Simulation prediction method and system for random vibration fatigue of underwater vehicle equipment support

Abstract

The invention provides an underwater vehicle equipment support random vibration fatigue simulation prediction method and system. The method comprises the steps that a finite element model is constructed based on the actual installation postures of a halogen lamp support and a halogen lamp in the transportation process; analyzing the modal distribution of the halogen lamp bracket in the installation state, identifying the weak link of the key modal, and analyzing the coupling condition of the modal frequency and the PSD excitation frequency; carrying out random vibration analysis, and determining a stress frequency response function and a stress root mean square RMS stress of the key position; and based on a random vibration analysis result, predicting the fatigue life of the halogen lamp bracket and reproducing a fracture phenomenon. And optimizing the support structure through a strategy of combining free shape optimization and multi-model optimization. According to the method, the service life of the halogen lamp bracket is predicted more accurately, the halogen lamp bracket is optimized, the modal frequency of the bracket is improved, the stress amplitude is reduced, and the fatigue life is prolonged.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater submersibles, and in particular to a random vibration fatigue simulation prediction method and system for underwater submersible equipment brackets. Background Art

[0002] The underwater submersible equipment bracket is a key load-bearing structure of deep-sea exploration equipment, and its reliability directly affects the execution efficiency of scientific research tasks and the service life of equipment. In recent years, with the increasing frequency of deep-sea exploration activities, the frequency of road transportation of underwater submersible equipment has increased significantly. However, due to the requirements of lightweight design of underwater submersible structures, equipment brackets are often designed to be relatively light and thin while meeting the strength design. This design feature gradually exposes the problem of structural fatigue fracture caused by random vibration during transportation, and has become an important factor affecting the safe service of equipment. The present invention takes the halogen lamp bracket of a certain type of 4,000-meter-class autonomous underwater submersible as an example. The bracket performed well in the deep-sea high-pressure environment during the sea trial stage, but during the road transportation from Xiamen to Shanghai, many fatigue fracture accidents occurred (such as Figure 1 This typical case highlights the shortcomings of traditional underwater submersible structural design methods in coping with complex transportation vibration loads, and it is urgent to carry out targeted research to improve its vibration resistance.

[0003] The broadband random vibrations generated during road transportation can not only trigger structural resonance, but their cumulative damage effects can even exceed the rigors of deep-sea operations. Currently, underwater submersible structural design research focuses primarily on optimizing performance under marine environmental loads, while insufficient consideration is given to the effects of transportation vibration spectral loading, which complies with national standards. In particular, the application of the power spectral density (PSD) load spectrum specified in national standards to underwater submersible engineering practice requires further research.

[0004] In the field of vibration fatigue analysis, scholars have established a relatively mature methodological system. Wang Kenan and others used finite element simulation methods to deeply analyze the response characteristics of unmanned electric vehicle frames under random vibration of the road surface, extracted the inherent modal and vibration characteristic parameters of the frame, and provided a theoretical basis for frame design. You Yongzhong carried out modal analysis, frequency response analysis, and vibration fatigue analysis on the vibration fracture problem of the gas tank bracket of a light truck. Not only did he accurately identify the cause of the fracture, but he also significantly improved the reliability of the bracket through optimized design. Lin Jianfeng used the ANSYS Workbench platform to conduct a comprehensive static and random vibration analysis of the electric heating bracket structure, effectively identifying the stress concentration area and significantly improving the transportation reliability of the bracket through optimized design.

[0005] Significant research progress has also been made in recent years in the optimization design of bracket structures. Wang Shuai et al. constructed a random vibration fatigue analysis model for fuel tanks based on the Abaqus platform, using a sweep frequency method to determine simulation damping parameters. Through optimization techniques, they significantly improved the strength of the strapping structure and shortened the development cycle. Zeng Weihe et al. conducted random fatigue simulation analysis of on-board charger brackets based on measured road load spectra. They not only accurately located the origin of fatigue cracks but also effectively reduced the bracket's stress level through design optimization, significantly extending its service life. Zeng Chao et al. conducted a fatigue reliability assessment of a urea tank bracket, identified weak points, and proposed an improvement plan. Test results demonstrated significant improvement. Zhang Zheng et al. used finite element software to conduct a random vibration fatigue analysis of a power battery bracket. By comparing the fatigue life and structural quality of the bracket before and after improvement, they proposed an optimized design. The optimized bracket structure reduced its mass by approximately 19.5% and met fatigue durability requirements, providing a useful reference for the design and optimization of power battery brackets for pure electric vehicles. Deng Saibang et al. addressed the vibration cracking problem of the BCM bracket of a certain vehicle model. They predicted its random vibration fatigue life based on frequency response analysis and improved the durability of the bracket through optimized design.

[0006] The above research provides a wealth of theoretical and methodological references for the vibration fatigue analysis and optimization design of underwater submersible equipment brackets. However, the vibration fatigue problem of underwater submersible equipment brackets under complex transportation vibration loads still needs to be further studied in combination with specific engineering practices.

[0007] This invention is the first to introduce the PSD spectrum of Class III highway transportation specified in the national standard into the fatigue analysis of underwater submersible structures. By combining the high-precision finite element model with the Dirlik probabilistic model, the fracture mode of the halogen lamp bracket was successfully simulated and reproduced. On this basis, through the strategy of combining free shape optimization with multi-model optimization (Multi-Model Optimization, MMO), the limitations of traditional single-objective optimization were broken through, and multi-objective optimization with the coordinated reduction of modal frequency and stress amplitude was achieved. The fatigue life of the bracket after optimized design was extended to more than twice the original one, and it passed the strength verification of the offshore lifting condition and the verification of the random vibration test. Summary of the Invention

[0008] In view of the defects in the prior art, the purpose of the present invention is to provide a random vibration fatigue simulation prediction method and system for underwater submersible equipment brackets.

