Method and system for analyzing vibration response of an elastic support structure under a maneuvering flight state

Abstract

The application discloses a kind of motor flight state under elastic support structure vibration response analysis method and system, method includes by establishing rotor-bearing-elastic support system dynamics model under motor flight state, by establishing oil film cavitation Reynolds equation under mass conservation boundary condition, the transient oil film force generated by extrusion oil film damper is analyzed out;When motor flight complex motion leads to extrusion oil film damper transient rub, analyze the rub force model generated by it;By establishing bearing complex dynamics model, the differential equation of bearing dynamics model can be directly established and coupled with motor flight, to establish the coupled bearing dynamics model under motor flight state;Finally, the dynamics differential equation of complex rotor system is established, and the vibration response of elastic support structure is obtained by using numerical solution method;It is helpful to realize accurate analysis on the dynamics characteristics and vibration response mechanism of aero-engine elastic support structure under motor flight state.

Description

Technical Field

[0001] This invention belongs to the field of mechanical engineering and relates to a method and system for analyzing the vibration response of an elastic support structure under maneuvering flight conditions. Background Technology

[0002] The elastic support structure comprises a squeeze film damper and elastic elements (squirrel cage or elastic ring type elastic support). Squeeze film dampers, as a support structure capable of altering the overall stiffness and damping of rotating machinery, are widely used in aero-engines, reducing resonance amplitude and attenuating support force transmission. Especially during maneuvering flight, the aggressive nature of aircraft operation places higher demands on the support structure. Extensive testing has demonstrated that the proper use of squeeze film dampers can effectively improve the stability and performance of aero-engine rotor structures. The elastic elements connect the bearings to the casing, reducing support stiffness and consequently lowering the rotor's first and second natural frequencies. This allows the rotor's natural frequencies to move away from the operating speed of the rotor system, ultimately improving the overall performance of the rotor system and reducing the likelihood of resonance.

[0003] Establishing a coupled dynamic model of the aero-engine rotor-bearing-elastic support is crucial for conducting dynamic analysis of elastic supports. Currently, extrusion film dampers are widely used in rotating machinery. Based on whether they have a centering elastic support, extrusion film dampers can be classified into two typical types: concentric and non-concentric. A concentric extrusion film damper is a structure with a centering elastic support. In the non-concentric type, the rotor load acts directly on the extrusion film damper through the bearing, without any elastic elements. The application of SFDs in various rotating machinery, including aero engines, gas turbines, turbochargers, compressors, and machine tools, has been the subject of long-term and systematic research by Professor Luis San Andres (L San Andrés, SH Jeung, S Den, et al. Squeeze film dampers: An experimental appraisal of their dynamic performance. First Asia Turbomachinery and Pump Symposium, Singapore, 2016: 22-25.) and others from the Turbomechanics Group at Texas A&M University. Through the design of a test apparatus specifically for squeeze film dampers, they conducted a series of theoretical and experimental studies, analyzing the damping coefficient and inertia coefficient of SFDs. Furthermore, they analyzed the influence of various structural characteristics of the damper, including oil film length, oil film gap variation, and the forms of lubrication cavities, sealing methods, oil inlets, and oil grooves, on the structural dynamics of SFDs. The research group of Professor Liao Mingfu at Northwestern Polytechnical University (Li Yan, Liao Mingfu, Wang Siji, et al. Influence of concentricity and rubbing of extrusion oil film damper on rotor vibration characteristics [J]. Vibration and Shock, 2020, 39(01):150-156+174.) studied the influence of concentricity and rubbing of extrusion oil film damper on the vibration characteristics of rotor system. The results showed that as the rotor whirl radius increases, the influence of the damper's installation eccentricity on rotor vibration becomes stronger. When the damper eccentricity ratio is too large, the inner and outer rings of the oil film may rub against each other, which will excite the rotor's reverse precession natural frequency, causing the vibration amplitude to fluctuate violently. Professor Luo Guihuo of Nanjing University of Aeronautics and Astronautics (Zhao Xiangwei, Luo Guihuo, Wang Fei. Numerical analysis of the influence of static eccentricity on the vibration reduction characteristics of extrusion film dampers [J]. Aero Engine, 2018, 44(03):42-48.) derived the SFD Reynolds equation under static eccentricity conditions to study the influence of static eccentricity caused by gravity or assembly errors on the vibration characteristics of rotor systems, and analyzed the nonlinear response of the rotor.

