Engine bolt random vibration fatigue life evaluation method and device

Abstract

The invention belongs to the technical field of simulation data processing, and particularly relates to an engine bolt random vibration fatigue life evaluation method and device. The method comprises the following steps: S1, applying a pre-tightening force to a finite element model constructed by bolt connection, then carrying out modal analysis and frequency response analysis, inputting a specified acceleration power spectral density curve to carry out random vibration analysis, and extracting a stress response power spectral density curve of a bolt dangerous point; s2, determining an inertia moment according to the power spectral density curve; s3, determining root mean square stress, peak frequency and coefficients in a Dirlik equation according to the inertia moment; and S4, calculating fatigue damage and fatigue life of the engine bolt according to the root-mean-square stress, the peak frequency and coefficients in the Dirlik equation. According to the method, the fatigue life of the bolt in the random vibration environment can be quickly and accurately evaluated, and a basis is provided for bolt model selection in engine design.

Description

Technical Field

[0001] The present application belongs to the technical field of simulation data processing, and in particular relates to a method and device for evaluating the random vibration fatigue life of engine bolts. Background Art

[0002] The engine is the most important core component of the aircraft, and its reliability is of vital importance. The engine and its fuel accessories are widely connected by bolts. Bolts are the hub of the overall structural load transmission. Under the action of the structural working load, the threads of the screws and bolts will yield, loosen, and break late, which will cause accidents due to bolt breakage.

[0003] The fracture and failure of bolts will affect or even completely destroy the functions of related components, and even worse, will cause significant personal and economic losses. The main failure form of bolts is fatigue fracture. By estimating the fatigue life of bolts in combination with existing fatigue analysis theory, it is possible to replace them in advance before they break to avoid accidents. Therefore, it is necessary to conduct in-depth research on the dynamic characteristics and fatigue problems of bolts to provide a more practical reference for engine design and maintenance.

[0004] Most existing technologies conduct fatigue life analysis on a certain component. The force transmission path is relatively clear and the boundary conditions are easy to simulate. However, the bolt connection system is relatively more complex and the stress conditions of the bolts cannot be clearly analyzed, which brings challenges to the fatigue life analysis of the bolts. Summary of the invention

[0005] In order to solve the above problems, the present application provides a method and device for evaluating the random vibration fatigue life of engine bolts, which uses the finite element method combined with the frequency domain method to perform random vibration fatigue analysis of engine bolts.

[0006] The first aspect of the present application provides a method for evaluating the random vibration fatigue life of an engine bolt, mainly comprising: Step S1, after applying a preload force to a finite element model constructed by bolt connection, modal analysis, frequency response analysis and inputting a specified acceleration power spectrum density curve to perform random vibration analysis, and extracting a stress response power spectrum density curve of a bolt danger point; Step S2, determining the moment of inertia according to the power spectrum density curve; Step S3, determining the root mean square stress, the peak frequency and the coefficient in the Dirlik equation according to the moment of inertia; Step S4: Calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

[0007] Preferably, in step S1, constructing a finite element model of the engine bolt includes: connecting two engine casings through engine bolts, with a sealing ring between the two engine casings, the engine bolts and the engine casings are contact-bound, the engine bolts and the sealing rings are not in contact, the engine casings are connected to other engine structures through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

[0008] Preferably, in step S2, the nth-order moment of inertia m of the power spectral density function is determined by the following formula: n : ; Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

[0009] Preferably, in step S3, the root mean square stress is determined by the following formula: : ; The peak frequency is determined by the following formula : ; The coefficients in the Dirlik equation are determined by the following formula , , , , : ; in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

[0010] Preferably, in step S4, the fatigue damage of the engine bolt is determined by the following formula: : ; The fatigue life of engine bolts is determined by the following formula : ; Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

