CN114429060A - Method for assessing structure dislocation failure and service life prediction in fatigue vibration - Google Patents

Method for assessing structure dislocation failure and service life prediction in fatigue vibration Download PDF

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CN114429060A
CN114429060A CN202111459422.1A CN202111459422A CN114429060A CN 114429060 A CN114429060 A CN 114429060A CN 202111459422 A CN202111459422 A CN 202111459422A CN 114429060 A CN114429060 A CN 114429060A
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CN114429060B (en
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李一舒
张澧桐
曹贺全
王佰超
高永亮
陈巍
赵岩
陈达宇
宗铎
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China Weapon Science Academy Ningbo Branch
Changchun University of Science and Technology
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Changchun University of Science and Technology
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Abstract

The invention relates to a method for assessing structure dislocation failure and service life prediction in fatigue vibration, which comprises the following steps of S100, establishing a three-dimensional geometric structure model of a product to be examined; s200, establishing a finite element structure model of the product to be examined on the basis of the three-dimensional geometric structure model; s300, performing free mode calculation in a solver based on the finite element structure model; s400, performing uninterrupted fatigue vibration response calculation on a product to be examined based on vibration schemes in different directions and different amplitudes, and forming a data sample; s500, fitting a mathematical function of product assessment structure displacement based on a neural network, and establishing a structural dislocation limit state equation; s600, selecting the data samples in the S400 to perform test verification on the fitted mathematical function; and S700, establishing a conversion relation among frequency, resolution and a time domain based on the mathematical function verified in the S600, obtaining a connection coefficient equation of the reliability prediction model based on the service life, and predicting the fatigue life of the product in the specified vibration environment according to the extreme state equation. The method makes product design and maintenance easier.

Description

Method for assessing structure dislocation failure and service life prediction in fatigue vibration
Technical Field
The invention relates to the field of product reliability research, in particular to a method for assessing structure dislocation failure and predicting service life in fatigue vibration.
Background
The vibration load is widely existed in the transportation or working environment of various products, the product structure generates vibration response under the excitation of the vibration load, the structural dislocation of each group of components can be caused, the product structure is in the fatigue vibration working environment for a long time, the tiny dislocation can be accumulated along with the time to form large dislocation, the service performance and the service life of the product are reduced to a great extent, the prediction of the service life of the product has important significance for guiding the product design and maintenance, and the assessment of the structural dislocation failure and the service life prediction in the fatigue vibration is significant.
However, the fatigue vibration environment is characterized by small vibration amplitude, random vibration frequency, small influence on the performance of the product in a short time and large accumulated damage to the product in a long time. The fatigue vibration response performance of the product is evaluated at the present stage mainly by loading a random vibration frequency spectrum in an actual working environment or a fatigue vibration test bed, and the problems that the evaluation time is long, the internal vibration response damage of the product cannot be observed in real time and the like exist, so that the adverse factors of the internal structure of the product to the fatigue vibration cannot be effectively improved when the product is designed and maintained.
Therefore, a method for rapidly checking the structure dislocation failure and the service life prediction in the fatigue vibration is needed.
Disclosure of Invention
In view of the above problems, the present invention provides a method for rapidly checking the structure dislocation failure and life prediction in fatigue vibration.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for assessing structure dislocation failure and service life prediction in fatigue vibration is characterized by comprising the following steps: the method comprises the following steps of,
s100, establishing a three-dimensional geometric structure model of a product to be examined;
s200, establishing a finite element structure model of the product to be examined on the basis of the three-dimensional geometric structure model;
s300, performing free mode calculation in a solver based on the finite element structure model;
s400, performing uninterrupted fatigue vibration response calculation on a product to be examined based on vibration schemes in different directions and different amplitudes, and forming a data sample;
s500, fitting a mathematical function of product assessment structure displacement based on a neural network, and establishing a structural dislocation limit state equation; s600, selecting the data samples in the S400 to perform test verification on the fitted mathematical function;
and S700, establishing a conversion relation among frequency, resolution and a time domain based on the mathematical function verified in the S600, obtaining a connection coefficient equation of the reliability prediction model based on the service life, and predicting the fatigue life of the product in the specified vibration environment according to the extreme state equation.
