Modeling method of flexible shaft system of multi-stage feedwater pump considering impeller fault excitation

Abstract

The present invention discloses a method for modeling a flexible shaft system of a multi-stage water feed pump considering impeller fault excitation, comprising the following steps: establishing a shaft segment dynamics model of a flexible shaft segment of a multi-stage water feed pump; establishing an impeller dynamics model of an impeller of a multi-stage water feed pump; establishing a bearing dynamics model of a bearing; considering impeller fault excitation, establishing a shaft system unbalanced mechanical model and a shaft system misalignment mechanical model; combining the above models to obtain a group of dynamic equations of a flexible shaft system of a multi-stage water feed pump; solving the group of dynamic equations by a numerical integration method to obtain the vibration response law of each component of the flexible shaft system of a multi-stage water feed pump. The present application models a flexible shaft system of a multi-stage water feed pump by considering flexible shaft segments, rigid impellers, bearings, and impeller fault excitations, and obtains the vibration response law by a numerical integration method, thereby improving the modeling accuracy of the flexible shaft system of a multi-stage water feed pump and the efficiency of vibration response analysis.

Description

Technical Field

[0001] The present application relates to the technical field of underwater vehicle modeling, and in particular to a method for modeling a flexible shaft system of a multi-stage feedwater pump taking into account impeller fault excitation. Background Art

[0002] Compared with traditional single-stage pumps, multi-stage feedwater pumps for underwater vehicles have better performance in terms of head and efficiency, but also have higher requirements in terms of processing, manufacturing and use. As a key component of the multi-stage feedwater pump system, the quality of the multi-stage feedwater pump shaft system determines the performance of the feedwater pump unit. In practical applications, the high performance, low noise and stable operation of the multi-stage feedwater pump system for underwater vehicles have become the focus of scholars. Therefore, it is necessary to study the modeling method of the flexible shaft system of the multi-stage feedwater pump.

[0003] At present, the finite element analysis method and multi-body dynamics method based on 3D software such as Ansys and Fluent are generally used to carry out dynamic modeling of the water feed pump shaft system and vibration response analysis of the water feed pump shaft system structure.

[0004] Among them, the finite element analysis method is more dependent on mesh accuracy, and high-quality meshes will occupy a large amount of computer resources and have a long calculation time, resulting in low efficiency in analyzing the vibration response of the feed pump shaft system structure; the existing multi-body dynamics method has a fast calculation speed, but generally does not consider the flexible deformation effect of the shaft segment. In addition, shaft impeller failure will cause vibration noise, hydraulic performance degradation, efficiency loss and cavitation in the multi-stage feed pump system during operation. In severe cases, it may also cause the feed pump unit to shut down. However, the existing technology has not studied the impeller fault excitation, and the modeling accuracy of the flexible shaft system of the multi-stage feed pump is low. Summary of the invention

[0005] The present application provides a method for modeling a flexible shaft system of a multi-stage water feed pump taking into account impeller fault excitation, so as to solve the problems of low efficiency in analyzing the vibration response of the shaft system structure of the water feed pump and low accuracy in modeling the flexible shaft system of the multi-stage water feed pump in the prior art.

[0006] On the one hand, the present application provides a method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation, comprising the following steps:

[0007] Step 1: Establish a shaft segment dynamic model of the flexible shaft segment of a multi-stage water supply pump.

[0008] Step 2: Establish the impeller dynamics model of the multi-stage feedwater pump impeller.

[0009] Step three, establish the bearing dynamics model of the bearing.

[0010] Step 4: Consider the impeller fault excitation and establish the shaft imbalance mechanical model and shaft misalignment mechanical model.

[0011] Step five, combining the shaft segment dynamics model, the impeller dynamics model, the bearing dynamics model, the shaft system unbalanced mechanical model and the shaft system misalignment mechanical model to obtain a group of dynamic equations for the flexible shaft system of the multi-stage water feed pump.

[0012] Step six, solving the dynamic equations by numerical integration method to obtain the vibration response law of each component of the flexible shaft system of the multi-stage water pump.

