Turbine disk topology optimization design method and system for additive manufacturing

Abstract

This invention discloses a turbine disk topology optimization design method and system for additive manufacturing. The method first identifies the thermal convection boundary of the turbine disk based on the convection-diffusion equation and applies thermal convection, achieving variable boundary thermal convection application. This accurately simulates the thermal convection effect. Furthermore, after applying variable boundary thermal convection, thermo-mechanical coupling loading constraints and stress constraints considering thermal convection heat dissipation are set, which, together with the self-supporting internal hole constraints, serve as constraints for the topology optimization objective function. This achieves synergistic optimization of the three, enabling the optimization algorithm to converge to a reasonable 0-1 density distribution. The optimized design result, while achieving lightweight turbine disk design, satisfies additive manufacturing geometric constraints, improving machinability, effectively controlling stress levels, improving service reliability, and considering thermo-mechanical coupling loading for thermal convection heat dissipation. This allows for turbine disk design under complex operating conditions, improving applicability.

Description

Technical Field

[0001] This invention relates to the field of turbine disk topology optimization technology, and in particular, to a turbine disk topology optimization design method and system for additive manufacturing, electronic equipment, and computer-readable storage medium. Background Technology

[0002] Turbine disks account for a significant proportion of the mass of aero-engines, and lightweight design of turbine disks is crucial for improving aero-engine efficiency. Structural topology optimization provides a solution for lightweight turbine disk design. Topology-optimized turbine disks often have complex geometries, typically including internal holes, making the optimized structure difficult to manufacture using traditional techniques. Additive manufacturing, however, offers a possibility for processing topology-optimized turbine disks. However, laser selective melting additive manufacturing, which offers high-precision forming, requires auxiliary supports when machining overhanging surfaces with small inclinations. For internal holes, these supports are difficult to remove after machining, significantly increasing the cost and difficulty of additive manufacturing. Therefore, it is necessary to consider internal hole overhang angle constraints during turbine disk topology optimization design to improve the feasibility of additive manufacturing. Currently, relevant research has proposed structural topology optimization methods with self-supporting internal hole constraints.

[0003] Furthermore, during engine operation, the turbine disk must withstand not only the thermal load from the high-temperature combustion gases but also the enormous centrifugal force generated by high-speed rotation and the complex mechanical loads transmitted by the blades. This requires the turbine disk to possess excellent thermodynamic and mechanical properties to ensure stable and efficient engine operation under various conditions. The complex external contours and internal pores of the turbine disk after topology optimization directly affect the convective heat transfer efficiency, thereby affecting the turbine disk's thermo-coupling performance. Therefore, accurately simulating the thermal convection effect is a prerequisite for achieving synergistic optimization of structural performance and manufacturing process during turbine disk topology optimization. However, thermal convection heat dissipation is a variable boundary load, meaning it changes with the structural boundary. Due to the lack of explicit description of the structural boundary in variable density topology optimization, it is difficult to identify the external boundary and internal cavity surface of the structure, making it difficult to apply thermal convection. Moreover, the thermal convection load depends on the length of the structural boundary, while the self-supporting internal hole constraint affects the inclination and length of the structural boundary. The interaction between the two affects the change of the structural boundary and may even lead to sharp corners in the internal holes, thus affecting the structural stress distribution and convergence, making it difficult to obtain a reasonable 0 / 1 density distribution. Existing turbine disk topology optimization methods do not consider thermal convection heat dissipation, nor do they consider the interaction between thermal convection loads and self-supporting internal hole constraints, thus making it difficult to converge to a reasonable 0 / 1 density distribution. Summary of the Invention

[0004] This invention provides a turbine disk topology optimization design method and system for additive manufacturing, electronic equipment, and computer-readable storage medium. It can accurately identify external boundaries and apply thermal convection to variable boundaries, accurately simulate thermal convection effects, and achieve synergistic optimization of the three based on thermo-mechanical coupling loading constraints, stress constraints, and self-supporting internal hole constraints, so that the optimization algorithm can converge to a reasonable 0-1 density distribution.

[0005] According to one aspect of the present invention, a turbine disk topology optimization design method for additive manufacturing is provided, comprising the following:

[0006] The internal bore region and thermal convection boundary of the turbine disk are identified based on the convection-diffusion equation, and thermal convection is applied to the thermal convection boundary.

[0007] Thermo-coupling loading constraints and stress constraints are set to take into account thermal convection and heat dissipation, and self-supporting internal hole constraints are set based on the identified internal hole regions and density gradients.

[0008] With the goal of minimizing the amount of solid material used, and with constraints such as thermo-coupling loading, stress constraints, and self-supporting internal hole constraints, an objective function for turbine disk topology optimization is constructed.