[0009] A method for simulating and predicting random vibration fatigue of a support for underwater submersible equipment provided by the present invention includes:

[0010] Step S1: constructing a finite element model based on the actual installation posture of the halogen lamp bracket and the halogen lamp during transportation;

[0011] Step S2: Analyze the modal distribution of the halogen lamp bracket in the installed state, identify the weak links of the key modes, and analyze the coupling between the modal frequency and the PSD excitation frequency;

[0012] Step S3: Perform random vibration analysis to determine the stress frequency response function and root mean square (RMS) stress at key locations;

[0013] Step S4: Based on the random vibration analysis results, the fatigue life of the halogen lamp bracket is predicted and the fracture phenomenon is reproduced.

[0014] Preferably, said constructing of the finite element model includes meshing, model simplification and boundary condition setting;

[0015] The halogen lamp bracket is discretized using a three-dimensional hexahedral grid;

[0016] The L-shaped aluminum alloy gasket between the halogen lamp and the bracket is simulated using a two-dimensional plate-shell element. The bolt connection between the L-shaped aluminum alloy gasket and the halogen lamp is simulated using an equivalent RBE2+BEAM+RBE2 combined connection element. The halogen lamp itself is simulated using RBE3+mass point CONM2, where the mass point is located at the center of mass of the halogen lamp. The mass point is connected to the halogen lamp and the four bolt holes of the mounting bracket using RBE3 elements.

[0017] The halogen lamp bracket is connected to the main structure of the underwater submersible through two mounting screw holes. The two bolt holes are connected to a main node using the RBE2 rigid unit, and the boundary conditions of the halogen lamp single system are equivalently simulated by constraining all degrees of freedom of the main node. At the same time, the main node also serves as the basic loading point for random vibration fatigue analysis.

[0018] Preferably, the halogen lamp bracket includes three-order natural modes, namely the first-order mode, the second-order mode and the third-order mode, wherein the key mode is the first-order mode;

[0019] The weak link of the key mode includes the starting area of ​​the semicircular waist hole structure.

[0020] Preferably, the input load of the random vibration analysis is expressed in the form of a spectrum of power spectrum density PSD, and the characterization indicators include the power spectrum density PSD of the response and the standard deviation of the Gaussian distribution of the response.

[0021] Preferably, step S3 includes:

[0022] Step S3.1: Solve the transfer function H between the loading point and the structure to characterize the dynamic relationship between the input excitation and the structural response. The formula is as follows:

[0023] H(f)=Y(f) / X(f)

[0024] Where Y(f) represents the Fourier transform of the output response, and X(f) represents the Fourier transform of the input stimulus;

[0025] Step S3.2: Based on the transfer function H and the given input power spectrum density PSD, a random vibration response analysis is performed to obtain the dynamic response characteristics of the halogen lamp bracket under the random vibration load.

[0026] Preferably, step S4 includes:

[0027] Step S4.1: Based on the PSD data of the random vibration response, a frequency domain-time domain conversion algorithm is used to construct the probability density function of the stress amplitude;

[0028] Step S4.2: Combine the PSD curve and the total vibration duration, and estimate the total number of cycles in each stress amplitude range using the stress amplitude-cycle number relationship in Miner's linear damage accumulation theory;

[0029] Step S4.3: Based on the material stress-life curve, calculate the fatigue damage factor D corresponding to each stress amplitude range i , the calculation formula is as follows:

[0030]

[0031] Where n i Indicates the number of cycles corresponding to a specific stress amplitude, N i (S) represents the number of cycles to failure at this stress level;

[0032] Step S4.4: Apply Miller’s linear damage accumulation criterion to linearly superimpose the damage in each stress amplitude range to obtain the total structural damage, as shown in the following formula:

[0033]

[0034] When the cumulative damage reaches a preset critical value, the structure fails due to fatigue, and the corresponding total vibration duration is the fatigue life.

[0035] Preferably, the method further includes step S5: optimizing the support structure in stages, with the following sub-steps:

[0036] Step S5.1: Perform free-form shape optimization on the two sides of the stent to determine the optimized boundary geometry.

[0037] Step S5.2: Based on the free shape optimization, the bracket structure is further optimized by multiple models.

[0038] Preferably, the step S5.1 includes determining and defining optimization variables, constraints and objective functions;

[0039] The optimization variables select the node coordinates on both sides of the bracket as design variables;

[0040] The constraint condition refers to the constraint imposed on the first-order natural frequency of the bracket, and the constraint value is not less than 30Hz;

[0041] The optimization objective is to minimize the mass of the support structure as the optimization objective function.

[0042] Preferably, the step S5.2 includes:

[0043] Step S5.2.1: Create seven shape variables based on the changes in local dimensions and plate thickness, and use optimization design software to automatically explore the best combination of these shape variables;

[0044] Step S5.2.2: Divide the model into multiple sub-regions. Define shape variables and mesh deformation rules independently for each region. Combine static, modal, and fatigue responses to achieve multi-objective optimization through a weighted objective function.

[0045] Among them, the fatigue damage value is directly constrained to be less than 1, and the mass minimization is the optimization goal.

