Turbine disk topology optimization method based on sensitivity and dynamic grayscale suppression

Abstract

The present invention provides a topology optimization method based on sensitivity and dynamic grayscale suppression, which is used to solve the difficulty and inaccuracy of solving the topology optimization of turbine disks under inertial loads and fixed loads, as well as the grayscale unit problem in the topology structure optimization process. The method comprises the following steps: (1) establishing a topology optimization design domain for the radial section of the turbine disk; (2) designing a mathematical model for topology optimization; (3) calculating the elastic modulus E(x i ) is punished; (4) according to the finite element calculation, the displacement matrix U of the turbine disc section is obtained, and the objective function - structural strain energy C is further calculated; (5) sensitivity calculation; (6) according to the optimization criterion method, the update iteration is designed; (7) load sensitivity suppression method; (8) dynamic grayscale suppression method; (9) convergence judgment. The three-spoke turbine disc designed according to the present invention has the following beneficial effects: effectively bearing the centrifugal load of the turbine blades on the rim and the turbine disc itself, the arc structure of the rear spoke and the supporting structure is conducive to bearing the aerodynamic tangential load transmitted by the turbine blades on the rim; the setting of the holes makes the turbine disc lightweight; and meets the strength and stiffness requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of aeroengine and high-pressure gas turbine, and specifically, relates to a topology optimization method based on sensitivity and dynamic grayscale suppression. The asymmetric three-spoke plate structure of the turbine disk connecting the hub and the rim improves the ability of the turbine disk to withstand centrifugal load, radial load and tangential load. The overall stress distribution of the turbine disk is improved. At the same time, due to the presence of holes, the mass of the turbine disk is also reduced. Background Art

[0002] Traditional turbine discs use a single-spoke plate structure, which has reached its structural design limit, severely restricting the further development of engines. With the development of 3D printing technology, the manufacturing bottleneck of novel turbine disc structures has been overcome, and the innovative design of turbine discs with higher load-bearing capacity and lighter weight has become one of the core technologies in the design of aircraft engines and gas turbines.

[0003] The patent Twin-web rotor disk (U.S. Patent No. 5,961,287, 1999-10-5) mentions a new type of double-web turbine disk that is different from the previous single-web. This turbine disk is composed of two front and rear webs in the axial direction, and the two webs form a central disk cavity. Compared with the single-web turbine disk, the double-web can reduce the weight by 1 / 4 compared with the single-web turbine disk while meeting the requirements of wheel strength and stiffness. Due to the outstanding advantages of the double-web turbine disk, the United States' Integrated High Performance Turbine Engine Technology Program (IHPTET) (USDepartment of Defense. Integrated high performance turbine engine technology (IHPTET) [R]. Gas Turbine Forecast, Archived, 2006) designated the double-web turbine disk as the future development trend of the high-pressure turbine disk structure.

[0004] The typical structure of the double-web turbine disk proposed in the patent Twin-web rotor disk (U.S. Patent No. 5,961,287, 1999-10-5) generally has a symmetrical structure in the radial section. However, for different types of aircraft engines and high-pressure gas turbines, the radial and tangential forces of the turbine disk are different under centrifugal loads and aerodynamic loads. The load state is very complex and asymmetrical. A symmetrical structure is subjected to complex asymmetric loads, and its stress uniformity is inevitably affected. Therefore, the double-web structure is not the optimal structure for the turbine disk. Further research on the load conditions of the turbine disk during operation and designing a turbine disk with uniform force and light weight while meeting the strength and stiffness requirements are of great significance for improving the performance of aircraft engines and gas turbines.

[0005] With the expansion of the application field of structural topology optimization, the research on topology optimization methods of structures under various load conditions has attracted attention in the engineering field. Inertial loads, as common design-related loads, exist in many structures. For example, in large civil buildings, the deadweight of the structure is usually one of the important loads that cannot be ignored; in steam turbines and aerospace vehicles, the structure is subject to inertial loads caused by acceleration or angular velocity. For example, the turbine of an aircraft engine has to withstand huge centrifugal forces when working, and the load-bearing structure of the aircraft has to withstand inertial loads caused by acceleration during the launch phase.

