A simulation method for the crack fault of a gas turbine rotor

Abstract

The present invention belongs to the technical field related to rotor dynamics, and discloses a simulation method for crack faults of a gas turbine rotor. The method includes the following steps: S1 Simplify the disk structure of the gas turbine rotor into a multi-disk rotor system, and construct the overall dynamic equation of the multi-disk rotor system; S2 Solve the area of the crack closure region and the crack stiffness matrix; S3 Use the overall stiffness matrix of the multi-disk rotor system at the current moment to solve the displacement vector at the current moment and the crack stiffness matrix at the current moment, and use the crack stiffness matrix at the current moment to update the overall stiffness matrix; S4 Use the updated overall stiffness matrix as the overall stiffness matrix at the next moment, and return to step S3, and iterate in this way to calculate the displacement vectors at all moments, thereby realizing the simulation of the gas turbine rotor fault. Through the present invention, the problem that the existing crack fault model cannot accurately simulate the crack fault of the actual gas turbine rotor is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to rotor dynamics, and more specifically, relates to a simulation method for crack faults of a gas turbine rotor. Background Art

[0002] For gas turbine units, rotor crack faults are one of the faults that cannot be ignored during their operation. The rotors of these large-scale devices usually need to operate under complex and harsh conditions such as high temperature, high pressure, and high rotational speed. And during the working process, affected by aerodynamic excitation and mechanical excitation, cracks are more likely to initiate in a general rotor system. If such faults are not detected and eliminated in time, it is extremely easy to cause significant economic losses. Therefore, carrying out research on cracks in gas turbines, and deeply analyzing the fault generation mechanism and deterioration process, has extremely important theoretical and application values.

[0003] The influence of crack faults on the rotor system is reflected through the change of stiffness. Due to the existence of cracks, the flexibility of the system increases and the stiffness weakens, causing the vibration characteristics of the system to change, which brings strong non-linear factors to the system and greatly affects the vibration characteristics of the system.

[0004] Currently, in the research on gas turbine cracks, the main crack models used are: switch model, cosine model, Gao-Zhu model, breathing model based on neutral axis theory, crack closure line model, etc. The first few models fail to effectively combine the opening and closing law of cracks with the rotor motion, so they cannot truly reflect the state change of cracks during rotor operation. The crack closure line model determines the crack state by calculating the position of the crack closure line in real time, and then updates the system stiffness. In comparison, the crack closure line model is more in line with the actual crack condition. However, most of the current literature still uses the first few models for crack models. For the crack closure line model, the crack is only simplified to a horizontal and straight crack model, and the influence of the actual crack front shape on the model is not considered. In addition, in the current literature on researching gas turbine rotor cracks, the disk-shaft models established are mostly single-disk or double-disk with symmetric distribution to explore general laws, and there is less research on the actual gas turbine rotor structure. Therefore, there is room for optimization between the existing models and the crack fault models of actual gas turbine rotors.

[0005] Therefore, in view of the problem that the existing crack fault models cannot accurately simulate the crack faults of actual gas turbine rotors, the present invention invented a simulation method for crack faults of a gas turbine rotor. By considering the influence of the actual crack front shape and the gas turbine disk-shaft layout on the rotor characteristics, a more appropriate rotor crack fault simulation model is established, and numerical calculation methods are used to calculate the response of the gas turbine rotor under the action of crack faults. Summary of the Invention

[0006] In view of the above deficiencies or improvement requirements of the prior art, the present invention provides a simulation method for the crack fault of a gas turbine rotor, which solves the problem that the crack fault model cannot accurately simulate the actual crack fault of the gas turbine rotor.

[0007] To achieve the above object, according to the present invention, there is provided a simulation method for the crack fault of a gas turbine rotor, the method comprising the following steps:

[0008] S1 Simplify the structure of the gas turbine rotor disk into a multi-disk rotor system, and construct the overall dynamic equation of the multi-disk rotor system with respect to the displacement vector;

[0009] S2 For the cracked shaft section on the rotating shaft in the multi-disk rotor system, construct a crack stiffness matrix relation of the cracked shaft section with respect to the area of the crack closure interval; determine the position where the crack closure line is located and solve the area of the crack closure region, and solve the crack stiffness matrix by using the area of the crack closure region;

[0010] S3 Use the overall stiffness matrix of the multi-disk rotor system at the current moment, solve the displacement vector at the current moment according to the overall dynamic equation in step S1, obtain the crack stiffness matrix at the current moment by using the method in step S2, and update the overall stiffness matrix by using the crack stiffness matrix at the current moment;

[0011] S4 Take the updated overall stiffness matrix as the overall stiffness matrix at the next moment, return to step S3, and iteratively calculate in this way to obtain the displacement vectors at all moments, thereby realizing the simulation of the gas turbine rotor fault.

