A Dynamics Optimization Method for Rotor Systems Based on Perturbation Principle

Abstract

This application belongs to the field of dynamics optimization technology. It provides a rotor system dynamics optimization method based on the perturbation principle. The embodiments of this disclosure can determine the corresponding adjustable parameters for the energy distribution of the substructure of a dual-rotor-support system of an aero-engine without repeated iterative dynamic calculations, thereby implementing dynamic optimization and redistributing the energy of the system substructure to achieve optimization. This method is particularly suitable for optimizing complex, high-dimensional aero-engine rotor systems, significantly saving the time and manpower costs required by traditional algorithm optimization methods. It can play a role in the dynamics-related design of rotating machinery such as aero-engines or gas turbines.

Description

Technical Field

[0001] This disclosure relates to the field of dynamics optimization technology, and in particular to a method for optimizing the dynamics of a rotor system based on the principle of perturbation. Background Technology

[0002] Aero engines are core components of modern aerospace engineering, and their performance and reliability are crucial for the safe operation of aircraft. With the continuous development of the aviation industry and the rapid growth of global air traffic, the need for optimization of aero engines is becoming increasingly urgent. Advanced aero engines / gas turbines have complex system structures, resulting in numerous factors contributing to overall engine vibration. Vibration coupling exists between rotors and between the rotor and the support structure, making structural states difficult to predict, dynamic analysis challenging, and troubleshooting difficult. Therefore, during the aero engine design phase, it is essential to meet vibration specifications, primarily by assessing the critical speed and energy distribution of the dual-rotor-support system, minimizing overall engine vibration sensitivity, and avoiding harmful resonances.

[0003] Rotor dynamics optimization design is often based on parameter optimization using mathematical algorithms, which lacks clear physical meaning and pays insufficient attention to the intrinsic relationship between the optimization objective and the optimization variables. Furthermore, using pure algorithms for dynamics optimization is time-consuming and labor-intensive, especially for high-dimensional rotor system models, where the time from modeling to dynamics calculation is lengthy. Using traditional optimization algorithms for iterative dynamics optimization calculations is too costly. Strain energy analysis in energy analysis has always been an indispensable part of aero-engine rotor system design and dynamics research. Energy-based rotor dynamics optimization design, built on energy analysis, provides the influence of optimization variables (structural parameters) on the optimization objective, with clear physical meaning and easy understanding. In the structural design guidelines for gas turbine engines, the rotor system design requirements state that strain energy analysis should be performed on the rotor-support-casing system to reduce the sensitivity of the rotor system to unbalanced vibration response and avoid instability caused by self-excited vibration.

[0004] Among related technologies, Ren Guangming et al. from Beihang University were the first to use strain energy analysis to study the dynamics of complex rotor casing systems in "Strain Energy Analysis of Complex Rotor Casing System Using Overall Transfer Matrix Method [J]. Journal of Aeronautical Power, 1997, 12(1): 87-89+111." Zhang Dayi et al. used a three-dimensional model of the whole engine to model the dual-rotor turbofan engine in "Establishment of Whole Engine Dynamics Model and Vibration Characteristics Analysis [J]. Propulsion Technology, 2015, 36(5): 768-773," and applied strain energy analysis to calculate and analyze its vibration characteristics. Zheng Xudong et al. conducted vibration research on the rotor-support-casing system in "Vibration Characteristics and Strain Energy Calculation and Analysis of Whole Engine [J]. Aero Engine, 2000, 26(2): 42-46," and used the overall transfer matrix method to calculate the whole engine vibration characteristics and strain energy distribution of a certain type of counter-rotating engine. In their paper "Vibration characteristic investigation of counter-rotating dual-rotor in aero-engine [J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2012, 29(01): 33-39," Feng Guoquan et al. from the China Aero Engine Research Institute used the energy method to perform dynamic optimization of a certain type of aero-engine and conducted experimental verification.

[0005] Most aero-engines employ strain energy analysis for dynamic analysis and optimization. While this method can represent the modal characteristics of the rotor system to some extent and characterize its stiffness, it lacks characterization of rotor inertia. Therefore, using strain energy alone for dynamic optimization is incomplete. Thus, both kinetic and strain energy analysis should be used as research methods for dynamic optimization.

[0006] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0007] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0008] The purpose of this disclosure is to provide a method for optimizing the dynamics of a rotor system based on the perturbation principle, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0009] According to embodiments of this disclosure, a method for optimizing the dynamics of a rotor system based on the perturbation principle is provided, the method comprising:

[0010] The rotor-support system of an aero-engine is simplified and modeled, and its critical speeds at each order are calculated.