[0006] However, in the case of variable density topology optimization, firstly, the traditional SIMP interpolation model will have "material attachment effect" under inertial load, and secondly, the overall flexibility of the structure under inertial load is not monotonic to the structural parameters (unit density), and its sensitivity is no longer always negative. Therefore, the solution algorithm of the optimization criterion method cannot solve the topology optimization problem under inertial load conditions. Third, excessive grayscale suppression in the solution process will lead to convergence to a non-optimal solution, while too weak will lead to non-convergence or too many grayscale units. The present invention uses the EAMP interpolation model to propose a load sensitivity suppression method and a dynamic grayscale suppression method. Based on the present invention, an optimized structure of a three-spoke turbine disk is obtained, and a method is provided to solve the sensitivity non-monotonicity problem and the problem of many grayscale units and unclear boundaries in the topological structure in the topological optimization of inertial loads based on the optimization criterion method, which is suitable for the structural topology optimization design method of inertial loads. Summary of the invention

[0007] In view of the above technical problems, the present invention provides a topology optimization method based on sensitivity and dynamic grayscale suppression, aiming to provide a turbine disk structure that adapts to the working environment of aircraft engines and gas turbine turbines, improves the stress distribution uniformity of the turbine disk under centrifugal load and aerodynamic load, improves the load-bearing capacity of the turbine disk, and reduces the weight of the turbine disk body structure.

[0008] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0009] A three-spoke turbine disc, the turbine disc comprising a rim 1, a hub 2 and a spoke plate structure connecting the rim 1 and the hub 2, the spoke plate structure comprising a front spoke plate 3, a middle spoke plate and a rear spoke plate, the front spoke plate 3, the middle spoke plate and the rear spoke plate are connected to the rim 1 at their upper ends and to the hub 2 at their lower ends.

[0010] Furthermore, the middle spoke plate and the rear spoke plate are arranged crosswise.

[0011] Furthermore, the middle spoke plate and the rear spoke plate are cross-arranged to form a middle spoke plate upper portion 7, a middle spoke plate lower portion 4, a rear spoke plate upper portion 6 and a rear spoke plate lower portion 5, the middle spoke plate upper portion 7 and the rear spoke plate upper portion 6 are connected to the wheel rim 1, and the middle spoke plate lower portion 4 and the rear spoke plate lower portion 5 are connected to the wheel hub 2.

[0012] Furthermore, a first hole 8 is formed between the front spoke 3, the upper portion of the rear spoke 6 and the lower portion of the middle spoke 4, a third hole 10 is formed between the upper portion of the middle spoke 7, the upper portion of the rear spoke 6 and the rim 1, and a second hole 9 is formed between the lower portion of the middle spoke 4, the lower portion of the rear spoke 5 and the wheel hub 2.

[0013] Furthermore, the rear spoke plate has an arc-shaped structure.

[0014] Furthermore, the three-spoke turbine disc is made by 3D printing.

[0015] A three-spoke turbine disc, the turbine disc comprising a rim 1, a hub 2 and a spoke plate structure connecting the rim 1 and the hub 2, the spoke plate structure comprising a front spoke plate 3, a middle spoke plate and a rear spoke plate, the front spoke plate 3, the middle spoke plate and the rear spoke plate are connected to the rim 1 at their upper ends and to the hub 2 at their lower ends, the middle spoke plate and the rear spoke plate are arranged crosswise; the middle spoke plate and the rear spoke plate are arranged crosswise to form a middle spoke plate upper part 7, a middle spoke plate lower part 4, and a rear spoke plate upper part 6 and the rear spoke lower part 5, the middle spoke upper part 7 and the rear spoke upper part 6 are connected to the wheel rim 1, and the middle spoke lower part 4 and the rear spoke lower part 5 are connected to the wheel hub 2; a first hole 8 is formed between the front spoke 3, the rear spoke upper part 6 and the middle spoke lower part 4, a third hole 10 is formed between the middle spoke upper part 7, the rear spoke upper part 6 and the wheel rim 1, and a second hole 9 is formed between the middle spoke lower part 4, the rear spoke lower part 5 and the wheel hub 2; the rear spoke has an arc-shaped structure.

[0016] An engine is provided with the above three-spoke turbine disk.

[0017] A design method for manufacturing the above-mentioned three-spoke turbine disk based on topology optimization is characterized by comprising the following steps:

[0018] (1) Establish a topology optimization design domain for the radial section of the turbine disk, with a length of L and a width of D. Set the non-topology optimization design domain on the rim of the turbine disk according to the size of the turbine blades. The radius of the turbine disk shaft is r, and the speed is ω. The displacement constraint is fixed on one side of the turbine disk shaft. The global centrifugal force is F1, the radial component of the impeller centrifugal force and the aerodynamic load is F2, and the tangential component of the aerodynamic load is F3. The material density is ρ0, the elastic modulus is E0, and the volume constraint fraction is f.