[0009] The objective function is solved to obtain the turbine disk topology optimization results.

[0010] Furthermore, the process of identifying the thermal convection boundary of the turbine disk based on the convection-diffusion equation includes the following:

[0011] Based on the given topological description function, the illumination direction is set to the positive y-axis, and the convection-diffusion equation is solved to obtain the first shadow region;

[0012] By adjusting the illumination direction to the negative y-axis and solving the convection-diffusion equation again, the second shadow region is obtained.

[0013] Calculate the intersection of the first and second shaded regions to obtain the solid material region containing the internal hole;

[0014] Based on the design principle that the density gradient is non-zero only at the solid-void interface and zero elsewhere in the design region, and combined with the solid material region containing internal pores, the thermal convection loading terms are determined so that thermal convection is applied only to the external convection boundary.

[0015] Furthermore, the thermal convection loading term is:

[0016] ;

[0017] in, Indicates the movable design-related load boundary. Indicates the thermal convection coefficient. Represents the temperature field The test function, Represents the physical density gradient. Indicates the design area. Indicates reference temperature. A function to identify solid material regions containing internal holes. This represents the external region identification function that includes the external convection boundary.

[0018] Furthermore, the thermo-coupling loading constraint is as follows:

[0019] ;

[0020] ;

[0021] in, Represents the bilinear form of thermal energy. , Indicates linear heat load form, , This represents the virtual solution space of the temperature field. Represents physical density The corresponding thermal conductivity, Represents the temperature gradient. Indicates the radius of rotation relative to the axis of rotation. Indicates the loaded heat source. Represents the bilinear term of strain energy. Represents a linear purely mechanical load term. Indicates the thermo-coupling term. , , , Represents physical density The corresponding Young's modulus, This represents the pure mechanical stress at a unit Young's modulus. Represents a virtual strain field. Indicates traction boundary The traction load on it, Indicates the density of the material. Indicates rotational speed. Indicates displacement. Indicates virtual displacement. This represents the virtual solution space for displacement. Represents the space for displacement trial solutions. Indicates the coefficient of thermal expansion. and Represents Lamé constant, This represents the divergence.

[0022] Furthermore, the stress constraint is:

[0023] ;

[0024] in, This represents the total stress based on the stress step function mapping. Represents the stress step function. , The parameter representing the kurtosis of the stress step function. This indicates the upper limit of the stress constraint. Indicates the penalty coefficient. Indicates von Mises stress, Indicates failure stress, Indicates the design area.

[0025] Furthermore, the self-supporting internal hole constraint is as follows:

[0026] ;

[0027] in, This indicates the projected length of the non-self-supporting overhanging surface of the internal hole onto the printing plane. Indicates the angle of suspension. Indicates the critical slack angle. This represents the projection length limit value corresponding to the critical overhang angle. Indicates the printing direction in additive manufacturing. This represents the function for identifying internal hole regions. This represents a step function based on the density gradient. , Represents the optically compliant step function. , This represents a parameter that controls the steepness of the smooth step function.

[0028] Furthermore, the objective function is:

[0029] ;

[0030] in, Indicates the amount of physical material used. The design variable represents the structural density distribution. This represents the weak solution form of the convection-diffusion equation. Represents the bilinear form. Representing linear form, Represents the field variable of light intensity distribution. This represents the test function. This represents the trial solution space of the light intensity distribution field variables.

[0031] In addition, the present invention also provides a turbine disk topology optimization design system for additive manufacturing, comprising:

[0032] The thermal convection loading module is used to identify the internal hole region and thermal convection boundary of the turbine disk based on the convection-diffusion equation, and to apply thermal convection on the thermal convection boundary;

[0033] The constraint construction module is used to establish thermo-mechanical coupling loading constraints and stress constraints that take into account thermal convection and heat dissipation, and to establish self-supporting internal hole constraints based on the internal hole region and density gradient.

[0034] The objective function construction module is used to construct the objective function for turbine disk topology optimization with the minimum amount of solid material as the optimization objective and thermal coupling loading constraints, stress constraints, and self-supporting internal hole constraints as constraints.

[0035] The objective function solution module is used to solve the objective function and obtain the turbine disk topology optimization results.

[0036] In addition, the present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor executes the steps of the method described above by calling the computer program stored in the memory.

[0037] In addition, the present invention provides a computer-readable storage medium for storing a computer program for optimizing turbine disk topology design for additive manufacturing, wherein the computer program performs the steps of the method described above when run on a computer.

