A random vibration fatigue life analysis method considering damage equivalence

Abstract

The present invention discloses a random vibration fatigue life analysis method taking into account damage equivalence, which belongs to the field of engineering technology vibration fatigue testing. The method includes the following steps: determining the frequency response function of the test structure; calculating the equivalent test power spectrum density of the vibration acceleration; calculating the stress response of the test structure; predicting the number of time-series load cycles of the stress response spectrum; counting the rain flow of the time-domain load cycle; calculating the fatigue damage of the test structure; and evaluating the fatigue life results of the test structure. The present invention provides a new analysis method for vibration fatigue life analysis of mechanical structures. The method performs vibration life analysis on mechanical structures while taking into account damage equivalence, and by adjusting the equivalent test time, it can achieve the purpose of frequency domain accelerated testing, providing a basis and method for vibration fatigue life analysis and vibration accelerated testing; it can more accurately evaluate the fatigue life of mechanical structures under random vibration, and improve the reliability and safety of the structure.

Description

Technical Field

[0001] The present invention relates to the field of engineering technology vibration fatigue testing, and more particularly to a random vibration fatigue life analysis method taking damage equivalence into consideration. Background Art

[0002] Currently, in modern industrial manufacturing, mechanical equipment and structures need to withstand various types of vibration loads. Among them, random vibration is a common type of vibration. Since its vibration characteristics are difficult to predict, random vibration fatigue life analysis has always been a challenging problem. The fatigue life analysis methods of random vibration are mainly divided into time domain analysis and frequency domain analysis. In time domain analysis, the fatigue life is analyzed by recording the time history of the vibration acceleration load, but this method has high computational complexity and high requirements on the sampling rate and sampling length of the signal. In frequency domain analysis, the vibration acceleration load can be converted into a frequency domain signal and analyzed, thereby improving computational efficiency and reducing the requirements on the sampling rate and sampling length.

[0003] However, most existing technologies use a frequency-domain Fourier transform of random vibration acceleration loads to obtain a power spectral density (PSD), and then use its envelope as the input for vibration fatigue life analysis. This method has two drawbacks: (1) the power spectral density (PSD) obtained by Fourier transform does not take into account damage information; (2) the envelope of the PSD load results in a conservative fatigue life result, which is not conducive to lightweight design of the structure. Therefore, a more accurate random acceleration vibration fatigue life analysis method is needed to solve this problem. Summary of the Invention

[0004] In view of this, the present invention provides a random vibration fatigue life analysis method taking into account damage equivalence to solve the complex problems in the vibration fatigue accelerated test process. While ensuring that the failure mode remains unchanged, it can effectively shorten the vibration fatigue test time and facilitate the timely discovery of design defects.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a random vibration fatigue life analysis method taking into account damage equivalence, comprising the following steps:

[0007] S1. Determine the frequency response function of the target test mechanical structure;

[0008] S2. Calculate the equivalent test power spectrum density of the vibration acceleration of the target test mechanical structure;

[0009] S3, calculate the target test according to the frequency response function and the equivalent test power spectrum density

[0010] machine

[0011] The stress response of the mechanical structure is calculated to obtain the stress response spectrum;

[0012] S4. predicting the number of time series load cycles of stress response based on the stress response spectrum;

[0013] S5. Count the rain flow of the time series load cycle according to the number of time series load cycles, and obtain the rain flow.

[0014] flow

[0015] matrix;

[0016] S6. Calculating fatigue damage of the target test mechanical structure based on the rain flow matrix and the stress-life curve;

[0017] S7. Evaluate the remaining fatigue life of the target test mechanical structure based on the fatigue damage.