[0013] In a possible implementation, step one includes:

[0014] Establish the node displacement vector of the flexible shaft section of the multi-stage water supply pump.

[0015] Establish the shaft segment mass matrix of the flexible shaft segment of the multi-stage water supply pump.

[0016] Establish the segment stiffness matrix of the flexible segment of the multi-stage water supply pump.

[0017] Establish the shaft segment damping matrix of the flexible shaft segment of the multi-stage water supply pump.

[0018] A shaft segment dynamics model of the flexible shaft segment of a multi-stage water supply pump is established based on the node displacement vector, the shaft segment mass matrix, the shaft segment stiffness matrix and the shaft segment damping matrix.

[0019] In a possible implementation, step 2 includes:

[0020] Establish the impeller displacement vector of the multi-stage feedwater pump impeller.

[0021] Establish the impeller mass matrix of the multi-stage feedwater pump impeller.

[0022] Establish the impeller damping matrix of the multi-stage feedwater pump impeller.

[0023] An impeller dynamics model of a multi-stage feedwater pump impeller is established based on the impeller displacement vector, the impeller mass matrix and the impeller damping matrix.

[0024] In a possible implementation, step three includes:

[0025] The rolling bearing balance equation is established according to Newton's law, and the rolling bearing balance equation is the bearing dynamics model.

[0026] In a possible implementation, in step 4, the impeller fault excitation includes: impeller imbalance fault excitation and impeller misalignment fault excitation.

[0027] In a possible implementation, in step 4, the impeller unbalance fault excitation is obtained based on the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity and the unbalance mass initial phase angle.

[0028] The relationship between the impeller unbalance fault excitation and the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity, and the initial phase angle of the unbalance mass is the shaft system unbalance mechanical model.

[0029] In a possible implementation, in step 4, the impeller misalignment fault excitation is obtained based on the impeller misalignment mass, the impeller misalignment distance, the rotational angular velocity and the initial phase angle of the misalignment mass.

[0030] The relationship between the impeller misalignment fault excitation and the impeller misalignment mass, the impeller misalignment distance, the rotational angular velocity, and the initial phase angle of the misalignment mass is the shaft system misalignment mechanical model.

[0031] In a possible implementation, in step six, the numerical integration method adopts the Newmark-β method.

[0032] The flexible shafting modeling method of a multi-stage feedwater pump considering impeller fault excitation in this application has the following advantages:

[0033] The flexible shaft system of the multi-stage water feed pump is modeled by considering the flexible shaft section, rigid impeller, bearing, and impeller fault excitation, and the vibration response law is obtained through the numerical integration method, which improves the modeling accuracy of the flexible shaft system of the multi-stage water feed pump and the efficiency of vibration response analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 A schematic flow chart of a method for modeling a flexible shaft system of a multi-stage feedwater pump taking into account impeller fault excitation provided in an embodiment of the present application;

[0036] Figure 2 A schematic diagram of the structure of a flexible shaft system model of a multi-stage water supply pump provided in an embodiment of the present application;

[0037] Figure 3 A time domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the X direction under normal working conditions provided in an embodiment of the present application;

[0038] Figure 4 A time domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the Y direction under normal working conditions provided in an embodiment of the present application;

[0039] Figure 5 A frequency domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the X direction under normal working conditions provided in an embodiment of the present application;

[0040] Figure 6 A frequency domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the Y direction under normal working conditions provided in an embodiment of the present application;

[0041] Figure 7 A time domain diagram of the vibration response of the shaft system structure of a multi-stage water supply pump in the X direction under unbalanced working conditions provided in an embodiment of the present application;

[0042] Figure 8 A time domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the Y direction under unbalanced working conditions provided in an embodiment of the present application;

[0043] Fig. 9 A frequency domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the X direction under unbalanced working conditions provided in an embodiment of the present application;

[0044] Fig.10 A frequency domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the Y direction under unbalanced working conditions provided in an embodiment of the present application;

[0045] Fig.11 A time domain diagram of the vibration response of the shaft system structure of a multi-stage water supply pump in the X direction under the misalignment condition provided in an embodiment of the present application;