Further, the S300 includes the steps of,
s3100, calculating power spectral density of road excitation according to actual application working conditions and narrow-band random vibration program data of goods fastened by a tracked vehicle;
s3200, calculating a mean value, a variance and a peak acceleration based on excitation energy and spectral characteristics reflected by power spectral density;
s3300, determining a frequency range of free mode calculation according to the mean value, the variance and the peak acceleration, performing free mode calculation in a nanostran solver on the basis of a finite element structure model to obtain inherent properties of free vibration of the product structure, and analyzing states of all groups of parts of the structure during vibration.
Further, the S400 includes the steps of,
s4100, designing a random full-combination scheme for narrow-band random vibration program data of goods fastened by the tracked vehicle based on different directions and different normal distribution characteristics;
s4200, obtaining continuous non-fault working time based on a conversion relation between kilometers and time agreed in narrow-band random vibration program data of goods fastened by the crawler, wherein the corresponding relation is as follows:
MTBF=Sb/TSthe method comprises the following steps of A, judging whether MTBF is a continuous fault-free working time in a limit state, Sb is a minimum fault-free mileage of a product driven by a vehicle, and Ts is a vehicle speed corresponding to a vibration frequency spectrum in program data;
and S4300, for each vibration scheme obtained in S4100, calculating a displacement value of a system target fault point in the vibration scheme by using a finite element mode-based forced response durability simulation method, wherein the loading time is a continuous non-fault working time MTBF, and obtaining data samples between the continuous non-fault working time MTBF and the vibration response, wherein the data samples comprise vibration acceleration in an X/Y/Z direction, accumulated displacement error of the system fault point and MTBF.
Further, the S500 includes the steps of,
s5100, establishing a structure misalignment evaluation mathematical function r ═ f (Δ x, Δ y, Δ z) according to a structure position relationship between the group components in the product, where r is a relative displacement between the group components, and Δ x, Δ y, Δ z are change values of the group components after displacement in X, Y, Z directions from an initial position;
s5200, inputting all groups of component influence factors under X, Y, Z three-direction vibration acceleration excitation and structural tolerance as input quantities into a three-layer neural network, and training the neural network to obtain a neural network model, wherein the input quantities are subjected to normalization processing during input, and the mathematical expression of the input quantities is as follows:
Figure BDA0003389302430000031
wherein i ═ X, Y, Z, D1,D2,...,DnINPUT when i takes value of X, Y, ZiRespectively representing the vibration acceleration in the direction of X, Y, Z, and INPUT when the value of i is DniRepresents all sets of component influences under structural tolerances;
the first layer of the three-layer neural network is
Figure BDA0003389302430000032
i takes a value of 1-15; the second layer of neural network is
Figure BDA0003389302430000033
i takes a value of 1-5; the third layer of neural network is
Figure BDA0003389302430000034
i takes a value of 1-5; the normalized processing equation of the output layer is
Figure BDA0003389302430000035
S5300, performing fitting training on the neural network model, wherein the fitting training times are more than or equal to 300, obtaining a fitting curve of output structure displacement under the influence of different groups of component structures after multidirectional fatigue stress loading, and obtaining a fitted mathematical function based on the fitting curve;
s5400, establishing a limit state function of product structure dislocation failure according to a fault mode and a fault influence analysis structure of a product, wherein the limit state function is g (x) ═ N (x) -place, the place is a displacement value of product structure dislocation in a fatigue vibration process but not causing product function failure, and N (x) is used for representing the limit state function of a test point in a system structure.
Further, the S700 includes the steps of,
s7100, under a time domain environment of a continuous excitation working state, a frequency spectrum range is 5 Hz-500 Hz, a maximum resolution fn is 0.2S and is used as a vibration period, and a conversion equation of working time and vibration times is established as follows:
t=T/fn
in the formula, T is working time.
