Fatigue life analysis method based on frequency domain method

Abstract

The invention provides a frequency domain method-based fatigue life analysis method, which comprises the following steps of: 1, importing an FEA analysis result, and reading field variable information in the result; 2, importing a material database to obtain fatigue life data under the conditions of different temperatures and stress ratios R; step 3, reading a mises stress process in the FEA; taking the obtained influence PSD stress curve as the input of fatigue calculation; 4, performing spectral moment calculation by using a PSD response curve, and calculating accumulated damage through a probability density function of a stress amplitude; and 5, calculating accumulated damage to accurately predict the fatigue life. According to the method, the development of random vibration fatigue research to actual engineering application is realized, calculation is performed by utilizing a PSD response curve and a probability density function of stress amplitude, and the problems of quick calculation of fatigue damage and accurate prediction of service life under multiple influences caused by randomness of vibration frequency and complex external load in the loading process are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue damage analysis and research, and particularly relates to a fatigue life analysis method based on the frequency domain method. Background Art

[0002] Fatigue failure is one of the main causes of engineering structure and machinery failure. The peak value of the cyclic load that causes fatigue failure is often much smaller than the "safe" load estimated according to static fracture analysis. Therefore, it is of great significance to carry out structural fatigue research. The maximum load that causes the failure of materials or structures under a single load is called static strength. The situation where materials or structures fail under multiple loads is called fatigue. The number of times of load application is called fatigue life, and the corresponding load value is called fatigue strength.

[0003] When an engineering structure works in a vibration load environment, it will suffer fatigue failure due to the action of vibration loads, such as structures like aircraft intakes, wings, tails, fuel pipelines, and cannon mounts. The vibration loads received by engineering structures are usually a random process. Therefore, vibration fatigue is a fatigue failure problem of structures under random vibration loads. In order to predict the fatigue life under random loading conditions, a fatigue model that correlates the equivalent damage parameter with the uniaxial SN fatigue characteristics is used. Compared with the external load of conventional fatigue, the magnitude and number of internal stress and strain in the structure caused by a single action of the external load of random vibration fatigue are not only related to the magnitude and action duration of the external load, but also related to the dynamic characteristics of the structure. This makes the prediction of random fatigue life more challenging than ordinary mechanical fatigue.

[0004] In recent years, many mature fatigue models based on the narrowband method and the Steinberg method have been developed. However, existing models often rely on specific vibration frequency characteristics, and most of these criteria have significant errors in predicting fatigue life under random vibration loads. At present, some scholars have noticed that vibration characteristics exhibit different fatigue behaviors under random vibration loads, and thus established different fatigue models to analyze different vibration frequency loads. However, the current related methods still have the defects of large prediction accuracy errors and poor actual application effects. Summary of the Invention

[0005] The main purpose of the present invention is to provide a fatigue life analysis method based on the frequency domain method, which can effectively solve the problems in the background art, realize the development of random vibration fatigue research towards practical engineering applications, and solve the rapid calculation of fatigue damage and accurate prediction of life under the randomness of vibration frequency during the loading process and the multiple influences caused by complex external loads.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A fatigue life analysis method based on the frequency domain method, comprising the following steps:

[0008] First step, import the FEA analysis results, and read the field variable information in the results, including stress, strain, displacement, and temperature field; Second step, import the material database to obtain fatigue life data under different temperatures and stress ratio R conditions;

[0009] Third step, read the mises stress history in the FEA; and use the obtained PSD stress curve as the input for fatigue calculation;

[0010] Fourth step, use the PSD response curve to calculate the spectral moment, and calculate the cumulative damage through the probability density function of the stress amplitude;

[0011] Fifth step, accurately predict the fatigue life by calculating the cumulative damage.

[0012] Furthermore, in the first step, directly import the FEA analysis results from the TT-FEM module of the TURBOTIDES analysis platform through the SeniorFatigue software, and the SeniorFatigue software can improve the calculation efficiency by automatically identifying the analysis steps and increment steps in the results and by identifying and reading the fatigue failure data of the structural surface elements / nodes.

