Gas turbine pull rod rotor wheel disc vibration analysis method, system and device

Abstract

The invention discloses a gas turbine pull rod rotor wheel disc vibration analysis method, system and device, and relates to the technical field of gas turbines.The method comprises the steps that a three-dimensional finite element kinetic equation of a rotating part is constructed; the contact stiffness of adjacent contact units is deduced by considering the rough contact characteristic of the contact interface and combining a microscopic contact mechanical model of the contact interface and a rough consolidation interface contact mechanical model based on the statistical theory; a stress strengthening effect is considered, and a stress stiffness matrix and a contact stiffness matrix are iteratively calculated; a central pull rod end face tooth structure considering local contact nonlinearity is constructed, and an end face tooth contact model considering collision separation is constructed; carrying out vibration response solution on the three-dimensional finite element kinetic equation by adopting a degree-of-freedom reduction method; according to the method, the vibration analysis model is established, the pull rod rotor does not need to be simplified, and geometric features, contact surface features and load effects of an original model can be reserved to a great extent.

Description

Technical Field

[0001] The present invention relates to the technical field of gas turbines, and in particular to a method, system and device for analyzing vibration of a gas turbine pull rod rotor disc. Background Art

[0002] The dynamic modeling of a gas turbine rotor system with a multi-disc tie-rod structure is highly complex due to the numerous contact surfaces between the discs. The stiffness characteristics of these contact surfaces influence the rotor's operating state and are a key factor influencing its dynamic characteristics. The stiffness of these contact surfaces is determined by the tie-rod preload. Therefore, determining the contact model and its parameters under different preload conditions presents a complex challenge in dynamic modeling and simulation analysis.

[0003] Current research primarily uses simplified models, which require significant simplifications of the rod rotor geometry, making it difficult to delve into these issues. Furthermore, the center-rod rotors of heavy-duty gas turbines, due to their unique structure and operating environment, can lead to unique failure modes, such as uneven preload distribution, poor contact between the discs, and even separation. These issues introduce nonlinearity into the rotor, potentially exacerbating rotor vibration. For a modular center-rod rotor connected by Hirth teeth, ideally, each pair of Hirth teeth bears a uniform preload to ensure good contact between the contact surfaces. The contact surface pressure in this state is referred to as "saturation pressure."

[0004] However, the simplified models used in previous vibration analysis of gas turbine multi-disc tie-rod rotors significantly simplified the geometric structure of the tie-rod rotors. However, in practice, certain conditions may cause poor contact or separation between the disc hirth teeth, introducing nonlinearity into the rotor and potentially exacerbating rotor vibration. However, the simplified models are unable to provide in-depth analysis of such issues. Summary of the Invention

[0005] In response to the shortcomings of the existing technology that have greatly simplified the geometric structure of the rod rotor and are unable to deeply analyze the conditions such as poor contact or separation of the wheel disk hirth tooth contact surface caused by certain circumstances, the present invention proposes a gas turbine rod rotor wheel disk vibration analysis method, system and device. By establishing a vibration analysis model of the gas turbine rod rotor wheel disk with a full three-dimensional multi-scale contact interface, the geometric characteristics, contact surface characteristics and load effects of the original model can be retained to a great extent without simplifying the rod rotor, thereby solving the problems existing in the existing technology.

[0006] A method for analyzing vibration of a gas turbine pull rod rotor disc comprises the following steps: Construct the three-dimensional finite element dynamic equations of the gas turbine pull rod rotor disc including the stress stiffening matrix and contact stiffness matrix; The rough surface of the rotor disc is considered as a surface formed by a series of micro-asperities of different heights on a smooth surface. According to the elastic-plastic contact model, the deformation stage of a single micro-asperity is divided into the elastic stage, the elastic-plastic stage, and the plastic stage, and the normal contact load of each stage is calculated. The normal contact load of all micro-asperities involved in the contact is integrated to obtain the functional relationship between the contact variable and the contact surface distance. Based on the functional relationship between the contact variable and the contact surface distance, the current contact stiffness matrix is ​​determined. Perform static analysis based on the current contact stiffness matrix to obtain the displacement field and the corresponding stress field. Update the contact stiffness matrix and stress stiffening matrix based on the displacement field and the corresponding stress field. After multiple iterations, until the residual of the contact stiffness matrix between two adjacent iterations is less than the set tolerance, the final contact stiffness matrix and stress stiffening matrix are output. After introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation, the three-dimensional finite element dynamic equation is analyzed and solved to obtain the vibration response of the gas turbine pull rod rotor disk.

[0007] Furthermore, the three-dimensional finite element dynamic equation for constructing the gas turbine pull rod rotor disc containing the stress stiffening matrix and the contact stiffness matrix is ​​expressed as: ; in represents the mass matrix; is the rotational speed; is the Coriolis force matrix; represents the bearing damping matrix; represents the structural stiffness matrix; represents the rotation softening matrix; Represents the linear load force vector calculated from the preload force; represents the centrifugal load vector; represents the stiffness matrix of the bearing, is the displacement vector, is the velocity vector, is the acceleration vector.

