A multi-objective optimization verification method for anti-loosening fatigue life of in-shaft oil pipe connection

Abstract

The present invention discloses a multi-objective optimization verification method for fatigue life of an inner-shaft oil pipe connection to prevent loosening, the method comprising: step 1: establishing a three-dimensional geometric model of the inner-shaft oil pipe under real working conditions; step 2: setting boundary conditions in the model, the boundary conditions reflecting the real working conditions of the inner-shaft oil pipe; step 3: simulating the fatigue life of the real working conditions; step 4: establishing a three-dimensional geometric model of the inner-shaft oil pipe under test conditions; step 5: using a non-dominated sorting genetic algorithm II to perform multi-objective optimization, and determining a test loading condition equivalent to the real working condition of the inner-shaft oil pipe through fatigue life simulation and comparison with the result of step 3; step 6: performing test verification on a test device under the test loading condition.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue life multi-objective optimization verification, and in particular to a method for multi-objective optimization verification of fatigue life of an inner-shaft oil pipe connection to prevent loosening. Background Art

[0002] In industrial applications, especially in the fields of shipbuilding, oil drilling and offshore engineering, the reliability of the connection of the oil pipe in the shaft is crucial. These connection parts often work under high pressure and complex stress conditions, and are easily affected by factors such as vibration, wear and corrosion, which can lead to loose connections and failure. Therefore, improving the anti-loosening ability of the oil pipe connection in the shaft and ensuring its long-term stable operation is an important engineering challenge.

[0003] With the development of simulation technology, a three-dimensional geometric model of the oil pipe in the shaft is often designed, and the actual working conditions are simulated in simulation software such as finite element analysis (FEA) to perform simulation predictions such as fatigue life to ensure the stable operation of the equipment. In the final stage, it is usually necessary to conduct real-condition test verification on real equipment to confirm the accuracy of the finite element analysis prediction. It can be said that the consistency between the simulation results and the final test verification data results is crucial to verifying the entire methodology and confirming the reliability of the calculation model used.

[0004] However, the oil pipe inside the controllable pitch propeller shaft is a large-sized thin-walled structure, and traditional equivalent methods (such as dimensional analysis) are increasingly limited. This is firstly because it is limited by the test equipment conditions and cannot directly test and verify the actual size of the oil pipe inside the controllable pitch propeller shaft in real working conditions. Secondly, its wall thickness or single layer thickness cannot be reduced in proportion to the overall size, so traditional methods will encounter difficulties in the model design stage. Due to these limitations, the experimental results of the scaled model will produce deviations in the prediction of the prototype dynamic characteristics. Summary of the invention

[0005] The purpose of the present invention is to propose a nonlinear equivalent method based on finite element analysis and multi-objective optimization algorithm to solve the problem of using a scaled model to predict the actual size model in large-size thin-walled structures such as oil pipes in controllable pitch propeller shafts.

[0006] To achieve the above object, the present invention provides a multi-objective optimization verification method for anti-loosening fatigue life of an inner-shaft oil pipe connection, characterized in that the method comprises:

[0007] Step 1: Establish a 3D geometric model of the oil pipe in the shaft with actual dimensions for real working conditions;

[0008] Step 2: setting boundary condition loading parameters for the three-dimensional geometric model of the actual-size in-shaft oil pipe, wherein the boundary condition loading parameters reflect the actual working conditions of the actual in-shaft oil pipe;

[0009] Step 3: Use the Dirlik method, Bendat method and boundary condition loading parameters to simulate the fatigue life of the oil pipe in the actual size shaft;

[0010] Step 4: Establish a three-dimensional geometric model of the in-shaft oil pipe of the test size for test verification conditions;

[0011] Step 5: using a non-dominated sorting genetic algorithm II to perform multi-objective optimization, specifically, continuously adjusting the loading parameters of the three-dimensional geometric model of the test-sized in-shaft oil pipe, using the Dirlik method and the Bendat method to perform fatigue life simulation on the test-sized in-shaft oil pipe, and when the fatigue life simulation results obtained by the Dirlik method and the Bendat method are substantially the same as the fatigue life simulation results obtained in step 3, determining the current loading parameters as the test verification loading parameters;

[0012] Step 6: On the test equipment, use the test verification loading parameters to conduct fatigue life test verification on the test size inner shaft oil pipe, and use the test verification results as a reference for the fatigue life of the actual size inner shaft oil pipe under real working conditions.