[0011] The second aspect of the present application provides an engine bolt random vibration fatigue life assessment device, which mainly includes: The power spectrum density curve extraction module is used to perform modal analysis, frequency response analysis, and random vibration analysis by inputting a specified acceleration power spectrum density curve after applying a preload to the finite element model constructed by bolt connection, and extract the stress response power spectrum density curve of the bolt danger point; A moment of inertia calculation module, used to determine the moment of inertia according to the power spectrum density curve; A parameter calculation module, used for determining the root mean square stress, the peak frequency and the coefficients in the Dirlik equation according to the moment of inertia; The fatigue analysis module is used to calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

[0012] Preferably, in the power spectral density curve extraction module, constructing a finite element model of the engine bolts includes: connecting two engine casings through engine bolts, with a sealing ring between the two engine casings, the engine bolts and the engine casings are contact bound, the engine bolts and the sealing rings are not in contact, the engine casings are connected to other engine structures through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

[0013] Preferably, in the moment of inertia calculation module, the nth-order moment of inertia m of the power spectrum density function is determined by the following formula: n : ; Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

[0014] Preferably, the parameter calculation includes: The root mean square stress calculation unit is used to determine the root mean square stress using the following formula : ; Peak frequency calculation unit, used to determine the peak frequency using the following formula : ; The Dirlik equation coefficient calculation unit is used to determine the coefficients in the Dirlik equation using the following formula , , , , : ; in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

[0015] Preferably, the fatigue analysis module comprises: Fatigue damage calculation unit, used to determine the fatigue damage of engine bolts using the following formula : ; Fatigue life calculation unit, used to determine the fatigue life of engine bolts using the following formula : ; Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

[0016] This application can quickly and accurately evaluate the fatigue life of bolts in a random vibration environment, providing a basis for the selection of bolts in engine design. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a preferred embodiment of the random vibration fatigue life assessment method for engine bolts of the present application.

[0018] Figure 2 It is a schematic diagram of the finite element model of the bolted connection assembly.

[0019] Figure 3 It is a schematic diagram of the acceleration power spectrum density curve of broadband superimposed on narrowband. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the implementation of this application will be described in more detail in combination with the drawings in the implementation of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described implementation is a part of the implementation of this application, not all of the implementations. The implementation described below with reference to the drawings is exemplary and is intended to be used to explain this application, and cannot be understood as a limitation on this application. Based on the implementation in this application, all other implementations obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The implementation of this application is described in detail below in combination with the drawings.

[0021] The first aspect of the present application provides a method for evaluating the random vibration fatigue life of an engine bolt, such as Figure 1 As shown, it mainly includes: Step S1, after applying a preload force to a finite element model constructed by bolt connection, modal analysis, frequency response analysis and inputting a specified acceleration power spectrum density curve to perform random vibration analysis, and extracting a stress response power spectrum density curve of a bolt danger point; Step S2, determining the moment of inertia according to the power spectrum density curve; Step S3, determining the root mean square stress, the peak frequency and the coefficient in the Dirlik equation according to the moment of inertia; Step S4: Calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

[0022] In step S1, the present application calculates the dynamic response of the engine bolts under random vibration loads by means of the finite element method, and then in steps S2-S4, the fatigue damage and fatigue life of the bolts are calculated in combination with the Dirlik formula. In the finite element pre-processing, the model is simplified, and the details of the bolt connection are simulated, which reduces the calculation scale and improves the simulation accuracy. The analysis method of the present application can quickly and effectively analyze and predict the fatigue life of aircraft engine bolts under random vibration loads, and provide a reference for the selection of bolts in engine design.