[0008] Furthermore, according to the elastic-plastic contact model, the deformation stage of a single asperity is divided into an elastic stage, an elastic-plastic stage, and a plastic stage, and the normal contact load of each stage is obtained; wherein: The normal contact load in the elastic stage is expressed as: ; The normal contact load in the elastic-plastic stage is expressed as: ; ; The normal contact load in the fully plastic stage is expressed as: ; in represents the critical deformation of the asperity, ; represents the contact deformation of a single asperity; represents the equivalent elastic modulus of the contact interface; represents the approximate curvature radius of the asperity tip; Indicates contact microhardness; Represents the hardness coefficient, which is related to the Poisson's ratio of the material; By integrating the normal contact loads of all asperities involved in contact, we can obtain the functional relationship between the contact variable and the distance between the contact surfaces. The functional relationship is: ; in, ; ; ; ; in represents the dimensionless Gaussian distribution, ; 、 and Parameters that represent surface roughness include the number of asperities per unit area, the average radius of the asperities, and the standard deviation of the asperity heights.

[0009] Furthermore, the static analysis is performed based on the current contact stiffness matrix to obtain a displacement field and a corresponding stress field, and the contact stiffness matrix and the stress stiffening matrix are updated using the displacement field and the corresponding stress field; after multiple iterative updates, until the residual of the contact stiffness matrix between two adjacent iterations is less than a set tolerance, the final contact stiffness matrix and the stress stiffening matrix are output, which specifically includes the following steps: Let the initial stress stiffening matrix be zero and obtain the current contact stress. The calculation process is: ; ; in and Indicates the contact force of the end tooth contact surface; Indicates preload; Indicates the tangential force converted from torque; represents the coefficient of sliding friction; φrepresents the pressure angle of the face teeth, ; According to the current contact stress, the current contact stiffness matrix is ​​calculated by the finite element formula of the contact stiffness matrix; Substitute the current contact stiffness matrix and stress toughening matrix into the dynamic equation and solve it without considering the time term to obtain the displacement vector; The contact pressure is calculated based on the displacement vector, and the contact stiffness matrix and stress stiffening matrix are updated through the displacement field and the corresponding stress field; the stress stiffening matrix is ​​calculated by the finite element calculation formula; the finite element calculation formula of the stress stiffening matrix is ,in Related to Cauchy stress; Represents the geometric matrix, which describes the influence of the geometric state on the strain when the unit is deformed; After multiple iterative updates, the residual of the contact stiffness matrix between adjacent time steps is determined: ; If the residual is less than the tolerance tol , then the final calculated contact stiffness matrix and stress stiffening matrix are output; the tolerance tol Defined as: .

[0010] Furthermore, the contact stiffness matrix finite element formula is expressed as: ;in represents the shape function of the contact element, Represents the contact matrix of adjacent contact elements; the contact matrix of adjacent contact elements Expressed as: ; in, and They represent the element normal contact stiffness and tangential contact stiffness respectively; In the natural coordinate system, the shape function of the contact element is expressed as: , in, ; in and Represents the natural coordinates of the contact element.

[0011] Furthermore, it also includes constructing an end face tooth contact model considering collision separation by considering the normal pressure and tangential pressure per unit area of ​​the contact surface of the center tie rod end face tooth structure with local contact nonlinearity and the node normal displacement and tangential displacement of the end tooth surface contact surface before introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation; and obtaining the contact pressure of the end face tooth under different contact states according to the end face tooth contact model.

[0012] Furthermore, after introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation, the vibration response of the gas turbine pull rod rotor disc is analyzed using the degree of freedom reduction method. The specific steps include: Under the action of periodic excitation, according to the harmonic balance method, the displacement vector in the dynamic equation is expressed as a finite-order Fourier form; Substitute the finite-order Fourier form of the displacement vector into the dynamic equation to calculate the multi-order harmonic vector expression of the nonlinear force and linear force; A Newton-Raphson iteration method is used to obtain a steady-state solution for the multi-order harmonic vector expression of nonlinear force and linear force; a sampling degree of freedom reduction method is used to ignore the damping term, time-varying term and load term on the right side in the dynamic equation; a fixed interface modal synthesis method is used to obtain a reduced equation for the system's degrees of freedom based on a main modal matrix, a reduced modal matrix, modal coordinates and retained node displacement vectors; wherein the reduced modal matrix is ​​obtained based on a stiffness matrix divided into slave displacement vectors and a stiffness matrix of bearing node displacements and contact surface node displacement vectors that produce poor contact; the main modal matrix is ​​composed of the retained first k-order modal vectors after constraining the bearing node displacements and the contact surface node displacements that produce poor contact; The vibration response of the pull-rod rotor disc is analyzed based on the equation after modal reduction.

[0013] The present invention also includes a gas turbine pull rod rotor disc vibration analysis system, comprising: A construction module for constructing the three-dimensional finite element dynamic equations of the gas turbine pull rod rotor disc including the stress stiffening matrix and the contact stiffness matrix; The contact stiffness matrix calculation module treats the rough surface of the rotor disc as a surface formed by a series of asperities of different heights on a smooth surface. Based on the elastic-plastic contact model, the deformation stage of a single asperity is divided into the elastic stage, the elastic-plastic stage, and the plastic stage, and the normal contact load in each stage is calculated. The normal contact load of all the asperities involved in the contact is integrated to obtain the functional relationship between the contact variable and the contact surface distance. Based on the functional relationship between the contact variable and the contact surface distance, the current contact stiffness matrix is ​​determined. The update module is used to perform static analysis based on the current contact stiffness matrix to obtain the displacement field and the corresponding stress field, and update the contact stiffness matrix and stress stiffening matrix based on the displacement field and the corresponding stress field. After multiple iterations of updates, the contact stiffness matrix residual between two adjacent iterations is less than the set tolerance, and the final contact stiffness matrix and stress stiffening matrix are output. The analysis module is used to analyze and solve the three-dimensional finite element dynamic equations by introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equations to obtain the vibration response of the gas turbine pull rod rotor wheel.