[0013] Further preferably, in step 1, the three-dimensional geometric model includes the diameter, length and wall thickness of the oil pipe, and establishing the three-dimensional geometric model also includes defining material properties, and the material properties include elastic modulus, density and Poisson's ratio.

[0014] Further preferably, in step 2, setting the boundary conditions specifically includes: power spectral density (PSD) analysis, wherein the power spectral density (PSD) analysis is used to simulate frequency-dependent energy distribution;

[0015] Modal reduction analysis to determine the modes of the structure and their corresponding modal masses; and applying simulated air pressure, torque, and random vibration loads.

[0016] Further preferably, in step 3, the estimation of fatigue life is based on the cumulative distribution function of stress amplitude, which is mathematically expressed as:

[0017]

[0018] Where σ represents the stress amplitude and f(σ) is the distribution function of the stress amplitude.

[0019] Further preferably, in step 5, the multi-objective optimization using non-dominated sorting genetic algorithm II specifically includes the following steps:

[0020] Step 51: defining an optimization objective function, wherein the optimization objective function includes a first optimization objective function and a second optimization objective function, wherein the first optimization objective function is to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size by the Dirlik method; and to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size by the Bendat method;

[0021] Step 52: defining decision variables and constraints, wherein the decision variables include the amplitude and frequency of torque loading, air pressure level and vibration characteristics;

[0022] Step 53: Using a non-dominated sorting genetic algorithm II (NSGA-II) to solve the multi-objective optimization problem; wherein the mathematical model of the non-dominated sorting genetic algorithm II (NSGA-II) algorithm is expressed as an optimization problem:

[0023] min x {f1(x),f2(x)},

[0024] Among them, x is the decision variable vector, f1 and f2 are the first and second optimization objective functions.

[0025] Further preferably, in step 53, using a non-dominated sorting genetic algorithm II (NSGA-II) to solve the multi-objective optimization problem specifically includes the following steps:

[0026] Step 53-1: Population initialization: randomly generating a group of initial solutions, wherein the group of initial solutions represents different design schemes;

[0027] Step 53-2: Fitness evaluation: evaluating the fitness of each individual, where the fitness is the performance of the individual in meeting different optimization objectives;

[0028] Step 53-3: Non-dominated sorting and crowding calculation: Sort by individual fitness and calculate crowding to maintain the diversity of solutions;

[0029] Step 53-4: Selection, crossover and mutation operations: select excellent individuals according to non-dominated sorting and crowding, and generate new solutions through crossover and mutation operations;

[0030] Step 53-5: Population replacement: Replace the individuals in the current population with the newly generated more optimized Pareto frontier solution and enter the next generation of iteration.

[0031] Further preferably, the “substantially the same” in step 5 means that the calculated result of the objective function is ≤ one thousandth of the fatigue life simulation result in step 2, that is, when the above condition is met, the iteration in step 53-5 is terminated.

[0032] Further preferably, in step 6, the test verification is specifically as follows: on the test equipment, the working environment of the in-shaft oil pipe of the test size is simulated, which is affected by random vibration, torque and air pressure, so as to evaluate the anti-loosening performance of the oil pipe connection.

[0033] Further preferably, the test verification specifically includes the following steps:

[0034] Step 61: designing a tooling structure and a control system, wherein the tooling structure includes a base plate, an adjustment bracket, a sliding base, a torque sensor adapter and a bearing support, wherein the control system is a PLC control system, and the PLC control system is responsible for controlling the servo motor to apply torque and vibration load;

[0035] Step 62: Applying and monitoring the load: applying the test verification loading parameters determined in step 5 based on the simulation results to the oil pipe in the test size shaft;

[0036] Step 63: Anti-loosening performance evaluation: After completing the predetermined load cycle, the oil pipe in the test size shaft is inspected and evaluated, wherein the evaluation includes whether there is leakage at the connection.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. The present invention combines finite element analysis (FEA) with a fatigue life prediction model. First, the fatigue life of the actual-size in-shaft oil pipe connection under actual working conditions is accurately predicted based on loading conditions such as stress and strain analysis under complex load conditions. Then, based on the predicted fatigue life, equivalent loading conditions corresponding to the actual working conditions of the test-size in-shaft oil pipe and the actual-size in-shaft oil pipe are found, and verification is performed on the test equipment based on the loading conditions as a reference for the fatigue life of the actual-size in-shaft oil pipe under real working conditions, thereby solving the problem of using a scaled model to predict the actual-size model in a large-size thin-walled structure.

