A fast calculation method for structural fatigue life

Abstract

The present invention relates to a method for rapid calculation of structural fatigue life, comprising obtaining harmonic loads of dynamic loads by Fourier transforming each dynamic load on the structure; applying all harmonic loads to the structural finite element model at one time, performing harmonic response analysis to obtain stress spectrum calculation results of the structural finite element model; extracting the stress spectrum of the concerned part of the structure from the stress spectrum calculation results, performing stress synthesis to obtain time-domain dynamic stress; and performing fatigue life assessment analysis on the concerned part based on the time-domain dynamic stress. The present invention is based on Fourier transform and structural finite element harmonic response analysis, and solves the technical problems of high calculation cost and low calculation accuracy of existing structural fatigue assessment methods.

Description

Technical Field

[0001] The invention belongs to the technical field of structural fatigue assessment, and in particular relates to a method for quickly calculating structural fatigue life based on Fourier transform and structural finite element harmonic response analysis. Background Art

[0002] Fatigue fracture has always been the main mode of structural failure. This is caused by the fact that structural components (such as wheelsets, bogies and car bodies in the rail vehicle industry) are subjected to dynamic loads for a long time during their service. To this end, many researchers are committed to studying structural fatigue strength or life assessment analysis methods. At present, the structural fatigue assessment analysis method is achieved by applying Miner's linear fatigue damage accumulation theory, combining material fatigue performance test data (SN curve) and structural finite element strength calculation analysis. With the continuous deepening of theoretical research on fatigue assessment methods and the rapid development of computer technology, structural fatigue assessment methods considering dynamic loads have been developed. There are currently two main methods:

[0003] (1) Time domain analysis method: The measured or predefined dynamic load data is applied to the structural finite element model, and the structural dynamic stress is obtained through structural transient analysis. The dynamic stress data is then analyzed using the rain flow meter method to obtain the number of cycles at each stress level. Finally, fatigue life assessment is performed based on Miner's linear fatigue damage accumulation theory and the SN curve.

[0004] (2) Frequency domain analysis method: First, perform harmonic response analysis (or steady-state response analysis) on the structural finite element model to obtain the stress frequency response function under the i-th load. Then, perform Fourier transform on the dynamic load data to obtain the load's autopower spectrum and the mutual power spectrum with other loads. Then, calculate the stress power spectrum of the structural focus point. Then, apply the Dirlik method to obtain the structural stress probability density function and count the stress change range and frequency of occurrence per unit time. Finally, fatigue life assessment is performed based on Miner's linear fatigue damage accumulation theory and SN curve.

[0005] When the time domain analysis method is used to evaluate and analyze the fatigue life of the structure, the transient analysis of the structural finite element is extremely time-consuming; when the frequency domain analysis method is used, the stress frequency response function under each load needs to be obtained through the structural finite element harmonic response analysis, and the autopower spectrum of each load and the mutual power spectrum with other loads need to be calculated. When there are many loads, the calculation process is very cumbersome and complicated. In addition, since the results of the rain flow counting method are consistent with the stress-strain characteristics of the material and have a more reliable mechanical basis, the cycle counting method based on the rain flow meter method is simpler and faster than the probability density function method, and can reflect the characteristics of the load. Therefore, in the fatigue strength design and fatigue life calculation of most projects, the cycle counting method of the rain flow meter method is still used. Therefore, in recent years, it has been recognized as the most advanced counting method at home and abroad, and has been increasingly valued and used. Summary of the invention

[0006] In view of the shortcomings existing in the related technologies, the present invention provides a method for quickly calculating the fatigue life of a structure to solve the technical problems of high calculation cost and low calculation accuracy of the existing structural fatigue assessment methods.

