A fuel tank life calculation method based on low-frequency working condition additional mass method

Abstract

This invention belongs to the field of fuel tank fatigue life prediction technology, and particularly relates to a fuel tank life calculation method based on the added mass method under low-frequency operating conditions. Its key feature is the introduction of the added mass method under low-frequency operating conditions for equivalent fluid-structure interaction (FSI) calculations under random loads, combined with the three-interval method and the nominal stress method to calculate the weld life of the fuel tank. Specifically, it includes: 1) fuel tank model establishment and mesh generation; 2) temporal reconstruction of random loads; 3) equivalent FSI calculations using the added mass method; 4) verification of the equivalent FSI calculations; and 5) weld fatigue life calculations. The beneficial effects of this invention are that by introducing the added mass method under low-frequency operating conditions for equivalent FSI calculations under random loads, and combining it with the three-interval method and the nominal stress method to calculate the weld life of the fuel tank, this invention provides a framework for analyzing the FSI fatigue characteristics of fuel tanks, and solves the technical problems of high cost of FSI calculations and difficulty in predicting weld life under random loads.

Description

Technical Field

[0001] This invention belongs to the field of fuel tank fatigue life prediction technology, and particularly relates to a fuel tank life calculation method based on the added mass method under low-frequency operating conditions. Background Technology

[0002] In the design of integral metal fuel tanks for aircraft, the tank cap and tank body are often welded using precision welding processes to ensure structural strength and sealing. During takeoff, landing, or maneuvering, the fuel in the tank may slosh due to changes in aircraft speed, encounters with unstable airflow, and other factors. The complex vibration loads generated by this sloshing can cause stress concentration at geometric abrupt changes such as weld roots and fusion lines, leading to weld fatigue failure and affecting flight safety.

[0003] In the existing technology, the fluid-structure interaction analysis of oil tank sloshing mainly relies on theoretical methods, numerical simulation and experimental means. The theoretical analysis method is difficult to apply to the calculation of large structures, and the experimental method is costly and time-consuming. Numerical simulation has become the mainstream technology, but it has the problem of difficulty in predicting the weld life under random loads. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the life of a fuel tank based on the added mass method under low-frequency operating conditions. This method overcomes the shortcomings of existing technologies by introducing the added mass method under low-frequency operating conditions for equivalent fluid-structure interaction calculations under random loads. It also combines the three-interval method and the nominal stress method to calculate the weld life of the fuel tank, providing a new approach for analyzing the fluid-structure interaction fatigue characteristics of fuel tanks and solving the technical problems of high calculation costs for fluid-structure interaction and difficulty in predicting weld life under random loads.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for calculating the life of an oil tank based on the added mass method under low-frequency operating conditions is proposed. This method introduces the added mass method under low-frequency operating conditions for equivalent fluid-structure interaction calculations under random loads, and combines the three-interval method and the nominal stress method to calculate the weld life of the oil tank. Specifically, the method includes the following steps: 1) Fuel tank model establishment and mesh generation: Based on the target fuel tank as a prototype, after simplifying the geometric model, hexahedral meshes containing the solid domain and fluid domain of the fuel tank body and weld are generated respectively, and the meshes pass the independence verification. 2) Random load time-domain reconstruction: The frequency domain load data of random vibration of the oil tank is obtained, and converted into time-domain acceleration data by inverse Fourier transform. The time-domain acceleration is verified to conform to the Gaussian normal distribution. 3) Equivalent fluid-structure interaction calculation using the additional mass method: The mass and static pressure of water are applied to the surface where the oil tank and water are in contact to represent the actual effect of the liquid on the solid. 4) Verification of equivalent fluid-structure interaction calculation: After selecting a low-frequency load of 20Hz~80Hz and confirming that there is no obvious sloshing of the liquid surface through simulation, the equivalent fluid-structure interaction calculation is performed using the added mass method. 5) Weld fatigue life calculation: Based on the three-interval method, the load interval is divided, and the weld fatigue life is calculated using the nominal stress method. (N) 总 The final number of cycles is given by N = f0 × t, where t is the final lifetime.

[0006] In step 1), simplifying the geometric model involves removing details such as small holes, chamfers, fillets, and bosses that would severely degrade mesh quality and increase the number of elements. The average mesh width is gradually reduced by a factor of 0.8, and the key eigenvalues, namely maximum stress, maximum displacement, or natural frequency, are calculated for each set of meshes. When the change in eigenvalues ​​between two adjacent sets of meshes is less than 5%, the current mesh density is considered to meet the mesh independence requirement.