[0023] In some optional embodiments, in step S1, constructing a finite element model of the engine bolt includes: connecting two engine casings through engine bolts, with a sealing ring between the two engine casings, the engine bolts and the engine casings are contact bound, the engine bolts and the sealing rings are not in contact, the engine casings are connected to other engine structures through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

[0024] In this embodiment, an overall engine model including engine bolts is constructed and divided into 3D finite element meshes. The overall mesh scale is large and the connection relationship is complex, resulting in a large amount of calculation. Therefore, it is necessary to simplify the overall structure. This application uses concentrated mass to simulate the structure outside the engine casing connected by the engine bolts, and connects it to the engine casing with RBE3 units. Then, for the engine bolts, all the bolts are screwed into the bottom parts, and torque is applied to the upper part by nuts to assemble the parts together. The bolts and nuts are regarded as a whole, and the part of the bolts that exceeds the nuts is not subjected to force, so this part of the unit can be deleted. The meshing part of the engine bolts and the engine casing uses contact binding. There is a thin sealing ring between the two casings that does not contact the engine bolts. The interfaces of the components are connected to each other using frictional contact connection properties to prevent the interface units of the components from penetrating each other. The finite element model of the bolted assembly is shown in the figure below. Figure 2 shown.

[0025] There is a preload between bolt connections. The preload is applied at the cross section of the bolt. The theoretical formula for the preload is as follows: ; Among them, M is the tightening torque, F is the preload force determined during design, d is the nominal diameter of the thread, d2 is the thread pitch, and P is the thread pitch. is the friction coefficient between the nut and the supported surface (washer), determined by test or experience. is the friction coefficient of the thread pair, determined by test or experience, The half angle of the thread profile. is the thread lead angle, , is the equivalent friction angle of the bolt and nut connection, , A is the outer radius of the nut support surface. Generally, A=0.475S, S is the width across the nut, r is the inner radius of the nut support surface. Generally, r=D / 2, and D is the nominal diameter of the nut thread.

[0026] After the finite element model is constructed, modal analysis can be carried out. This application calculates the natural frequency and vibration mode of the finite element model within 15~2000Hz. After the modal analysis, frequency response analysis is performed. Frequency response analysis is a method for evaluating the response capability of a system or device to signals of different frequencies. It determines the gain and phase changes of different frequency signals by measuring the relationship between the input and output of the system or device at different frequencies. In this embodiment, the overall structure is constrained according to the constraint relationship during assembly, and unit acceleration excitations in the three directions of X, Y, and Z are applied at the constraint points to analyze the response of the engine components to different frequencies.

[0027] On the basis of frequency response analysis and calculation, the acceleration power spectrum density curves in the three directions of X, Y, and Z are input respectively for random vibration analysis. The acceleration power spectrum density curve is a broadband superimposed narrowband random vibration curve, such as Figure 3 After the analysis is completed, the stress response power spectrum density curve of the bolt danger point is extracted. The danger point here refers to the point with the largest stress, which can be obtained through the above finite element analysis.

[0028] Then, in step S2, the moment of inertia of the power spectral density function is determined. In some optional implementations, in step S2, the nth-order moment of inertia m of the power spectral density function is determined by the following formula: n : ; Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

[0029] It should be noted that the power spectrum density function given in step S1 is usually in the form of , that is, the independent variable is , the unit is rad / s, and the frequency unit commonly used in engineering is Hz, that is, according to , we can get the power spectrum density function form commonly used in engineering .

[0030] Then, the root mean square stress can be calculated in step S3 according to the moments of inertia of each order: : .

[0031] The moment of inertia also characterizes the important time domain characteristics of the random process. In the frequency domain, the above moment of inertia is usually used to approximate the zero-mean positive crossing frequency E[0] and the peak frequency E[P]. The peak frequency E[P] is determined by the following formula: .

[0032] The present application also introduces the Dirlik equation in step S3. This is because the coefficients in the Dirlik equation will be used in step S4 of the present application to solve the fatigue life of the engine bolts. In some optional embodiments, the coefficients in the Dirlik equation are determined by the following formula: , , , , : ; in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

[0033] In some optional embodiments, in step S4, the fatigue damage of the engine bolt is determined by the following formula: : ; The fatigue life of engine bolts is determined by the following formula : ; Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

[0034] The principles of step S3 and step S4 are described as follows: Bandwidth Factor It is an important parameter describing the power spectral density function and is defined as: .

[0035] From the above formula, we can see that is a dimensionless number, , where n can take non-integer values.