[0007] The present invention provides a method for quickly calculating the fatigue life of a structure, which is characterized by comprising:

[0008] S1. Obtain the harmonic load of each dynamic load on the structure by Fourier transform;

[0009] S2. applying all the harmonic loads to the structural finite element model at once, performing harmonic response analysis to obtain the stress spectrum calculation results of the structural finite element model;

[0010] S3. extracting the stress spectrum of the concerned part of the structure from the stress spectrum calculation result, performing stress synthesis to obtain the time domain dynamic stress;

[0011] S4. Perform fatigue life assessment analysis on the concerned parts based on the time domain dynamic stress.

[0012] In some embodiments, the step S2 further includes: the harmonic response analysis selects the modal superposition method for calculation.

[0013] In some embodiments, the step S1 further comprises:

[0014] After the harmonic load is calculated, the harmonic load is stored in M ​​N h ×2 load array; where M is the number of dynamic loads to which the structure is subjected, N is the number of load sampling points; the load array is used for the harmonic response analysis in the structural finite element model.

[0015] In some embodiments, the step S2 further comprises:

[0016] In the harmonic response analysis of the structural finite element model, the values ​​of each row of the M load arrays are sequentially applied to the structural finite element model, and the harmonic response of the corresponding discrete circumferential frequency is solved and calculated, and all N h The harmonic response of each frequency is calculated to obtain the stress spectrum calculation result.

[0017] In some embodiments, step S3 further comprises:

[0018] The formula for extracting the stress spectrum of the focus area is:

[0019]

[0020] In the formula, is the stress spectrum, a k ,φ k are the discrete circular frequencies ω k The amplitude and phase of the stress spectrum at .

[0021] In some embodiments, step S3 further comprises:

[0022] The formula for obtaining the time domain dynamic stress by performing stress synthesis on the stress spectrum is:

[0023]

[0024] Where σ(t) is the dynamic stress in the time domain, and t is the continuous time variable of the dynamic load.

[0025] In some embodiments, step S4 further comprises:

[0026] The time domain dynamic stress analysis is performed using a rain flow meter method to obtain the number of cycles at each stress level.

[0027] In some embodiments, step S4 further comprises:

[0028] According to Miner's linear fatigue damage accumulation theory and SN curve, fatigue life assessment and analysis are performed on the concerned parts.

[0029] In some embodiments, the step S1 further comprises:

[0030] First, a discrete Fourier transform of the dynamic load is calculated, and then the harmonic load is calculated according to the discrete Fourier transform.

[0031] In some embodiments, the step S1 further comprises:

[0032] The formula for calculating the harmonic load according to the discrete Fourier transform is:

[0033]

[0034] In the formula, is the harmonic load, is the discrete Fourier transform value of the dynamic load, They are The numerical values ​​of the imaginary and real parts.

[0035] Based on the above technical solution, the present invention realizes a fast calculation method of structural fatigue life based on Fourier transform and structural finite element harmonic response analysis, ingeniously utilizes Fourier transform, and fully utilizes and gives play to the calculation efficiency of structural finite element harmonic response and the calculation accuracy of rain flow meter method, and its advantages are:

[0036] 1. Compared with the frequency domain method, the present invention applies the dynamic load to the finite element model once after Fourier transformation, eliminating the calculation of the stress frequency response function of each load, as well as the calculation of the load autopower spectrum, cross-power spectrum and stress power spectrum, thus reducing the calculation links and significantly reducing the complexity of the calculation;

[0037] 2. Compared with the time domain method, the harmonic response analysis of the structural finite element model is performed to obtain the stress spectrum results, and then the stress synthesis is performed to obtain the dynamic stress time history results, which avoids the transient analysis of the structural finite element model and greatly improves the calculation efficiency;

[0038] 3. The stress-time history results are obtained through structural finite element harmonic response analysis and stress synthesis, and then the rain flow meter method is used to calculate the number of cycles at each stress level to ensure the reliability of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0040] Figure 1 This is a flow chart of the method for quickly calculating the fatigue life of a structure of the present invention; DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments. 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 work are within the scope of protection of the present invention.