[0011] Based on the critical speeds and design speeds of each order, the critical speeds to be optimized and the non-optimized critical speeds are selected.

[0012] The aero-engine rotor-support system is divided into substructures, and the energy proportions of each substructure at each order of the critical speed to be optimized and the energy proportions of each substructure at the non-optimized critical speed are obtained by combining the critical speeds to be optimized and the non-optimized critical speeds.

[0013] The objective function for optimization design is determined based on the critical speed ratios to be optimized at each order and the corresponding energy proportions of the substructures; the constraint function for optimization design is determined based on the non-optimized critical speed ratios at each order and the corresponding energy proportions of the substructures.

[0014] Determine the optimization parameters and their optimization range according to the engineering design requirements;

[0015] Based on the objective function, the constraint function, the optimization parameters, and the optimization range of the optimization parameters, a dynamic optimization process is performed using an optimization algorithm to determine the change in the optimization parameters in order to form an initial optimization scheme.

[0016] The initial optimization scheme is dynamically verified to determine whether the modal rotation speeds in the initial optimization scheme meet the preset vibration criterion requirements. If they do, the initial optimization scheme is output as the target optimization scheme; otherwise, optimization continues.

[0017] Furthermore, the steps of simplifying the structure of the aero-engine rotor-support system and calculating its critical speeds for each order include:

[0018] The structure of the aero-engine rotor-support system is simplified;

[0019] Based on the system's material characteristic data, structural characteristic data, support characteristic data, and rotational speed characteristic data, a Mechanical APDL finite element model is constructed.

[0020] Based on the Mechanical APDL finite element model, the Campbell diagram, modal rotation speeds, and modal array are calculated.

[0021] Based on the Campbell diagram, determine the local monotonicity of the dynamic frequency line, and calculate the gyroscope kinetic energy at each modal speed based on the modal speed.

[0022] The local monotonicity of the dynamic frequency line and the kinetic energy of the rotational speed gyroscope of each mode are correlated to obtain the critical speed of each order.

[0023] Furthermore, the substructure division step of the aero-engine rotor-support system includes:

[0024] The aero-engine rotor-support system is divided into several substructures; wherein the substructures include at least bladed disk components, shaft components, and support components.

[0025] Furthermore, the energy calculation expression for the bladed disk component is as follows:

[0026]

[0027] in, i Indicates order, j Indicates the substructure number. The kinetic energy of the bladed disk includes mass kinetic energy, diameter rotational inertia kinetic energy, and gyro kinetic energy. For the first i The mass of the bladed disk-like components of the stage, for x velocity in direction, for y velocity in direction, The moment of inertia of the diameter. The moment of inertia is the polar rotation. for x Direction swing angle, for y Direction swing angle, It is the axial angular velocity;

[0028] The energy calculation expression for the shaft-type component is as follows:

[0029]

[0030]

[0031] in, The kinetic energy of the rotating shaft For the density of the shaft material, The area of ​​the axial section, The moment of inertia of the axial section, for x Direction swing angle, for y Direction and swing angle; For the strain energy of the rotating shaft, Let be the cross-sectional bending stiffness of the shaft. Poisson's ratio, Let be the shear stiffness of the shaft section. and The axes are respectively x and y The partial derivative of the displacement in the axial direction;

[0032] The energy calculation expression for the support component is as follows:

[0033]

[0034] in, The total support strain energy of the system, For the first i fulcrum x directional support stiffness, For the first i fulcrum y Support stiffness in the direction.

[0035] Furthermore, the method also includes:

[0036] Based on the principle of energy perturbation, the relationship between the substructure energy of the aero-engine rotor-support system and the critical speed is obtained;

[0037] Based on the relationship between the substructure energy of the aero-engine rotor-support system and the critical speed, and combining the critical speeds to be optimized and the non-optimized critical speeds of each order, the first energy proportion of each substructure under the critical speeds to be optimized and the second energy proportion of each substructure under the non-optimized critical speed are obtained.

[0038] The relationship between the substructure energy of the aero-engine rotor-support system and the critical speed is expressed as follows:

[0039]

[0040] in, This represents the critical speed after the structural changes. This is the critical speed before the structural changes. This is the substructure designation for the rotor-support system. and These represent the strain energy and kinetic energy of each substructure after the rotor-support structure change. and These represent the strain energy and equivalent kinetic energy of each substructure before the rotor-support structure changes.

