Fault rotor dynamics simulation method and system, electronic device and storage medium

Abstract

The application belongs to the technical field of rotor dynamics, and discloses a fault rotor dynamics simulation method, a system, an electronic device and a storage medium, wherein the method comprises the following steps: establishing a finite element model of a rotor system; a crack model is established, and a stiffness matrix of a crack element is obtained according to the crack model and physical parameters of the crack element; a loose stiffness model and a loose damping model of a bearing are established, and the stiffness and damping of the loose bearing are obtained; the stiffness matrix of the crack element and the stiffness and damping of the loose bearing are used to reassemble and obtain a system stiffness matrix and a system damping matrix of the rotor system; and the dynamic response characteristics of the rotor system are obtained according to the system stiffness matrix and the system damping matrix. The application adopts a finite element numerical simulation method, comprehensively considers the coupling fault situation of cracks and bearing seat looseness, and proposes a simulation analysis method of the rotor system under the coupling fault, so that the simulation analysis method has higher calculation precision under the coupling fault situation and is more practical.

Description

Technical Field

[0001] This invention belongs to the field of rotor dynamics technology, and more specifically, relates to a fault rotor dynamics simulation method, system, electronic device and storage medium. Background Technology

[0002] Rotating machinery plays a vital role in modern industrial society, widely used in transportation, energy, mining, metallurgy, and manufacturing industries. Typical examples include generators, steam turbines, centrifugal compressors, and aircraft engines. The core component of rotating machinery is the rotor system. Due to its own weight, the rotor system experiences significant transverse bending fatigue stress during high-speed rotation, making it prone to transverse cracks. Rotor system rotation also easily leads to loosening of bearing housings. Rotor cracks and loose bearing housings are common faults in rotating machinery. Rotor system failures occur frequently, and if not monitored promptly, they can seriously threaten the operational safety of the system. Therefore, research on the dynamic characteristics of rotor systems under fault conditions is particularly important.

[0003] Invention patent CN115270577A discloses a simulation method for rotor cracks. This method addresses the case where the crack is located on the shaft segment at the junction of the disk load and the rotor shaft. Noise is introduced into the simulated signal, and then CYCBD noise reduction and Teager energy envelope spectrum analysis are performed on the noise-introduced signal to achieve fault diagnosis of the crack. While this existing rotor system simulation method incorporates fault diagnosis, it suffers from limitations in studying a single type of fault and fails to consider the possibility of simultaneous bearing housing loosening faults. This could lead to reduced identification accuracy if the system exhibits both crack and loosening coupled faults. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a fault rotor dynamics simulation method, system, electronic device, and storage medium. It solves the problem that existing rotor system simulation methods only study a single type of fault and do not consider the possible simultaneous occurrence of bearing housing loosening faults. This leads to a potential decrease in identification accuracy if the system has both crack and loosening coupled faults. This invention enables simulation analysis of the dynamic response characteristics of rotor systems under crack and loosening coupled faults.

[0005] To achieve the above objectives, according to a first aspect of the present invention, a fault rotor dynamics simulation method is provided, characterized by comprising:

[0006] The three-dimensional model of the rotor system is divided into multiple shaft segment elements to establish the finite element model of the rotor system.

[0007] A crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element, wherein the crack element is the shaft segment element with crack fault.

[0008] Establish a loosening stiffness model and a loosening damping model for the bearing, and obtain the stiffness and damping of the loose bearing based on the loosening stiffness model, the loosening damping model, and the displacement of the loose bearing with loosening fault.

[0009] Based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing, the system stiffness matrix and system damping matrix of the rotor system are reassembled and obtained.

[0010] The dynamic response characteristics of the rotor system are obtained based on the system stiffness matrix and the system damping matrix.

[0011] According to the fault rotor dynamics simulation method provided by this invention, a crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element. Specifically, this includes:

[0012] Establish a coordinate system for the rotor system, wherein the axial direction of the rotor system is set along the X-axis;

[0013] Based on the inner diameter, outer diameter, crack depth, and crack angle of the cracked element, the mechanical parameters of the cracked element during the rotation of the rotor system are obtained. The mechanical parameters include the moment of inertia of the cracked part of the cracked element about the Y-axis, the moment of inertia about the Z-axis, the eccentricity, and the area of ​​the uncracked part on the cross section of the cracked element.

[0014] Based on the mechanical parameters and the physical parameters of the crack element, obtain the additional stiffness matrix generated by the crack;

[0015] Based on the crack model and the additional stiffness matrix, the stiffness matrix of the crack element in the rotating coordinate system is obtained.

[0016] According to the fault rotor dynamics simulation method provided by the present invention, a crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element. The method further includes:

[0017] Based on the stiffness matrix of the crack element in the rotating coordinate system, the stiffness matrix of the crack element in the static coordinate system is obtained.