[0007] In step 2), when using inverse Fourier transform for time-domain reconstruction, each frequency component is assigned a random phase angle that is uniformly distributed in the range of [0, 2π] so that the reconstructed time-domain signal conforms to Gaussian random characteristics.

[0008] The formula for calculating the additional mass in step 3) is as follows: In the formula, C m It is the additional mass coefficient, which depends on the structural shape, vibration modes and boundary conditions; ρ is the fluid density; V is the volume of fluid displaced by the structure.

[0009] Whether there is obvious swaying of the liquid level inside the oil tank in step 4) shall be determined by the results of finite element analysis.

[0010] In step 5), based on the three-interval method, the reconstructed time-domain acceleration load is divided into three amplitude intervals: "0~1.23m / s²". 2 1.23m / s 2 ~2.46m / s 2 2.46 m / s 2 ~3.69m / s 2 The values ​​1σ, 2σ, and 3σ correspond to stress levels of 0.683N, 0.271N, and 0.0433N, respectively, and the percentage of cycles corresponding to each load level is determined to be 0.683N, 0.271N, and 0.0433N, respectively. In the formula, N is the total number of cycles, f0 is the average frequency of the random vibration load, t is the time, and the equivalent sinusoidal load period is 1 / f0.

[0011] In step 5), the nominal stress method is used to determine the nominal stress spectrum of the critical parts of the weld, and combined with the stress concentration factor and the SN curve of the material, fatigue damage under each load level is calculated. Then, the damage caused by each load level is superimposed to obtain the formula for the total fatigue life of the oil tank: .

[0012] In the formula, N 总 N represents the total number of vibration cycles. 3σ N is the number of vibration cycles in the 3σ interval. 2σ The number of vibration cycles in the 2σ interval.

[0013] Compared with the prior art, the beneficial effects of the present invention are: 1) This invention introduces the additional mass method under low-frequency conditions for equivalent fluid-structure interaction calculation under random loads, and combines the three-interval method and nominal stress method to calculate the weld life of the oil tank, providing a way to analyze the fatigue characteristics of oil tank fluid-structure interaction and solving the technical problems of high cost of fluid-structure interaction calculation and difficulty in predicting weld life under random loads. 2) The present invention has verified the fuel tank under empty, half-load and full-load conditions respectively. The predicted life is close to the actual life, which verifies the feasibility of the method of the present invention. 3) This invention boldly adopts the added mass method under low-frequency operating conditions and significantly improves efficiency while ensuring acceptable engineering accuracy. Problems that could only be solved through expensive experiments or large-scale simulations can now be completed quickly on ordinary workstations. It has high computational efficiency and strong engineering applicability, providing an effective solution for predicting the fatigue life of aircraft fuel tanks. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the algorithm flow of an embodiment of the present invention; Figure 2 This is the hexahedral mesh model of the fuel tank in this embodiment of the invention; Figure 3 This is the fluid domain hexahedral mesh model in this embodiment of the invention; Figure 4 These are the frequency domain load data from the random vibration experiment of the fuel tank in this embodiment of the invention; Figure 5 This is a schematic diagram of the Gaussian normal distribution of time-domain acceleration in an embodiment of the present invention; Figure 6 This describes the changes in the oil tank level under different loads and the same liquid level height in this embodiment of the invention. Figure 7 This is a schematic diagram of the oil tank level change at a frequency of 1Hz in an embodiment of the present invention, showing obvious shaking. Detailed Implementation

[0015] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The components of the embodiments of the present invention described and shown in the accompanying drawings can typically be arranged and designed in many different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0017] See Figure 1-7 This is a schematic diagram of the algorithm flow of an embodiment of the fuel tank life calculation method based on the low-frequency operating condition additional mass method of the present invention. It introduces the low-frequency operating condition additional mass method under random loads to perform equivalent fluid-structure interaction calculations, and combines the three-interval method and the nominal stress method to calculate the weld life of the fuel tank. Specifically, it includes the following steps: 1) Fuel Tank Model Establishment and Mesh Generation: Using the target fuel tank (preferably a hypersonic aircraft fuel tank) as a prototype, detailed features that do not affect the overall mechanical properties are deleted to obtain a simplified model. The simplified model has dimensions of 600mm (length) × 400mm (width) × 350mm (height), a tank wall thickness of 1.5mm, a weld thickness of 2.5mm, and a weld width of 3mm. Eight fixed support bases are provided at the bottom of the fuel tank. HyperMesh is used to generate a hexahedral mesh of the solid domain (fuel tank body and welds), with a total mesh size of 217,554 and a total of 421,046 nodes. Figure 2 As shown; a hexahedral mesh of the fluid domain (fuel equivalent to water) was generated using Spaceclaim, with a total mesh size of 1,744,284 and a total of 1,862,415 nodes. Figure 3 As shown, both the solid domain and fluid domain meshes passed the mesh independence verification.