[0041] Furthermore, the expressions for the critical speed ratios to be optimized at each order are as follows:

[0042]

[0043] in, This is the critical speed ratio. , This represents the coefficient representing the proportion of strain energy in the substructure. This represents the proportion of kinetic energy of the substructure. This indicates the proportion of strain energy in the substructure. This indicates the proportion of kinetic energy in the substructure. This represents the structural optimization ratio coefficient. , , .

[0044] Furthermore, the expression for the objective function is:

[0045]

[0046] in, This represents the proportion of strain energy in the substructure. The strain energy corresponding to each substructure at the critical speed to be optimized is given. To optimize the ratio of critical speeds before and after. This represents the proportion of kinetic energy of the substructure. This represents the kinetic energy corresponding to each substructure at the critical speed to be optimized. For the first i The critical speed to be optimized is of order 1. For the first i The target critical speed is determined based on the critical speed requirements of aero-engines. ≥ 1.2 , The design speed includes the idle speed, the design point speed, and the maximum speed.

[0047] The expression for the constraint function is:

[0048]

[0049] in, To optimize the first and second parts i The ratio of the non-critical speed to be optimized. This represents the proportion of strain energy corresponding to each substructure at the non-critical rotational speed. This represents the kinetic energy percentage of each substructure at the non-critical rotational speed.

[0050] Further, the step of determining the change in the optimization parameters to form an optimization scheme by performing a dynamic optimization process using an optimization algorithm based on the objective function, the constraint function, the optimization parameters, and the optimization range of the optimization parameters includes:

[0051] When the parameters change, the energy proportion coefficient of each substructure is determined according to the optimization parameters and the optimization range of the optimization parameters;

[0052] The energy proportion coefficient of the substructure is substituted into the objective function and iteratively filtered until the constraint function is satisfied, thus obtaining the optimized scheme.

[0053] Furthermore, the substructure kinetic energy ratio coefficient corresponding to the mass kinetic energy is:

[0054]

[0055] in, Indicates the critical speed. and The mass kinetic energy before and after optimization is respectively calculated. Indicates the mass of the substructure. This indicates the change in the mass of the substructure.

[0056] The substructure kinetic energy ratio coefficient corresponding to the diameter rotational inertia kinetic energy is:

[0057]

[0058] in, and These represent the diameter rotational inertia and kinetic energy before and after optimization, respectively. This represents the rotational inertia of the substructure's diameter. This represents the change in the moment of inertia of the substructure diameter.

[0059] The substructure kinetic energy ratio coefficient corresponding to the kinetic energy of the gyroscope is:

[0060]

[0061] in, and denoted as the polar rotational inertia kinetic energy before and after optimization, respectively. This represents the polar rotational inertia of the substructure. This represents the change in the polar moment of inertia of the substructure.

[0062] The substructure kinetic energy ratio coefficient corresponding to the kinetic energy of the rotating shaft is:

[0063]

[0064] in, and These represent the optimized kinetic energy of the front and rear axles, respectively. d , D Δ d Δ D This indicates the outer diameter of the shaft and its change. and Indicates the length of the shaft and its change;

[0065] The proportion coefficient of the substructure strain energy corresponding to the strain energy of the rotating shaft is:

[0066]

[0067] in, and These represent the strain energy of the shaft before and after optimization, respectively. Indicates the elastic modulus. 、 This represents the interface moment of inertia of the shaft and its change. and Indicates the length of the shaft and its change;

[0068] The substructure strain energy ratio coefficient corresponding to the support strain energy is:

[0069]

[0070] in, and These represent the strain energy of the support before and after optimization, respectively. 、 It indicates the support stiffness of the shaft and its variation.

[0071] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0072] In the embodiments of this disclosure, the rotor system dynamics optimization method based on the perturbation principle described above achieves two main advantages. Firstly, this method can determine the corresponding adjustable parameters for the energy distribution of the dual rotor-support system substructure of an aero-engine without requiring iterative dynamic calculations. This allows for dynamic optimization by redistributing the energy of the system substructure, thus achieving optimization. Secondly, this method is particularly effective for optimizing complex, high-dimensional aero-engine rotor systems, saving the time and manpower costs required by traditional optimization methods. It can play a role in the dynamics-related design of rotating machinery such as aero-engines or gas turbines. Attached Figure Description

[0073] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0074] Figure 1 The diagram illustrates the steps of a rotor system dynamics optimization method based on the perturbation principle in an exemplary embodiment of this disclosure.

[0075] Figure 2 This diagram illustrates a specific flowchart of the rotor system dynamics optimization method based on the perturbation principle in an exemplary embodiment of this disclosure.

[0076] Figure 3 This diagram illustrates the substructure division of the aero-engine rotor system in an exemplary embodiment of this disclosure.