[0046] Fig.12 A time domain diagram of the vibration response of the shaft system structure of a multi-stage water supply pump in the Y direction under the misalignment condition provided in an embodiment of the present application;

[0047] Fig.13 A frequency domain diagram of the vibration response of the shaft structure of a multi-stage water supply pump in the X direction under the misalignment condition provided in an embodiment of the present application;

[0048] Fig.14 This is a frequency domain diagram of the vibration response of the multi-stage water supply pump shaft system structure in the Y direction under the misalignment condition provided in an embodiment of the present application. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0050] like Figure 1 As shown, the embodiment of the present application provides a method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation, including the following steps:

[0051] Step 1: Establish a shaft segment dynamic model of the flexible shaft segment of a multi-stage water supply pump.

[0052] Step 2: Establish the impeller dynamics model of the multi-stage feedwater pump impeller.

[0053] Step three, establish the bearing dynamics model of the bearing.

[0054] Step 4: Consider the impeller fault excitation and establish the shaft imbalance mechanical model and shaft misalignment mechanical model.

[0055] Step five, combining the shaft segment dynamics model, the impeller dynamics model, the bearing dynamics model, the shaft system unbalanced mechanical model and the shaft system misalignment mechanical model to obtain a group of dynamic equations for the flexible shaft system of the multi-stage water feed pump.

[0056] Step six, solving the dynamic equations by numerical integration method to obtain the vibration response law of each component of the flexible shaft system of the multi-stage water pump.

[0057] Specifically, Figure 2 The figure shows a schematic diagram of the structure of the flexible shaft system model of a multi-stage water supply pump. The shaft system model structure includes nine shaft segments, five impellers and two bearings. The nine shaft segments correspond to ten nodes. The axial direction of the nine shaft segments is defined as the Z axis, the opposite direction of the gravity direction is defined as the Y axis, and the horizontal plane direction perpendicular to both the Z axis and the Y axis is defined as the X axis. The modeling method of the flexible shaft system of the multi-stage water supply pump in this embodiment is based on Figure 2 Take the flexible shaft system model structure of a multi-stage water supply pump as an example.

[0058] Exemplarily, step one includes:

[0059] Establish the node displacement vector of the flexible shaft section of the multi-stage water supply pump.

[0060] Establish the shaft segment mass matrix of the flexible shaft segment of the multi-stage water supply pump.

[0061] Establish the segment stiffness matrix of the flexible segment of the multi-stage water supply pump.

[0062] Establish the shaft segment damping matrix of the flexible shaft segment of the multi-stage water supply pump.

[0063] A shaft segment dynamics model of the flexible shaft segment of a multi-stage water supply pump is established based on the node displacement vector, the shaft segment mass matrix, the shaft segment stiffness matrix and the shaft segment damping matrix.

[0064] Specifically, in this embodiment, the node displacement vector of the flexible shaft section of the multi-stage water supply pump is as shown in formula (1):

[0065] (1)

[0066] in, represents the displacement vector of the ith node, , , They represent the vibration displacement in the X direction, Y direction and Z direction of the i-th node respectively. , , Respectively represent the torsion angle of the i-th node around the X-axis, Y-axis and Z-axis. Each node has three translational degrees of freedom and three rotational degrees of freedom. Except for the first and tenth nodes, the two ends of each node correspond to a node with a displacement vector of six degrees of freedom.