[0018] 2) Temporal reconstruction of random loads: such as Figure 4 The frequency domain load data of the random vibration of the oil tank shown is converted into time domain acceleration data through inverse Fourier transform. A random phase generation method is used in this process: for each frequency component, a random phase angle uniformly distributed in the range [0, 2π] is assigned to ensure that the reconstructed time domain signal has Gaussian random characteristics, consistent with the statistical assumptions of actual vibration load. The sampling frequency is set to 4000Hz, and the sampling time is set to 1000s. After load reconstruction, the acceleration is 0.04m / s². 2To count the occurrences of time-domain accelerations over intervals, we verified that they conform to a Gaussian normal distribution. The mean of the Gaussian normal distribution is 0, and the standard deviation is 1.23 m / s². 2 ,like Figure 5 As shown.

[0019] 3) Equivalent Fluid-Structure Coupling Calculation Using the Added Mass Method: The mass and hydrostatic pressure of water are applied to the surface where the tank and water meet to represent the actual effect of the liquid on the solid. When the structure vibrates in the fluid, the surrounding fluid generates dynamic pressure due to inertia, opposite to the direction of the structure's acceleration. This dynamic pressure is equivalent to adding mass to the structure, and is called added mass. Added mass lowers the structure's natural frequency, affecting its vibration response.

[0020] Added mass is usually expressed by the added mass coefficient C. m The product of fluid density ρ and displaced fluid volume V is expressed as: Formula (1) In formula (1), C m It is the added mass coefficient, which depends on the structural shape, vibration modes, and boundary conditions; ρ is the fluid density; V is the volume of fluid displaced by the structure. Assuming the fluid is incompressible and inviscid (potential flow assumption), the fluid's motion can be expressed through the velocity potential function. The description states that it satisfies the Laplace equation: Formula (2) The dynamic pressure p exerted by the fluid on the surface of the structure is given by the unsteady Bernoulli equation: Formula (3) Let the vibration displacement of the structure be u(x,t), and its acceleration be... At the fluid-structure interface Above, the normal velocity of the fluid and the velocity of the structural surface must satisfy the motion coordination condition: Formula (4) In formula (4), n is the normal vector. The total inertial force of the fluid on the structure can be obtained by integrating the interfacial pressure: Formula (5) Assume the structure undergoes simple harmonic motion (u=U) eiωt The velocity potential can be separated into the following variables: Substituting into the above equation, we get: Formula (6) make Formula (7) The fluid force can then be expressed as: Formula (8) After considering the added mass, the structural vibration equation is corrected as follows: Formula (9) In formula (9), M is the structural mass matrix; M add is the additional mass matrix (related to structural geometry and vibration modes); C is the damping matrix; K is the stiffness matrix; F(t) is the external excitation force; In the study of oil tank sloshing, water is present in the tank, necessitating consideration of the fluid-solid coupling effect. To reduce the computational cost of fluid-structure interaction (FSI), this invention employs an equivalent FSI method, namely the added mass method. The added mass method involves applying hydrostatic pressure and weight to corresponding locations on the oil tank during simulation calculations.

[0021] Because of the presence of water, the oil tank will be subjected to an additional force to suppress its vibration when it vibrates. Therefore, the mass and hydrostatic pressure of water should be applied to the surface where the oil tank and water come into contact to be equivalent to the actual effect of the liquid on the solid.

[0022] 4) Verification of Equivalent Fluid-Structure Coupling Calculation: A low-frequency load of 20Hz~80Hz was selected. After simulation confirmed that there was no significant sloshing of the liquid surface, the added mass method was used for equivalent fluid-structure coupling calculation. Water has viscosity; therefore, the water in the tank exhibits a certain hysteresis in response to the load. Under high-frequency loads, this hysteresis will cause the load on the water to cancel out, thus preventing displacement. Therefore, the motion state analysis of the fluid under equivalent loads mainly focuses on low-frequency loads (20Hz~80Hz).

