A multi-axis random vibration life prediction method considering the influence of bandwidth

Abstract

The present invention discloses a multi-axis random vibration life prediction method considering bandwidth influence, which involves data acquisition, processing and life calculation of wide-band random vibration tests, and belongs to the field of fatigue performance of materials under random vibration loads. The present invention corrects the error of the frequency-domain equivalent von Mises stress method in the wide-band case, and proposes an improved von Mises equivalent criterion by adding a bandwidth influence factor to better estimate the damage in the wide-band case, so as to make the fatigue life prediction of aluminum alloy under wide-band multi-axis vibration more accurate.

Description

Technical Field

[0001] The present invention is applied to the field of broadband multi - axis random vibration fatigue life prediction in the frequency domain, and particularly refers to a multi - axis random vibration fatigue life prediction method considering the influence of bandwidth. Background Art

[0002] With the rapid development of the material field and the stringent requirements put forward in engineering applications, higher requirements are also put forward for the mechanical strength and durability design. On the one hand, whether it is ships, heavy machinery or the recently much - concerned hypersonic aircraft, it is required that the fatigue life of many components be above 10 7 . Using the traditional time - domain method will bring extremely long design, test, and measurement time investment, which is obviously too time - consuming. On the other hand, the time - domain method is to perform cyclic rain - flow counting on the entire load history based on knowing the entire load spectrum, and then perform damage calculation, with a large amount of work. Therefore, the frequency - domain method came into being. The frequency - domain method is to obtain the relevant statistical parameters of the corresponding power spectrum through the stress power spectral density (PSD) of the structural critical - point response, combine with the probability density function of the stress amplitude, select applicable damage accumulation criteria and failure criteria, and conduct fatigue life prediction. This method requires fewer data samples and less data processing volume than the time - domain method, and is more practical in engineering.

[0003] At the same time, during their working life, many structures are subjected to not only unidirectional loads. Due to the randomness and complexity of the external environment and the diversity of the loading history, they are more likely to be subjected to multi - axis loads. Therefore, it is more meaningful to study the fatigue life prediction method under multi - axis stress states. Summary of the Invention

[0004] The purpose of the present invention is to propose a prediction method for multi - axis random vibration fatigue life considering the influence of bandwidth in the frequency domain based on a condition that conforms to the real multi - axis random vibration working condition, so as to improve the accuracy of the frequency - domain method for predicting fatigue life. The frequency - domain equivalent von Mises stress method equivalentizes the power spectral densities in multiple directions into an equivalent power spectral density function. This method has good prediction results for narrow - band conditions, but the prediction results for broadband conditions are on the small side. Therefore, by adding a bandwidth influence factor m to correct the von Mises equivalent criterion, the damage under broadband conditions can be better estimated, making the equivalent von Mises stress method more accurate for predicting the broadband multi - axis random vibration fatigue life of aluminum alloys.

[0005] The multi - axis random vibration fatigue life prediction method considering the influence of bandwidth provided by the present invention comprises the following steps:

[0006] (1) Conduct a multi - axis random vibration test on the specimen. The multi - axis specimen is symmetrically designed, and strain rosettes are pasted at the critical point to obtain strain data in three directions;

[0007] (2) The linear strains ε in three directions measured by the strain rosette a1 , ε a2 , ε a3 are used to calculate the actual strain ε x , ε y , γ xy . The specific formula is as follows:

[0008]

[0009]

[0010]

[0011] where a1, a2, and a3 are the measurement angles;

[0012] (3) Obtaining the power spectrum of the stress response signal. Take the strain time-domain data for a certain period, convert it into stress time-domain data x(t), perform autocorrelation on it, and then perform continuous Fourier transform on the autocorrelation function to obtain the bilateral power spectral density. Since negative frequencies are not considered, the negative-frequency power spectral density is folded into positive frequencies to obtain the unilateral power spectral density of the stress response. The autocorrelation function R x (τ), the bilateral power spectral density S x (ω), and the unilateral power spectral density function G x (ω) are expressed as follows:

[0013]

[0014]

[0015]

[0016] where ω represents frequency, t represents time, and τ represents the interval time;

[0017] (4) Obtaining the cross-power spectrum of the stress response signal: Take the cross-correlation function of the response stresses in two directions, and then perform continuous Fourier transform on the cross-correlation function to obtain the bilateral power spectral density, and then convert it into the unilateral power spectral density. The cross-correlation function is expressed as:

[0018]

