22) solving a linear equation of the local stress strain and the component load of the fatigue damage check point, wherein the expression is as follows:

σ(c,t)＝K_σ(c)·F(t)

ε(c,t)＝K_ε(c)·F(t)

wherein c is a component fatigue damage checking point, t is a load time, and σ (c, t), ε (c, t) and F (t) are respectively a stress vector, a strain vector and an external load vector of the component fatigue damage checking point, wherein the matrix expression form of the vectors is as follows:

wherein, K_σ(c)、K_ε(c) A matrix of coefficients of stress, strain, respectively, versus external load matrix, and which is constant over the time course of the load; sigma_xx(c,t)、σ_yy(c,t)、σ_zz(c,t)、τ_yz(c,t)、τ_xz(c,t)、τ_xy(c, t) respectively representing the normal stress and the shear stress under an xyz coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx(c,t)、ε_yy(c,t)、ε_zz(c,t)、γ_yz(c,t)、γ_xz(c,t)、γ_xy(c, t) respectively representing positive strain and shear strain under an xyz coordinate system, wherein subscripts of the positive strain and the shear strain correspond to the directions of the coordinate system; f₁(t)、F₂(t)、...F_m(t) represents the m external loads to which the member is subjected;

performing multiple linear equation calculation according to the stress strain history obtained in the step (21) to obtain a coefficient matrix K_σ(c)、K_ε(c) The numerical solution of (c).

(3) Carrying out time discretization on the stress-strain history of the fatigue examination point, and determining a critical plane by using a weight function based on damage time-varying parameters; the method comprises the following specific steps:

(31) setting a discrete degree variable s, selecting a discrete time interval delta T of each load variable according to the sampling time delta T of the original load, wherein the relation among the variables is as follows:

△T＝s·△t

T＝N·△T

wherein T, N represents the total sampling time and total number of samples of the original load, so that the original load history σ (c, T), ε (c, T) with time interval of Δ T is refined into discrete data with time history of Δ T as load

(32) Discrete data of load time history according to step (31)

For the strain data of each discrete load point, determining the critical plane position (theta) of the discrete load time point by calculating the shear strain of any plane in space through coordinate rotation_cr(t_p),φ_cr(t_p) And then carrying out weight averaging on the critical plane position of the load process according to a weight function to obtain a weighted critical plane of the fatigue damage examination point, wherein the strain coordinate rotation calculation expression 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

wherein the content of the first and second substances,

wherein, the theta angle and the phi angle are coordinate rotation variables, the theta is an included angle between the projection of an X ' axis of a new coordinate system (X ' -Y ' -Z ') on an X-Y plane and the X axis, and the phi is an included angle between the X ' axis and the Z axis; sigma_xx、σ_yy、σ_zz、τ_yz、τ_xz、τ_xyRespectively representing normal stress and shear stress under an (X-Y-Z) coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx、ε_yy、ε_zz、γ_yz、γ_xz、γ_xyRespectively represent positive strain and shear strain, sigma 'in a (X-Y-Z) coordinate system'_xx、σ′_yy、σ′_zz、τ′_yz、τ′_xz、τ′_xyRespectively representing normal stress and shear stress under a (X ' -Y ' -Z ') coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon'_xx、ε′_yy、ε′_zz、γ′_yz、γ′_xz、γ′_xyRespectively representing positive strain and shear strain under a (X ' -Y ' -Z ') coordinate system; [ phi ] of_ε]、[Φ_σ]Representing a strain, stress rotation matrix;

the stress coordinate rotation calculation only needs to convert the corresponding strain into stress, i.e. sigma_x、σ_y、σ_zSubstitution of epsilon_x、ε_y、ε_z，τ_yz、τ_xz、τ_xyReplacement 1/2 gamma_yz、1/2γ_xz、1/2γ_xy(ii) a And the influence of the damage parameters on the critical plane based on each moment is the same, and the weight function is defined as:

wherein, tau_-1The range of variation is (0, 1) for shear fatigue limit, G is shear modulus, c is constant coefficient]，D(t_p) Is defined by the maximum shear strain gamma_max(t_p) The corresponding fatigue damage is calculated by the following expression:

D(t_p)＝1/N_p

wherein E is the elastic modulus of the material, N_pIs multiaxial fatigue life, σ'_f、b、ε′_fC represents a fatigue strength coefficient, a fatigue strength index, a fatigue ductility coefficient and a fatigue ductility index, respectively;

according to the critical plane (theta) at each moment in the load course_cr(t_p),φ_cr(t_p) Weight averaging is performed as follows:

wherein the content of the first and second substances,

for weighted critical plane locations, W is the sum of the weight coefficients.