[0014] The present invention also includes a gas turbine pull rod rotor disc vibration analysis computer device, comprising: a memory, a processor and a computer program stored in the memory, and when the processor executes the computer program, the steps of the gas turbine pull rod rotor disc vibration analysis method are implemented.

[0015] The present invention also includes a readable storage medium, which stores a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the gas turbine pull rod rotor disc vibration analysis method.

[0016] The present invention provides a method for analyzing vibration of a gas turbine pulley rotor disc, which has the following beneficial effects: The present invention constructs a vibration analysis model of a full three-dimensional multi-scale contact interface without simplifying the rod rotor, and retains the geometric features, contact surface features and load effects of the original model to a great extent, thereby significantly improving the accuracy of the analysis; the contact stiffness of adjacent contact units is derived through a microscopic contact mechanics model, and the elastic-plastic deformation (elastic, elastic-plastic, and plastic stages) of the rough surface can be accurately simulated, thereby more realistically reflecting the actual contact state; by iteratively updating the contact stiffness matrix and the stress stiffening matrix until the residual is less than the set tolerance, the convergence and reliability of the calculation results are ensured, and the nonlinear problem caused by the preload force is effectively solved; this method considers the complex contact state between multiple contact surfaces, based on the elastic-plastic contact theory and the high-fidelity finite element method, to establish a gas turbine vibration analysis model of a full three-dimensional multi-scale contact interface, without simplifying the rod rotor, and can retain the geometric features, contact surface features and load effects of the original model to a great extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of a rough surface contact model for end face tooth contact in an embodiment of the present invention; Figure 2 Schematic diagram of the relationship between normal contact stiffness and contact pressure of different contact surfaces in an embodiment of the present invention; Figure 3Schematic diagram of the iterative process for calculating the contact stiffness matrix in an embodiment of the present invention; Figure 4 Schematic diagram of the end face gear structure of the center tie rod considering local contact nonlinearity in an embodiment of the present invention; Figure 5 Schematic diagram of a multi-disk center-tie rod rotor experimental system with a Hirth tooth structure according to an embodiment of the present invention; Figure 6 Schematic diagram of the surface profile curve of the contact surface of the experimental rod rotor in an embodiment of the present invention; Figure 7 Schematic diagram showing the comparison of the first three free vibration frequencies under different preload forces in an embodiment of the present invention; Figure 7 (a) is a schematic diagram comparing the experimental value and the calculated value. Figure 7 (b) is a schematic diagram of the relative error between the experimental value and the calculated value; Figure 8 The flowchart of a method for analyzing the vibration of a gas turbine pull-rod rotor is shown in FIG.

[0018] Description of reference numerals: 11-main wheel disc, 12-No. 1 test disc, 13-No. 2 test disc, 14-center pull rod, 15-nut, 21-impact hammer, 31-acceleration sensor, 32-dynamic data acquisition instrument, 33-data analysis computer, 41-strain gauge, 42-strain gauge, 51-suspension rope; C#1-contact between nut 15 and No. 1 test disc 12, C#2-end face tooth contact between No. 1 test disc 12 and main wheel disc 11, C#3-end face tooth contact between No. 2 test disc 13 and main wheel disc 11. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0020] The present invention proposes a vibration analysis method for a gas turbine pull-rod rotor disk. Aiming at the vibration response analysis problem of a gas turbine multi-stage disk, the present invention considers the complex contact state between the contact surfaces of the gas turbine pull-rod rotor and establishes a vibration analysis model of a gas turbine pull-rod rotor disk with a full three-dimensional multi-scale contact interface based on elastic-plastic contact theory and high-fidelity finite element method. Without simplifying the pull-rod rotor, the geometric features, contact surface features, and load effects of the original model can be retained to a great extent. The correctness of the proposed method has been verified through experimental research. Figure 8 As shown, the method specifically includes the following steps: S1. Construct the three-dimensional finite element dynamic equations for the rotating component (gas turbine pull rod rotor disc). For a rotating coordinate system with the Z axis and a rotational speed of Ω, the coordinate transformation relationship between point P in the rotating coordinate system and the fixed coordinate system can be written as:

[0021] (1) in Represents the coordinate vector of point P in the rotating coordinate system; Represents the coordinate vector of point P in the fixed coordinate system; Represents the coordinate transformation matrix, which is expressed as follows: (2).

