A turbine disc structure optimization method based on thermal coupling

Abstract

The application provides a turbine disc structure optimization method based on thermal coupling, a topology optimization model is established by taking the relative density of each unit in a finite element analysis model of the turbine disc as a design variable; the elastic modulus of the material of the unit in the topology optimization model at different temperatures is extracted and linearly fitted as a first-order function to construct a mapping relationship between the elastic modulus of any unit in an optimization domain and the design variable, and a topology optimization problem of the structure is converted into an optimal distribution problem of the material; the sensitivity of all units in the optimization domain is calculated, the sensitivity is normalized and filtered, the processed sensitivity is sorted to obtain an array, and the array is updated; an iteration termination judgment condition is set, when the structure volume meets the design requirement and reaches a convergence standard, the optimized structure is output, and the turbine disc structure optimization design is completed. The optimization method provided by the application meets the lightweight design of the turbine disc structure and improves the overall stiffness performance of the disc structure.

Description

[Technical Field]

[0001] This invention relates to the field of aero-engine technology, and more specifically to a method for optimizing turbine disk structure based on thermo-coupling. [Background Technology]

[0002] Aero engines mainly consist of a compressor, combustion chamber, and gas turbine. The gas turbine, as the power core of the aero engine, converts some of the thermal and pressure energy of the high-temperature combustion gases into mechanical energy, thereby driving the compressor and accessories. The turbine disk, as a typical component of the gas turbine, is characterized by high power output, the ability to withstand extremely high gas temperatures, and extremely high rotational speeds. Therefore, its performance needs to be optimized to meet the requirements of long-term operation in harsh environments with high temperature and pressure. Thus, it is necessary to provide a turbine disk structure optimization method based on thermo-coupling to solve the aforementioned problems. [Summary of the Invention]

[0003] The technical problem to be solved by the present invention is to provide a turbine disk structure optimization method based on thermo-coupling, which improves the overall stiffness performance of the turbine disk structure while satisfying the lightweight design of the turbine disk structure.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A method for optimizing turbine disk structures based on thermo-coupling, characterized by comprising the following steps:

[0006] S1: Establish a simplified spatial geometric model of the turbine disk, and construct a finite element analysis model of the turbine disk in combination with the actual operating conditions of the aero-engine;

[0007] S2: Using the relative density of each element in the finite element analysis model of the turbine disk as the design variable, the minimum overall structural flexibility as the optimization objective, and volume as the constraint condition, a topology optimization model is established.

[0008] S3: Extract the elastic modulus of the material of the unit in the topology optimization model at different temperatures, and linearly fit it to a linear function f. E (T), construct the elastic modulus E(i) and design variable x of any element in the optimization domain. i The mapping relationship transforms the topology optimization problem of the structure into the optimal distribution problem of materials, where the elastic modulus E(i) of any element is related to the design variable x. i The mapping relationship is represented as follows:

[0009] E(i)=f E (T)·f(x i E0

[0010] f E (T) = 214.5 - 0.069T

[0011]

[0012] In the formula, E0 represents the elastic modulus of the solid element in the topology optimization model; f E (T) represents the function of linear fitting between temperature and elastic modulus, derived from the linear fitting of the material's elastic modulus at temperatures of 20℃, 100℃, 200℃, 300℃, 400℃, 500℃, 600℃, 700℃, 800℃, 900℃, and 1000℃; f(x i ) is the material interpolation function, used to interpolate the design variable x. i Approximates a 0-1 distribution; T is the temperature of the unit in the topology optimization model, and p is the penalty coefficient of the interpolation function;

[0013] S4: Calculate the sensitivity of all units in the optimization domain, normalize and filter the sensitivity, sort the processed sensitivity to obtain an array, and update the array.

[0014] S5: Set the iteration termination condition. When the structural volume meets the design requirements and reaches the convergence standard, output the optimized structure and complete the turbine disk structure optimization design.

[0015] Preferably, the turbine disk structure includes a disk body located at the center and multiple blades distributed along the disk body. The step S1 of "establishing a simplified spatial geometric model of the turbine disk" specifically means: simulating the effect of the blades on the disk body by removing the blades and applying equivalent nodal forces, thereby simplifying the spatial geometric model of the turbine disk.