S7200, calculating a connection coefficient equation of the reliability prediction model based on the service life based on the acceleration excitation-displacement data sample obtained in S400 as follows:
Figure BDA0003389302430000036
in the formula, s is the dislocation displacement between two adjacent parts, and sigma is the variance of the maximum displacement of the reference national military standard loading capacity;
s7300, obtaining a reliability calculation equation of single excitation according to a connection coefficient equation of the reliability prediction model based on the service life of S7200:
R=Φ(Z)
the service life reliability calculation equation after N times of vibration is as follows:
Rn=Φ(Z)N
the service life reliability equation after using n hours of vibration is:
Figure BDA0003389302430000041
the probability of failure F (t) after t hours can be expressed as:
F(t)=1-R(t)
the failure rate after t hours λ (t) is expressed as:
Figure BDA0003389302430000042
the equations for the reliable life, median life and characteristic life are then expressed as follows:
t=R-1(t)
Figure BDA0003389302430000043
Figure BDA0003389302430000044
compared with the prior art, the invention has the advantages that:
the invention solves the technical problems that the product fatigue vibration test in the prior art is long in test period and the structure dislocation in the product can not be observed in real time, solves the problem that the reliability of the product is reduced and can not be quantified due to the structure dislocation under the vehicle-mounted condition, solves the problem of random matching in three directions, and is more scientific and effective for the limit test of the fatigue vibration.
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FIG. 1 is a flow chart of a method for accelerating structural dislocation failure in assessment of fatigue vibration and a service life prediction method provided by the invention.
Fig. 2 is a data diagram of a narrow-band random vibration program of goods fastened by a crawler in GJB 150.16A-2009 military equipment laboratory environment test method part 16.
Fig. 3 is a diagram of road excitation power spectral density obtained by a crawler running according to an embodiment of the present invention.
FIG. 4 is a diagram showing the results of free mode calculations for a product according to an embodiment of the present invention in the frequency range of 0-600 Hz.
Fig. 5 is a diagram of a neural network computational model scenario in accordance with an embodiment of the present invention.
FIG. 6 is a graph of a fit of the structural displacement of the product set components after multidirectional fatigue stress loading in accordance with embodiments of the present invention.
FIG. 7 is a schematic diagram of a product fatigue vibration test arrangement according to an embodiment of the present invention.
FIG. 8 is a graph of product reliability versus time according to an embodiment of the present invention.
Fig. 9 is characteristic data of excitation normal distribution of roads in different directions according to an embodiment of the present invention.
Fig. 10 is a diagram illustrating part of the input-output database created in step S400 according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention provides a method for accelerating the examination of structural dislocation failure in fatigue vibration and a service life prediction method, which can be used for accelerating the examination of the function loss of a certain product arranged on a tracked vehicle caused by structural dislocation and can effectively solve the technical problems that the test period of a product fatigue vibration test is long and the structural dislocation in the product can not be observed in real time; the reliability of the product is reduced and the service life of the product cannot be predicted due to structural dislocation under a vehicle-mounted condition; the existing testing method is divided into the technical problems of X-axis, Y-axis and Z-axis unidirectional respective testing and poor operability.
Referring to fig. 1, the invention provides a method for accelerating the structural dislocation failure in the examination of fatigue vibration and a service life prediction method, comprising the following steps:
step S100: establishing a three-dimensional geometric structure model of the assessment product;
and (3) carrying out equal-proportion modeling according to the component structure of the product, assembling the component of the product according to the machining tolerance, and completing the modeling of the three-dimensional geometric structure model of the product, wherein the structure meets the static strength standard.
Step S200: establishing a product structure finite element model;
establishing a finite element model of the product based on the three-dimensional geometric structure model, carrying out meshing on the finite element model, and then loading the material model.
Step S300: calculating a mode;
and based on the finite element structure model, performing free modal calculation in a nanostran solver.
Preferably, step S300 includes the steps of:
step S3100: according to the actual application working condition of the product, narrow-band random vibration program data (see figure 2) of goods fastened by the tracked vehicle in GJB 150.16A-2009 military equipment laboratory environment test method part 16 vibration test is selected as a basis; the power spectral density of the road excitation is calculated based on narrowband random vibration program data of the tracked vehicle securing cargo, as shown in fig. 3.
Step S3200: based on the excitation energy and the spectral characteristics reflected by the power spectral density, the power spectral density meets the normal distribution, and key parameter values such as a mean value, a variance and a peak acceleration are calculated and obtained, as shown in table 1;
step S3300: determining the frequency range of free mode calculation to be 0-600Hz according to key parameter values such as mean value, variance and peak acceleration obtained by calculation; based on the finite element structure model, performing free mode calculation in a nanostran solver, wherein the calculation result is shown in FIG. 4; and obtaining the inherent property of free vibration of the product structure according to the calculation result, and analyzing the states of all groups of parts of the structure during vibration.