[0018] The stiffness matrix of the crack element in the static coordinate system is:

[0019] k st =T T k ce T;

[0020]

[0021]

[0022] Where, k st k is the stiffness matrix of the crack element in the static coordinate system. ce T is the stiffness matrix of the crack element in the rotating coordinate system; T is the element transformation matrix from the rotating coordinate system to the static coordinate system; T e Ω is the node transformation matrix from the rotating coordinate system to the static coordinate system; Ω is the rotational angular velocity of the crack element; and t is the rotation time.

[0023] According to the fault rotor dynamics simulation method provided by the present invention, the crack model is as follows:

[0024]

[0025] Where Ω is the rotational angular velocity of the crack element; t is the rotation time; α = cos -1 (1-d / r2), where d is the crack depth, r2 is the outer radius of the crack element, and j is the number of rotations, which is 0, 1, 2, ...

[0026] According to the fault rotor dynamics simulation method provided by the present invention, the loosening stiffness model is as follows:

[0027]

[0028] Where, k ac k represents the stiffness of the loose bearing. b1 k b2 and k b3 σ is the set value; σ is the maximum loose clearance of the loose bearing; y is the displacement of the loose bearing in the vertical direction;

[0029] The loosening damping models are as follows:

[0030]

[0031] Among them, c ac c is the damping of the loose bearing; b1 c b2 c b3 This is the set value.

[0032] According to the fault rotor dynamics simulation method provided by the present invention, the system stiffness matrix and system damping matrix of the rotor system are reassembled based on the stiffness matrix of the cracked element and the stiffness and damping of the loose bearing, specifically including:

[0033] The rotor system includes an inner shaft and an outer shaft that are sleeved together. The bearings of the rotor system include intermediate bearings. The intermediate bearings are numbered m and n on the inner shaft and the outer shaft, respectively. The stiffness k of the intermediate bearings in the horizontal direction is... bz and vertical stiffness k by Size k bz =k by =k b Damping in the horizontal direction c bz and vertical damping c by Size is c bz =c by =c b Then the stiffness matrix K of the intermediate bearing ib and damping matrix C ib They are respectively:

[0034]

[0035]

[0036] According to the fault rotor dynamics simulation method provided by the present invention, the dynamic response characteristics of the rotor system are obtained based on the system stiffness matrix and the system damping matrix, specifically including:

[0037] The displacement, velocity, and acceleration of the rotor system are calculated using the following formulas:

[0038]

[0039]

[0040]

[0041] [RC] st =α[M] st +β[K] st ;

[0042]

[0043]

[0044]

[0045] Among them, [M] st [K] st and [G] stThe mass matrix, stiffness matrix, and gyroscope matrix of the rotor system are respectively derived from the corresponding shaft segment element matrices; M1 is the mass matrix of the inner shaft; M2 is the mass matrix of the outer shaft; K1 is the stiffness matrix of the inner shaft; K2 is the stiffness matrix of the outer shaft; G1 is the gyroscope matrix of the inner shaft; G2 is the gyroscope matrix of the outer shaft; K bearing C is a matrix composed of the stiffness matrices of multiple bearings. bearing A matrix consisting of the damping matrices of multiple bearings, including the intermediate bearing; [RC] st Here, ζ1 and ζ2 are the system's viscous damping matrix; ω1 is the first-order critical speed of the rotor system; ω2 is the second-order critical speed of the rotor system; [u] st , These are the generalized displacement, velocity, and acceleration vectors of the rotor system, respectively; [F g ] st [F] ub ] st These are the gravity and unbalanced force vectors of the rotor system, respectively.

[0046] According to a second aspect of the present invention, a fault rotor dynamics simulation system is provided, comprising:

[0047] The finite element model building module is used to divide the three-dimensional model of the rotor system into multiple shaft segment elements and build the finite element model of the rotor system.

[0048] The first analysis module is used to establish a crack model and obtain the stiffness matrix of the crack element based on the crack model and the physical parameters of the crack element, wherein the crack element is the shaft segment element with crack fault.

[0049] The second analysis module is used to establish a loosening stiffness model and a loosening damping model for the bearing, and to obtain the stiffness and damping of the loose bearing based on the loosening stiffness model, the loosening damping model, and the displacement of the loose bearing with loosening fault.

[0050] The third analysis module is used to reassemble and obtain the system stiffness matrix and system damping matrix of the rotor system based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing.

[0051] The calculation module is used to obtain the dynamic response characteristics of the rotor system based on the system stiffness matrix and the system damping matrix.

[0052] According to a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the fault rotor dynamics simulation method described in any of the preceding claims.

[0053] According to a fourth aspect of the present invention, a non-transitory computer-readable storage medium is provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the fault rotor dynamics simulation method described in any of the preceding claims.

[0054] In summary, compared with the prior art, the fault rotor dynamics simulation method, system, electronic equipment, and storage medium provided by this invention offer the following advantages:

[0055] 1. The finite element numerical simulation method is used to analyze the rotor system. It has the characteristics of unconditional convergence, wide applicability and strong transferability. The finite element model is established based on the three-dimensional model of the rotor system, and the results are closer to the real fault data. In addition, considering the coupled faults of cracks and loose bearing housings, a simulation analysis method for the rotor system under coupled faults is proposed. This makes the simulation method applicable to a variety of fault conditions and has high calculation accuracy under coupled fault conditions, making it more practical.