[0077] Figure 4 This illustrates the strain energy distribution of each substructure under low-pressure rotor excitation in different modes in an exemplary embodiment of this disclosure;

[0078] Figure 5 This illustrates the kinetic energy distribution of each substructure under low-pressure rotor excitation in different modes in an exemplary embodiment of this disclosure;

[0079] Figure 6 This illustrates the strain energy distribution of each substructure under different modes of high-pressure rotor excitation in an exemplary embodiment of this disclosure;

[0080] Figure 7 This illustration shows the kinetic energy distribution of each substructure under different modes of high-voltage rotor excitation in an exemplary embodiment of this disclosure. Detailed Implementation

[0081] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0082] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0083] This example implementation provides a method for optimizing the dynamics of a rotor system based on the perturbation principle. (Reference) Figure 1 As shown, the rotor system dynamics optimization method based on the perturbation principle may include steps S101 to S107.

[0084] Step S101: Simplify and model the rotor-support system of the aero-engine, and calculate its critical speeds for each order;

[0085] Step S102: Based on the critical speeds of each order and the design speed, select the critical speeds to be optimized and the non-optimized critical speeds;

[0086] Step S103: Divide the aero-engine rotor-support system into substructures, and combine the critical speeds to be optimized and the non-optimized critical speeds of each order to obtain the energy proportion of each substructure at the critical speeds to be optimized and the energy proportion of each substructure at the non-optimized critical speeds.

[0087] Step S104: Determine the objective function of the optimization design based on the critical speed ratios to be optimized at each order and the corresponding energy proportions of the substructures; determine the constraint function of the optimization design based on the non-optimized critical speed ratios at each order and the corresponding energy proportions of the substructures.

[0088] Step S105: Determine the optimization parameters and their optimization range according to the engineering design requirements;

[0089] Step S106: Based on the objective function, the constraint function, the optimization parameters, and the optimization range of the optimization parameters, perform a dynamic optimization process using an optimization algorithm to determine the change in the optimization parameters, thereby forming an initial optimization scheme;

[0090] Step S107: Perform dynamic verification on the initial optimization scheme, and determine whether the modal rotation speed in the initial optimization scheme meets the preset vibration criterion requirements. If it meets the requirements, output the initial optimization scheme as the target optimization scheme.

[0091] The aforementioned perturbation-based rotor system dynamics optimization method offers several advantages. Firstly, it allows for dynamic optimization of the energy distribution within the dual-rotor-support substructure of an aero-engine without requiring iterative dynamic calculations. This method determines adjustable parameters and redistributes energy across the substructure, achieving optimal results. Secondly, it is particularly effective for optimizing complex, high-dimensional aero-engine rotor systems, saving the time and manpower required by traditional optimization methods. This approach can play a significant role in the dynamics-related design of rotating machinery such as aero-engines and gas turbines.

[0092] Below, we will refer to Figures 1 to 7 The steps of the rotor system dynamics optimization method based on the perturbation principle described in this example embodiment will be explained in more detail.

[0093] In step S101, as Figure 2 The diagram shows a flowchart of the rotor system dynamics optimization method based on the perturbation principle. The rotor-support system of the aero-engine is structurally simplified, and its critical speeds for each order are calculated.

[0094] Specifically, firstly, the rotor-support system of the aero-engine is structurally simplified, and modeled based on engine material characteristic data, structural characteristic data, and support characteristic data. Data files are generated from these data, and then MATLAB is used to transform them into parameterized command files. A Mechanical APDL finite element model is generated based on the parameterized command files, and modal calculations are performed on the Mechanical APDL finite element model to obtain Campbell's plot, modal speeds, and modal patterns. The local monotonicity of the dynamic frequency line is determined based on the Campbell's plot, and the corresponding gyroscopic kinetic energy is calculated based on the modal speeds. The local monotonicity of the dynamic frequency line and the gyroscopic kinetic energy at each modal speed are correlated to obtain the critical speeds for each order.

[0095] In steps S102 and S103, as follows Figure 2 As shown, based on the critical speed and design speed of each order, the critical speed to be optimized and the non-optimized critical speed of each order are screened out; the aero-engine rotor-support system is divided into substructures, and combined with the critical speed to be optimized of each order, the energy proportion of each substructure under the critical speed to be optimized of each order is obtained.

[0096] Specifically, the critical speed within 20% of the design speed is selected, and the safe speed outside the margin is used as the optimization target.