Step S400: calculating vibration response;
and based on vibration schemes in different directions and different amplitudes, calculating the uninterrupted fatigue vibration response of the product.
Preferably, step S400 includes the steps of:
s4100, designing a random full-combination scheme for narrow-band random vibration program data of goods fastened by the tracked vehicle based on different directions and different normal distribution characteristics;
s4200, obtaining continuous non-fault working time based on a conversion relation between kilometers and time agreed in narrow-band random vibration program data of goods fastened by the crawler, wherein the corresponding relation is as follows:
MTBF=Sb/TSthe method comprises the following steps that MTBF is continuous fault-free working time in a limit state, Sb is the minimum fault-free mileage of a product in vehicle running, and Ts is the vehicle speed corresponding to a vibration frequency spectrum in program data;
and S4300, for each vibration scheme obtained in S4100, calculating a displacement value of a system target fault point in the vibration scheme by using a finite element mode-based forced response durability simulation method, wherein the loading time is a continuous non-fault working time MTBF, and obtaining data samples between the continuous non-fault working time MTBF and the vibration response, wherein the data samples comprise vibration acceleration in an X/Y/Z direction, accumulated displacement error of the system fault point and MTBF.
Step S500: fitting a mathematical function of product assessment structure displacement based on a neural network, and establishing a limit state equation of structure dislocation;
determining a neural network computational model scheme based on the data samples established in step S400, the neural network computational model scheme being shown in fig. 5; training the neural network model for multiple times, setting a fitting program, fitting to obtain a mathematical polynomial of product assessment structure displacement, and establishing a structural dislocation extreme state equation;
preferably, step S500 includes the steps of:
s5100, establishing a structure misalignment evaluation mathematical function r ═ f (Δ x, Δ y, Δ z) according to a structure position relationship between the group components in the product, where r is a relative displacement between the group components, and Δ x, Δ y, Δ z are change values of the group components after displacement in X, Y, Z directions from an initial position;
s5200, inputting all groups of component influence factors under X, Y, Z three-direction vibration acceleration excitation and structural tolerance as input quantities into a three-layer neural network, and training the neural network to obtain a neural network model, wherein the input quantities are subjected to normalization processing during input, and the mathematical expression of the input quantities is as follows:
Figure BDA0003389302430000061
wherein i ═ X, Y, Z, D1,D2,...,DnINPUT when i takes value of X, Y, ZiRespectively representing the vibration acceleration in the direction of X, Y, Z, and INPUT when the value of i is DniRepresents all sets of component influences under structural tolerances;
the first layer of the three-layer neural network is
Figure BDA0003389302430000071
i takes a value of 1-15; the second layer of neural network is
Figure BDA0003389302430000072
i takes a value of 1-5; the third layer of neural network is
Figure BDA0003389302430000073
i takes a value of 1-5; the normalized processing equation of the output layer is
Figure BDA0003389302430000074
S5300, performing fitting training on the neural network model, wherein the fitting training times are more than or equal to 300, obtaining a fitting curve of output structure displacement under the influence of different groups of component structures after multidirectional fatigue stress loading, and obtaining a fitted mathematical function based on the fitting curve;
s5400, establishing a limit state function of product structure dislocation failure according to a fault mode and a fault influence analysis structure of a product, wherein the limit state function is g (x) ═ N (x) -place, the place is a displacement value of product structure dislocation in a fatigue vibration process but not causing product function failure, and N (x) is used for representing the limit state function of a test point in a system structure.
Step S600: performing experimental verification on a mathematical fitting function;
based on the mathematical fitting function, selecting individual cases in the data sample of the step S400 for test verification; a vibration system is adopted, parameters such as vibration amplitude and the like are input, and the product structure dislocation failure time under individual conditions is obtained to verify the feasibility of a mathematical fitting function.
The product was subjected to a fatigue vibration test, the test layout being shown in fig. 7.
Firstly, designing a mounting bracket 2 according to the actual working condition of a product 3; thereafter, the mounting bracket 2 is fastened to the vibration table 1, and the product 3 is mounted on the bracket 2; the product 3 comprises a component 4 and a part 5, wherein the part 5 consists of a plurality of parts 6 and parts 7; the center of the part 6 is on the midline of the part 7, and the structural dislocation of the part 6 and the part 7 can cause the product performance to be greatly reduced, and when the center of the part 6 deviates from the boundary of the part 7, the product fails.