[0016] Preferably, the topology optimization model is expressed as:

[0017]

[0018] In the formula, C(X) is the total strain energy under the coupled structural field, U is the total structural displacement matrix, K is the total structural stiffness matrix, T represents the transpose of the matrix, N is the number of all elements in the entire optimization domain, and u i To optimize the displacement matrix of any element within the domain, k i To optimize the stiffness matrix of any element within the optimization domain, V(X) represents the total volume of the structure after optimization, and V0 represents the total volume of the structure before optimization; F represents the total load in the optimization domain. For temperature-independent element node external loads, x represents the element node thermal load caused by temperature changes. i Let be a design variable, representing the relative density of any element within the optimization domain, and its value is in the range [x]. min Between [1], x min Represents design variable x iThe minimum value of , where X represents the set of relative densities of all elements in the optimization domain, and R represents the set of real numbers.

[0019] Preferably, step S4, "sorting the processed sensitivities to obtain an array and updating the array," specifically includes the following steps:

[0020] S41: Calculate the maximum number of deleted units (Cycle); where the Cycle value represents the maximum number of deleted units during the iteration process, and its value increases with the increase of the iteration steps, and is positively correlated with the unit deletion rate;

[0021] S42: Sort the sensitivity values ​​of all units in the optimization domain to obtain an array, and use the sensitivity value corresponding to the Cycle-th unit as the threshold;

[0022] S43: Compare the sensitivity values ​​of all units within the optimization domain with the threshold. If the sensitivity value of a unit is greater than the threshold, the design variable value corresponding to that unit is increased by one step value; otherwise, it is decreased by one step value.

[0023] S44: Filter and retain cells with design variables greater than 0.5, delete other cells, and complete the array update.

[0024] Preferably, the unit sensitivity α i The calculation process is as follows:

[0025]

[0026] In the formula, u i Let k represent the displacement matrix of element i. i f represents the stiffness matrix of element i. i This represents the load on element i.

[0027] Compared with related technologies, the present invention takes a simplified turbine disk structure as the optimization object, applies corresponding centrifugal force and thermal boundary conditions according to the actual working conditions of the turbine disk, constructs a finite element analysis model, and uses the relative density of each element in the finite element model of the turbine disk structure as the design variable in the optimization process. It adopts an asymptotic structural optimization algorithm based on an interpolation model, takes the minimum overall structural flexibility as the optimization objective, and establishes a topology optimization model with volume as the constraint condition. It assigns a certain mapping relationship between the elastic modulus and the design variables and performs finite element solution. By setting reasonable optimization parameters, the topology optimization result with the optimal material distribution is obtained, which improves the stiffness of the turbine disk under the condition of weight reduction and meets the requirements of turbine disk performance optimization design. [Attached Image Description]

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0029] Figure 1 This is a flowchart of a turbine disk structure optimization method based on thermo-coupling provided by the present invention;

[0030] Figure 2 This is a schematic diagram of the turbine disk geometric model structure constructed in Example 1;

[0031] Figure 3 yes Figure 2 A simplified model of the turbine disk is shown.

[0032] Figure 4 This is a schematic diagram of the mesh generation structure of the turbine disk finite element model in Example 1;

[0033] Figure 5 This is a schematic diagram of the turbine disk finite element model in Example 1;

[0034] Figure 6 It is a flowchart of the update process for design variables during the iteration process;

[0035] Figure 7 This is a schematic diagram showing the division of the design optimization domain for the turbine disk model in Example 1;

[0036] Figure 8 This is the result of the turbine disk structure topology optimization in Example 1;

[0037] Figure 9 This is a comparison of the wheel temperature cloud map results before and after optimization in Example 1;

[0038] Figure 10 This is a comparison of the Von Mises equivalent stress cloud diagrams of the wheel before and after optimization in Example 1;

[0039] Figure 11 This is a comparison of the wheel strain energy density cloud map results before and after optimization in Example 1.

Detailed Implementation Methods

[0040] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, and to make the above-mentioned objectives, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0041] Please refer to the following: Figure 1-11This invention provides a method for optimizing turbine disk structures based on thermo-coupling, comprising the following steps:

[0042] S1: Establish a simplified spatial geometric model of the turbine disk, and construct a finite element analysis model of the turbine disk in combination with the actual operating conditions of the aero-engine.

[0043] The turbine disk structure consists of a central disk and multiple blades distributed along the disk. Due to the large number of blades, and the fact that the blades are not within the optimization domain, directly meshing and calculating would result in cumbersome computation and low solution accuracy. Therefore, a method is adopted to remove the blades and apply equivalent nodal forces to simulate the effect of the blades on the disk, simplifying the spatial geometry model of the turbine disk. After simplification, the disk is rotationally symmetric throughout, which can greatly improve optimization efficiency, mesh quality, and computational accuracy.