[0019] (2) Design of mathematical model for topology optimization: The mathematical model for topology optimization based on variable density method and taking structural flexibility as the target is as shown in formula (1):

[0020]

[0021] Where x is the relative density of the finite element in the design domain; n is the total number of elements; C is the structural flexibility; K, U and F are the overall stiffness matrix, displacement vector and load vector of the structure respectively; v i is the unit volume; V0 and f are the initial design domain volume and volume fraction respectively; x min is the lower limit of the design variable;

[0022] (3) Using an EAMP material interpolation model, the mathematical expression is as shown in formula (2). Based on this model, according to the unit relative density and the unit elastic modulus E(x i )for:

[0023]

[0024]

[0025] (4) According to the finite element calculation, the displacement matrix U of the turbine disk section is obtained, and the objective function, i.e., the structural strain energy C, is further calculated;

[0026] (5) Sensitivity calculation, the sensitivity of the objective function to the unit density.

[0027]

[0028] in

[0029]

[0030]

[0031] (6) According to the optimization criterion method, the mathematical model (1) is solved iteratively:

[0032]

[0033] Where k is the number of iterations, η is the damping coefficient, and m is the moving step size; is an iterative solution format, λ1 is the Lagrange multiplier; based on the Lagrange function and the KT condition, expression (8) can be easily derived:

[0034]

[0035] (7) A load sensitivity suppression method is proposed. A load sensitivity suppression factor is added to expression (8); through the suppression effect of this factor, the objective function remains monotonic; the expression after adding the load sensitivity suppression factor is shown in equation (9):

[0036]

[0037] in, is the load sensitivity suppression factor, and the value of s is as follows (10):

[0038]

[0039] The value range of l can be from extremely small to infinite. Different values ​​of l represent different degrees of suppression of load sensitivity. The smaller l is, the smaller the suppression is, that is, the more load sensitivity is retained; the larger l is, the greater the suppression is, that is, the less load sensitivity is retained;

[0040] (8) A dynamic grayscale suppression method is proposed. Based on the grayscale suppression method, the new iterative format (11) is:

[0041]

[0042] Where q is the dynamic grayscale suppression factor that changes with the number of optimization steps, as shown in equation (12);

[0043] q=1+δk (12)

[0044] Among them, δ is the suppression step length, which can take different values ​​according to the specific optimization problem, generally 0.02 or less, which is related to the number of iterations of the optimization problem;

[0045] (9) Convergence judgment: According to the convergence condition formula (13), it is judged whether the updated design variable-unit density has reached convergence; if the convergence condition is not met, the next step of iteration is continued until the convergence condition is met;

[0046]

[0047] in, and are the i-unit densities of the k+1th and kth times respectively, ε is the convergence accuracy, which can generally be taken as 0.001 or less.

[0048] Compared with the prior art, the present invention has the following beneficial effects: it can effectively bear the centrifugal load of the turbine blades on the wheel rim and the turbine disc itself; the arc structure of the rear spoke plate and the supporting structure is conducive to bearing the aerodynamic tangential load transmitted by the turbine blades on the wheel rim; the arrangement of the holes makes the turbine disc lightweight; and the strength and stiffness requirements are met. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic diagram of the structure of a three-hole three-spoke turbine disk of the present invention;

[0050] Figure 2 The topological optimization geometric model of the present invention;

[0051] Figure 3 The EAMP material interpolation model of the present invention;

[0052] Figure 4 The present invention optimizes the flow chart;

[0053] Figure 5 A schematic diagram of the structure of a turbine disk with four holes and three spokes according to the present invention;

[0054] Figure 6 A schematic diagram of the structure of a turbine disk with five holes and three spokes according to the present invention;

[0055] Figure 7 The conventional single-spoke turbine disc structure, the typical double-spoke turbine disc and the three-spoke turbine disc structure of the present invention;

[0056] Figure 8 Finite element analysis of traditional single-spoke turbine disk structure;

[0057] Fig. 9 Finite element analysis of a typical double-spoke turbine disk structure;