[0097] like Figure 3 As shown, the aero-engine rotor-support system is divided into several substructures; wherein, the substructure includes at least bladed disk components, shaft components, and support components; the bladed disk components include the fan, compressor, high-pressure turbine, and low-pressure turbine; the shaft components include the high-pressure turbine shaft, low-pressure turbine shaft, and the drum of the fan and compressor; the support components include bearings and support structures connected to the bearings.

[0098] The energy of each substructure is calculated using energy analysis.

[0099] 1) The main components of the fan, compressor, high-pressure turbine, and low-pressure turbine are bladed disks, and their energy expression is as follows:

[0100] (1)

[0101] The kinetic energy of the bladed disk and its mass Diameter Moment of Inertia Polar moment of inertia They are positively correlated.

[0102] 2) The high-pressure turbine shaft, low-pressure turbine shaft, and the blowers of the fan and compressor are all rotating shaft components, and their energy expression is as follows:

[0103] a. Kinetic energy:

[0104] (2)

[0105] When the rotational speed and mode shape remain constant, the kinetic energy of the shaft is proportional to the shaft's mass and moment of inertia.

[0106] b. Strain energy:

[0107] (3)

[0108] The strain energy of a shaft is positively correlated with its bending stiffness.

[0109] 3) The supporting components mainly consist of bearings and the supporting structures connected to the bearings. Their strain energy expression is as follows:

[0110] (4)

[0111] The strain energy of a support is proportional to its support stiffness. k i .

[0112] The problem of small changes in structural parameters causing variations in structural vibration characteristics is of great significance for the optimal design of engineering structures. Using the perturbation principle, the relative variational expression for the natural frequency of the rotor system can be obtained:

[0113] (5)

[0114] Furthermore, the natural frequency relationship before and after the structural change of the rotor-support system can be obtained:

[0115] (6)

[0116] (7)

[0117] Where: ω is the natural frequency after the structural change, and ω0 is the natural frequency before the structural change. j This is the code for the substructure of the rotor-support system. and These represent the strain energy and kinetic energy of each substructure after the rotor-support structure change. and These represent the strain energy and kinetic energy of each substructure before the rotor-support structure changes.

[0118] Substituting the kinetic energy into the formula, we get:

[0119] (8)

[0120] in: The structural optimization ratio is: .make , , According to the perturbation principle, we have:

[0121] (9)

[0122] Expressing each absolute energy as a relative quantity, that is:

[0123] (10)

[0124] in: The speed ratio between the new structure and the original structure; This represents the coefficient representing the proportion of strain energy in the substructure. This represents the kinetic energy ratio of the substructure. This represents the relative strain energy of the substructure; This represents the relative kinetic energy of the substructure. From the above formula, it can be seen that when the rotational speed ratio and the proportion of strain energy and kinetic energy of each substructure are known, the corresponding proportion coefficients of strain energy and kinetic energy can be derived, thereby guiding the relative optimization of the substructure.

[0125] In steps S104 and S105, the objective function for optimization design is determined based on the critical speed to be optimized and the energy ratio of the rotor system substructure, and the constraint function for optimization design is determined based on the non-optimized critical speed and the energy ratio of the rotor system substructure; the optimization parameters and the optimization range of the optimization parameters are determined according to the engineering design requirements.

[0126] Specifically, the expression for the objective function is:

[0127] (11)

[0128] in: The first one to be optimized i Critical speed. Let be the target critical speed of the i-th order, based on the critical speed requirements of aero-engines. ≥ 1.2 ( This indicates the design speed, including: idle speed, design point speed, and maximum speed.

[0129] This function represents the objective function for dynamic optimization under high-pressure rotor excitation or low-pressure rotor excitation. The number of objectives is determined by the number of critical speeds to be adjusted: when there is only one critical speed, the optimization problem is a single-objective optimization problem; when there are multiple critical speeds, the optimization problem becomes a multi-objective optimization problem. When the objective critical speed is determined, the function value... When ≥ 0, the first rank under this structure is considered to be 0. i The critical speed meets the vibration requirements of aero-engines.

[0130] Constraint functions. All critical speeds not involved in optimization meet the dynamic design requirements, meaning that each critical speed is within the safe range of the design speed.

[0131] (12)

[0132] in: , These represent the relative strain energy and kinetic energy of each substructure at the critical speed before optimization, respectively. It refers to the engine design speed, including: idle speed, design point speed, and maximum speed.

[0133] Optimize design parameters

[0134] 1) Parameters corresponding to the strain energy term:

[0135] a) The strain energy of a support is proportional to its support stiffness. k ;

[0136] b) The strain energy of the shaft is proportional to the stiffness of the shaft. ;

[0137] 2) The kinetic energy term mainly includes three parameters: mass kinetic energy, diameter rotational inertia kinetic energy, and polar rotational inertia kinetic energy.