[0012] Further preferably, in step S1, the construction of the overall dynamic equation is carried out according to the following steps:

[0013] S11 Construct the rotor dynamic equation of the multi-disk rotor system and the disk motion equation of the disk;

[0014] S12 Couple the rotor dynamic equation, the disk motion equation, and the stiffness and damping of the bearing to obtain the overall dynamic equation.

[0015] Further preferably, in step S11, the rotor dynamic equation is in accordance with the following relation:

[0016]

[0017] where M s , G s , C s , K s are respectively the mass matrix, gyro matrix, damping matrix and stiffness matrix of the shaft section unit, Ω is the rotor rotation speed, is the external excitation force vector of the rotating shaft, is the gravity term of the rotating shaft, and q is the generalized displacement vector.

[0018] Further preferably, in step S11, the motion equation of the disk is as follows:

[0019]

[0020] where M i d and G i d are the mass matrix and the gyro matrix of the i-th disk respectively, F ui and F gi are the eccentric excitation vector and the gravity vector of the i-th disk respectively, Ω is the rotor rotation speed, and q i is the displacement vector of the i-th disk.

[0021] Further preferably, in step S12, the relationship of the overall dynamic equation is as follows:

[0022]

[0023] where M is the system mass matrix, including the mass matrices of the rotating shaft and the disks; G is the system gyro matrix, assembled by the gyro matrices G s and G i d of each shaft segment unit and each disk; C is the system damping matrix, assembled by the damping matrix C s of each shaft segment unit and the bearing damping; K is the system stiffness matrix, assembled by the stiffness matrix K s of each shaft segment unit and the bearing stiffness; Ω is the rotor rotation speed; F includes the gravity term of the rotating shaft, the external excitation vector, the eccentric excitation vector and the gravity vector of the disks, and q is the generalized displacement vector.

[0024] Further preferably, in step S2, the relationship of the crack stiffness matrix is as follows:

[0025] S21 Equivalent the cracked shaft segment to multiple equal-thickness thin plates, and construct the relationship of the additional strain energy of the cracked shaft segment in the crack closure region;

[0026] S22 Use the additional strain energy of the cracked shaft segment and the strain energy without crack to construct the total strain energy relationship of the cracked shaft segment, and use this total strain energy to construct the stiffness matrix relationship of the crack.

[0027] Further preferably, in step S21, the relationship of the additional strain energy of the cracked shaft segment is as follows:

[0028]

[0029] where E' = E(1 - ν 2 ), E is Young's modulus of elasticity, ν is Poisson's ratio, correspond to the stress intensity factors of type I, type II, and type III cracks caused by the nodal forces in the j - degree - of - freedom direction respectively, A is the area of the crack - closure region, U c is the additional strain energy of the crack - axis segment.

[0030] Further preferably, in step S21, the stiffness - matrix relation of the crack is carried out according to the following relation:

[0031] K c = TG -1 T -1

[0032]

[0033] where K c is the crack - element stiffness matrix, T is the element transformation matrix, G is the crack - element flexibility matrix, g mn is the value of the m - th row and n - th column in G, m, n = 1 - 6, U is the total strain energy of the crack element, U 0 is the strain energy of the rotor without cracks, P m , P n are the nodal forces along the m - and n - coordinate directions respectively.

[0034] Further preferably, in step S2, the position of the crack - closure line is determined in the following manner:

[0035] Calculate the total stress intensity factors at the crack tips of each thin plate, and determine the opening and closing conditions of the crack according to the total stress intensity factors K k of each thin plate:

[0036] If the value of K k is greater than 0, the crack opens at this node; if the value of K k is less than 0, the crack closes at this node; the boundary line between crack opening and closing is the crack - closure line, and thus the position of the crack - closure line is determined.

[0037] Further preferably, the total stress intensity factors of each thin plate are carried out according to the following relation:

[0038]

[0039] where K k is the total stress intensity factor at the crack tip of the k - th thin plate, is the value of the stress intensity factor of the type I crack of the thin plate caused by the nodal force in the j - degree - of - freedom direction.

