A multi-objective optimization method for determining hydrogen charging parameters of high-strength bolts based on finite element method

Abstract

The present invention discloses a method for determining hydrogen charging parameters of high-strength bolts based on multi-objective optimization of finite elements. The method comprises: step a: selecting a set of initial hydrogen charging parameters T0 and I0, and calculating the values ​​of objective functions f1(T0, I0) and f2(T0, I0); step b: randomly selecting a set of new hydrogen charging parameters T′ and I′ in the neighborhood of the current solution, and calculating the values ​​of objective functions f1(T′, I′) and f2(T′, I′); step c: if the value of the new solution on at least one objective function is better than the current solution, and the values ​​on all objective functions are not worse than the current solution, then T0 and I0 are updated to T′ and I′; otherwise, T0 and I0 remain unchanged; step d: if a preset termination condition is met, then the iteration is stopped and the current solutions T0 and I0 are output; otherwise, the process returns to step b and the iterative search is continued.

Description

Technical Field

[0001] The present invention relates to the technical field of metallurgy, and in particular to a method for determining hydrogen charging parameters of high-strength bolts based on multi-objective optimization of finite elements. Background Art

[0002] Despite the increasing popularity of high-strength bolts in marine environments, existing technologies for addressing hydrogen embrittlement in bolts have limitations. Due to the unique characteristics of the marine environment, such as direct contact with seawater and complex electrochemical reactions, high-strength bolts are susceptible to hydrogen absorption during use. This hydrogen absorption not only reduces the fatigue strength of the bolts but also accelerates the growth of fatigue cracks, severely impacting their performance and reliability.

[0003] The present invention targets three typical high-strength bolts: cylinder bolts (M42), blade root bolts (M56), and shaft flange bolts (M60). These bolts are typically installed with a specific tightening torque and employ various measures to enhance their sealing and corrosion resistance, such as sealant on the bolt end faces, sealing rings at the chamfers, and molybdenum disulfide powder treatment on the threads. While these treatments can alleviate hydrogen embrittlement to a certain extent, the risk of hydrogen-induced failure remains significant under the dual conditions of high-pressure oil environments (e.g., 0.3 MPa) and direct seawater contact.

[0004] Therefore, in view of the application background of high-strength bolts in marine environments, the present invention aims to propose an effective method for determining hydrogen charging parameters to improve the performance and safety of these critical fasteners. Summary of the Invention

[0005] To achieve the above object, the present invention provides a method for determining hydrogen charging parameters of high-strength bolts based on multi-objective optimization of finite element method, characterized in that the method comprises:

[0006] Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0);

[0007] Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′);

[0008] Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged;

[0009] Step d: If the preset termination condition is met, stop the iteration and output the current solutions T0 and I0; otherwise, return to step b and continue the iterative search.

[0010] In a preferred embodiment, the preset termination condition includes that the number of iterations reaches a preset maximum value, or the value of the objective function does not improve significantly in a certain number of iterations.

[0011] In a preferred embodiment, f1(T0, I0) is a hydrogen content concentration target function, where f1(T, I) = -C(T, I);

[0012] Wherein, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I).

[0013] In a preferred embodiment, the hydrogen content concentration is determined by the following formula:

[0014]

[0015] Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time;

[0016] Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula:

[0017]

[0018] Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model.

[0019] In a preferred embodiment, the hydrogen binding energy is determined by the following formula:

[0020]

[0021] Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ij is the expansion tensor of each hydrogen atom, σ ij is the total stress tensor;

[0022] The binding energy can be calculated using a stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t, and the target hydrogen concentration C0, the binding energy W int It can be calculated by the following formula:

[0023] W int =-σ(C-C0)VH

[0024] Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

[0025] The present invention provides a multi-objective optimization system for determining hydrogen charging parameters of high-strength bolts based on finite elements, characterized in that the system includes a memory and a processor, wherein the memory stores processor-executable instructions, and when executed by the processor, the instructions cause the processor to perform the following operations:

[0026] Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0);

[0027] Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′);

[0028] Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged;

[0029] Step d: If the preset termination condition is met, stop the iteration and output the current solutions T0 and I0; otherwise, return to step b and continue the iterative search.