[0036] In particular, when n=2 in the above formula, the spectral irregularity factor describing the bandwidth distribution of the power spectral density function with frequency can be obtained: and spectral width coefficient for: ; .

[0037] when (or ), it is an ideal narrowband process (approximately a simple harmonic process); when (or ), it is represented as an ideal broadband process (approximately a white noise process).

[0038] Assuming the critical stress level is S, the expectation of the critical crossing frequency is expressed as , the peak distribution function of the stationary Gaussian random process at time t can be written as: ; Taking the differential equation of the above formula, we can get the probability density function of the peak value as: .

[0039] The above formula can be used to obtain a more general peak probability density function: .

[0040] in, is the error function: .

[0041] when When , the peak probability density function can be expressed as: .

[0042] in, The peak probability density function exhibits a Rayleigh distribution.

[0043] when When , the peak probability density function can be expressed as: , this peak probability density function exhibits a Gaussian distribution.

[0044] The Dirlik method is relatively accurate for both broadband and narrowband power spectral density functions. The method applicable to this example is the broadband superimposed narrowband acceleration power spectral density curve.

[0045] The Dirlik equation is: .

[0046] As mentioned above, the various parameters in the equation can be obtained through the four moments of inertia. Although the Dirlik equation does not consider the influence of the mean value of each stress cycle, practice shows that the Dirlik equation can usually give a relatively accurate life estimation result. Then in step S4, the fatigue damage and life are expressed in the form of a Gamma function through mathematical transformation, and finally the fatigue life and fatigue damage of the bolt can be obtained.

[0047] In step S4, the parameters C and m are further described as follows.

[0048] The SN curve expression of the material is as follows: .

[0049] S is the maximum stress amplitude that the material can withstand. As the number of cycles increases, the stress amplitude that the material can withstand gradually decreases. N is the fatigue life, that is, the maximum number of cycles that the material can withstand at a given stress level. The constants C and m are parameters related to material properties, load type and test conditions. C is a symbol of the fatigue strength of the material, and m is the fatigue index of the material, which represents the relationship between stress amplitude and fatigue life.

[0050] The second aspect of the present application provides an engine bolt random vibration fatigue life assessment device corresponding to the above method, mainly comprising: The power spectrum density curve extraction module is used to perform modal analysis, frequency response analysis, and random vibration analysis by inputting a specified acceleration power spectrum density curve after applying a preload to the finite element model constructed by bolt connection, and extract the stress response power spectrum density curve of the bolt danger point; A moment of inertia calculation module, used to determine the moment of inertia according to the power spectrum density curve; A parameter calculation module, used for determining the root mean square stress, the peak frequency and the coefficients in the Dirlik equation according to the moment of inertia; The fatigue analysis module is used to calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

[0051] In some optional embodiments, in the power spectral density curve extraction module, constructing a finite element model of the engine bolts includes: connecting two engine casings through engine bolts, with a sealing ring between the two engine casings, the engine bolts and the engine casings are contact bound, the engine bolts and the sealing rings are not in contact, the engine casings are connected to other engine structures through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

[0052] In some optional implementations, in the moment of inertia calculation module, the nth-order moment of inertia m of the power spectral density function is determined by the following formula: n : ; Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

[0053] In some optional implementations, the parameter calculation includes: The root mean square stress calculation unit is used to determine the root mean square stress using the following formula : ; Peak frequency calculation unit, used to determine the peak frequency using the following formula : ; The Dirlik equation coefficient calculation unit is used to determine the coefficients in the Dirlik equation using the following formula , , , , : ; in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

[0054] In some optional implementations, the fatigue analysis module includes: Fatigue damage calculation unit, used to determine the fatigue damage of engine bolts using the following formula : ; Fatigue life calculation unit, used to determine the fatigue life of engine bolts using the following formula : ; Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