[0022] The dynamic equation of the rotor-bearing system in the rotating coordinate system is: (3) in represents the mass matrix; is the Coriolis force matrix; represents the bearing damping matrix; represents the structural stiffness matrix; represents the rotation softening matrix; Represents the linear load force vector calculated from the preload force; represents the centrifugal load vector; represents the stiffness matrix of the bearing, which is expressed as follows: (4) (5) Where: and In the central tie rod rotor-bearing system, each stage of the wheel is positioned and torque-transmitted through the end face teeth, forming multiple contact surfaces. In order to simulate this connection relationship in a three-dimensional finite element, a zero-thickness surface element is used to calculate the contact stiffness between the two contact surfaces. The present invention uses the Goodman zero-thickness element, and the two adjacent nodes of the Goodman zero-thickness element correspond one to one. t1 、e t2 and e n Represent the tangential and normal directions of the contact surface respectively, and the potential energy of the unit is:

[0023] (6) in represents the element contact stiffness coefficient matrix per unit area, represents the unit displacement per unit area, S eRepresents the contact unit area. The finite element formula of the contact stiffness matrix can be derived from the potential energy of the contact unit:

[0024] (7) in represents the shape function of the contact element, Represents the contact matrix of adjacent contact elements. The contact matrix expression is as follows, where and They represent the element normal contact stiffness and tangential contact stiffness respectively.

[0025] (8) In the natural coordinate system, the shape function of the contact element can be expressed as: (9) (10) in and Represents the natural coordinates of the contact element.

[0026] S2. Considering the rough contact characteristics of the contact interface, the contact stiffness of adjacent contact units is derived by combining the microscopic contact mechanics model of the contact interface and the rough consolidation interface contact mechanics model based on statistical theory.

[0027] At the microscopic scale, a rough surface can be viewed as a surface formed by a series of micro-convex bodies of different heights on a smooth surface, and the distribution of the height of the micro-convex bodies can be considered to satisfy the Gaussian distribution. Figure 1 The rough surface contact model is considered to be a uniform, random, isotropic face-to-face contact model. The top of the asperity is approximately a curvature radius of R n sphere, height z s Represents the distance between the vertex of the micro-asperity and the average height of the micro-asperity. When the rough surface is subjected to a normal load, the contact deformation of a single micro-asperity is:

[0028] (11) in Represents the distance between the mean height of the rough surface and the rigid plane, It represents the distance between the mean height of the rough surface and the mean height of the asperities.

[0029] According to the elastic-plastic contact model, the deformation of a single asperity is considered and its deformation stages are divided into elastic stage, elastic-plastic stage and plastic stage, and the normal contact load in each stage can be obtained.

[0030] The normal contact load in the elastic stage is: (12) The normal contact load in the elastic-plastic stage is: (13) (14) The normal contact load in the fully plastic stage is: (15) in represents the critical deformation of the asperity, ; Represents the equivalent elastic modulus of the contact interface / Pa; Indicates contact microhardness / Pa; Indicates the hardness coefficient and the Poisson's ratio of the material related, .

[0031] By integrating the normal contact loads of all asperities involved in contact, we can obtain the functional relationship between the contact variable and the distance between the contact surfaces: (16) (17) (18) (19) (20) in represents the dimensionless Gaussian distribution, s represents the distance between the vertex of the micro-asperity and the mean line of the micro-asperity height, ; 、 and Parameters that represent surface roughness include the number of asperities per unit area, the average radius of the asperities, and the standard deviation of the asperity heights.

[0032] For the contact surface morphology s ( x ) surface, the surface roughness parameters are calculated as follows: (twenty one) (twenty two) (twenty three) in , , , , Represents the length of the contact surface; on the element contact surface, it is assumed that the local roughness parameter and the overall roughness parameter of the contact surface obey the same statistical distribution law. The element normal contact stiffness can be expressed as the derivative of the contact pressure relative to the dimensionless distance:

[0033] (twenty four) The tangential contact stiffness is calculated as follows: (25).

[0034] Figure 2 The figure shows the curve of contact stiffness changing with contact pressure under different surface roughness parameters. Figure 2 It can be seen that under the same contact pressure, the surface normal contact stiffness decreases with the increase of surface roughness. In addition, the normal contact stiffness increases with the increase of contact pressure. On the smoother surface, the normal contact stiffness increases faster with the contact pressure. However, the normal contact stiffness cannot increase infinitely with the increase of contact pressure, and there are certain limitations. According to the microscopic contact mechanics model of the contact interface, when h = 0, that is, when the surface contact pressure causes the interface asperities to completely deform, the contribution of the asperities to the normal contact stiffness is zero. At this point, the contact stiffness is already very large. In order to avoid numerical calculation problems, the normal contact stiffness is set to remain unchanged with the increase of contact pressure. Figure 2 As shown by the horizontal line in .

[0035] S3. Considering the stress hardening effect, iteratively calculate the stress stiffening matrix and contact stiffness matrix.

[0036] In rod-type rotors, stress intensification is an important consideration in preload structural analysis. The natural frequency may be sensitive to local stress due to the stress intensification effect. For example, when the structure is under axial tension, the ability to resist bending deformation will increase. On the contrary, if the structure is under axial compression, the ability to resist bending will decrease. The rod preload is regarded as an external force factor in the preload structural analysis. In the finite element analysis, this effect is considered through the auxiliary stiffness matrix of the stress stiffness matrix (StressStiffness). Therefore, the stress stiffness matrix caused by the preload should also be included in the system dynamics equation. K σ The finite element calculation formula for the element stress stiffening matrix is:

[0037] (26) in Related to Cauchy stress; Represents the geometric matrix, which describes the influence of the geometric state on the strain when the element is deformed.

