Equal stress amplitude vibration fatigue S-N curve determination method and device

Abstract

The invention belongs to the technical field of aircraft fatigue life design, and particularly relates to an equal stress amplitude vibration fatigue S-N curve determination method and device. The method comprises the following steps: carrying out random vibration response analysis on a structural dynamic finite element model of a cantilever beam with one end clamped and supported, and obtaining a vibration stress power spectral density function and a vibration stress root-mean-square; determining a k-order moment of the vibration stress power spectrum density function; determining a coefficient value of a vibration stress amplitude probability density function formula according to the k-order moment; determining a constant C of the equal stress amplitude vibration fatigue S-N curve; determining a stress amplitude S corresponding to the specified cycle index N according to the constant C; and determining a vibration fatigue SRMS-N curve parallel to the random stress amplitude and a curve passing through the corresponding coordinate points of the cycle index N and the stress amplitude S as an equal stress amplitude vibration fatigue S-N curve. The equal stress amplitude vibration fatigue S-N curve constructed by the invention improves the efficiency of evaluating the vibration fatigue life of the structure.

Description

Technical Field

[0001] This application belongs to the field of aircraft fatigue life design technology, and specifically relates to a method and apparatus for determining the SN curve of vibration fatigue with constant stress amplitude. Background Technology

[0002] Currently, in the design of structural dynamic strength vibration fatigue life, it is necessary to consult the random vibration stress amplitude SN curve in the dynamic fatigue handbook, i.e., the root mean square of vibration stress S. RMS -N curves are available, but in some cases, it is necessary to consult the constant stress amplitude vibration fatigue SN curve. If the constant stress amplitude vibration fatigue SN curve cannot be found, then the root mean square of the vibration stress S needs to be used. RMS The -N curve can be converted into the SN curve of constant stress amplitude vibration fatigue, but there is currently no conversion method. This situation makes vibration fatigue life design difficult for engineers. Summary of the Invention

[0003] To address the aforementioned problems, this application provides a method and apparatus for determining the root mean square stress (S) curve of vibration fatigue with constant stress amplitude, thereby realizing the root mean square stress (S) curve of random vibration. RMS The conversion from the -N curve to the SN curve of equal stress vibration amplitude.

[0004] The first aspect of this application provides a method for determining the SN curve of constant stress amplitude vibration fatigue, mainly including:

[0005] Step S1: Perform random vibration response analysis on the dynamic finite element model of the cantilever beam structure with one end fixed, and obtain the vibration stress power spectral density function and the root mean square of the vibration stress.

[0006] Step S2: Determine the k-th moment of the vibration stress power spectral density function;

[0007] Step S3: Determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th order moment;

[0008] Step S4: Determine the constant C for the constant stress amplitude vibration fatigue SN curve;

[0009] Step S5: Determine the stress amplitude S corresponding to the specified number of cycles N based on the constant C;

[0010] Step S6: Determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

[0011] Preferably, step S4 further includes:

[0012] Step S41: Vibration fatigue based on random stress amplitude S RMS The -N curve determines the fatigue index of the material;

[0013] Step S42: Determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

[0014] Preferably, in step S42, the constant C of the constant stress amplitude vibration fatigue SN curve is determined by the following formula:

[0015] ;

[0016] Where N is the given number of cycles, and D is the fatigue damage caused by continuous stress in the structure. It is the zeroth moment.

[0017] Preferably, in step S5, the stress amplitude S corresponding to the specified number of cycles N is determined according to the following formula:

[0018] ;

[0019] Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

[0020] The second aspect of this application provides a device for determining the SN curve of vibration fatigue with constant stress amplitude, mainly comprising:

[0021] The random vibration response analysis module is used to perform random vibration response analysis on the dynamic finite element model of a cantilever beam structure with one end fixed, and to obtain the vibration stress power spectral density function and the root mean square of the vibration stress.

[0022] The k-th moment calculation module is used to determine the k-th moment of the vibration stress power spectral density function;

[0023] The probability density function coefficient determination module is used to determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th moment.

[0024] The constant determination module is used to determine the constant C of the constant-frequency (SN) curve of constant stress amplitude vibration fatigue.

[0025] The stress amplitude determination module is used to determine the stress amplitude S corresponding to a specified number of cycles N based on a constant C.

[0026] The curve generation module is used to determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

[0027] Preferably, the constant determination module includes:

[0028] Fatigue index determination unit, used to determine the vibration fatigue S based on random stress amplitude. RMS The -N curve determines the fatigue index of the material;

[0029] The constant calculation unit is used to determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

[0030] Preferably, in the constant calculation unit, the constant C of the constant stress amplitude vibration fatigue SN curve is determined by the following formula:

[0031] ;

[0032] Where N is the given number of cycles, and D is the fatigue damage caused by continuous stress in the structure. It is the zeroth moment.

