Topological optimization design method for grillwork spring

Abstract

A topological optimization design method for a grillage spring relates to the technical field of grillage spring design, and comprises the following steps: S1, creating a geometric model of the grillage spring through parametric modeling; s2, on the basis of the geometric model, constructing a numerical simulation model to simulate the stress state of the grillwork spring under the full-life working condition, and performing stress calculation analysis to obtain the stress peak value of the spring and the stress sensitive area of the spring; s3, taking reduction of the stress peak value and the stress sensitive area of the spring as an optimization target, and carrying out structural topological optimization on the geometric model; s4, carrying out stress optimization evaluation on the novel spring structure obtained after topological optimization, and if an evaluation result does not meet requirements, returning to S1 or S2 to carry out iterative optimization until an optimization scheme meeting the requirements is obtained; the method breaks through the limitation that a traditional design method depends on empirical type selection, and the obtained spring optimized structure can effectively reduce the risk of stress corrosion cracking.

Description

Technical Field

[0001] This invention relates to the field of grid spring design technology, and more specifically to a grid spring topology optimization design method. Background Technology

[0002] As one of the most critical functional structural components of the fuel assembly, the positioning grid consists of a clamping structure made up of rigid protrusions stamped from the grid strip and springs. The springs are fixed to the inner strip by spot welding at both ends. Within each grid cell, rigid protrusions and springs are arranged in opposite directions. When a fuel rod is inserted into a grid cell, the spring is compressed, and simultaneously, the fuel rod is pressed against the opposite rigid protrusion, achieving clamping and positioning. For example, the positioning grid clamping structure of the French AFA3G is as follows... Figure 1 As shown, the fuel rod is positioned at 6 contact points within a single cell. This clamping structure has several advantages: the high stiffness of the convex protrusions provides better fuel rod positioning stiffness; the low stiffness of the springs provides lower fuel rod clamping stiffness to reduce clamping force fluctuations; and the separate upper and lower convex protrusions provide higher cell torsional stiffness to resist fuel rod vibration.

[0003] However, because fuel assemblies are subjected to high temperatures, high pressures, radiation, and complex aquatic environments for extended periods, the grid clamping springs are required to maintain their clamping effect on the fuel rods at all times during operation. Therefore, the spring structure is constantly under significant deformation and high internal stress. This condition easily leads to stress corrosion cracking (SCC) in the springs, affecting the positioning accuracy and structural stability of the fuel assemblies, and consequently impacting the safety of nuclear reactor operation. Currently, SCC fractures of grid springs have been observed in operating units both domestically and internationally. Therefore, reducing the high stress sensitivity of grid springs and improving the structure's resistance to SCC are important trends in current grid spring design.

[0004] Stress corrosion cracking (SCC) in lattice springs is primarily influenced by material properties, water chemistry, and stress factors. Under constant material and stress environment conditions, optimizing the spring's structural design to reduce stress concentration and minimize stress-sensitive areas is an effective way to reduce SCC risk. Low-stress optimization design of clamping springs faces technical challenges such as limited structural space, compatibility with existing structural systems, and the contradiction between clamping function and low-stress conditions. Existing lattice spring design processes often employ empirical iterative methods, i.e., local optimization based on existing mature structures. This results in the final design's stress distribution and magnitude being similar to the original structure, making it difficult to fundamentally improve the stress state.

[0005] Chinese patent CN117556672A discloses an efficient topology optimization method for minimizing structural stress in intelligent manufacturing. This method focuses on minimizing the peak stress of spring structures, constructs a P-norm function to improve accuracy, and emphasizes the stability of the topology optimization process. However, the analysis direction is relatively singular, and it cannot effectively avoid the risk of stress corrosion cracking, resulting in hidden dangers in the optimization results.

[0006] Therefore, we propose an optimization design method for obtaining low-stress spring structures. Summary of the Invention

[0007] The purpose of this invention is to provide a topology optimization design method for lattice springs. This method can overcome the limitations of traditional design methods that rely on experience-based selection, and the resulting optimized spring structure can effectively reduce the risk of stress corrosion cracking.