[0004] Currently, in the dynamic models of extrusion film dampers, the existing formulas for calculating the film force are simplified from the Reynolds equation. However, the film pressure and thickness in the Reynolds equation are influenced by a combination of factors, including aircraft maneuvering loads, temperature changes, viscosity changes, and the interconversion of gas and liquid phases. Under unsteady conditions of maneuvering flight, the dynamic characteristics of the film exhibit a high degree of nonlinearity. When aero-engines are subjected to pitch, yaw, roll, and other complex maneuvers, a simple dynamic model cannot accurately describe them. Summary of the Invention

[0005] The purpose of this invention is to provide a vibration response analysis method for elastic support structures under maneuvering flight conditions, in order to solve one or more of the aforementioned technical problems. Considering the effects of additional inertial torque, transient oil film force of the squeezed oil film, and inner and outer ring friction force of the squeezed oil film under maneuvering flight conditions, a coupled modeling method considering highly nonlinear elastic support, complex bearing dynamics model, and rotor is established to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of aero-engine under maneuvering flight conditions, and to fundamentally reveal the generation mechanism and dynamic characteristics of the vibration response of the elastic support structure of aero-engine under maneuvering flight conditions.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions, comprising the following steps:

[0007] S1, obtain the attribute parameters and operating status of the rotor system, bearings, elastic support structure, and wheel of the aero-engine;

[0008] S2. Based on the property parameters and operating status of the rotor system, bearings, elastic support structure, and wheel disk of the aero-engine, analyze the additional gyroscopic torque under different complex flight motion states, and establish a dynamic model of the rotor-bearing-squirrel cage elastic support-squeezed oil film damper coupled system, and couple the additional gyroscopic torque to the dynamic model.

[0009] S3. For the extrusion oil film damper, a fluid dynamics physical model considering oil film cavitation is established to obtain the instantaneous oil film force generated by the extrusion oil film damper.

[0010] S4. For elastic elements, a squirrel cage elastic support is used to establish a stiffness calculation formula for the squirrel cage elastic support.

[0011] S5. Based on the complexity of the maneuvering flight process and the variability of the working conditions, a model of the inner and outer ring friction force of the squeeze oil film damper caused by maneuvering flight is established to obtain the friction force of the squeeze oil film damper caused by transient static eccentricity.

[0012] S6. For bearings, establish a bearing dynamics model that considers the time-varying and nonlinear changes in bearing height;

[0013] S7 considers various additional inertial moments and inertial forces generated during maneuvering flight. Based on the rotor-bearing-elastic support coupling model established in S2, it considers the instantaneous oil film force generated by the squeeze oil film damper obtained in S3, the influence of the squirrel cage elastic support stiffness on the overall stiffness of the rotor system obtained in S4, the friction force of the squeeze oil film damper caused by transient static eccentricity obtained in S5, and the bearing dynamic model obtained in S6. Numerical integration is used to solve the problem, so as to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of the aero-engine.

[0014] A further improvement of the present invention is that, in S1, the attribute parameters of the rotor and the disk include: geometric structural parameters and material property parameters; the attribute parameters of the bearing include: geometric parameters, material property parameters, installation position, preload, initial contact angle, axial clearance / radial clearance, and number of rolling balls; the attribute parameters of the squeeze oil film damper include: inner ring radius of the oil film, outer ring radius of the oil film, oil film length, oil viscosity, and oil film gap; the attribute parameters of the squirrel cage elastic support include: number of squirrel cage bars, effective length of the squirrel cage bars, cross-sectional width of the squirrel cage bars, cross-sectional height of the squirrel cage bars, and elastic modulus; the motion parameters include the rotational speed of the rotor, the unbalance of the rotor system itself, and the motion load spectrum of maneuvering flight.

[0015] A further improvement of this invention is that, in S2, the dynamic model of the coupled system of the aero-engine rotor-bearing-squirrel cage elastic support-squeezing oil film damper under maneuvering flight conditions is as follows:

[0016]

[0017] M = M b +M d

[0018] Q = F e +F sfd +F b +F J +G e +F rub

[0019] Where: M—system mass matrix; M b — Beam element mass matrix; M d —Disc unit mass matrix; C —System damping matrix; C B —Additional damping matrix; G—System gyroscope matrix; K—Beam element system stiffness matrix; K s —Elastic support stiffness matrix; q t —System generalized displacement; G e—Gravity vector; F e —Unbalanced force vector; F sfd — Vector of damping force of the squeezed oil film; F b —Dynamic bearing force vector; ω —Shaft rotation speed; F J —The vector of additional excitation force caused by maneuvering flight; F rub —The friction force vector of the squeeze oil film damper.