[0039] 2. By introducing the non-dominated sorting genetic algorithm II (NSGA-II), the present invention achieves an optimal balance between multiple design objectives. This method takes into account the interaction of different design variables and comprehensively considers the fatigue life (Dirlik method) and stress resistance (Bendat method) of the in-shaft oil pipe during use to ensure the effectiveness and stability of iterative search for the equivalent load of the actual workpiece of the scaled workpiece.

[0040] 3. The Dirlik model can effectively simulate random vibrations under actual working conditions, and can more accurately and effectively predict the fatigue life of the in-shaft oil pipe working under complex working conditions; while the Bendat model is more suitable for processing nonlinear stress-life relationships, and can better simulate the stress resistance of specific material structural parts according to the material and loading conditions. Therefore, the scheme of the present invention is particularly suitable for the fatigue life prediction of the in-shaft oil pipe in complex working environments such as high pressure, vibration and irregular stress in scenes such as ships, oil drilling and marine engineering.

[0041] 4. The present invention does not rely solely on simulation data, but also includes experimental verification steps to ensure the consistency between the theoretical model and the actual application. This method of combining simulation and experiment enhances the application value of the invention and the credibility in actual operation. Under the premise of ensuring function and safety, it improves design efficiency, optimizes material and design costs, and achieves the optimization of overall performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the process of the present invention. DETAILED DESCRIPTION

[0043] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation modes.

[0044] Unless explicitly stated otherwise, throughout the specification and claims, the term “comprise” or variations such as “include” or “comprising”, etc., will be understood to include the stated elements or components but not to exclude other elements or components.

[0045] Example 1

[0046] Figure 1 1 is a process flow chart of the present invention. As shown in the figure, the method of the present invention comprises the following steps:

[0047] Step 1: Establish a detailed finite element analysis model of the oil pipe in the actual size shaft; In a specific calculation example, establishing a detailed finite element analysis model of the oil pipe in the actual size shaft includes:

[0048] 1) Establishment of 3D geometric model

[0049] In a specific calculation example, an example of a three-dimensional geometric model can be the following model: the total length of the oil pipe is 2660mm. The diameter of the middle thickened part is φ525±3mm, and the diameters of the two ends are φ136mm and φ88±0.1mm respectively. The diameter of the connecting thread part is φ136mm. The thread is M160×4 and the length is 25mm. The inner diameter is φ500mm and the wall thickness is 12.5mm.

[0050] 2) Material property definition

[0051] In a specific calculation example, the material properties can be as follows: Elastic modulus: 210 GPa. Density: 7850 kg / m 3 . Poisson's ratio: 0.3.

[0052] Step 2: Set boundary conditions in the model. The boundary conditions reflect the working environment of the oil pipe in the actual size shaft in actual operation, including:

[0053] Establish the kinetic equation;

[0054] In a specific calculation example, the dynamic equation is set as follows: Structural response estimation: Dynamic equation Used to estimate the response of a structure in a random vibration analysis. The modal mass matrix M, damping coefficients C, stiffness matrix K, displacement vector x, and external forces F(t) are set based on actual conditions and material properties.

[0055] Parameter setting of the kinetic equation:

[0056] Modal mass matrix M: It is assumed to be a diagonal matrix, and the main diagonal elements are set to 100kg.

[0057] Damping coefficient C: Assuming the critical damping ratio is 0.05, the damping coefficient calculation formula is:

[0058] Stiffness matrix K: Assume that the stiffness coefficient of each mode is 10000N / m.

[0059] Displacement vector x: Set the initial displacement to zero, that is, x=0.

[0060] Time-dependent external force F(t): Assume that the external force is periodic, for example, F(t) = F0sin(ωt), where F0 = 500N and the frequency ω is 5Hz to 200Hz.