[0018] Furthermore, the step S1 includes:

[0019] S101. Establish a three-dimensional model of the target test mechanical structure, import the three-dimensional model into finite element analysis software, and select the modal analysis module and the harmonic response analysis module;

[0020] S102. Assigning material properties of the target test mechanical structure according to the actual material properties of the target test mechanical structure, including density, Young's modulus, elastic modulus, and ultimate tensile strength;

[0021] S103, meshing the three-dimensional model using a tetrahedral mesh or a hexahedral mesh;

[0022] S104, applying boundary conditions of composite actual constraints to the target test mechanical structure;

[0023] S105, performing modal analysis on the target test mechanical structure according to the modal analysis module to determine the natural frequency and vibration mode of the target test mechanical structure;

[0024] S106, importing the modal analysis results into the harmonic response analysis module, and obtaining an analytical expression of the frequency response function using the modal superposition principle;

[0025] S107, applying a unit load excitation to the target test mechanical structure to obtain a vibration response of the target test mechanical structure at a corresponding frequency, including amplitude and phase;

[0026] S108. Superimpose the harmonic responses at different corresponding frequencies to obtain a frequency response function of the structure.

[0027] Furthermore, the step S2 includes:

[0028] S201. Using an acceleration sensor to record the random vibration acceleration load of the target test mechanical structure in a working environment;

[0029] S202. Calculate the vibration response of the single-degree-of-freedom system to acceleration in the form of relative displacement. The relative displacement depends on the selected natural frequency of the single-degree-of-freedom system. The relationship between the displacement response and the generalized stress is:

[0030]

[0031] Where K is the displacement constant with respect to stress, σ is the generalized stress, z is the displacement response, and f n is the natural frequency; n is the frequency point, which is a positive integer greater than or equal to 0;

[0032] S203. The Basquin equation is used to describe the stress-life curve of the material. According to Miner's law, the damage calculation follows the linear accumulation principle of equations (2) and (3):

[0033]

[0034]

[0035] Among them, N i is the stress amplitude σ i The maximum number of cycles; C, b are material parameters; n i is the stress amplitude σ i The actual number of cycles; D is fatigue damage; i is the stress level of the variable amplitude load, which is a positive integer greater than or equal to 1;

[0036] S204. Calculate the fatigue damage spectrum. Combine formulas (1) to (3) to obtain formula (4). Formula (4) is the calculation formula for the fatigue damage spectrum:

[0037]

[0038] Among them, FDS is fatigue damage spectrum, z i is the amplitude of the relative displacement at level i, and by changing the natural frequency f of the single degree of freedom system n To cover all target frequencies and obtain a complete fatigue damage spectrum;

[0039] S205. If the target test mechanical structure has multiple test conditions, calculate the fatigue damage spectrum of each condition and sum them up to obtain ∑FDS. Formula (5) is the calculation formula for the test power spectrum density taking into account damage equivalence:

[0040]

[0041] Where P(f) is the equivalent power spectrum density, ∑FDS is the power spectrum density of each frequency f under all working conditions. n The sum of the fatigue damage spectra under eq is the time of the equivalent test, Q is the dynamic amplification factor of the single-degree-of-freedom system, and Γ(·) is the gamma function.

[0042] Furthermore, the step S3 specifically includes:

[0043] The frequency response function of step S1 and the equivalent test power spectrum density of step S2 are multiplied to obtain the stress response of the target test mechanical structure under the random vibration load, and the calculation formula is:

[0044] G(f)=|G FRF (f)| 2 ·P(f) (6)

[0045] Among them, G FRF (f) is the frequency response function of the target test mechanical structure, P(f) is the equivalent test power spectrum density, G(f) is the stress response spectrum of the structure, and f is the frequency.

[0046] Furthermore, the step S4 includes:

[0047] S401. Calculate the area moment of the stress response power spectrum density using the formula:

[0048] m n =∫f n ·G n (f)·df (7)

[0049] Where m n is the nth-order area moment, G n (f) is the single-sided area of ​​the power spectral density, and f is the frequency; calculate the 0th-order area moment m0, the 2nd-order area moment m2, and the 4th-order moment m4;

[0050] S402, calculate the expected number of zero crossings E[0] and the expected number of peak crossings E[P], the formula is:

[0051]

[0052]

[0053]

[0054] Among them, m0 is the 0th order area moment, m2 is the 2nd order area moment, m4 is the 4th order area moment, and γ is the irregularity coefficient;

[0055] S403. Use the Lalanne PSD cycle counting method to estimate the stress cycle number of the time series load signal. The formula is:

[0056] N(S)=E[P]·T·p(S) (11)

[0057] where N(S) is the expected number of stress cycles within a time period of T seconds and a stress range of S, E[P] is the expected number of peak crossings, T is the time in seconds, and p(S) is the probability density function of the peak distribution.