[0023] like Figure 4 As shown, there are significant differences in power spectral density at different frequencies, with loads below 100 Hz exhibiting relatively smaller power spectral densities. This invention selects the extreme operating conditions within the low-frequency load range for liquid surface sloshing analysis. The derivation method for the extreme operating conditions is as follows: First, the power spectral density within the 0~80 Hz frequency range is selected and processed using the load reconstruction method to obtain a Gaussian normal distribution of the time-domain acceleration within this frequency band. Then, the 3σ acceleration value is taken as the extreme operating condition corresponding to the 80 Hz operating condition, i.e., frequency 80 Hz, acceleration 2.63 m·s⁻¹. -2 This frequency is defined as the limiting operating condition. Following this method, the limiting load conditions corresponding to 60 Hz, 40 Hz, and 20 Hz are further derived, and the results are summarized in Table 1. Figure 6 The finite element analysis results show no obvious shaking. Figure 7 The calculation at 1 Hz showed significant sloshing. Simulation analysis of the liquid surface sloshing confirmed that there was no significant sloshing within this frequency range, meeting the application conditions of the added mass method.

[0024] Table 1. Low-frequency conditions Accelerometer The final stress and life of the oil tank welds under no-load, half-load, and full-load conditions are shown in Table 2.

[0025] Table 2. Stress and life of welds 5) Weld fatigue life calculation: Based on the three-interval method, the load interval is divided, and the weld fatigue life is calculated using the nominal stress method. The maximum principal stress is selected for life prediction. The specific process is as follows: 5.1) Load range division: Based on the three-range method, the three amplitude ranges are 0~1.23m / s. 2 1.23m / s 2 ~2.46m / s 2 2.46 m / s 2 ~3.69m / s 2 , The corresponding value is 1.23 m / s 2 , The corresponding value is 2.46 m / s 2 , The corresponding value is 3.69 m / s 2 The fatigue damage from a sinusoidal load superimposed at a certain ratio can be equivalent to the fatigue damage to the fuel tank caused by random vibration loads. Assuming the total number of random vibration cycles is N, the amplitude of the superimposed fatigue damage is 1.23 m / s². 2 The load cycles were 0.683 N, and the amplitude was 2.46 m / s. 2 The load cycles were 0.271 N, and the amplitude was 3.69 m / s. 2 The number of load cycles was 0.0433 N.

[0026] In the formula: N is the total number of cycles, f0 is the average frequency of the random vibration load, t is the time, and the equivalent sinusoidal load period is 1 / f0.

[0027] 5.2) Nominal stress calculation: The specific procedure for evaluating the fatigue life of components using the nominal stress method is as follows: (a) Analyze the components for which fatigue life assessment is required to identify the critical locations; (b) Calculate the nominal stress and stress concentration factor Kt at the critical location; (c) Further determine the nominal stress spectrum at the evaluation location based on the load spectrum; (d) Find a suitable SN curve based on the stress concentration factor, and determine the fatigue life under a single working condition using interpolation. (e) Based on the three-interval fatigue damage accumulation theory, the fatigue life at the critical location is calculated.

[0028] The stress generated by the corresponding load is relatively small and has little impact on the fatigue life, so it can be ignored. Substituting the maximum stress and stress concentration factor into the formula yields the corresponding fatigue life cycle number. According to the three-interval method, the total fatigue life cycle number N is calculated as shown in formula (10): Formula (10) 5.3) Experimental Results Verification: Vibration table fatigue tests were conducted on the target oil tank under three working conditions: no-load, half-load, and full-load. The dimensions of the test piece were consistent with the simulation model. During the experiment, a vertical load spectrum was applied, consistent with the simulation. The test piece was connected to the vibration table via bolts. The lifespan under no-load, half-load, and full-load conditions was measured during the experiment. When the test piece failed, the lifespan was recorded, and the experiment ended.

[0029] The experimental results and the comparison of predicted lifespan are shown in Table 3. No damage occurred to the fuel tank within 2 hours under no-load conditions. However, the no-load state is almost impossible to occur in actual flight, and the stress on the weld is also minimal under this condition; therefore, the experimental lifespan under no-load conditions is not very meaningful. The test specimen lifespan was 0.48 hours under half-load and 0.17 hours under full-load conditions. For both half-load and full-load conditions, the predicted lifespan is close to the actual lifespan, verifying the feasibility of the method used in this paper. Furthermore, the predicted lifespan is slightly less than the actual lifespan, indicating sufficient conservatism in lifespan prediction and leaving a large safety margin.

[0030] Table 3 Comparison of Experimental Lifetime and Predicted Lifetime This invention breaks through the existing technical bias that "tank vibration must be handled using strong fluid-structure interaction methods (such as CEL) to ensure accuracy." It boldly employs the added mass method under low-frequency conditions, significantly improving efficiency while maintaining acceptable engineering accuracy. The synergistic effect of the overall solution: demonstrating that all stages of the entire methodology (from meshing to equivalent simulation to simplified fatigue) are interconnected and work together, enabling problems that previously could only be solved through expensive experiments or large-scale simulations to be quickly completed on ordinary workstations, producing unexpected technical effects beyond simple superposition.