[0046] According to the present invention, a random vibration fatigue simulation prediction system for underwater submersible equipment bracket is provided, comprising:

[0047] Module M1: Construct a finite element model based on the actual installation posture of the halogen lamp bracket and the halogen lamp during transportation;

[0048] Module M2: Analyze the modal distribution of the halogen lamp bracket in the installed state, identify the weak links of the key modes, and analyze the coupling between the modal frequency and the PSD excitation frequency;

[0049] Module M3: Perform random vibration analysis to determine the stress frequency response function and RMS stress at key locations;

[0050] Module M4: Based on the results of random vibration analysis, the fatigue life of the halogen lamp bracket is predicted and the fracture phenomenon is reproduced.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. The present invention successfully reproduces the fracture mode of halogen lamp brackets during actual transportation by constructing a refined finite element model and performing simulation analysis based on the power spectral density (PSD) load spectrum of third-level highway transportation specified in the national standard.

[0053] 2. This paper uses a combination of freeform shape optimization and multi-model shape optimization (MMO) to optimize the design of a halogen lamp bracket. The optimized bracket's modal frequency increased to 22 Hz, the stress amplitude decreased by 18%, and the fatigue life was extended to over 30 hours.

[0054] 3. To ensure the practicality and reliability of the optimized design, the present invention conducted a strength verification test on the optimized bracket under offshore hoisting conditions. The verification results showed that under offshore hoisting conditions, the maximum stress of the bracket was only 11.3 MPa, far below the material's allowable stress of 192 MPa. This demonstrates that the optimized bracket meets the strength and safety requirements for offshore hoisting conditions. Furthermore, random vibration test results demonstrate that the optimized design effectively improves the bracket's fatigue resistance, ensuring its reliability during actual transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0056] Figure 1 This is a schematic diagram of the fracture position of the halogen lamp bracket in a fatigue fracture accident;

[0057] Figure 2 Schematic diagram of 3D model for halogen lamp installation;

[0058] Figure 3 SN curve of 6061-T6 aluminum alloy material and its correction diagram;

[0059] Figure 4 is the general transportation random vibration PSD curve;

[0060] Figure 5 It is a schematic flow chart of the working method of the present invention;

[0061] Figure 6 Schematic diagram of the overall finite element calculation model in the present invention;

[0062] Figure 7 It is the modal and strain energy cloud diagram of the present invention;

[0063] Figure 8 It is the distribution diagram of the modal frequency on the load excitation PSD curve in the present invention;

[0064] Figure 9 This is a schematic diagram of the problem diagnosis results based on modality in the present invention;

[0065] Figure 10 Schematic diagram of RMS stress distribution in the present invention;

[0066] Figure 11 This is a PSD response curve diagram of the high stress area unit in the present invention;

[0067] Figure 12 This is a schematic diagram of the random vibration fatigue analysis results of the present invention;

[0068] Figure 13 This is a schematic diagram of the actual fracture position in an embodiment of the present invention;

[0069] Figure 14 This is a life distribution diagram of the halogen lamp bracket in the present invention;

[0070] Figure 15 Schematic diagram of free-form optimization design variables in the present invention;

[0071] Figure 16 Schematic diagram of the free shape optimization results in the present invention;

[0072] Figure 17 This is a comparison diagram of the first-order modes before and after free-form optimization in the present invention;

[0073] Figure 18 This is a comparison diagram of the random vibration 1σ stress before and after the free shape optimization in the present invention;

[0074] Figure 19 This is a comparison diagram of fatigue damage before and after free-form optimization in the present invention;

[0075] Figure 20 Optimizing the shape variable graph in the present invention;

[0076] Figure 21 These are four installation posture diagrams of the present invention;

[0077] Figure 22 This is the result diagram of the multi-model MMO shape optimization in the present invention;

[0078] Figure 23 Fatigue damage for the optimized design scheme in the present invention;

[0079] Figure 24 To optimize the design of the rear support structure in the present invention;

[0080] Figure 25 The stress results of the optimized design of the front and rear brackets in this invention are

[0081] Figure 26 This is a diagram of random vibration test samples before and after the optimization design in the present invention;

[0082] Figure 27 These are the random vibration test loading curves of the test specimens before and after the optimized design in the present invention. DETAILED DESCRIPTION

[0083] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0084] This study addresses the fatigue fracture issues associated with underwater vehicle equipment brackets during road transportation. Using a combination of finite element simulation and experimental verification, we systematically conducted vibration fatigue analysis and design optimization research. By constructing a refined finite element model of the equipment bracket and combining it with the power spectral density (PSD) load spectrum for random vibration during road transportation, as specified in national standards, we conducted modal analysis, random vibration response calculations, and fatigue life prediction.

[0085] In actual application, the halogen lamp needs to adjust the installation angle according to the site requirements, so the bracket is designed as follows Figure 2 The semicircular waist hole structure shown. The halogen lamp bracket structure is made of 6061-T6 aluminum alloy profiles with a yield strength of 240MPa. According to the China Classification Society's "Diving System and Submersible Classification Rules" (2018 edition) and the British Lloyd's Register's "LR-CO-001 Code for Lifting Appliances in a Marine Environment" (2024 edition), and with reference to the "Aluminum Alloy Structure Design Code", the equipment bracket is manufactured by machining. The material stress coefficient is taken as 0.8, and the allowable stress of the 6061-T6 aluminum alloy material is calculated as follows:

[0086] Allowable stress = stress coefficient × σ s =0.8×240=192MPa

[0087] The fatigue curve characteristics of 6061-T6 aluminum alloy are based on the literature

[13] The SN curve provided is simulated, and the fitting formula is:

[0088]

[0089] Where, the material fatigue limit σ fl =96.5MPa, the slope b in the double logarithmic coordinates is -0.5, and the stress amplitude S1 corresponding to a single cycle (N=1) life is 14575.5MPa. When the stress amplitude to which the structure is subjected exceeds its yield strength, the structure tends to suffer static strength failure rather than failure caused by fatigue cyclic load. Therefore, for the part of the SN curve where the stress amplitude exceeds the yield strength, it needs to be corrected according to the actual failure mode. The corrected SN curve is as follows Figure 3As shown in the figure, in regions where the stress amplitude exceeds the yield strength (i.e., the horizontal section in the figure), the fatigue damage is set to 1, indicating that the structure will directly fail at this stress level. Subsequent fatigue simulation analysis will use this modified SN curve to estimate life under random vibration loading.