[0058] Furthermore, p(S) is the probability density function of the peak distribution, and the formula is as follows:

[0059]

[0060]

[0061] Where rms is the root mean square value, S is the stress range, γ is the irregularity coefficient, and erf(x) is the error function.

[0062] Furthermore, the step S5 includes:

[0063] S501, extracting a cycle using four consecutive load points S1, S2, S3, and S4, where the four consecutive stress points define an internal stress interval ΔS1 = |S2-S3| and an external stress interval ΔS0 = |S1-S4|;

[0064] S502. If the external stress interval is greater than or equal to the internal stress interval: ΔS0 ≥ ΔS1, and the points constituting the internal stress interval are included in the external stress interval, then S2 and S3 are considered to form a cycle; if not, no cycle is counted; the two internal stress points S2 and S3 are discarded, and the two external stress points S1 and S4 are connected;

[0065] S503: Apply the same comparison method as step S502 to the next four consecutive stress points until all data points are counted to obtain a rain flow matrix.

[0066] Furthermore, step S6 includes:

[0067] According to the rain flow matrix and the stress-life curve of the target test mechanical structure material, the Miner linear damage accumulation criterion is used to calculate the damage of the stress load, and the formula is:

[0068]

[0069] Where D is fatigue damage, n i is the number of cycles under the i-th level load, N iIt represents the fatigue life under the i-th level load, and i represents the stress level level of the variable amplitude load.

[0070] The present invention discloses a random vibration fatigue life analysis method taking into account damage equivalence, which has the following beneficial effects compared with the prior art:

[0071] (1) The present invention provides a standardized and streamlined random acceleration vibration fatigue life analysis method. Modal analysis and harmonic response analysis are used to calculate the frequency response function of the test structure, taking into account the influence of load frequency and achieving high calculation accuracy. The finite element analysis results are combined with the measured vibration acceleration load to analyze the fatigue life of the test structure under vibration conditions.

[0072] (2) The method proposed in this invention takes into account damage equivalence. The power spectral density of random vibration acceleration calculated directly by the frequency domain Fourier transform method does not contain information about damage accumulation and therefore cannot be directly used as input for random vibration analysis. This invention takes into account damage equivalence, introduces the fatigue damage spectrum, and derives the power spectral density containing durability information as input for vibration fatigue life analysis.

[0073] (3) The method proposed in this invention can achieve the purpose of frequency domain accelerated testing. By adjusting the equivalent test time, the duration of the power spectrum density can be changed, shortening the simulation analysis time and the bench test time, achieving the purpose of frequency domain accelerated fatigue testing, quickly discovering structural design defects, and reducing the development cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0075] Figure 1 A flow chart of the random vibration fatigue life analysis method taking into account damage equivalence provided by the present invention;

[0076] Figure 2 A three-dimensional model of the test structure provided by the present invention;

[0077] Figure 3 A graph showing the frequency response function of the test structure provided by the present invention;

[0078] Figure 4 A schematic diagram of the random vibration acceleration load provided by the present invention;

[0079] Figure 5 A schematic diagram of the fatigue damage spectrum provided by the present invention;

[0080] Figure 6 Schematic diagram of equivalent test power spectrum density provided by the present invention;

[0081] Figure 7 Schematic diagram of the stress response spectrum of the test structure provided by the present invention;

[0082] Figure 8 A schematic diagram of the spectral moment calculation method provided by the present invention;

[0083] Figure 9 A schematic diagram of the expected number of zero crossings and peak crossings provided by the present invention;

[0084] Figure 10 Schematic diagram of the probability density function of Lalanne cycle counting provided by the present invention;

[0085] Figure 11 A graph showing cycle counting results provided by the present invention;

[0086] Figure 12 The stress-life curve diagram of the test structure material provided by the present invention;

[0087] Figure 13 The cumulative damage diagram provided by the present invention;

[0088] Figure 14 This is the fatigue life result diagram provided by the present invention. DETAILED DESCRIPTION