[0138] a) The kinetic energy of the impeller is proportional to its mass. The kinetic energy of the diameter's rotational inertia is proportional to its rotational inertia. The kinetic energy of a polar rotation is proportional to its polar moment of inertia. ;

[0139] b) The kinetic energy of the shaft is proportional to the mass of the shaft. The kinetic energy of the diameter's rotational inertia is proportional to its rotational inertia. The kinetic energy of a polar rotation is proportional to its polar moment of inertia. .

[0140] In steps S106 and S107, based on the objective function, constraint function, optimization parameters, and optimization range of the optimization parameters, a dynamic optimization process is performed using an optimization algorithm to determine the change in the optimization parameters and form an initial optimization scheme. The initial optimization scheme is then dynamically verified to determine whether the modal rotation speeds in the initial optimization scheme meet the preset vibration criterion requirements. If they do, the initial optimization scheme is output as the target optimization scheme.

[0141] Specifically, when the parameters change, the energy proportion coefficient of each substructure is determined based on the optimization parameters and their optimization range.

[0142] 1) The strain energy of the support is proportional to its stiffness. Then the substructure strain energy ratio coefficient corresponding to the support strain energy term is:

[0143] (13)

[0144] 2) The strain energy of a shaft segment is proportional to the stiffness of the shaft. Then, the substructure strain energy ratio coefficient corresponding to the strain energy term of the shaft is:

[0145] (14)

[0146] 3) The kinetic energy of the bladed disk consists of three parts: mass kinetic energy, diameter rotational inertia kinetic energy, and gyro kinetic energy.

[0147] The kinetic energy of a bladed disk is proportional to its mass. Then the substructure kinetic energy ratio coefficient corresponding to the mass kinetic energy term of the impeller is:

[0148] (15)

[0149] The kinetic energy of the impeller disk is proportional to its diameter moment of inertia. Then, the substructure kinetic energy ratio coefficient corresponding to the inertial kinetic energy term of the bladed disk is:

[0150] (16)

[0151] The kinetic energy of a bladed disk is proportional to its polar moment of inertia. Then the substructure kinetic energy ratio coefficient corresponding to the gyroscopic kinetic energy term of the bladed disk is:

[0152] (17)

[0153] 4) Kinetic energy of the shaft segment

[0154] The kinetic energy of the shaft is proportional to the mass of the shaft. Then, the kinetic energy ratio coefficient of the substructure corresponding to the kinetic energy term of the shaft is:

[0155] (18)

[0156] Given the energy proportions of each substructure in the model and the critical rotational speeds of each order, the optimization critical rotational speed, optimization design objective, and optimization design objective function are determined. As the parameters change, the energy proportion coefficients of the substructures are determined and substituted into the objective function. The process is iteratively refined until the optimization constraints are met, yielding the optimization result.

[0157] Thus, the dynamic optimization method for aero-engine rotor systems based on the principle of energy perturbation has been established. The kinetic and strain energies of each substructure have been parameterized. The dynamic optimization of the rotor-support system is based on the energy method, using support stiffness, shaft stiffness, disc mass, and shaft mass as optimization parameters. These parameters are adjusted within the allowable range of engineering design to achieve optimized vibration characteristics.

[0158] In one specific embodiment, to make the technical solution and advantages of the present invention clearer, specific implementation methods of the present invention are given below and described in further detail with reference to the accompanying drawings.

[0159] The structure of the aero-engine rotor-support system is simplified and its critical speeds of each order are calculated. The critical speeds within 20% of the design speed are selected, and the safe speeds outside the margin are used as the optimization target.

[0160] Determine the optimization parameters and the parameter optimization range according to the engineering design requirements;

[0161] Divide the rotor-support system of an aero-engine into substructures, such as... Figure 3 As shown, the strain energy and kinetic energy distribution of each substructure at each critical speed are calculated. Figures 4 to 7 As shown. Among them, Figure 4 The strain energy distribution of each substructure under different modes under low-pressure rotor excitation is shown. Figure 5 This shows the kinetic energy distribution of each substructure under different modes of low-voltage rotor excitation. Figure 6 The strain energy distribution of each substructure under different modes under high-voltage rotor excitation is shown. Figure 7 This shows the kinetic energy distribution of each substructure in different modes under high-voltage rotor excitation.