[0013] Furthermore, in the second step, the material database is used to store the conventional properties of the material, S-N related parameters, E-N related parameters, and can obtain fatigue life data under different temperatures and stress ratio R conditions through linear interpolation and curve interpolation.

[0014] Furthermore, the specific method of the third step is divided into two types. One is: (1), directly read the random vibration mises stress history in the FEA results; the other is: (2), automatically calculate the mises stress history after response according to the frequency response function and the power spectral density of the excitation signal in the FEA.

[0015] Furthermore, in the fourth step: the equation for calculating the spectral moment of the PSD response curve is:

[0016]

[0017] where ω is the frequency, G X (ω) is the response PSD stress, i is the order, and m0 is the mean square value of the response.

[0018] Furthermore, in the fourth step: the bandwidth coefficient ε and the irregularity factor γ are introduced into the equation for calculating the spectral moment of the PSD response curve,

[0019]

[0020] Wherein, its value range is 0 ≤ ε ≤ 1. When ε approaches 1, it is a wideband random process, and when ε approaches 0, it is a narrowband random process.

[0021] Furthermore, in the fourth step: the probability density function calculation equation is:

[0022]

[0023] The cumulative damage is calculated through the probability density function of the stress amplitude. Assuming the signal history is T:

[0024]

[0025] Wherein, is the number of peaks per unit time (peak rate), N(S) = aS -b is an S-N curve in exponential form.

[0026] Furthermore, for the narrowband process, P(S) is a Raileigh distribution, and the analytical solution for the exponential form of the S-N curve is:

[0027]

[0028] Wherein, Γ() is the Gamma function.

[0029] Furthermore, for the wideband process, the peak probability density function of wideband random vibration is a combination of a normal distribution and a Rayleigh distribution, and its expression equation is:

[0030]

[0031] Wherein,

[0032] D3 = 1 - D1 - D2, S is the stress range.

[0033] Furthermore, in the fifth step, it is displayed and accurately predicted through the cumulative damage cloud map and the random vibration fatigue life cloud map.

[0034] Compared with the prior art, the fatigue life analysis method based on the frequency domain method of the present invention has the following beneficial effects: The present invention realizes the development of random vibration fatigue research towards practical engineering applications. Around the stress response power spectral density and the stress probability density function, the narrowband method and the Dirlik method are applied to solve the rapid calculation of fatigue damage and the accurate prediction of life under the randomness of vibration frequency during the loading process and the multiple effects on engineering components caused by complex external loads. Description of the Drawings

[0035] Figure 1This is the principle flow chart of the present invention.

[0036] Figure 2 This is the schematic diagram of non-uniform sampling in the power spectral density frequency domain of the present invention.

[0037] Figure 3 This is the imported display diagram of the FEA analysis result of the present invention.

[0038] Figure 4 This is the interface diagram of the material database of the present invention.

[0039] Figure 5 This is the schematic diagram of the random vibration load that can be processed by the present invention.

[0040] Figure 6 This is the interface of the Dirlik method fatigue calculation method for life estimation based on broadband random vibration of the present invention.

[0041] Figure 7 This is the interface of the Narrowband method fatigue calculation method for life estimation based on narrowband random vibration of the present invention.

[0042] Figure 8 This is the cloud map of the random vibration fatigue life of the present invention. Detailed implementation manners

[0043] To make the purpose, technical means for implementation, advantages, and the achievements of the purpose and effects of the present invention easy to understand, the present invention will be further described below in conjunction with specific implementation manners.

[0044] Example 1, as Figures 1 to 8As shown, a fatigue life analysis method based on the frequency domain method includes the following steps: First step, import the FEA analysis results and read the field variable information in the results, including stress, strain, displacement, and temperature field; Second step, import the material database to obtain fatigue life data under different temperatures and stress ratios R; Third step, read the mises stress history in the FEA; and use the obtained PSD stress curve as the input for fatigue calculation; Fourth step, use the PSD response curve to calculate the spectral moment and calculate the cumulative damage through the probability density function of the stress amplitude; Fifth step, accurately predict the fatigue life by calculating the cumulative damage. Most mechanical structures work under vibration loads and will experience fatigue due to the action of vibration loads, and fatigue failure is closely related to the characteristics of vibration loads. Since these key components often have complex geometric features and variable vibration environments, these factors will inevitably cause fatigue at the weak parts of the actual mechanical structure; The present invention realizes the development of random vibration fatigue research towards practical engineering applications. By combining the narrowband method and the Dirlik method around the stress response power spectral density and the stress probability density function, it solves the problems of rapid calculation of fatigue damage and accurate prediction of life under the randomness of vibration frequency during the loading process and the multiple effects on engineering components caused by complex external loads, and develops corresponding software, establishes a simulation analysis model, and clarifies the physical mechanism of fatigue failure under external loads and random vibration loads, which can provide scientific guidance for the fatigue life calculation of mechanical structures in service.