[0020] A further improvement of the present invention is that, in S3, for the extrusion oil film damper, based on the law of conservation of mass and the changes in gas-liquid two-phase flow, the Renolds equation and the Fischer-Burmeister equation are solved simultaneously to obtain the instantaneous oil film force generated by the extrusion oil film damper, as shown below:

[0021]

[0022]

[0023] In the formula, H is the local oil film thickness; P is the oil film pressure; X is the sliding direction; Y is the direction perpendicular to the sliding direction; and θ is the porosity.

[0024] A further improvement of the present invention is that, in S4, the stiffness K is established based on the structure of the elastic support of the squirrel cage. s The calculation expression is:

[0025]

[0026] In the formula, n is the number of cage bars; L is the effective length of the cage bar; a is the width of the cage bar cross section; b is the height of the cage bar cross section; and E is the elastic modulus.

[0027] A further improvement of the present invention is that S5 specifically includes, considering the transient static eccentricity of the squeeze film damper during maneuvering flight, which leads to the generation of discontinuous cavitation in the oil film exceeding half a circumference, causing the squeeze film damper to fail and generate rubbing, establishing a rubbing force model for the squeeze film damper, based on Schweitzer's rubbing theory, the elastic normal impact force F of the inner and outer rings of the squeeze film damper and the friction force F f The expression is:

[0028]

[0029] S contact — Friction stiffness between the inner and outer rings of the extrusion film damper; α — Energy consumption coefficient; δ — Precession displacement of the inner ring of the extrusion film damper; —Precession speed of the inner ring of the squeeze film damper.

[0030] A further improvement of the present invention is that S6 specifically includes, on the main bearing of an aero-engine with high speed, variable load, and especially maneuvering flight, considering the interaction between various bearing components, using differential equations to simulate and describe the motion process of each bearing component, and considering the factors of complex maneuvering flight in the process of establishing differential equations, and coupling the gyroscopic torque and additional excitation force generated by maneuvering flight into the differential equations.

[0031] A further improvement of the present invention is that, based on the assumption that the Gupta bearing model does not constrain the motion of bearing elements, the resultant force acting on the entire rotor coupling system is obtained according to the calculation formulas for the resultant force between the rolling balls and the races, the torque of the center of mass of the rolling balls, and the resultant torque of the center of mass of the races.

[0032] A further improvement of the present invention is that the various additional inertial moments and inertial forces generated during maneuvering flight include: simplifying the process by aligning one end of the aero-engine rotor with the center of gravity of the aircraft; establishing a fixed coordinate system oxyz for the rotor system, wherein the fixed coordinate system oxyz is a relative coordinate system with respect to the aircraft fuselage; taking the rotor axis as the z-axis; and establishing x and y axes at the radial support nodes. For basic maneuvering flight motion, when the aircraft rolls, the rotor system is equivalent to the change in rotational angular velocity around the z-axis; when the aircraft pitches, the rotor system is equivalent to the change in rotational angular velocity around the x-axis. Based on the influence of the changes in maneuvering flight conditions, an expression for the total kinetic energy of the rotor disk is established, thereby calculating the various additional inertial moments and inertial forces generated during maneuvering flight.

[0033] Based on the same inventive concept, the present invention also provides a vibration response analysis system for elastic support structures under maneuvering flight environment, including a rotor system dynamics model construction module, an instantaneous oil film force acquisition module, a squirrel cage elastic support stiffness acquisition module, an extrusion oil film damper rubbing force acquisition module, a bearing dynamics model construction module, and an analysis and solution module.

[0034] The rotor system dynamics model building module is used to analyze the additional gyroscopic torque under different complex flight motion states based on the property parameters and operating states of the rotor system, bearings, elastic support structure, and wheel disk of the aero-engine, and to establish a dynamic model of the rotor-bearing-squirrel cage elastic support-squeezed oil film damper coupled system, and to couple the additional gyroscopic torque to the dynamic model.

[0035] The instantaneous oil film force acquisition module is used to establish a fluid dynamics physical model that takes into account oil film cavitation for the extrusion oil film damper, and to acquire the instantaneous oil film force generated by the extrusion oil film damper.

[0036] The stiffness acquisition module for squirrel cage elastic supports is used to establish a stiffness calculation formula for squirrel cage elastic supports for elastic elements.