[0008] This invention is achieved through the following technical solution: A topology optimization design method for lattice springs includes the following steps: S1: Create the geometric model of the lattice spring through parametric modeling; S2: Based on the geometric model, a numerical simulation model is constructed to simulate the stress state of the lattice spring under full-life working conditions, and stress calculation and analysis are performed to obtain the peak stress of the spring and the area of ​​the stress-sensitive region of the spring. S3: To optimize the geometric model by reducing the peak stress of the spring and the area of ​​the stress-sensitive region; S4: Perform stress optimization evaluation on the new spring structure obtained after topology optimization. If the evaluation result does not meet the requirements, return to S1 or S2 for iterative optimization until an optimized solution that meets the requirements is obtained.

[0009] Furthermore, in S1, the objects of parametric modeling include parameters such as the length, width, height, and chord length of the lattice spring, and the correlation between the various dimensional parameters can be established based on geometric constraints.

[0010] Furthermore, in S2, the input parameters of the simulation model include operating temperature, neutron flux, coolant environmental parameters, grid structure geometric constraints, and changes in the physical properties of the spring material caused by irradiation relaxation.

[0011] Furthermore, the changes in physical properties include the material's yield strength. Neutron flux The changes are as follows:

[0012] In the formula, The initial yield strength of the material. This represents the irradiation hardening coefficient.

[0013] Furthermore, in S2, a numerical simulation model is constructed using the finite element analysis method, and the geometric features of the lattice spring are discretized into shell elements, beam elements, or solid elements.

[0014] Furthermore, in S2, the region where the stress value exceeds a certain proportion of the yield strength of the spring material is defined as the stress-sensitive region.

[0015] Furthermore, the certain ratio is set to 0.8 times.

[0016] Furthermore, in S3, the goal of topology optimization is to reduce the peak stress and the area of ​​the stress-sensitive region within a specified optimization area while maintaining or optimizing the clamping force, and the clamping force is obtained by extracting the contact reaction force between the spring and the fuel rod in the simulation model.

[0017] Furthermore, the evaluation results in S4 require that the peak stress of the optimized spring and the area of ​​the stress-sensitive region of the spring both decrease; if the evaluation fails, the iteration is repeated by modifying the geometric model parameters of S1 or the stress calculation and analysis conditions of S2.

[0018] Furthermore, the parameters of the initial geometric model are provided by the AFA 3G lattice spring.

[0019] The technical solution of the present invention has at least the following advantages and beneficial effects: This invention discloses a topology optimization design method for lattice springs. By establishing a parametric model and a finite element simulation model that includes the entire life cycle operating conditions, a design process for lattice springs based on simulation data and optimization algorithms is proposed, avoiding the dilemma in traditional design where it is difficult to make breakthrough improvements in stress state due to the limitations of the initial structure.

[0020] In addition, by optimizing the topology, the stress peak and stress-sensitive area of ​​the spring structure are actively sought and reduced, which reduces the risk of SCC from the source. Furthermore, by quantitatively controlling and optimizing the stress-sensitive area, the prevention of SCC is more targeted, thereby greatly improving the safety and reliability of fuel assemblies in the reactor.

[0021] Furthermore, by setting a mathematical optimization model with the explicit objectives of reducing peak stress and the area of ​​stress-sensitive regions, it is possible to simultaneously consider clamping force constraints and volume constraints, ensuring the unity of optimization results in terms of performance, safety, and economy, which is more convincing and superior than the empirical iteration method.

