A method and system for constructing an aero-engine multi-component coupling rub simulation model

Abstract

The application discloses a kind of aero-engine multi-component coupling rub-impact simulation model construction method and system, construct aero-engine multi-component finite element model, obtain the mass matrix, stiffness matrix and gyro matrix of each component, establish the coupling relationship of blade and rotating disc, and bearing and casing using equivalent stiffness and coordinate transformation, establish the coupling relationship between each rotating disc, and rotating disc and bearing using simulation rotating shaft, form multi-component coupling model;According to the relative displacement between the normal vibration displacement of blade and the vibration displacement of casing and the non-uniform circumferential gap, determine the rub-impact force by Lankarani-Nikravesh rub-impact force model;Rub-impact force is applied as external force term in multi-component coupling model, and multi-component coupling rub-impact simulation model is obtained.The multi-component coupling rub-impact simulation model constructed by the method can reflect the mutual transmission and coupling effect of vibration energy between rotating and stationary components when rub-impact fault occurs.

Description

Technical Field

[0001] This invention relates to the field of technology for constructing dynamic models of blade-casing collision faults in aero-engines, and more specifically to a method and system for constructing a simulation model of multi-component coupled collisions in aero-engines. Background Technology

[0002] Under continuous high-speed, high-load operation, the extremely small gap between the blades and casing of an aero-engine leads to frequent contact between them, resulting in rubbing failures. Rubbing failures not only cause wear of the sealing coating and aerodynamic performance degradation, but can also seriously compromise flight safety. Due to the involvement of nonlinear contact forces, multi-source excitation, and complex coupled structural responses, the vibration characteristics of rubbing failures are extremely complex, making fault identification and localization a significant challenge. Therefore, in-depth research into the dynamic response characteristics of blade-casing rubbing failures is of great engineering significance for improving the health monitoring and fault prediction capabilities of aero-engines.

[0003] Currently, in existing research on rubbing failures, Song Xuyuan's team, in their paper "Vibration performance of rotating thin-walled cylindrical shell with tip-rubbing excitation between drum and stator vane segment of aero-engine," proposed a method that simplifies the engine drum into a rotating thin-walled cylindrical shell structure with one end fixed, starting from the perspective of casing model construction. A dynamic model was established based on Donnel's thin-shell theory and Lagrange's equations. To simulate the single-point rubbing process between the blade cascade and the drum, the team introduced an equivalent contact stiffness and a Coulomb friction model, equating the rubbing excitation to a time-varying nonlinear additional stiffness matrix acting on the shell. This theoretically revealed the abrupt change in the drum structure stiffness at the moment of rubbing and analyzed the nonlinear vibration phenomena under different rotational speeds and rubbing parameters.

[0004] However, in order to simplify the calculation, the above-mentioned existing technical methods have simplified the complex structure of the actual aero-engine and ignored the physical properties of the blades themselves. They only use a time-varying additional stiffness matrix to make the overall equivalent of the rubbing excitation, which makes it difficult for the model to effectively analyze the influence of the blade's own property changes on the rubbing fault response characteristics. It also limits the true reflection of the feedback effect of rotor system vibration on the rubbing process. Summary of the Invention

[0005] To address the problems existing in the above-mentioned fields, this invention proposes a method and system for constructing a multi-component coupled collision simulation model for aero-engines. The constructed multi-component coupled collision simulation model can realistically reflect the mutual transmission and coupling effect of vibration energy between rotating and stationary components during collision failure.

[0006] To address the aforementioned technical problems, this invention discloses a method for constructing a multi-component coupled collision simulation model for aero-engines, comprising the following steps: Based on the geometric and material parameters of the turntable, blades, casing, and bearings, a multi-component finite element model of an aero-engine is constructed. Among them, a non-uniform circumferential gap is set between the casing and the blade tip. The blade finite element model is constructed using plate theory. The blade finite element model has radial and chordal vibration displacement degrees of freedom. Based on the finite element model of multiple components of an aero-engine, the mass matrix, stiffness matrix, and gyro matrix of each component are obtained. Based on the mass matrix, stiffness matrix, and gyro matrix, the coupling relationship between the blade and the turntable, and between the bearing and the casing are established using equivalent stiffness and coordinate transformation. The coupling relationship between each turntable and between the turntable and the bearing is established using a simulated rotating shaft, thus forming a multi-component coupling model. Based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, the friction force is determined by the Lankarani-Nikravesh friction force model; the friction force is applied as an external force to the multi-component coupled model to obtain the multi-component coupled friction simulation model.