[0037] Based on the complexity of the maneuvering flight process and the variability of the working conditions, the module for obtaining the friction force of the extrusion oil film damper establishes a model of the friction force of the inner and outer rings of the extrusion oil film damper caused by the maneuvering flight, and obtains the friction force of the extrusion oil film damper caused by transient static eccentricity.

[0038] The bearing dynamics model building module is used to build a bearing dynamics model that takes into account the time-varying and nonlinear changes in bearing height.

[0039] The analysis and solution module is used to consider various additional inertial moments and inertial forces generated during maneuvering flight. Based on the established rotor-bearing-elastic support coupling model, it considers the instantaneous oil film force generated by the squeeze oil film damper, the influence of the squirrel cage elastic support stiffness on the overall stiffness of the rotor system, the rubbing force of the squeeze oil film damper caused by transient static eccentricity, and the bearing dynamic model. Numerical integration is used to solve the problem, so as to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of the aero-engine.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects: Existing modeling methods for bearings generally use simple bearing models or fixed bearing stiffness damping to simulate bearings. Considering the effects of additional inertial torque, transient oil film force of the squeezed oil film, and inner and outer ring friction force of the squeezed oil film under maneuvering flight conditions, a coupled modeling method considering highly nonlinear elastic support, complex bearing dynamics model, and rotor is established to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of aero-engine under maneuvering flight conditions, and to reveal the generation mechanism and dynamic characteristics of the vibration response of the elastic support structure of aero-engine under maneuvering flight conditions in essence.

[0041] Furthermore, in terms of modeling the extrusion film damper, existing modeling methods generally use the short bearing support theory and the assumptions of full oil film and half oil film to solve the oil pressure. This invention uses mass conservation and boundary conditions of gas-liquid two-phase flow change to solve the oil pressure of the extrusion film damper. Attached Figure Description

[0042] Figure 1 This is a diagram illustrating a rotor-bearing-elastic support modeling method for a maneuvering flight environment according to the present invention.

[0043] Figure 2 This is a diagram showing the vibration response characteristics of an elastic support under kinetic loads.

[0044] Figure 3 A simplified model diagram of the rotor-bearing-elastic support system.

[0045] Figure 4 This is a static eccentric model diagram of a squeeze oil film damper.

[0046] Figure 5 This is a model diagram of a pressure oil film damper. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the embodiments and accompanying drawings.

[0048] refer to Figure 1 This invention discloses a method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions, comprising the following steps:

[0049] 1) Collect the geometric parameters, material properties, and operating conditions of the rotor, bearings, extrusion oil film damper, and squirrel cage elastic support to provide data support for rotor system dynamic modeling. The property parameters of the rotor and disk include: geometric dimensions and material properties. The property parameters of the bearings include: geometric dimensions, material properties, installation position, preload, initial contact angle, axial / radial clearance, and number of balls. The property parameters of the extrusion oil film damper include: inner ring radius, outer ring radius, oil film length, oil viscosity, and oil film gap. The property parameters of the squirrel cage elastic support include: number of cage bars, effective length of cage bars, cross-sectional width of cage bars, cross-sectional height of cage bars, and elastic modulus. The motion parameters include the rotor's rotational speed, the unbalance of the rotor system itself, and the motion load spectrum of maneuvering flight.

[0050] 2) Maneuvering flight load calculation considers both single maneuvering flight actions and load calculations involving coupled complex maneuvers. The process is as follows: Figure 2 As shown, the motion of an aircraft in the air can be decomposed into translational motion with respect to the center of mass and rotational motion about the center of mass. Maneuvering not only includes changes in the aircraft's trajectory but also changes in its speed and acceleration during flight. Furthermore, the basic typical maneuvers of an aircraft can be categorized into three types: vertical plane maneuvers, horizontal plane maneuvers, and roll motion around an axis. Typical vertical plane maneuvers include dives, loops, and climbs; typical horizontal plane maneuvers include turns and circles. The calculation process sequentially includes: aeronautical Euler angle transformation, conversion between flight parameters and rotor basic motion parameters, decomposition of maneuvering motion, and decomposition of the excitation forms experienced by the aircraft during maneuvers. Flight parameters include the aircraft's speed, acceleration, yaw angle, pitch angle, and roll angle during maneuvers; the decomposition of aircraft excitation forms includes the mutual conversion process between steady-state excitation and harmonic excitation, transient excitation and impact excitation, etc.