[0089] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0090] The present invention provides a random vibration fatigue life analysis method taking into account damage equivalence. Taking a certain bracket structure as the research object, the present invention is introduced in combination with the random vibration acceleration load of actual test. Figure 1 As shown, the following steps are included:

[0091] Step 1: Determine the frequency response function of the target test mechanical structure

[0092] Using modal analysis, the vibration modes of the structure are decomposed. By solving the structure's natural frequencies and modal vibration shapes, the modal response of the structure can be obtained. Using harmonic response analysis, the vibration response of the structure at that frequency, including amplitude and phase, can be obtained by applying a unit load excitation to the structure. By superimposing the harmonic responses at different frequencies, the frequency response function of the structure can be obtained. The specific steps are as follows:

[0093] Step 1.1: Create a three-dimensional model of the test structure. Figure 2 Import the 3D model into the finite element analysis software and select the modal analysis module and the harmonic response analysis module;

[0094] Step 1.2: Assign the material properties of the target test mechanical structure according to its actual material properties, including density, Young's modulus, elastic modulus, and tensile strength limit. For example, the support structure material is titanium aluminum alloy, and the density of titanium aluminum alloy is 4.54g / cm 3 , Poisson's ratio is 0.35, Young's modulus is 461.5MPa, elastic modulus is 110GPa, and ultimate tensile strength is 700MPa;

[0095] Step 1.3 uses tetrahedral mesh or hexahedral mesh to mesh the three-dimensional model. Figure 2 The structure of the bracket structure is divided into three-dimensional models using hexahedral grids;

[0096] Step 1.4 applies boundary conditions to the bracket structure, and the two holes on the left are fixed constraints, such as Figure 2 As shown;

[0097] Step 1.5: Perform modal analysis on the bracket structure to determine the natural frequency and vibration mode of the bracket structure;

[0098] Step 1.6: Import the modal analysis results into the harmonic response analysis module and use the modal superposition principle to obtain the analytical expression of the frequency response function;

[0099] In step 1.7, apply a vertical upward unit load excitation to the hole below the support structure to obtain the vibration response of the support structure at a certain frequency. The frequency range is selected from 0 to 300 Hz.

[0100] In step 1.8, the harmonic response results of 0 to 300 Hz are superimposed to obtain the frequency response function (FRF) of the structure, as shown in Figure 3 shown.

[0101] Step 2 Calculate the equivalent test power spectrum density of vibration acceleration

[0102] The power spectral density PSD obtained by Fourier transform does not contain damage information and therefore cannot be directly used as input for random vibration analysis. Taking into account damage equivalence, fatigue damage spectrum is introduced. The definition of fatigue damage spectrum (FDS) is that for a single degree of freedom system, given the damping ratio ξ and material parameter b, the natural frequency f of the single degree of freedom system is n Perform fatigue damage tracking to obtain the relationship between frequency and damage.

[0103] Step 2.1 Use an accelerometer to record the random vibration acceleration load of the support structure in the working environment, such as Figure 4 As shown, the maximum acceleration load is 4.6m / s 2 , the sampling frequency is 100Hz, the load time length is 900s,

[0104] Step 2.2 calculates the vibration response of the single-degree-of-freedom system to acceleration in the form of relative displacement. The relative displacement depends on the selected natural frequency of the single-degree-of-freedom system. Assume that the relationship between the displacement response and the generalized stress is:

[0105]

[0106] where K is the displacement constant with respect to stress, σ is the generalized stress and z displacement response, and f n is the natural frequency, n is the frequency point, and its value ranges from 0 to 300.

[0107] Step 2.3 The stress-life curve of the material is assumed to be described by the Basquin equation. According to Miner's law, the damage calculation follows the linear accumulation principle of equations (2) and (3):

[0108]

[0109]

[0110] Among them, N i is the stress amplitude σ i The maximum number of cycles, parameters C and b are material parameters, n i is the stress amplitude σ i The actual number of cycles, D is the fatigue damage, i represents the stress level of the variable amplitude load, and the value is 1, 2, 3…

[0111] Step 2.4: Combine formulas (1) to (3) to obtain formula (4), which is the calculation formula for the fatigue damage spectrum:

[0112]

[0113] Among them, FDS is fatigue damage spectrum, z iis the amplitude of the relative displacement at level i, and by changing the natural frequency f of the single degree of freedom system n To cover all target frequencies 0-300 Hz, a complete fatigue damage spectrum is obtained, such as Figure 5 shown.