[0007] Preferably, the determination of the friction force based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing, and the non-uniform circumferential gap, using the Lankarani-Nikravesh friction force model, specifically includes: When the relative displacement exceeds the non-uniform circumferential gap, the friction force consists of radial friction force and tangential friction force; when the relative displacement does not exceed the non-uniform circumferential gap, the friction force is zero. The radial friction force is determined based on the Lankarani-Nikravesh model, the tangential friction force is determined based on the chordal vibration velocity of the blade and Coulomb's law of friction, and the chordal vibration velocity is determined based on the chordal vibration displacement.

[0008] Preferably, the finite element model of the blade also has axial vibration displacement degree of freedom, and takes into account its gyroscopic effect, geometric nonlinearity, and centrifugal potential energy generated by rotation on the bias disk.

[0009] Preferably, establishing the coupling relationship between the blade and the turntable, and between the bearing and the casing, using equivalent stiffness and coordinate transformation specifically includes: Based on the equivalent stiffness of the connection between the blade and the turntable, the stiffness matrix of the blade is transformed to the turntable coordinate system through a rotation transformation matrix to determine the coupling relationship between the blade and the turntable. Based on the equivalent stiffness of the bearing housing, the normal and tangential vibration displacement degrees of freedom of the casing are mapped to the horizontal and vertical vibration displacement degrees of freedom of the bearing through a coordinate transformation matrix, thereby determining the coupling relationship between the bearing and the casing.

[0010] Preferably, the step of establishing the coupling relationship between the turntables and between the turntables and the bearings using a simulated rotating shaft specifically includes: By simulating the rotating shaft using beam elements, the connection relationships between each turntable and between the turntable and the bearing are established; When the components at both ends of the shaft segment of the rotating shaft undergo relative displacement, the beam element generates elastic potential energy; Based on the elastic potential energy generated by the beam unit, the coupling relationship between each turntable and between the turntable and the bearing is established.

[0011] Preferably, the non-uniform circumferential gap is determined based on a preset initial gap, variable gap, gap angle, and gap range.

[0012] Preferably, the radial friction force is determined based on the Lankarani-Nikravesh model, specifically including: Obtain the preset impact stiffness and coefficient of restitution; The penetration depth is determined based on the normal vibration displacement of the blades and the vibration displacement of the casing at the current time step. The normal vibration velocity is obtained by differentiating the normal vibration displacement of the blade, and the rubbing velocity is determined based on the normal vibration velocity. Based on the aforementioned friction stiffness, coefficient of restitution, penetration depth, and friction velocity, the current radial friction force is determined.

[0013] Preferably, the Newmark-β method is used to numerically solve the multi-component coupling model.

[0014] Preferably, the casing is constructed using the finite element method, with both ends of the casing rigidly fixed. Its nodal displacement vector includes radial, tangential, and axial vibration displacements, as well as rotation angles around the radial, tangential, and axial axes.

[0015] Preferably, it also includes a system for constructing a multi-component coupled collision simulation model of an aero-engine, comprising: The finite element model construction module is used to construct finite element models of multiple components of an aero-engine based on the geometric and material parameters of the turntable, blades, casing, and bearings. Among them, a non-uniform circumferential gap is set between the casing and the blade tip, and the blade finite element model is constructed using plate theory. The blade finite element model has radial and chordal vibration displacement degrees of freedom. The coupling relationship establishment module is used to obtain the mass matrix, stiffness matrix and gyro matrix of each component according to the finite element model of the multi-component aero-engine; based on the mass matrix, stiffness matrix and gyro matrix, the coupling relationship between the blade and the turntable and the bearing and the casing is established by using equivalent stiffness and coordinate transformation; the coupling relationship between each turntable and between the turntable and the bearing is established by using the simulated rotating shaft, thus forming a multi-component coupling model. The collision simulation model generation module is used to determine the collision force based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, using the Lankarani-Nikravesh collision force model; the collision force is applied as an external force term to the multi-component coupled model to obtain the multi-component coupled collision simulation model.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes a method for constructing a multi-component coupled collision-rubbing simulation model for aero-engines. It employs plate theory to construct a blade model with normal and chordal vibration displacement degrees of freedom, reflecting the direct influence of the blade's mass, stiffness, geometry, and vibration mode on the collision-rubbing process. This overcomes the shortcomings of existing technologies that equate the blade to a time-varying stiffness matrix, thus failing to analyze the influence of blade parameters. The multi-component coupled model formed by this invention can realistically reflect the mutual transmission and coupling effects of vibration energy between rotating and stationary components during collision-rubbing failures. The Lankarani-Nikravesh collision-rubbing force model is used to determine the collision-rubbing force. This model, based on Hertzian contact theory, calculates the collision-rubbing force in real time according to the penetration depth between the blade and the casing and the collision-rubbing velocity. It can capture the nonlinear impact characteristics caused by changes in penetration depth during collision and the energy loss during the collision process. Applying the collision-rubbing force as an independent external force term to the multi-component coupled model differs from existing technologies that equate the collision-rubbing force to a time-varying stiffness matrix. This method can realistically simulate the physical process of collision-rubbing failures, where they occur only when they happen and disappear when they don't, providing precise force boundary conditions for analyzing the nonlinear vibration response under collision-rubbing failures. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method for constructing a multi-component coupled collision simulation model of an aero-engine proposed in this invention; Figure 2 A schematic diagram of the aero-engine collision fault simulation model constructed according to the present invention; Figure 3 This is a schematic diagram of the casing coordinate transformation provided in an embodiment of the present invention; Figure 4 The overall simulation flowchart of the aircraft engine collision fault simulation model provided in the embodiment of the present invention is shown. Detailed Implementation

