Rotor hot bending fault positioning analysis method

Abstract

The invention relates to the field of nuclear power maintenance, in particular to a rotor hot bending fault positioning analysis method. The method comprises the following steps that S1, the position where thermal bending occurs is preliminarily judged; s2, calculating a thermal bending moment, a bending curve and exciting force caused by thermal bending; s3, establishing a kinetic equation of a rotor thermal bending system; s4, calculating by utilizing the rotor thermal bending system kinetic equation to obtain a thermal bending calculation vibration response curve of a typical position; and S5, comparing the actual vibration response with the thermal bending calculation response curve, and judging the thermal bending position and the bending degree. According to the invention, the position of the thermal bending fault of the rotor system can be quickly and conveniently analyzed, and the severity of thermal bending is judged.

Description

Technical Field

[0001] The invention relates to the field of nuclear power maintenance, and in particular to a rotor thermal bending fault location analysis method. Background Art

[0002] In order to maintain high efficiency and minimize leakage during operation, the rotor system often sets the gap between the rotating parts and the stationary parts to be very small. However, a smaller gap will lead to another problem, that is, the rotating parts and the stationary parts are prone to friction. The rotation speed of the rotor is generally very high, and its surface linear velocity is large. Once friction occurs, the rotor will be thermally bent, causing imbalance, which will lead to severe vibration. The severe vibration will further aggravate the friction and further cause thermal bending. When installing the rotor system, there are many locations with small installation gaps, all of which may cause friction and thermal bending. The gap between the rotating parts and the stationary parts is often measured during installation. After the rotor system is started and operated, the gap between the rotating parts and the stationary parts will change. The data at installation alone is not enough to accurately determine where friction and thermal bending occur.

[0003] Since the generator and motor rotors are equipped with wires, the rotor wires will generate heat when the rotor system is running. When the heat of each part is inconsistent, a temperature difference will occur on the rotor surface, causing the rotor to thermally bend and induce vibration. At this time, it is necessary to know where the thermal bending of the rotor occurs for further processing.

[0004] Thermal bending is related to the running state of the rotor. Currently, the position and extent of the bending can only be determined when the thermal bending has caused permanent bending of the rotor and the machine is shut down for disassembly inspection. Permanent bending caused by thermal bending must be prevented. However, most thermal bending is restorative bending, which generally occurs during the running stage and will gradually disappear after shutdown. At this time, it cannot be detected by disassembly inspection.

[0005] Thermal bending is a common fault that causes high vibration. Currently, vibration analysis can be used to diagnose whether the rotor has thermal bending. In order to deal with thermal bending vibration, dynamic balancing methods for thermal bending have also been invented, such as patents such as ZL201410270217.4. However, these methods only reduce vibration, and further positioning and analysis of the thermal bending phenomenon is required to find the exact thermal bending location, and then deal with the location where the thermal bending occurs, such as adjusting the rotor dynamic and static clearance and other maintenance.

[0006] In order to accurately diagnose the thermal bending position of the rotor system, it is necessary to invent a rotor thermal bending fault location analysis method. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a method for rotor thermal bending fault location and analysis, which can quickly and conveniently analyze the location of the rotor system thermal bending fault and judge the severity of the thermal bending.

[0008] The present invention provides a method for rotor thermal bending fault location and analysis, including the following steps:

[0009] Step S1: Preliminarily judge the location where thermal bending occurs;

[0010] Step S2: Calculate the thermal bending moment, bending curve and exciting force caused by thermal bending;

[0011] Step S3: Establish the dynamic equation of the rotor thermal bending system;

[0012] Step S4: Use the dynamic equation of the rotor thermal bending system to calculate and obtain the vibration response curve of thermal bending calculation at typical positions;

[0013] Step S5: Compare according to the actual vibration response and the thermal bending calculation response curve to determine the thermal bending position and the degree of bending.

[0014] In a specific embodiment of the present invention, the step S1 specifically includes:

[0015] Step S1-1: Analyze the possible sources of thermal bending of the rotor system, including self-friction and external heating;

[0016] When analyzing self-friction, analyze the clearance between the rotating parts and the stationary parts, diagnose the parts and possibilities where thermal bending is likely to occur, and sort them according to the size of the possibilities;

[0017] When analyzing external heating, analyze the parts of the rotor heated by external heat sources, diagnose the parts and possibilities where thermal bending is likely to occur, and sort them according to the size of the possibilities;

[0018] Step S1-2: Based on the above analysis, preliminarily diagnose the possible temperature difference positions of the rotor to further narrow the analysis range of the rotor thermal bending position.