[0056] 2. It is proposed to first obtain the additional stiffness matrix of crack generation through mechanical analysis, and then obtain the stiffness matrix of crack element through the additional stiffness matrix. Compared with directly calculating the stiffness matrix of crack element, the calculation process is simpler and helps to reduce computational complexity and time consumption.

[0057] 3. Using a high-resolution hybrid model to describe the crack can accurately describe the state changes of the crack during the rotation of the rotor system, thus improving the accuracy of simulation calculations. Attached Figure Description

[0058] Figure 1 This is a flowchart illustrating the fault rotor dynamics simulation method provided by the present invention;

[0059] Figure 2 This is a schematic cross-sectional view of the three-dimensional model of the rotor system provided by the present invention;

[0060] Figure 3 This is a schematic diagram of the shaft segment unit provided by the present invention in a coordinate system;

[0061] Figure 4 This is a cross-sectional schematic diagram of a crack element with shallow cracks provided by the present invention;

[0062] Figure 5 This is a cross-sectional schematic diagram of a crack element in a deep crack provided by the present invention;

[0063] Figure 6 This is a schematic diagram of the numerical simulation process provided by the present invention;

[0064] Figure 7 This is a waveform diagram of the vertical displacement of the crack element node provided by the present invention;

[0065] Figure 8 This is the axisymmetric trajectory diagram of the crack element node provided by the present invention;

[0066] Figure 9 This is a schematic diagram of the electronic device provided by the present invention;

[0067] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0068] 1-17 are the wheel; Ⅰ-Ⅴ are the bearings. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0070] Please see Figure 1 This invention provides a method for simulating the dynamics of a faulty rotor, the method comprising:

[0071] S1, the three-dimensional model of the rotor system is divided into multiple shaft segment elements to establish a finite element model of the rotor system; to more accurately investigate the vibration signal characteristics of the rotor system during faults, this embodiment uses the finite element simulation method. Taking the study of the engine rotor system as an example, refer to... Figure 2 Based on the actual design structure of the engine, a three-dimensional structural model can be established after simplification. The three-dimensional model can then be divided into shaft segment units along the axial direction, thereby transforming the three-dimensional model into a finite element model.

[0072] S2. Establish a crack model. Based on the crack model and the physical parameters of the crack elements, obtain the stiffness matrix of the crack elements. The crack elements are the shaft segment elements with crack faults; the crack model describes the crack variation. Shaft segment elements with crack faults are called crack elements, meaning they have cracks. The physical parameters of the crack elements are known, and mechanical analysis can be performed on the crack elements based on these parameters to obtain their stiffness matrix.

[0073] S3. Establish a loosening stiffness model and a loosening damping model for the bearing. Based on these models and the displacement of the loose bearing with the loosening fault, obtain the stiffness and damping of the loose bearing. Bearing housing loosening is a common fault in rotor systems, leading to bearing loosening. The rotor system includes multiple bearings; the bearing that experiences a loosening fault is the loose bearing. The loosening stiffness model and the loosening damping model are predefined loosening models. Based on these models and the displacement of the loose bearing, the stiffness and damping of the loose bearing can be determined.

[0074] S4. Based on the stiffness matrix of the cracked unit, the stiffness and damping of the loose bearing, the system stiffness matrix and system damping matrix of the rotor system are reassembled and obtained. By reassembling the stiffness matrix of each shaft segment unit and the stiffness and damping matrix of each bearing, the system stiffness matrix and system damping matrix of the rotor system under the coupled fault of crack and loosening can be obtained.

[0075] S5. Based on the system stiffness matrix and the system damping matrix, the dynamic response characteristics of the rotor system are obtained. With the system stiffness matrix and system damping matrix known, the dynamic equations of the rotor system can be calculated, thereby obtaining the dynamic response characteristics of the rotor system, such as vibration data like displacement, velocity, and acceleration, thus enabling simulation analysis of the rotor system under fault conditions.

[0076] The fault rotor dynamics simulation method provided in this embodiment uses the finite element numerical simulation method to analyze the rotor system. It has the characteristics of unconditional convergence of numerical simulation, wide applicability, and strong transferability. The finite element model is established based on the three-dimensional model of the rotor system, and the results obtained are closer to the real fault data. Furthermore, considering the coupled faults of cracks and loose bearing housings, a simulation analysis method for the rotor system under coupled faults is proposed, making the simulation method applicable to a variety of fault conditions. It also has high calculation accuracy under coupled fault conditions, making it more practical.

[0077] Furthermore, establishing the finite element model of the rotor system also includes setting parameters, specifically: setting the physical parameters of any shaft segment element, including parameters such as length, density, Poisson's ratio, inner diameter, and outer diameter; among which, the physical parameters of the crack element also include crack depth and crack angle; it is also necessary to set parameters such as the loosening clearance of the loose bearing. These set parameters are known parameters set during model establishment.