[0018] The following will refer to the appendices in the embodiments of the present invention. Figures 1-4 The technical solutions in the embodiments of the present invention will be clearly and completely described. It should be understood that the terminology used in the present invention is only for describing particular implementation methods and is not intended to limit the present invention.

[0019] Example like Figure 1 As shown, this invention proposes a method for constructing a multi-component coupled collision simulation model of an aero-engine, comprising the following steps: S1: Construct a multi-component finite element model of an aero-engine, which includes a turntable, blades, bearings, and casing, such as... Figure 2 As shown, it includes two bearings (bearing 1 and bearing 2), three turntables (disc 1, disc 2 and disc 3), each turntable having multiple blades, a housing, and a shaft. l 1 indicates the distance between the fixed end on the left side of the casing and the connection point between the casing and bearing 1. l 2 indicates the distance between the left side connection point of the casing and bearing 1 and the corresponding axial position of the disc 1. l 3 indicates the distance between the axial position of disk 1 and the connection point between the casing and bearing 2. l 4 indicates the distance between the connection point of disc 1 and bearing 1 on the same rotating shaft. l 5 indicates the distance between the connection point of bearing 1 and the shaft and disc 2. l 6 represents the distance between disk 2 and disk 3. l 7 indicates the distance between the connection point of disc 3 and bearing 2 on the same rotating shaft. l a This indicates the total axial length of the casing.

[0020] The non-uniform circumferential gap between the casing and the blade tip is expressed as follows: ; In the formula, These represent the preset initial gap, variable gap, gap angle, and gap range, respectively. Indicates the first k The angular position of each blade, subscript k Indicates the blade number.

[0021] The blade model is constructed using plate theory, and the blade model has normal and chord vibration displacement degrees of freedom.

[0022] The blade model also has axial vibration displacement degree of freedom, and takes into account its gyroscopic effect, geometric nonlinearity, and centrifugal potential energy generated by rotation on the bias disk.

[0023] S2: Based on the finite element model of multiple components of the aero-engine, obtain the mass matrix, stiffness matrix and gyro matrix of each component; based on the mass matrix, stiffness matrix and gyro matrix of each component, establish the coupling relationship between the blade and the turntable, and between the bearing and the casing using equivalent stiffness and coordinate transformation, and establish the coupling relationship between each turntable and between the turntable and the bearing using simulated rotating shaft, thus forming a multi-component coupling model.

[0024] This embodiment defines the first n The vibration displacement vector of each turntable is ,in , , , They represent the first n The vertical displacement, horizontal displacement, and rotation of each turntable Y Rotation angle in the axial direction, around Z Angle of rotation along the axis.

[0025] S21: Based on the finite element model of multiple components of an aero-engine, obtain the mass matrix, stiffness matrix, and gyro matrix of each component, specifically including: Considering the gyroscopic effect caused by each turntable being located outside the mid-span of the axis of rotation, the kinetic energy of each turntable in the multi-component finite element model simultaneously includes rotational and translational kinetic energy under the condition of mass eccentricity. Its expression is as follows: ; ; In the formula, They represent the first n Mass, eccentricity, and initial phase angle of each turntable; Indicates the rotational speed of the shaft; They represent the first n The diameter moment of inertia and polar coordinate moment of inertia of each turntable.

[0026] Based on the kinetic energy expression of the turntable mentioned above, the mass matrix and gyroscope matrix of the turntable are derived through the Lagrange equation.

[0027] For the two bearings involved in the aforementioned finite element model of multiple components of an aero-engine, this invention only considers their translational kinetic energy and elastic potential energy, the expressions of which are: ; ; In the formula, They represent the first n The mass, damping, vertical displacement, and horizontal displacement of each bearing.

[0028] Based on the above expressions for the kinetic and potential energy of the bearing, the mass matrix and stiffness matrix of the bearing are derived through the Lagrange equation.

[0029] In this invention, the Shell181 element in ANSYS is used to construct the finite element model of the casing. The two ends of the casing are rigidly fixed, and its nodal displacement vectors include radial, tangential, and axial vibration displacements as well as rotation angles about the radial, tangential, and axial axes.