[0040] Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

[0041] 1. The present invention adopts the finite element method, reasonably simplifies the gas turbine disk-shaft layout into a multi-disk rotor system, and transforms the gas turbine rotor crack fault model into a multi-disk rotor system crack fault model, ensuring a certain degree of accuracy while simplifying the calculation;

[0042] 2. When calculating the area of the crack closure region, the present invention considers the influence of the crack front line shape on the response of the rotor system to obtain a more accurate crack stiffness matrix; considering the breathing effect of the crack, the crack closure line model is applied to simulate the breathing effect of the crack, and a more appropriate gas turbine rotor crack fault simulation model is established. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flowchart of a gas turbine rotor crack fault simulation method constructed according to a preferred embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of a crack front constructed according to a preferred embodiment of the present invention, where (a) is the real crack front and (b) is the elliptical front;

[0045] Figure 3 is a finite element model of a multi-disk rotor system constructed according to a preferred embodiment of the present invention;

[0046] Figure 4 is the response of the gas turbine system under crack fault calculated according to an embodiment of the present invention, where (a) is the time-domain diagram of the y-direction vibration response, (b) is the frequency-domain diagram of the y-direction vibration response; (c) is the time-domain diagram of the z-direction vibration response, and (d) is the frequency-domain diagram of the z-direction vibration response.

[0047] In all the drawings, the same reference numerals are used to represent the same elements or structures, where:

[0048] 1 - rotating shaft, 2 - node, 3 - bearing, 4 - disk. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0050] A gas turbine rotor crack fault simulation method includes the following steps:

[0051] S1 Simplify the actual gas turbine rotor disk layout into a multi-disk rotor system, model the shaft segment elements of the system based on the basic theory of six-degree-of-freedom Timoshenko beam elements, and establish a finite element model of the gas turbine multi-disk rotor. Among them, the structure of the multi-disk rotor system describes that the multi-disk rotor system includes a rotating shaft with multiple nodes, disks and bearings arranged on the rotating shaft. As Figure 3 shown, the central axis in the figure is the rotating shaft 1, the circle on the central axis is the node 2, the triangles below the nodes at both ends of the central axis are the bearings 3, and the disk 4 is sleeved on the rotating shaft 1.

[0052] S2 Apply fracture mechanics theory, and calculate the stiffness matrix of the crack element in combination with the actual crack front shape; adopt the crack closure line model to simulate the breathing effect of the crack.

[0053] S3 Combine the models in steps 1 and 3, and use numerical calculation methods to calculate the response of the rotor system under crack faults.

[0054] The following further details the content of the present invention with reference to the accompanying drawings:

[0055] The implementation process of the method proposed by the present invention is as Figure 1 shown, and the main steps are described in detail as follows:

[0056] S1 Construct the overall dynamic equation of the multi-disk rotor system:

[0057] (1) Simplify the gas turbine into a multi-disk rotor system according to the layout of the actual gas turbine rotor disk. The gas turbine structure is usually relatively complex, and equivalent reduction methods are generally used for simulation calculations. For the crack fault model, the weak influence of turbine blades and compressor blades is ignored, and only the main rotor structure is considered. Its proportion can be scaled to a certain extent, but its natural frequency and critical speed need to be kept consistent with the original structure. Among them, the compressor disk and the turbine disk are both simplified as disks attached to the main shaft. For the bearings, they are simplified into a simple spring-damper system, and only the radial stiffness and damping of the bearings are considered during calculation.

[0058] (2) Divide the elements of the simplified rotor system, model the shaft segment elements based on the basic theory of six-degree-of-freedom Timoshenko beam elements, and the dynamic equation of the shaft segment element in the static coordinate system is expressed as:

[0059]

[0060] In the formula, M s , G s , C s , K sare the mass matrix, gyro matrix, damping matrix, and stiffness matrix of the shaft segment unit respectively, Ω is the rotor rotation speed, is the external excitation force vector of the rotating shaft, is the gravity term of the rotating shaft, and q is the generalized displacement vector.

[0061] For a disk, it is equivalent to a concentrated mass and applied to the corresponding element nodes. Let the mass of the i-th disk be m di , the generalized displacement vector is q i , the motion equation of the i-th disk in the static coordinate system can be expressed as:

[0062]

[0063] In the formula, M i d 、G i d are the mass matrix and gyro matrix of the i-th disk respectively, Ω is the rotor rotation speed, F ui 、F gi are the eccentric excitation vector and gravity vector of the i-th disk respectively.