(4) Calculating the total accumulated damage of the original load spectrum according to the multi-axial fatigue damage model; the method comprises the following specific steps:

(41) converting the original multi-parameter random load history of the component check point into a stress-strain history on the critical plane based on the critical plane obtained in the step (3), wherein the calculation expression is as follows:

wherein the content of the first and second substances,

respectively representing the weighted critical plane position determinations obtained in step (32)A fixed strain stress coordinate rotation matrix;

(42) converting the original multi-parameter random load history of the component into a series of stress and strain cycles by using a multi-axis cycle counting method, calculating the fatigue damage of each cycle by using a multi-axis fatigue damage model, and performing multi-axis damage accumulation of the whole original load spectrum to obtain the total damage D of the multi-axis fatigue of the original load spectrum_squenceExpressed as follows:

N_f＝f(σ_cr,ε_cr)

wherein N is_f、σ_cr、ε_crRepresenting the service life and the stress strain in the multi-axial fatigue damage model; n is_iRepresenting the number of cycles of the load cycle, N_iIndicating the multi-axial fatigue life of the load cycle.

(5) Establishing a relation between external load and multi-axis damage based on a linear equation of a weight function critical plane, local stress strain and component load, determining a series of multi-axis fatigue damage values representing load cycle combination, and performing optimization search solution on the optimization parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency; the method comprises the following specific steps:

(51) establishing a relation between external load and multi-axis damage based on the critical plane direction of the weight function obtained in the step (3) and a linear equation of local stress strain and component load, and calculating damage of a series of typical load cycle combinations according to the damage calculation method in the step (4), wherein the relation between stress strain and external load cycle on the critical plane is as follows:

wherein, F₁(t)、F₂(t)、...、F_m(t) represents the external load to which the member is subjected; [ K ]_σ]、[K_ε]A matrix of coefficients of stress, strain versus external load matrix determined for step (22) { (A)_1,k,M_1,k),(A_2,h,M_2,h),...,(A_m,q,M_m,q) Determined by step (1), and phase information between the loads of the channels and the number of load cycles, i.e. the number of load cycles

The optimization selection is carried out by the following step (53), namely, the optimization vector is

(52) Carrying out optimization search solving on the optimized parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency, wherein the load combination cycle number meets the following proportional relation:

......

wherein the content of the first and second substances,

the number of cycles for each combination of loads is indicated,

the cycle number of the ith load and the jth load grade of the original load spectrum is represented;

(53) performing multivariate optimization search based on the multi-parameter fatigue test spectrum load parameter model, the average amplitude load grade information and the load cycle proportion equation, wherein the optimization target is that the total damage of each representative load cycle combined spectrum block after optimization is consistent with the total damage of the original load spectrum; the method for calculating the total damage of the optimized multi-parameter spectrum block is consistent with the step (41), and the optimization objective function is as follows:

wherein the content of the first and second substances,

(N_k,h,...,q)_{k,h,...,q∈{1,2,3,..,n}}e.N (natural number);

wherein D is_squenceTotal damage to multiaxial fatigue, D, representing the original load spectrum_block,jRepresenting the total damage of the multi-axial fatigue of each load combination cycle spectrum block;

N_k,h,...,q(k, h,., q ∈ {1,2, 3., n }) represents the phase and cycle number, respectively, of each load combination cyclic spectrum block;

therefore, the load average amplitude, the phase difference and the load combined cycle number information of the component multi-parameter fatigue test load spectrum block which is consistent with the original load spectrum damage are obtained.

(6) And randomly splicing each level of load, and synthesizing a multi-parameter fatigue test spectrum with the same load characteristics and damage as the original load spectrum.

The present invention will be further described with reference to the following examples and accompanying drawings.

Examples

Example analyses of the present invention were conducted as random tension-torsion load spectra of hollow thin-walled open-celled cylindrical members.