[0045] Further, as Figure 2 shown, in the first step, directly import the FEA analysis results from the TT-FEM module of the TURBOTIDES analysis platform through the SeniorFatigue software, and the SeniorFatigue software can improve the calculation efficiency by automatically identifying the analysis steps and increment steps in the results and by identifying and reading the fatigue failure data of the structural surface elements / nodes.

[0046] Further, as Figure 3 shown, in the second step, the material database is used to store the conventional properties of the material, S-N related parameters, E-N related parameters, and can obtain fatigue life data under different temperatures and stress ratios R through linear interpolation and curve interpolation.

[0047] Further, the specific method of the third step is divided into two types. One is: (1), directly read the random vibration mises stress history in the FEA results; the other is: (2), automatically calculate the mises stress history after response according to the frequency response function and the power spectral density of the excitation signal in the FEA.

[0048] Further, in the fourth step: The equation for calculating the spectral moment of the PSD response curve is:

[0049]

[0050] where ω is the frequency, G X (ω) is the response PSD stress, i is the order, and m0 is the mean square value following the response.

[0051] Furthermore, in the fourth step: in the PSD response curve spectral moment calculation equation, the bandwidth coefficient ε and the irregularity factor γ are introduced.

[0052]

[0053]

[0054] where: its value range is 0 ≤ ε ≤ 1. When ε approaches 1, it is a wideband random process, and when ε approaches 0, it is a narrowband random process.

[0055] Furthermore, in the fourth step: the probability density function calculation equation is:

[0056]

[0057] The cumulative damage is calculated through the probability density function of the stress amplitude. Assuming the signal history is T:

[0058]

[0059] where is the number of peaks per unit time (peak rate), N(S) = aS -b is the S-N curve in exponential form; the power spectral density is used to describe the characteristics of a stationary random process varying with frequency (i.e., the frequency-domain characteristics). PSD characterizes the distribution of the average power of the random process with frequency, and its dimension is: the square of the physical quantity dimension / HZ. The power spectral density has no phase information, and its integral is the average power; in random vibration analysis, the power corresponds to the square value of the physical quantity, and the integral of the power spectral density is the mean square value of the corresponding physical quantity; for a stationary random process, its power spectral density function S X (ω) and its autocorrelation function R X (τ) exactly form a Fourier transform pair:

[0060]

[0061] Statistical moments can be used to describe the numerical characteristics of the probability density distribution function (PDF) of a random process, and spectral moments can be used to describe the numerical characteristics of the power spectral density of a stationary random process. The expression for the i-th spectral moment m i of the stationary process X(t) is:

[0062]

[0063] According to the different shapes of their power spectral densities, stationary random processes, such as Figure 5 shown, can be divided into narrowband stationary random processes and broadband stationary random processes. The spectral density of a narrowband stationary random process is mainly distributed in a narrow frequency range, and the power spectral density has a peak, which is close to the form of simple harmonic vibration. The power spectral density of a broadband random process is relatively flat, distributed in a relatively wide frequency band range, and has great randomness.

[0064] Furthermore, as Figure 6 and Figure 7 shown, for a narrowband process, P(S) follows a Rayleigh distribution, and when the S-N curve is in exponential form, the analytical solution is:

[0065]

[0066] where Γ() is the Gamma function.