[0030] In the system provided by the present invention, the preset termination conditions include the number of iterations reaching a preset maximum value, or the value of the objective function not being significantly improved in a certain number of iterations.

[0031] The system provided by the present invention, wherein f1(T0, I0) is a hydrogen content concentration target function, wherein f1(T, I) = -C(T, I);

[0032] Wherein, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I).

[0033] The system provided by the present invention, wherein the hydrogen content concentration is determined by the following formula:

[0034]

[0035] Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time;

[0036] Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula:

[0037]

[0038] Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model.

[0039] The present invention provides a system wherein the hydrogen binding energy is determined by the following formula:

[0040]

[0041] Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ij is the expansion tensor of each hydrogen atom, σ ij is the total stress tensor;

[0042] The binding energy can be calculated by the stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t and the target hydrogen content concentration C0, the binding energy W int It can be calculated by the following formula:

[0043] W int =-σ(C-C0)V H

[0044] Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

[0045] Compared with the prior art, the present invention has the following advantages: the method of this patent not only improves the performance and safety of high-strength bolts, but also has good practicality and operability, and is suitable for actual industrial production environments, especially in the fields of shipbuilding and marine engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of a method according to an embodiment of the present invention.

[0047] Figure 2 It is a schematic diagram of the distribution of the electrolyte current density vector at the bolt interface after the optimization of the hydrogen charging process.

[0048] Figure 3 It is a schematic diagram of the total interfacial current density on the bolt surface after the optimization of the hydrogen charging process. DETAILED DESCRIPTION

[0049] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific embodiments.

[0050] In this method, a 3D model of a high-strength bolt is first created using CAD software. This model is then imported into finite element analysis software for meshing. In SolidWorks, the bolt's geometry (including diameter, length, thread shape, and dimensions) and material physical properties (such as density, elastic modulus, and Poisson's ratio) are first defined. These parameters are crucial for subsequent finite element analysis.

[0051] After the model is created, meshing is performed, a key step in finite element analysis. Meshing divides the 3D model into multiple small elements, each representing an independent physical entity whose internal physical processes are described by differential equations. In SolidWorks, automatic meshing tools are used to generate a high-quality mesh and define the boundary and initial conditions of the bolts, including fixed boundaries, hydrogen charging boundaries (i.e., hydrogen concentration limits), initial temperature, and stress state.

[0052] After the finite element model is established and meshed, the model is solved using COMSOL software. COMSOL is a multi-physics simulation software suitable for handling complex physics and engineering problems. First, the bolt model and mesh created in SolidWorks are imported into COMSOL, and the physics field and solver are set. In the present invention, the diffusion physics field is set to simulate the hydrogen charging process of the bolt, where the diffusion coefficient and concentration of hydrogen are key parameters.

[0053] COMSOL is used to perform iterative calculations until a solution that satisfies all equations and boundary conditions is found. After the solution is completed, the post-processing tool of COMSOL is used to analyze the results. In order to achieve subsequent multi-objective optimization, the COMSOL model and results are exported to MATLAB. Using the LiveLink function of COMSOL Multiphysics and MATLAB, the model can be easily modified and the data processed in MATLAB to optimize the hydrogen charging parameters. The above-mentioned software and the operating methods of the software are common knowledge in the field and will not be described in detail in the present invention.

[0054] Example 1

[0055] Figure 1 1 is a flow chart of a method according to an embodiment of the present invention. As shown in the figure, the method of the present invention includes the following steps:

[0056] Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0);

[0057] Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′);

[0058] A new set of hydrogen charging parameters P' and T' is randomly selected in the neighborhood of the current solution. These parameters are within the set difference limit with the parameters P and T of the current solution and will not significantly change the predicted values ​​of hydrogen content concentration and hydrogen binding energy. Calculate the objective function F under the new parameters H (P′,T′) and F E The value of (P′,T′).

[0059] Among them, P′ and T′ represent the newly selected current density and hydrogen charging time parameters, respectively, and F H and F E represent the objective functions of hydrogen content concentration and hydrogen binding energy, respectively.

[0060] Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged;

[0061] Step d: If the preset termination condition is met, stop the iteration and output the current solutions T0 and I0; otherwise, return to step b and continue the iterative search.