[0114] In this example, b is set to 3, where b is the damage index of the material. From formula (5), we can see that the larger the value of b, the more damage is considered for loads with larger amplitudes, and the influence of small loads is ignored; the smaller the value of b, the more the effect of small loads is ignored. After analysis, b is set to 3 in this example.

[0115] Step 2.5: This example only considers one set of load data. If the test structure has multiple test conditions, calculate the fatigue damage spectrum of each condition and sum them to obtain ∑FDS. Formula (5) is the calculation formula for the test power spectrum density derived from the fatigue damage spectrum taking into account damage equivalence:

[0116]

[0117] Where P(f) is the equivalent power spectrum density, FDS is the fatigue damage spectrum calculated in step 2.4, k is the safety factor, which is 1.2, and T eq is the time of equivalent test, which is 450s, Q is the dynamic amplification factor of single degree of freedom system, which is 10, Γ(·) is the gamma function, b and C are material parameters, b is 3, C is 1, Figure 6 Schematic diagram of equivalent test power spectrum density.

[0118] Step 3: Calculate the stress response of the test structure

[0119] Multiplying the frequency response function in step 1 and the equivalent power spectrum density in step 2 yields the stress response of the test structure under random vibration loads. The calculation formula is:

[0120] G(f)=|G FRF (f)| 2 ·P(f) (6)

[0121] Among them, G FRF (f) is the frequency response function of the test structure, P(f) is the equivalent test power spectrum density, G(f) is the stress response spectrum of the structure, f is the frequency, and the stress response spectrum of the bracket structure is as follows: Figure 7 shown.

[0122] Step 4: Estimate the number of time series load cycles for the stress response spectrum

[0123] Based on the shape of the stress response spectrum G(f) in step 3, the number of loading cycles of the stress response is predicted.

[0124] Step 4.1 calculates the area moment of the stress response PSD. The area moment is defined as Figure 8 As shown, the calculation formula of area moment is:

[0125] m n =∫f n ·G n (f)·df (7)

[0126] Among them, m n is the nth-order area moment, G n (f) is the single-sided area of ​​the PSD, and f is the frequency. Calculate the 0th-order area moment m0, the 2nd-order area moment m2, and the 4th-order area moment m4.

[0127] Step 4.2 calculates the expected number of zero crossings E[0] and peak crossings E[P] of the stress response spectrum. Figure 9 This is a diagram of the expected number of zero crossings and peak crossings, and the formula is:

[0128]

[0129]

[0130]

[0131] Among them, m0 is the 0th order area moment, m2 is the 2nd order area moment, m4 is the 4th order area moment, and γ is the irregularity coefficient.

[0132] Step 4.3 uses the Lalanne PSD cycle counting method to estimate the number of stress cycles of the time series load signal. The formula is:

[0133] N(S)=E[P]·T·p(S) (11)

[0134] Where N(S) is the expected number of stress cycles within a time of T seconds and a stress range of S, E[P] is the expected number of peak crossings, and p(S) is the probability density function of the peak distribution, as shown in Figure 10 As shown, the formula is:

[0135]

[0136]

[0137] Where rms is the root mean square value, S is the stress range, γ is the irregularity coefficient, and erf(x) is the error function.

[0138] Step 5 Rainflow counting for time domain load cycles

[0139] Select four consecutive load points S1, S2, S3, and S4 to extract a cycle. The four consecutive stress points define the internal stress interval ΔS1 = |S2-S3| and the external stress interval ΔS0 = |S1-S4|. If the external stress interval is greater than or equal to the internal stress interval (ΔS0 ≥ ΔS1), and the points that make up the internal stress interval are included in the external stress interval, then the second and third points are considered to form a cycle. If this is not satisfied, no cycle is counted. Discard the two internal stress points and connect the two external stress points (the first and fourth points). In addition, the same comparison method is used for the subsequent four consecutive stress points until all data points are counted to obtain the rain flow matrix. Figure 11 To display the results of rainflow counting in the form of frequency-amplitude.