[0030] Define the global vibration displacement vector of the casing, which consists of multiple nodes, as follows: , of which i Vibration displacement vector of each node for: ; in, They represent the first i The vibration displacement of each casing node in the radial, tangential, and axial directions, as well as the rotation angle around the radial, tangential, and axial axes.

[0031] Mass matrix based on casing and stiffness matrix The kinetic and potential energies of the casing are obtained as follows: ; ; Based on the above expressions for the kinetic and potential energy of the casing, combined with the mass and stiffness matrices of the casing, the dynamic characteristics of the casing can be determined.

[0032] This invention constructs a finite element model of the blade based on the plate theory assumption, and sets the blades on each turntable to have a common... Each, its length, width, and thickness are defined as follows: a , b , h .

[0033] This invention considers the vibration displacement of the blade in three degrees of freedom: axial, normal, and chord (where the radial direction is consistent with the blade's normal direction) and the gyroscopic effect on the bias disk.

[0034] The kinetic energy expression for the blade is: ; In the formula, These represent the vibration displacement matrix and density of the blade, respectively.

[0035] The potential energy of the blade consists of two parts: one part is the potential energy generated by the bending and deformation of the blade, and the other part is the centrifugal potential energy generated by the rotation of the blade on the turntable. Specifically: The expression for the bending potential energy of the blade is as follows: ; In the formula, These represent Young's modulus and Poisson's ratio of the blade, respectively. They represent the first k Deformation of the neutral surface of each blade.

[0036] The neutral plane is the intermediate reference plane along the thickness direction of the blade. In classical thin-plate theory, the blade thickness is relatively small, and it is generally assumed that a straight line perpendicular to the neutral plane before deformation remains straight and approximately perpendicular to the deformed neutral plane after deformation. Therefore, the three-dimensional deformation of the blade can be described by the displacement on the neutral plane. When the blade vibrates, axial and chordal displacements directly cause in-plane tension or compression on the neutral plane; simultaneously, normal deflection changes the actual distance between adjacent points on the neutral plane, causing additional tensile deformation. Therefore, when considering geometric nonlinearity, the strain on the neutral plane includes not only the first derivative of the displacement but also the quadratic term of the normal displacement gradient.

[0037] The in-plane strain of the neutral plane consists of components in three directions, namely axial strain. Normal strain and shear strain The three components have the following corresponding expressions: ; The expression for the centrifugal potential energy of the blade is: ; in, They represent the first n The radius of the first turntable and the first k The normal deformation component of each blade.

[0038] Based on the above expressions for the kinetic and potential energy of the blade, the mass matrix, stiffness matrix, and gyroscope matrix of the blade are derived using the Lagrange equation.

[0039] S22: Based on the mass matrix, stiffness matrix, and gyro matrix of each component, the coupling relationship between the blade and the turntable, and between the bearing and the casing, is established using equivalent stiffness and coordinate transformation. The coupling relationship between the turntables and between the turntable and the bearing is established using a simulated rotating shaft, forming a multi-component coupling model, specifically including: Based on the equivalent stiffness of the connection between the blade and the turntable, the stiffness matrix of the blade is transformed to the turntable coordinate system through a rotation transformation matrix to determine the coupling relationship between the blade and the turntable. Based on the equivalent stiffness of the bearing housing, the normal and tangential vibration displacement degrees of freedom of the casing are mapped to the horizontal and vertical vibration displacement degrees of freedom of the bearing through a coordinate transformation matrix, thereby determining the coupling relationship between the bearing and the casing.

[0040] By simulating the rotating shaft using beam elements, the connection relationships between each turntable and between the turntable and the bearing are established; When the components at both ends of the shaft segment of the rotating shaft undergo relative displacement, the beam element generates elastic potential energy; Based on the elastic potential energy generated by the beam elements, the coupling relationship between each turntable and between the turntable and the bearing is established.

[0041] Based on the coupling relationship between the bearing and the casing, as well as the coupling relationships between each turntable and between the turntable and the bearing, a multi-component coupling model is formed.

[0042] Specifically, the present invention connects the blades and the turntable, as well as the bearings and the casing, based on equivalent stiffness and a rotating coordinate system. By setting the connections between the blades, the turntable, the bearings and the casing, the vibration response between the components is coupled.

[0043] This invention constructs the connection between turntables and between turntables and bearings using beam units, specifically, as follows: Figure 2 As shown, each turntable and bearing is connected by a rotating shaft. When the first... n When relative displacement occurs between the components at both ends of a shaft segment (such as two turntables, or a turntable and a bearing), the shaft segment is stretched, bent, or twisted, thereby generating elastic potential energy, which is the basis for constructing the overall stiffness matrix of the rotor system.