[0033] Preferably, in the stress amplitude determination module, the stress amplitude S corresponding to a specified number of cycles N is determined according to the following formula:

[0034] ;

[0035] Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

[0036] The constant stress amplitude vibration fatigue SN curve constructed in this application improves the efficiency of evaluating the vibration fatigue life of structures. Attached Figure Description

[0037] Figure 1 This is a flowchart of a preferred embodiment of the method for determining the SN curve of vibration fatigue with equal stress amplitude in this application.

[0038] Figure 2 yes Figure 1 A schematic diagram of the constant stress amplitude vibration fatigue SN curve of the embodiment shown. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0040] The first aspect of this application provides a method for determining the SN curve of vibration fatigue with constant stress amplitude, such as... Figure 1 As shown, it mainly includes:

[0041] Step S1: Perform random vibration response analysis on the dynamic finite element model of the cantilever beam structure with one end fixed, and obtain the vibration stress power spectral density function and the root mean square of the vibration stress.

[0042] Step S2: Determine the k-th moment of the vibration stress power spectral density function;

[0043] Step S3: Determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th order moment;

[0044] Step S4: Determine the constant C for the constant stress amplitude vibration fatigue SN curve;

[0045] Step S5: Determine the stress amplitude S corresponding to the specified number of cycles N based on the constant C;

[0046] Step S6: Determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

[0047] First, in step S1 of this application, a finite element model of the cantilever beam structure with one end fixed is established. The vibration stress response analysis results of the cantilever beam are obtained through random vibration response analysis, and the vibration stress power spectral density function of the cantilever beam is obtained. and root mean square of vibration stress , It is frequency The corresponding one-sided stress power spectral density.

[0048] Then, in step S2, the power spectral density is calculated according to the following formula. Moment of order:

[0049] ;

[0050] in, Known as power spectral density Step moment.

[0051] Then, in step S3, the coefficient values ​​of the vibration stress amplitude probability density function are determined.

[0052] First, the formula for the probability density function of vibration stress amplitude is as follows:

[0053] .

[0054] Based on the above formula, the coefficient values ​​are determined as follows:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] Where S is the stress amplitude.

[0064] Next, in step S4, the constant C of the constant stress amplitude vibration fatigue SN curve is determined. In some optional embodiments, step S4 further includes:

[0065] Step S41: Vibration fatigue based on random stress amplitude S RMS The -N curve determines the fatigue index of a material.

[0066] This step involves consulting the random stress amplitude vibration fatigue S in the material handbook. RMS The fatigue index of the material is determined using the -N curve and the following formula. ;

[0067] ;

[0068] Among them, S RMS For random stress amplitude vibration fatigue S RMSThe stress amplitude in the -N curve, where N is the fatigue number and C is the stress amplitude. RMS This is the fatigue constant.

[0069] Step S42: Determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

[0070] First, calculate the integral function formula as shown below. For fatigue damage caused by continuous stress in a structure, D is usually set to 1;

[0071] .

[0072] Then, based on Miner's damage accumulation theory, the constant of the constant-strain (SN) curve for constant stress amplitude fatigue is derived as shown in the formula. :

[0073] .

[0074] Step S5 is used to determine the stress amplitude S corresponding to a specified number of cycles N. In some optional embodiments, in step S5, the stress amplitude S corresponding to the specified number of cycles N is determined according to the following formula:

[0075] ;

[0076] Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

[0077] Finally, in step S6, the constant stress amplitude vibration fatigue SN curve is plotted. In a double logarithmic coordinate system, the coordinate point P determined by N and S calculated in step six and this step is found. Through coordinate point P, a curve parallel to the random stress amplitude vibration fatigue SN curve is plotted. RMS -N curve is the constant stress amplitude vibration fatigue SN curve, such as Figure 2 The solid line shown.

[0078] This application establishes a method based on random stress amplitude vibration fatigue S RMS The method, steps, and formulas for converting -N curves to constant stress amplitude vibration fatigue SN curves have the following advantages and positive effects:

[0079] 1. This method fills the gap in the research on vibration fatigue under random stress amplitude. RMS The blank space in the transformation of the -N curve to the SN curve of constant stress amplitude vibration fatigue;

[0080] 2. The constant stress amplitude vibration fatigue SN curves obtained by this method can enrich the material vibration fatigue database;

[0081] 3. The constant stress amplitude vibration fatigue SN curve obtained by this method can be used for vibration fatigue design of aircraft structures.

[0082] 4. This method uses numerical calculation, resulting in high computational efficiency;

[0083] 5. Engineering designers can obtain the vibration fatigue SN curve by querying this method, and quickly assess the vibration fatigue life of the structure, which is highly efficient and saves time and costs.