[0061] Step 3: Estimation of fatigue life of the oil pipe in the actual size shaft under real working conditions, wherein fatigue life estimation is performed using the Dirlik and Bendat methods; specifically, in the present invention, fatigue analysis of the oil pipe is performed using the Dirlik cycle counting model and the Bendat cycle counting model. The model can effectively predict the fatigue life of the oil pipe under severe boundary conditions, such as torque or vibration levels beyond the normal operating range. The Dirlik model and the Bendat model are advanced fatigue analysis methods based on statistics and probability theory, which can accurately predict the fatigue behavior of materials under complex load conditions. In a specific calculation example, fatigue life estimation can be achieved by the following method: Dirlik method: Using the Dirlik method, where the fatigue strength coefficient σ′f and the Basquin fatigue strength index b is set to σ′ f =500MPa and b=-0.25.

[0062] Fatigue strength coefficient (σ′ f ): Set to 500MPa, used to characterize the fatigue limit of the material.

[0063] Basquin fatigue strength index (b): set to -0.25, describes the fatigue behavior of the material under repeated loading.

[0064] Stress amplitude (σ a ): is set to 200MPa as a typical stress level to simulate actual working conditions.

[0065] Fatigue life (N f )Calculation formula:

[0066]

[0067] Used to predict fatigue life under given stress conditions.

[0068] Bendat Cycle Counting Model: The Bendat model is used for fatigue prediction of narrow-band random processes. In this model, the stress cycles in the load history are counted and analyzed using the same Basquin criterion as the Dirlik model.

[0069] Step 4: Establish a three-dimensional geometric model of the in-shaft oil pipe of the test size under the test verification conditions. The method is similar to step 1 and will not be repeated here.

[0070] Step 5: Use non-dominated sorting genetic algorithm II for multi-objective optimization; In the present invention, the simulation results of the actual size in-shaft oil pipe are used as the optimization benchmark for the simulation parameters of the test size in-shaft oil pipe. The core here is to use a multi-objective optimization algorithm (such as NSGA-II) to accurately adjust the loading conditions of the test size in-shaft oil pipe so that it more truly reflects the actual working conditions of the actual size in-shaft oil pipe. The goal of this step is to ensure that the fatigue life simulation results of the test size in-shaft oil pipe are as close as possible to the simulation results of the actual size in-shaft oil pipe.

[0071] Step 6: Test verification.

[0072] In a preferred embodiment, in step 1, the detailed three-dimensional geometric model includes the diameter, length, wall thickness and detailed structure of the connection part of the oil pipe, and establishing the detailed three-dimensional geometric model of the oil pipe in the actual size shaft also includes defining material properties, and the material properties include elastic modulus, density and Poisson's ratio. The method of the present invention uses COMSOL Multiphysic to perform finite element analysis. By establishing a detailed geometric model of the oil pipe in the actual size shaft, the model accurately reflects the size, shape and material properties in actual use. A comprehensive simulation analysis is performed for loading conditions, including air pressure, random vibration and torque load. The purpose of the simulation analysis is to obtain the stress, strain, acceleration and predict fatigue life at the oil pipe connection under various working conditions.

[0073] In a preferred embodiment, in step 2, setting the boundary conditions specifically includes: power spectrum density (PSD) analysis, power spectrum density (PSD) analysis is used to simulate frequency-dependent energy distribution; in a specific example, power spectrum density (PSD) analysis is particularly used to simulate frequency-dependent energy distribution in a high-frequency vibration environment;

[0074] Application Calculation Example 1

[0075] In application calculation example 1, the specific steps of power spectral density (PSD) analysis are introduced:

[0076] 1. First, you need to determine the frequency range and PSD function, specifically:

[0077] Determination of frequency range: The frequency range of the analysis was limited to 150 Hz to 800 Hz to capture the enhanced response that may occur in the structure near the natural frequency.

[0078] PSD function setting: In the axial direction, the PSD function is set to P X (f) = Alog(f) B , and in the vertical direction, the function is set to P Z (f) = Cexp(Dlog(f)). These functions describe the frequency-dependent energy distribution of the vibration load in a selected frequency range.

[0079] Axial direction: In the axial direction, the PSD function is a logarithmic function of the frequency, defined as P X (f) = 0.001log(f) 2 .

[0080] Vertical direction: The vertical PSD is directly exponentially defined by the logarithm of the frequency as P Z (f)=0.0005exp(0.03log(f)).

[0081] 2. Perform power spectral density (PSD) analysis. The power spectral density (PSD) analysis specifically includes the following steps:

[0082] Determination of power spectral density value

[0083] At a specific reference frequency f ref , determine the power spectral density value S0, which is usually taken from the material properties or the vibration response data measured by experiment. For example, for the oil pipe in the shaft made of low carbon steel, it can be ref =1Hz using S0=0.1g 2 / Hz.