The specific steps of the step (1) are as follows:

(11) carrying out peak-valley value detection and rain flow circulation counting processing aiming at a multi-parameter random load spectrum (as shown in figure 1) of a complex mechanical component, wherein the peak-valley value detection is to judge the peak value or the valley value of each load time course, if so, the peak-valley value is reserved, otherwise, the peak-valley value is removed, the data is judged by a three-point method, namely, three adjacent data points F (i-1), F (i) and F (i +1) are read, and if the three adjacent data points F (i-1), F (i) and F (i +1) meet the following requirements:

[ F (i) -F (i-1) ] [ F (i +1) -F (i) ] is not less than 0 and F (i) -F (i-1) ≠ 0

F (i) is the peak or valley point, as shown in fig. 2, which is the external load time history curve of the component with the non-peak-valley data points removed, wherein 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.

And the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of the material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following conditions: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely 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)|

therefore, the statistical result of the load full-cycle peak-valley value of each load path can be obtained, and further the statistical information of the load full-cycle average amplitude can be obtained, and the calculation expression is as follows:

C_amp＝(F_peak-F_valley)/2

C_mean＝(F_peak+F_valley)/2

wherein, F_peak、F_valleyRespectively representing the peak value and the valley value of the rain flow counting cycle; c_amp、C_meanRepresenting the magnitude and valley of the rain flow counting cycle, respectively. Fig. 3 is a three-dimensional frequency histogram of the average amplitude of the random tensile load and the torsional load applied to the member of this example after rain flow statistics.

(12) Based on the statistical information of the load full-cycle average amplitude in the step (11), a load accumulated frequency curve (as shown in fig. 4) is drawn by taking the load amplitude as a vertical coordinate and the accumulated frequency as a horizontal coordinate, further, discrete grade division is carried out on a load amplitude interval according to the accumulated frequency curve by using an equal interval method or according to actual load distribution to determine the load amplitude of each grade, and the tensile load amplitude (A) can be obtained by adopting a three-grade equal interval division method in the embodiment_1,1,A_1,2,A_1,3) Amplitude of torsional load (A)_2,1,A_2,2,A_2,3) As shown by the horizontal dotted line in fig. 5, the load frequency corresponding to each level of load is determined by using the principle of equal damage interval, so that the average value of each level of load is averaged, and the average value (M) of each level of step load is obtained_1,1,M_1,2,M_1,3) And (M)_2,1,M_2,2,M_2,3) Whereby a series of representative load cycles per channel load can be obtained, i.e.

Tensile load:

and torsional load:

wherein

For the number of cycles per load, j is 1,2, i is 1,2,3, and the result of the ranking and the representative load cycle information are shown in fig. 5.

(13) Further, based on a series of representative load cycles determined by each load, traversal matching combination of the multi-parameter load spectrum shown in fig. 6 is performed, and a multi-parameter fatigue test spectrum model fully including actual multi-parameter load characteristics is obtained, wherein the number of the load matching combination is 9, that is, 9 multi-parameter load spectrum blocks are generated, wherein each spectrum block parameter includes 4 load average amplitude parameters, 1 phase parameter and 1 load combination cycle number, that is, each spectrum block parameter includes 4 load average amplitude parameters, 1 phase parameter and 1 load combination cycle number

Wherein each represents a representative multi-parameter duty cycle combined spectrum block. From this, a parametric representation of the multi-parameter fatigue test spectrum model can be obtained, wherein the load-averaged amplitude parameter is obtained from the measured load statistics, as shown in fig. 5, and the phase parameter and the load combination cycle number are optimized and valued by the following step (53) based on the damage agreement principle.

The specific steps of the step (2) are as follows:

(21) determining the stress-strain course of the fatigue examination point of the component under the multi-parameter load spectrum,

the stress-strain history calculation of the fatigue examination point under the multi-parameter load spectrum is mainly carried out by means of finite element software, and comprises the following steps: the method comprises the steps of firstly, giving material attributes and unit types, secondly, modeling and grid division of components, thirdly, solving in multiple load steps, fourthly, analyzing stress-strain data, and enabling stress and strain time history curves of fatigue damage examination points to be as shown in fig. 7 and fig. 8.