[0067] In this embodiment, the shaft segment mass matrix of the flexible shaft segment of the multi-stage water supply pump is shown in formula (2):

[0068] (2)

[0069] in, represents the mass matrix of the nth axis segment, ρ represents the material density of the shaft segment, l Indicates the length of the shaft segment, represents the inertia matrix of the nth axis segment, represents the interpolation matrix corresponding to the mass matrix, and The expressions of are shown in formula (3) and formula (4):

[0070] (3)

[0071] (4)

[0072] in, A represents the cross-sectional area of ​​the shaft segment, , They represent the section inertia moment of the shaft segment in the YZ plane and the XZ plane respectively. N x1 , N θx1 , N x2 , N θx2 , N y1 , N θy1 , N y2 , N θy2 , L x1 , L θx1 , L x2, L θx2 , L y1 , L θy1 , L y2 , L θy2 are the shape functions of the shaft segment units, as shown in formula (5):

[0073] ; ;

[0074] ; ;

[0075] ; ;

[0076] ; ;

[0077] ; ;

[0078] ; ;

[0079] ; ;

[0080] ; ;

[0081] ; (5)

[0082] in, γ is the dimensionless unit length of the flexible shaft segment unit, l is the length of the differential axis segment, , , , are shear deformation parameters.

[0083] In this embodiment, the shaft segment stiffness matrix K of the flexible shaft segment of the multi-stage water supply pump is established based on the virtual displacement principle. n , as shown in formula (6):

[0084] (6)

[0085] Where B represents the interpolation matrix of the shaft segment unit stiffness matrix, and D represents the interpolation matrix of the shaft segment unit stiffness, as shown in formula (7):

[0086]

[0087] (7)

[0088] in, k represents the correction parameter. In this embodiment, k =10 / 9, G represents the shape function matrix of the shaft segment element, E Represents the elastic modulus.

[0089] In this embodiment, based on the Rayleigh damping assumption, the shaft segment damping matrix is ​​calculated by the linear combination of the shaft segment mass matrix and the shaft segment stiffness matrix. The shaft segment damping matrix C of the flexible shaft segment of the multi-stage water supply pump is n As shown in formula (8):

[0090] (8)

[0091] in, and They represent the proportionality coefficients of the shaft segment mass matrix and the shaft segment stiffness matrix respectively.

[0092] In this embodiment, based on the node displacement vector, the shaft segment mass matrix, the shaft segment stiffness matrix and the shaft segment damping matrix, combined with Newton's law, the shaft segment dynamics model of the flexible shaft segment of the multi-stage water supply pump is established as shown in formula (9):

[0093] (9)

[0094] in, represents the vibration velocity vector of the ith node, Represents the vibration acceleration vector of the i-th node.

[0095] Exemplarily, step two includes:

[0096] Establish the impeller displacement vector of the multi-stage feedwater pump impeller.

[0097] Establish the impeller mass matrix of the multi-stage feedwater pump impeller.

[0098] Establish the impeller damping matrix of the multi-stage feedwater pump impeller.

[0099] An impeller dynamics model of a multi-stage feedwater pump impeller is established based on the impeller displacement vector, the impeller mass matrix and the impeller damping matrix.

[0100] Specifically, the impeller is usually made of cast iron or cast steel, which has a small aspect ratio, high rigidity, and is not prone to bending and twisting. Based on the theory of Newton's second law, ignoring the gyroscopic effect of the rigid impeller, taking the displacement at the center of the rigid impeller, the impeller displacement vector of the multi-stage feedwater pump impeller is established as shown in formula (10):

[0101] (10)

[0102] in, represents the displacement vector of the dth impeller, , , They represent the vibration displacement in the X direction, Y direction and Z direction at the center of the dth impeller, respectively. , , They represent the torsion angles around the X-axis, Y-axis and Z-axis at the center of the d-th impeller respectively.

[0103] In this embodiment, the impeller mass matrix of the multi-stage feedwater pump impeller is shown in formula (11):

[0104] (11)

[0105] in, represents the mass matrix of the d-th impeller, m d represents the mass of the dth impeller, J d is the diameter moment of inertia, J p Represents the polar moment of inertia.

[0106] In this embodiment, the impeller damping matrix of the multi-stage feedwater pump impeller is shown in formula (12):

[0107] (12)

[0108] in, represents the damping matrix of the d-th impeller, Represents the proportionality factor of the impeller mass matrix.

[0109] In this embodiment, the impeller dynamics model of the multi-stage feedwater pump impeller is established based on the impeller displacement vector, the impeller mass matrix and the impeller damping matrix, as shown in formula (13):

[0110] (13)

[0111] in, represents the vibration velocity vector at the center of the dth impeller, Represents the vibration acceleration vector at the center of the dth impeller.