[0084] Frequency Response Index Selection

[0085] The frequency response index n reflects the sensitivity of the material to frequency changes. In typical engineering situations, n=2 is used to reflect the trend that energy increases with increasing frequency.

[0086] Calculation of power spectral density value:

[0087] For the natural frequency f of the structure nat , calculate the PSD value at that frequency, for example:

[0088]

[0089] With f nat =50Hz as an example, calculate the PSD value at this frequency:

[0090]

[0091] In step 2, setting boundary conditions specifically also includes: modal reduction analysis, which is used to determine the various modes of the structure and their corresponding modal masses, which is the key to understanding the structural response.

[0092] Application Calculation Example 2

[0093] In application calculation example 2, the specific steps of modal reduction analysis are introduced.

[0094] In application calculation example 2, the modal reduction analysis includes the calculation of modal mass, where the calculation of modal mass is specifically: the modal mass m of each structure i It is determined through a natural frequency study and estimated by integrating the PSD function with frequency as shown below: where f low ,f high The lower and upper frequency limits of the integration are 150 Hz and 800 Hz respectively.

[0095] Modal reduction analysis includes:

[0096] 1. Determine the natural frequency of the structure:

[0097] Finite element analysis (FEA) software was used to determine the natural frequencies of the structure. For the long specimen inner shaft oil pipe, the first three natural frequencies were f1 = 30 Hz, f2 = 75 Hz and f3 = 150 Hz.

[0098] 2. Calculation of modal mass:

[0099] In FEA software, the modal mass m of each mode is obtained through modal analysis. i The calculated modal masses are m1=10kg, m2=5kg and m3=2kg respectively.

[0100] 3. Calculate the modal participation factor:

[0101] Modal participation factor g i It can be obtained by integrating the vibration shape vector of each mode with the PSD function, expressed as:

[0102]

[0103] where φ i (f) is the value of the vibration shape vector of the ith mode at frequency f, and we get g1 = 0.8, g2 = 0.3, g3 = 0.1

[0104] 4. Calculate the total energy of the modal participation:

[0105] Calculate each mode participation factor to get the energy contribution of each mode:

[0106]

[0107] For example, for the above modal participation factors and modal masses, the calculated energy contributions are E1 = 3.2 J, E2 = 0.45 J and E3 = 0.01 J respectively.

[0108] 5. Add the energy contributions of all modes to obtain the total energy of the structure:

[0109]

[0110] For the above example, the total energy is E total =3.66J.

[0111] In a preferred embodiment, the kinetic equation is expressed as:

[0112]

[0113] Where M is the modal mass matrix, C is the damping coefficient, K is the stiffness matrix, x is the displacement vector, and F(t) is the time-dependent external force. The natural frequencies of the structure are calculated using classical dynamic equations. These equations take into account the modal mass and probability density function parameters and provide a basis for predicting the response of the structure in random vibration analysis.

[0114] The above dynamic equation is used to describe the dynamic response of the structure under random loads. The external force F(t) is time-dependent and represents the random vibration load borne by the structure. In order to solve the dynamic equation, it is necessary to consider the influence of three physical quantities, mass, damping and stiffness, on the dynamic response of the structure. The dynamic equation describes the vibration response of the structure under random loads, including displacement, velocity, acceleration, etc., reflecting the interaction between the inherent characteristics of the structure (mass, stiffness, damping) and external excitation (random load).

[0115] In a preferred embodiment, in step 3, the estimation of fatigue life is based on the cumulative distribution function of stress amplitude, which is mathematically expressed as:

[0116]

[0117] Where σ represents the stress amplitude and f(σ) is the distribution function of the stress amplitude.

[0118] Step 4: Establish a three-dimensional geometric model of the in-shaft oil pipe of the test size under test verification conditions. The method is similar to step 1 and will not be repeated here.

[0119] In a preferred embodiment, in step 5, the multi-objective optimization using the non-dominated sorting genetic algorithm II specifically includes the following steps:

[0120] Step 51: defining an optimization objective function, wherein the optimization objective function includes a first optimization objective function and a second optimization objective function, wherein the first optimization objective function is to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size by the Dirlik method; the second optimization objective function is to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size by the Bendat method;

[0121] Step 52: Define decision variables and constraints, where the decision variables include the amplitude and frequency of torque loading, air pressure level and vibration characteristics, where the constraints are used to ensure that all solutions in the optimization process are practically feasible based on the feasibility and safety of actual operating parameters. The decision variables correspond to the key factors that affect the anti-loosening performance of the oil pipe.

