Rotor system integrated topological optimization design method considering critical rotating speed

Abstract

The invention relates to a rotor system integrated topological optimization design method considering dynamic performance, and belongs to the technical field of high-performance calculation science, and the method comprises the following steps: taking statics and rotor dynamics as constraint conditions for a rotor two-dimensional structure, carrying out two-dimensional topological optimization design, and obtaining a new rotor two-dimensional structure; and on the basis of the new two-dimensional structure of the rotor, three-dimensional topological optimization design is carried out on the sector model of the rotor by taking the rotation period structure frequency and the statics property as constraint conditions, and a new three-dimensional configuration is obtained. According to the method, on the basis of traditional topological optimization which only considers the static performance, the constraint on the dynamic performance is increased, the dynamic performance requirement needed by the rotor system can be met while the maximum rigidity design is completed, the design period can be effectively shortened, and the design efficiency can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of major equipment design technology, and relates to an integrated topology optimization design method for rotor systems that considers critical speed. Background Technology

[0002] Structural optimization design, based on structural analysis techniques, is a technology that aims to design engineering structures within a given design space that meet usage requirements and achieve optimal performance or lowest cost. Structural optimization design generally consists of three levels: dimensional optimization, shape optimization, and topology optimization. Dimensional optimization corresponds to the detailed design stage of the structure. In this stage, the structure type, materials, and topology are fixed, and the design parameters are the geometric dimensions of the components, such as plate thickness and the length and width of beam interfaces. Shape optimization corresponds to the basic design stage, focusing on the geometric shape of the structure's boundary contours or internal voids, but the initial and optimized structures share the same topological layout. The goal of shape optimization is mostly to reduce stress concentration and improve the stress distribution of the structure. Topology optimization corresponds to the conceptual design stage, focusing on the material distribution of the structure to seek the optimal distribution of structural stiffness in the design space or the optimal force transmission path within the design domain. Compared to dimensional and shape optimization, topology optimization offers more design freedom, a larger design space, and better optimization results, and has developed rapidly in the last thirty years, making it a challenging research direction in the field of structural optimization.

[0003] According to the type of design variables and the difficulty of solving the problem, the optimization of continuum structures can be divided into three levels: size optimization (size variables), shape optimization (shape variables), and topology optimization (topology variables), which correspond to three different product design stages: conceptual design, basic design, and detailed design.

[0004] Sizing optimization seeks the optimal combination of cross-sectional dimensions and material properties for structural components while maintaining the shape and topology of the structure. This includes optimizing the optimal area of ​​cross-sections (e.g., trusses) and selecting the optimal thickness of plates. Its advantages include: easily expressible design variables and mature solution theories and methods.

[0005] Shape optimization: Optimization maintains the structural topology while changing the shape and boundary of the design domain, seeking the most ideal boundary and geometry of the structure. In skeleton structures, this manifests as optimizing the optimal position of nodes, while in solid structures, it manifests as optimizing the boundary shape of the structure.

[0006] Topology optimization seeks the optimal configuration of the location and quantity of non-solid regions within a defined continuous region, optimizing the component layout and node connections to ensure the structure can transfer external loads to supports while meeting stress and displacement constraints, and simultaneously optimizing certain structural performance indicators. A subset Ω is selected on the continuum Ω. m The goal is to satisfy the objective function and constraints. For truss structures, topology optimization involves determining the optimal connection relationships between nodes given their locations. For continuous structures, topology optimization requires not only changing the boundary shape but also optimizing the number and shape distribution of voids. The main difficulty lies in the fact that there are many possible topologies that meet certain requirements, which are difficult to quantitatively describe or parameterize. Furthermore, the area to be designed is often unknown beforehand, significantly increasing the difficulty of solving topology optimization problems.

[0007] Topology optimization is a higher-level optimization method than size optimization and shape optimization, and it is also one of the most complex problems in structural optimization. Topology optimization is performed in the conceptual design stage of a structure, and its optimization result forms the basis for all subsequent designs. When the initial topology of a structure is not optimal, size and shape optimization may lead to suboptimal structures; therefore, it is necessary to determine the optimal topology of the structure in the initial conceptual design stage. The three levels of structural optimization play different roles and have different tasks in the optimization process, playing a crucial role in the product design and development process. Summary of the Invention

[0008] To address the aforementioned problems, the technical solution adopted by this invention is: an integrated topology optimization design method for rotor systems considering dynamic performance, comprising the following steps:

[0009] S1. For the two-dimensional rotor structure, statics and rotor dynamics are used as constraints to perform two-dimensional topology optimization design to obtain a new two-dimensional rotor structure.