[0042] In the description of the present invention, it is necessary to understand that the orientations or positional relationships indicated by terms such as “upper”, “front”, “back”, “top”, “bottom” and “inside” are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0043] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "fixation" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0044] The invention discloses a method for quickly calculating the structural fatigue life based on Fourier transform and structural finite element harmonic response analysis, which can be used for structural fatigue strength or life assessment analysis of structural parts, and is particularly suitable for wheelsets, bogies and car bodies in the rail vehicle industry.

[0045] As attached Figure 1 As shown, the embodiment of the present application includes the following steps:

[0046] S1. Each dynamic load on the structure is transformed by Fourier transform to obtain the harmonic load of the dynamic load.

[0047] Optionally, the discrete Fourier transform of the dynamic load is first calculated, and then the harmonic load is calculated based on the discrete Fourier transform. The formula for calculating the harmonic load based on the discrete Fourier transform is:

[0048]

[0049] In the formula, is the harmonic load, is the discrete Fourier transform value of the dynamic load, They are The numerical values ​​of the imaginary and real parts.

[0050] Optionally, after the harmonic load is calculated, the harmonic load is stored in M ​​N h ×2 load array; where M is the number of dynamic loads on the structure, N is the number of load sampling points; the load array is used for harmonic response analysis in the structural finite element model.

[0051] In the specific implementation, suppose the structure is subjected to M dynamic loads, the discrete time of the dynamic load is Δt, and there are N load sampling points in total. Then the i-th dynamic load at t n =nΔt The load value at the time can be expressed as

[0052] f i (t n ) = f i [n], (n=0,1,2,…N-1)

[0053] Its discrete Fourier transform (DFT) can be expressed by the following formula:

[0054]

[0055] In the formula, is the discrete circular frequency Dynamic load at f i (t). The harmonic load of this load in the harmonic response analysis is obtained as

[0056]

[0057] In the formula, They are The values ​​of the imaginary and real parts, Express Round down to an integer, for example, when N=5, N h =2, when N=6, N h =3. When analyzing harmonic response, only dynamic loads with frequencies greater than zero are considered, so k = 1, 2, ..., N h Using the above formula, we can get the M dynamic loads at each discrete frequency ω k The harmonic load value is stored in M ​​N h ×2 load array, then the i-th load at frequency ω k The real and imaginary parts of the load are

[0058]

[0059]

[0060] S2. All harmonic loads are applied to the structural finite element model at one time, and harmonic response analysis is performed to obtain the stress spectrum calculation results of the structural finite element model.

[0061] Optionally, the harmonic response analysis uses the modal superposition method for calculation.

[0062] Optionally, in the harmonic response analysis of the structural finite element model, each row value of the M load array is sequentially applied to the structural finite element model, and the harmonic response of the corresponding discrete circumferential frequency is solved and calculated, and all N h The harmonic response of each frequency is calculated to obtain the stress spectrum calculation results.

[0063] In the specific implementation, in the harmonic response analysis of the structural finite element model, the values ​​of the first row of the M load array are first applied to the model and the harmonic response of the ω1 frequency is solved and calculated. Then, the values ​​of the second row of the M load array are applied to the model to solve the harmonic response of the ω2 frequency. All N loads are loaded and solved in the above loading and solving manner. h The above calculation steps can be expressed by the following vibration theory formula:

[0064]

[0065] In the formula, the degree of freedom vector is

[0066]

[0067] M, C and K are the mass, damping and stiffness matrices of the structural finite element model, respectively. The harmonic load vector is

[0068]

[0069] The stress spectrum calculation results of the discrete frequency of the structural finite element model can be obtained through harmonic response analysis. In order to further improve the calculation efficiency, the modal superposition method is preferred for harmonic response analysis.

[0070] S3. Extract the stress spectrum of the concerned part of the structure from the stress spectrum calculation results, perform stress synthesis and obtain the time domain dynamic stress.