[0051] 3) Establish a simplified rotor-bearing-support model, such as Figure 3As shown, the left end of the rotor is supported by a roller bearing-squeezing oil film damper-squirrel cage elastic support, and the right end of the rotor is supported by a deep groove ball bearing. The rotor is modeled using Timoshenko beam elements, the wheel disk is discretized into a rigid disk, and the bearing adopts a complex dynamic model. The bearing force is calculated using Hertz contact theory.

[0052] The rotor motion equations are derived using Lagrange equations with generalized coordinates as variables, where the second kind of Lagrange equation is:

[0053]

[0054] In the formula, q is the generalized coordinate; T is the kinetic energy; U is the potential energy; and Q is the external force.

[0055] According to the second type of Lagrange equations, the differential equations of motion for the rotor system, i.e., the dynamic model of the coupled system of aero-engine rotor-bearing-squirrel cage elastic support-squeezing oil film damper, can be expressed as:

[0056]

[0057] M = M b +M d

[0058] Q = F e +F sfd +F b +F J +G e +F rub

[0059] Where: M—system mass matrix; M b — Beam element mass matrix; M d —Disc unit mass matrix; C —System damping matrix; C B —Additional damping matrix; G—System gyroscope matrix; K—Beam element system stiffness matrix; K s —Elastic support stiffness matrix; q t —System generalized displacement; G e —Gravity vector; F e —Unbalanced force vector; F sfd — Vector of damping force of the squeezed oil film; F b —Dynamic bearing force vector; ω —Shaft rotation speed; F J —The vector of additional excitation force caused by maneuvering flight; F rub —The friction force vector of the squeeze oil film damper.

[0060] 4) Based on the complexity of maneuvering flight, a dynamic model of the oil film force in the transient static eccentricity of the squeeze oil film damper under maneuvering flight conditions is established, such as... Figure 4 As shown, based on the law of conservation of mass and the changes in gas-liquid two-phase flow, the Renolds equation and the Fischer-Burmeister equation are solved simultaneously, as shown in the following equation:

[0061]

[0062]

[0063] In the formula, H is the local oil film thickness; P is the oil film pressure; X is the sliding direction; Y is the direction perpendicular to the sliding direction; and θ is the porosity.

[0064] 5) Under maneuvering flight conditions, the transient static eccentricity of the squeeze film damper may further lead to rubbing between the inner and outer rings of the squeeze film damper, such as... Figure 5 As shown. A friction force model for the extrusion film damper is established to address its failure. Based on Schweitzer's friction theory, the elastic contact force Fo of the inner and outer rings of the extrusion film damper and the friction force Fo are calculated. f The expression is:

[0065]

[0066] S contact — Friction stiffness between the inner and outer rings of the extrusion film damper; α — Energy consumption coefficient; δ — Precession displacement of the inner ring of the extrusion film damper; —Precession speed of the inner ring of the squeeze film damper.

[0067]

[0068] After decomposing the frictional force along the X and Y directions, we can obtain:

[0069]

[0070] 6) On the main bearing of aero-engines with high speed, variable load, and especially maneuvering flight, the interaction between various bearing components is considered. Differential equations are used to simulate and describe the motion process of each bearing component. In the process of establishing the differential equations, the factors of complex maneuvering flight are considered, and the gyroscopic torque and additional excitation force generated by maneuvering flight are coupled into the differential equations.

[0071] Based on the assumption that the Gupta bearing model does not constrain the motion of bearing elements, and considering the complex operating conditions during maneuvering flight, the motion of each moving element in the bearing is simulated using differential equations, taking into account the additional gyroscopic torque and gyroscopic force caused by external operating conditions. The Gupta bearing dynamics model considers the interaction between the three main bearing elements: rolling elements, raceways, and cage. The formula for calculating the resultant force between the rolling balls and raceways is shown below:

[0072] F k c =Q k c +f k c -c br v c

[0073] Q k c —Contact force perpendicular to the contact surface; f k c —The traction force parallel to the contact surface; c br —Damping coefficient caused by lubrication in the contact area; v c —The relative velocity of the ball and the ring at the point of contact.

[0074] Torque M of the center of mass of the rolling ball c Calculation formula and resultant moment M of the ring's center of mass rk The calculation formula is shown below:

[0075]

[0076] —The position vector of the contact point relative to the center of the ball; —The position vector of the contact point relative to the center of the ring; T crk —Transformation matrix from contact coordinate system to ring coordinate system; z k — The number of balls in the k-th bearing; the subscript j — the j-th ball in the bearing.