[0038] The present invention has the following beneficial effects:

[0039] The present invention provides a turbine disk topology optimization design method for additive manufacturing. First, it identifies the thermal convection boundary of the turbine disk based on the convection-diffusion equation and applies thermal convection. Since the convection-diffusion equation depends on the structural topology, for variable-density topology optimization, the convection-diffusion equation changes accordingly when the structural topology changes. This causes the identified thermal convection boundary to change as well, thus achieving variable-boundary thermal convection application and accurately simulating the thermal convection effect. Furthermore, after applying variable-boundary thermal convection, thermo-mechanical coupling loading constraints and stress constraints, considering thermal convection heat dissipation, are set as constraints for the topology optimization objective function along with self-supporting internal hole constraints. This achieves synergistic optimization of the three, enabling the optimization algorithm to converge to a reasonable 0-1 density distribution. The optimized design result, while achieving lightweight turbine disk design, satisfies additive manufacturing geometric constraints, improving manufacturability, effectively controlling stress levels, improving service reliability, and considering thermo-mechanical coupling loading for thermal convection heat dissipation. This allows for turbine disk design under complex operating conditions, improving applicability.

[0040] In addition, the turbine disk topology optimization design system for additive manufacturing of the present invention also has the above-mentioned advantages.

[0041] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0042] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0043] Figure 1 This is a schematic flowchart of a turbine disk topology optimization design method for additive manufacturing according to a preferred embodiment of this application;

[0044] Figure 2 yes Figure 1 A schematic diagram of the sub-process of step S1;

[0045] Figure 3 This is a schematic diagram of a certain topology provided in a preferred embodiment of this application;

[0046] Figure 4 This is a preferred embodiment of the present application. Figure 3 A schematic diagram of the first shadow region is obtained by applying illumination along the positive y-axis to the topological structure and solving the convection-diffusion equation.

[0047] Figure 5 This is a preferred embodiment of the present application. Figure 3 A schematic diagram of the second shadow region is obtained by applying illumination along the negative y-axis to the topological structure and solving the convection-diffusion equation.

[0048] Figure 6 This is a preferred embodiment of the present application. Figure 4 The first shaded area and Figure 5 Find the intersection of the second shaded region to obtain a schematic diagram of the solid material region containing the internal hole;

[0049] Figure 7 This is a schematic diagram of the external boundary identified in the preferred embodiment of this application;

[0050] Figure 8 This is a schematic diagram of applying heat convection to the outer boundary in a preferred embodiment of this application;

[0051] Figure 9 This is a schematic diagram of the axisymmetric thermal model of the turbine disk in a preferred embodiment of this application;

[0052] Figure 10This is a schematic diagram of the axisymmetric force model of the turbine disk in a preferred embodiment of this application;

[0053] Figure 11 This is a schematic diagram of the module structure of a turbine disk topology optimization design system for additive manufacturing, according to another embodiment of this application. Detailed Implementation

[0054] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0055] Reference Figure 1 A preferred embodiment of this application provides a turbine disk topology optimization design method for additive manufacturing, including the following:

[0056] Step S1: Identify the internal hole region and thermal convection boundary of the turbine disk based on the convection-diffusion equation, and apply thermal convection to the thermal convection boundary;

[0057] Step S2: Set thermo-mechanical coupling loading constraints and stress constraints that take into account thermal convection and heat dissipation, and set self-supporting internal hole constraints based on the identified internal hole region and density gradient;

[0058] Step S3: With the minimum amount of solid material as the optimization objective, and with thermal coupling loading constraints, stress constraints, and self-supporting internal hole constraints as constraints, construct the objective function for turbine disk topology optimization;

[0059] Step S4: Solve the objective function to obtain the turbine disk topology optimization results.

[0060] It is understood that the turbine disk topology optimization design method for additive manufacturing in this embodiment first identifies the thermal convection boundary of the turbine disk based on the convection-diffusion equation and applies thermal convection. Since the convection-diffusion equation depends on the structural topology, for variable density topology optimization, the convection-diffusion equation changes accordingly when the structural topology changes, causing the identified thermal convection boundary to change as well. This achieves the application of thermal convection at variable boundaries, accurately simulating the thermal convection effect. Furthermore, after applying the variable boundary thermal convection, thermo-mechanical coupling loading constraints and stress constraints considering thermal convection heat dissipation are set, which, together with the self-supporting internal hole constraints, serve as constraints for the topology optimization objective function. This achieves synergistic optimization of the three, enabling the optimization algorithm to converge to a reasonable 0-1 density distribution. The optimized design result, while achieving lightweight turbine disk design, satisfies the geometric constraints of additive manufacturing, improving manufacturability, effectively controlling stress levels, improving service reliability, and considering thermo-mechanical coupling loading for thermal convection heat dissipation. This allows it to be used for turbine disk design under complex operating conditions, improving its applicability.