[0067] Furthermore, for a broadband process, the peak probability density function of broadband random vibration is a combination of a normal distribution and a Rayleigh distribution, and its expression equation is:

[0068]

[0069] where

[0070] D3 = 1 - D1 - D2, S is the stress range; the peak probability density function of broadband random vibration is a combination of a normal distribution and a Rayleigh distribution. The Dirlik method uses Monte Carlo techniques to perform a large number of computer simulations to obtain an empirical closed solution for the fatigue analysis method of frequency-domain signals.

[0071] Furthermore, as Figure 8 shown, in the fifth step, it is demonstrated and accurately predicted through the cumulative damage contour map and the random vibration fatigue life contour map. Engineering structures usually bear variable amplitude loads and gradually fail. How to calculate damage accumulation is of great significance for the accurate prediction of fatigue life. The fatigue damage accumulation theory mainly includes three aspects: (1) damage caused by a single cycle; (2) damage caused by the interaction between different levels of loads; (3) critical damage value. From the perspective of the methods for describing fatigue damage accumulation, it can be mainly divided into two categories: linear damage accumulation and nonlinear damage accumulation. Linear damage accumulation is represented by the Miner criterion, In the formula, n i is the number of cycles under a given cyclic stress or strain level, and N iwhere \(N_f\) is the number of cycles at the same stress or strain level for fatigue failure life, and \(m\) is the total number of load levels. The Miner's criterion assumes that fatigue failure occurs when the critical damage \(D\) equals 1, but the critical damage is not always 1. Instead, it follows a lognormal distribution with a mean value of 1. Nonlinear damage accumulation is represented by the Starkey criterion: where \(\eta\) i is a variable related to the \(i\)th stress loading level. As the stress level increases, the variable \(\eta\) i gradually approaches 1.

[0072] This invention starts with random vibration fatigue experiments and theoretical analysis methods, summarizes the advantages and disadvantages of existing random vibration fatigue assessment models, and applies the narrowband method and Dirlik method around the stress response power spectral density and stress probability density function. It has been applied in random vibration fatigue life prediction, with small computational volume and fast operation speed, and can accurately predict fatigue life at the same time.

[0073] Example 2: The invention also provides a three - interval method for calculating random vibration fatigue. By Steinberg's arrangement and rearrangement of a large amount of experimental data, it is a simplified method based on the Gaussian distribution and Miner's criterion, which can be used to analyze the fatigue life of structures in a random vibration environment. It has reasonable accuracy and precision and can meet most engineering requirements. First, assume that the random excitation received by the structure follows a Gaussian distribution. The time when the instantaneous acceleration at the 1σ level acts between - 1σ and + 1σ accounts for 68.3%, the time when the instantaneous acceleration at the 2σ level acts between - 2σ and + 2σ accounts for 27.1% (95.4% - 68.3%), and the time when the instantaneous acceleration at the 3σ level acts between - 3σ and + 3σ accounts for 4.33% (99.73% - 95.4%). Using the 1σ, 2σ, and 3σ stress levels and vibration frequencies, and then using the S - N curve and Miner's criterion to calculate the fatigue damage at the critical point, the vibration fatigue life can be obtained. The specific calculation formula for fatigue damage is as follows:

[0074]

[0075] where \(N_1\), \(N_2\), \(N_3\) 1σ , \(N_1\) 2σ , \(N_2\) 3σ are the number of cycles corresponding to the 1σ, 2σ, and 3σ stress levels obtained from the S - N curve respectively. The trigonometric series method, also known as the harmonic superposition method, is a relatively mature time - domain simulation method in time - domain fatigue calculation and is applicable to various spectrum shapes. The basic idea of time - domain simulation of a random process is to approximate the target random process with a discrete spectrum. Suppose the power spectral density of a random process is as Figure 1 shown. Take \(m\) points on the frequency axis, \(f_1\), \(f_2\), …, \(f\) i , …, \(f\) m, each point corresponds to a spectral density value G(f i ). According to the idea of the trigonometric series method, a random process can be approximated by the superposition of an infinite number of simple harmonic vibrations. The amplitude of the simple harmonic vibration is determined by the root mean square of the random process, the vibration frequency depends on the frequency points of the power spectral density function, and the initial phase of the simple harmonic vibration is uniformly distributed within (0, 2π]. The mean square value of a stationary random process is determined by the area under the curve of the spectral density in the frequency domain. From this, the mean square stress amplitude a i 2 of the response spectrum within this frequency range is obtained as:

[0076] a i 2 = (f i+1 - f i )(G(f i ) + G(f i+1 )) for i = 2, 3,..., m - 1;

[0077] The frequency ω i of the simple harmonic vibration is determined by the following formula:

[0078] ω i = π(f i + f i+1 ) for i = 2, 3,..., m - 1

[0079] A subsample of the true random process is obtained by the improved angular series method:

[0080]

[0081] The obtained subsample is subjected to rainflow processing to filter out the load value cycles that have little influence on structural fatigue damage, and a load-time history that can be used for fatigue life analysis is obtained, which can also be used in conjunction with this method for accurate prediction of fatigue life.

[0082] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes, equivalent substitutions, improvements, etc., all of which should fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A fatigue life analysis method based on the frequency domain method, characterized in that It includes the following steps: The first step: Import the FEA analysis results, and read the field variable information in the results, including stress, strain, displacement, and temperature field; The second step: Import the material database to obtain the fatigue life data under different temperatures and stress ratio R conditions; The third step: Read the mises stress history in the FEA; and use the obtained PSD stress curve as the input for fatigue calculation; The fourth step: Use the PSD response curve to calculate the spectral moment, and calculate the cumulative damage through the probability density function of the stress amplitude; The fifth step: Accurately predict the fatigue life by calculating the cumulative damage.

2. The fatigue life analysis method based on the frequency domain method according to claim 1, wherein: In the first step, directly import the FEA analysis results from the TT-FEM module of the TURBOTIDES analysis platform through the SeniorFatigue software, and the SeniorFatigue software can improve the calculation efficiency by automatically identifying the analysis steps and increment steps in the results and by identifying and reading the fatigue failure data of the structural surface elements / nodes.

3. A fatigue life analysis method based on the frequency domain method according to claim 1, characterized in that: In the second step, the material database is used to store the conventional properties of the material, S-N related parameters, E-N related parameters, and the fatigue life data under different temperatures and stress ratio R conditions can be obtained by means of linear interpolation and curve interpolation.

4. The fatigue life analysis method based on the frequency domain method according to claim 1, wherein: The specific method of the third step is: (1) Directly read the random vibration mises stress history in the FEA results; (2) Automatically calculate the mises stress history after response according to the frequency response function and the power spectral density of the excitation signal in the FEA.

5. A fatigue life analysis method based on the frequency domain method according to claim 1, characterized in that: In the fourth step: The equation for calculating the spectral moment of the PSD response curve is: where ω is the frequency, G X (ω) is the response PSD stress, i is the order, and m0 is the mean square value following the response.

6. The fatigue life analysis method based on the frequency domain method according to claim 5, characterized in that: In the fourth step: The bandwidth coefficient ε and the irregularity factor γ are introduced into the equation for calculating the spectral moment of the PSD response curve, where: The value range is 0 ≤ ε ≤ 1. When ε approaches 1, it is a wideband random process, and when ε approaches 0, it is a narrowband random process.

7. A fatigue life analysis method based on the frequency domain method according to claim 1, characterized in that: In the fourth step: The equation for calculating the probability density function is: Calculate the cumulative damage through the probability density function of the stress amplitude. Assume the signal history is T: Among them, is the number of peaks per unit time (peak rate), and N(S) = aS -b is an S-N curve in exponential form.

8. The fatigue life analysis method based on the frequency domain method according to claim 6, wherein: For the narrowband process, P(S) is the Raileigh distribution, and there is an analytical solution when the S-N curve is in exponential form: where Γ() is the Gamma function.

9. A fatigue life analysis method based on the frequency domain method according to claim 1, characterized in that: For the wideband process, the peak probability density function of wideband random vibration is a combination of the normal distribution and the Rayleigh distribution, and its expression equation is: where, D3 = 1 - D1 - D2, S is the stress range.

10. A fatigue life analysis method based on the frequency domain method according to claim 1, characterized in that: In the fifth step, display and accurate prediction are carried out through the cumulative damage cloud map and the random vibration fatigue life cloud map.

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