[0044] No. n Elastic potential energy of each axis segment The expression is: ; in, Indicates the first n The stiffness matrix of the beam element corresponding to each axis segment Indicates the first n The displacement vectors at both ends of each shaft segment (including the lateral displacement and rotation of the nodes at both ends).

[0045] The rotation transformation matrices of the blade along the three coordinate axes of the spatial coordinate system are: ; Based on this, the elastic potential energy generated between the blade and the turntable due to the blade vibration is: ; In the formula, These represent the stiffness matrix of the blade in the axial direction, the stiffness matrix in the tangential direction, and the stiffness matrix in the normal direction, respectively.

[0046] Based on the translational kinetic energy of the turntable under mass eccentricity, this energy is combined with the casing vibration at the axial position corresponding to the support position. Then, the elastic potential energy of the casing is calculated based on the displacement difference between the casing and the bearing and the equivalent stiffness. for: ; In the formula, These represent the relative displacement between the bearing and the casing at the connection point, and the equivalent stiffness matrix of the bearing housing, respectively.

[0047] The vibration displacements of the casing in the normal and tangential directions can be converted into horizontal and vertical directions through coordinate transformation, such as... Figure 3 As shown in the figure, O i Indicates the first i The position coordinates of each node casing U i Indicates the first i Normal vibration displacement of each node casing V i Indicates the first i Tangential vibration displacement of each node casing Indicates the first i The angular position of each node in the casing corresponds to the rotation angle in the generalized coordinate system and the casing's local coordinate system. The casing model constructed using the finite element method vibrates in the local coordinate system, and its vibration needs to be transformed to the generalized coordinate system before it can be connected to the bearing.

[0048] Therefore, combining The normal and tangential vibration displacements of each node casing can be converted into the expressions for the horizontal and vertical displacements: ; ; After completing the kinetic and potential energy analysis of the turntable, blades, casing, bearings, and various connecting components, a rotor system model is constructed based on Hamilton's principle. The expression for Hamilton's principle is: ; In the formula, These represent kinetic energy, potential energy, and the work done by external forces (including frictional forces).

[0049] Hamilton's principle can be used to obtain the mass matrix, stiffness matrix, gyroscope matrix, and external force matrix of the corresponding analyzed component / equipment.

[0050] Meanwhile, to address the unavoidable damping effects during normal equipment operation, this invention constructs a damping matrix based on the Rayleigh damping method. D z for: ; In the formula, M z andK z These represent the mass matrix and stiffness matrix of the corresponding analyzed component / equipment, respectively. These represent the Rayleigh damping ratio.

[0051] Based on the above analysis, by combining this elastic potential energy with the mass matrices of each component of the rotor system and the gyroscope matrix obtained above, the rotor system model can be obtained through the Lagrange equation as follows: ; In the formula, These represent the mass matrix, damping matrix, gyroscope matrix, stiffness matrix, external force matrix, and vibration displacement matrix of the rotor system, respectively.

[0052] S3: Based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, the friction force is determined by the Lankarani-Nikravesh friction force model; the friction force is applied as an external force term to the multi-component coupled model to obtain the multi-component coupled friction simulation model.

[0053] Specifically, based on the equivalent stiffness of the connection between the blade and the turntable, the stiffness matrix of the blade is transformed to the turntable coordinate system through a rotation transformation matrix to determine the coupling stiffness matrix between the blade and the turntable. Based on the equivalent stiffness of the bearing housing, the normal and tangential degrees of freedom of the casing are mapped to the horizontal and vertical degrees of freedom of the bearing through a coordinate transformation matrix to determine the rotation-static coupling stiffness matrix. The mass matrix, stiffness matrix, damping matrix, and gyroscope matrix of each component are combined with the coupling stiffness matrix and the static-rotation coupling stiffness matrix, and assembled according to the degree of freedom correspondence to form the overall mass matrix, overall stiffness matrix, overall damping matrix, and overall gyroscope matrix of the complete coupled system. Based on the overall mass matrix, overall stiffness matrix, overall damping matrix, and overall gyroscope matrix of the complete coupled system, construct the motion differential equations of the complete coupled system.

[0054] In this embodiment, based on the rotor system model constructed in step S22 above, and combining the elastic potential energy between the blades and the turntable due to blade vibration, the elastic potential energy between the casing and the bearings, the coordinate changes between the rotating coordinate system and the generalized coordinate system, the mass matrix of the blades and the casing, the Coriolis force matrix (specifically, the matrix generated by the gyroscopic effect on the eccentric mass, which is a variation of the gyroscopic matrix), the stiffness matrix, and the damping matrix, the matrix expressions are combined to obtain a complete multi-component coupling model as follows: ; In the formula, These represent the mass matrix, damping matrix, gyroscope matrix, stiffness matrix, external force matrix, and vibration displacement matrix of the rotor-bearing-casing system, respectively.