(22) Solving a linear equation of the local stress strain and the component load of the fatigue damage check point, wherein the expression is as follows:

σ(c,t)＝K_σ(c)·F(t)

ε(c,t)＝K_ε(c)·F(t)

wherein c is a component fatigue damage checking point, t is a load time, and σ (c, t), ε (c, t) and F (t) are respectively a stress vector, a strain vector and an external load vector of the component fatigue damage checking point, wherein the matrix expression form of the vectors is as follows:

wherein, K_σ(c)、K_ε(c) A matrix of coefficients of stress, strain, respectively, versus external load matrix, and which is constant over the time course of the load; sigma_xx(c,t)、σ_yy(c,t)、σ_zz(c,t)、τ_yz(c,t)、τ_xz(c,t)、τ_xy(c, t) respectively representing the normal stress and the shear stress under an xyz coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx(c,t)、ε_yy(c,t)、ε_zz(c,t)、γ_yz(c,t)、γ_xz(c,t)、γ_xy(c, t) respectively representing positive strain and shear strain under an xyz coordinate system, wherein subscripts of the positive strain and the shear strain correspond to the directions of the coordinate system; f₁(t)、F₂(t)、...F_m(t) represents the m external loads to which the member is subjected.

According to the response obtained in step (21)The force strain process is subjected to multiple linear equation calculation to obtain a coefficient matrix K_σ(c)、K_ε(c) The numerical solution of (c) is calculated for this example as:

the specific steps of the step (3) are as follows:

(31) setting a variable s of the discrete degree as 10, selecting a discrete time interval delta T of each load variable as 0.1 according to a sampling time delta T of an original load as 1, and obtaining a relation formula among variables as follows:

△T＝s·△t

T＝N·△T

wherein T, N represents the total sampling time and total number of original loads, and the stress-strain history at the fatigue-examination point is time-discretized based on the above-mentioned variation, so that the original load histories σ (c, T) and ε (c, T) at time intervals of Δ T are refined into discrete data of load time history at time intervals of Δ T

(32) According to the load time history discrete data processed in the step (31), aiming at the strain data of each discrete load point, the critical plane position (theta) of the discrete load time point is determined by calculating the shear strain of any plane in space through coordinate rotation_cr(t_p),φ_cr(t_p) For example, as shown in fig. 9, which is a schematic diagram of three-dimensional coordinate rotation and strain on an arbitrary plane, the weighted critical plane of the fatigue damage examination point is obtained by performing weight averaging on the critical plane position of the load history according to a weight function, where the strain coordinate rotation calculation expression 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

wherein the content of the first and second substances,

wherein the theta angle and the phi angle are coordinate rotation variables, theta is an included angle between the projection of an X ' axis of a new coordinate system (X ' -Y ' -Z ') on an X-Y plane and the X axis, and phi is an included angle between the X ' axis and the Z axis; sigma_xx、σ_yy、σ_zz、τ_yz、τ_xz、τ_xyRespectively representing normal stress and shear stress under an (X-Y-Z) coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx、ε_yy、ε_zz、γ_yz、γ_xz、γ_xyRespectively represent positive strain and shear strain, sigma 'in a (X-Y-Z) coordinate system'_xx、σ′_yy、σ′_zz、τ′_yz、t′_xz、t′_xyRespectively representing normal stress and shear stress under a (X ' -Y ' -Z ') coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon'_xx、ε′_yy、ε′_zz、γ′_yz、γ′_xz、γ′_xyRespectively representing positive strain and shear strain under a (X ' -Y ' -Z ') coordinate system; [ phi ] of_ε]、[Φ_σ]Representing a strain, stress rotation matrix.

The stress coordinate rotation calculation only needs to convert the corresponding strain into stress, i.e. sigma_x、σ_y、σ_zSubstitution of epsilon_x、ε_y、ε_z，τ_yz、τ_xz、τ_xyReplacement 1/2 gamma_yz、1/2γ_xz、1/2γ_xy. And on the assumption that the impact of the damage parameter at each time instant on the critical plane is the same,the weight function is defined as:

wherein, tau_-1The range of variation is (0, 1) for shear fatigue limit, G is shear modulus, c is constant coefficient]，D(t_p) Is defined by the maximum shear strain gamma_max(t_p) The corresponding fatigue damage is calculated by the following expression:

D(t_p)＝1/N_p

wherein E is the elastic modulus of the material, N_pIs multiaxial fatigue life, σ'_f、b、ε′_fAnd c represents a fatigue strength coefficient, a fatigue strength index, a fatigue ductility coefficient, and a fatigue ductility index, respectively.

Further, according to the critical plane (theta) at each moment in the load history_cr(t_p),φ_cr(t_p) Weight averaging, which is generally as follows:

wherein the content of the first and second substances,

for weighted critical plane locations, W is the sum of the weight coefficients.