[0019] In a specific embodiment of the present invention, the positions where friction is likely to occur are: floating oil baffle, floating seal ring, contact steam seal, end steam seal of steam turbine, diaphragm steam seal, end cover oil seal;

[0020] The positions where heating is likely to cause bending are: the heating position of the generator excitation current, the heating position of the motor rotor cage bar current, the heating position of the steam flow in the steam turbine cylinder, the heating position of the shaft diameter in the bearing.

[0021] In a specific embodiment of the present invention, the step S2 specifically includes:

[0022] The rotor shafting is discretized axially into N node beam elements, and the temperature differences of each node form a temperature difference matrix as follows:

[0023]

[0024] 1 to N refer to each node;

[0025] The displacement and moment relationship matrix at the rotor nodes is as follows:

[0026]

[0027] v is the bending deformation of each node section, M is the bending moment of each node section, I is the moment of inertia of the rotor section about the axis, E is the elastic modulus of the rotor shaft material, and λ is the length of the shaft section between each node; N is a natural number;

[0028] According to the selected temperature difference value, the bending moment at this temperature can be obtained from the calculation formulas of Mx and My. According to the matrix, the bending deformation of each point can be solved, and by connecting the bending deformations of each node, the bending curve of the shafting can be obtained.

[0029] In a specific embodiment of the present invention, in step S2, the consequences of thermal bending are divided into two types of exciting forces, namely unbalanced exciting force and thermal bending exciting force.

[0030] In a specific embodiment of the present invention, in step S2,

[0031] The matrix {Q m} of the unbalanced exciting force is as follows:

[0032]

[0033] m is the concentrated mass of the node, and ω is the rotational circular frequency;

[0034] The matrix {Q T} of the thermal bending exciting force:

[0035]

[0036] In the formula, k i is the shaft section stiffness between i and node i + 1, and i is a natural number from 1 to N; {Q T} is the rotor thermal bending exciting force matrix.

[0037] In a specific embodiment of the present invention, step S3 specifically includes:

[0038] Determine the vibration displacement vectors formed by each node in the x and y directions as follows:

[0039] {D x} = [x1, θy1 , x2, θ y2 , …, x n , θ yN T

[0040] {D y} = [y1, -θ x1 , y2, -θ x2 , …, y n , -θ xN T

[0041] D x 、D y are respectively vectors composed of nodal displacements and deflection angles in the x and y directions. x i and y i are displacement variables of the node in the x and y directions, and θ x and θ y are deflection angle variables in the two directions;

[0042] Combine the total mass matrix, gyroscopic matrix and stiffness matrix of the shafting with the displacement vector to establish the dynamic equation of the shafting:

[0043]

[0044] where M0 and J0 are respectively the mass matrix and gyroscopic force matrix of the rotor system, K x and K y are the stiffness matrices in the x and y directions, Q m is the unbalanced exciting force; Q T is the thermal bending exciting force;

[0045] is the acceleration and velocity vectors corresponding to the vibration displacement vectors D x 、D y ;

[0046] Combine the matrix equation into the standard form:

[0047]

[0048] where {Q m} is the unbalanced exciting force, {Q T} is the thermal bending exciting force, c xx , c xy , c yx , c yy are the four damping coefficients of the bearing, Jx and Jy are the moments of inertia about the x-axis and y-axis, k xx , k xy , y yx ​​, k yy are the four stiffness coefficients of the bearing, and K0 is the stiffness of the shaft section.

[0049] In a specific embodiment of the present invention, the step S4 specifically includes:

[0050] Select several other parts that are prone to thermal bending, and determine the corresponding node positions of the rotor.

[0051] Set different temperature differences.

[0052] Use the dynamic equation of the rotor thermal bending system to calculate and obtain the corresponding curves of thermal bending calculations at each typical position.

[0053] In a specific embodiment of the present invention, in the step S5,

[0054] When it is diagnosed that the increase in vibration during the operation of the rotor is caused by thermal bending, compare the on-site vibration response with the trend of the typical thermal bending vibration calculation response curve. If the curve trends are consistent, the thermal bending position in the dynamic equation of the rotor thermal bending system is the same as or close to the on-site thermal bending position.