[0062] In a preferred embodiment, the preset termination condition includes that the number of iterations reaches a preset maximum value, or the value of the objective function does not improve significantly in a certain number of iterations.

[0063] In a preferred embodiment, f1(T0, I0) is a hydrogen content concentration target function, where f1(T, I) = -C(T, I);

[0064] Wherein, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I).

[0065] In a preferred embodiment, the hydrogen content concentration is determined by the following formula:

[0066]

[0067] Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time;

[0068] Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula:

[0069]

[0070] Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model.

[0071] In a preferred embodiment, the hydrogen binding energy is determined by the following formula:

[0072]

[0073] Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ij is the expansion tensor of each hydrogen atom, σ ij is the total stress tensor;

[0074] The binding energy can be calculated using a stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t, and the target hydrogen concentration C0, the binding energy W int It can be calculated by the following formula:

[0075] W int =-σ(C-C0)V H

[0076] Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

[0077] Figure 2 The distribution of electrolyte current density vector at the bolt interface after the optimized hydrogen charging process is depicted under different hydrogen charging time and current density conditions.

[0078] Figure 3 The total interfacial current density on the bolt surface after the optimized hydrogen charging process is completed is depicted. The chromatogram scale in the figure indicates the current density in different areas.

[0079] Example 2

[0080] The present invention provides a multi-objective optimization system for determining hydrogen charging parameters of high-strength bolts based on finite elements, characterized in that the system includes a memory and a processor, wherein the memory stores processor-executable instructions, and when executed by the processor, the instructions cause the processor to perform the following operations:

[0081] Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0);

[0082] Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′);

[0083] Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged;

[0084] Step d: If the preset termination condition is met, stop the iteration and output the current solutions T0 and I0; otherwise, return to step b and continue the iterative search.

[0085] In the system provided by the present invention, the preset termination conditions include the number of iterations reaching a preset maximum value, or the value of the objective function not being significantly improved in a certain number of iterations.

[0086] The system provided by the present invention, wherein f1(T0, I0) is a hydrogen content concentration target function, wherein f1(T, I) = -C(T, I);

[0087] Wherein, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I).

[0088] The system provided by the present invention, wherein the hydrogen content concentration is determined by the following formula:

[0089]

[0090] Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time;

[0091] Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula:

[0092]

[0093] Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model.

[0094] The present invention provides a system wherein the hydrogen binding energy is determined by the following formula:

[0095]

[0096] Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ijis the expansion tensor of each hydrogen atom, σ ij is the total stress tensor;

[0097] The binding energy can be calculated by the stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t and the target hydrogen content concentration C0, the binding energy W int It can be calculated by the following formula:

[0098] W int =-σ(C-C0)V H

[0099] Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

[0100] Example 3

[0101] The NSGA-II algorithm is used. This algorithm is an effective multi-objective optimization tool, especially suitable for dealing with problems such as hydrogen charging parameter optimization with multiple conflicting objectives. The following is a detailed description of the NSGA-II algorithm in this application scenario:

[0102] (a) Algorithm Overview

[0103] The NSGA-II algorithm effectively searches the solution space for multi-objective optimization problems by simulating natural selection and genetic mechanisms. Its core features are fast non-dominated sorting and crowding distance calculation, which help generate diverse and high-quality solution sets.

[0104] (b) Encoding method

[0105] Real encoding: In this application, the charging parameters (e.g., charging time and current density) are encoded as real number vectors as input to the algorithm.

[0106] (c) Fitness function

[0107] -Define: Define fitness functions for hydrogen concentration and binding energy

[0108]

[0109] Among them, C H represents the hydrogen concentration, a and b are coefficients for adjusting the shape of the function, and p is a power exponent used to adjust the degree of nonlinearity of the function.

[0110] -Fitness function f2 of binding energy: Considering the relationship between binding energy and hydrogen charging parameters, it can be designed as follows:

[0111]

[0112] Among them, Eb represents the binding energy, c and d are coefficients that adjust the shape of the function, which is in exponential form to emphasize the importance of low binding energy, reflecting the trade-off between the optimization objectives, namely minimizing the binding energy while maximizing the hydrogen content concentration.

[0113] (d) Population initialization

[0114] -Encoding method: Each individual consists of two parameters t (charging time) and I (current density), both of which are randomly selected within a given range.