[0122] Step 53: Using a non-dominated sorting genetic algorithm II (NSGA-II) to solve the multi-objective optimization problem; wherein the mathematical model of the non-dominated sorting genetic algorithm II (NSGA-II) is expressed as an optimization problem:

[0123] min x {f1(x),f2(x)},

[0124] Among them, x is the decision variable vector, f1 and f2 are the first and second optimization objective functions.

[0125] In a preferred embodiment, in step 53, using a non-dominated sorting genetic algorithm II (NSGA-II) to solve the multi-objective optimization problem specifically includes the following steps:

[0126] Step 53-1: Population initialization: randomly generate a set of initial solutions, each of which represents different design schemes;

[0127] Step 53-2: Fitness evaluation: Evaluate the fitness of each individual, where fitness is the performance of the individual in meeting different optimization goals; wherein the optimization goals may also include maximizing anti-loosening performance and minimizing costs;

[0128] Step 53-3: Non-dominated sorting and crowding calculation: Sort by individual fitness and calculate crowding to maintain the diversity of solutions;

[0129] Step 53-4: Selection, crossover and mutation operations: select excellent individuals according to non-dominated sorting and crowding, and generate new solutions through crossover and mutation operations;

[0130] Step 53-5: Population replacement: Replace the individuals in the current population with the newly generated more optimized Pareto front solution and enter the next generation of iteration. In the actual iteration process, if the objective function threshold is not reached after 100 iterations, the iteration is terminated and the condition closest to the threshold is used as the loading condition.

[0131] Application Calculation Example 3

[0132] In Application Calculation Example 3, a specific calculation example of using a non-dominated sorting genetic algorithm II (NSGA-II) to solve a multi-objective optimization problem is given. The calculation example specifically includes the following steps:

[0133] 1. Problem Definition

[0134] (1-1) Determine the decision variables: The decision variables include: the outer pipe oil pressure P E , Inner pipe oil pressure P I , outer tube torque T E And the inner tube torque T I .

[0135] (1-2) Determine the optimization goal:

[0136] Objective function 1: f1 = 1 / 2 × (L D -L LD ) 2

[0137] Objective function 2: f2 = 1 / 2 × (L B -L LB ) 2

[0138] Where L D and L B The fatigue life simulation results of the oil pipe in the test-size shaft calculated by Dirlik and Bendat models are respectively L It is the fatigue life simulation result corresponding to the oil pipe in the actual size shaft.

[0139] 2. NSGA-II algorithm implementation

[0140] The NSGA-II algorithm specifically includes the following steps:

[0141] S1. Population initialization: The population size is set to 50. The initial solution is constructed by randomly generating values ​​for each decision variable.

[0142] S2. Fitness evaluation

[0143] The Dirlik and Bendat models are used to calculate the two fatigue lives respectively. The calculation formulas are as follows:

[0144] L D =f Dirlik (P E , P I , T E , T I )

[0145] L B =f Bendat (P E , P I , T E , T I )

[0146] Calculate the values ​​of objective functions f1 and f2.

[0147] S3, non-dominated sorting and congestion calculation

[0148] Among them, non-dominated sorting: each individual is assigned a rank according to its dominance relationship. The definition of dominance relationship is as follows:

[0149] If individual A is not inferior to individual B for any goal f1 or f2, and A is superior to B on at least one goal, then A is said to dominate B.

[0150] Crowding calculation: For each individual in each level, calculate its crowding on each objective function. The formula is as follows:

[0151]

[0152] Where m is the number of objective functions, f i j (max) and f i j (min) are the maximum and minimum values ​​of the jth objective function in level i, respectively. For the implementation of the present application, the actual m=2.

[0153] S4. Selection, crossover, and mutation

[0154] Selection: Based on tournament selection, parents are chosen based on non-dominated ordering and crowding.

[0155] Crossover: Randomly select a crossover point and perform a single-point crossover. The formula is as follows:

[0156]

[0157] where k c is the intersection point, C1 and $C_2$ are children, and P1 and P2 are parents.