[0019] (5) The obtained response power spectral density functions are grouped into a power spectrum matrix G σ (f), and it is converted into an equivalent power spectrum matrix G σeq using the improved von Mises equivalent criterion M;

[0020]

[0021] In the formula, G kk (f) is the auto-power spectral density function of a stress component (k = 1, 2, 3)

[0022] G hk (f) is the cross-power spectral density function of stress components (h = 1, 2, 3; k = 1, 2, 3);

[0023]

[0024] In the formula, m is the bandwidth influence factor, and Q is the original von Mises equivalent criterion;

[0025] G σeq = Trace{MG σ (f)} (10)

[0026] In the formula, Trace{} is the sum of the main diagonal components of the square matrix;

[0027] (6) Calculate the spectral parameters using the obtained equivalent power spectral density matrix. The spectral distance calculation formula is:

[0028]

[0029] (7) Calculate the amplitude probability density function p(S), using the Dirlik model as:

[0030]

[0031] In the formula

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] D3 = 1 - D1 - D2 (18)

[0038]

[0039]

[0040] (8) Calculate the number of cycles within the time according to the probability density function:

[0041] n s = v a*T* p(s) (21)

[0042] where *v* a is the mean crossing rate and *T* is the action time of the random vibration response;

[0043] (9) Combine the Miner's linear cumulative theory and the material S-N curve to obtain the final damage *D*;

[0044]

[0045] where *n* s is the actual number of cycles at stress *s*; *N* s is the number of failure cycles at stress *s*, which can be determined by the S-N curve equation:

[0046] *S* K *N* S = *C* (23)

[0047] where *K* and *C* are the material fatigue index and constant, which are the index and constant of the S-N curve of the structural fatigue characteristics;

[0048]

[0049] When the cumulative damage reaches the critical damage *D* = 1, the structure undergoes fatigue failure, and the obtained *T* value is the structural fatigue life. Description of the Drawings

[0050] Figure 1 is a multi-axial specimen;

[0051] Figure 2 is the strain rosette paste position;

[0052] Figure 3 is the flow chart of a multi-axial random vibration fatigue life prediction method considering bandwidth influence provided by the present invention. Detailed Embodiments

[0053] Combine the drawings to describe the detailed embodiments of the present invention.

[0054] Step 1) Conduct a multi-axial random vibration test on the specimen. The multi-axial specimen is symmetrically designed. As Figure 1 shown, paste a strain rosette at the rounded edge, and the paste position is as Figure 2 shown to obtain the strain data in three directions at this critical point.

[0055] Step 2) Use the three linear strains ε a1 , ε a2 , ε a3 measured by the strain rosette to calculate the actual strains ε x , ε y , γ xy, the specific formula is:

[0056]

[0057]

[0058]

[0059] where a1, a2, and a3 are the measured angles;

[0060] Step 3) Obtaining the power spectrum of the stress response signal. Take the strain time-domain data for a certain period of time, convert it into the stress time-domain data x(t), perform autocorrelation on it, and then perform continuous Fourier transform on the autocorrelation function to obtain the bilateral power spectral density. Since negative frequencies are not considered, the negative-frequency power spectral density is folded into the positive frequency to obtain the unilateral power spectral density of the stress response. The autocorrelation function R x (τ), the bilateral power spectral density S x (ω), and the unilateral power spectral density function G x (ω) are expressed as follows:

[0061]

[0062]

[0063]

[0064] where ω represents frequency, t represents time, and τ represents the interval time;

[0065] Step 4) Obtaining the cross-power spectrum of the stress response signal: Take the cross-correlation function of the response stresses in two directions, and then perform continuous Fourier transform on the cross-correlation function to obtain the bilateral power spectral density, and then convert it into the unilateral power spectral density. The cross-correlation function is expressed as:

[0066]

[0067] Step 5) Combine the obtained response power spectral density functions to form a power spectrum matrix G σ (f), and use the improved von Mises equivalent criterion M to convert it into an equivalent power spectrum matrix G σeq ;

[0068]

[0069] where G kk (f) - the auto-power spectral density function of the stress component (k = 1, 2, 3)

[0070] G hk(f) - Cross - power spectral density function of stress components (h = 1, 2, 3; k = 1, 2, 3),

[0071]

[0072] where m is the bandwidth influence factor and Q is the original von Mises equivalent criterion,

[0073] G σeq = Trace{MG σ (f)} (34)