[0022] Furthermore, this invention forms a closed-loop iterative process of "parametric modeling - simulation analysis - topology optimization - comprehensive evaluation"; once the initial model is established, new schemes can be quickly generated and automatically evaluated by adjusting parameters, which greatly shortens the design cycle and reduces development costs; this method is based on parametric driving and does not depend on a specific spring configuration, so it can be flexibly applied to the structural optimization of different types of lattice springs, and has good versatility and promotion value. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a traditional grid spring structure according to the present invention; Figure 2 This is a schematic diagram of a method flow of the present invention; Figure 3 This is a schematic diagram of the electronic device in this invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0025] Example 1 like Figure 2 The illustrated lattice spring topology optimization design method includes the following steps: S1: Create the geometric model of the lattice spring through parametric modeling; Specifically, the objects modeled parametrically include the length of the lattice springs. ,width ,high chord length Dimensional parameters, and the ability to establish relationships between these parameters based on geometric constraints; Specifically, the relationships between the various dimensional parameters include: derived from the chord length... and height The radius of curvature of the spring arch profile can be determined. :

[0026] Relationship between the geometry of the spring end and its total length:

[0027] In the formula, The length of the straight or specially shaped end segment of the spring; The relationship between the end width and the main body width must meet the following requirements. ,in, The width of the spring's end; In addition, the parameters of the initial geometric model were provided by AFA 3G lattice springs.

[0028] S2: Based on the geometric model, a numerical simulation model is constructed to simulate the stress state of the lattice spring under full-life working conditions, and stress calculation and analysis are performed to obtain the peak stress of the spring and the area of ​​the stress-sensitive region of the spring. Among them, the input parameters of the simulation model Including operating temperature neutron fluence The changes in coolant environmental parameters, grid structure geometric constraints, and spring material properties caused by radiation relaxation; In addition, changes in physical properties include the material's yield strength. Neutron flux The changes, that is, the manifestation of material properties, are specifically as follows:

[0029] In the formula, The initial yield strength of the material. This is the irradiation hardening coefficient; Temperature changes will induce thermal stress. When there is a temperature difference between the spring and the fuel rod or the grid strip, or when the temperature is uneven, thermal stress will be generated. This stress needs to be superimposed on the mechanical stress. Furthermore, temperature directly affects the properties of materials, such as elastic modulus and coefficient of thermal expansion. The flow of coolant will generate flow-induced vibration loads on the spring. This dynamic load is the basis of fatigue analysis and an important supplement to the steady-state stress field. The high-pressure environment itself is an external load, which will affect the contact state and stress. The geometric constraints of the grid structure determine the boundary conditions of the spring. Since the spring is welded to the grid strip, the constraint conditions of these connection parts directly affect the deformation mode and stress distribution of the spring. At the same time, the grid space restricts the maximum possible displacement of the spring during the compression deformation process, preventing it from interfering with adjacent components.

[0030] The stress calculation and analysis are performed by solving the finite element equilibrium equations, specifically:

[0031] In the formula, Here is the stiffness matrix. It is a displacement vector. For load vectors; The stiffness matrix is ​​determined by the input parameters of the simulation model. The displacement vector is obtained by solving the finite element equilibrium equations, and then the strain matrix is ​​obtained by solving the geometric equations (strain-displacement relationship). Finally, the stress field of the spring is calculated by the physical equations (constitutive relations), thereby determining the peak stress of the spring. .

[0032] Area of ​​stress-sensitive region For the region where the stress on the spring is higher than 0.8 times the yield strength of the spring material, the following integral formula is used for calculation:

[0033] In the formula, It is a step function, meaning that the integral is 1 when it is greater than 0, and 0 otherwise; The equivalent stress is calculated from the stress field. For the spring optimization domain, This is the threshold coefficient, which is 0.8.

[0034] In addition, stress calculation and analysis require enabling nonlinear calculation functionality. The solver will employ an iterative algorithm, updating the stiffness matrix and contact conditions based on the current deformation, stress, and contact state at each incremental load step, progressively solving until an equilibrium state satisfying the convergence criterion is obtained. Only in this way can the calculated peak stress and contact force have engineering guiding significance and provide reliable input for topology optimization. Furthermore, since the amount of spring compression is determined by the geometry of the grid cells, which is a displacement boundary condition, the amount of displacement applied by the fuel rod is defined. The fact that the displacement is equal to the spring compression means that in the finite element model, we are using a displacement-controlled loading method rather than a force-controlled one, and the displacement applied by the fuel rod satisfies:

[0035] In the formula, The free height of the spring, This represents the working height of the spring; that is, simulating the process of the spring being compressed from its free state to its working height, thus truly reflecting the working stress state.