[0158] Mutation: Each gene is randomly mutated with a certain probability. The formula is as follows:

[0159]

[0160] Among them, M i,k is the mutated gene, G i,k It is the original gene, lb k andub k are the lower and upper bounds of the gene, p m is the mutation probability.

[0161] In step 6, the test verification is specifically: test verification of the test size specimen, wherein the test verification of the test size inner shaft oil pipe is specifically: placing the test size inner shaft oil pipe on the test equipment, in a simulated working environment, under the influence of precisely controlled random vibration, torque and air pressure, so as to evaluate the anti-loosening performance of the oil pipe connection. In order to ensure the accuracy and reliability of the simulation results, the method includes the step of test verification of the test size inner shaft oil pipe. This step uses a high-precision random vibration test machine with specially designed fixtures to ensure the accurate execution of the test.

[0162] In a preferred embodiment, the test verification of the oil pipe in the test-size shaft specifically includes the following steps:

[0163] Step 61: Design of tooling structure and control system, where the tooling structure includes a base plate, an adjustment bracket, a sliding base, a torque sensor adapter and a bearing support, where the control system is a PLC control system, which is responsible for controlling the servo motor to accurately apply torque and vibration loads; the design of the tooling structure is crucial, as it ensures the stability and accuracy of the specimen during the test. The PLC control system is the core of the test. The system can automatically adjust according to preset parameters to ensure that the test conditions are consistent with the simulation analysis.

[0164] Step 62: Load application and monitoring: Apply the load conditions determined based on the simulation results to the oil pipe in the test size shaft; this includes alternating torque loading, application of air pressure, and vibration control. Use monitoring equipment such as torque sensors and vibration testers to record load data in real time during the test to ensure the accuracy and repeatability of the test.

[0165] Step 63: Anti-loosening performance evaluation: After completing the predetermined load cycle, the oil pipe in the test size shaft is inspected and evaluated, wherein the evaluation includes whether there is leakage at the connection to further verify the accuracy of the simulation model and method.

[0166] Example 2

[0167] The experimental verification stage of the present invention specifically includes the following steps:

[0168] 1. Test equipment and sample preparation: Use a 121-type short sample of the inner oil pipe of the shaft (test size sample) for the test. Prepare the necessary equipment, including a random vibration tester, a PLC servo motor control system, and an airtightness test bench.

[0169] 2. Tooling design and installation: Design the tooling structure according to the test requirements, including the base plate, adjustment bracket, sliding base, etc., to ensure the stability and accuracy of the test.

[0170] 3. Test process: Conduct the test according to the set parameters (test verification loading parameters), including air pressure, torque and vibration loading. Monitor the changes in key parameters during the test, such as torque and vibration frequency, as well as the response of the oil pipe.

[0171] 4. Data collection and analysis: Collect test data, including air pressure, torque, vibration frequency and amplitude, etc. By comparing simulation analysis results and test verification data, evaluate the anti-loosening performance of the oil pipe connection.

[0172] 5. Result evaluation: Comparison between simulation and test results: The simulation results of the actual size in-shaft oil pipe and the test size in-shaft oil pipe are compared with the test data to verify the accuracy of the simulation model and the effectiveness of the prediction.

[0173] 6. Performance evaluation: The reliability of the oil pipe design is evaluated based on the anti-loosening performance of the oil pipe joints observed in the test.

[0174] It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principles of the present invention, and do not constitute a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modifications that fall within the scope and boundaries of the appended claims, or the equivalent forms of such scope and boundaries.

Claims

1. A multi-objective optimization verification method for the anti-loosening fatigue life of an in-shaft oil pipe connection, characterized in that: The method comprises: Step 1: Establish a 3D geometric model of the oil pipe in the shaft with actual dimensions for real working conditions; Step 2: setting boundary condition loading parameters for the three-dimensional geometric model of the actual-size in-shaft oil pipe, wherein the boundary condition loading parameters reflect the actual working conditions of the actual in-shaft oil pipe; Step 3: Use the Dirlik method, Bendat method and boundary condition loading parameters to simulate the fatigue life of the oil pipe in the actual size shaft; Step 4: Establish a three-dimensional geometric model of the in-shaft oil pipe of the test size for test verification conditions; Step 5: using a non-dominated sorting genetic algorithm II to perform multi-objective optimization, specifically, continuously adjusting the loading parameters of the three-dimensional geometric model of the test-sized in-shaft oil pipe, using the Dirlik method and the Bendat method to perform fatigue life simulation on the test-sized in-shaft oil pipe, and when the fatigue life simulation results obtained by the Dirlik method and the Bendat method are substantially the same as the fatigue life simulation results obtained in step 3, determining the current loading parameters as the test verification loading parameters; Step 6: On the test equipment, use the test verification loading parameters to conduct fatigue life test verification on the test size inner shaft oil pipe, and use the test verification results as a reference for the fatigue life of the actual size inner shaft oil pipe under real working conditions.