[0078] Further, S2, a crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element, specifically including:

[0079] S21, Reference Figure 3Establish a coordinate system for the rotor system, wherein the axial direction of the rotor system is set along the X-axis;

[0080] S22, based on the inner diameter, outer diameter, crack depth, and crack angle of the cracked unit, obtain the mechanical parameters of the cracked unit during the rotation of the rotor system. The mechanical parameters include the moment of inertia of the cracked part of the cracked unit about the Y-axis, the moment of inertia about the Z-axis, the eccentricity, and the area of ​​the uncracked part on the cross section of the cracked unit.

[0081] S23, Based on the mechanical parameters and the physical parameters of the crack element, obtain the additional stiffness matrix generated by the crack;

[0082] S24. Based on the crack model and the additional stiffness matrix, obtain the stiffness matrix of the crack element in the rotating coordinate system.

[0083] In this embodiment, axial tensile and compressive deformation and torsional deformation around the axis are ignored for any shaft segment element. Mechanical analysis can be performed on the cross-section of the crack element, and the mechanical parameters of the crack element can be calculated based on its physical parameters, thereby obtaining the additional stiffness matrix generated by the crack on the crack element. Then, the stiffness matrix of the crack element is obtained based on the additional stiffness matrix.

[0084] This embodiment proposes to first obtain the additional stiffness matrix generated by the crack through mechanical analysis, and then obtain the stiffness matrix of the crack element through the additional stiffness matrix. Compared with directly calculating the stiffness matrix of the crack element, the calculation process is simpler and helps to reduce computational complexity and time consumption.

[0085] Furthermore, based on the inner diameter, outer diameter, crack depth, and crack angle of the cracked element, the mechanical parameters of the cracked element during the rotation of the rotor system are obtained. These mechanical parameters include the moment of inertia of the cracked portion of the cracked element about the Y-axis, the moment of inertia about the Z-axis, the eccentricity, and the area of ​​the uncracked portion on the cross-section of the cracked element. Specifically, they include:

[0086] The cracks on the crack element are transverse breathing cracks. Based on whether the crack depth exceeds the difference between the inner and outer radii of the axis of rotation it occupies, crack failures can be classified as shallow cracks or deep cracks. The cross-sectional geometric diagrams of the crack element under both failure conditions are shown below. Figure 4 and Figure 5 As shown.

[0087] like Figure 4 and Figure 5Let o be the centroid of the section before cracking, c be the centroid of the section when the crack is fully open, e be the eccentricity, d be the crack depth, τ be the crack angle, and τ1 be the inner crack angle of the deep crack. r1 and r2 are the inner and outer radii of the shaft segment element, respectively. For a given rotor system, assume that when the crack depth is constant, the moment of inertia of the crack section about the coordinate axes oz and oy of the rotating coordinate system is... It is a constant value.

[0088] refer to Figure 4 For shallow cracks, where the crack depth is less than the difference between the inner and outer radii of the crack element, the moments of inertia of the cracked portion about oz and oy during rotation are... and Area A of the uncracked region of the crack element unopen The eccentricity e and crack angle τ are calculated according to the following formulas:

[0089]

[0090]

[0091] A unopen =r2 2 (π-cos -1 (1-λ)+(1-λ)η)-πr1 2 ;

[0092]

[0093] τ=2cos -1 (1-λ);

[0094] Where λ = d / r² is the dimensionless crack depth, also known as the relative crack depth.

[0095] refer to Figure 5 For deep cracks, where the crack depth is greater than the difference between the inner and outer radii of the crack element, the moment of inertia I of the cracked portion about oz and oy during rotation... z ce and I y ce Area A of the uncracked region of the crack element unopen The eccentricity e and the internal crack angle τ1 are calculated according to the following formulas:

[0096]

[0097]

[0098]

[0099]

[0100] Where τ1=2cos -1 ((r2-d) / r1).

[0101] make The moments of inertia of the uncracked region about the new centroidal axes cz and cy are respectively:

[0102]

[0103]

[0104] In the formula, let I = π(r2) 4 -r1 4 ) / 4; is the moment of inertia of the cross section without cracks.

[0105] Additional stiffness matrix k generated by crack ap for:

[0106]

[0107] In the formula, l is the axial length of the crack element;

[0108]

[0109] G is the shear modulus; E is the elastic modulus. ψ is the shear coefficient, expressed as:

[0110]

[0111] The stiffness matrix k of the shaft segment element containing the crack in the rotating coordinate system at time t can be obtained from the crack model and the aforementioned additional stiffness model. ce for:

[0112] k ce =k n -g(t)k ap ;

[0113] Where, k n This is the stiffness matrix of a crack-free shaft segment element.

[0114] Furthermore, a crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element. This also includes:

[0115] Based on the stiffness matrix of the crack element in the rotating coordinate system, the stiffness matrix of the crack element in the static coordinate system is obtained.