[0112] Exemplarily, step three includes:

[0113] The rolling bearing balance equation is established according to Newton's law, and the rolling bearing balance equation is the bearing dynamics model.

[0114] Specifically, in this embodiment, the rolling bearing balance equation is shown in formula (14):

[0115] (14)

[0116] in, m is the mass of the inner ring of the rolling bearing and the shaft, , , , , , , , , They are the vibration displacement, vibration velocity and vibration acceleration of the inner ring of the rolling bearing in the X, Y and Z directions respectively. is the damping of the rolling bearing, is the support stiffness of the inner ring of the rolling bearing, , and The rolling element is subjected to external loads in the X, Y and Z directions respectively. , and They are the contact forces between the rolling element and the inner ring in the X, Y, and Z directions respectively. , and As shown in formula (15):

[0117] (15)

[0118] in, is the number of rolling elements, , and They are i Rolling elements and inner ring j contact load, position angle and contact angle, It is the inner circle j and i The drag force between the rolling elements along the rolling direction.

[0119] Exemplarily, in step 4, the impeller fault excitation includes: impeller imbalance fault excitation and impeller misalignment fault excitation.

[0120] Exemplarily, in step 4, the impeller unbalance fault excitation is obtained based on the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity and the initial phase angle of the unbalance mass.

[0121] The relationship between the impeller unbalance fault excitation and the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity, and the initial phase angle of the unbalance mass is the shaft system unbalance mechanical model.

[0122] Specifically, in this embodiment, the unbalanced mechanical model of the shaft system is shown in formula (16):

[0123] (16)

[0124] in, F ux and F uy Respectively represent the impeller unbalance fault excitation in the X and Y directions, m u is the equivalent mass of the impeller unbalance mass at the geometric center, e is the impeller unbalance distance, ω is the angular velocity of rotation, θ is the initial phase angle of the unbalanced mass.

[0125] Exemplarily, in step 4, the impeller misalignment fault excitation is obtained based on the impeller misalignment mass, the impeller misalignment distance, the rotational angular velocity and the initial phase angle of the misalignment mass.

[0126] The relationship between the impeller misalignment fault excitation and the impeller misalignment mass, the impeller misalignment distance, the rotational angular velocity, and the initial phase angle of the misalignment mass is the shaft system misalignment mechanical model.

[0127] Specifically, in this embodiment, the mechanical model of shaft misalignment is shown in formula (17):

[0128] (17)

[0129] in, F mx and F my Respectively represent the impeller misalignment fault excitation in the X and Y directions, m i is the equivalent mass of the impeller misalignment mass at the geometric center, Δ E is the impeller misalignment distance, ω is the angular velocity of rotation, is the initial phase angle of the misaligned mass.

[0130] Specifically, in this embodiment, in step five, the shaft segment dynamics model, the impeller dynamics model, the bearing dynamics model, the shaft system unbalanced mechanical model and the shaft system misaligned mechanical model are combined, that is, equations (1) to (16) are combined to obtain the dynamics equation group of the flexible shaft system of the multi-stage water supply pump as shown in equation (18):

[0131] (18)

[0132] Where u = [ xyzθ x θ y θ z ] T is the generalized displacement vector of each node of the flexible shaft system of the multi-stage feedwater pump, and are the vibration velocity vector and vibration acceleration vector of each node of the flexible shaft system of the multi-stage feedwater pump; F f is the fault excitation of the multi-stage water supply pump; M, C, K are the mass matrix, damping matrix and stiffness matrix of the multi-stage water supply pump as a whole. Specifically, as shown in formula (19):

[0133]

[0134]

[0135] (19)

[0136] In the formula, , , , Represents the mass matrix element corresponding to segment 1 (superscript (1) represents segment 1, superscript (2) represents segment 2, and so on. Subscripts 11, 12, 21, 22 represent different mass matrix components); , , , Represents the stiffness matrix element corresponding to shaft segment 1 (superscript (1) represents shaft segment 1, superscript (2) represents shaft segment 2, and so on. Subscripts 11, 12, 21, 22 represent different stiffness matrix components); α 0 and α 1 They respectively represent the proportional coefficient of the mass matrix of the multi-stage water supply pump as a whole and the proportional coefficient of the stiffness matrix of the multi-stage water supply pump as a whole.