[0090] Under offshore hoisting conditions, according to the British Lloyd's Register regulations, when operating in Beaufort Scale 4 sea conditions, the operating coefficient is taken as 1.2 and the dynamic load coefficient is taken as 1.7. The load safety factor is calculated as follows:

[0091] Load safety factor = stress factor × dynamic load factor = 1.2 × 1.7 = 2.04

[0092] During the road transportation process from Xiamen to Shanghai, the underwater submersible suffered fatigue fracture of the halogen lamp bracket due to random vibration for more than ten hours.

[0093] This paper refers to the general highway transportation random vibration power spectrum density (PSD) curve specified in the national standard, and conducts random vibration fatigue simulation analysis on the halogen lamp bracket to reproduce the fatigue fracture phenomenon that occurs during actual transportation. On this basis, combined with the specific working conditions, the fatigue optimization design of the halogen lamp bracket is carried out to ensure that its transportation life can exceed 30 hours, which is sufficient to meet the actual highway transportation needs from Shanghai to Xiamen, Qingdao, Sanya and other ports. Random vibration loads such as Figure 4 As shown, the specific data can be found in Table 1, and the random vibration time is set to 20 hours.

[0094] Table 1

[0095]

[0096] Example 1

[0097] According to the present invention, a method for predicting the random vibration fatigue of a support for underwater submersible equipment is provided. Figure 5 Shown, including:

[0098] Step S1: Construct a finite element model based on the halogen lamp bracket and the actual installation posture of the halogen lamp during transportation, including meshing, model simplification, and boundary condition setting. The halogen lamp bracket is discretized using a three-dimensional hexahedral mesh. The average cell size is precisely controlled to 1 mm, and at least four layers of mesh are ensured in the thickness direction to improve calculation accuracy. To ensure the accuracy and reliability of the finite element calculation, the mesh quality is strictly controlled using the Jacobian ratio to ensure that its value is not less than 0.7.

[0099] The L-shaped aluminum alloy gasket between the halogen lamp and the bracket is simulated using a two-dimensional plate and shell element. The average unit size is set to 1mm, and the unit Jacobian ratio is also controlled above 0.7. The bolt connection between the L-shaped aluminum alloy gasket and the halogen lamp is simulated using an equivalent RBE2+BEAM+RBE2 combined connection unit to reflect the actual connection status. The halogen lamp itself is simulated using RBE3+mass point (CONM2), where the mass point is located at the center of mass of the halogen lamp; the mass point is connected to the halogen lamp and the four bolt holes of the mounting bracket through the RBE3 unit. The mass of the halogen lamp is 1kg, and the mass of the halogen lamp bracket is 84.3g; the entire model contains a total of 60051 units. The overall model and its connection relationship are shown as follows. Figure 6 As shown in (a).

[0100] The halogen lamp bracket is connected to the main structure of the underwater submersible through two mounting screw holes. The two bolt holes are connected to a main node using RBE2 rigid elements, and the boundary conditions of the halogen lamp single system are equivalently simulated by constraining all degrees of freedom of the node. At the same time, the main node is also used as the basic loading point for random vibration fatigue analysis (such as Figure 6 (b) shows that the external load is transmitted to the entire halogen lamp system through these two bolt holes.

[0101] Step S2: Analyze the modal distribution of the installed halogen lamp bracket, identify key modal weaknesses, and examine the coupling between modal frequencies and PSD excitation frequencies, providing a theoretical basis for subsequent design optimization. Modal analysis reveals the system's natural frequencies and modal shapes. By implementing a frequency avoidance design strategy—rationally adjusting the structural modal frequencies to avoid external excitation frequencies—structural resonance can be effectively suppressed, thereby reducing the amplitude of the structure's dynamic response under vibration excitation and significantly improving its fatigue life and performance.

[0102] For the halogen lamp bracket system, within the PSD load excitation frequency range (2-200Hz) during road transportation, modal analysis identified the existence of three natural modes in the system. The corresponding frequency values, modal vibration characteristics and strain energy distribution are as follows: Figure 7 As shown in the figure, the strain energy distribution shows that the strain energy is mainly concentrated in the starting area of ​​the semicircular waist hole structure, indicating that this area is a weak link in the structure. Therefore, in the subsequent structural optimization and design improvement process, it is necessary to focus on strengthening this area to improve the overall structural strength and reliability of the halogen lamp bracket system.

[0103] The distribution of each modal frequency on the load excitation PSD spectrum is as follows: Figure 8As shown in Figure 2. It's worth noting that the first-order mode plays a decisive role in the structural dynamic response. Because its frequency is very close to the primary excitation frequency band (4-20 Hz), it can easily induce resonance, accelerating fatigue damage and ultimately reducing the fatigue life of the structure. Therefore, in subsequent optimization designs, adjusting the first-order modal frequency should be prioritized to avoid the primary excitation frequency band, thereby effectively improving the structure's fatigue resistance.