[0116] The stiffness matrix k of the crack element in the static coordinate systemst for:

[0117] k st =T T k ce T;

[0118]

[0119]

[0120] Where, k st k is the stiffness matrix of the crack element in the static coordinate system. ce T is the stiffness matrix of the crack element in the rotating coordinate system; T is the element transformation matrix from the rotating coordinate system to the static coordinate system; T e Ω is the node transformation matrix from the rotating coordinate system to the static coordinate system; Ω is the rotational angular velocity of the crack element; and t is the rotation time.

[0121] Furthermore, the crack model is as follows:

[0122]

[0123] Where Ω is the rotational angular velocity of the crack element; t is the rotation time; α = cos -1 (1-d / r2), where d is the crack depth, r2 is the outer radius of the crack element, and j is the number of rotations, which is 0, 1, 2, ...

[0124] This embodiment uses a Gao-Zhu hybrid model to describe the crack, which can accurately describe the state change of the crack during the rotation of the rotor system, thereby improving the accuracy of simulation calculation.

[0125] Furthermore, when a bearing housing becomes loose, the horizontal stiffness drops sharply to zero. Therefore, for a rotor system with this fault, only its vertical displacement, stiffness, and damping need to be analyzed. This embodiment uses a piecewise linear model to represent the stiffness and damping of the loose bearing. Assumptions Figure 2 The bearing housings of bearings I and V have become loose, with a maximum loosening clearance of σ. The segmented stiffness depending on the relative position of the loosening is k. ac The loosening stiffness model is as follows:

[0126]

[0127] Where, k ac k represents the stiffness of the loose bearing. b1 k b2 and k b3σ is a pre-set known parameter representing the bearing housing stiffness in the three loosening stages; σ is the maximum loosening clearance of the loosened bearing; y is the displacement of the loosened bearing in the vertical direction.

[0128] The loosening damping models are as follows:

[0129]

[0130] Among them, c ac c is the damping of the loose bearing; b1 c b2 c b3 The setpoints are pre-set, known parameters representing the bearing damping at three stages of loosening. This allows the determination of the stiffness and damping of the loosened bearing.

[0131] Furthermore, based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing, the system stiffness matrix and system damping matrix of the rotor system are reassembled and obtained, specifically including:

[0132] The rotor system includes an inner shaft and an outer shaft that are sleeved together. The bearings of the rotor system include intermediate bearings. The intermediate bearings are numbered m and n on the inner shaft and the outer shaft, respectively. The stiffness k of the intermediate bearings in the horizontal direction is... bz and vertical stiffness k by Size k bz =k by =k b Damping in the horizontal direction c bz and vertical damping c by Size is c bz =c by =c b Then the stiffness matrix K of the intermediate bearing ib and damping matrix C ib They are respectively:

[0133]

[0134]

[0135] Because the system structure contains an intermediate bearing that couples the two shafts, for example... Figure 2 Therefore, the way the stiffness and damping of the intermediate bearing are grouped in the system stiffness matrix is ​​also one of the key steps of this invention. The matrix grouping method of the intermediate bearing is different from that of ordinary bearings. Assuming that the inner ring of the intermediate bearing is located at the m-th node of the inner shaft and the outer ring is located at the n-th node of the outer shaft, the force balance equations of nodes m and n can be obtained by the following derivation process.

[0136] Let the horizontal and vertical stiffness of the intermediate bearing be k. bz =k by =k b The magnitudes of the horizontal and vertical damping are c. bz =c by =c b Every bearing has stiffness and damping; these are inherent properties of the bearing itself. For example, attached... Figure 2 Each of the five bearings has its own stiffness and damping, which are parameters that need to be preset by the simulation engineer before the simulation begins. Generally, the horizontal and vertical stiffness and damping of the same bearing are equal, but the specific values ​​can be determined based on the actual situation. The typical bearing stiffness is 10. 6 ~10 10 The damping is 1000 N / (m / s), and the specific value is not limited.

[0137] There is relative motion between nodes m and n, and the coupling forces of the intermediate bearing on node m are as follows:

[0138]

[0139] Similarly, the coupling forces of the intermediate bearing at node n are as follows:

[0140]

[0141] Combining the two sets of formulas above and writing them in matrix form, we get:

[0142]

[0143] The stiffness matrix K of the intermediate bearing can be obtained from the above formula. ib and damping matrix C ib Wherein, ΔF mz ΔF is the horizontal force (z-direction) exerted by the intermediate bearing on node m. my Let ΔF be the vertical (y-direction) force exerted by the intermediate bearing on node m; nz ΔF is the horizontal force (z-direction) exerted by the intermediate bearing on node n. ny Z represents the vertical (y-direction) force exerted by the intermediate bearing on node n; m Let y be the displacement of node m in the horizontal direction (z direction); m Let z be the displacement of node m in the vertical direction (y direction); n Let y be the displacement of node n in the horizontal direction (z direction); n Let n be the displacement of node n in the vertical direction (y direction); Let be the velocity of node m in the horizontal direction (z direction); Let be the velocity of node m in the vertical direction (y direction); Let n be the velocity of node n in the horizontal direction (z direction); Let n be the velocity of node n in the vertical direction (y direction).