[0115] - Population size: N, usually 50 to 100 individuals.

[0116] (e) Genetic manipulation

[0117] -Selection: Use the tournament selection method to select the best individual from k random individuals, denoted as S(P,k).

[0118] -Crossover: Single-point crossover, randomly select the crossover point c, denoted as C(P x ,P y ,c).

[0119] - Mutation: Gaussian mutation, add Gaussian noise to individual parameters, denoted as M(P i ,σ).

[0120] (f) Evolutionary process

[0121] - Generation: Each generation produces new individuals Q through selection, crossover and mutation.

[0122] -Update: Combine the parent P and the child Q, and use non-dominated sorting and crowding calculation to form a new population P new .

[0123] (g) Termination conditions

[0124] - Criteria: The number of iterations M or the fitness change Δf is less than the threshold ò.

[0125] Application Calculation Examples

[0126] The following is a specific computational example of using the NSGA-II algorithm to effectively search the solution space of a multi-objective optimization problem by simulating natural selection and genetic mechanisms. The computational example includes the following steps:

[0127] 1. Parameter setting and model initialization

[0128] Population size: 100 individuals.

[0129] Maximum number of iterations: 50 generations.

[0130] Current density range: 0.01 to 0.1 A / mm2 .

[0131] Hydrogen charging time range: 1 to 10 hours.

[0132] Objective function:

[0133] -F1(I,t): Hydrogen content concentration (unit: \%).

[0134] -F2(I,t): hydrogen binding energy (unit: kJ / mol). The specific form of the objective function has been given in Example 1 and will not be repeated here.

[0135] 2. Initial population generation and evaluation

[0136] A random strategy is used to generate the initial population, and the current density and hydrogen charging time of each individual are randomly determined within a preset range.

[0137] 3. Calculation of objective function

[0138] For each individual, the hydrogen content concentration and hydrogen binding energy are calculated based on the current density and hydrogen charging time. The formula for calculating the hydrogen content concentration and hydrogen binding energy can be found in Example 1.

[0139] 4. Non-dominated sorting and congestion calculation

[0140] A non-dominated sorting is performed on the initial population, each individual is ranked according to its performance on the objective function, and the crowding degree is calculated.

[0141] 5. Genetic manipulation

[0142] Implement single-point crossover and Gaussian mutation operations to generate new population individuals.

[0143] 6. Iteration process and intermediate results analysis

[0144] Representative data during the iteration process:

[0145]

[0146] During the iteration process, individuals showed obvious optimization trends in hydrogen content concentration and hydrogen binding energy.

[0147] 7. Final result analysis and optimization

[0148] Optimization results: After 50 generations of iteration, a series of Pareto optimal solutions were obtained, such as:

[0149] Solution A: Current density 0.06A / mm 2 , hydrogen charging time is 8 hours, hydrogen content concentration is 0.018%, and hydrogen binding energy is 65kJ / mol.

[0150] Solution B: Current density 0.08A / mm 2 , hydrogen charging time is 6 hours, hydrogen content concentration is 0.022%, and hydrogen binding energy is 58kJ / mol.

[0151] According to actual application requirements, if you attach importance to reducing the hydrogen concentration, choose solution A; if you attach importance to increasing the hydrogen binding energy, choose solution B.

[0152] The above calculation example demonstrates the effectiveness of the NSGA-II algorithm in optimizing the hydrogen charging parameters of high-strength bolts. This algorithm not only improves the performance and safety of the bolts, but also provides a scientific basis for parameter selection for the practical application of high-strength bolts in marine environments.

[0153] Example 4

[0154] The present invention also provides the following method:

[0155] Step 1: Preheat the hydrogen filling equipment and perform system inspection to confirm that the equipment is performing normally;

[0156] Step 2: Select corresponding hydrogen charging parameters according to the preset hydrogen charging level, wherein the hydrogen charging parameters include hydrogen charging time and current density;

[0157] Step 3: Start the hydrogen charging equipment and conduct the hydrogen charging experiment according to the set parameters; in the process of hydrogen charging, monitor the status of the hydrogen charging equipment in real time to ensure that all parameters are stable during the experiment. After the experiment is completed, turn off the equipment and remove the high-strength bolts from the hydrogen charging equipment.