[0010] S2. Based on the new two-dimensional rotor structure, the rotational periodic structure frequency and static performance are used as constraints to perform three-dimensional topology optimization design on the rotor sector model to obtain a new three-dimensional configuration.

[0011] Furthermore: the topology optimization formula used in the two-dimensional topology optimization design is as follows:

[0012]

[0013] Where α is a topology design variable vector, used to describe the presence or absence of support points within a region; ρ eThis refers to the material density of the e-th element, N is the number of mesh elements, K is the structural stiffness matrix, and M is the mass moment.

[0014] C is the damping matrix, G is the gyroscope matrix, F is the load vector, and U is the displacement vector. For velocity vectors, Let Ω be the acceleration vector. i Ω0 is the structural critical speed, ε is the structural operating speed, and v is the avoidance margin. e V is the unit volume. * ρ represents the volumetric material usage, and ρ is a topology design variable vector used to describe the presence or absence of material within a region.

[0015] Furthermore: the topology optimization formula used in the three-dimensional topology optimization design is as follows:

[0016]

[0017] Where: ρ is the pseudo-density vector of the structural design domain, where each design variable ρ i The range of values ​​is from the minimum value ρ min Between and the maximum value of 1, K r φ r =λ r M r φ r Here are the eigenvalue equations for each section of the structure, and the physical equilibrium equations for finite element analysis. K r M is the stiffness matrix of the structure. r Let λ be the mass matrix. r φ is the eigenvalue of the structure. r ρ is the vibration mode vector; e For the pseudo density of the unit cell, v e Let f be the volume of the element, used as the optimization objective; r,j To specify the natural frequency of a structure with a given nodal diameter and order, f lower f is the lower bound of the natural frequency constraint. upper This is the upper limit of the constraint on the natural frequency.

[0018] Furthermore, the topology optimization design and the three-dimensional topology optimization design employ the following topology methods:

[0019] Step 1: Initialize the pseudo-density design variable ρ, construct the Helmholtz anisotropic linear filter field, and initialize the Heaviside function;

[0020] Step 2: Apply a Helmholtz field to ρ using linear filtering to obtain the density after linear filtering. Using the Heaviside nonlinear mapping function to The density is obtained after processing and nonlinear mapping.

[0021] Step 3: Use the MSIMP interpolation model to map the variables after nonlinear mapping. Interpolate to material properties and solve for the stiffness matrix K of the current iteration step. r and mass matrix M r And solve the structural eigenvalue equations to obtain the natural frequency response of the structure, and at the same time solve the volume fraction of the current iteration step;

[0022] Step 4: Construct a target with a specific frequency and a volume fraction function;

[0023] Step 5: Solve for the density after nonlinear mapping of the constraint function and the objective function. The sensitivity of the constraint function and the objective function to the pseudo-density ρ is determined by the chain rule.

[0024] Step 6: Based on the values ​​and sensitivities of the objective function and constraint functions, use the moving asymptote method to solve the structural optimization problem and update the design variables;

[0025] Step 7: Update the Heaviside function;

[0026] Step 8: Perform optimization convergence condition judgment, that is, when the residual of the objective function is less than ε0, or the number of iterations reaches the maximum, if the convergence condition is further determined: the solution process of the constraint value of the rotor dynamics is as follows:

[0027] S11. In the dynamic analysis of axisymmetric rotor structures based on traditional dynamic formulas, add a gyroscope matrix G;

[0028] S12. Solve the dynamic equilibrium equations of the structural rotor using the complex characteristic solution method, and obtain the dynamic characteristics of the structural rotor.

[0029] S13. When the rotor's critical speed equals the excitation force acting on the rotor, which is the rotor's own unbalanced force, the corresponding eigenvector solution of the synchronous positive precession of the rotor system caused by this excitation force is:

[0030]

[0031] φ(t) is the eigenvector, φ0 is the magnitude of the eigenvector, e is the base, i is the complex number, t is the frequency, and Ω is the eigenvector. i It is the critical speed.