[0038] Extrapolate the element contact stiffness matrix and stress stiffening matrix to the overall structure and substitute them into the system dynamics equation to obtain: (27) If the contact pressure of the contact surface is obtained in advance, then the contact stiffness matrix of the contact surface can be calculated in theory. When the preload at both ends of the face gear connection section is determined, the contact pressure of the Hirth gear can be approximately calculated using the following two equations:

[0039] (28) (29) in and Indicates the contact force of the end tooth contact surface; Indicates preload; Indicates the tangential force converted from torque; represents the coefficient of sliding friction; φ represents the pressure angle of the face teeth, .

[0040] However, in most cases, the contact pressure of the contact surface is difficult to obtain in advance, so an iterative method is required to obtain the contact stiffness matrix. Considering the effect of the preload on the center-tie rod rotor, the implicit relationship of the stiffness matrix can be expressed as:

[0041] (30) in and Represent the total stiffness matrix of the current iteration step and the previous iteration step respectively.

[0042] refer to Figure 3 The iterative process of obtaining the contact stiffness matrix is ​​described in the following. First, given the displacement and force boundary conditions, when n = 0, set the stress stiffening matrix to zero. At this time, the contact pressure is calculated using Equations (28) and (29), and then the initial contact stiffness matrix is ​​calculated using Equations (7) to (25). Considering static analysis, ignore the time term of Equation (27), solve the finite element equation to obtain the displacement vector, calculate the contact stress, repeat the calculation process of Equations (7) to (25), update the contact stiffness matrix, and calculate the stress stiffening matrix using Equation (26). The convergence condition is judged, that is, the residual of the contact stiffness matrix calculated in two adjacent steps (defined as: ) is less than the tolerance. If it is greater than the tolerance tol , then repeat the above process, otherwise stop the iteration and output the contact stiffness matrix and stress stiffening matrix calculated in the current step. tol Defined as:

[0043] (31) S4. Considering the local contact nonlinearity of the center tie rod end face tooth structure, a face tooth contact model considering collision separation is constructed.

[0044] Figure 4 The figure shows the center tie rod end face tooth structure considering local contact nonlinearity. Under the action of gravity and unbalanced forces, relative movement occurs between the end face teeth of adjacent wheels with poor contact, resulting in a relatively obvious contact nonlinear phenomenon. Specifically, it can be simplified into two components: parallel end face tooth surface and perpendicular end face tooth surface.

[0045] The normal pressure and tangential pressure per unit area under different contact states are expressed as: (32) (33) in and Indicates the normal pressure and tangential pressure per unit area of ​​the contact surface in the initial state, and represents the node normal displacement of the left and right end tooth contact surfaces, and Represents the tangential displacement of the nodes of the left and right face tooth contact surfaces.

[0046] S5. Use the degree of freedom reduction method to solve the vibration response of the above dynamic equations and obtain the displacement response.

[0047] The dynamic equations of structures containing linear and nonlinear forces can be uniformly expressed in the form of partial differential equations: (34) Under periodic excitation, according to the harmonic balance method, the displacement vector u( t ) can be expressed in finite-order Fourier form: (35) in, represents the static displacement component, Nh represents the total harmonic order, and Indicates the i Coefficient vector of the cosine and sine harmonics of order .

[0048] Substituting Equation (35) into Equation (34), calculating the multi-order harmonic vector expressions of nonlinear force and linear force, and rearranging the left and right sides of the equation, Equation (35) can be rearranged into the following form: (36) Where R(U) represents the residual matrix, represents the multiharmonic vector of the nonlinear force, The Fourier coefficient vector representing the system response, represents the multi-harmonic vector of linear force, U represents the harmonic coefficient vector of node displacement, , It consists of the linear dynamic stiffness matrix, which is composed of mass, damping and stiffness matrices.

[0049] The Newton-Raphson iteration method is used to find the steady-state solution. The iteration process is: (37) in k Indicates the current iteration step.

[0050] Using a three-dimensional model for modeling will increase the system's degrees of freedom, making it difficult to directly solve the dynamic equations. Therefore, degree of freedom reduction is necessary. The fixed interface modal synthesis method is used to retain some degrees of freedom of the wheel contact surface and bearing. Ignoring the damping term, time-varying term, and load term on the right side in Equation (34), we can obtain:

[0051] (38) Main mode matrix The reduced modal matrix is ​​composed of the first k-order modal vectors retained after constraining the displacement of the bearing nodes and the displacement of the contact surface nodes that produce poor contact. .

[0052] According to the fixed interface modal synthesis method, the reduction equation of the system's degree of freedom can be expressed as: (39) in is the transformation matrix, is the coordinate vector of the system, are the modal coordinates, is the retained node displacement vector.

[0053] According to the fixed interface mode synthesis method, the reduced mode matrix can be expressed as: (40) (41) in represents the stiffness matrix divided into subordinate displacement vectors in the matrix K, Represents the stiffness matrix composed of the bearing node displacement in matrix K and the contact surface node displacement vector that produces poor contact, Represents the coupling stiffness matrix between the slave displacement vector and the bearing node displacement vector and the contact surface node displacement vector with poor contact, Represents the coupling stiffness matrix between the bearing node displacement vector, the contact surface node displacement vector with poor contact, and the slave displacement vector.