[0158] Step 4: Based on the test results of hydrogen charging, record the hydrogen content and analyze the experimental data;

[0159] Step 5: Based on the experimental results, if the difference between the actual hydrogen charge amount and the expected hydrogen charge amount is within 5% of the actual hydrogen charge concentration, then record the hydrogen charge test parameters at this time as the final actual hydrogen charge test parameters. If the difference between the actual hydrogen charge amount and the expected hydrogen charge amount is greater than 5% of the actual hydrogen charge concentration, then adjust the hydrogen charge parameters to perform parameter fine-tuning tests and continue to optimize the hydrogen charge parameters.

[0160] Step 6: Calculate the difference between the actual hydrogen charging amount and the expected hydrogen charging amount, and use the proportionality principle formula to calculate the new hydrogen charging time and current density based on the calculated difference;

[0161] Step 7: Conduct a new hydrogen charging experiment using a new hydrogen charging time and current density. After the experiment is completed, measure and record the new actual hydrogen charging amount.

[0162] Step 8: Calculate the difference between the new actual hydrogen charge and the expected hydrogen charge. If the difference is within 5% of the actual hydrogen charge concentration, apply the new hydrogen charge time and current density to subsequent experiments. If the difference is greater than 5% of the actual hydrogen charge concentration, return to step 6 and recalculate the difference and adjust the parameters.

[0163] In one embodiment, the high-strength bolt hydrogen charging test equipment of the present invention should have precise time and current control functions and should have highly stable and reliable performance. The uses of different equipment are as follows:

[0164] 1) Hydrogen charging equipment: DC regulated power supply, which can accurately control the hydrogen charging time and current density.

[0165] 2) Hydrogen source: electrolyte, used to provide high-purity hydrogen.

[0166] 3) Measuring device: Oxygen, nitrogen and hydrogen analyzer, used to measure the hydrogen content results of the hydrogen charging test.

[0167] The test equipment includes: a DC regulated power supply, an oxygen, nitrogen, and hydrogen analyzer, a beaker, several conductive wires, several graphite rods, a 0.1 mol / L NaOH electrolyte, and a 0.1 g / L sodium thiocyanate solution. The hydrogen charging equipment is shown in the figure above and includes a DC regulated power supply, conductive wires, a beaker, and electrolytes (0.1 mol / L NaOH and 0.1 g / L sodium thiocyanate).

[0168] The main parameters of the test equipment of the present invention are as follows:

[0169] (1) DC regulated power supply

[0170] Main performance parameters of DC regulated power supply:

[0171] Frequency: 50Hz Output current: 0~100A

[0172] Output voltage: 0~60.0V

[0173] Output power 0~6000W

[0174] 0-100%Δ output voltage stability: <0.2%

[0175] Related certifications: EMC & LVD.

[0176] (2) Oxygen, nitrogen and hydrogen analyzer

[0177] Model: Oxygen, nitrogen and hydrogen analyzer

[0178] Working principle: Pulse melting reduction - infrared absorption, thermal conductivity method

[0179] Application range: oxygen, nitrogen and hydrogen content in steel, cast iron, alloys, copper, zirconium, titanium, ceramics and other inorganic substances

[0180] Sample mass: ≤1000 "mg" (generally)

[0181] Sensitivity:

[0182] Oxygen: 0.1 μg / g

[0183] Nitrogen: 0.1 μg / g

[0184] Hydrogen: 0.01 μg / g

[0185] Accuracy:

[0186] Oxygen: 2μg / g (low content) or 2% (high content)

[0187] Nitrogen: 2μg / g (low content) or 2% (high content)

[0188] Hydrogen: 0.2μg / g (low content) or 2% (high content)

[0189] Analysis scope:

[0190] Oxygen: 0.0002% to 0.01% (low oxygen, 1g sample), to 2% (high oxygen, 1g sample)

[0191] Nitrogen: 0.0002% to 0.05% (low nitrogen, 1g sample), to 2% (high nitrogen, 1g sample)

[0192] Hydrogen: 0.00001% to 0.1%

[0193] Analysis cycle: ~3min

[0194] Sample: Solid sample or powder sample smaller than 5mm*8mm

[0195] Carrier gas pressure: High-purity helium (high-purity argon or high-purity nitrogen) pressure reducing valve adjusted to ~0.3MPa, instrument pressure stabilized to 0.15MPa, pressure gauge displayed 0.15MPa

[0196] Power gas pressure: The nitrogen pressure reducing valve is adjusted to ~0.3MPa, and the instrument pressure is stabilized to ~0.25Mpa.