[0036] Furthermore, the spring sheet is a thin-shell structure of uniform thickness. Both ends of the spring are welded to the strip, restricting out-of-plane displacement and rotation. Other parts of the spring may come into contact during deformation. The simulation model applies the following boundary conditions based on the spring's service conditions: fixed constraints are set on the edge lines, only the fuel rod is allowed translational freedom in the axial direction, and the fuel rod, rigid convexity, and spring are in frictional contact with a friction coefficient of 0.325. Nonlinearity must be enabled during calculation. Initially, the fuel rod is in contact with the spring surface. The deformation state when the spring clamps the fuel rod is simulated by displacing the fuel rod towards the spring.

[0037] Furthermore, in this embodiment, the spring is simplified to a shell element model. In reality, the spring can also be discretized into solid elements and beam elements, among others. The principle of discretization is to transform the complex continuum problem into a combination of simple, discrete, numerically solvable problems. This process is based on variational principles and the weighted residual method. Because a lattice spring is a continuous body with complex geometry, its mechanical behavior (such as stress and strain) should theoretically be described by a set of partial differential equations (governing equations) over the entire domain. Directly solving these equations is almost impossible for complex geometries. Therefore, the finite element method divides the continuous spring structure into a finite number of simple-shaped blocks, which are called elements, and the elements are connected by nodes. In this way, the differential equations that originally needed to be solved at an infinite number of points are simplified to solving algebraic equations at a finite number of nodes. Solid elements divide the three-dimensional solid spring into small blocks (such as tetrahedrons and hexahedrons). Each solid element has dimensions in three spatial directions, which can describe the complex stress state inside the structure in detail. When it is necessary to accurately analyze areas with significant three-dimensional stress concentration effects, such as the root of the spring, near holes, or rigid protrusions, this is the most accurate but computationally most expensive method. Shell elements are used when the size (thickness) of a spring in one direction is much smaller than the size in the other two directions. They can be simplified into a mid-surface and a thickness property can be assigned to this mid-surface. Shell elements can describe tensile / compressive stress in the plane and bending stress out of the plane at the same time. The computational efficiency of this method is much higher than that of solid elements because it greatly reduces the number of elements and nodes while ensuring sufficient accuracy. Beam elements are used when a spring can be idealized as a line with cross-sectional properties (such as area and moment of inertia), primarily bearing axial forces, shear forces, and bending moments. If the spring's width is comparable to its thickness, and its primary mechanical behavior is bending about its weak axis, it can be simplified to a beam element. This simplification offers the highest degree of precision and the fastest computation speed, but it may not capture the stress distribution along the width direction.

[0038] S3: To optimize the geometric model by reducing the peak stress of the spring and the area of ​​the stress-sensitive region; The goal of the topology optimization is to reduce the peak stress and the area of ​​the stress-sensitive region within a specified optimization area while maintaining or optimizing the clamping force. The objective function for structural topology optimization is:

[0039] In the formula, and These are the weights for the peak stress of the spring and the area of ​​the stress-sensitive region of the spring, respectively. The clamping force is obtained by extracting the contact reaction force between the spring and the fuel rod in the simulation model. Physically, the clamping force of a spring is often positively correlated with its internal stress level. To provide sufficient clamping force, the spring typically requires a certain stress level. Since the objective function aims to achieve the lowest stress while satisfying the basic function (i.e., the clamping force requirement), the clamping force becomes the constraint condition in the objective function.

[0040] Furthermore, during topology optimization, weight is removed from the model before optimization, thus improving material utilization and economic efficiency, demonstrating that the method of this invention can achieve low-stress optimization design of lattice springs.