[0104] Comprehensive analysis of the system modal characteristics and comparison with the excitation conditions show that the first-order modal frequency of the halogen lamp bracket system is at a low level. The weak areas of the system are mainly concentrated in the three areas near the semicircular waist hole and closest to the structural boundary. The specific locations are as follows: Figure 9 Based on the above analysis results, these three areas should be identified as key areas for subsequent structural optimization. Notably, these three areas are located where the force transmission path abruptly changes and the width decreases sharply, making them key areas prone to stress concentration in the structure. The modal analysis results are consistent with the judgment based on engineering experience.

[0105] Step S3: Perform random vibration analysis to examine the stress frequency response function and 1σ stress level and its distribution pattern at key locations.

[0106] Random vibration analysis is a frequency-domain analysis method primarily used to study the dynamic response characteristics of stationary and ergodic Gaussian random processes. In this method, the input load is expressed as a spectrum in the form of a power spectral density (PSD). The analysis focuses on the statistically significant output parameters of the response, with the power spectral density (PSD) and the standard deviation of the Gaussian distribution of the response being the most commonly used characterization metrics. The mathematical expression for random vibration analysis is as follows:

[0107] [S YY (f)] n*n =[H(f)] n*m *[S XX (f)] m*m *[H(f)] H m*n

[0108] In the formula, [S YY (f)] n*n Represents the power spectrum density matrix of the response, [S XX (f)] m*m represents the power spectral density matrix of the input load, [H(f)] n*m represents the frequency response function matrix of the system, [H(f)] H m*n represents the conjugate transposed matrix of the frequency response function matrix, where f represents frequency.

[0109] From the above expression, we can see that random vibration analysis is essentially a numerical calculation process based on the transfer function H and the input load PSD. In the case of only one input, the above expression can be simplified to:

[0110] S YY (f)=|H(f)| 2 S XX (f)

[0111] The present invention relates to random vibration analysis under a typical single-input base excitation condition. In finite element analysis software, random vibration problems are usually solved using a phased, step-by-step approach. Step S3 includes:

[0112] Step S3.1: Determine the transfer function H between the loading point and the structure. This function is the ratio of the Fourier transform of the output response, Y(f), to the Fourier transform of the input excitation, X(f). The mathematical expression is: H(f) = Y(f) / X(f). This transfer function characterizes the dynamic relationship between the input excitation and the structural response and is an important foundation for subsequent random vibration response analysis.

[0113] Step S3.2: Based on the transfer function H and the given input power spectral density (PSD), a random vibration response analysis is performed. This step allows the dynamic response characteristics of the structure under random vibration loads to be determined, providing a key basis for structural optimization design and reliability assessment.

[0114] In highway transport power spectral density (PSD) ( Figure 8 ) excitation, the 1σ, 2σ and 3σ responses of the structure are as follows Figure 10 The analysis results show that the main stress concentration area of ​​the structure is located at the crack position of the bracket, and the stress distribution characteristics of this area are highly consistent with the modal strain energy distribution law, further verifying that this area is the weak link of the structure and requires special attention in the subsequent optimization design.

[0115] Based on the fundamental principles of Gaussian distribution, under conditions of random pavement excitation, the probability that the structure will experience stress values ​​below 56.7 MPa is as high as 99.3%. The detailed σ levels and their corresponding probability distributions are shown in Table 2. This table provides important data support for in-depth analysis of the structure's stress response characteristics under random pavement excitation, aiding in further assessment of the structure's reliability and durability.

[0116] Table 2

[0117]

[0118] like Figure 11As shown in the figure, the stress power spectral density (PSD) response curve in the high-stress area exhibits two significant peaks, located at 21 Hz and 45 Hz, respectively. These two peak frequencies are highly consistent with the first-order and second-order modal natural frequencies of the structure. It can be inferred that the peak response at 21 Hz is mainly excited by the first-order mode, while the peak response at 45 Hz is mainly induced by the second-order mode. It is worth noting that the peak stress amplitude at 21 Hz is significantly higher than that at 45 Hz, with its peak response value reaching approximately 10 MPa. This indicates that the first-order mode contributes more significantly to the dynamic response of the high-stress area and should be given special attention in structural optimization.

[0119] Step S4: Based on the random vibration analysis results, the fatigue life of the structure under 20 hours of transportation is predicted, reproducing the actual transportation fracture phenomenon. The core of this step is to construct a stress amplitude probability distribution model using power spectral density (PSD) data and combine it with the fatigue properties of the material to achieve life estimation. Step S4 includes:

[0120] Step S4.1: Based on the PSD data of the random vibration response, a frequency-to-time domain conversion algorithm, such as the rainflow counting method or the Dirlik method, is used to construct a probability density function of the stress amplitude. This step converts the continuous frequency-domain signal into a discrete stress amplitude distribution, providing the basis for subsequent cycle counting.

[0121] Step S4.2: Combine the PSD curve and the total vibration duration, and estimate the total number of cycles in each stress amplitude range using the stress amplitude-cycle number relationship in Miner's linear damage accumulation theory.

[0122] Step S4.3: Based on the material SN curve (stress-life curve), calculate the fatigue damage factor corresponding to each stress amplitude range. The calculation formula is as follows:

[0123]

[0124] Where n i is the number of cycles corresponding to a specific stress amplitude, N i (S) represents the number of cycles to failure at this stress level.