[0162] Establish the engine objective function and constraint function based on the optimization objective and optimization parameters;

[0163] The dynamic optimization process is carried out using optimization algorithms (such as genetic algorithms) to determine the changes in structural optimization parameters and form an optimization scheme.

[0164] Dynamic calculations were performed on the optimized scheme to verify whether the rotational speeds of each modal met the vibration criteria requirements of the aero-engine rotor system.

[0165] The optimized solution meets the vibration standard, and the optimization process is complete.

[0166] The aforementioned perturbation-based rotor system dynamics optimization method offers several advantages. Firstly, it allows for dynamic optimization of the energy distribution within the dual-rotor-support substructure of an aero-engine without requiring iterative dynamic calculations. This method determines adjustable parameters and redistributes energy across the substructure, achieving optimal results. Secondly, it is particularly effective for optimizing complex, high-dimensional aero-engine rotor systems, saving the time and manpower required by traditional optimization methods. This approach can play a significant role in the dynamics-related design of rotating machinery such as aero-engines and gas turbines.

[0167] It should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., in the above description indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this disclosure and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this disclosure.

[0168] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0169] In the embodiments of this disclosure, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.

[0170] In embodiments of this disclosure, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0171] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0172] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for optimizing the dynamics of a rotor system based on the perturbation principle, characterized in that, The method includes: The rotor-support system of an aero-engine is simplified and modeled, and its critical speeds at each order are calculated. Based on the critical speeds and design speeds of each order, the critical speeds to be optimized and the non-optimized critical speeds are selected. The aero-engine rotor-support system is divided into substructures, and the energy proportions of each substructure at each order of the critical speed to be optimized and the energy proportions of each substructure at the non-optimized critical speed are obtained respectively. Based on the critical speed ratios to be optimized at each order and the energy proportion of the engine substructure, the objective function of the optimization design is determined, and the constraint function of the optimization design is determined based on the non-optimized critical speed ratios at each order and the non-optimized critical speeds. Determine the optimization parameters and their optimization range according to the engineering design requirements; Based on the objective function, the constraint function, the optimization parameters, and the optimization range of the optimization parameters, a dynamic optimization process is performed using an optimization algorithm to determine the change in the optimization parameters in order to form an initial optimization scheme. The initial optimization scheme is dynamically verified to determine whether the modal rotation speeds in the initial optimization scheme meet the preset vibration criterion requirements. If they do, the initial optimization scheme is output as the target optimization scheme; otherwise, optimization continues. The expression for the objective function is: in, i Indicates order, j Indicates the substructure number. This represents the proportion of strain energy in the substructure. The strain energy corresponding to each substructure at the critical speed to be optimized is given. To optimize the ratio of critical speeds before and after. This represents the proportion of kinetic energy of the substructure. This represents the kinetic energy corresponding to each substructure at the critical speed to be optimized. For the first i The critical speed to be optimized is of order 1. For the first i The target critical speed is determined based on the critical speed requirements of aero-engines. ≥ 1.2 , The design speed includes the idle speed, the design point speed, and the maximum speed. The expression for the constraint function is: in, To optimize the first and second parts i The ratio of the non-critical speed to be optimized. This represents the proportion of strain energy corresponding to each substructure at the non-critical rotational speed. This represents the kinetic energy percentage of each substructure at the non-critical rotational speed.

2. The rotor system dynamics optimization method based on the perturbation principle according to claim 1, characterized in that, The steps of simplifying the structure of the aero-engine rotor-support system and calculating its critical speeds for each order include: The structure of the aero-engine rotor-support system is simplified; Based on the system's material characteristic data, structural characteristic data, support characteristic data, and rotational speed characteristic data, a Mechanical APDL finite element model is constructed. Based on the Mechanical APDL finite element model, the Campbell diagram, modal rotation speeds, and modal array are calculated. Based on the Campbell diagram, determine the local monotonicity of the dynamic frequency line, and calculate the gyroscope kinetic energy at each modal speed based on the modal speed. The local monotonicity of the dynamic frequency line and the kinetic energy of the rotational speed gyroscope of each mode are correlated to obtain the critical speed of each order.

3. The rotor system dynamics optimization method based on the perturbation principle according to claim 2, characterized in that, The substructure division step of the aero-engine rotor-support system includes: The aero-engine rotor-support system is divided into several substructures; wherein the substructures include at least bladed disk components, shaft components, and support components.