[0137] Exemplarily, in step six, the numerical integration method adopts the Newmark-β method.

[0138] Specifically, in this embodiment, the Newmark-β method is used to solve the dynamic equations to obtain the vibration response law of each component of the flexible shaft system of the multi-stage water supply pump. The process is as follows:

[0139] Initialization: Given initial conditions, including displacement vector u, velocity vector and the acceleration vector The initial vector condition.

[0140] Determine parameters: Select Newmark-β method parameters: In this embodiment, β=0.25 and γ=0.5, at which time the algorithm has good convergence.

[0141] Solving acceleration: Based on the displacement, velocity, and external force or constraints at the current moment, calculate the acceleration, shaft load, and vibration displacement at the current moment.

[0142] Update displacement and velocity: Use the iterative formula of the Newmark-β method to calculate the displacement and velocity of the next time step.

[0143] Iteration: Repeatedly solves for acceleration and repeatedly updates displacement and velocity until the desired solution time step is reached or convergence criteria are met.

[0144] Output results: At the end of each time step, displacement, velocity, acceleration, shaft load and vibration displacement parameters are recorded.

[0145] In a possible embodiment, Figures 3 to 6 The figure shows the vibration response diagram of the shaft structure of the multi-stage feedwater pump under normal working conditions, including the time domain and frequency domain diagrams in the X and Y directions. At this time, the impeller unbalance fault excitation and impeller misalignment fault excitation are not considered. Figures 7 to 10 The figure shows the vibration response diagram of the shaft structure of a multi-stage feedwater pump under unbalanced working conditions, including the time domain and frequency domain diagrams in the X and Y directions, and the impeller unbalance fault excitation is considered at this time. Figures 11 to 14 The figure shows the vibration response diagram of the shaft structure of the multi-stage feedwater pump under the misalignment condition, including the time domain and frequency domain diagrams in the X and Y directions, when the impeller misalignment fault excitation is considered. By comparing the vibration response diagrams of the shaft structure of the multi-stage feedwater pump under three working conditions, it can be seen that after considering the impeller unbalance fault excitation or the impeller misalignment fault excitation, the amplitude characteristics in the time domain and frequency domain change significantly.

[0146] The embodiment of the present application models the flexible shaft system of a multi-stage water feed pump by considering flexible shaft segments, rigid impellers, bearings, and impeller fault excitations, and obtains the vibration response law through a numerical integration method, thereby improving the modeling accuracy of the flexible shaft system of the multi-stage water feed pump and the efficiency of vibration response analysis.