Secondly, according to the calculation result of the step S4300, selecting the vibration frequency and amplitude which have serious influence on the structure dislocation in the simulation vibration scheme, inputting the vibration frequency and amplitude into a control program of the vibration table, and starting the vibration program. If the vibration test time is too long, methods such as improving the vibration amplitude and the like can be adopted to shorten the vibration time.
Thirdly, comparing the difference between the structure dislocation displacement and the simulation vibration result after the vibration program is finished, analyzing errors possibly existing in the simulation, and correcting.
And finally, according to the corrected data, obtaining a mathematical function of the product assessment structure displacement based on neural network fitting.
Step S700: according to the model, the fatigue life of the product in a specified vibration environment is predicted.
And (3) establishing a conversion relation between parameters such as frequency and resolution and a time domain based on the product structure dislocation mathematical fitting function established in the step (S600), obtaining a connection coefficient equation of the reliability prediction model based on the service life, and predicting the fatigue life of the product in the specified vibration environment according to the extreme state equation.
According to the road spectrum requirement in the GJB 150.16A part 16 vibration test table D.1 (shown in figure 2), the reliability prediction model core based on the service life is to establish the relation between the excitation times and the time. Since the whole vibration test is a continuous excitation working state in a time domain environment, and the frequency spectrum ranges from 5Hz to 500Hz, the maximum resolution fn is 0.2s as a vibration period, and the conversion equation of the working time and the vibration frequency is as follows:
t=T/fn
wherein T is the working time.
According to the input (acceleration excitation) -output (displacement) database obtained after the calculation in the step S4300, a connection coefficient equation of the reliability prediction model based on the service life is calculated as follows:
Figure BDA0003389302430000081
in the formula, s is the dislocation displacement of the part 6 and the part 7, and sigma is the variance of the maximum displacement of the reference national military standard load;
the reliability calculation equation for a single excitation is then:
R=Φ(Z)
the service life reliability calculation equation after N times of vibration is as follows:
Rn=Φ(Z)N
the service life reliability equation after using n hours of vibration is:
Figure BDA0003389302430000082
the probability of failure F (t) after t hours can be expressed as:
F(t)=1-R(t)
the failure rate after t hours λ (t) is expressed as:
Figure BDA0003389302430000083
equations of the reliable life, the median life and the characteristic life are respectively expressed as follows:
t=R-1(t)
Figure BDA0003389302430000084
Figure BDA0003389302430000085
by combining the above relational expressions, the relationship between the reliability of the product and the operating time can be obtained as shown in fig. 8, and the reliability life, the median life and the characteristic life of the product can be calculated.
While embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (5)

1. A method for assessing structure dislocation failure and service life prediction in fatigue vibration is characterized by comprising the following steps: the method comprises the following steps of,
s100, establishing a three-dimensional geometric structure model of a product to be checked;
s200, establishing a finite element structure model of the product to be examined on the basis of the three-dimensional geometric structure model;
s300, performing free mode calculation in a solver based on the finite element structure model;
s400, performing uninterrupted fatigue vibration response calculation on a product to be examined based on vibration schemes in different directions and different amplitudes, and forming a data sample;
s500, fitting a mathematical function of product assessment structure displacement based on a neural network, and establishing a structural dislocation limit state equation; s600, selecting the data samples in the S400 to perform test verification on the fitted mathematical function;
and S700, establishing a conversion relation among frequency, resolution and a time domain based on the mathematical function verified in the S600, obtaining a connection coefficient equation of the reliability prediction model based on the service life, and predicting the fatigue life of the product in the specified vibration environment according to the extreme state equation.
2. The method of claim 1, further comprising: the S300 includes the steps of,
s3100, calculating power spectral density of road excitation according to actual application working conditions and by taking narrow-band random vibration program data of goods fastened by a tracked vehicle as a basis;
s3200, calculating a mean value, a variance and a peak acceleration based on excitation energy and spectral characteristics reflected by power spectral density;
s3300, determining a frequency range of free mode calculation according to the mean value, the variance and the peak acceleration, performing free mode calculation in a nanostran solver on the basis of a finite element structure model to obtain inherent properties of free vibration of the product structure, and analyzing states of all groups of parts of the structure during vibration.