[0055] Compare the on-site vibration amplitude with the thermal bending response value calculated according to the model; when the measured vibration amplitude at the vibration measurement position is close to the vibration response value calculated by the dynamic equation of the rotor thermal bending system, the actual temperature difference on the shaft should be close to the temperature difference value input in the simulation calculation, thereby judging the severity of thermal bending.

[0056] In a specific embodiment of the present invention, the calculation method of the bending moment M of each node section is as follows:

[0057] Set the rotor to have a circular shaft section, M x = M y = M;

[0058] The temperature difference T generates bending moments M x , M y about the x and y axes in the middle of the rotor cross-section. The bending moment at the left cross-section of the rotor shaft section is M L , and the bending moment at the left cross-section of the rotor shaft section is M R . The middle deflection angle of the rotor shaft section is θ.

[0059] M x = ∫∫γ0·E·T·ydxdy

[0060] M y = ∫∫γ0·E·T·xdxdy

[0061] Where γ0 is the linear expansion coefficient of the rotor, E is the elastic modulus of the rotor shaft material, T is the temperature distribution in the circumferential direction of the cross-section, x and y are the coordinates of the points on the rotor cross-section along the x and y axes, and dx and dy are the integration variables along the x and y axes respectively.

[0062] Compared with the prior art, the rotor thermal bending fault location analysis method of the present invention analyzes the possible sources of thermal bending of the rotor system first. By constructing the dynamic equation of the rotor thermal bending system and calculating the vibration response curve of the thermal bending at typical positions, the positions prone to thermal bending are simulated and analyzed. Thus, the vibration characteristics when the rotor rubs at different positions can be judged by using the large model, and the severity of the rotor thermal bending can be inferred from the vibration condition. Further, the efficiency and accuracy of the thermal bending fault are improved. Moreover, the method of the present invention can monitor the operation of the rotor in real time, timely detect the parts that may have faults, and prevent problems before they occur. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a flow chart of the rotor thermal bending fault location analysis method;

[0064] Figure 2 is a schematic diagram for calculating and analyzing the expansion force during the thermal bending of the shaft section;

[0065] Figure 3 is an application example of a simply supported beam rotor;

[0066] Figure 4 is an example of the bending curve of the middle thermal bending;

[0067] Figure 5 is the vibration response curve of the simulation calculation at the bearing;

[0068] Figure 6 is the vibration response curve of the on-site measurement at the bearing. DETAILED DESCRIPTION OF THE INVENTION

[0069] In order to further understand the present invention, the implementation of the present invention will be described below in conjunction with embodiments. However, it should be understood that these descriptions are only for further explaining the features and advantages of the present invention, rather than limiting the present invention.

[0070] An embodiment of the present invention discloses a rotor thermal bending fault location analysis method, as Figure 1 shown, including the following steps:

[0071] Step S1: Initially judge the position where thermal bending occurs;

[0072] First, analyze the possible sources of thermal bending of the rotor system. The temperature non-uniformity of thermal bending is divided into the following two aspects: self-friction and external heating.

[0073] For self-friction, analyze the clearances between rotating components and stationary components, diagnose the locations and probabilities of thermal bending prone to occur, and rank them in order of probability. The locations prone to friction are: floating oil seals, floating sealing rings, contact steam seals, end steam seals of steam turbines, diaphragm steam seals, end cover oil seals, etc.

[0074] For external heating, analyze the parts of the rotor heated by external heat sources, diagnose the locations and probabilities of thermal bending prone to occur, and rank them in order of probability. The locations prone to bending caused by heating are: excitation current heating of generators, rotor bar current heating of motors, air flow heating in steam turbine cylinders, shaft diameter heating in bearings, etc.

[0075] Based on the above analysis, a preliminary diagnosis can be made on the possible temperature difference locations of the rotor, narrowing the analysis scope of the rotor thermal bending locations in the next step.