[0125] Step S4.4: Apply Miller’s linear damage accumulation criterion to linearly superimpose the damage in each stress amplitude range to obtain the total structural damage, as shown in the following formula:

[0126]

[0127] When the cumulative damage reaches a critical value (usually D total =1), the structure fails due to fatigue, and the corresponding total vibration duration is the fatigue life.

[0128] This paper uses the Dirlik fatigue damage model to model the stress amplitude probability density function under random vibration excitation. The total vibration test duration is set to 20 hours. The structural fatigue damage results calculated based on this model are as follows:

[0129] Maximum fatigue damage value of the structure D max is 1.391. According to Miner's linear damage accumulation criterion, when the damage value D≥1, the structure will fail due to fatigue. It can be inferred that the fatigue life of the halogen lamp bracket under random vibration excitation is T fail It is approximately 14.38 hours, and the calculation formula is:

[0130]

[0131] Where, T total is the total vibration duration.

[0132] The simulation results of fatigue fracture location are as follows Figure 12 The results are highly consistent with the predicted results of modal strain energy distribution under random vibration excitation: the simulation results show that the maximum strain energy density is concentrated in the area where the semicircular waist hole of the bracket is closest to the structure boundary; Figure 13 As shown in Figure 2, the actual fracture location is also located in this area, which verifies the Dirlik model's ability to predict the location of fatigue crack initiation. Figure 14 shown.

[0133] Step S5: Simulate and diagnose fatigue fracture issues and implement targeted optimization designs. Given that halogen lamps may be installed at different angles and undergo varying transportation times during service, this study simultaneously conducts multi-model optimization (MMO) for various installation positions and the longest transportation time (30 hours) to comprehensively improve fatigue performance.

[0134] Based on the above analysis results, the main causes of fatigue fracture can be attributed to the following two points: First, the natural frequency of the first-order mode is low, and its frequency range is close to the high stress amplitude range of the transport load spectrum (such as Figure 8 There is a significant overlap between the two frequencies (as shown in Figure 2), which leads to a significant amplification of the dynamic response of the structure in this frequency band, and thus a surge in the local stress level. Secondly, the modal strain energy distribution analysis shows that (as shown in Figure 2) Figure 9 As shown in ), the key response area of ​​the first-order mode is located at the geometric mutation point of the force transmission path. Due to the stiffness discontinuity, the modal strain energy density in this area is significantly higher than that in other parts, which leads to local stress concentration under random vibration excitation (as shown in Figure 10 The coupling effect of the above two factors leads to vibration fatigue cracking in this area under transportation vibration conditions (as shown in Figure 12 The crack initiation position is completely consistent with the modal strain energy concentration area.

[0135] Based on the above problem diagnosis results, the present invention uses finite element optimization design software to carry out phased optimization of the bracket structure, and the step S5 includes:

[0136] Step S5.1: Perform free-form optimization on the two sides of the bracket to explore and determine the optimized boundary geometry, providing a basis for subsequent optimization. The mathematical modeling of the free-form optimization problem requires clear definition of the optimization variables, constraints, and objective function, as follows:

[0137] Optimization variables: The node coordinates on both sides of the bracket are selected as design variables. During the optimization process, these nodes can be freely moved in the design space to change their position coordinates (such as Figure 15 shown).

[0138] Constraints: A constraint is imposed on the first-order natural frequency of the structure, requiring its value to be no less than 30 Hz to ensure that the structure has sufficient stiffness.

[0139] Optimization objective: Minimizing the mass of the support structure is the optimization objective function, aiming to reduce the weight of the structure.

[0140] Free shape optimization results are as follows Figure 16 The optimization results show that in areas with high strain energy distribution in the original design, particularly where the load-bearing path on both sides of the bracket narrows, the boundaries undergo significant outward expansion deformation, with the expansion direction primarily perpendicular to the original boundary surface. This optimization result effectively increases the load-bearing area in this area, thereby reducing stress concentration.

[0141] The first-order modal frequency after optimization is 22 Hz, which is 1 Hz higher than 21 Hz before optimization (e.g. Figure 17 The optimized bracket weighs 116.9 g, a 38.7% increase compared to the original design. However, this result still fails to meet the frequency constraint (>30 Hz) established during the free-form optimization phase. Analysis indicates that simply adjusting the geometry of this specific region is insufficient to achieve a significant increase in modal frequency. This indicates the need for a more in-depth structural optimization strategy.

[0142] Nevertheless, the 1σ stress level of the bracket after optimization is 15.4 MPa, which is 3.5 MPa lower than 18.9 MPa before optimization (e.g. Figure 18 As shown in the figure, it shows a certain stress improvement effect. In addition, the fatigue damage value of the bracket after optimization design is 0.89, which is 0.5 lower than that before optimization design (as shown in the figure). Figure 19However, since the goal of this optimization design is to make the structural life greater than 30 hours, the current results still do not meet the predetermined requirements and further optimization is needed to increase the fatigue life of the structure.

[0143] Step S5.2: Based on the free-form shape optimization, the bracket structure is further optimized using multiple models. This stage aims to achieve more comprehensive performance optimization by incorporating multiple possible halogen lamp installation angles and conditions, ensuring that the optimized bracket structure exhibits good mechanical properties under various operating conditions. Based on the free-form shape optimization of the bracket structure, and ensuring a fatigue life of at least 30 hours, the present invention further conducts multiple model shape optimization.

[0144] The step S5.2 includes:

[0145] Step S5.2.1: Create seven shape variables (such as Figure 20 ), and use optimization design software to automatically explore the best combination of these shape variables to achieve more refined structural optimization.