[0064] After coupling and assembling equations (1), (2) and the stiffness and damping of the bearings in the node order, the overall dynamic equation of the system is obtained, specifically expressed as:

[0065]

[0066] In the formula, M is the system mass matrix, including the mass matrices of the rotating shaft and the disks; G is the system gyro matrix, assembled by the gyro matrices G s and G i d of each shaft segment unit and each disk; C is the system damping matrix, assembled by the damping matrix C s of each shaft segment unit and the bearing damping; K is the system stiffness matrix, assembled by the stiffness matrix K s of each shaft segment unit and the bearing stiffness; Ω is the rotor rotation speed; F includes the gravity term and external excitation vector of the rotating shaft, as well as the eccentric excitation vector and gravity vector of the disks, and q is the generalized displacement vector.

[0067] S2 Construct the crack stiffness matrix relation and solve the crack stiffness matrix

[0068] S21 Construct the crack stiffness matrix relation

[0069] (1) Using the thin plate crack strain energy calculation method, the cracked shaft segment is equivalent to a combination of many equal-thickness thin plates. The additional strain energy of the cracked shaft segment is obtained by calculating the sum of the strain energies of these thin plates. The specific formula is:

[0070]

[0071] where E' = E(1 - ν 2 ), E is Young's modulus of elasticity, and ν is Poisson's ratio. They respectively correspond to the stress intensity factors of type-I (opening mode), type-II (sliding mode), and type-III (tearing mode) cracks caused by the nodal forces in the j-degree-of-freedom direction. A is the area of the crack closure region, and U c is the additional strain energy of the crack shaft segment.

[0072] (2) Consider the influence of the crack front shape on the rotor system. As shown in Figure 2 (a) thereof, the actual crack front shape is not a straight horizontal shape, but has certain undulations, and its influence on the stiffness of the cracked rotor cannot be ignored. Fit the crack front curve as a function under the coordinate system shown in Figure 2 (a) as the lower limit of the integral in Equation (4). Taking the elliptical front crack in Figure 2 (b) as an example, where b is half of the crack width, h1 is the z-direction coordinate of the front line in the coordinate system, and β is the lateral distance between the thin plate and the center of the shaft segment.

[0073] (3) Calculate the total strain energy of the crack element, and determine the stiffness matrix of the crack according to the total strain energy model. The specific formula is:

[0074]

[0075] K c = TG -1 T -1 (6)

[0076] where K c is the crack element stiffness matrix, T is the element transformation matrix, G is the crack element flexibility matrix, g mn is the value of the m-th row and n-th column in G, m, n = 1 - 6, U is the total strain energy of the crack element, U 0 is the strain energy of the rotor without cracks, and P m , P n are the nodal forces along the m and n coordinate directions respectively.

[0077] S22 Solve the crack stiffness matrix

[0078] Adopt the crack closure line model to simulate the breathing effect of the crack.

[0079] During the process of calculating the crack stiffness, it is necessary to perform integral calculations on the crack closure region, and the crack closure region changes continuously during the operation of the rotor. To capture the opening and closing conditions of the crack, calculate the total stress intensity factor at the crack tip of each thin plate divided in Step 2, and determine the opening and closing conditions of the crack on it according to the values of the total stress intensity factors of each thin plate. The specific formula is as follows:

[0080]

[0081] In the formula, K k is the total stress intensity factor at the crack tip of the k-th thin plate, is the value of the stress intensity factor of the mode I crack of the thin plate caused by the nodal force in the j degree-of-freedom direction, which can be calculated by the empirical formula through the nodal force, and its value changes with the change of the nodal force.

[0082] Define the total stress intensity factor at the crack tip of each thin plate as follows: If the value of K k is greater than 0, it is considered that the point is in tensile stress and the crack opens at this point; if the value of K k is less than 0, it is considered that the point is in compressive stress and the crack closes at this point. The boundary line between crack opening and closing is the crack closure line. During the operation of the rotor, the nodal force changes continuously, and the opening and closing conditions of each thin plate also change accordingly, and this process forms the breathing effect of the crack.

[0083] S3 Solve the displacement vectors at all times

[0084] Combined with Steps 2 and 3, calculate the system response under the crack fault of the gas turbine.

[0085] (1) Divide the position interval of the crack closure line. According to Steps 2 and 3, the state of the crack changes continuously during operation, which also causes the stiffness matrix of the crack shaft section to change continuously. Since the crack closure line only exists on both sides of the thin plate, determine the possible positions of the crack closure line according to the number of thin plates divided. Usually, this number is set to 100 to achieve a higher calculation accuracy. That is, there are 100 positions for the crack closure line, and each position corresponds to a different crack state, and there are 100 stiffness matrices corresponding to different crack states.