[0031] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating fuel tank life based on the added mass method under low-frequency operating conditions, characterized in that, The equivalent fluid-structure interaction calculation is performed by introducing the additional mass method under low-frequency conditions under random loads, and the weld life of the oil tank is calculated by combining the three-interval method and the nominal stress method. The specific steps include: 1) Fuel tank model establishment and mesh generation: Based on the target fuel tank as a prototype, after simplifying the geometric model, hexahedral meshes containing the solid domain and fluid domain of the fuel tank body and weld are generated respectively, and the meshes pass the independence verification. 2) Random load time-domain reconstruction: The frequency domain load data of random vibration of the oil tank is obtained, and converted into time-domain acceleration data by inverse Fourier transform. The time-domain acceleration is verified to conform to the Gaussian normal distribution. 3) Equivalent fluid-structure interaction calculation using the additional mass method: The mass and static pressure of water are applied to the surface where the oil tank and water are in contact to represent the actual effect of the liquid on the solid. 4) Verification of equivalent fluid-structure interaction calculation: After selecting a low-frequency load of 20Hz~80Hz and confirming that there is no obvious sloshing of the liquid surface through simulation, the equivalent fluid-structure interaction calculation is performed using the added mass method. 5) Weld fatigue life calculation: Based on the three-interval method, the load interval is divided, and the weld fatigue life is calculated using the nominal stress method. (N) 总 The final number of cycles is given by N = f0 × t, where t is the final lifetime.

2. The method for calculating fuel tank life based on the added mass method under low-frequency operating conditions according to claim 1, characterized in that, In step 1), simplifying the geometric model involves removing details such as small holes, chamfers, fillets, and bosses that would severely degrade mesh quality and increase the number of elements. The average mesh width is gradually reduced by a factor of 0.8, and the key eigenvalues, namely maximum stress, maximum displacement, or natural frequency, are calculated for each set of meshes. When the change in eigenvalues ​​between two adjacent sets of meshes is less than 5%, the current mesh density is considered to meet the mesh independence requirement.

3. The method for calculating fuel tank life based on the added mass method under low-frequency operating conditions according to claim 1, characterized in that, In step 2), when using inverse Fourier transform for time-domain reconstruction, each frequency component is assigned a random phase angle that is uniformly distributed in the range of [0, 2π] so that the reconstructed time-domain signal conforms to Gaussian random characteristics.

4. The method for calculating fuel tank life based on the added mass method under low-frequency operating conditions according to claim 1, characterized in that, The formula for calculating the additional mass in step 3) is as follows: In the formula, C m It is the additional mass coefficient, which depends on the structural shape, vibration modes and boundary conditions; ρ is the fluid density; V is the volume of fluid displaced by the structure.

5. The method for calculating fuel tank life based on the added mass method under low-frequency operating conditions according to claim 1, characterized in that, Whether there is obvious swaying of the liquid level inside the oil tank in step 4) shall be determined by the results of finite element analysis.

6. The method for calculating fuel tank life based on the added mass method under low-frequency operating conditions according to claim 1, characterized in that, In step 5), based on the three-interval method, the reconstructed time-domain acceleration load is divided into three amplitude intervals: "0~1.23m / s". 2 1.23m / s 2 ~2.46m / s 2 2.46 m / s 2 ~3.69m / s 2 The values ​​1σ, 2σ, and 3σ correspond to stress levels of 0.683N, 0.271N, and 0.0433N, respectively, and the percentage of cycles corresponding to each load level is determined to be 0.683N, 0.271N, and 0.0433N, respectively. In the formula, N is the total number of cycles, f0 is the average frequency of the random vibration load, t is the time, and the equivalent sinusoidal load period is 1 / f0. According to claim 1, a method for calculating the life of a fuel tank based on the added mass method under low-frequency operating conditions is characterized in that, in step 5), the nominal stress method is used to determine the nominal stress spectrum of the critical part of the weld, and the fatigue damage under each load is calculated by combining the stress concentration factor and the SN curve of the material. Then, the damage caused by each load is superimposed to obtain the formula for the total fatigue life of the fuel tank: 。 7. In the formula, N 总 N represents the total number of vibration cycles. 3σ N is the number of vibration cycles in the 3σ interval. 2σ The number of vibration cycles in the 2σ interval.

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