[0146] Step S5.2.2: Multi-Model Shape Optimization (MMO): Comprehensive Consideration Figure 21 Four common halogen lamp installation postures were selected, and multi-model shape optimization was performed on the seven shape variables mentioned above. The goal was to obtain a unified optimization result applicable to all postures, ensuring that the optimized bracket structure has greater versatility and robustness. Multi-model shape optimization divides the model into multiple sub-regions, independently defining shape variables and mesh deformation rules for each region. Combining static, modal, and fatigue responses, multi-objective optimization is achieved through a weighted objective function.

[0147] Step S5.2.3: Directly constrain the fatigue damage value to be less than 1 to ensure that the support structure has no fatigue failure within 30 hours and meets the design life requirements.

[0148] Step S5.2.4: Minimize mass as the optimization goal, taking into account both lightweighting and performance improvement of the structure.

[0149] The shape optimization results are as follows Figure 22 As shown in Figure 1, the results of different degree combinations of seven shape variables are shown. The fatigue damage value of the optimized structure in each posture is controlled below 1, ensuring the integrity of the structure (such as Figure 23 The shape change after optimization and the final optimization results are shown in Table 3:

[0150] Table 3

[0151]

[0152] Based on the optimization results and combined with the size of the specific profile for rounding, the following is finally determined: Figure 24 The bracket design shown in the figure increases the thickness of the short and long plates of the L-shaped bracket from 5 mm before optimization to 5.5 mm and 7 mm, respectively. The overall plate width (excluding the local protrusion) is widened from 50 mm before optimization to 55 mm. The weight of the bracket after optimization is 126.6 g, a 50.2% increase compared to the original weight.

[0153] In order to verify the effectiveness of the optimized design, the present invention conducted a comparative analysis on the strength of the halogen lamp bracket under offshore lifting conditions. The maximum stress value of the bracket before the optimized design was 26.3MPa, while after the optimized design, it was reduced to 11.3MPa, a reduction of 57% (e.g. Figure 25 (as shown). This significant reduction in stress clearly demonstrates the significant improvement in the bracket's strength due to the optimized design. Considering that both stress values ​​before and after optimization are well below the specified allowable stress, it can be concluded that the bracket's strength meets safety requirements under offshore lifting conditions. Despite the increase in bracket mass, the optimized design not only improves fatigue resistance and strength but also achieves optimal mass control, effectively avoiding excessive weight gain in the bracket structure and demonstrating excellent structural performance.

[0154] In order to verify the durability and reliability of the optimized design, the halogen lamp brackets before and after the optimization were installed on the vibration test bench, and two groups of random vibration tests were carried out for 20 hours and 30 hours respectively. The vibration direction was set to vertical. The specific arrangement is as follows: Figure 26 The loading curve of the random vibration test is shown in Figure 27 shown.

[0155] During the test, cracking and failure of the test specimens were continuously monitored, and the failure times were recorded in detail. The test results showed that the test specimens before the optimization design developed cracks after approximately 17.5 hours of vertical vibration. The crack locations were highly consistent with the actual situation and simulation results. However, the appearance of the test specimens after the optimization design remained unchanged after 30 hours of vertical vibration.

[0156] In summary, the first-order modal frequency (20.1 Hz) of the bracket in the present invention is coupled with the main frequency band of road transport excitation (4-20 Hz), resulting in stress concentration in the weak area. The simulation predicts a fatigue life of 14.38 hours, which is highly consistent with the 17.5-hour fracture phenomenon in the test. Based on free-form optimization and multi-model optimization (MMO) technology, the modal frequency of the optimized bracket is increased to 22 Hz, the stress amplitude is reduced by 18%, the fatigue life is significantly extended to more than 30 hours, and it has passed the strength verification of offshore lifting conditions (maximum stress 11.3 MPa, far below the allowable value of 192 MPa). The research results provide an important theoretical basis and technical reference for improving the reliability of deep-sea equipment. From an economic point of view, the processing and manufacturing cost of underwater submersible equipment mounting brackets is relatively low, while underwater equipment, especially deep-sea equipment, is usually expensive, with limited spare parts and long ordering cycles. Once equipment damage occurs, it is very likely to directly affect the smooth execution of the sea trial mission. Therefore, for underwater submersible equipment that is easy to disassemble, it is recommended that it be clearly stipulated in the underwater submersible manual that it must be disassembled and stored after sea trials to reduce the risk of equipment damage caused by factors such as vibration fatigue during transportation. For underwater submersibles that require long-distance transportation, in order to ensure the reliability of the equipment mounting bracket, a more reliable approach is to, in addition to performing strength verification according to conventional methods during the design phase, also follow the random vibration fatigue analysis and optimization design process proposed in this paper (such as Figure 5 Random vibration fatigue analysis is performed using a process (as shown). This process comprehensively evaluates the fatigue performance of equipment brackets in complex transportation environments, effectively identifies potential fatigue damage risks, and enables targeted optimization design to ensure the safe transportation and long-term reliable service of underwater vehicles.

[0157] Example 2

[0158] The present invention also provides a random vibration fatigue simulation prediction system for an underwater submersible equipment bracket. The random vibration fatigue simulation prediction system for an underwater submersible equipment bracket can be realized by executing the process steps of the random vibration fatigue simulation prediction method for an underwater submersible equipment bracket. That is, those skilled in the art can understand the random vibration fatigue simulation prediction method for an underwater submersible equipment bracket as an optimal implementation of the random vibration fatigue simulation prediction system for an underwater submersible equipment bracket.