[0086] (2) Calculate the nodal forces in the initial state and deduce the crack stiffness matrix at the next moment. By default, the crack is in a closed state in the initial state, and its system response is the same as that of the crack-free system. Numerically calculate Equation (3) using the Newmark method. The product of the calculated generalized displacement vector q of the system and the system stiffness matrix K at the current moment is the nodal force vector of each node in the system at the current moment. Intercept the nodal forces of the shaft segment where the crack is located in the nodal force vector to deduce the total stress intensity factors at the crack tips of each thin plate in Equation (7). Subsequently, the position of the crack closure line can be determined according to the model described in Step 3. Once the position of the crack closure line is determined, the closure condition of the crack cross-section is also determined. The crack stiffness matrix in the current state can be calculated according to Equations (4), (5), and (6).

[0087] (3) Update the system stiffness and perform iterative calculations. Replace the stiffness matrix of the shaft segment where the crack is located with the calculated crack stiffness matrix K c , and recombine to obtain a new system stiffness matrix K for the calculation at the next moment. The calculated generalized displacement vector q at the next moment is then processed as above. Continuously update the system stiffness in this way for calculation until the set calculation duration is reached. Recording the displacement vector q at each moment can obtain the response data of the system.

[0088] The present invention will be further described below with reference to specific embodiments.

[0089] Embodiment

[0090] After reasonable simplification in combination with the actual layout of a certain type of gas turbine, a finite element model of the multi-disk rotor system as shown in Figure 3 was established to verify the effectiveness of the solution.

[0091] First, simplify the structure of the gas turbine. The basic parameters of the obtained multi-disk rotor system are as follows: The total length of the rotor is 1500 mm, the diameter is 50 mm, and it is divided into 34 elements in total. The shaft segment element numbers are 1 to 34. Except for the shaft segment elements 13 to 23 with a length of 30 mm, the lengths of the other shaft segment elements are all 50 mm. There are 21 disks in total from left to right, and the disk numbers are sequentially 1 to 21. Among them, the first 17 disks correspond to the 17-stage compressor disks of the gas turbine, and the last 4 disks correspond to the 4-stage turbine disk structure of the gas turbine. The disk diameters are between 140 mm and 284 mm, and the thicknesses are in the range of 16 mm to 40 mm. This system adopts a two-end support structure, where bearing 1 acts on node 5 and bearing 2 acts on node 32. The elastic modulus E of the rotating shaft and the disk is 2.11×10 11 Pa, the Poisson's ratio ν = 0.3, and the eccentricity of the disks is all e = 1.6×10 -5 m.

[0092] Select the shaft segment unit 12 as the crack unit for simulation calculation. The crack is located at the middle position of the shaft segment unit. Temporarily select Figure 2 the elliptical leading edge shown in (b) of Figure 4 for simulation. The diameter of the shaft segment unit 12 is 50 mm. Take the crack depth a = 5 mm, that is, the crack depth ratio r = a / R = 0.2. The time-domain waveform and frequency-domain waveform of the system response calculated are as shown in Figure 4 . It can be seen from

[0093] that the influence of the crack fault on the vibration response of the gas turbine rotor system is mainly reflected in the 1st, 2nd, and 3rd harmonic components, which is consistent with the frequency-domain characteristics monitored in actual production under crack faults, verifying the effectiveness of the method. Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A simulation method for gas turbine rotor crack faults, characterized in that, The method includes the following steps: S1 Simplify the structure of the gas turbine rotor disk into a multi-disk rotor system, and construct the overall dynamic equation of the multi-disk rotor system with respect to the displacement vector; S2 For the cracked shaft section on the rotating shaft in the multi-disk rotor system, construct the crack stiffness matrix relation of the cracked shaft section with respect to the area of the crack closure interval; determine the position where the crack closure line is located and solve the area of the crack closure region, and use the area of the crack closure region to solve the crack stiffness matrix; S3 Use the overall stiffness matrix of the multi-disk rotor system at the current moment, solve the displacement vector at the current moment according to the overall dynamic equation in step S1, obtain the crack stiffness matrix at the current moment in the manner of step S2, and use the crack stiffness matrix at the current moment to update the overall stiffness matrix; S4 Take the updated overall stiffness matrix as the overall stiffness matrix at the next moment, return to step S3, and iteratively calculate in this way to obtain the displacement vectors at all moments, thereby realizing the gas turbine rotor fault simulation; In step S2, the crack stiffness matrix relation is carried out according to the following steps: S21 Equivalent the cracked shaft section to multiple equal-thickness thin plates, and construct the relation of the additional strain energy of the cracked shaft section in the crack closure region; S22 Use the additional strain energy of the cracked shaft section and the strain energy without cracks to construct the total strain energy relation of the cracked shaft section, and use the total strain energy to construct the crack stiffness matrix relation; In step S21, the relation of the additional strain energy of the cracked shaft section is carried out as follows: where E' = E(1 - ν 2 ), E is Young's modulus of elasticity, ν is Poisson's ratio, correspond to the stress intensity factors of type-I, type-II, and type-III cracks caused by the nodal forces in the j-degree-of-freedom direction respectively, A is the area of the crack closure region, U c is the additional strain energy of the crack shaft segment.