4. The rotor system dynamics optimization method based on the perturbation principle according to claim 3, characterized in that, The energy calculation expression for the bladed disk component is as follows: in, i Indicates order, j Indicates the substructure number. The kinetic energy of the bladed disk includes mass kinetic energy, diameter rotational inertia kinetic energy, and gyro kinetic energy. For the first i The mass of the bladed disk-like components of the stage, for x velocity in direction, for y velocity in direction, The moment of inertia of the diameter. The moment of inertia is the polar rotation. for x Direction swing angle, for y Direction swing angle, It is the axial angular velocity; The energy calculation expression for the shaft-type component is as follows: in, The kinetic energy of the rotating shaft, For the density of the shaft material, The area of ​​the axial section, The moment of inertia of the axial section, for x Direction swing angle, for y Direction and swing angle; For the strain energy of the rotating shaft, Let be the cross-sectional bending stiffness of the shaft. Poisson's ratio, Let be the shear stiffness of the shaft section. and The axes are respectively x and y The partial derivative of the displacement in the axial direction; The energy calculation expression for the support component is as follows: in, The total support strain energy of the system, For the first i fulcrum x directional support stiffness, For the first i fulcrum y Support stiffness in the direction.

5. The rotor system dynamics optimization method based on the perturbation principle according to claim 4, characterized in that, The method also includes: Based on the principle of energy perturbation, the relationship between the substructure energy of the aero-engine rotor-support system and the critical speed is obtained; Based on the relationship between the substructure energy of the aero-engine rotor-support system and the critical speed, and combining the critical speeds to be optimized and the non-optimized critical speeds of each order, the energy proportion of each substructure under the critical speeds to be optimized and the energy proportion of each substructure under the non-optimized critical speeds are obtained. The relationship between the substructure energy of the aero-engine rotor-support system and the critical speed is expressed as follows: in, This represents the critical speed after the structural changes. This is the critical speed before the structural changes. This is the substructure designation for the rotor-support system. and These represent the strain energy and kinetic energy of each substructure after the rotor-support structure change. and These represent the strain energy and equivalent kinetic energy of each substructure before the rotor-support structure changes.

6. The rotor system dynamics optimization method based on the perturbation principle according to claim 5, characterized in that, The expressions for the critical speed ratios to be optimized at each order are: in, This is the critical speed ratio. , This represents the coefficient representing the proportion of strain energy in the substructure. This represents the proportion of kinetic energy of the substructure. This indicates the proportion of strain energy in the substructure. This indicates the proportion of kinetic energy in the substructure. This represents the structural optimization ratio coefficient. , , .

7. The rotor system dynamics optimization method based on the perturbation principle according to claim 6, characterized in that, The step of determining the changes in the optimization parameters to form an optimization scheme, based on the objective function, the constraint function, the optimization parameters, and the optimization range of the optimization parameters, using an optimization algorithm to perform a dynamic optimization process, includes: When the parameters change, the energy proportion coefficient of each substructure is determined according to the optimization parameters and the optimization range of the optimization parameters; The energy proportion coefficient of the substructure is substituted into the objective function and iteratively filtered until the constraint function is satisfied, thus obtaining the optimized scheme.

8. The rotor system dynamics optimization method based on the perturbation principle according to claim 7, characterized in that, The substructure kinetic energy ratio coefficient corresponding to the mass kinetic energy is: in, Indicates the critical speed. and The mass kinetic energy before and after optimization are respectively calculated. Indicates the mass of the substructure. This indicates the change in the mass of the substructure. The substructure kinetic energy ratio coefficient corresponding to the diameter rotational inertia kinetic energy is: in, and These represent the diameter rotational inertia and kinetic energy before and after optimization, respectively. This represents the moment of inertia of the substructure diameter. This represents the change in the moment of inertia of the substructure diameter. The substructure kinetic energy ratio coefficient corresponding to the gyroscope kinetic energy is: in, and denoted as the polar rotational inertia kinetic energy before and after optimization, respectively. This represents the polar rotational inertia of the substructure. This represents the change in the polar moment of inertia of the substructure. The substructure kinetic energy ratio coefficient corresponding to the kinetic energy of the rotating shaft is: in, and These represent the optimized kinetic energy of the front and rear axles, respectively. d , D Δ d Δ D This indicates the outer diameter of the shaft and its change. and Indicates the length of the shaft and its change; The proportion coefficient of the substructure strain energy corresponding to the strain energy of the rotating shaft is: in, and These represent the strain energy of the shaft before and after optimization, respectively. Indicates the elastic modulus. 、 This represents the interface moment of inertia of the shaft and its change. and Indicates the length of the shaft and its change; The substructure strain energy ratio coefficient corresponding to the support strain energy is: in, and These represent the strain energy of the support before and after optimization, respectively. 、 It indicates the support stiffness of the shaft and its variation.

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