[0061] In step S1, the structural density distribution design variable used in the variable density topology optimization process of the turbine disk is... The filter density is usually obtained by density filtering based on the Helmholtz equation. Then, the physical density is obtained based on the step function mapping. The specific density filtering and step function mapping are existing technologies and will not be elaborated here. Therefore, this application uses physical density. To describe the form of the topological structure, =1 indicates solid material. =0 indicates an empty phase or no material. Since the convection-diffusion equation can simulate the illumination process and identify shadowed regions, for a given topological form or physical density... This application identifies the internal hole region and thermal convection boundary of the turbine disk by solving the convection-diffusion equation, and applies thermal convection to the thermal convection boundary.

[0062] Specifically, the state equation of the convection-diffusion equation can be expressed as: ,in, L This represents the projected length of the design area in the machining direction. Represents the diffusion tensor. Denotes divergence, Represents the advection vector. The solution to the convection-diffusion equation represents the distribution field of light intensity. Indicates the shaded area. Indicates the bright area. Represents the light intensity gradient. Indicates the size of the source item. , representing physical density This refers to physical density. The density after density filtering and step function mapping, where the partial differential equation used for density filtering can be expressed as: , This indicates the physical density after filtration. To represent the control scale, the step function can be expressed as: , Indicates the density threshold. This represents a parameter used to control the sharpness of the step function mapping; when a large value is given... When, the step function mapping forces less than Filtration density Approaching 0, while being greater than 0 The value approaches 1.

[0063] The weak solution form of the convection-diffusion equation is as follows: , Represents the bilinear form. Representing linear form, i.e., light source loading terms. Represents the field variable of light intensity distribution. This represents the test function. Let represent the trial solution space of the light intensity distribution field variable, and the bilinear and linear forms are defined as follows:

[0064] ;

[0065] ;

[0066] in, Indicates the design area. Represents the gradient of the test function. This represents the gradient of the field variable, i.e., the gradient of light intensity.

[0067] Therefore, for a given topological form or physical density Since the auxiliary supports are added along the printing direction during additive manufacturing, by setting the illumination direction to be consistent with the printing direction and solving the convection-diffusion equation to obtain the shaded area, this shaded area can be considered as the area where the auxiliary supports cannot be removed during additive manufacturing, i.e., the internal hole area. Furthermore, in the actual optimization process, to ensure that the shaded area has a clear boundary, the solution to the convection-diffusion equation is also... Step function mapping was performed to obtain the final internal hole region identification function. The solution process for the convection-diffusion equation is existing technology and will not be elaborated here.

[0068] In addition, such as Figure 2 As shown, the process of identifying the thermal convection boundary of the turbine disk based on the convection-diffusion equation includes the following:

[0069] Step S11: Based on the given topological description function, set the illumination direction to the positive y-axis, solve the convection-diffusion equation, and obtain the first shadow region;

[0070] Step S12: Adjust the illumination direction to the negative y-axis and solve the convection-diffusion equation again to obtain the second shadow region;

[0071] Step S13: Calculate the intersection of the first shaded region and the second shaded region to obtain the solid material region containing the internal hole;

[0072] Step S14: Based on the design principle that the density gradient is non-zero only at the solid-void interface and zero elsewhere in the design region, and in combination with the solid material region containing internal pores, determine the thermal convection loading term so that thermal convection is only applied to the external convection boundary.

[0073] Specifically, for a given topological description function (i.e., physical density) ,like Figure 3 As shown, the blue area represents the empty phase / no material region, i.e., the bright region, and the brown area represents the solid material region, i.e., the shadow region. Since the load boundary changes with topology evolution, although the design principle based on the density gradient being non-zero only at the solid-void interface and zero elsewhere in the design region can be applied using the physical density gradient... The domain integral implicitly applies design-related boundary loads, but due to the physical density gradient... The identified boundaries may include internal hole boundaries, making it impossible to apply heat convection only to the external boundaries. This application addresses this by first setting the illumination direction... That is, the direction of illumination is set along the positive y-axis, where the coordinate system is based on... Figure 3 The image is defined with the bottom left corner as the origin, the positive x-axis to the right, and the positive y-axis upwards. The convection-diffusion equations are solved to simulate the illumination process. For illumination along the positive y-axis, the first shadow region is formed due to occlusion by solid materials. ,like Figure 4 As shown. Then, adjust the lighting direction to be along the negative y-axis, that is, set the lighting direction to... Solving the convection-diffusion equations again, a second shadow region will form due to the obstruction of solid materials. ,like Figure 5 As shown. Next, the first shaded area is calculated. Second shadow area The intersection of these points yields a solid material region containing internal holes, such as... Figure 6 As shown, a function for identifying solid material regions containing internal holes can be obtained. Finally, based on the design principle that the density gradient is non-zero only at the solid-void interface and zero elsewhere in the design region, and based on the solid material region identification function containing internal pores... The external region identification function is determined as follows: This allows us to determine the thermal convection loading term and the external boundary, wherein the thermal convection loading term is:

[0074] ;

[0075] in, Indicates the movable design-related load boundary. Indicates the thermal convection coefficient. Represents the temperature field The test function, Represents the physical density gradient. Indicates the design area. Indicates reference temperature. A function to identify solid material regions containing internal holes. This represents the external region identification function containing external convection boundaries, and the identified external boundaries are as follows: Figure 7 As shown, it can be seen that The value is greater than 0 only at the outer boundary, and 0 at all other locations. After determining the thermal convection loading term, thermal convection can be applied only to the outer boundary using a volume integral method, such as... Figure 8 As shown, the specific volume fractionation process is existing technology and will not be described in detail here.

[0076] It is understood that this application, based on the characteristic that the convection-diffusion equation depends on the structural topology, solves the convection-diffusion equation by setting the illumination direction to the positive and negative y-axis directions respectively. It utilizes the principle that solid materials can cause shading to obtain the shadow regions formed by light shining from top to bottom and from bottom to top respectively. The intersection of these two shadow regions is the solid material region containing the internal pores. Combined with the design principle that the density gradient is non-zero only at the solid-void interface and zero in other parts of the design region, the external boundary can be accurately identified and thermal convection can be applied. Even if the structural topology changes during the optimization process, the identified external boundary will also change accordingly, thus realizing the application of thermal convection with variable boundaries, which can accurately simulate the thermal convection effect of the turbine disk.

[0077] In addition, in step S2, after identifying the thermal convection boundary and applying thermal convection, thermal convection heat dissipation needs to be considered when performing thermo-mechanical coupling analysis. The thermo-mechanical coupling analysis actually solves the heat conduction problem and the linear elasticity problem in the design area. Here, it is necessary to first assume that the material is linear elastic and isotropic.

[0078] For heat conduction problems, such as Figure 9 As shown, the axisymmetric thermal model of the turbine disk uses cylindrical coordinates to describe its structure. r The radial direction is represented by 'z', the axis direction by 'x', and the rectangular area is the design area. The geometry of the turbine disk can be defined by three parameters: the inner radius R, the outer radius L0, and the width H0. T l and T r Let represent the temperatures applied at the left and right boundaries of the design region, respectively. The equation for the heat conduction problem can be expressed as:

[0079] ;

[0080] in, Denotes divergence, Represents the temperature gradient. Indicates the thermal conductivity coefficient. and Representing the design area The left and right boundaries. The weak solution to this equation can be expressed as: ,in, This represents the bilinear form of thermal energy, which characterizes the energy changes within a structure during heat conduction. , This represents a linear heat load form, which characterizes the work done by the external heat load. , This represents the virtual solution space of the temperature field. Represents physical density The corresponding thermal conductivity, Represents the temperature gradient. Indicates the radius of rotation relative to the axis of rotation. This indicates the heat source being loaded, which is set to zero in this application. Additionally, It can be obtained based on SIMP function interpolation, and can be represented as: , Indicates the thermal conductivity coefficient of a fixed material. This can avoid singularities in the finite element matrix. This represents the penalty coefficient, typically set to 3. It can be understood that the temperature field can be obtained by solving the weak solution form in the open-source finite element analysis platform FEniCS. .

[0081] For linear elastic problems, the axisymmetric force model of the turbine disk is as follows: Figure 10 As shown, the equilibrium equation for the linear elastic problem can be expressed as:

[0082] ;

[0083] in, Represents the Cauchy stress tensor. Indicates the density of the material. Indicates rotational speed. Indicates traction boundary The unit normal vector on, Indicates the traction load on the traction boundary. Indicates displacement. Indicates the Dirichlet boundary The specified displacement. In linear elastic problems considering thermoelastic loads, the stress tensor... It can be defined as: ,in, Indicates Young's modulus. This represents the pure mechanical stress at a unit Young's modulus. Indicates the coefficient of thermal expansion. Represents a unit tensor. and Represents Lamé constant, , , It represents Poisson's ratio.

[0084] Therefore, considering thermo-coupling, the weak solution form of the axisymmetric thermo-coupling model of the turbine disk can be expressed as:

[0085] ;

[0086] in, Represents the bilinear term of strain energy. Represents a linear purely mechanical load term. Indicates the thermo-coupling term. , , , This represents the virtual solution space for displacement. Represents the space for displacement trial solutions. Indicates virtual displacement. Represents physical density The corresponding Young's modulus, This represents the virtual strain field. The strain energy bilinear term... Characterized by the energy change of an elastic body due to deformation, the linear pure mechanical load term Characterized by the total virtual work done by all external loads on the virtual displacement, the thermo-mechanical coupling term This characterizes the coupling effect between the temperature field and the virtual displacement. Additionally, Young's modulus... Similarly, it can be obtained based on SIMP function interpolation, with the specific interpolation formula as described above. The formula for the difference is the same, and will not be repeated here.