[0058] Fig.10 Finite element analysis of turbine disk structure with three spokes 1;

[0059] Fig.11 Finite element analysis of three-spoke plate structure 2 turbine disk structure

[0060] In the figure, the rim 1, the hub 2, the front spoke 3, the lower part of the middle spoke 4, the lower part of the rear spoke 5, the upper part of the rear spoke 6, the upper part of the middle spoke 7, the first hole 8, the second hole 9, the third hole 10, the first fork 11, the second fork 12, and the fourth hole 13. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0062] In the description of the present invention, it is to be understood that the terms “center”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “axial”, “circumferential”, etc., indicating orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0063] In the present invention, unless otherwise clearly specified and limited, the terms "set", "install", "connect", "connect", "fix" and the like should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection; it can be a mechanical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0064] In addition, the terms "first", "second", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features.

[0065] Embodiment 1

[0066] like Figure 1 As shown, a three-spoke turbine disc comprises a rim 1, a hub 2 and a spoke structure connecting the rim 1 and the hub 2, wherein the spoke structure comprises a front spoke 3, a middle spoke and a rear spoke, wherein the upper ends of the front spoke 3, the middle spoke and the rear spoke are connected to the rim 1, and the lower ends are connected to the hub 2.

[0067] Embodiment 2

[0068] On the basis of the first embodiment, it is further configured that the middle spoke plate and the rear spoke plate are cross-arranged.

[0069] Embodiment 3

[0070] On the basis of embodiment 1, it is further configured that the middle spoke plate and the rear spoke plate are cross-arranged to form a middle spoke plate upper portion 7, a middle spoke plate lower portion 4, a rear spoke plate upper portion 6 and a rear spoke plate lower portion 5, the middle spoke plate upper portion 7 and the rear spoke plate upper portion 6 are connected to the wheel rim 1, and the middle spoke plate lower portion 4 and the rear spoke plate lower portion 5 are connected to the wheel hub 2.

[0071] Embodiment 4

[0072] On the basis of the third embodiment, the fourth embodiment is that a first hole 8 is formed between the front spoke 3, the upper part of the rear spoke 6 and the lower part of the middle spoke 4, a third hole 10 is formed between the upper part of the middle spoke 7, the upper part of the rear spoke 6 and the rim 1, and a second hole 9 is formed between the lower part of the middle spoke 4, the lower part of the rear spoke 5 and the wheel hub 2.

[0073] Embodiment 5

[0074] On the basis of the fourth embodiment, the fifth embodiment is that the rear spoke plate has an arc-shaped structure.

[0075] The three spokes in the above embodiments can all be made by 3D printing. Based on the above improvements to the turbine disk, the turbine disk in the present invention can be applied to aircraft engines.

[0076] Since the turbine disc not only needs to bear the centrifugal load generated by high-speed rotation but also needs to bear the large radial force and tangential force brought by the turbine blades, compared with the ordinary single-spoke plate and double-spoke plate structures, the three-spoke plate turbine disc not only adds a middle spoke plate, but also adds an oblique support structure. By adding the middle spoke plate and the support structure, the overall bearing capacity of the turbine disc is enhanced, so that the overall comprehensive displacement and stress of the turbine disc are effectively reduced. The stress distribution of the turbine disc is improved, and the life of the turbine disc is increased.

[0077] For the above three-spoke turbine disc, the design method of the present invention is as follows:

[0078] 1. Establish the topology optimization design domain of the turbine disk radial section as follows Figure 2 As shown in the figure, the length L and width D of the design domain are taken according to the actual engineering values; the turbine disk rim is set as the non-topological optimization design domain according to the size of the turbine blades, that is, the size of the turbine disk rim where the turbine blades are installed ( Figure 2 The black part in the figure is the non-topology optimization design domain; the radius of the turbine disk shaft is r, and the speed is ω; the displacement constraint on one side of the turbine disk shaft is fixed; the global centrifugal force is F1, the radial component of the impeller centrifugal force and the aerodynamic load is F2, and the tangential component of the aerodynamic load is F3; the material density is ρ0, and the elastic modulus is E0; the volume constraint fraction is f;

[0079] 2. Design of topology optimization mathematical model: The topology optimization mathematical model based on variable density method with structural flexibility as the target is as shown in formula (1):

[0080]

[0081] Where x is the relative density of the finite element in the design domain; n is the total number of elements; C is the structural flexibility; K, U and F are the overall stiffness matrix, displacement vector and load vector of the structure respectively; v i is the unit volume; V0 and f are the initial design domain volume and volume fraction respectively; x min is the lower limit of the design variable;

[0082] 3. Use an EAMP material interpolation model, the mathematical expression is as shown in formula (2). Based on this model, according to the unit relative density and the unit elastic modulus E(x i )for:

[0083]

[0084]

[0085] 4. According to the finite element calculation, the displacement matrix U of the turbine disk section is obtained, and the objective function, i.e., the structural strain energy C, is further calculated;

[0086] 5. Sensitivity calculation, the sensitivity of the objective function to the unit density.