[0055] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for evaluating the random vibration fatigue life of engine bolts, characterized in that: include: Step S1, after applying a preload force to a finite element model constructed by bolt connection, modal analysis, frequency response analysis and inputting a specified acceleration power spectrum density curve to perform random vibration analysis, and extracting a stress response power spectrum density curve of a bolt danger point; Step S2, determining the moment of inertia according to the power spectrum density curve; Step S3, determining the root mean square stress, the peak frequency and the coefficient in the Dirlik equation according to the moment of inertia; Step S4: Calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

2. The random vibration fatigue life assessment method for engine bolts according to claim 1, characterized in that: In step S1, constructing a finite element model of an engine bolt includes: connecting two engine casings through engine bolts, a sealing ring is provided between the two engine casings, the engine bolts are contact-bound with the engine casing, the engine bolts are not in contact with the sealing ring, the engine casing is connected with other engine structures through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

3. The random vibration fatigue life assessment method for engine bolts according to claim 1, characterized in that: In step S2, the nth-order moment of inertia m of the power spectral density function is determined by the following formula: n : ； Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

4. The random vibration fatigue life assessment method for engine bolts according to claim 1, characterized in that: In step S3, the root mean square stress is determined by the following formula: : ； The peak frequency is determined by the following formula : ； The coefficients in the Dirlik equation are determined by the following formula , , , , : ； in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

5. The random vibration fatigue life assessment method for engine bolts according to claim 1, characterized in that: In step S4, the fatigue damage of the engine bolt is determined by the following formula: : ； The fatigue life of engine bolts is determined by the following formula : ； Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

6. An engine bolt random vibration fatigue life assessment device, characterized in that: include: The power spectrum density curve extraction module is used to perform modal analysis, frequency response analysis, and random vibration analysis by inputting a specified acceleration power spectrum density curve after applying a preload to the finite element model constructed by bolt connection, and extract the stress response power spectrum density curve of the bolt danger point; A moment of inertia calculation module, used to determine the moment of inertia according to the power spectrum density curve; A parameter calculation module, used for determining the root mean square stress, the peak frequency and the coefficients in the Dirlik equation according to the moment of inertia; The fatigue analysis module is used to calculate the fatigue damage and fatigue life of the engine bolts according to the root mean square stress, peak frequency and coefficients in the Dirlik equation.

7. The random vibration fatigue life assessment device for engine bolts according to claim 6, characterized in that: In the power spectral density curve extraction module, constructing a finite element model of an engine bolt includes: connecting two engine casings through engine bolts, a sealing ring is provided between the two engine casings, the engine bolts and the engine casings are contact-bound, the engine bolts and the sealing rings are not in contact, the engine casings and other engine structures are connected through RBE3 units, and other engine structures are simulated using concentrated mass, and a preload is applied at the cross section of the engine bolts.

8. The random vibration fatigue life assessment device for engine bolts according to claim 6, characterized in that: In the inertia moment calculation module, the nth order inertia moment m of the power spectrum density function is determined by the following formula: n : ； Where n is the frequency order and is a natural number greater than or equal to 1, f n is the nth-order frequency, and G(f) is the power spectral density function.

9. The random vibration fatigue life assessment device for engine bolts according to claim 6, characterized in that: The parameter calculation includes: The root mean square stress calculation unit is used to determine the root mean square stress using the following formula : ； Peak frequency calculation unit, used to determine the peak frequency using the following formula : ； The Dirlik equation coefficient calculation unit is used to determine the coefficients in the Dirlik equation using the following formula , , , , : ； in, , , is the 0th-order moment of inertia, is the first-order moment of inertia, is the second-order moment of inertia, is the fourth-order moment of inertia.

10. The random vibration fatigue life assessment device for engine bolts according to claim 6, characterized in that: The fatigue analysis module includes: Fatigue damage calculation unit, used to determine the fatigue damage of engine bolts using the following formula : ； Fatigue life calculation unit, used to determine the fatigue life of engine bolts using the following formula : ； Where C is the fatigue strength of the engine bolt material, m is the fatigue index of the engine bolt material, is the Gamma function.

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