[0197] In one embodiment, the specific test method of the present invention is as follows:

[0198] 1) Electrochemical hydrogen charging

[0199] The specific test steps for electrochemical hydrogen charging are as follows:

[0200] (a) Material preparation: Clean the bolts to remove grease and impurities on the surface.

[0201] (b) Electrochemical hydrogen charging setup: In a 0.1 mol / L NaOH solution, use the bolt as the working electrode. Set the current density to the value obtained by multi-objective optimization. Charge for a predetermined time to achieve the desired hydrogen charge (1 ppm, 4 ppm, 8 ppm, 12 ppm). The hydrogen charging time needs to be determined through preliminary experiments.

[0202] (c) Post-hydrogen charging treatment: After hydrogen charging is completed, the bolts should be immediately removed from the electrolyte and cleaned. Post-treatment should be performed under appropriate conditions, such as low-temperature baking, to reduce hydrogen emission.

[0203] (d) Fine-tuning hydrogen charging parameters: If the measured hydrogen content deviates significantly from the expected hydrogen charging amount, the current density and charging time during the hydrogen charging process need to be fine-tuned to achieve the desired hydrogen charging amount.

[0204] 2) Hydrogen content determination

[0205] The hydrogen content in the bolt material needs to be determined using the melting-thermal conductivity method. The specific steps are as follows:

[0206] (a) Sample preparation: Ensure that the bolt sample is clean after hydrogen filling to avoid external contamination affecting the measurement results.

[0207] (b) Melting process: Place the sample under a power of 50W to 100W and keep it in a molten state for 3 minutes. During this process, hydrogen in the sample will be released, preparing for the subsequent hydrogen content determination.

[0208] (c) Hydrogen Content Determination: According to GB / T 223.82-2018, hydrogen content determination must be performed immediately under inert gas after sample melting to prevent atmospheric hydrogen from affecting the measurement results. The hydrogen content in the sample is measured using the melting-thermal conductivity method, and the determination process must strictly follow relevant regulations and procedures.

[0209] (d) Data Recording: Record the hydrogen content measurement results in μg / g. All experimental data and results must be properly stored for subsequent analysis and reporting.

[0210] Example 5

[0211] The difference between the actual hydrogen charge amount and the expected hydrogen charge amount of the present invention is calculated according to the following formula:

[0212] ΔP=|P A -P E |

[0213] Among them, ΔP is the difference between the actual hydrogen charging amount and the expected hydrogen charging amount, P Ais the actual hydrogen charge, P E is the expected hydrogen charge;

[0214] Calculate the new hydrogen charging time according to the following formula:

[0215] T N =T O *(1+ΔP / P E )

[0216] Among them, T N is the new hydrogen filling time, T O is the original hydrogen charging time;

[0217] Calculate the new current density according to the following formula:

[0218] I N =I O *(1+ΔP / P E )

[0219] Among them, I N is the new current density, I O is the original current density.

[0220] Example 6

[0221] The hydrogen charging time and current density in step 2 of the present invention (i.e., the initial values ​​of the hydrogen charging time and current density) are determined by the following method:

[0222] Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0);

[0223] Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′);

[0224] Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged;

[0225] Step d: If the preset termination condition is met, the iteration is stopped and the current solution T0 and I0 are output; otherwise, the process returns to step b and the iterative search continues. After determining the optimal solution hydrogen charging time and current density based on the iterative method, the expected hydrogen charging amount P_expected can be calculated based on the optimal solution hydrogen charging time and current density. In addition, in the present invention, the range of values ​​for hydrogen charging time and current density is specified as follows:

[0226] Hydrogen filling time: T∈[T min ,Tmax ]

[0227] Current density: I∈[I min ,I max ]

[0228] Among them, T min ,T max ,I min and I max These are the minimum and maximum values ​​of these parameters. Refer to relevant literature and they can be set to 0h, 120h, 0mA / cm 2 , 100mA / cm 2 .