[0087]

[0088] in

[0089]

[0090]

[0091] 6. According to the optimization criterion method, the mathematical model (1) is solved iteratively:

[0092]

[0093] Where k is the number of iterations, η is the damping coefficient, and m is the moving step size; is the iterative solution format; λ1 is the Lagrange multiplier. Based on the Lagrange function and the KT condition, it is easy to derive the expression (8):

[0094]

[0095] 7. A load sensitivity suppression method is proposed. A load sensitivity suppression factor is added to expression (8); through the suppression effect of this factor, the objective function remains monotonic; the expression after adding the load sensitivity suppression factor is shown in equation (9):

[0096]

[0097] in, is the load sensitivity suppression factor, and the value of s is as follows (10):

[0098]

[0099] The value range of l can be from extremely small to infinite. Different values ​​of l represent different degrees of suppression of load sensitivity. The smaller l is, the smaller the suppression is, that is, the more load sensitivity is retained; the larger l is, the greater the suppression is, that is, the less load sensitivity is retained;

[0100] 8. A dynamic grayscale suppression method is proposed. Based on the grayscale suppression method, the new iterative format (11) is:

[0101]

[0102] Where q is the dynamic grayscale suppression factor that changes with the number of optimization steps, as shown in equation (12);

[0103] q=1+δk (12)

[0104] Among them, δ is the suppression step length, which can take different values ​​according to the specific optimization problem, generally 0.02 or less, which is related to the number of iterations of the optimization problem;

[0105] 9. Convergence judgment: According to the convergence condition formula (13), it is judged whether the updated design variable - unit density has reached convergence; if the convergence condition is not met, the next step of iteration is continued until the convergence condition is met;

[0106]

[0107] in, and are the i-unit densities of the k+1th and kth times respectively, ε is the convergence accuracy, which can generally be taken as 0.001 or less.

[0108] Compared with traditional single-spoke and double-spoke turbine discs, the present invention is suitable for more complex load conditions. The added middle spoke and supporting structure improve the circumferential, radial and axial load-bearing capacity of the connection between the spoke and the rim and the hub, improve the uniformity of stress distribution of the turbine disc, and at the same time, due to the presence of the holes, the mass of the turbine disc is also reduced.

[0109] like Figure 7 As shown, the traditional single-spoke plate, double-spoke plate turbine disc structure and two three-spoke plate structures based on the present invention are shown, wherein the two three-spoke plate structures are designed under the conditions of Table 1 using the topology optimization method of the present invention: the three-spoke plate structure 1 is equivalent to the single-spoke plate structure in mass (reduced by 1%) and equivalent to the typical double-spoke plate structure in mass (reduced by 2%); the three-spoke plate structure 2 is 11% lighter than the single-spoke plate structure and 12% lighter than the typical double-spoke plate structure.

[0110] Through finite element calculation, the comprehensive displacement, maximum VM stress of the radial plate, and overall average stress of various turbine disks are compared as shown in the following table:

[0111] Table 1 Comparison between the conventional single-spoke turbine disc and the three-spoke structure 1

[0112]

[0113] Table 2 Comparison between the conventional single-spoke turbine disc and the three-spoke structure 2

[0114]

[0115]

[0116] Table 3 Typical double-spoke turbine disc compared with three-spoke structure 1

[0117]

[0118] Table 4 Typical double-spoke turbine disc compared with three-spoke structure 2

[0119]