[0032] Based on the feature vectors, we obtain:

[0033]

[0034] The critical speed of the structure can be obtained by solving the above formula.

[0035] Furthermore, the process for determining the constraint value of the frequency of the rotating periodic structure is as follows:

[0036] The eigenvalue equations of the three-dimensional structure are as follows:

[0037] K=λM

[0038] Where K and M are the stiffness matrix and mass matrix of the structure, respectively, and λ is the eigenvalue of the structure, relating the natural frequency of the structure to the following equation: λ = 4π 2 f 2 Where Φ is the modal vector of the structure; and simultaneously, U = e iωt Mφ ensures that the orthogonal normalization condition is met:

[0039]

[0040] For rotationally periodically symmetric boundary conditions, there is an interaction between the two symmetric planes, which allows the eigenvalue response of the structure to be solved using the wave propagation principle.

[0041] This invention provides an integrated topology optimization design method for rotor systems considering critical speeds. By considering critical speeds, this invention can simultaneously perform traditional topology optimization design and take into account the critical speeds of the rotor system, thus achieving better integrated rotor system design, improving design efficiency, and shortening the rotor system design cycle. The method includes: using structural strength as the objective and mass, critical speed, and dynamic performance as constraints, conducting topology optimization design considering the structural rotor dynamic performance. The beneficial effects of this invention are manifested in the following aspects:

[0042] 1. The method of the present invention adds constraints on dynamic performance to the traditional topology optimization that only considers static performance. It can meet the dynamic performance requirements of the rotor system while completing the maximum stiffness design, which can effectively shorten the design cycle and improve the design efficiency.

[0043] 2. The method of the present invention adds a method for solving the frequency sensitivity of rotating periodic structures to the traditional solution method, thereby realizing the sensitivity solution at the element level.

[0044] 3. The method of this invention adds a critical speed sensitivity analysis method to the traditional solution method, thereby realizing the solution of the critical speed of the structure. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is an integrated topology optimization design method for rotor systems that considers critical speeds;

[0047] Figure 2 Example 1 - Two-dimensional rotor dynamics calculation model;

[0048] Figure 3 The results of topology optimization for the static objective of a multi-level roulette wheel are shown in Example 1.

[0049] Figure 4 The results of topology optimization for multi-stage wheel rotor dynamics are shown in Example 1.

[0050] Figure 5 Example 2-1 / 24 sector wheel calculation;

[0051] Figure 6 The results of the 2-1 / 24 sector wheel calculation example are shown in (a) and (b) respectively. Detailed Implementation

[0052] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] An integrated topology optimization design method for rotor systems considering dynamic performance includes the following steps:

[0055] S1. For the two-dimensional rotor structure, statics and rotor dynamics are used as constraints to perform two-dimensional topology optimization design to obtain a new two-dimensional rotor structure.

[0056] S2. Based on the new two-dimensional rotor structure, the rotational periodic structure frequency and static performance are used as constraints to perform three-dimensional topology optimization design on the rotor sector model to obtain a new three-dimensional configuration.

[0057] Steps S1 and S2 are executed sequentially;

[0058] The topology optimization methods used in two-dimensional and three-dimensional topology optimization designs are as follows:

[0059] Step 1: Initialize the pseudo-density design variable ρ, construct the Helmholtz anisotropic linear filter field, and initialize the Heaviside function;

[0060] Step 2: Apply a Helmholtz field to ρ using linear filtering to obtain the density after linear filtering. Using the Heaviside nonlinear mapping function to The density is obtained after processing and nonlinear mapping.

[0061] Step 3: Use the MSIMP interpolation model to map the variables after nonlinear mapping. Interpolate to material properties and solve for the stiffness matrix K of the current iteration step. r and mass matrix M r And solve the structural eigenvalue equations to obtain the natural frequency response of the structure, and at the same time solve the volume fraction of the current iteration step;

[0062] Step 4: Construct a target with a specific frequency and a volume fraction function;

[0063] Step 5: Solve for the density after nonlinear mapping of the constraint function and the objective function. The sensitivity of the constraint function and the objective function to the pseudo-density ρ is determined by the chain rule.