[0055] in, M It is derived from the corresponding mass matrices of the rotor system, blades, bearings, and casing through coordinate system transformation based on their degrees of freedom. Similarly, it is obtained... D , G , K and F .

[0056] Specifically, in the multi-component coupling model, the friction force between the blade and the casing is determined based on whether the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing exceeds the non-uniform circumferential gap. This friction force includes radial friction force and tangential friction force. The radial friction force is determined based on the Lankarani-Nikravesh model, and the tangential friction force is determined based on the chordal vibration velocity of the blade and Coulomb's law of friction. The chordal vibration velocity is determined based on the chordal vibration displacement.

[0057] In this embodiment, when the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing exceeds the non-uniform circumferential gap, contact occurs at the current time step. The magnitude of the radial friction force generated at the current time step is calculated using the Lankarani-Nikravesh model, and its expression is as follows: ; In the formula, These represent the rubbing stiffness, coefficient of restitution, penetration depth, rubbing velocity, and initial rubbing velocity at the current time step, respectively.

[0058] Based on Coulomb's law of friction and the chordal vibration velocity of the blade, the expression for the tangential friction force can be obtained: ; In the formula, These represent the sign function and the tangential vibration velocity of the blade, respectively.

[0059] In this embodiment, vibration damping of the turntable and bearings is introduced through parameter settings, while Rayleigh damping is used for the structural damping of the casing and blades.

[0060] In the overall solution, the beam function combination method is used to solve the radial and chordal vibration displacements of the blades, and the Newmark-β method is used to numerically solve the multi-component coupled model, thereby obtaining the vibration response characteristics of the turntable, bearings, blades and casing under the rubbing fault condition.

[0061] like Figure 4 The diagram shown is a detailed simulation flowchart of the aero-engine collision fault simulation model provided in this embodiment. For a specified time step, Total duration.

[0062] ① Set initial parameters, including: motion conditions, physical properties of the overall system (including the mass, stiffness, radius and length of each connecting section, damping ratio of the rotor system; length, width, height, density, number, angular position, Young's modulus, Poisson's ratio of the blades; length, thickness, radius, Young's modulus, Poisson's ratio of the casing), number of casing nodes, number of calculated blade modes, rubbing fault parameters (including initial clearance, varying clearance, clearance angle, clearance range, coefficient of restitution, Coulomb friction coefficient), and total calculation duration and time step; ② Set the initial motion conditions for the turntable, support, casing, and blades, namely the initial vibration displacement, velocity, and acceleration; ③ Based on the initial motion conditions of the turntable, support, casing, and blades, calculate the penetration depth of each component under the current conditions (specifically, by subtracting the vibration displacement of the casing from the vibration displacement of the blade tip and the gap value), and determine whether the object currently being simulated by the model has failed. If a failure occurs, calculate the friction force using the Lankarani-Nikravesh model. If no failure occurs, the friction force is 0. ④ Transform the obtained friction force to the local coordinate system of the blade and apply it to the finite element model of the blade. Combine the current motion state of the blade in the finite element model with the mass matrix, stiffness matrix, Coriolis force matrix and damping matrix of the blade. Solve the motion state of the blade after being subjected to friction force using the Newmark-β method, and use it as the new motion state of the blade. ⑤ Combine the new blade motion state with the equivalent stiffness of the blade-turntable connection, calculate the elastic potential energy between the blade and the turntable, and change the force on the turntable to the turntable coordinate system through coordinate transformation. Then, calculate the vibration state of the turntable after receiving the force using the Newmark-β method. ⑥ By using the shaft stiffness and the change in motion state of the turntable after the blade force, calculate the elastic potential energy of the shaft. Combine the mass, stiffness, and damping matrix of the rotor system, and use the Newmark-β method to calculate the vibration state of the bearings and other turntables that have not experienced rubbing failures after being subjected to force. ⑦ By using the equivalent stiffness of the connection between the bearing and the casing, combined with the new vibration state of the bearing, the force on the casing is calculated. Then, through coordinate transformation, the force is decomposed to each new connection node of the casing, and the new vibration state of the casing is calculated using the Newmark-β method. ⑧ Thus, a new vibration state calculation for all components is completed. The calculation is compared to see if the required total calculation time has been reached. If not, the current motion state is used as the starting point to continue the cycle calculation of the motion state update of each component at the next time step.

[0063] This invention also includes step S4: using Fast Fourier Transform, extracting the power frequency amplitude values ​​of each stage of the disc and the casing under normal and different axial positions during blade-casing rubbing fault conditions, quantifying and analyzing the ability of the rubbing fault response to be transmitted from the fault location along the shaft or along the bearing to the casing, and defining the vibration transmission coefficient and the absolute sensitivity coefficient. Wherein:

[0064] The expression for the vibration transmission coefficient is: ; In the formula, The values ​​represent the changes in the power frequency vibration displacement amplitude at the turntable where the rubbing failure occurred and at other turntables where the rubbing failure did not occur.