[0159] (Ignore this for now and let the agent complete it)

[0160] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0161] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for predicting the random vibration fatigue of underwater submersible equipment brackets, characterized in that: include: Step S1: constructing a finite element model based on the actual installation posture of the halogen lamp bracket and the halogen lamp during transportation; Step S2: Analyze the modal distribution of the halogen lamp bracket in the installed state, identify the weak links of the key modes, and analyze the coupling between the modal frequency and the PSD excitation frequency; Step S3: Perform random vibration analysis to determine the stress frequency response function and root mean square (RMS) stress at key locations; Step S4: Based on the random vibration analysis results, the fatigue life of the halogen lamp bracket is predicted and the fracture phenomenon is reproduced.

2. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 1 is characterized in that: The constructing of the finite element model includes meshing, model simplification and boundary condition setting; The halogen lamp bracket is discretized using a three-dimensional hexahedral grid; The L-shaped aluminum alloy gasket between the halogen lamp and the bracket is simulated using a two-dimensional plate-shell element. The bolt connection between the L-shaped aluminum alloy gasket and the halogen lamp is simulated using an equivalent RBE2+BEAM+RBE2 combined connection element. The halogen lamp itself is simulated using RBE3+mass point CONM2, where the mass point is located at the center of mass of the halogen lamp. The mass point is connected to the halogen lamp and the four bolt holes of the mounting bracket using RBE3 elements. The halogen lamp bracket is connected to the main structure of the underwater submersible through two mounting screw holes. The two bolt holes are connected to a main node using the RBE2 rigid unit, and the boundary conditions of the halogen lamp single system are equivalently simulated by constraining all degrees of freedom of the main node. At the same time, the main node also serves as the basic loading point for random vibration fatigue analysis.

3. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 1 is characterized in that: The halogen lamp bracket includes three natural modes, namely the first-order mode, the second-order mode and the third-order mode, among which the key mode is the first-order mode; The weak link of the key mode includes the starting area of ​​the semicircular waist hole structure.

4. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 1 is characterized in that: The input load of the random vibration analysis is expressed as a frequency spectrum of power spectrum density PSD, and the characterization indicators include the power spectrum density PSD of the response and the Gaussian distribution standard deviation of the response.

5. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 4 is characterized in that: Step S3 includes: Step S3.1: Solve the transfer function H between the loading point and the structure to characterize the dynamic relationship between the input excitation and the structural response. The formula is as follows: H(f)=Y(f) / X(f) Where Y(f) represents the Fourier transform of the output response, and X(f) represents the Fourier transform of the input stimulus; Step S3.2: Based on the transfer function H and the given input power spectrum density PSD, a random vibration response analysis is performed to obtain the dynamic response characteristics of the halogen lamp bracket under the random vibration load.

6. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 1 is characterized in that: The step S4 comprises: Step S4.1: Based on the PSD data of the random vibration response, a frequency domain-time domain conversion algorithm is used to construct the probability density function of the stress amplitude; Step S4.2: Combine the PSD curve and the total vibration duration, and estimate the total number of cycles in each stress amplitude range using the stress amplitude-cycle number relationship in Miner's linear damage accumulation theory; Step S4.3: Based on the material stress-life curve, calculate the fatigue damage factor D corresponding to each stress amplitude range i , the calculation formula is as follows: Where n i Indicates the number of cycles corresponding to a specific stress amplitude, N i (S) represents the number of cycles to failure at this stress level; Step S4.4: Apply Miller’s linear damage accumulation criterion to linearly superimpose the damage in each stress amplitude range to obtain the total structural damage, as shown in the following formula: When the cumulative damage reaches a preset critical value, the structure fails due to fatigue, and the corresponding total vibration duration is the fatigue life.

7. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 1 is characterized in that: The step S5 is also included: optimizing the support structure in stages, with the following sub-steps: Step S5.1: Perform free-form shape optimization on the two sides of the stent to determine the optimized boundary geometry. Step S5.2: Based on the free shape optimization, the bracket structure is further optimized by multiple models.

8. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 7 is characterized in that: The step S5.1 includes determining and defining optimization variables, constraints and objective functions; The optimization variables select the node coordinates on both sides of the bracket as design variables; The constraint condition refers to the constraint imposed on the first-order natural frequency of the bracket, and the constraint value is not less than 30Hz; The optimization objective is to minimize the mass of the support structure as the optimization objective function.

9. The random vibration fatigue simulation prediction method for underwater submersible equipment bracket according to claim 7, characterized in that: The step S5.2 includes: Step S5.2.1: Create seven shape variables based on the changes in local dimensions and plate thickness, and use optimization design software to automatically explore the best combination of these shape variables; Step S5.2.2: Divide the model into multiple sub-regions. Define shape variables and mesh deformation rules independently for each region. Combine static, modal, and fatigue responses to achieve multi-objective optimization through a weighted objective function. Among them, the fatigue damage value is directly constrained to be less than 1, and the mass minimization is the optimization goal.

10. A random vibration fatigue simulation prediction system for underwater submersible equipment bracket, characterized in that: include: Module M1: Construct a finite element model based on the actual installation posture of the halogen lamp bracket and the halogen lamp during transportation; Module M2: Analyze the modal distribution of the halogen lamp bracket in the installed state, identify the weak links of the key modes, and analyze the coupling between the modal frequency and the PSD excitation frequency; Module M3: Perform random vibration analysis to determine the stress frequency response function and RMS stress at key locations; Module M4: Based on the results of random vibration analysis, the fatigue life of the halogen lamp bracket is predicted and the fracture phenomenon is reproduced.

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