[0064] Step 6: Based on the values ​​and sensitivities of the objective function and constraint functions, use the Moving Asymptotic Method (MMA) to solve the structural optimization problem and update the design variables;

[0065] Step 7: Update the Heaviside function;

[0066] Step 8: Perform optimization convergence condition judgment, that is, when the residual of the objective function is less than ε0, or when the number of iterations reaches the maximum, if convergence is achieved, the optimization iteration converges; otherwise, return to step 2 to continue iteration.

[0067] The topology optimization formula used in the two-dimensional topology optimization design is as follows:

[0068]

[0069] Where α is a topology design variable vector, used to describe the presence or absence of support points within a region; ρ e This refers to the material density of the e-th unit.

[0070] N represents the number of meshes, K is the structural stiffness matrix, M is the mass matrix, C is the damping matrix, G is the gyroscope matrix, F is the load vector, and U is the displacement vector. For velocity vectors, Let Ω be the acceleration vector. i Ω0 is the structural critical speed, ε is the structural operating speed, and v is the avoidance margin. e V is the unit volume. * ρ represents the volumetric material usage, and ρ is a topology design variable vector used to describe the presence or absence of material within a region.

[0071] The topology optimization formula used in the three-dimensional topology optimization design is as follows:

[0072]

[0073] Where: ρ is the pseudo-density vector of the structural design domain, where each design variable ρ i The range of values ​​is from the minimum value ρ min Between and the maximum value of 1, K r φ r =λ r M r φ r Here are the eigenvalue equations for each section of the structure, and the physical equilibrium equations for finite element analysis. K r M is the stiffness matrix of the structure. r Let λ be the mass matrix. r φ is the eigenvalue of the structure. r ρ is the vibration mode vector; e For the pseudo density of the unit cell, v e Let f be the volume of the element, used as the optimization objective; r,j To specify the natural frequency of a structure with a given nodal diameter and order, f lower f is the lower bound of the natural frequency constraint. upper This is the upper limit of the constraint on the natural frequency.

[0074] The process of solving the constraint values ​​of the rotor dynamics is as follows:

[0075] S11. In the dynamic analysis of axisymmetric rotor structures based on traditional dynamic formulas, add a gyroscope matrix G;

[0076] S12. Solve the dynamic equilibrium equations of the structural rotor using the complex characteristic solution method, and obtain the dynamic characteristics of the structural rotor.

[0077] S13. When the rotor's critical speed equals the excitation force acting on the rotor, which is the rotor's own unbalanced force, the corresponding eigenvector solution of the synchronous positive precession of the rotor system caused by this excitation force is:

[0078]

[0079] Where: φ(t) is the eigenvector, φ0 is the magnitude of the eigenvector, e is the base, i is the complex number, t is the frequency, and Ω is the eigenvalue. i It is the critical speed;

[0080] Based on the feature vectors, we obtain:

[0081]

[0082] The critical speed of the structure can be obtained by solving the above formula.

[0083] The process for solving the constraint value of the frequency of the rotating periodic structure is as follows:

[0084] The eigenvalue equations of the three-dimensional structure are as follows:

[0085] K=λM

[0086] Where K and M are the stiffness matrix and mass matrix of the structure, respectively, and λ is the eigenvalue of the structure, relating the natural frequency of the structure to the following equation: λ = 4π 2 f 2 Where Φ is the modal vector of the structure; and simultaneously, U = e iωt Mφ ensures that the orthogonal normalization condition is met:

[0087]

[0088] For rotationally periodically symmetric boundary conditions, there is an interaction between the two symmetric planes, which allows the eigenvalue response of the structure to be solved using the wave propagation principle.

[0089] Example 1

[0090] Reconstruct the simple multi-level roulette wheel example, the example model is as follows: Figure 2 As shown, the bottom shaft and the 10mm area at the top of each disc are defined as the non-design domain. The three discs have simulated blade loads added to their tops from left to right, which are 1e6, 1e6, and 1e7N respectively. The areas of the three discs are the design domains.

[0091] First, considering only the minimum static compliance without regard to rotor dynamics, and with a body ratio of 0.8 as a constraint, a structural optimization design is performed. The calculation results are as follows: Figure 3 As shown, the volume fraction is 0.612, and the critical speed of the optimal solution is shown in Table 1.