The specific steps of the step (4) are as follows:

(41) based on the critical plane obtained in the step (3), converting the original multi-parameter random load history of the component check point into a stress-strain history on the critical plane, wherein the calculation expression is as follows:

wherein the content of the first and second substances,

respectively representing the strain stress coordinate rotation matrixes determined by the weighted critical plane positions obtained in the step (32).

(42) In the embodiment, the original multi-parameter random load course of the member is converted into a series of stress and strain cycles by using a multi-axis cycle counting method proposed by Wang-Brown, and the maximum shear strain amplitude gamma in each cycle is obtained_maxMaximum positive strain increment δ ε_nAnd the mean value of the positive stress σ_n,meanThe calculation expression is as follows:

wherein v is the total discrete load step number in the load cycle, and r and s are discrete load step numbers.

Further the fatigue damage per cycle was calculated therefrom using the Wang-Brown multiaxial fatigue damage model,and multi-axis damage accumulation of the whole original load spectrum is carried out, so that the multi-axis fatigue total damage D of the original load spectrum can be obtained_squenceExpressed as follows:

wherein, γ_max、δε_n、σ_n,meanRespectively representing the maximum shear strain, the maximum positive strain increment and the mean value of the positive stress on a critical plane; upsilon 'and E are equivalent Poisson' S ratio and elastic modulus of the material, and S is a material constant; n is a radical of_fIs multiaxial fatigue life, σ'_f、b、ε′_fC represents a fatigue strength coefficient, a fatigue strength index, a fatigue ductility coefficient and a fatigue ductility index, respectively; n is_iRepresenting the number of cycles of the load cycle, N_iIndicating the multi-axial fatigue life of the load cycle.

The specific steps of the step (5) are as follows:

(51) establishing a relation between external load and multi-axis damage based on the critical plane direction of the weight function obtained in the step (3) and a linear equation of local stress strain and component load, and calculating damage of a series of typical load cycle combinations according to the damage calculation method in the step (4), wherein the cyclic relation between the stress strain and the external load on the critical plane is as follows:

wherein, F₁(t)、F₂(t)、...、F_m(t) represents the external load to which the member is subjected; [ K ]_σ]、[K_ε]A matrix of coefficients of stress, strain versus external load matrix determined for step (22) { (A)_1,k,M_1,k),(A_2,q,M_2,q) Determined by the above step (1), and phase information between the loads of the channels and the number of load cycles, i.e., the number of load cycles

N_k,qThe optimization selection is carried out by the following step (53), namely, the optimization vector is

(52) And carrying out optimization search solving on the optimization parameters of the multi-parameter fatigue test spectrum model established in the step according to the principle of damage consistency, wherein the load combination cycle number meets the following proportional relation:

wherein N is_k,h(k, h e {1,2,3}) represents the number of cycles per load combination,

and the cycle number of the ith load and the jth load grade of the original load spectrum is shown.

(53) Further, multivariate optimization search can be performed based on the multi-parameter fatigue test spectrum load parameter model, the average amplitude load grade information and the load cycle proportion equation, and the optimization target is that the total damage of each representative load cycle combined spectrum block after optimization is consistent with the total damage of the original load spectrum. The method for calculating the total damage of the optimized multi-parameter spectrum block is consistent with the step (41), and the optimization objective function is as follows:

wherein the content of the first and second substances,

(N_k,q)_{k,q∈{1,2,3}}e.N (natural number).

Therefore, the load average amplitude, the phase difference and the load combined cycle number information of the component multi-parameter fatigue test load spectrum block which is consistent with the original load spectrum damage can be obtained. Thus, an optimization search is performed according to the present example, and fig. 10 is the multi-parameter fatigue test load spectrum block optimization information of the component damage consistency.

The specific steps of the step (6) are as follows:

and randomly splicing each multi-parameter load combination spectrum block to obtain a multi-parameter fatigue test spectrum which has the same load characteristics and damage with the original load spectrum, such as the multi-parameter program fatigue test spectrum with different spectrum block sequences shown in fig. 11 and 12.

The above description is only a specific embodiment of the present invention, and further details of the object, technical solution and advantageous effects of the present invention are described. Finally, it should be noted that: the foregoing is merely a preferred embodiment of the invention and is not intended to limit the invention in any manner. For those skilled in the art, the non-innovative modifications, variations and alterations of the technical solutions of the present invention made by the above-mentioned contents should be considered as falling within the protection scope of the present invention without departing from the technical solutions of the present invention.