2. The method according to claim 1, wherein: In step 1, the three-dimensional geometric model includes the diameter, length and wall thickness of the oil pipe. Establishing the three-dimensional geometric model also includes defining material properties, and the material properties include elastic modulus, density and Poisson's ratio.

3. The method according to claim 1, wherein: In step 2, setting boundary conditions specifically includes: power spectrum density (PSD) analysis, wherein the power spectrum density (PSD) analysis is used to simulate frequency-dependent energy distribution; modal reduction analysis for determining the modes of the structure and their corresponding modal masses; and Apply simulated air pressure, torque, and random vibration loads.

4. The method according to claim 1, wherein: In step 3, the fatigue life is estimated based on the cumulative distribution function of stress amplitude, which is mathematically expressed as: Where σ represents the stress amplitude and f(σ) is the distribution function of the stress amplitude.

5. The method according to claim 1, wherein: In step 5, the multi-objective optimization using non-dominated sorting genetic algorithm II specifically includes the following steps: Step 51: defining an optimization objective function, wherein the optimization objective function includes a first optimization objective function and a second optimization objective function, wherein the first optimization objective function is to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size using the Dirlik method; the second optimization objective function is to minimize the difference between the fatigue life simulation values ​​of the oil pipe in the shaft of the test size and the oil pipe in the shaft of the actual size using the Bendat method; Step 52: defining decision variables and constraints, wherein the decision variables include the amplitude and frequency of torque loading, air pressure level and vibration characteristics; Step 53: Using a non-dominated sorting genetic algorithm II (NSGA-II) to solve the multi-objective optimization problem; wherein the mathematical model of the non-dominated sorting genetic algorithm II (NSGA-II) is expressed as an optimization problem: min x {f1(x),f2(x)}, Among them, x is the decision variable vector, f1 and f2 are the first and second optimization objective functions.

6. The method according to claim 5, wherein: In step 53, the non-dominated sorting genetic algorithm II (NSGA-II) is used to solve the multi-objective optimization problem, which specifically includes the following steps: Step 53-1: Population initialization: randomly generating a group of initial solutions, wherein the group of initial solutions represents different design schemes; Step 53-2: Fitness evaluation: evaluating the fitness of each individual, where the fitness is the performance of the individual in meeting different optimization objectives; Step 53-3: Non-dominated sorting and crowding calculation: Sort by individual fitness and calculate crowding to maintain the diversity of solutions; Step 53-4: Selection, crossover and mutation operations: select excellent individuals according to non-dominated sorting and crowding, and generate new solutions through crossover and mutation operations; Step 53-5: Population replacement: Replace the individuals in the current population with the newly generated more optimized Pareto frontier solution and enter the next generation of iteration.

7. The method according to claim 6, wherein: The "substantially the same" in step 5 means that the calculated result of the objective function is ≤ one thousandth of the fatigue life simulation result in step 2, that is, when the above condition is met, the iteration in step 53-5 is terminated.

8. The method according to claim 1, wherein: In step 6, the test verification is specifically as follows: on the test equipment, the working environment of the in-shaft oil pipe of the test size is simulated, which is affected by random vibration, torque and air pressure, so as to evaluate the anti-loosening performance of the oil pipe connection.

9. The method according to claim 8, wherein: The test verification specifically includes the following steps: Step 61: designing a tooling structure and a control system, wherein the tooling structure includes a base plate, an adjustment bracket, a sliding base, a torque sensor adapter and a bearing support, wherein the control system is a PLC control system, and the PLC control system is responsible for controlling the servo motor to apply torque and vibration load; Step 62: Applying and monitoring the load: applying the test verification loading parameters determined in step 5 based on the simulation results to the oil pipe in the test size shaft; Step 63: Anti-loosening performance evaluation: After completing the predetermined load cycle, the oil pipe in the test size shaft is inspected and evaluated, wherein the evaluation includes whether there is leakage at the connection.

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