[0077] The resultant force acting on the entire rotor coupling system can be expressed as follows:

[0078]

[0079] —The resultant force of the rolling balls of the k-th bearing acting on the inner ring; —The weight of the rotor; n—The number of bearings mounted on the rotor; T ci —Transformation matrix from contact coordinate system to inertial coordinate system.

[0080] The resultant torque acting on the rotor's center of mass can be expressed as follows:

[0081]

[0082] —The torque caused between the k-th bearing ball and the inner ring; T cr —Transformation matrix from contact coordinate system to rotor coordinate system;

[0083] 7) For the calculation of maneuvering flight loads, various additional inertial moments and inertial forces generated during maneuvering flight are obtained. Specifically, the center of gravity of the aero-engine rotor is simplified by aligning one end with the aircraft's center of gravity, and a fixed coordinate system oxyz is established for the rotor system, which is used as a relative coordinate system with respect to the aircraft fuselage. The rotor's axial direction is taken as the z-axis, and x and y axes are established at the radial support nodes. For basic maneuvering flight motions, when the aircraft rolls, the rotor system can be equivalently represented by the change in angular velocity about the z-axis; when the aircraft pitches, the rotor system can be equivalently represented by the change in angular velocity about the x-axis. Based on the influence of changes in maneuvering flight conditions, the total kinetic energy expression of the rotor disk is established as follows:

[0084]

[0085] v n —The aircraft's entrainment velocity; r—The relative displacement vector of the turntable center with respect to the oxyz coordinate system; ω—The angular velocity vector of the rotor disk; I d —Diameter of the turntable and moment of inertia; I p —The extreme moment of inertia of the turntable; —The angular velocity component of the rotor about the x-axis in the oxyz coordinate system; —The angular velocity component of the rotor about the y-axis in the oxyz coordinate system; θ n,z —The angular velocity component of the rotor about the z-axis in the oxyz coordinate system; Ω —The rotor speed; θ x —The angle of rotation of the rotor system relative to the x-axis; θ y —The angle of rotation of the rotor system relative to the y-axis.

[0086] The additional excitation force vector generated by the maneuvering flight on the turntable can be represented as follows:

[0087]

[0088] —The acceleration of the aircraft in the X direction; —The acceleration of the aircraft in the Y direction.

[0089] 8) The additional inertial torque and additional inertial force generated during complex maneuvering flight are used as excitation sources; based on the fluid dynamics physical model of the squeeze oil film damper considering oil film cavitation established in 4), the analysis of transient oil film changes is completed; based on 5), the analysis of the influence of different maneuvering aggression on rotor eccentricity is completed, considering the transient static eccentricity caused by maneuvering flight and the inner and outer ring rubbing of the squeeze oil film; based on 6), the dynamic model of the bearing is established, considering the influence of complex dynamic interactions between bearing components under complex maneuvering flight conditions; the results of transient oil film changes, the rubbing force caused by static eccentricity, and the complex dynamic model of the bearing are coupled with the rotor system for analysis, and finally the dynamic response of the rotor system with elastic support structure under maneuvering flight conditions is studied.

[0090] In summary, the method described in this invention establishes a dynamic model of the rotor-bearing-elastic support system under maneuvering flight conditions to analyze the vibration response of the elastic support under such conditions. It also establishes the Reynolds equation for oil film cavitation under mass conservation boundary conditions to analyze the transient oil film force generated by the extrusion oil film damper. Furthermore, it studies the transient rubbing force model generated when the complex motion of maneuvering flight causes the extrusion oil film damper to rub against each other. By establishing a complex bearing dynamic model, the differential equations of the bearing dynamic model can be directly coupled with the maneuvering flight, thus establishing a coupled bearing dynamic model under maneuvering flight conditions. Finally, it establishes the dynamic differential equations of the complex rotor system and solves them using numerical methods to obtain the vibration response of the elastic support structure. Considering the effects of additional inertial torque, transient oil film force of the extrusion oil film, and rubbing forces between the inner and outer rings of the extrusion oil film under maneuvering flight conditions, a coupled modeling method considering highly nonlinear elastic support, complex bearing dynamic model, and rotor is established. This enables accurate analysis of the dynamic characteristics and vibration response mechanism of the aero-engine elastic support structure under maneuvering flight conditions, fundamentally revealing the generation mechanism and dynamic characteristics of the vibration response of the aero-engine elastic support structure under maneuvering flight conditions.