[0065] The vibration transmission coefficient is used to characterize the ability of a rubbing fault response at different axial positions to be transmitted along the shaft. It compares the relative change in the power frequency amplitude of other discs that did not experience a rubbing fault relative to the disc at the fault location. TR A value close to or greater than 1 indicates that the axial transmission of the rubbing fault at that location is relatively strong; if TR A value much less than 1 indicates that the axial rubbing fault will not affect other turntables on the shaft.

[0066] The expression for the absolute sensitivity coefficient is: ; in, These represent the changes in the power frequency amplitude of the housing under fault state 1, the changes in the power frequency amplitude of the housing under fault state 2, the changes in the power frequency amplitude of the rubbing position turntable under fault state 1, and the changes in the power frequency amplitude of the rubbing position turntable under fault state 2, respectively.

[0067] The absolute sensitivity coefficient is used to measure the significance of the casing vibration response at different axial positions. If a blade-casing rubbing fault at a certain axial position produces a larger absolute sensitivity coefficient, it means that the response change on the casing is closer to the vibration response change of the turntable at the location of the rubbing fault, and the rubbing fault at that axial position is more likely to be reflected in the casing.

[0068] This invention also proposes a system for constructing a multi-component coupled collision simulation model for aero-engines, comprising: The finite element model construction module is used to construct finite element models of multiple components of an aero-engine based on the geometric and material parameters of the turntable, blades, casing, and bearings. Among them, a non-uniform circumferential gap is set between the casing and the blade tip, and the blade finite element model is constructed using plate theory. The blade finite element model has radial and chordal vibration displacement degrees of freedom. The coupling relationship establishment module is used to obtain the mass matrix, stiffness matrix and gyro matrix of each component based on the finite element model of the multi-component aero-engine; based on the mass matrix, stiffness matrix and gyro matrix, the coupling relationship between the blade and the turntable, and between the bearing and the casing is established by using equivalent stiffness and coordinate transformation; the coupling relationship between each turntable and between the turntable and the bearing is established by using the simulated rotating shaft, thus forming a multi-component coupling model. The collision simulation model generation module is used to determine the collision force based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, using the Lankarani-Nikravesh collision force model; the collision force is then applied as an external force term to the multi-component coupled model to obtain the multi-component coupled collision simulation model.

[0069] The multi-component coupled collision simulation model constructed in this invention has the following advantages: High fidelity: The fine-grained design takes into account the physical properties of the blades and multiple vibration degrees of freedom, overcoming the shortcomings of oversimplification in existing technologies.

[0070] Strong coupling: It achieves complete dynamic coupling of the rotor-bearing-casing system and can reflect the vibration transmission between rotating and stationary components.

[0071] Closely reflects operating conditions: It can simulate non-uniform thermal gaps and time-varying friction forces, which is closer to the actual operating conditions of the engine.

[0072] Accurate calculation: The simulation process employs time-step integration and dynamic update strategies to achieve accurate solutions for the nonlinear response of the collision, providing reliable model support for analyzing the fault transmission characteristics of different bearing structures and axial positions.

[0073] In summary, the proposed method for constructing a multi-component coupled collision-rubbing simulation model for aero-engines utilizes plate theory to build a blade model with radial and chordal vibration displacement degrees of freedom, reflecting the direct influence of the blade's mass, stiffness, geometry, and vibration mode on the collision-rubbing process. By employing beam element connections, coordinate transformation, and equivalent stiffness coupling, the vibration responses of the rotor and stator systems are unified into a single coupled system dynamic equation, reflecting the mutual transfer and coupling effects of vibration energy between the rotor and stator components during collision-rubbing faults. Using the Lankarani-Nikravesh contact model and Coulomb's friction law, combined with the radial vibration displacement and chordal velocity of the blade, the radial and tangential collision-rubbing forces are dynamically calculated at each time step and updated in real-time to the external force terms of the dynamic equations. This achieves stepwise time-history integration calculation of the collision-rubbing force, capturing the nonlinear impact and friction effects at the moment of collision, and providing accurate force boundary conditions for analyzing the nonlinear vibration response under collision-rubbing faults.