[0092] Table 1

[0093] Critical speed number / nodal diameter Value (rad / s) 1 / 0 130.22 2 / 1 168.30 3 / 0 272.89 4 / 1 335.77 5 / 0 435.21 6 / 1 447.13

[0094] Based on the above static results, a new optimization problem constrained by rotor dynamic performance is constructed. The new problem is constrained by compliance, a volume fraction ratio of 0.8, an upper limit of 120 rad / s for the first critical speed, and a lower limit of 340 rad / s for the fourth critical speed. Topology optimization design is then performed, and the calculation results are as follows: Figure 4 As shown, the volume ratio is 0.601, and the critical speeds of the optimal solution are shown in Table 2. Both critical speeds satisfy the constraints, verifying the effectiveness of the topology optimization method.

[0095] Table 2

[0096] Critical speed number Value (rad / s) 1 / 0 119.52 2 / 1 160.71 3 / 0 270.67 4 / 1 339.96 5 / 1 403.72 6 / 0 450.60

[0097] Example 2

[0098] This section constructs a 1 / 24-sector disk example, such as Figure 5 As shown. The two sector-shaped periodic surfaces satisfy the cyclic periodic constraint, and one side of the inner ring surface has an axial constraint. One-fifth of the model's height is set as an unspecified domain to ensure the material has a positive impact on the target. The design domain is shown in green in the figure. The Young's modulus of the material is E = 2 × 10⁻⁶. 5 MPa, Poisson's ratio v = 0.3, density p = 7.8 × 10 3 kg / m 3 .

[0099] The Minmax strategy for topology optimization based on the maximum fundamental frequency constructs an independent scalar variable and uses the first-order frequencies of all nodal diameters as objects subject to inequality constraints, aiming to maximize the minimum frequency. The volume fraction constraint is set to 0.5, and the MSIMP interpolation model is chosen for material interpolation, with a penalty of 3. The Young's modulus E of the weak material is... min =E0×10 -6 To avoid numerical singularities in finite element analysis, a Helmholtz PDE filter and Heaviside projection method are used, with the linear filter radius approximately three times the element size. The maximum number of iterations is limited to 180. Figure 6 As shown, (a) is the sector result and (b) is the array result; the obtained material is mainly distributed in the direction away from the base plate, and each part has an inclined support to ensure structural stiffness. In the region near the inner ring constraint, the material distribution is more concentrated. The inclined support structure has many holes and is dendritic in shape.

[0100] The volume fraction eventually converges to 0.264, which is a loose constraint. Changes in structure shape begin to slow around step 90, and the objective function stabilizes rapidly. The volume fraction function converges slowly after step 120.

[0101] The results were compared with the fundamental frequency of the original model. The frequency increased from 1616.01 Hz to 2906.84 Hz, both within the first nodal diameter. This verifies the effectiveness of the maximization topology optimization method for the fundamental frequency. Before and after optimization, the modal shapes of each sector are basically the same. By comparing the nodal diameter and the color of the vibration region, it can be seen that the color gradient of the 0-2Nd region is smaller after optimization, while the color gradient of the 3-12Nd region is larger.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An integrated topology optimization design method for a rotor system considering dynamic performance, characterized in that, Includes the following steps: S1. For the two-dimensional rotor structure, statics and rotor dynamics are used as constraints to perform two-dimensional topology optimization design to obtain a new two-dimensional rotor structure. S2. Based on the new two-dimensional rotor structure, the rotational periodic structure frequency and static performance are used as constraints to perform three-dimensional topology optimization design on the rotor sector model to obtain a new three-dimensional configuration.

2. The integrated topology optimization design method for rotor systems considering dynamic performance according to claim 1, characterized in that: The topology optimization formula used in the two-dimensional topology optimization design is as follows: find:ρ={ρ1,ρ2,...,ρ N ,a1,a2,...,a M } T min:F T U st:KU=F (Oh i -Ω0) 2 ≥e 2 0<ρ min ≤ρ e ≤1,e=1,2,...,N Where α is a topology design variable vector, used to describe the presence or absence of support points within a region; ρ e This refers to the material density of the e-th element, N is the number of meshes, K is the structural stiffness matrix, M is the mass matrix, C is the damping matrix, G is the gyroscope matrix, F is the load vector, and U is the displacement vector. For velocity vectors, Let Ω be the acceleration vector. i Ω0 is the structural critical speed, ε is the structural operating speed, and v is the avoidance margin. e V is the unit volume. * ρ represents the volumetric material usage, and ρ is a topology design variable vector used to describe the presence or absence of material within a region.