[0147] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0148] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A flexible shaft modeling method for a multi-stage feedwater pump considering impeller fault excitation, characterized in that: The following steps are involved: Step 1, establishing a shaft segment dynamics model of the flexible shaft segment of the multi-stage water feed pump, including: establishing a shaft segment dynamics model of the flexible shaft segment of the multi-stage water feed pump based on the node displacement vector, shaft segment mass matrix, shaft segment stiffness matrix and shaft segment damping matrix of the flexible shaft segment of the multi-stage water feed pump; Step 2, establishing an impeller dynamics model of the multi-stage feedwater pump impeller, including: establishing an impeller dynamics model of the multi-stage feedwater pump impeller based on an impeller displacement vector, an impeller mass matrix and an impeller damping matrix of the multi-stage feedwater pump impeller; Step 3, establishing a bearing dynamics model of the bearing; Step 4: Considering the impeller fault excitation, establish the shaft system unbalance mechanical model and shaft system misalignment mechanical model; Step 5, combining the shaft segment dynamics model, the impeller dynamics model, the bearing dynamics model, the shaft system unbalanced mechanical model and the shaft system misalignment mechanical model to obtain a group of dynamics equations of the flexible shaft system of the multi-stage water feed pump; Step six, solving the dynamic equations by numerical integration method to obtain the vibration response law of each component of the flexible shaft system of the multi-stage water supply pump; In step 4, the impeller fault excitation includes: impeller imbalance fault excitation and impeller misalignment fault excitation; In step 4, the impeller unbalance fault excitation is obtained based on the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity and the unbalance mass initial phase angle; The relationship between the impeller unbalance fault excitation and the impeller unbalance mass, the impeller unbalance distance, the rotation angular velocity, and the initial phase angle of the unbalance mass is the shaft system unbalance mechanical model; The mechanical model of shaft imbalance is as follows: ； in, F ux and F uy Respectively represent the impeller unbalance fault excitation in the X and Y directions, m u is the equivalent mass of the impeller unbalance mass at the geometric center, e is the impeller unbalance distance, ω is the angular velocity of rotation, θ is the initial phase angle of the unbalanced mass; In step 4, the impeller misalignment fault excitation is obtained based on the impeller misalignment mass, the impeller misalignment distance, the rotation angular velocity and the initial phase angle of the misalignment mass; The relationship between the impeller misalignment fault excitation and the impeller misalignment mass, the impeller misalignment distance, the rotational angular velocity, and the initial phase angle of the misalignment mass is the shaft misalignment mechanical model; The mechanical model of shaft misalignment is as follows: ； in, F mx and F my Respectively represent the impeller misalignment fault excitation in the X and Y directions, m i is the equivalent mass of the impeller misalignment mass at the geometric center, Δ E is the impeller misalignment distance, ω is the angular velocity of rotation, is the initial phase angle of the misaligned mass; In step 5, the shaft segment dynamics model, impeller dynamics model, bearing dynamics model, shaft system unbalanced mechanical model and shaft system misalignment mechanical model are combined to obtain the dynamics equations of the flexible shaft system of the multi-stage feedwater pump as shown below: ； Where u = [ xyzθ x θ y θ z ] T is the generalized displacement vector of each node of the flexible shaft system of the multi-stage feedwater pump, and are the vibration velocity vector and vibration acceleration vector of each node of the flexible shaft system of the multi-stage feedwater pump; F f is the fault excitation of the multi-stage water supply pump; M, C, K are the mass matrix, damping matrix and stiffness matrix of the multi-stage water supply pump as a whole respectively; ； In the formula, α 0 and α 1 respectively represent the proportional coefficient of the mass matrix of the multi-stage water supply pump as a whole and the proportional coefficient of the stiffness matrix of the multi-stage water supply pump as a whole.

2. The method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation according to claim 1 is characterized in that: Step one includes: Establish the node displacement vector of the flexible shaft section of the multi-stage water supply pump; Establish the shaft mass matrix of the flexible shaft of the multi-stage feedwater pump; Establish the segment stiffness matrix of the flexible segment of the multi-stage water supply pump; Establish the shaft segment damping matrix of the flexible shaft segment of the multi-stage water supply pump; A shaft segment dynamics model of the flexible shaft segment of a multi-stage water supply pump is established based on the node displacement vector, the shaft segment mass matrix, the shaft segment stiffness matrix and the shaft segment damping matrix.

3. The method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation according to claim 1 is characterized in that: Step 2 includes: Establish the impeller displacement vector of the multi-stage feedwater pump impeller; Establish the impeller mass matrix of the multi-stage feedwater pump impeller; Establish the impeller damping matrix of the multi-stage feedwater pump impeller; An impeller dynamics model of a multi-stage feedwater pump impeller is established based on the impeller displacement vector, the impeller mass matrix and the impeller damping matrix.

4. The method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation according to claim 1 is characterized in that: Step three includes: The rolling bearing balance equation is established according to Newton's law, and the rolling bearing balance equation is the bearing dynamics model.

5. The method for modeling a flexible shaft system of a multi-stage feedwater pump considering impeller fault excitation according to claim 1 is characterized in that: In step six, the numerical integration method adopts the Newmark-β method.

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