[0071] Optionally, the formula for extracting the stress spectrum of the area of ​​interest is

[0072]

[0073] In the formula, is the stress spectrum, a k ,φ k are the discrete circular frequencies ω k The amplitude and phase of the stress spectrum at .

[0074] Optionally, the formula for obtaining the time domain dynamic stress by performing stress synthesis on the stress spectrum is:

[0075]

[0076] Where σ(t) is the dynamic stress in the time domain, and t is the continuous time variable of the dynamic load.

[0077] In the specific implementation, the stress spectrum of the node of interest is extracted from the structural finite element harmonic response analysis results. The spectrum can be expressed in amplitude and phase or in complex form. Let the frequency ω k The amplitude and phase of the stress spectrum at k ,φ k , then the stress spectrum expression is

[0078]

[0079] The stress spectrum obtained by harmonic response analysis is synthesized to obtain the time domain dynamic stress expression:

[0080]

[0081] S4. According to the time domain dynamic stress, fatigue life assessment analysis is performed on the concerned parts. Each dynamic load is transformed by Fourier Transform (FT) to obtain its harmonic load.

[0082] Optionally, the rain flow meter method is used to analyze the time domain dynamic stress to obtain the number of cycles at each stress level; optionally, the fatigue life assessment analysis of the concerned parts is performed based on Miner's linear fatigue damage accumulation theory and SN curve.

[0083] In the specific implementation, the rain flow meter method is used to analyze the time domain dynamic stress σ(t) to obtain the number of cycles under each stress level. According to Miner's linear fatigue damage accumulation theory and SN curve, the fatigue life evaluation analysis of the focus point is carried out.

[0084] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0085] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A method for rapid calculation of structural fatigue life, characterized in that: include: S1. Obtain the harmonic load of each dynamic load on the structure by Fourier transform; S2. applying all the harmonic loads to the structural finite element model at once, performing harmonic response analysis to obtain the stress spectrum calculation results of the structural finite element model; S3. extracting the stress spectrum of the concerned part of the structure from the stress spectrum calculation result, performing stress synthesis to obtain the time domain dynamic stress; S4. performing fatigue life assessment analysis on the concerned part according to the time domain dynamic stress; Wherein, the step S1 comprises: After the harmonic load is calculated, the harmonic load is stored in indivual The payload array of ; among them, is the amount of dynamic load to which the structure is subjected, , is the number of load sampling points; the load array is used for the harmonic response analysis in the structural finite element model; Wherein, the step S2 further comprises: In the harmonic response analysis of the structural finite element model, Each row value of the load array is applied to the structural finite element model in turn, and the harmonic response of the corresponding discrete circumferential frequency is solved and calculated, and all the The harmonic response calculation of each frequency is performed to obtain the stress spectrum calculation result; Wherein, the step S3 further comprises: The formula for extracting the stress spectrum of the focus area is: In the formula, is the stress spectrum, , Discrete circular frequencies The amplitude and phase of the stress spectrum at ; The formula for obtaining the time domain dynamic stress by performing stress synthesis on the stress spectrum is: In the formula, is the dynamic stress in time domain, is the continuous time variable of the dynamic load; Wherein, the step S1 further comprises: Firstly, a discrete Fourier transform of the dynamic load is calculated, and then the harmonic load is calculated according to the discrete Fourier transform; The formula for calculating the harmonic load according to the discrete Fourier transform is: In the formula, is the harmonic load, is the discrete Fourier transform value of the dynamic load, , They are The numerical values ​​of the imaginary and real parts.

2. The calculation method according to claim 1, characterized in that: The step S2 further comprises: The harmonic response analysis uses the modal superposition method for calculation.

3. The calculation method according to claim 1 or 2, characterized in that: The step S4 further comprises: The time domain dynamic stress analysis is performed using a rain flow meter method to obtain the number of cycles at each stress level.

4. The calculation method according to claim 3, characterized in that: The step S4 further comprises: According to Miner's linear fatigue damage accumulation theory and SN curve, fatigue life assessment and analysis are performed on the concerned parts.

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