[0074] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0075] Furthermore, unless otherwise stated, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. All references to this specification are incorporated by way of citation to disclose and describe methods relating to those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

Claims

1. A method for constructing a multi-component coupled collision simulation model of an aero-engine, characterized in that, Includes the following steps: Based on the geometric and material parameters of the turntable, blades, casing, and bearings, a multi-component finite element model of an aero-engine is constructed. Among them, a non-uniform circumferential gap is set between the casing and the blade tip. The blade finite element model is constructed using plate theory. The blade finite element model has radial and chordal vibration displacement degrees of freedom. Based on the finite element model of multiple components of an aero-engine, the mass matrix, stiffness matrix, and gyro matrix of each component are obtained. Based on the mass matrix, stiffness matrix, and gyro matrix, the coupling relationship between the blade and the turntable, and between the bearing and the casing are established using equivalent stiffness and coordinate transformation. The coupling relationship between each turntable and between the turntable and the bearing is established using a simulated rotating shaft, thus forming a multi-component coupling model. Based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, the friction force is determined by the Lankarani-Nikravesh friction force model; the friction force is applied as an external force to the multi-component coupled model to obtain the multi-component coupled friction simulation model.

2. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The friction force is determined using the Lankarani-Nikravesh friction force model based on the relative displacement between the normal vibration displacement of the blades and the vibration displacement of the casing, and the non-uniform circumferential gap. Specifically, this includes: When the relative displacement exceeds the non-uniform circumferential gap, the friction force consists of radial friction force and tangential friction force; when the relative displacement does not exceed the non-uniform circumferential gap, the friction force is zero. The radial friction force is determined based on the Lankarani-Nikravesh model, the tangential friction force is determined based on the chordal vibration velocity of the blade and Coulomb's law of friction, and the chordal vibration velocity is determined based on the chordal vibration displacement.

3. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The blade finite element model also has axial vibration displacement degree of freedom, and takes into account its gyroscopic effect, geometric nonlinearity, and centrifugal potential energy generated by rotation on the bias disk.

4. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The establishment of the coupling relationship between the blade and the turntable, and between the bearing and the casing, using equivalent stiffness and coordinate transformation specifically includes: Based on the equivalent stiffness of the connection between the blade and the turntable, the stiffness matrix of the blade is transformed to the turntable coordinate system through a rotation transformation matrix to determine the coupling relationship between the blade and the turntable. Based on the equivalent stiffness of the bearing housing, the normal and tangential vibration displacement degrees of freedom of the casing are mapped to the horizontal and vertical vibration displacement degrees of freedom of the bearing through a coordinate transformation matrix, thereby determining the coupling relationship between the bearing and the casing.

5. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The establishment of coupling relationships between turntables and between turntables and bearings using a simulated rotating shaft specifically includes: By simulating the rotating shaft using beam elements, the connection relationships between each turntable and between the turntable and the bearing are established; When the components at both ends of the shaft segment of the rotating shaft undergo relative displacement, the beam unit generates elastic potential energy; Based on the elastic potential energy generated by the beam unit, the coupling relationship between each turntable and between the turntable and the bearing is established.

6. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The non-uniform circumferential gap is determined based on the preset initial gap, variable gap, gap angle, and gap range.

7. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 2, characterized in that, The radial friction force is determined based on the Lankarani-Nikravesh model and specifically includes: Obtain the preset impact stiffness and coefficient of restitution; The penetration depth is determined based on the normal vibration displacement of the blades and the vibration displacement of the casing at the current time step. The normal vibration velocity is obtained by differentiating the normal vibration displacement of the blade, and the rubbing velocity is determined based on the normal vibration velocity. Based on the aforementioned friction stiffness, coefficient of restitution, penetration depth, and friction velocity, the current radial friction force is determined.

8. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The Newmark-β method was used to numerically solve the multi-component coupling model.

9. The method for constructing a multi-component coupled collision simulation model of an aero-engine according to claim 1, characterized in that, The casing is constructed using the finite element method. Both ends of the casing are rigidly fixed, and its nodal displacement vectors include radial, tangential, and axial vibration displacements as well as rotation angles around the radial, tangential, and axial axes.

10. A system for constructing a multi-component coupled collision simulation model for an aero-engine, characterized in that, include: The finite element model construction module is used to construct finite element models of multiple components of an aero-engine based on the geometric and material parameters of the turntable, blades, casing, and bearings. Among them, a non-uniform circumferential gap is set between the casing and the blade tip, and the blade finite element model is constructed using plate theory. The blade finite element model has radial and chordal vibration displacement degrees of freedom. The coupling relationship establishment module is used to obtain the mass matrix, stiffness matrix and gyro matrix of each component according to the finite element model of the multi-component aero-engine; based on the mass matrix, stiffness matrix and gyro matrix, the coupling relationship between the blade and the turntable and the bearing and the casing is established by using equivalent stiffness and coordinate transformation; the coupling relationship between each turntable and between the turntable and the bearing is established by using the simulated rotating shaft, thus forming a multi-component coupling model. The collision simulation model generation module is used to determine the collision force based on the relative displacement between the normal vibration displacement of the blade and the vibration displacement of the casing and the non-uniform circumferential gap, using the Lankarani-Nikravesh collision force model; the collision force is applied as an external force term to the multi-component coupled model to obtain the multi-component coupled collision simulation model.

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