[0144] For example, the stiffness matrix K of an intermediate bearing ib and damping matrix C ib The meaning of each item in the matrix should be interpreted as follows when adding the stiffness and damping of the intermediate bearing to the system: k should be added to the 4m-3 row and 4m-3 column of the system stiffness matrix. bz (corresponding stiffness matrix K) ib The top-left element), in the system damping matrix, should have c added to the 4m-3 row and 4m-3 column. bz (corresponding damping matrix C) ib The top-left element), in the system stiffness matrix, should have -k added to the 4m-3 row and 4n-3 column. bz (corresponding stiffness matrix K) ib The element in the first row and third column of the system damping matrix (the element in the first row and third column) should have -c added to the 4m-3 row and 4n-3 column. bz (corresponding damping matrix C) ib The element in the first row and third column), where m and n are the node numbers of the intermediate bearing on the inner and outer shafts, respectively, and the meanings of the other items are similar.

[0145] The reason why there are zero terms in the intermediate bearing stiffness matrix and damping matrix is ​​that during simulation, only the stiffness and damping of the bearing in the horizontal direction (z direction) and vertical direction (y direction) are generally considered, while the stiffness and damping in the horizontal and vertical intersection directions are ignored (set to 0), so zero terms will appear.

[0146] Furthermore, based on the system stiffness matrix and the system damping matrix, the dynamic response characteristics of the rotor system are obtained, specifically including:

[0147] The displacement, velocity, and acceleration of the rotor system are calculated using the following formulas:

[0148]

[0149]

[0150]

[0151] [RC] st =α[M] st +β[K] st ;

[0152]

[0153]

[0154]

[0155] Among them, [M] st [K] st and [G] st The mass matrix, stiffness matrix, and gyroscope matrix of the rotor system are respectively derived from the corresponding shaft segment element matrices; M1 is the mass matrix of the inner shaft; M2 is the mass matrix of the outer shaft; K1 is the stiffness matrix of the inner shaft; K2 is the stiffness matrix of the outer shaft; G1 is the gyroscope matrix of the inner shaft; G2 is the gyroscope matrix of the outer shaft; K bearing C is a matrix composed of the stiffness matrices of each bearing in the rotor system. bearing The matrix is ​​composed of the damping matrices of each bearing, including the intermediate bearing; [RC] st Here, ζ1 and ζ2 are the system's viscous damping matrix; ω1 is the first-order critical speed of the rotor system; ω2 is the second-order critical speed of the rotor system; [u] st , These are the generalized displacement, velocity, and acceleration vectors of the rotor system, respectively; [F g ] st [F] ub ] st These are the gravity and unbalanced force vectors of the rotor system, respectively, [F ub ] st Of all the elements, only the wheel node containing the unbalanced quantity is non-zero; all other elements are zero.

[0156] After obtaining the stiffness matrix of the cracked element and the stiffness and damping of the loose bearing in the static coordinate system, the stiffness and damping matrices of each shaft segment element and each bearing are reassembled to obtain the new system stiffness matrix and system damping matrix. For a two-axis system, let the system mass, stiffness, and gyroscope matrices of the inner and outer shafts be M1, M2, K1, K2, G1, and G2, respectively. Then, the total system mass matrix, stiffness matrix, and gyroscope matrix in the static coordinate system are [M]. st [K] st and [G] st Based on the above matrix parameters, the system dynamics equations in the static coordinate system are:

[0157]

[0158] refer to Figure 6When performing numerical simulations using Matlab, before each time step, the stiffness matrix of the crack element and the stiffness and damping matrix of the loose bearing seat (i.e., the loose bearing) are updated based on the current time t and the vertical displacement of the bearing seat at the previous time step. Then, the system stiffness and damping matrices are reassembled. Finally, based on the dynamic equations, the Newmark-β method is used for numerical calculation to obtain the displacement, velocity, and acceleration of the node at the current time step. By repeating this process, vibration data at any time step can be obtained.

[0159] Finally, the vertical displacement waveform and the axial trajectory of the crack element can also be obtained, as shown below. Figure 7 , Figure 8 As shown.

[0160] Of course, other models can be used to describe the behavior of transverse cracks. Other numerical algorithms, such as the Runge-Kutta method, can also be used for solution. Similarly, wavelet analysis and wavelet packet decomposition can be used for post-processing of the results.