[0041] S4: Perform stress optimization evaluation on the new spring structure obtained after topology optimization. If the evaluation result does not meet the requirements, return to S1 or S2 for iterative optimization until an optimized solution that meets the requirements is obtained. The specific evaluation results are as follows: after optimization, both the peak stress of the spring and the area of ​​the spring's stress-sensitive region should be reduced. If the peak stress of the spring is reduced but the area of ​​the spring's stress-sensitive region is increased, or if the peak stress of the spring is increased but the area of ​​the spring's stress-sensitive region is reduced, then the evaluation is unqualified. If the evaluation is unqualified, the geometric model parameters of S1 or the stress calculation and analysis conditions of S2 should be modified and the iteration should be repeated. Finally, the optimized geometric model is extracted from the completed simulation model. The corresponding lattice spring structure has the ability to resist stress corrosion cracking, which greatly improves the safety and reliability of fuel assemblies in reactor operation. This method forms a closed-loop iterative process of "parametric modeling - simulation analysis - topology optimization - comprehensive evaluation". Once the initial model is established, new schemes can be quickly generated and automatically evaluated by adjusting parameters, which greatly shortens the design cycle and reduces development costs. This method is based on parametric driving and does not depend on a specific spring configuration. Therefore, it can be flexibly applied to the structural optimization of different types of lattice springs and has good versatility and promotion value.

[0042] Example 2 As attached Figure 3 An electronic device shown includes: Processor, memory, communication interface; The memory is used to store the executable instructions of the processor; The processor is configured to execute the above-described lattice spring topology optimization design method by executing the executable instructions.

[0043] A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described lattice spring topology optimization design method.

[0044] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A lattice spring topology optimization design method, characterized by, The method comprises the following steps: S1. creating a geometric model of the grid spring through parameterized modeling; S2. based on the geometric model, constructing a numerical simulation model to simulate the stress state of the grid spring under full-life working conditions, and performing stress calculation analysis to obtain the stress peak value of the spring and the stress sensitive area of the spring; S3. taking the reduction of the stress peak value and the stress sensitive area of the spring as the optimization target, performing structural topology optimization on the geometric model; S4. performing stress optimization evaluation on the new spring structure obtained after topology optimization, and if the evaluation result does not meet the requirements, returning to S1 or S2 for iterative optimization until an optimization scheme meeting the requirements is obtained.

2. The lattice spring topology optimization design method of claim 1, wherein: In S1, the objects of parameterized modeling include the length, width, height and chord length size parameters of the grid spring, and the correlation between the size parameters can be established according to the geometric constraint conditions.

3. The lattice spring topology optimization design method of claim 1, wherein: In S2, the input parameters of the simulation model include the operating temperature, neutron flux, coolant environmental parameters, grid cell structure geometric constraints and the changes of material physical properties caused by irradiation relaxation.

4. The lattice spring topology optimization design method of claim 3, wherein: The property parameter change includes a material yield strength With a change in neutron fluence Specifically, wherein is the initial yield strength of the material, is the irradiation hardening coefficient.

5. The lattice spring topology optimization design method of claim 1, wherein: In S2, the finite element analysis method is used to construct the numerical simulation model, and the geometric characteristics of the grid spring are discretized into shell elements, beam elements or solid elements.

6. The lattice spring topology optimization design method of claim 1, wherein: In S2, the region where the stress value exceeds a certain proportion of the yield strength of the spring material is defined as the stress sensitive area.

7. The lattice spring topology optimization design method of claim 6, wherein: The certain proportion is set to 0.8 times.

8. The lattice spring topology optimization design method of claim 1, wherein: In S3, the topology optimization aims to reduce the stress peak value and the stress sensitive area in the specified optimization region while maintaining or optimizing the clamping force, and the clamping force is obtained by extracting the contact reaction force between the spring and the fuel rod in the simulation model.

9. The lattice spring topology optimization design method of claim 1, wherein: The evaluation result in S4 requires that the stress peak value of the optimized spring and the stress sensitive area of the spring are both smaller; if the evaluation is not qualified, the geometric model parameters in S1 or the stress calculation analysis conditions in S2 are modified to reiterate.

10. The lattice spring topology optimization design method of claim 1, wherein: The parameters of the initial geometric model are provided by the AFA 3G grid spring.

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