[0087] Therefore, after applying thermal convection on the external boundary, the thermo-mechanical coupling loading constraint considering thermal convection heat dissipation can be expressed as:

[0088] ;

[0089] .

[0090] It is understood that the thermal coupling loading constraint of this application takes into account thermal convection heat dissipation, and can be used for turbine disk topology optimization design under complex working conditions, thereby improving the applicability of the algorithm.

[0091] Furthermore, for stress constraint, this application uses von Mises stress as the stress measurement to facilitate the prediction of yielding of ductile materials under complex loading conditions. Von Mises stress can be calculated based on the deviatoric stress tensor, and the calculation formula is as follows: ,in, Indicates von Mises stress, Represents the deviatoric stress tensor. , Represents the stress tensor. The trace of the stress tensor is obtained by adding the elements on the diagonal of the tensor. This represents the unit tensor. Conventional optimization methods typically set stress constraints so that each material point must satisfy the following condition: , This represents the failure stress, but conventional stress constraints are local constraints and are difficult to apply during the optimization process.

[0092] Therefore, this application constructs a global stress constraint based on a step function mapping, which can be expressed as:

[0093] ;

[0094] in, This represents the total stress based on the stress step function mapping. Represents the stress step function. , The parameter representing the kurtosis of the stress step function is typically taken as 0.005. This represents the upper limit of the stress constraint, typically taken as 0.001. This represents the penalty coefficient, which is typically set to 2. The larger the value, the stronger the penalty for exceeding the stress limit.

[0095] It is understood that this application constructs an overall stress constraint based on a step function mapping, and no longer applies local stress constraints to each material point, so as to apply stress constraints during the topology optimization process. This can effectively control the stress level of the optimized turbine disk and improve the service reliability of the turbine disk.

[0096] Additionally, in step S2, during the variable-density topology optimization of the turbine disk, the physical density used to describe the topology configuration... The gradient exists only at the interface between the solid and empty phase materials, and points from the empty phase material region to the solid material region. Therefore, the physical density gradient is usually referred to as the physical density gradient. With printing direction The angle between them is defined as the suspension angle. When the angle of the internal hole overhang is less than the critical overhang angle When this happens, auxiliary support is required. Therefore, in order to eliminate auxiliary support and achieve self-support for the internal holes, it is necessary to ensure during the topology optimization process that... ≥ However, this method of directly using the overhang angle for constraint is a typical local constraint, which is difficult to implement in the topology optimization process. Therefore, this application uses the internal pore region identification function obtained by solving the convection-diffusion equation in step S1. and physical density gradient To construct the internal hole overhang angle constraint, i.e., the self-supporting internal hole constraint, it can be expressed as:

[0097] ;

[0098] in, This indicates the projected length of the non-self-supporting overhanging surface of the internal hole onto the printing plane. Indicates the angle of suspension. This represents the critical slack angle, typically taken as 45°. This represents the projection length limit corresponding to the critical overhang angle; in this application, it is set to 0.01. Indicates the printing direction in additive manufacturing. This represents the function for identifying internal hole regions. This represents a step function based on the density gradient. , Represents the optically compliant step function. , This parameter controls the steepness of the smooth step function, and is typically set to 10. This is understandable because... Physically, it represents the projected length of the non-self-supporting overhanging surface of the internal hole on the printing plane. Therefore, by limiting... This allows for the constraint of the overhang length, thus achieving a self-supporting design.

[0099] Furthermore, in step S3, with the minimum amount of solid material used as the optimization objective, and using thermo-coupling loading constraints, stress constraints, and self-supporting internal hole constraints as constraints, an objective function for turbine disk topology optimization is constructed, wherein the objective function is:

[0100] ;

[0101] in, Indicates the amount of physical material used. The structural density distribution design variable is represented. It can be seen that, from top to bottom, the first constraint equation is the convection-diffusion equation. The shaded area obtained by solving it is used to identify the thermal convection boundary and the internal hole region. The thermal convection boundary facilitates the application of thermal convection to the external boundary, while the internal hole region facilitates the application of internal hole overhang angle constraints. The second and third equations are the heat conduction equation and the thermo-mechanical coupling equation; the fourth equation is the stress constraint; and the fifth equation is the internal hole overhang angle constraint.