[0140] Step 6 Calculate the fatigue damage of the test structure

[0141] According to the rain flow matrix, combined with the real stress-life curve of the support structure material, such as Figure 12 As shown in Figure 2, the Miner linear damage accumulation criterion is used to calculate the damage of stress load, and the formula is:

[0142]

[0143] Where D is fatigue damage, n i Indicates the number of cycles under the i-th level load, N i represents the fatigue life under the i-th level load, i represents the stress level of the variable amplitude load. The cumulative damage results are as follows Figure 13 shown.

[0144] Step 7: Evaluate the fatigue life results of the test structure

[0145] like Figure 14 As shown, combined with the number of failures and the damage assessment in step 6, the remaining fatigue life results of the test structure are evaluated and the causes of errors are analyzed to ensure the reliability and accuracy of the results.

[0146] The present invention provides a random vibration fatigue life analysis method that takes damage equivalence into account. Through the present invention, the fatigue life of mechanical structures under random vibration can be more accurately evaluated, the reliability and safety of the structure can be improved, and it is expected to be widely used in industrial manufacturing.

[0147] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0148] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A random vibration fatigue life analysis method taking into account damage equivalence, characterized in that: The following steps are involved: S1. Determine the frequency response function of the target test mechanical structure; S2. Calculate the equivalent test power spectrum density of the vibration acceleration of the target test mechanical structure; S3. Calculating the stress response of the target test mechanical structure according to the frequency response function and the equivalent test power spectrum density to obtain a stress response spectrum; S4. predicting the number of time series load cycles of stress response based on the stress response spectrum; S5. Counting rain flow of the time series load cycle according to the number of time series load cycles to obtain a rain flow matrix; S6. Calculating fatigue damage of the target test mechanical structure based on the rain flow matrix and the stress-life curve; S7. Evaluate the remaining fatigue life of the target test mechanical structure based on the fatigue damage; Wherein, the step S2 includes: S201. Using an acceleration sensor to record the random vibration acceleration load of the target test mechanical structure in a working environment; S202. Calculate the vibration response of the single-degree-of-freedom system to acceleration in the form of relative displacement. The relative displacement depends on the selected natural frequency of the single-degree-of-freedom system. The relationship between the displacement response and the generalized stress is: Where K is the displacement constant with respect to stress, σ is the generalized stress, z is the displacement response, and f n is the natural frequency; n is the frequency point, which is a positive integer greater than or equal to 0; S203. The Basquin equation is used to describe the stress-life curve of the material. According to Miner's law, the damage calculation follows the linear accumulation principle of equations (2) and (3): Among them, N i is the stress amplitude σ i The maximum number of cycles; C, b are material parameters; n i is the stress amplitude σ i The actual number of cycles; D is fatigue damage; i is the stress level of the variable amplitude load, which is a positive integer greater than or equal to 1; S204. Calculate the fatigue damage spectrum. Combine formulas (1) to (3) to obtain formula (4). Formula (4) is the calculation formula for the fatigue damage spectrum: Among them, FDS is fatigue damage spectrum, z i is the amplitude of the relative displacement at level i, and by changing the natural frequency f of the single degree of freedom system n To cover all target frequencies and obtain a complete fatigue damage spectrum; S205. If the target test mechanical structure has multiple test conditions, calculate the fatigue damage spectrum of each condition and sum them up to obtain ∑FDS. Formula (5) is the calculation formula for the test power spectrum density taking into account damage equivalence: Where P(f) is the equivalent power spectrum density, ∑FDS is the power spectrum density of each frequency f under all working conditions. n The sum of the fatigue damage spectra under eq is the time of the equivalent test, Q is the dynamic amplification factor of the single-degree-of-freedom system, and Γ(·) is the gamma function.