[0044] Based on a simplified spatial geometric model of the turbine disk, the 3D coupled element SOLID5 in ANSYS was selected as the mesh element type, and the mesh was generated according to 8-node hexahedral elements. Next, according to the actual operating conditions of the turbine disk, temperature-displacement boundary conditions were set and corresponding external loads, such as centrifugal loads and blade equivalent loads, were applied.

[0045] S2: Using the relative density of each element in the finite element analysis model of the turbine disk as the design variable, the minimum overall structural flexibility as the optimization objective, and volume as the constraint, a topology optimization model is established:

[0046]

[0047] In the formula, C(X) is the total strain energy under the coupled structural field, U is the total structural displacement matrix, K is the total structural stiffness matrix, T represents the transpose of the matrix, N is the number of all elements in the entire optimization domain, and u i To optimize the displacement matrix of any element within the domain, k i To optimize the stiffness matrix of any element within the optimization domain, V(X) represents the total volume of the structure after optimization, and V0 represents the total volume of the structure before optimization; F represents the total load in the optimization domain. For temperature-independent element node external loads, x represents the element node thermal load caused by temperature changes. i Let be a design variable, representing the relative density of any element within the optimization domain, and its value is in the range [x]. min Between [1], x min Represents design variable x i The minimum value of , where X represents the set of relative densities of all units in the optimization domain, and R represents the set of real numbers;

[0048] In related technologies, the BESO algorithm is commonly used for topology optimization. During the evolutionary process, it can both remove inefficient elements and add efficient ones, giving the asymptotic optimization method strong shape optimization capabilities. It more easily reduces maximum stress and stress concentration, resulting in a more uniform stress distribution in the structure, finding better force transmission paths, and obtaining a superior topology. In the BESO algorithm, the design variable x... i This variable reflects the state of each element in the optimization domain. Its value can only be 0 or 1. When the design variable is 0, it indicates that the element is in a closed state and is a void element; when the design variable is 1, it indicates that the element is in an open state and is a solid element. By using the design variable to determine whether an element is deleted, some elements that have a weak effect on structural performance are continuously removed, while elements that are useful for structural performance are retained.

[0049] In traditional structural topology models, the design variable x i As the element stiffness matrix is ​​a discrete 0,1 distribution, it is prone to singularities, and there is no intermediate density between 0 and 1 in the element density. This makes the BESO algorithm too reliant on intuition when adding material strategies, which leads to unclear design objectives and evolutionary instability caused by drastic changes in design variables. Ultimately, this results in less than ideal optimization results. This phenomenon is particularly evident in topology optimization problems of three-dimensional configurations with a large number of elements.

[0050] Therefore, this invention introduces x using the variable density method. min The concept makes the design variable x i It is continuous between (0,1).

[0051] S3: Extract the elastic modulus of the material of the unit in the topology optimization model at different temperatures, and linearly fit it to a linear function f. E (T), construct the elastic modulus E(i) and design variable x of any element in the optimization domain. i The mapping relationship transforms the topology optimization problem of the structure into the optimal distribution problem of materials, where the elastic modulus E(i) of any element is related to the design variable x. i The mapping relationship is represented as follows:

[0052] E(i)=f E (T)·f(x i E0

[0053] f E (T) = 214.5 - 0.069T

[0054]

[0055] In the formula, E0 represents the solid element (x) i =1) elastic modulus, fE (T) represents the function for linear fitting of temperature and elastic modulus. The elastic modulus of the material at temperatures of 20℃, 100℃, 200℃, 300℃, 400℃, 500℃, 600℃, 700℃, 800℃, 900℃, and 1000℃ is extracted and linearly fitted, f(x) i ) is the material interpolation function, used to interpolate the design variable x. i Approximates a 0-1 distribution; T is the temperature of the cell, and p is the penalty coefficient of the interpolation function.

[0056] The variable density method uses the relative density of structural elements as the design variable, artificially assuming a functional relationship between the material's elastic modulus and the element's relative density, thus transforming the topology optimization problem of the structure into a problem of optimal material distribution. Compared to the homogenization method, it requires far fewer design variables, has a simpler optimization procedure, and is more efficient. Because transforming discrete optimization into continuous topology optimization can introduce intermediate density values, making it difficult to determine whether material should be removed, a penalty coefficient is added to the variable density method. This penalty coefficient pushes the intermediate density closer to the 0 and 1 extremes, preventing intermediate density elements from appearing in the structural topology optimization results.

[0057] Meanwhile, by linearly fitting the function of temperature and elastic modulus, the elastic model of the unit material is affected by both the design variables and the unit temperature during the optimization and iterative calculation process, thereby achieving material redistribution under thermo-mechanical coupling conditions.