[0120] It can be seen from the above table that when the mass of the typical double-web plate is equivalent to that of the traditional single-web plate, the comprehensive displacement, maximum VM stress, and overall average stress of the double-web plate are reduced, indicating that the performance of the double-web turbine disk proposed based on the patent Twin-web rotor disk (U.S. Patent No. 5,961,287, 1999-10-5) is improved compared with the traditional single-web turbine disk. It can be seen from Tables 1 and 3 that when the overall mass of the three-web plate 1 is basically equivalent to that of the traditional single-web plate and the typical double-web plate, its comprehensive displacement, maximum VM stress, and overall average stress are greatly reduced. It can be seen from Tables 2 and 4 that when the overall mass of the three-web plate 2 is reduced by 11% and 12% respectively compared with the traditional single-web plate and the typical double-web plate, the comprehensive displacement, maximum VM stress, and overall average stress of the three-web plate 2 are also greatly reduced. Therefore, it can be concluded that the three-web turbine disk of the present invention has better working performance than the traditional single-web plate and the typical double-web turbine disk, and its excellent effect can be seen from Figure 8 , 9 , 10, and 11.

[0121] Reference Figure 5 , Figure 6 The number of holes can be three, four, five or more. It is just a structural change without deviating from the essence of the three-spoke plate.

[0122] Compared with the prior art, the present invention has the following beneficial effects: it can effectively bear the centrifugal load of the turbine blades on the wheel rim and the turbine disc itself; the arc structure of the rear spoke plate and the supporting structure is conducive to bearing the aerodynamic tangential load transmitted by the turbine blades on the wheel rim; the arrangement of the holes makes the turbine disc lightweight; and the strength and stiffness requirements are met.

[0123] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A topology optimization method based on sensitivity and dynamic grayscale suppression, characterized in that: The following steps are included: (1) Establish a topology optimization design domain for the radial section of the turbine disk, with a length of L and a width of D. Set the non-topology optimization design domain on the rim of the turbine disk according to the size of the turbine blades. The radius of the turbine disk shaft is r, and the speed is ω. The displacement constraint is fixed on one side of the turbine disk shaft. The global centrifugal force is F1, the radial component of the impeller centrifugal force and the aerodynamic load is F2, and the tangential component of the aerodynamic load is F3. The material density is ρ0, the elastic modulus is E0, and the volume constraint fraction is f. (2) Design of mathematical model for topology optimization: The mathematical model for topology optimization based on variable density method and taking structural flexibility as the target is as shown in formula (1): Where x is the relative density of the finite element in the design domain; n is the total number of elements; C is the structural flexibility; K, U and F are the overall stiffness matrix, displacement vector and load vector of the structure respectively; v i is the unit volume; V0 and f are the initial design domain volume and volume fraction respectively; x min is the lower limit of the design variable; (3) Using an EAMP material interpolation model, the mathematical expression is as shown in formula (2). Based on this model, according to the unit relative density and the unit elastic modulus E(x i )for: (4) According to the finite element calculation, the displacement matrix U of the turbine disk section is obtained, and the objective function, i.e., the structural strain energy C, is further calculated; (5) Sensitivity calculation: the sensitivity of the objective function to the cell density. in (6) According to the optimization criterion method, the mathematical model (1) is solved iteratively: Where k is the number of iterations, η is the damping coefficient, and m is the moving step size; It is an iterative solution format; based on the Lagrangian function and the KT condition, expression (8) can be easily derived: (7) A load sensitivity suppression method is proposed, in which a load sensitivity suppression factor is added to expression (8); through the suppression effect of this factor, the objective function remains monotonic; the expression after adding the load sensitivity suppression factor is shown in equation (9): in, is the load sensitivity suppression factor, and the value of s is as follows (10): The value range of l can be from extremely small to infinite. Different values ​​of l represent different degrees of suppression of load sensitivity. The smaller l is, the smaller the suppression is, that is, the more load sensitivity is retained; the larger l is, the greater the suppression is, that is, the less load sensitivity is retained; (8) A dynamic grayscale suppression method is proposed. Based on the grayscale suppression method, the new iterative format (11) is: Where q is the dynamic grayscale suppression factor that changes with the number of optimization steps, as shown in equation (12); q=1+δk (12) Among them, δ is the suppression step length, which can take different values ​​according to the specific optimization problem, taking 0.02 or less, which is related to the number of iterations of the optimization problem; (9) Convergence judgment: According to the convergence condition formula (13), it is judged whether the updated design variable-unit density has reached convergence; if the convergence condition is not met, the next step of iteration is continued until the convergence condition is met; in, and are the i-unit densities of the k+1th and kth times respectively, and ε is the convergence accuracy, which can be 0.001 or less.

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