[0054] After mode reduction, Equation (36) can be rewritten as: (42) Where: .

[0055] Figure 5 A multi-disk center rod rotor experimental system with a Hirth tooth structure is provided to verify a rod rotor disc vibration analysis method based on a rough surface contact model. The system includes: The pull-rod rotor main system 1, the excitation system 2, the data acquisition and analysis system 3, the strain measurement system 4 and the support system 5; the pull-rod rotor main system 1 includes the main wheel 11, the No. 1 test plate 12, the No. 2 test plate 13, the central pull rod 14 and the nut 15; the excitation system 2 includes the striking hammer 21; the data acquisition and analysis system 3 includes the acceleration sensor 31, the dynamic data acquisition instrument 32 and the data analysis computer 33; the strain measurement system 4 includes the strain gauge 41 and the strain gauge 42; the support system 5 includes the suspension rope 51.

[0056] The main rod rotor system consists of an axially extending center rod 14, which secures the second test disc 13, the main wheel disc 11, the first test disc 12, and a nut 15. To facilitate description of the contact state of the test rod rotor, the contact surface between the nut 15 and the first test disc 12 is designated NF, the contact surface between the first test disc 12 and the nut 15 is designated SF, and the end surface of the first test disc 12 is designated H1F. In the figure, the end surface of the main wheel disc 11 on the left is designated H2F, and on the right is designated H3F. The end surface of the second test disc 13 is designated H4F. There are three pairs of contact surfaces in the test pull rod rotor, namely the contact between the nut 15 and the No. 1 test disc 12 (C#1: NF-SF), the end face tooth contact between the No. 1 test disc 12 and the main wheel disc 11 (C#2: H1F-H2F), and the end face tooth contact between the No. 2 test disc 13 and the main wheel disc 11 (C#3: H4F-H3F).

[0057] The striking hammer 21 is connected to the dynamic data acquisition instrument 32 via a wire to record the striking force signal during the experiment and process and analyze the striking force signal in the subsequent process. The acceleration sensor 31 is installed on the No. 1 test plate 12 and connected to the dynamic data acquisition instrument 32 via a wire. The dynamic data acquisition instrument 32 is connected to the data analysis computer 33 to complete the data acquisition, transmission, processing and analysis tasks during the experiment. The strain gauge 42 is attached to the shaft of the No. 1 test plate 12 and connected to the strain gauge 41 via a wire. The strain is read during the experiment to estimate the preload of the tie rod. The suspension rope 51 is installed to the outer ends of the No. 1 test plate 12 and the No. 2 test plate 13 to support the tie rod rotor main body system.

[0058] During the experiment, a torque wrench was used to apply a clamping force to the rotor assembly. This force generates tension in the tie rod and compression on the shaft. Basic mechanics dictates that tension and compression are equal. Therefore, the tie rod preload can be estimated by attaching strain gauges to the test disc shaft and reading the strain. During the application of the preload, the corresponding strain values ​​were sequentially read and recorded using the strain gauges. To ensure reliable measurement results, the experiment was repeated, with the strain gauges reattached at the same locations after each experiment and the process repeated. To determine the surface roughness parameters of the experimental rotor, a surface profiler was used to measure the surface profile of the contact surface between the experimental tie rod and the rotor. Three random areas on each tooth surface were measured three times. The surface roughness parameters were calculated based on the profile curves, and the average of these multiple measurements was taken. The rotor assembly was then struck with a force hammer. The response signals collected by the accelerometers were input into a data acquisition and analysis system for recording and processing. In post-processing, the response curves were used to identify the rotor's natural frequency, enabling measurement of the rotor's natural frequency.

[0059] The experimental verification method provided by the present invention is to study the influence of the preload force of the pull rod and the roughness of the contact surface on the free vibration natural frequency of the rotor assembly, and compare the experimental measurement results with the calculation results of the numerical model to verify the accuracy of the proposed method.

[0060] Example: Utilizing the pull-rod rotor wheel vibration analysis method and the multi-disk center pull-rod rotor experimental system with a Hirth tooth structure provided by the present invention, numerical calculations are performed on the multi-disk center pull-rod rotor model with a Hirth tooth structure in the experimental system, and experimental measurements are performed. The experimental measurement results are compared with the numerical model calculation results to verify the accuracy of the method proposed by the present invention.

[0061] The strain gauge used in the experiment is the SDY2102 dynamic and static strain gauge with a resolution of 1 μe , the measurement range is 0~±19999 μe The model of the impact hammer is LC-04A; the broadband resolution of the accelerometer is 0.005m / s 2 rms The acceleration amplitude measurement uncertainty is ±5% within the frequency range of 1 to 4000 Hz. The model is 356A24. Data collected by the accelerometer is input into a data acquisition system for recording and processing at a sampling rate of 10 kHz. The rotor's natural frequency is identified in post-processing using the response curve.