[0076] Step S2: Calculate the thermal bending moment, bending curve and exciting force caused by thermal bending;

[0077] Discretize the rotor shafting into N node beam elements along the axial direction, and the temperature of each node forms a temperature difference matrix as follows:

[0078]

[0079] 1 to N refer to each node;

[0080] Select a part within the analysis scope in Step S1 for analysis. A temperature difference T has occurred in the cross-section of this part, and the temperature difference T will generate moments M x , M y , as Figure 2 shown, the moment of the cross-section on the left part of the rotor shaft section is M L , and the moment of the cross-section on the left part of the rotor shaft section is M R . The mid-span deflection angle of the rotor shaft section is θ,

[0081] M x =∫∫γ0·E·T·ydxdy

[0082] M y =∫∫γ0·E·T·xdxdy

[0083] In the formula, γ0 is the linear expansion coefficient of the rotor, E is the elastic modulus of the rotor shaft material, and T is the temperature distribution in the circumferential direction of the cross-section. x and y are the coordinates of points on the rotor cross-section along the x and y axes, and dx and dy are the integration variables along the x and y axes respectively.

[0084] Assume that the rotor has a circular shaft cross-section, then M x =M y =M.

[0085] According to this conclusion, the displacement and moment relationship matrix at the rotor node is as follows:

[0086]

[0087] v1 to v N are the bending deformation amounts of each node section, M1 to M N are the bending moments of each node section, I is the moment of inertia of the rotor section about the axis, E is the elastic modulus of the rotor shaft material, λ is the length of the shaft section between each node; N is a natural number;

[0088] According to the selected temperature difference value, the bending moment at this temperature can be obtained from the calculation formulas of Mx and My. According to the matrix, the bending deformation amount of each point can be solved, and by connecting the bending deformation amounts of each node, the bending curve of the shafting can be obtained.

[0089] The consequences of thermal bending are divided into two types of exciting forces, namely unbalanced exciting force and thermal bending exciting force.

[0090] The matrix {Q m} of the unbalanced exciting force is as follows:

[0091]

[0092] {Q m} is the unbalanced exciting force matrix, m is the concentrated mass of the node, and ω is the rotational circular frequency;

[0093] The matrix {Q T} of the thermal bending exciting force:

[0094]

[0095] In the formula, k i is the shaft section stiffness between node i and node i + 1, and i is a natural number from 1 to N; {Q T} is the rotor thermal bending exciting force matrix.

[0096] Step S3: Establish the dynamic equation of the rotor thermal bending system;

[0097] Determine the vibration displacement vectors formed by each node in the x and y directions as follows:

[0098] {D x} = [x1, θ y1 , x2, θ y2 , …, x n , θ yN T

[0099] {D y} = [y1, -θ x1 , y2, -θ​x2 ,…, y n , -θ xN T

[0100] D x 、D y are vectors composed of nodal displacements and flexure angles in the x and y directions respectively, where x i and y i are displacement variables of the node in the two directions of x and y, and θ x and θ y are flexure angle variables in the two directions; i is a natural number from 1 to N;

[0101] Combine the total mass matrix, gyroscopic matrix, and stiffness matrix of the shafting with the displacement vector to establish the dynamic equation of the shafting:

[0102]

[0103] where M0 and J0 are the mass matrix and gyroscopic force matrix of the rotor system respectively, K x and K y are the stiffness matrices in the x and y directions, Q m is the unbalanced excitation force; Q T is the thermal bending excitation force.

[0104] is the acceleration and velocity vector corresponding to the vibration displacement vector D x 、D y .

[0105] Combine the matrix equation into the standard form:

[0106]

[0107] where

[0108] {Q m} is the unbalanced excitation force matrix, and {Q T} is the thermal bending excitation force matrix.

[0109] c xx , c xy , c yx , c yy are the four damping coefficients of the bearing, Jx and Jy are the moments of inertia about the x-axis and y-axis respectively, k xx , k xy , y yx , k yy are the four stiffness coefficients of the bearing, and K0 is the shaft segment stiffness.

[0110] ​Step S4: Calculate using the dynamic equation of the rotor thermal bending system to obtain the vibration response curve of the thermal bending calculation at typical positions;

[0111] Select several other parts prone to thermal bending and determine the corresponding node positions of the rotor.

[0112] Set different temperature differences.

[0113] Calculate using the dynamic equation of the rotor thermal bending system to obtain the corresponding curves of the thermal bending calculation at each typical position.

[0114] Step S5: Compare according to the actual vibration response and the thermal bending calculation response curve to determine the thermal bending position and the degree of bending.