[0161] Furthermore, the technical problem this invention aims to solve is to overcome the limitations of existing methods in describing crack behavior, which fails to consider the potential simultaneous issue of bearing housing loosening, and to provide a more comprehensive finite element numerical simulation method. This method is applicable to the simulation analysis of aero-engines. For a specific type of aero-engine, it abstracts, for example... Figure 2 The 3D model cross-sectional view shown illustrates a multi-disc dual-rotor system, comprising an inner and outer shaft, with disks 1-17 and bearings I-V mounted on both shafts. Each disk 1-17 may contain a fan, a disc, and blades. The system is divided into several shaft segment units in a left-to-right order, starting with the inner shaft and then moving to the outer shaft. The mass of the fan and discs is added to the corresponding shaft segment nodes.

[0162] For a single shaft segment element, it can be simplified into several two-node Timoshenko beam elements, neglecting its axial tensile and compressive deformation and torsional deformation about the axis. Each node is considered to have four degrees of freedom in four directions: horizontal displacement z, vertical displacement y, and rotation θ about the horizontal axis. z Rotation θ about the vertical axis y ,like Figure 3 As shown. Therefore, for a given node, its generalized displacement vector can be expressed as:

[0163]

[0164] Any beam element has two nodes, node A and node B, and node A is rotated about the horizontal axis by θ. Az and rotation θ about the vertical axis Ay The rotation θ of node B about the horizontal axis Bzand rotation θ about the vertical axis By ,refer to Figure 3 As shown.

[0165] Furthermore, this method, based on a real aero-engine structure, simplifies it to establish a three-dimensional counter-rotating dual-rotor-bearing model. This three-dimensional model is then converted into a finite element model, comprehensively considering crack and bearing housing loosening faults. Numerical simulation is used to perform finite element simulation on the dual-rotor system containing both faults, obtaining the system's vibration data. The main steps include: For the aero-engine under study, a three-dimensional model is abstracted based on its design diagram. The model is rationally divided into elements according to structural parameters, fault types and key parameter values ​​are determined, and the three-dimensional model is converted into a finite element numerical simulation model. The Newmark-β numerical simulation method is used to perform simulation calculations on the model, obtaining vibration data for each element node. The vibration data is then post-processed to obtain the data type required for the study.

[0166] Furthermore, the object of this invention can also be other types of gas turbines, such as ground-based gas turbines.

[0167] The method proposed in this invention features unconditional convergence in numerical simulation, wide applicability, and strong transferability. Using this method to model and simulate aero-engines yields results that more closely resemble real-world fault data. Therefore, this method is suitable for numerical simulation analysis of crack-loosening coupling faults in multi-disc counter-rotating dual rotors, providing decision-making basis and technical support for identifying engine vibration faults.

[0168] The fault rotor dynamics simulation system provided by the present invention is described below. The fault rotor dynamics simulation system described below can be referred to in correspondence with the fault rotor dynamics simulation method described above.

[0169] Furthermore, the present invention also provides a fault rotor dynamics simulation system, the system comprising:

[0170] The finite element model building module is used to divide the three-dimensional model of the rotor system into multiple shaft segment elements and build the finite element model of the rotor system.

[0171] The first analysis module is used to establish a crack model and obtain the stiffness matrix of the crack element based on the crack model and the physical parameters of the crack element, wherein the crack element is the shaft segment element with crack fault.

[0172] The second analysis module is used to establish a loosening stiffness model and a loosening damping model for the bearing, and to obtain the stiffness and damping of the loose bearing based on the loosening stiffness model, the loosening damping model, and the displacement of the loose bearing with loosening fault.

[0173] The third analysis module is used to reassemble and obtain the system stiffness matrix and system damping matrix of the rotor system based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing.

[0174] The calculation module is used to obtain the dynamic response characteristics of the rotor system based on the system stiffness matrix and the system damping matrix.

[0175] Furthermore, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the fault rotor dynamics simulation method described above.

[0176] Furthermore, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the fault rotor dynamics simulation method described above.

[0177] Figure 9 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 9 As shown, the electronic device may include a processor, a communication interface, memory, and a communication bus, wherein the processor, communication interface, and memory communicate with each other via the communication bus. The processor can call logical instructions in the memory to execute a fault rotor dynamics simulation method.

[0178] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0179] On the other hand, the present invention also provides a computer program product, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to execute the fault rotor dynamics simulation method provided by the above methods.

[0180] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the fault rotor dynamics simulation methods provided above.

[0181] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0182] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0183] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simulating the dynamics of a faulty rotor, characterized in that, include: The three-dimensional model of the rotor system is divided into multiple shaft segment elements to establish the finite element model of the rotor system. A crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element, wherein the crack element is the shaft segment element with crack fault. Establish a loosening stiffness model and a loosening damping model for the bearing, and obtain the stiffness and damping of the loose bearing based on the loosening stiffness model, the loosening damping model, and the displacement of the loose bearing with loosening fault. Based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing, the system stiffness matrix and system damping matrix of the rotor system are reassembled and obtained. The dynamic response characteristics of the rotor system are obtained based on the system stiffness matrix and the system damping matrix. The crack model is as follows: ； in, The rotational angular velocity of the crack element; t For rotation time; , d The crack depth. r 2 represents the outer radius of the crack element; j The number of rotations is 0, 1, 2, ...; The loosening stiffness model is as follows: ； in, k ac The stiffness of the loose bearing; k b1 , k b2 and k b3 Set value; This represents the maximum loosening clearance of the loose bearing; y The displacement of the loose bearing in the vertical direction; The loosening damping models are as follows: ； in, c ac The damping of the loose bearing; c b1 , c b2 , c b3 This is the set value.