3. The method of claim 2, further comprising: the S400 includes the steps of,
s4100, designing a random full-combination scheme for narrow-band random vibration program data of goods fastened by the tracked vehicle based on different directions and different normal distribution characteristics;
s4200, obtaining continuous non-fault working time based on a conversion relation between kilometers and time agreed in narrow-band random vibration program data of goods fastened by the crawler, wherein the corresponding relation is as follows:
MTBF=Sb/TSthe method comprises the following steps that MTBF is continuous fault-free working time in a limit state, Sb is the minimum fault-free mileage of a product in vehicle running, and Ts is the vehicle speed corresponding to a vibration frequency spectrum in program data;
and S4300, for each vibration scheme obtained in S4100, calculating a displacement value of a system target fault point in the vibration scheme by using a finite element mode-based forced response durability simulation method, wherein the loading time is a continuous non-fault working time MTBF, and obtaining data samples between the continuous non-fault working time MTBF and the vibration response, wherein the data samples comprise vibration acceleration in an X/Y/Z direction, accumulated displacement error of the system fault point and MTBF.
4. The method of claim 3, wherein: the S500 includes the steps of,
s5100, establishing a structure dislocation evaluation mathematical function r which is f (delta x, delta y and delta z) according to a structure position relation between the group components in the product, wherein r is relative displacement between the group components, and delta x, delta y and delta z are change values of the group components in X, Y, Z three-direction coordinate axes compared with an initial position after the group components are displaced;
s5200, inputting all groups of component influence factors under X, Y, Z three-direction vibration acceleration excitation and structural tolerance as input quantities into a three-layer neural network, and training the neural network to obtain a neural network model, wherein the input quantities are subjected to normalization processing during input, and the mathematical expression of the input quantities is as follows:
Figure FDA0003389302420000021
wherein i ═ X, Y, Z, D1,D2,...,DnINPUT when i takes value of X, Y, ZiRespectively representing the vibration acceleration in the direction of X, Y, Z, and INPUT when the value of i is DniRepresents all sets of component influences under structural tolerances;
the first layer of the three-layer neural network is
Figure FDA0003389302420000022
i takes a value of 1-15; the second layer of neural network is
Figure FDA0003389302420000023
i takes a value of 1-5; the third layer of neural network is
Figure FDA0003389302420000024
i takes a value of 1-5; the normalized processing equation of the output layer is
Figure FDA0003389302420000025
S5300, performing fitting training on the neural network model, wherein the fitting training times are more than or equal to 300, obtaining a fitting curve of output structure displacement under the influence of different groups of component structures after multidirectional fatigue stress loading, and obtaining a fitted mathematical function based on the fitting curve;
s5400, establishing a limit state function of product structure dislocation failure according to a fault mode and a fault influence analysis structure of a product, wherein the limit state function is g (x) ═ N (x) -place, the place is a displacement value of product structure dislocation in a fatigue vibration process but not causing product function failure, and N (x) is used for representing the limit state function of a test point in a system structure.
5. The method of claim 4, further comprising: the S700 includes the steps of,
s7100, under a time domain environment of a continuous excitation working state, a frequency spectrum range is 5 Hz-500 Hz, a maximum resolution fn is 0.2S and is used as a vibration period, and a conversion equation of working time and vibration times is established as follows:
t=T/fn
in the formula, T is working time.
S7200, calculating a connection coefficient equation of the reliability prediction model based on the acceleration excitation-displacement data sample obtained in the S400, wherein the connection coefficient equation is as follows:
Figure FDA0003389302420000031
in the formula, s is the dislocation displacement between two adjacent parts, and sigma is the variance of the maximum displacement of the reference national military standard loading capacity;
s7300, obtaining a reliability calculation equation of single excitation according to a connection coefficient equation of the reliability prediction model based on the service life of S7200, wherein the reliability calculation equation comprises the following steps:
R=Φ(Z)
the service life reliability calculation equation after N times of vibration is as follows:
Rn=Φ(Z)N
the service life reliability equation after using n hours of vibration is:
Figure FDA0003389302420000032
the probability of failure F (t) after t hours can be expressed as:
F(t)=1-R(t)
the failure rate after t hours λ (t) is expressed as:
Figure FDA0003389302420000033
the equations for the reliable life, median life and characteristic life are then expressed as follows:
t=R-1(t)
Figure FDA0003389302420000034
Figure FDA0003389302420000035
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