[0062] The axial preload is applied by a torque wrench, and the torque is read directly from the torque wrench. The torque value increases from 10Nm to 10Nm, 20Nm, 30Nm, 40Nm and 50Nm respectively. When the preload is loaded, the corresponding strain values ​​are read in sequence by the strain gauge and recorded. To ensure the reliability of the measurement results, the experiment was repeated 5 times. After each experiment, the strain gauge was re-pasted at the same position and the experimental process was repeated. After removing the abnormal data from the 5 sets of experimental data, the remaining 3 experimental measurement results showed a trend of near consistency in the axial strain of the shaft, and no extreme values ​​appeared. Therefore, the average value of these 3 data was used as the final result. The relationship between torque and preload was calculated by measuring the axial strain and the 3D finite element results, and the results shown in Table 1 were obtained.

[0063] Table 1 Torque and preload The surface profile curve of the experimental rod rotor contact surface was obtained by surface profilometer test, as shown in the attached figure. Figure 6 Among them, three areas of each tooth surface were randomly selected for measurement three times, and the surface roughness parameters were calculated based on the profile curve. Then the average value of the multiple measurement results was taken. The calculation results are shown in Table 2.

[0064] Table 2 Surface roughness parameters of the experimental rotor The material parameters of each component of the experimental pull-rod rotor are shown in Table 3.

[0065] Table 3 Material parameters of various components of the experimental rod rotor Figure 7 The figure shows a comparison of the rotor frequency measured by the impact test and the results calculated by the numerical model. As can be seen from the figure, each order of frequency increases with increasing preload. The experimental test results are close to those calculated by the numerical model, with the absolute value of the relative error less than 5%, verifying the effectiveness of the proposed method.

[0066] The present invention addresses the vibration analysis problem of the rotor system of a gas turbine multi-disc tie-rod structure and provides a tie-rod rotor disc vibration analysis method based on a rough surface contact model. Taking into account the complex contact state between multiple contact surfaces, a gas turbine disc vibration analysis model with a full three-dimensional multi-scale contact interface is established based on elastic-plastic contact theory and a high-fidelity finite element method. This method does not require simplification of the tie-rod rotor and can retain the geometric features, contact surface features, and load effects of the original model to a great extent.

[0067] The present invention designs a multi-disc center-tie rod rotor experimental system with a Hirth tooth structure, and conducts experimental research on the natural frequency of the system. The experimental results are compared with the results calculated by the method in this paper to demonstrate the high precision and accuracy of the model and method proposed in the present invention, and further verify the applicability of the method proposed in the present invention to practical engineering problems.

[0068] The multi-disc center-tie rod rotor experimental system with a Hirth tooth structure designed in this invention experimentally verifies the proposed vibration analysis method, realizes the organic combination of method modeling, simulation calculation and experimental verification, and constructs a complete technical closed loop, which has certain academic value and engineering application value.

[0069] Based on the above inventive concept, the present invention further proposes a gas turbine pull rod rotor disc vibration analysis system, comprising: A building block for constructing the three-dimensional finite element dynamic equations for a gas turbine rotor disc including the stress stiffening matrix and the contact stiffness matrix.

[0070] The contact stiffness matrix calculation module is used to regard the rough surface of the rotor disc as a surface formed by a series of micro-asperities of different heights on a smooth surface; according to the elastic-plastic contact model, the deformation stage of a single micro-asperity is divided into the elastic stage, the elastic-plastic stage and the plastic stage, and the normal contact load of each stage is calculated; the normal contact loads of all micro-asperities involved in the contact are integrated to obtain the functional relationship between the contact variable and the contact surface distance; and the current contact stiffness matrix is ​​determined based on the functional relationship between the contact variable and the contact surface distance.

[0071] The update module is used to perform static analysis based on the current contact stiffness matrix to obtain the displacement field and the corresponding stress field, and update the contact stiffness matrix and stress stiffening matrix through the displacement field and the corresponding stress field; after multiple iterative updates, until the residual of the contact stiffness matrix between two adjacent iterations is less than the set tolerance, the final contact stiffness matrix and stress stiffening matrix are output.

[0072] The analysis module is used to analyze and solve the three-dimensional finite element dynamic equations by introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equations to obtain the vibration response of the gas turbine pull rod rotor wheel.

[0073] The present invention also includes a gas turbine pull rod rotor disc vibration analysis computer device, including: a memory, a processor and a computer program stored in the memory. When the processor executes the computer program, the steps of the gas turbine pull rod rotor disc vibration analysis method are implemented.

[0074] The present invention also includes a readable storage medium storing a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, the program instructions are used to execute the steps of the gas turbine pull rod rotor disk vibration analysis method.

[0075] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for analyzing vibration of a gas turbine pull rod rotor disc, characterized in that: The following steps are involved: Construct the three-dimensional finite element dynamic equations of the gas turbine pull rod rotor disc including the stress stiffening matrix and contact stiffness matrix; The rough surface of the rotor disc is considered as a surface formed by a series of asperities of different heights on a smooth surface. Based on the elastic-plastic contact model, the deformation stage of a single asperity is divided into the elastic stage, the elastic-plastic stage, and the plastic stage, and the normal contact load in each stage is calculated. The normal contact load of all the asperities involved in the contact is integrated to obtain the functional relationship between the contact variable and the distance between the contact surfaces. Determine the current contact stiffness matrix based on the functional relationship between the contact variable and the contact surface distance; Perform static analysis based on the current contact stiffness matrix to obtain the displacement field and the corresponding stress field, and update the contact stiffness matrix and stress stiffening matrix based on the displacement field and the corresponding stress field; After multiple iterations, the contact stiffness matrix residuals between two adjacent iterations are less than the set tolerance, and the final contact stiffness matrix and stress stiffening matrix are output; After introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation, the three-dimensional finite element dynamic equation is analyzed and solved to obtain the vibration response of the gas turbine pull rod rotor disk.