[0102] Furthermore, the specific solution method in step S4 is existing technology; for example, given initial design variables... The initial physical density is obtained through density filtering and step function mapping. First, the convection-diffusion equations are solved to identify the internal orifice region and the thermal convection boundary, and thermal convection is applied to the thermal convection boundary. Then, the heat conduction equation and the thermo-mechanical coupling equation are solved to obtain the displacement field. Next, the stress constraint equation is calculated based on the displacement field to apply stress constraints, and the internal orifice overhang constraint equation is calculated to apply internal overhang angle constraints. Finally, the sensitivity of the objective function, stress constraints, and overhang angle constraints is calculated. The objective function is solved using the moving asymptotic method until convergence. After convergence... Corresponding physical density This represents the optimized structural topology. The specific solution process is implemented in the existing open-source finite element analysis platform FEniCS; the detailed solution process and principles will not be elaborated here.

[0103] In addition, such as Figure 11 As shown, another embodiment of the present invention also provides a turbine disk topology optimization design system for additive manufacturing, preferably employing the turbine disk topology optimization design method for additive manufacturing as described above, including:

[0104] The thermal convection loading module is used to identify the internal hole region and thermal convection boundary of the turbine disk based on the convection-diffusion equation, and to apply thermal convection on the thermal convection boundary;

[0105] The constraint construction module is used to establish thermo-mechanical coupling loading constraints and stress constraints that take into account thermal convection and heat dissipation, and to establish self-supporting internal hole constraints based on the internal hole region and density gradient.

[0106] The objective function construction module is used to construct the objective function for turbine disk topology optimization with the minimum amount of solid material as the optimization objective and thermal coupling loading constraints, stress constraints, and self-supporting internal hole constraints as constraints.

[0107] The objective function solution module is used to solve the objective function and obtain the turbine disk topology optimization results.

[0108] It is understood that the turbine disk topology optimization design system for additive manufacturing in this embodiment first identifies the thermal convection boundary of the turbine disk based on the convection-diffusion equation and applies thermal convection. Since the convection-diffusion equation depends on the structural topology, for variable density topology optimization, the convection-diffusion equation changes accordingly when the structural topology changes, causing the identified thermal convection boundary to change as well. This achieves the application of thermal convection at variable boundaries, accurately simulating the thermal convection effect. Furthermore, after applying the variable boundary thermal convection, thermo-mechanical coupling loading constraints and stress constraints considering thermal convection heat dissipation are set, which, together with the self-supporting internal hole constraints, serve as constraints for the topology optimization objective function. This achieves synergistic optimization of the three, enabling the optimization algorithm to converge to a reasonable 0-1 density distribution. The optimized design result, while achieving lightweight turbine disk design, satisfies the geometric constraints of additive manufacturing, improving manufacturability, effectively controlling stress levels, improving service reliability, and considering the thermo-mechanical coupling loading of thermal convection heat dissipation. This allows it to be used for turbine disk design under complex operating conditions, improving its applicability.

[0109] In addition, another embodiment of the present invention provides an electronic device including a processor and a memory, wherein the memory stores a computer program, and the processor executes the steps of the method described above by calling the computer program stored in the memory.

[0110] In addition, another embodiment of the present invention provides a computer-readable storage medium for storing a computer program for optimizing the topology design of a turbine disk for additive manufacturing, wherein the computer program performs the steps of the method described above when run on a computer.

[0111] Common computer-readable storage media include: floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, any other optical media, punch cards, paper tape, any other physical media with perforated patterns, random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), flash erasable programmable read-only memory (FLASH-EPROM), any other memory chips or cartridges, or any other media readable by a computer. Instructions may further be transmitted or received by a transmission medium. The term transmission medium can include any tangible or intangible medium used to store, encode, or carry instructions for execution by a machine, and includes digital or analog carrier communication signals or intangible media that facilitate communication of such instructions. Transmission media include coaxial cables, copper wires, and optical fibers, which contain conductors for transmitting a bus of computer data signals.

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0117] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