2. The simulation method for the crack fault of a gas turbine rotor according to claim 1, characterized in that In step S1, the construction of the overall dynamic equation is carried out according to the following steps: S11 Construct the rotor dynamic equation of the multi-disk rotor system and the disk motion equation of the disk; S12 Couple the rotor dynamic equation, the disk motion equation, and the stiffness and damping of the bearing to obtain the overall dynamic equation.

3. The simulation method for a gas turbine rotor crack fault according to claim 2, characterized in that, In step S11, the rotor dynamic equation is carried out according to the following relation: Among them, M s , G s , C s , K s are respectively the mass matrix, gyro matrix, damping matrix and stiffness matrix of the shaft segment unit, Ω is the rotor rotation speed, is the external excitation force vector of the rotating shaft, is the gravity term of the rotating shaft, and q is the generalized displacement vector.

4. The simulation method for the crack fault of a gas turbine rotor according to claim 2, wherein, In step S11, the disk motion equation is carried out according to the following relation: Among them, M i d and G i d are respectively the mass matrix and the gyro matrix of the i-th disk, and F ui and F gi are respectively the eccentric excitation vector and the gravity vector of the i-th disk, Ω is the rotor rotation speed, and q i is the displacement vector of the i-th disk.

5. The simulation method for the crack fault of a gas turbine rotor according to claim 2, wherein In step S12, the relation of the overall dynamic equation is carried out as follows: Among them, M is the system mass matrix, including the mass matrices of the rotating shaft and the disks; G is the system gyro matrix, which is assembled by the gyro matrices G s and G i d of each shaft segment element and each disk; C is the system damping matrix, which is assembled by the damping matrices C s of each shaft segment element and the bearing damping; K is the system stiffness matrix, which is assembled by the stiffness matrices K s of each shaft segment element and the bearing stiffness; Ω is the rotational speed of the rotor; F includes the gravity term and the external excitation vector of the rotating shaft, as well as the eccentric excitation vector and the gravity vector of the disks, and q is the generalized displacement vector.

6. A simulation method for gas turbine rotor crack faults according to claim 1, characterized in that In step S22, the crack stiffness matrix relation is carried out according to the following relation: K c = TG -1 T -1 Among them, K c is the crack element stiffness matrix, T is the element transformation matrix, G is the crack element flexibility matrix, and g mn is the value of the m-th row and n-th column in G, where m, n = 1 to 6, U is the total strain energy of the crack element, and U 0 is the strain energy of the rotor without cracks, and P m and P n are the nodal forces along the m- and n-coordinate directions, respectively.

7. The simulation method for the crack fault of a gas turbine rotor according to claim 3, wherein, In step S2, the position where the crack closure line is located is determined in the following manner: Calculate the total stress intensity factor at the crack tip of each thin plate, and determine the crack opening and closing conditions based on the total stress intensity factor K of each thin plate k Determine the crack opening and closing conditions: If K k has a value greater than 0, the crack opens at this node; if K k has a value less than 0, the crack closes at this node; the boundary line between crack opening and closing is the crack closure line, and thus the position of the crack closure line is determined.

8. A simulation method for gas turbine rotor crack faults according to claim 7, characterized in that, The total stress intensity factor of each thin plate is carried out according to the following relation: Among them, K k is the total stress intensity factor at the crack tip of the k-th thin plate, is the value of the stress intensity factor of the mode I crack of the thin plate caused by the nodal force in the j degree-of-freedom direction.

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