2. The random vibration fatigue life analysis method taking into account damage equivalence according to claim 1 is characterized in that: The step S1 comprises: S101. Establish a three-dimensional model of the target test mechanical structure, import the three-dimensional model into finite element analysis software, and select the modal analysis module and the harmonic response analysis module; S102. Assigning material properties of the target test mechanical structure according to the actual material properties of the target test mechanical structure, including density, Young's modulus, elastic modulus, and ultimate tensile strength; S103, meshing the three-dimensional model using a tetrahedral mesh or a hexahedral mesh; S104, applying boundary conditions of composite actual constraints to the target test mechanical structure; S105, performing modal analysis on the target test mechanical structure according to the modal analysis module to determine the natural frequency and vibration mode of the target test mechanical structure; S106, importing the modal analysis results into the harmonic response analysis module, and obtaining an analytical expression of the frequency response function using the modal superposition principle; S107, applying a unit load excitation to the target test mechanical structure to obtain a vibration response of the target test mechanical structure at a corresponding frequency, including amplitude and phase; S108. Superimpose the harmonic responses at different corresponding frequencies to obtain a frequency response function of the structure.

3. The random vibration fatigue life analysis method taking into account damage equivalence according to claim 1 is characterized in that: The step S3 specifically includes: The frequency response function of step S1 and the equivalent test power spectrum density of step S2 are multiplied to obtain the stress response of the target test mechanical structure under the random vibration load, and the calculation formula is: G(f)=|G FRF (f)| 2 ·P(f) (6) Among them, G FRF (f) is the frequency response function of the target test mechanical structure, P(f) is the equivalent test power spectrum density, G(f) is the stress response spectrum of the structure, and f is the frequency.

4. The random vibration fatigue life analysis method taking into account damage equivalence according to claim 1, characterized in that: The step S4 comprises: S401. Calculate the area moment of the stress response power spectrum density, the formula is: m n =∫f n ·G n (f)·df (7) Where m n is the nth-order area moment, G n (f) is the single-sided area of ​​the power spectral density, and f is the frequency; calculate the 0th-order area moment m0, the 2nd-order area moment m2, and the 4th-order moment m4; S402, calculate the expected number of zero crossings E[0] and the expected number of peak crossings E[P], the formula is: Among them, m0 is the 0th order area moment, m2 is the 2nd order area moment, m4 is the 4th order area moment, and γ is the irregularity coefficient; S403. Use the Lalanne PSD cycle counting method to estimate the stress cycle number of the time series load signal. The formula is: N(S)=E[P]·T·p(S) (11) where N(S) is the expected number of stress cycles within a time period of T seconds and a stress range of S, E[P] is the expected number of peak crossings, T is the time in seconds, and p(S) is the probability density function of the peak distribution.

5. The random vibration fatigue life analysis method taking into account damage equivalence according to claim 4 is characterized in that: p(S) is the probability density function of the peak distribution, and the formula is as follows: Where rms is the root mean square value, S is the stress range, γ is the irregularity coefficient, and erf(x) is the error function.

6. The random vibration fatigue life analysis method considering damage equivalence according to claim 1, characterized in that: The step S5 comprises: S501, extracting a cycle using four consecutive load points S1, S2, S3, and S4, where the four consecutive stress points define an internal stress interval ΔS1 = |S2-S3| and an external stress interval ΔS0 = |S1-S4|; S502. If the external stress interval is greater than or equal to the internal stress interval: ΔS0 ≥ ΔS1, and the points constituting the internal stress interval are included in the external stress interval, then S2 and S3 are considered to form a cycle; if not, no cycle count is performed; the two internal stress points S2 and S3 are discarded, and the two external stress points S1 and S4 are connected; S503: Apply the same comparison method as step S502 to the next four consecutive stress points until all data points are counted to obtain a rain flow matrix.

7. The random vibration fatigue life analysis method considering damage equivalence according to claim 1, characterized in that: The step S6 comprises: According to the rain flow matrix and the stress-life curve of the target test mechanical structure material, the Miner linear damage accumulation criterion is used to calculate the damage of the stress load, and the formula is: Where D is fatigue damage, n i is the number of cycles under the i-th level load, N i It represents the fatigue life under the i-th level load, and i represents the stress level level of the variable amplitude load.

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