[0115] When it is diagnosed that the increase in vibration during the operation of the rotor is caused by thermal bending, compare according to the trend of the on-site vibration response and the typical thermal bending vibration calculation response curve. If the curve trends are consistent, the thermal bending position in the dynamic equation of the rotor thermal bending system is the same as or close to the on-site thermal bending position;

[0116] Compare the on-site vibration amplitude with the thermal bending response value calculated according to the model; when the measured vibration amplitude at the vibration measurement position is close to the vibration response value calculated by the dynamic equation of the rotor thermal bending system, the actual temperature difference on the shaft should be close to the temperature difference value input in the simulation calculation, thereby judging the severity of the thermal bending.

[0117] Verify the analysis method of the present invention, and the specific method is as follows:

[0118] The first step: According to the rotor installation situation, first sort out the positions prone to thermal bending. For example, Figure 3 As shown, the simply supported beam rotor is supported by two bearings. After sorting, there are 3 positions with relatively small static-dynamic clearances, which are more likely to cause friction and lead to thermal bending, namely positions 1, 2, and 3. These 3 positions can correspond to the front shaft seal, the middle diaphragm steam seal, and the rear shaft seal.

[0119] The second step: Set the temperature difference on the cross-section of the middle diaphragm steam seal, and calculate the nodal displacement and moment at this position.

[0120] Continuously change the input temperature difference to obtain a series of bending curves. The shapes of the bending curves composed of the nodal displacements are similar, and the overall shape is parabolic. The bending curves are shown in the appendix Figure 4 .

[0121] The third step: Input the calculated nodal bending deformation amounts and moments into the dynamic equation of the rotor thermal bending system constructed by the above technical solution;

[0122] Step 4: Calculate using the dynamic equations of the rotor thermal bending system. The calculation results of the vibration at the bearing are shown in the appendix Figure 5 . It can be found from the figure that as the rotational speed increases, the vibration gradually increases rapidly and reaches the maximum at the resonance peak; after crossing this resonance peak, the vibration rapidly decreases.

[0123] Step 5: On-site, the vibration curve when the rotor suffered frictional thermal bending on-site, resulting in high vibration and trip, was actually measured. See the appendix for details Figure 6 .

[0124] As Figure 5 and Figure 6 shown, by comparing the calculated results of the shaft vibration at the bearing with the measured results, it is found that the overall trends of the two are the same and the amplitudes are close.

[0125] Based on the comparison and analysis of the measured and calculated results, this method is verified to be feasible.

[0126] The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0127] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for rotor thermal bending fault location and analysis, characterized in that, It includes the following steps: Step S1: Initially determine the position where thermal bending occurs; Step S2: Calculate the thermal bending moment, bending curve and exciting force caused by thermal bending; Step S3: Establish the dynamic equation of the rotor thermal bending system; Step S4: Use the dynamic equation of the rotor thermal bending system to calculate and obtain the vibration response curve of thermal bending calculation at typical positions; Step S5: Compare according to the actual vibration response and the thermal bending calculation response curve to determine the thermal bending position and the degree of bending.

2. The rotor thermal bending fault location and analysis method according to claim 1, characterized in that The specific content of step S1 includes: Step S1-1: Analyze the possible sources of thermal bending of the rotor system, including self-friction and external heating; When analyzing self-friction, analyze the clearance between rotating parts and stationary parts, diagnose the parts and possibilities prone to thermal bending, and sort them according to the size of the possibilities; When analyzing external heating, analyze the parts of the rotor heated by external heat sources, diagnose the parts and possibilities prone to thermal bending, and sort them according to the size of the possibilities; Step S1-2: Based on the above analysis, initially diagnose the possible temperature difference positions of the rotor to further narrow the analysis range of the rotor thermal bending position.

3. The rotor thermal bending fault location and analysis method according to claim 2, characterized in that The positions prone to friction are: floating oil baffle, floating seal ring, contact steam seal, end steam seal of steam turbine, diaphragm steam seal, end cover oil seal; The positions prone to bending caused by heating are: the heating position of generator excitation current, the heating position of motor rotor cage bar current, the heating position of steam flow in steam turbine cylinder, the heating position of shaft diameter in bearing.

4. The rotor thermal bending fault location and analysis method according to claim 1, characterized in that The specific content of step S2 includes: Discretize the rotor shafting into N node beam elements along the axial direction, and the temperature of each node forms a temperature difference matrix as follows: 1 to N refer to each node; The displacement and moment relationship matrix at the rotor node is as follows: v is the bending deformation of each node section, M is the bending moment of each node section, I is the moment of inertia of the rotor section about the axis, E is the elastic modulus of the rotor shaft material, λ is the length of the shaft section between each node; N is a natural number; According to the selected temperature difference value, the bending moment at this temperature can be obtained from the calculation formulas of Mx and My. According to the matrix, the bending deformation of each point can be solved, and the bending curves of the shafting can be obtained by connecting the bending deformations of each node.