Claims (6)

1. A multi-parameter fatigue test spectrum compiling method based on damage equivalence is characterized in that: the method comprises the following steps:

(1) carrying out peak-valley value detection and rain flow cycle counting aiming at a multi-parameter random load spectrum of a complex mechanical component to obtain respective load amplitude and mean value statistical results, carrying out grade division on the load amplitude by utilizing a load accumulation frequency curve, and correspondingly carrying out averaging value taking on the mean value to obtain a series of representative load cycles of each load, and carrying out multi-parameter load matching combination on a typical load cycle series to obtain a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics;

(2) converting the preprocessed multi-parameter component load spectrum into a stress-strain history of a fatigue examination point according to a finite element principle, and solving a linear equation of local stress strain and component load;

(3) carrying out time discretization on the stress-strain history of the fatigue examination point, and determining a critical plane by using a weight function based on damage time-varying parameters;

(4) calculating the total accumulated damage of the original load spectrum according to the multi-axial fatigue damage model;

(5) establishing a relation between external load and multi-axis damage based on a linear equation of a weight function critical plane, local stress strain and component load, determining a series of multi-axis fatigue damage values representing load cycle combination, and performing optimization search solution on the optimization parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency;

(6) and randomly splicing each level of load, and synthesizing a multi-parameter fatigue test spectrum with the same load characteristics and damage as 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 method comprises the following steps: the specific steps of the step (1) are as follows:

(11) carrying out peak-valley value detection and rain flow circulation counting processing aiming at a multi-parameter random load spectrum of a complex mechanical component, wherein the peak-valley value detection is to judge the peak value or the valley value of each load time course, if so, retaining the peak value or the valley value, otherwise, removing the peak value or the valley value, and judging the data by a three-point method, namely reading three adjacent data points F (i-1), F (i) and F (i +1), and if the three adjacent data points are met:

[ F (i) -F (i-1) ] [ F (i +1) -F (i) ] is not less than 0 and F (i) -F (i-1) ≠ 0

Wherein, F (i) is the peak point or the valley point;

and the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of the material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following conditions: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely 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)|

therefore, the statistical result of the load full-cycle peak-valley value of each load is obtained, further the statistical information of the load full-cycle average amplitude value is obtained, and the calculation expression is as follows:

C_amp＝(F_peak-F_valley)/2

C_mean＝(F_peak+F_valley)/2

wherein, F_peak、F_valleyRespectively representing the peak value and the valley value of the rain flow counting cycle; c_amp、C_meanRespectively representing the amplitude and the valley of the rain flow counting cycle;

(12) based on the statistical information of the load full-cycle average amplitude in the step (11), a load accumulated frequency curve is drawn by taking the load amplitude as a vertical coordinate and the accumulated frequency as a horizontal coordinate, discrete grade division is carried out on a load amplitude interval according to the accumulated frequency curve by using an equal interval method or according to actual load distribution, and the load amplitude of each grade is determined, namely (A)_j,1,A_j,2,...,A_j,n) Determining the load frequency corresponding to each level of load by using the principle of equal damage interval, thereby averaging and taking the average value of each level of load to obtain the average value (M) of each level of step load_j,1,M_j,2,...,M_j,n) Thereby obtaining a series of representative load cycles for the jth load, i.e.

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)}

Wherein the content of the first and second substances,

is the number of cycles per load stage, j 1,2,.. the m, i 1,2,.. the n, m is the number of load channels, n is the number of stages per load division, and η is the number of stages per load division_j,iFor the normalized cycle count per load, the calculation expression is as follows:

(13) based on a series of representative load cycles determined by each load, traversing matching combination of multi-parameter load spectrums is carried out, and a multi-parameter fatigue test spectrum model fully containing actual multi-parameter load characteristics is obtained, wherein the number of load matching combination is n^mI.e. generating n^mA plurality of multi-parameter load spectrum blocks, wherein each spectrum block parameter comprises 2M load average amplitude parameters (A, M) and phase parameters

M-1 in total and 1 cycle number of load combination, i.e.

......