2. The fault rotor dynamics simulation method as described in claim 1, characterized in that, A crack model is established, and the stiffness matrix of the crack element is obtained based on the crack model and the physical parameters of the crack element. Specifically, this includes: Establish a coordinate system for the rotor system, wherein the axial direction of the rotor system is set along the X-axis; Based on the inner diameter, outer diameter, crack depth, and crack angle of the cracked element, the mechanical parameters of the cracked element during the rotation of the rotor system are obtained. The mechanical parameters include the moment of inertia of the cracked part of the cracked element about the Y-axis, the moment of inertia about the Z-axis, the eccentricity, and the area of ​​the uncracked part on the cross section of the cracked element. Based on the mechanical parameters and the physical parameters of the crack element, obtain the additional stiffness matrix generated by the crack; Based on the crack model and the additional stiffness matrix, the stiffness matrix of the crack element in the rotating coordinate system is obtained.

3. The fault rotor dynamics simulation method as described in claim 2, characterized in that, Establishing a crack model, and obtaining the stiffness matrix of the crack element based on the crack model and the physical parameters of the crack element, further includes: Based on the stiffness matrix of the crack element in the rotating coordinate system, the stiffness matrix of the crack element in the static coordinate system is obtained. The stiffness matrix of the crack element in the static coordinate system is: ； ； ； in, k st Here is the stiffness matrix of the crack element in the static coordinate system; k ce Let be the stiffness matrix of the crack element in the rotating coordinate system; This is the element transformation matrix from the rotating coordinate system to the static coordinate system; This is the node transformation matrix from the rotating coordinate system to the static coordinate system; The rotational angular velocity of the crack element is... t For rotation time.

4. The fault rotor dynamics simulation method as described in any one of claims 1-3, characterized in that, Based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing, the system stiffness matrix and system damping matrix of the rotor system are reassembled and obtained, specifically including: The rotor system includes an inner shaft and an outer shaft that are sleeved together. The bearings of the rotor system include intermediate bearings. The intermediate bearings are numbered m and n on the inner shaft and the outer shaft, respectively. The stiffness of the intermediate bearings in the horizontal direction is... k bz and vertical stiffness k by Size is Damping in the horizontal direction c bz and vertical damping c by Size is Then the stiffness matrix of the intermediate bearing K ib and damping matrix C ib They are respectively: ； 。 5. The fault rotor dynamics simulation method as described in claim 4, characterized in that, The dynamic response characteristics of the rotor system are obtained based on the system stiffness matrix and the system damping matrix, specifically including: The displacement, velocity, and acceleration of the rotor system are calculated using the following formulas: ； ； ； ； ； ； ； in, , and The mass matrix, stiffness matrix, and gyroscope matrix of the rotor system are respectively derived from the corresponding shaft segment element matrices; The mass matrix of the inner axis; The mass matrix of the outer shaft; Let be the stiffness matrix of the inner axis; Let be the stiffness matrix of the outer shaft; The gyroscope matrix of the inner axis; The gyroscope matrix of the outer axis; It is a matrix composed of the stiffness matrices of multiple bearings. It is a matrix composed of the damping matrices of multiple bearings, including the intermediate bearing; Here is the system's viscous damping matrix; , The damping coefficient; This refers to the first critical speed of the rotor system. This is the second critical speed of the rotor system; , , These are the generalized displacement, velocity, and acceleration vectors of the rotor system, respectively. , These are the gravity and unbalanced force vectors of the rotor system, respectively.

6. A fault rotor dynamics simulation system, characterized in that, The system for implementing the fault rotor dynamics simulation method as described in any one of claims 1 to 5 includes: The finite element model building module is used to divide the three-dimensional model of the rotor system into multiple shaft segment elements and build the finite element model of the rotor system. The first analysis module is used to establish a crack model and obtain the stiffness matrix of the crack element based on the crack model and the physical parameters of the crack element, wherein the crack element is the shaft segment element with crack fault. The second analysis module is used to establish a loosening stiffness model and a loosening damping model for the bearing, and to obtain the stiffness and damping of the loose bearing based on the loosening stiffness model, the loosening damping model, and the displacement of the loose bearing with loosening fault. The third analysis module is used to reassemble and obtain the system stiffness matrix and system damping matrix of the rotor system based on the stiffness matrix of the cracked element, the stiffness and damping of the loose bearing. The calculation module is used to obtain the dynamic response characteristics of the rotor system based on the system stiffness matrix and the system damping matrix.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the fault rotor dynamics simulation method as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the fault rotor dynamics simulation method as described in any one of claims 1 to 5.

Images