[0084] The second aspect of this application provides a device for determining the SN curve of constant stress amplitude vibration fatigue corresponding to the above method, mainly comprising:

[0085] The random vibration response analysis module is used to perform random vibration response analysis on the dynamic finite element model of a cantilever beam structure with one end fixed, and to obtain the vibration stress power spectral density function and the root mean square of the vibration stress.

[0086] The k-th moment calculation module is used to determine the k-th moment of the vibration stress power spectral density function;

[0087] The probability density function coefficient determination module is used to determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th moment.

[0088] The constant determination module is used to determine the constant C of the constant-frequency (SN) curve of constant stress amplitude vibration fatigue.

[0089] The stress amplitude determination module is used to determine the stress amplitude S corresponding to a specified number of cycles N based on a constant C.

[0090] The curve generation module is used to determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

[0091] In some alternative implementations, the constant determination module includes:

[0092] Fatigue index determination unit, used to determine the vibration fatigue S based on random stress amplitude. RMS The -N curve determines the fatigue index of the material;

[0093] The constant calculation unit is used to determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

[0094] In some alternative embodiments, in the constant calculation unit, the constant C of the constant-strain amplitude vibration fatigue SN curve is determined by the following formula:

[0095] ;

[0096] Where N is the given number of cycles, and D is the fatigue damage under continuous stress in the structure, typically D is set to 1. It is the zeroth moment.

[0097] In some alternative implementations, in the stress amplitude determination module, the stress amplitude S corresponding to a specified number of cycles N is determined according to the following formula:

[0098] ;

[0099] Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

[0100] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for determining the SN curve of vibration fatigue with constant stress amplitude, characterized in that, include: Step S1: Perform random vibration response analysis on the dynamic finite element model of the cantilever beam structure with one end fixed, and obtain the vibration stress power spectral density function and the root mean square of the vibration stress. Step S2: Determine the k-th moment of the vibration stress power spectral density function; Step S3: Determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th order moment; Step S4: Determine the constant C for the constant stress amplitude vibration fatigue SN curve; Step S5: Determine the stress amplitude S corresponding to the specified number of cycles N based on the constant C; Step S6: Determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

2. The method for determining the SN curve of constant stress amplitude vibration fatigue as described in claim 1, characterized in that, Step S4 further includes: Step S41: Vibration fatigue based on random stress amplitude S RMS The -N curve determines the fatigue index of the material; Step S42: Determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

3. The method for determining the SN curve of constant stress amplitude vibration fatigue as described in claim 2, characterized in that, In step S42, the constant C of the constant stress amplitude vibration fatigue SN curve is determined by the following formula: ； Where N is the given number of cycles, and D is the fatigue damage caused by continuous stress in the structure. It is the zeroth moment.

4. The method for determining the SN curve of constant stress amplitude vibration fatigue as described in claim 1, characterized in that, In step S5, the stress amplitude S corresponding to the specified number of cycles N is determined according to the following formula: ； Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

5. A device for determining the SN curve of vibration fatigue with constant stress amplitude, characterized in that, include: The random vibration response analysis module is used to perform random vibration response analysis on the dynamic finite element model of a cantilever beam structure with one end fixed, and to obtain the vibration stress power spectral density function and the root mean square of the vibration stress. The k-th moment calculation module is used to determine the k-th moment of the vibration stress power spectral density function; The probability density function coefficient determination module is used to determine the coefficient values ​​of the probability density function formula for vibration stress amplitude based on the k-th moment. The constant determination module is used to determine the constant C of the constant-frequency (SN) curve of constant stress amplitude vibration fatigue. The stress amplitude determination module is used to determine the stress amplitude S corresponding to a specified number of cycles N based on a constant C. The curve generation module is used to determine the vibration fatigue S parallel to the random stress amplitude. RMS The -N curve, and the curve passing through the coordinate points corresponding to the number of cycles N and the stress amplitude S is the constant stress amplitude vibration fatigue SN curve.

6. The device for determining the SN curve of vibration fatigue with constant stress amplitude as described in claim 5, characterized in that, The constant determination module includes: Fatigue index determination unit, used to determine the vibration fatigue S based on random stress amplitude. RMS The -N curve determines the fatigue index of the material; The constant calculation unit is used to determine the constant C of the constant stress amplitude vibration fatigue SN curve based on the coefficient value and the fatigue index of the material.

7. The device for determining the SN curve of vibration fatigue with constant stress amplitude as described in claim 6, characterized in that, In the constant calculation unit, the constant C of the constant stress amplitude vibration fatigue SN curve is determined by the following formula: ； Where N is the given number of cycles, and D is the fatigue damage caused by continuous stress in the structure. It is the zeroth moment.

8. The device for determining the SN curve of vibration fatigue with constant stress amplitude as described in claim 5, characterized in that, In the stress amplitude determination module, the stress amplitude S corresponding to a specified number of cycles N is determined according to the following formula: ； Where C is a constant of the constant stress amplitude vibration fatigue SN curve, and m is the fatigue index of the material.

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