And m parameters of k, h, and q are taken as values in {1,2, and so, n }, and each representative multi-parameter load cyclic spectrum block is represented, so that parameter expression of the multi-parameter fatigue test spectrum model is obtained.

3. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 1, wherein the method comprises the following steps: the specific steps of the step (2) are as follows:

(21) determining the stress-strain history of the fatigue examination point of the component under the multi-parameter load spectrum, wherein the calculation of the stress-strain history of the fatigue examination point under the multi-parameter load spectrum is carried out by means of finite element software, and the calculation comprises the following steps: endowing material attributes and unit types, modeling and grid division of components, multi-load step solving and stress-strain data analysis;

(22) solving a linear equation of the local stress strain and the component load of the fatigue damage check point, wherein the expression is as follows:

σ(c,t)＝K_σ(c)·F(t)

ε(c,t)＝K_ε(c)·F(t)

wherein c is a component fatigue damage checking point, t is a load time, and σ (c, t), ε (c, t) and F (t) are respectively a stress vector, a strain vector and an external load vector of the component fatigue damage checking point, wherein the matrix expression form of the vectors is as follows:

wherein, K_σ(c)、K_ε(c) A matrix of coefficients of stress, strain, respectively, versus external load matrix, and which is constant over the time course of the load; sigma_xx(c,t)、σ_yy(c,t)、σ_zz(c,t)、τ_yz(c,t)、τ_xz(c,t)、τ_xy(c, t) respectively representing the normal stress and the shear stress under an xyz coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx(c,t)、ε_yy(c,t)、ε_zz(c,t)、γ_yz(c,t)、γ_xz(c,t)、γ_xy(c, t) respectively representing positive strain and shear strain under an xyz coordinate system, wherein subscripts of the positive strain and the shear strain correspond to the directions of the coordinate system; f₁(t)、F₂(t)、...F_m(t) represents the m external loads to which the member is subjected;

according to the one obtained in the above step (21)Performing multivariate linear equation calculation on the stress strain process to obtain a coefficient matrix K_σ(c)、K_ε(c) The numerical solution of (c).

4. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 1, wherein the method comprises the following steps: the specific steps of the step (3) are as follows:

(31) setting a discrete degree variable s, selecting a discrete time interval delta T of each load variable according to the sampling time delta T of the original load, wherein the relation among the variables is as follows:

△T＝s·△t

T＝N·△T

wherein T, N represents the total sampling time and total number of samples of the original load, so that the original load history σ (c, T), ε (c, T) with time interval of Δ T is refined into discrete data with time history of Δ T as load

(32) Discrete data of load time history according to step (31)

For the strain data of each discrete load point, determining the critical plane position (theta) of the discrete load time point by calculating the shear strain of any plane in space through coordinate rotation_cr(t_p),φ_cr(t_p) And then carrying out weight averaging on the critical plane position of the load process according to a weight function to obtain a weighted critical plane of the fatigue damage examination point, wherein the strain coordinate rotation calculation expression 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

wherein the content of the first and second substances,

wherein, the theta angle and the phi angle are coordinate rotation variables, the theta is an included angle between the projection of an X ' axis of a new coordinate system (X ' -Y ' -Z ') on an X-Y plane and the X axis, and the phi is an included angle between the X ' axis and the Z axis; sigma_xx、σ_yy、σ_zz、τ_yz、τ_xz、τ_xyRespectively representing normal stress and shear stress under an (X-Y-Z) coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon_xx、ε_yy、ε_zz、γ_yz、γ_xz、γ_xyRespectively represent positive strain and shear strain, sigma 'in a (X-Y-Z) coordinate system'_xx、σ′_yy、σ′_zz、τ′_yz、τ′_xz、τ′_xyRespectively representing normal stress and shear stress under a (X ' -Y ' -Z ') coordinate system, wherein subscripts of the normal stress and the shear stress correspond to the directions of the coordinate system; epsilon'_xx、ε′_yy、ε′_zz、γ′_yz、γ′_xz、γ′_xyRespectively representing positive strain and shear strain under a (X ' -Y ' -Z ') coordinate system; [ phi ] of_ε]、[Φ_σ]Representing a strain, stress rotation matrix;

the stress coordinate rotation calculation only needs to convert the corresponding strain into stress, i.e. sigma_x、σ_y、σ_zSubstitution of epsilon_x、ε_y、ε_z，τ_yz、τ_xz、τ_xyReplacement 1/2 gamma_yz、1/2γ_xz、1/2γ_xy(ii) a And the influence of the damage parameters on the critical plane based on each moment is the same, and the weight function is defined as:

wherein, tau_-1The range of variation is (0, 1) for shear fatigue limit, G is shear modulus, c is constant coefficient]，D(t_p) Is defined by the maximum shear strain gamma_max(t_p) The corresponding fatigue damage is calculated by the following expression:

D(t_p)＝1/N_p

wherein E is the elastic modulus of the material, N_pIs multiaxial fatigue life, σ'_f、b、ε′_fC represents a fatigue strength coefficient, a fatigue strength index, a fatigue ductility coefficient and a fatigue ductility index, respectively;

according to the critical plane (theta) at each moment in the load course_cr(t_p),φ_cr(t_p) Weight averaging is performed as follows:

wherein the content of the first and second substances,

for weighted critical plane locations, W is the sum of the weight coefficients.

5. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 1, wherein the method comprises the following steps: the specific steps of the step (4) are as follows:

(41) converting the original multi-parameter random load history of the component check point into a stress-strain history on the critical plane based on the critical plane obtained in the step (3), wherein the calculation expression is as follows:

wherein the content of the first and second substances,

respectively representing the strain stress coordinate rotation matrixes determined by the weighted critical plane positions obtained in the step (32);

(42) converting the original multi-parameter random load history of the component into a series of stress and strain cycles by using a multi-axis cycle counting method, calculating the fatigue damage of each cycle by using a multi-axis fatigue damage model, and performing multi-axis damage accumulation of the whole original load spectrum to obtain the total damage D of the multi-axis fatigue of the original load spectrum_squenceExpressed as follows:

N_f＝f(σ_cr,ε_cr)

wherein N is_f、σ_cr、ε_crRepresenting the service life and the stress strain in the multi-axial fatigue damage model; n is_iRepresenting the number of cycles of the load cycle, N_iIndicating the multi-axial fatigue life of the load cycle.

6. The method for compiling a multi-parameter fatigue test spectrum based on damage equivalence according to claim 1, wherein the method comprises the following steps: the specific steps of the step (5) are as follows:

(51) establishing a relation between external load and multi-axis damage based on the critical plane direction of the weight function obtained in the step (3) and a linear equation of local stress strain and component load, and calculating damage of a series of typical load cycle combinations according to the damage calculation method in the step (4), wherein the relation between stress strain and external load cycle on the critical plane is as follows:

wherein, F₁(t)、F₂(t)、...、F_m(t) represents the external load to which the member is subjected; [ K ]_σ]、[K_ε]A matrix of coefficients of stress, strain versus external load matrix determined for step (22) { (A)_1,k,M_1,k),(A_2,h,M_2,h),...,(A_m,q,M_m,q) Determined by step (1), and phase information between the loads of the channels and the number of load cycles, i.e. the number of load cycles

The optimization selection is carried out by the following step (53), namely, the optimization vector is

(52) Carrying out optimization search solving on the optimized parameters of the multi-parameter fatigue test spectrum model established in the step (1) according to the principle of damage consistency, wherein the load combination cycle number meets the following proportional relation:

......

wherein the content of the first and second substances,

the number of cycles for each combination of loads is indicated,

the cycle number of the ith load and the jth load grade of the original load spectrum is represented;

(53) performing multivariate optimization search based on the multi-parameter fatigue test spectrum load parameter model, the average amplitude load grade information and the load cycle proportion equation, wherein the optimization target is that the total damage of each representative load cycle combined spectrum block after optimization is consistent with the total damage of the original load spectrum; the method for calculating the total damage of the optimized multi-parameter spectrum block is consistent with the step (41), and the optimization objective function is as follows:

wherein the content of the first and second substances,

(N_k,h,...,q)_{k,h,...,q∈{1,2,3,..,n}}e.N (natural number);

wherein D is_squenceTotal damage to multiaxial fatigue, D, representing the original load spectrum_block,jRepresenting total damage to multi-axial fatigue for each load combined cycle spectrum block；

N_k,h,...,q(k, h,., q ∈ {1,2, 3., n }) represents the phase and cycle number, respectively, of each load combination cyclic spectrum block;

therefore, the load average amplitude, the phase difference and the load combined cycle number information of the component multi-parameter fatigue test load spectrum block which is consistent with the original load spectrum damage are obtained.

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