[0058] S4: Calculate the sensitivity of all units within the optimization domain, normalize and filter the sensitivity, sort the processed sensitivity to obtain an array, and update the array.

[0059] The change in the average compliance of a structure caused by the removal of any element is defined as the element sensitivity α. i The calculation process is as follows:

[0060] In the formula, u i Let k represent the displacement matrix of element i. i f represents the stiffness matrix of element i. i This represents the load on element i.

[0061] Let ΔC represent the change in the total structural compliance, ΔU represent the change in the total structural displacement matrix, ΔK represent the change in the total structural stiffness matrix, and α represent the element sensitivity. i The derivation process is as follows:

[0062]

[0063] By utilizing the symmetry of the stiffness matrix, we can derive the following:

[0064]

[0065] ΔC can be considered as the sensitivity α of multiple units. i Therefore, after equivalent transformation of ΔC, the unit sensitivity α can be obtained from the integrated result. i The derivation formula.

[0066] Step S4, "sorting the processed sensitivities to obtain an array and updating the array," specifically includes the following steps:

[0067] S41: Calculate the maximum number of cells deleted (Cycle); the Cycle value increases with the number of iterations and is positively correlated with the cell deletion rate.

[0068] S42: Sort the sensitivity values ​​of all units in the optimization domain to obtain an array, and use the sensitivity value corresponding to the Cycle-th unit as the threshold;

[0069] S43: Compare the sensitivity values ​​of all units within the optimization domain with the threshold. If the sensitivity value of a unit is greater than the threshold, the design variable value corresponding to that unit is increased by one step value; otherwise, it is decreased by one step value.

[0070] S44: Filter and retain cells with design variables greater than 0.5, delete other cells, and complete the array update.

[0071] S5: Set the iteration termination condition. When the structural volume meets the design requirements and reaches the convergence standard, output the optimized structure and complete the turbine disk structure optimization design.

[0072] Example 1

[0073] The turbine disk structure optimization method based on thermo-coupling provided by this invention is used to carry out lightweight design of a certain type of aero-engine turbine disk structure. Its geometric model is as follows: Figure 1 As shown, the simplified model is as follows Figure 2 As shown. An 8-node hexahedral 3D coupled element SOLID5 was selected as the mesh element type to mesh the turbine disk model. The 3D display image of the meshed turbine disk is shown below. Figure 3 As shown. Next, the solid unit is assigned material properties, including an elastic modulus E = 200 GPa, a Poisson's ratio μ = 0.3, and a density ρ = 8010 kg / m³. 3Finally, load and temperature-displacement boundary constraints are applied to the turbine disk model. Specifically, this includes applying fixed constraints to the inner diameter contact surface of the turbine disk, applying a working temperature of 677℃ to the inner diameter contact surface, applying a heat source of 1380℃ to the outer diameter surface in contact with the blade base, applying a rotational speed ω0 around the central axis to the disk structure, and applying the blade forces on the disk as nodal equivalent loads to the outer diameter surface of the disk. This completes the construction of the turbine disk finite element model. Figure 4 As shown.

[0074] Before performing optimization iterations, the design domain and non-design domain are divided according to design requirements. Figure 7 The diagram shows the meridional cross-section of the turbine disk, where the black area represents the non-design optimization domain, and the remaining solid portion represents the design optimization domain. Secondly, by setting different optimization parameters, the accuracy and efficiency of the optimization iteration calculations are controlled to ensure the rationality of the optimization results. Specifically, the optimization volume constraint is set to 70% of the total volume of the model, with initial deletion rate RR0 = 0.01, evolution rate ER = 0.01, and design variable update step size move = 0.2.

[0075] During the optimization and iterative calculation process, the cross-sectional configuration of the turbine disk gradually evolved from a solid disk structure to a hollow spoked disk structure. The entire optimization process iterated 159 times. Figure 8 As shown. Through post-processing optimization, finite element analysis was performed on the optimized turbine disk structure to obtain the temperature distribution, Von Mises equivalent stress distribution, and element strain energy density distribution of the optimized turbine disk configuration, as shown below. Figure 9-11 As shown in the figure, by comparing the maximum stress and maximum element strain energy values ​​of the structure before and after optimization, it can be found that the maximum strain energy density of the optimized turbine disk structure is 62% lower than that before optimization, but the maximum Von Mises equivalent stress is 49% higher than that before optimization. Finally, from the perspective of the optimization objective, the turbine disk structure reduces the overall structural flexibility by 34% under the condition of a 30% weight reduction, thus meeting the goal of improving the overall structural stiffness.