[0118] The above description is merely a preferred embodiment of the present invention and is not intended to limit the 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 method for topology optimization design of a turbine disk for additive manufacturing, characterized in that, The method comprises the following steps: The heat convection loading constraint and the stress constraint considering heat convection heat dissipation are set, and the self-supporting internal hole constraint is set based on the identified internal hole region and the density gradient; The objective function of the turbine disc topology optimization is constructed with the minimum amount of solid material as the optimization objective and the heat convection loading constraint, the stress constraint and the self-supporting internal hole constraint as the constraint conditions; The objective function is solved to obtain the turbine disc topology optimization result; The heat convection loading constraint is: The stress constraint is: ； ； wherein, represents the bilinear thermal energy form, , represents the linear thermal load form, , represents the temperature field virtual solution space, represents the physical density corresponding thermal conductivity, represents the temperature gradient, represents the relative rotation radius of the shaft, represents the loaded heat source, represents the strain energy bilinear term, represents the linear pure mechanical load term, represents the thermal force coupling term, , , , represents the physical density corresponding Young's modulus, represents the pure mechanical stress under unit Young's modulus, represents the virtual strain field, represents the traction load on the traction boundary , represents the material density, represents the rotation speed, represents the displacement, represents the virtual displacement, represents the displacement virtual solution space, represents the displacement trial solution space, represents the thermal expansion coefficient, and represents the Lame constant, represents the divergence, represents the thermal convection coefficient, represents the test function of the temperature field, represents the solid material region identification function containing internal holes, represents the external region identification function containing external convection boundary, represents the physical density gradient, represents the design region, represents the reference temperature; The objective function is: ； wherein, represents the overall stress based on a stress ramp function mapping, represents a stress ramp function, , represents a parameter controlling the steepness of the stress ramp function, represents an upper stress constraint value, represents a penalty coefficient, represents a von Mises stress, represents a failure stress, represents a design region; The process of identifying the heat convection boundary of the turbine disc based on the convection-diffusion equation comprises the following steps: ； wherein, denotes the amount of solid material, denotes the structural density distribution design variable, denotes the weak form of the convection-diffusion equation, denotes the bilinear form, denotes the linear form, denotes the light intensity distribution field variable, denotes the test function, denotes the trial solution space of the light intensity distribution field variable, denotes the projected length of the internal hole non-self-supporting overhanging face in the printing plane, denotes the overhanging angle, denotes the critical overhanging angle, denotes the projected length limit value corresponding to the critical overhanging angle, denotes the printing direction of additive manufacturing, denotes the internal hole region identification function, denotes the step function based on the density gradient, , denotes the smoothing step function, , denotes the parameter for controlling the steepness of the smoothing step function.

2. The additive manufacturing oriented turbine disk topology optimization design method of claim 1, wherein, Based on the given topology description function, the light direction is set as the positive direction along the y-axis, the convection-diffusion equation is solved to obtain a first shadow region; The light direction is adjusted to the negative direction along the y-axis, and the convection-diffusion equation is solved again to obtain a second shadow region; The intersection of the first shadow region and the second shadow region is calculated to obtain a solid material region containing internal holes; Based on the design principle that the density gradient is only non-zero on the solid-void interface and zero elsewhere in the design region, and in combination with the solid material region containing internal holes, the heat convection loading term is determined so that heat convection is only applied to the external convection boundary. The heat convection loading term is:

3. The additive manufacturing oriented turbine disk topology optimization design method of claim 2, wherein, The self-supporting internal hole constraint is: ； wherein, denotes a movable design-dependent load boundary, denotes a thermal convection coefficient, denotes a temperature field of a test function, denotes a physical density gradient, denotes a design area, denotes a reference temperature, denotes a solid material area identification function comprising an internal hole, denotes an outer area identification function comprising an outer convection boundary.

4. The additive manufacturing-oriented turbine disk topology optimization design method of claim 3, wherein, The method comprises the following steps: ； wherein, denotes the projected length of the internal hole non-self-supporting overhanging face in the printing plane, denotes the overhang angle, denotes the critical overhang angle, denotes the projected length limit value corresponding to the critical overhang angle, denotes the printing direction of the additive manufacturing, denotes the internal hole region identification function, denotes the step function based on the density gradient, , denotes the smoothing step function, , denotes the parameter controlling the steepness of the smoothing step function.

5. A system for topology optimization design of a turbine disk for additive manufacturing, employing the method for topology optimization design of a turbine disk for additive manufacturing according to any one of claims 1 to 4, characterized in that The heat convection loading module is used to identify the internal hole region and the heat convection boundary of the turbine disc based on the convection-diffusion equation, and to apply heat convection on the heat convection boundary; The constraint construction module is used to establish the heat convection loading constraint and the stress constraint considering heat convection heat dissipation, and to establish the self-supporting internal hole constraint based on the internal hole region and the density gradient; The objective function construction module is used to construct the objective function of the turbine disc topology optimization with the minimum amount of solid material as the optimization objective and the heat convection loading constraint, the stress constraint and the self-supporting internal hole constraint as the constraint conditions; The objective function solving module is used to solve the objective function to obtain the turbine disc topology optimization result. The computer program runs on a computer to perform the steps of the method of any one of claims 1-4.

6. An electronic device, comprising: The computer program runs on a computer to perform the steps of the method of any one of claims 1-4.

7. A computer readable storage medium for storing a computer program for a topology optimization design of a turbine disk oriented to additive manufacturing, characterized in that, ​

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