[0229] In a preferred embodiment, the preset termination condition includes the number of iterations reaching a preset maximum value, or the value of the objective function not significantly improving in a certain number of iterations. In a specific example, the lack of significant improvement in a certain number of iterations can be defined as the improvement in the value of the objective function being less than 1%, 2%, 3%, 4%, 5%, or other suitable percentage values ​​in 5, 10, 15, 20, or more iterations.

[0230] It should be understood that the above-described specific embodiments of the present invention are merely illustrative or illustrative of the principles of the present invention and do not constitute limitations 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 within the scope of protection of the present invention. In addition, the appended claims are intended to cover all variations and modifications that fall within the scope and metes and bounds of the appended claims, or equivalents thereof.

Claims

1. A multi-objective optimization method for determining hydrogen charging parameters of high-strength bolts based on finite element analysis, characterized in that: The method comprises: Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0); Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′); Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged; Step d: If the preset termination condition is met, stop the iteration and output the current solutions T0 and I0; otherwise, return to step b and continue the iterative search; Wherein, f1(T0,I0) is the hydrogen content concentration objective function, where f1(T,I)=-C(T,I); Where, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I); The hydrogen content concentration is determined by the following formula: Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time; Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula: Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model; The hydrogen binding energy is determined by the following formula: Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ij is the expansion tensor of each hydrogen atom, σ ij is the total stress tensor; The binding energy is calculated by the stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t and the target hydrogen content concentration C0, the binding energy W int Calculated by the following formula: W int =-σ(C-C0)V H Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

2. The method according to claim 1, wherein The preset termination condition includes that the number of iterations reaches a preset maximum value, or the value of the objective function does not improve significantly in a certain number of iterations.

3. A multi-objective optimization system for determining hydrogen charging parameters of high-strength bolts based on finite element, characterized in that: The system includes a memory and a processor, wherein the memory stores processor-executable instructions. When executed by the processor, the instructions cause the processor to perform the following operations: Step a: Select a set of initial hydrogen charging parameters T0 and I0, and calculate the values ​​of objective functions f1(T0, I0) and f2(T0, I0); Step b: Randomly select a new set of charging parameters T′ and I′ in the neighborhood of the current solution and calculate the values ​​of the objective functions f1(T′, I′) and f2(T′, I′); Step c: If the new solution is better than the current solution in at least one objective function and is not worse than the current solution in all objective functions, then update T0 and I0 to T′ and I′; otherwise, T0 and I0 remain unchanged; Step d: If the preset termination condition is met, stop the iteration and output the current solution T0 and I0; otherwise , return to step b and continue iterative search; Wherein, f1(T0,I0) is the hydrogen content concentration objective function, where f1(T,I)=-C(T,I); Where, f2(T0,I0) is the hydrogen binding energy objective function, where f2(T,I)=-B(T,I); The hydrogen content concentration is determined by the following formula: Among them, I t is the current value at a certain time t, I ∞ is the current value when hydrogen permeation reaches steady state, L is the thickness of the sample, D is the diffusion coefficient of hydrogen in steel, and t is the cathode hydrogen charging time; Given the current density I and the hydrogen charging time t, the hydrogen concentration C is calculated by the following formula: Among them, I t is the current value at a certain time t calculated by the hydrogen permeation model; The hydrogen binding energy is determined by the following formula: Where μ is the chemical potential, μ0 is the chemical potential at the initial state, equivalent to C0, k is the Boltzmann constant, T is the temperature, and H ij is the expansion tensor of each hydrogen atom, σ ij is the total stress tensor; The binding energy is calculated by the stress-induced hydrogen diffusion model. Specifically, given the current density I, the hydrogen charging time t and the target hydrogen content concentration C0, the binding energy W int Calculated by the following formula: W int =-σ(C-C0)V H Where C is the hydrogen concentration calculated by the hydrogen permeation model, σ is the total stress tensor, and V H is the molar volume of hydrogen.

4. The system according to claim 3, wherein: The preset termination condition includes that the number of iterations reaches a preset maximum value, or the value of the objective function does not improve significantly in a certain number of iterations.

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