[0076] Compared with related technologies, the present invention takes a simplified turbine disk structure as the optimization object, applies corresponding centrifugal force and thermal boundary conditions according to the actual working conditions of the turbine disk, constructs a finite element analysis model, and uses the relative density of each element in the finite element model of the turbine disk structure as the design variable in the optimization process. It adopts an asymptotic structural optimization algorithm based on an interpolation model, takes the minimum overall structural flexibility as the optimization objective, and establishes a topology optimization model with volume as the constraint condition. It assigns a certain mapping relationship between the elastic modulus and the design variables and performs finite element solution. By setting reasonable optimization parameters, the topology optimization result with the optimal material distribution is obtained, which improves the stiffness of the turbine disk under the condition of weight reduction and meets the requirements of turbine disk performance optimization design.

[0077] The embodiments of the present invention have been described in detail above, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations made to these embodiments without departing from the principles and spirit of the present invention still fall within the protection scope of the present invention.

Claims

1. A method for optimizing turbine disk structures based on thermo-coupling, characterized in that, Includes the following steps: S1: Establish a simplified spatial geometric model of the turbine disk, and construct a finite element analysis model of the turbine disk in combination with the actual operating conditions of the aero-engine; S2: Using the relative density of each element in the finite element analysis model of the turbine disk as the design variable, the minimum overall structural flexibility as the optimization objective, and volume as the constraint condition, a topology optimization model is established. S3: Extract the elastic modulus of the material of the unit in the topology optimization model at different temperatures, and linearly fit it to a linear function. Construct the elastic modulus of any element within the optimization domain. E ( i ) and design variables The mapping relationship transforms the topology optimization problem of the structure into the optimal distribution problem of the material, and the elastic modulus of any element. E ( i ) and design variables The mapping relationship is represented as follows: In the formula, E0 This represents the elastic modulus of the solid element in the topology optimization model; The function representing the linear fit between temperature and elastic modulus is derived from the linear fit of the elastic modulus of the material at temperatures of 20℃, 100℃, 200℃, 300℃, 400℃, 500℃, 600℃, 700℃, 800℃, 900℃, and 1000℃. This is a material interpolation function, used to allow design variables to be interpolated. Approximates the 0-1 distribution; T The temperature of the element in the topology optimization model. p The penalty coefficient for the interpolation function; S4: Calculate the sensitivity of all units in the optimization domain, normalize and filter the sensitivity, sort the processed sensitivity to obtain an array, and update the array. S5: Set the iteration termination judgment condition. When the structural volume meets the design requirements and reaches the convergence criterion, output the optimized structure and complete the turbine disk structure optimization design. The topology optimization model is expressed as follows: In the formula, Let be the total strain energy under the coupled structural field. This is the total displacement matrix of the structure. Here is the overall stiffness matrix of the structure. T To represent the transpose of a matrix, The total number of elements in the entire optimization domain. To optimize the displacement matrix of any element within the domain, To optimize the stiffness matrix of any element within the domain, The total volume after structural optimization. This represents the total volume before structural optimization. F To optimize the total load of the domain, For temperature-independent element node external loads, For the element node thermal load caused by temperature change, Let be a design variable, representing the relative density of any element within the optimization domain, and its value is within [ ]. Between ,1] Represent design variables The minimum value, X This represents the set of relative densities of all elements within the optimization domain. R It represents the set of real numbers.

2. The turbine disk structure optimization method based on thermo-coupling according to claim 1, characterized in that, The turbine disk structure includes a disk body located at the center and multiple blades distributed along the disk body. The step S1 of "establishing a simplified spatial geometric model of the turbine disk" specifically means: simulating the effect of the blades on the disk body by removing the blades and applying equivalent nodal forces, thereby simplifying the spatial geometric model of the turbine disk.

3. The turbine disk structure optimization method based on thermo-coupling according to claim 1, characterized in that, Step S4, "sorting the processed sensitivities to obtain an array and updating the array," specifically includes the following steps: S41: Calculate the maximum number of deleted cells (Cycle); S42: Sort the sensitivity values ​​of all units in the optimization domain to obtain an array, and use the sensitivity value corresponding to the Cycle-th unit as the threshold; S43: Compare the sensitivity values ​​of all units within the optimization domain with the threshold. If the sensitivity value of a unit is greater than the threshold, the design variable value corresponding to that unit is increased by one step value; otherwise, it is decreased by one step value. S44: Filter and retain cells with design variables greater than 0.5, delete other cells, and complete the array update.

4. The turbine disk structure optimization method based on thermo-coupling according to claim 3, characterized in that, Unit sensitivity The calculation process is as follows: In the formula, Representation unit The displacement matrix, Representation unit stiffness matrix, Representation unit The load.

Images