3. The integrated topology optimization design method for rotor systems considering dynamic performance according to claim 1, characterized in that: The topology optimization formula used in the three-dimensional topology optimization design is as follows: find:ρ={ρ1,ρ2,...,ρ N } T min F T U stK0U=F K r f r =λ r M r f r 0<ρ min ≤ρ e ≤1,e=1,2,...,N Where: ρ is the pseudo-density vector of the structural design domain, where each design variable ρ i The range of values ​​is from the minimum value ρ min Between and the maximum value of 1, K r φ r =λ r M r φ r Here are the eigenvalue equations for each section of the structure, and the physical equilibrium equations for finite element analysis. K r M is the stiffness matrix of the structure. r Let λ be the mass matrix. r φ is the eigenvalue of the structure. r ρ is the vibration mode vector; e For the pseudo density of the unit cell, v e Let f be the volume of the element, used as the optimization objective; r,j To specify the natural frequency of a structure with a given nodal diameter and order, f lower f is the lower bound of the natural frequency constraint. upper This is the upper limit of the constraint on the natural frequency.

4. The integrated topology optimization design method for rotor systems considering dynamic performance according to claim 1, characterized in that: The topology optimization methods used in two-dimensional and three-dimensional topology optimization designs are as follows: Step 1: Initialize the pseudo-density design variable ρ, construct the Helmholtz anisotropic linear filter field, and initialize the Heaviside function; Step 2: Apply a Helmholtz field to ρ using linear filtering to obtain the density after linear filtering. Using the Heaviside nonlinear mapping function to The density is obtained after processing and nonlinear mapping. Step 3: Use the MSIMP interpolation model to map the variables after nonlinear mapping. Interpolate to material properties and solve for the stiffness matrix K of the current iteration step. r and mass matrix M r And solve the structural eigenvalue equations to obtain the natural frequency response of the structure, and at the same time solve the volume fraction of the current iteration step; Step 4: Construct a target for a specific frequency, and the volume fraction function; Step 5: Solve for the density after nonlinear mapping of the constraint function and the objective function. The sensitivity of the constraint function and the objective function to the pseudo-density ρ is determined by the chain rule. Step 6: Based on the values ​​and sensitivities of the objective function and constraint functions, use the moving asymptote method to solve the structural optimization problem and update the design variables; Step 7: Update the Heaviside function; Step 8: Perform optimization convergence condition judgment, that is, when the residual of the objective function is less than ε0, or when the number of iterations reaches the maximum, if convergence is achieved, the optimization iteration converges; otherwise, return to step 2 to continue iteration.

5. The integrated topology optimization design method for rotor systems considering dynamic performance according to claim 1, characterized in that: The process of solving the constraint values ​​of the rotor dynamics is as follows: S11. In the dynamic analysis of axisymmetric rotor structures based on traditional dynamic formulas, add a gyroscope matrix G; S12. Solve the dynamic equilibrium equations of the structural rotor using the complex characteristic solution method, and obtain the dynamic characteristics of the structural rotor. S13. When the rotor's critical speed is equal to the excitation force acting on the rotor, which is the rotor's own unbalanced force, the corresponding eigenvector solution of the synchronous positive precession of the rotor system caused by this excitation force is: φ(t) is the eigenvector, φ0 is the magnitude of the eigenvector, e is the base, i is the complex number, t is the frequency, and Ω is the eigenvector. i It is the critical speed. Based on the feature vectors, we obtain: The critical speed of the structure can be obtained by solving the above formula.

6. The integrated topology optimization design method for rotor systems considering dynamic performance according to claim 1, characterized in that: The process for solving the constraint value of the frequency of the rotating periodic structure is as follows: The eigenvalue equations of the three-dimensional structure are as follows: K=λM Where K and M are the stiffness matrix and mass matrix of the structure, respectively, and λ is the eigenvalue of the structure, relating the natural frequency of the structure to the following equation: λ = 4π 2 f 2 Where Φ is the modal vector of the structure; and simultaneously, U = e iωt Mφ ensures that the orthogonal normalization condition is met: For rotationally periodically symmetric boundary conditions, there is an interaction between the two symmetric planes, which allows the eigenvalue response of the structure to be solved using the wave propagation principle.

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