Claims

1. A method for analyzing the vibration response of an elastically supported structure under maneuvering flight conditions, characterized in that, Includes the following steps: S1, obtain the attribute parameters and operating status of the rotor system, bearings, elastic support structure, and wheel of the aero-engine; S2. Based on the property parameters and operating states of the rotor system, bearings, elastic support structure, and wheel disk of the aero-engine, analyze the additional gyroscopic torque under different complex flight motion states, and establish a dynamic model of the rotor-bearing-squirrel cage elastic support-squeezing oil film damper coupled system, coupling the additional gyroscopic torque into the dynamic model; wherein, the established dynamic model of the aero-engine rotor-bearing-squirrel cage elastic support-squeezing oil film damper coupled system under maneuvering flight state is as follows: In the formula: —System quality matrix; — Beam element mass matrix; —Disk unit mass matrix; —System damping matrix; —Additional damping matrix; —System gyroscope matrix; —Stiffness matrix of the beam element system; —Elastic support stiffness matrix; —System generalized displacement; —Gravity vector; —Unbalanced force vector; — Vector of damping force of the squeezed oil film; —Dynamic bearing force vector; —Shaft rotation speed; —The vector of additional excitation forces caused by maneuvering flight; —The friction force vector of the squeeze oil film damper; S3. For the extrusion oil film damper, a fluid dynamics physical model considering oil film cavitation is established to obtain the instantaneous oil film force generated by the extrusion oil film damper. S4. For elastic elements, a squirrel cage elastic support is used to establish a stiffness calculation formula for the squirrel cage elastic support. S5. Based on the complexity of the maneuvering flight process and the variability of the working conditions, a model of the inner and outer ring friction force of the squeeze oil film damper caused by maneuvering flight is established to obtain the friction force of the squeeze oil film damper caused by transient static eccentricity. S6. For bearings, establish a bearing dynamics model that considers the time-varying and nonlinear changes in bearing height; S7 considers various additional inertial moments and inertial forces generated during maneuvering flight. Based on the rotor-bearing-elastic support coupling model established in S2, it considers the instantaneous oil film force generated by the squeeze oil film damper obtained in S3, the influence of the squirrel cage elastic support stiffness on the overall stiffness of the rotor system obtained in S4, the friction force of the squeeze oil film damper caused by transient static eccentricity obtained in S5, and the bearing dynamic model obtained in S6. Numerical integration is used to solve the problem, so as to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of the aero-engine.

2. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, In S1, the attribute parameters of the rotor and disk include: geometric structural parameters and material property parameters; the attribute parameters of the bearing include: geometric parameters, material property parameters, installation position, preload, initial contact angle, axial clearance / radial clearance, and number of rolling balls; the attribute parameters of the squeeze oil film damper include: inner ring radius of the oil film, outer ring radius of the oil film, oil film length, oil viscosity, and oil film gap; the attribute parameters of the squirrel cage elastic support include: number of squirrel cage bars, effective length of squirrel cage bars, cross-sectional width of squirrel cage bars, cross-sectional height of squirrel cage bars, and elastic modulus; the motion parameters include the rotational speed of the rotor, the unbalance of the rotor system itself, and the motion load spectrum of maneuvering flight.

3. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, In S3, for the extrusion film damper, based on the law of conservation of mass and the changes in gas-liquid two-phase flow, the Renolds equation and the Fischer-Burmeister equation are solved simultaneously to obtain the instantaneous oil film force generated by the extrusion film damper, as shown below: In the formula, —Local oil film thickness; —Oil film pressure; —Sliding direction; —The direction perpendicular to the sliding direction; —Porosity.

4. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, In S4, the stiffness is established based on the structure of the elastic support of the squirrel cage. The calculation expression is: In the formula, —Number of bars in the rat cage; —Effective length of the cage bars; a —Width of the cage bar cross section; —Height of the cage bars; — Elastic modulus.

5. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, S5 specifically includes considering the transient static eccentricity of the squeeze film damper during maneuvering flight, which leads to cavitation exceeding half a circumference and discontinuous within the oil film, causing the squeeze film damper to fail and generate rubbing. A rubbing force model for the squeeze film damper is established, based on Schweitzer's rubbing theory, to calculate the elastic normal impact force F and friction force of the inner and outer rings of the squeeze film damper. The expression is: —The friction stiffness between the inner and outer rings of the squeeze film damper; —Energy consumption coefficient; —Precession displacement of the inner ring of the squeeze film damper; —Precession speed of the inner ring of the squeeze film damper.

6. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, S6 specifically includes, on the main bearing of an aero-engine with high speed, variable load, and especially maneuvering flight, considering the interaction between various bearing components, using differential equations to simulate and describe the motion process of each bearing component, and considering the factors of complex maneuvering flight in the process of establishing differential equations, coupling the gyroscopic torque and additional excitation force generated by maneuvering flight into the differential equations.

7. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 6, characterized in that, Based on the assumption that the Gupta bearing model does not constrain the motion of bearing elements, the resultant force acting on the entire rotor coupling system is obtained according to the calculation formulas for the resultant force between the rolling balls and the races, the torque of the center of mass of the rolling balls, and the resultant torque of the center of mass of the races.

8. The method for analyzing the vibration response of an elastic support structure under maneuvering flight conditions according to claim 1, characterized in that, The various additional inertial moments and forces generated during maneuvering flight include: simplifying the process by aligning one end of the aero-engine rotor with the center of gravity of the aircraft, establishing a fixed coordinate system oxyz for the rotor system, with oxyz as the relative coordinate system to the aircraft fuselage, using the rotor axis as the z-axis, and establishing x and y axes at the radial support nodes. For basic maneuvering flight motions, when the aircraft rolls, the rotor system is equivalent to the change in rotational angular velocity around the z-axis; when the aircraft pitches, the rotor system is equivalent to the change in rotational angular velocity around the x-axis. Based on the influence of changes in maneuvering flight conditions, an expression for the total kinetic energy of the rotor disk is established, thereby calculating the various additional inertial moments and forces generated during maneuvering flight.

9. A vibration response analysis system for an elastic support structure in a maneuvering flight state, characterized in that, It includes a rotor system dynamics model building module, an instantaneous oil film force acquisition module, a squirrel cage elastic support stiffness acquisition module, an extrusion oil film damper rubbing force acquisition module, a bearing dynamics model building module, and an analysis and solution module; The rotor system dynamics model construction module is used to analyze the additional gyroscopic torque under different complex flight motion states based on the property parameters and operating states of the rotor system, bearings, elastic support structure, and rotor disk of the aero-engine, and to establish a dynamic model of the rotor-bearing-squirrel cage elastic support-squeezing oil film damper coupled system, coupling the additional gyroscopic torque to the dynamic model; wherein, the established dynamic model of the aero-engine rotor-bearing-squirrel cage elastic support-squeezing oil film damper coupled system under maneuvering flight state is as follows: In the formula: —System quality matrix; — Beam element mass matrix; —Disk unit mass matrix; —System damping matrix; —Additional damping matrix; —System gyroscope matrix; —Stiffness matrix of the beam element system; —Elastic support stiffness matrix; —System generalized displacement; —Gravity vector; —Unbalanced force vector; — Vector of damping force of the squeezed oil film; —Dynamic bearing force vector; —Shaft rotation speed; —The vector of additional excitation forces caused by maneuvering flight; —The friction force vector of the squeeze oil film damper; The instantaneous oil film force acquisition module is used to establish a fluid dynamics physical model that takes into account oil film cavitation for the extrusion oil film damper, and to acquire the instantaneous oil film force generated by the extrusion oil film damper. The stiffness acquisition module for squirrel cage elastic supports is used to establish a stiffness calculation formula for squirrel cage elastic supports for elastic elements. Based on the complexity of the maneuvering flight process and the variability of the working conditions, the module for obtaining the friction force of the extrusion oil film damper establishes a model of the friction force of the inner and outer rings of the extrusion oil film damper caused by the maneuvering flight, and obtains the friction force of the extrusion oil film damper caused by transient static eccentricity. The bearing dynamics model building module is used to build a bearing dynamics model that takes into account the time-varying and nonlinear changes in bearing height. The analysis and solution module is used to consider various additional inertial moments and inertial forces generated during maneuvering flight. Based on the established rotor-bearing-elastic support coupling model, it considers the instantaneous oil film force generated by the squeeze oil film damper, the influence of the squirrel cage elastic support stiffness on the overall stiffness of the rotor system, the rubbing force of the squeeze oil film damper caused by transient static eccentricity, and the bearing dynamic model. Numerical integration is used to solve the problem, so as to achieve accurate analysis of the dynamic characteristics and vibration response mechanism of the elastic support structure of the aero-engine.

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