[0074] where Trace{} is the sum of the main diagonal components of the square matrix;

[0075] Step 6) Calculate the spectral parameters using the obtained equivalent power spectral density matrix. The spectral distance calculation formula is:

[0076]

[0077] Step 7) Calculate the amplitude probability density function p(S), using the Dirlik model as:

[0078]

[0079] where

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] D3 = 1 - D1 - D2 (42)

[0086]

[0087]

[0088] Step 8) Calculate the number of cycles within the time according to the probability density function:

[0089] n s = v a * T * p(s) (45)

[0090] where v a is the mean crossing rate and T is the action time of the random vibration response;

[0091] Step 9) Combine the miner linear cumulative theory and the material S-N curve to obtain the final damage D;

[0092]

[0093] where n s is the actual number of cycles at stress s; N s is the number of failure cycles at stress s, which can be determined by the S-N curve equation:

[0094] S K N S = C (47)

[0095] where K and C are the material fatigue index and constant, which are the index and constant of the S-N curve of the structural fatigue characteristics;

[0096]

[0097] When the cumulative damage reaches the critical damage D = 1, the structure undergoes fatigue failure, and the obtained T value is the fatigue life of the structure.

[0098] The present invention provides a method for predicting the fatigue life of multiaxial random vibration considering the influence of bandwidth, corrects the error of the frequency-domain equivalent von Mises stress method in the broadband case, and proposes an improved von Mises equivalent criterion by adding a bandwidth influence factor to better estimate the damage in the broadband case, making the fatigue life prediction of aluminum alloy under broadband multiaxial random vibration more accurate.

Claims

1. A multi-axis random vibration life prediction method considering the influence of bandwidth, characterized in that: The specific steps are as follows: Step 1) Conduct a multi-axial random vibration test on the specimen. The multi-axial specimen is symmetrically designed. Strain rosettes are pasted at the rounded edges to obtain the strain data in three directions at the critical points. Step 2) The linear strains in three directions measured by the strain rosette Calculate the actual strain ε x , ε y , γ xy , and the specific formula is as follows: Where a1, a2, and a3 are the measurement angles; Step 3) Obtaining the power spectrum of the stress response signal. Take the strain time-domain data for a certain period of time, convert it into the stress time-domain data x(t), take the autocorrelation function, and then perform a continuous Fourier transform on the autocorrelation function to obtain the bilateral power spectral density. Since negative frequencies are not considered, the negative-frequency power spectral density is folded into the positive frequency to obtain the unilateral power spectral density of the stress response. The autocorrelation function R x (τ), the bilateral power spectral density S x (ω), and the unilateral power spectral density function G x (ω) are expressed as follows: Where ω represents the frequency, t represents the time, τ represents the interval time, and T is the signal period; Step 4) Obtaining the cross-power spectrum of the stress response signal: Take the cross-correlation function of the response stresses in two directions, and then perform a continuous Fourier transform on the cross-correlation function to obtain the bilateral power spectral density, and then convert it into the unilateral power spectral density. The expression of the cross-correlation function is: Step 5) The obtained response power spectral density functions are grouped into a power spectral matrix G σ (f), and are transformed into an equivalent power spectral matrix G σeq ; where G kk (f) — the auto-power spectral density function of the stress component; G hk (f) — Cross-power spectral density function of stress components Where m is the bandwidth influence factor, and Q is the original von Mises equivalent criterion matrix, G σeq = Trace{MG σ (f)} (34) Where Trace{} is the sum of the main diagonal components of the square matrix; Step 6) Calculate the spectral parameters using the obtained equivalent power spectral density matrix. The formula for the spectral distance is: Step 7) Calculate the amplitude probability density function p(S), using the Dirlik model as: Where D3 = 1 - D1 - D2 (42) Step 8) Calculate the number of cycles within the time according to the probability density function: n s = v * T * p(S) (45) Where v is the mean crossing rate, T is the action time of the random vibration response, and s is the stress amplitude; Step 9) Combine the miner linear cumulative theory and the material S-N curve to obtain the final damage D; where n s is the actual number of cycles at a stress amplitude of s; N s is the number of failure cycles at a stress amplitude of s, which is determined by the S-N curve equation: S K N s = C(47) Where K and C are the material fatigue indices and constants, which are the indices and constants of the S-N curve of the structural fatigue characteristics; When the cumulative damage reaches the critical damage D = 1, the structure undergoes fatigue failure, and the obtained T value is the fatigue life of the structure.

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