5. The rotor thermal bending fault location and analysis method according to claim 1, wherein In step S2, the consequences of thermal bending are divided into two types of exciting forces, namely unbalanced exciting force and thermal bending exciting force.

6. The rotor thermal bending fault location and analysis method according to claim 5, characterized in that In step S2, The matrix {Q m} of the unbalanced exciting force is as follows: m is the concentrated mass of the node, ω is the rotational circular frequency; The matrix {Q of the thermal bending excitation force T}: where k i is the shaft segment stiffness between i and node i + 1, and i is a natural number from 1 to N; {Q T} is the exciting force matrix of rotor thermal bending.

7. The rotor thermal bending fault location and analysis method according to claim 6, wherein The specific content of step S3 includes: Determine the vibration displacement vector formed by each node in the x and y directions as follows: {D x} = [x1, θ y1 , x2, θ y2 , …, x n , θ yN T ​ {D y} = [y1, -θ x1 , y2, -θ x2 , …, y n , -θ xN T ​ D x and D y are vectors composed of nodal displacements and flexure angles in the x and y directions, respectively. x i and y i are displacement variables of the node in the x and y directions, respectively. θ x and θ y are flexure angle variables in the two directions; Combine the total mass matrix, gyroscopic matrix and stiffness matrix of the shafting with the displacement vector to establish the dynamic equation of the shafting: where \(M_0\) and \(J_0\) are the mass matrix and gyroscopic force matrix of the rotor system respectively, and \(K\) x and \(K\) y are the stiffness matrices in the \(x\) and \(y\) directions, \(Q\) m is the unbalanced excitation force; \(Q\) T is the thermal bending excitation force; is the vibration displacement vector D x , D y corresponding acceleration and velocity vectors; Synthesize the matrix equation into a standard form: In the formula {Q m} is the unbalanced exciting force, {Q T} is the thermal bending exciting force, c xx , c xy , c yx , c yy are the four damping coefficients of the bearing, Jx and Jy are the moments of inertia about the x-axis and y-axis, k xx , k xy , y yx , k yy are the four stiffness coefficients of the bearing, and K0 is the shaft section stiffness.

8. The rotor thermal bending fault location and analysis method according to claim 1, characterized in that The specific content of step S4 includes: Select several other parts prone to thermal bending, and determine the corresponding node positions of the rotor; Set different temperature differences; Use the dynamic equation of the rotor thermal bending system to calculate and obtain the thermal bending calculation corresponding curves at each typical position.

9. The rotor thermal bending fault location and analysis method according to claim 1, wherein In step S5, When it is diagnosed that the increase in rotor vibration during operation is caused by thermal bending, compare the on-site vibration response with the trend of the calculated response curve of typical thermal bending vibration. If the curve trends are consistent, the thermal bending position in the rotor thermal bending system dynamic equation is the same as or close to the on-site thermal bending position. Compare the on-site vibration amplitude with the thermal bending response value calculated according to the model; when the measured vibration amplitude at the vibration measurement position is close to the vibration response value calculated by the rotor thermal bending system dynamic equation, the actual temperature difference on the shaft should be close to the temperature difference value input in the simulation calculation, so as to judge the severity of thermal bending.

10. The rotor thermal bending fault location and analysis method according to claim 4, characterized in that The calculation method of the bending moment M of each node section is as follows: Set the rotor to have a circular shaft cross-section, M x = M y = M; The temperature difference T generates a bending moment M around the x and y axes in the middle of the rotor cross-section x , M y , the bending moment at the cross-section on the left part of the rotor shaft segment is M L , the bending moment at the cross-section on the left part of the rotor shaft segment is M R , the mid-span deflection angle of the rotor shaft segment is θ M x = ∫∫γ0·E·T·y dx dy M y = ∫∫γ0·E·T·x dx dy Where γ0 is the linear expansion coefficient of the rotor, E is the elastic modulus of the rotor shaft material, T is the temperature distribution in the circumferential direction of the section, x and y are the coordinates of the points on the rotor section along the x and y axes, and dx and dy are the integral variables along the x and y axes respectively.

Images