2. A gas turbine pull rod rotor disc vibration analysis method according to claim 1, characterized in that: The three-dimensional finite element dynamic equation for constructing the gas turbine pull rod rotor disc containing the stress stiffening matrix and the contact stiffness matrix is ​​expressed as: ； in represents the mass matrix; is the rotational speed; is the Coriolis force matrix; represents the bearing damping matrix; represents the structural stiffness matrix; represents the rotation softening matrix; Represents the linear load force vector calculated from the preload force; represents the centrifugal load vector; represents the stiffness matrix of the bearing, is the displacement vector, is the velocity vector, is the acceleration vector.

3. A gas turbine pull rod rotor disc vibration analysis method according to claim 1, characterized in that: According to the elastic-plastic contact model, the deformation stage of a single asperity is divided into an elastic stage, an elastic-plastic stage, and a plastic stage, and the normal contact load of each stage is obtained; wherein: The normal contact load in the elastic stage is expressed as: ； The normal contact load in the elastic-plastic stage is expressed as: ； ； The normal contact load in the fully plastic stage is expressed as: ； in represents the critical deformation of the asperity, ; represents the contact deformation of a single asperity; represents the equivalent elastic modulus of the contact interface; represents the approximate curvature radius of the asperity tip; Indicates contact microhardness; Represents the hardness coefficient, which is related to the Poisson's ratio of the material; By integrating the normal contact loads of all asperities involved in contact, we can obtain the functional relationship between the contact variable and the distance between the contact surfaces. The functional relationship is: ； in, ; ； ； ； in represents the dimensionless Gaussian distribution, ; 、 and Parameters that represent surface roughness include the number of asperities per unit area, the average radius of the asperities, and the standard deviation of the asperity heights.

4. A gas turbine pull rod rotor disc vibration analysis method according to claim 1, characterized in that: The static analysis is performed based on the current contact stiffness matrix to obtain a displacement field and a corresponding stress field, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; After multiple iterations, the contact stiffness matrix residuals between two adjacent iterations are less than the set tolerance, and the final contact stiffness matrix and stress stiffening matrix are output. Specifically, the following steps are included: Let the initial stress stiffening matrix be zero and obtain the current contact stress. The calculation process is: ； ； in and Indicates the contact force of the end tooth contact surface; Indicates preload; Indicates the tangential force converted from torque; represents the coefficient of sliding friction; φ represents the pressure angle of the face teeth, ; According to the current contact stress, the current contact stiffness matrix is ​​calculated by the finite element formula of the contact stiffness matrix; Substitute the current contact stiffness matrix and stress toughening matrix into the dynamic equation and solve it without considering the time term to obtain the displacement vector; The contact pressure is calculated based on the displacement vector, and the contact stiffness matrix and stress stiffening matrix are updated through the displacement field and the corresponding stress field; the stress stiffening matrix is ​​calculated by the finite element calculation formula; the finite element calculation formula of the stress stiffening matrix is ,in Related to Cauchy stress; Represents the geometric matrix, which describes the influence of the geometric state on the strain when the unit is deformed; After multiple iterative updates, the residual of the contact stiffness matrix between adjacent time steps is determined: ; If the residual is less than the tolerance tol , then the final calculated contact stiffness matrix and stress stiffening matrix are output; the tolerance tol Defined as: 。 5. A gas turbine pull rod rotor disc vibration analysis method according to claim 4, characterized in that: The contact stiffness matrix finite element formula is expressed as: ;in represents the shape function of the contact element, Represents the contact matrix of adjacent contact elements; the contact matrix of adjacent contact elements Expressed as: ； in, and They represent the element normal contact stiffness and tangential contact stiffness respectively; In the natural coordinate system, the shape function of the contact element is expressed as: ， in, ； in and Represents the natural coordinates of the contact element.

6. A gas turbine pull rod rotor disc vibration analysis method according to claim 5, characterized in that: It also includes constructing an end face tooth contact model considering collision separation by considering the normal pressure and tangential pressure per unit area of ​​the contact surface of the center tie rod end face tooth structure and the node normal displacement and tangential displacement of the end tooth surface contact surface before introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation; and obtaining the contact pressure of the end face teeth under different contact states according to the end face tooth contact model.

7. A gas turbine pull rod rotor disc vibration analysis method according to claim 1, characterized in that: After introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamics equations, the vibration response of the gas turbine pull rod rotor disk is analyzed using the degree of freedom reduction method. The specific steps include: Under the action of periodic excitation, according to the harmonic balance method, the displacement vector in the dynamic equation is expressed as a finite-order Fourier form; Substitute the finite-order Fourier form of the displacement vector into the dynamic equation to calculate the multi-order harmonic vector expression of the nonlinear force and linear force; A Newton-Raphson iteration method is used to obtain a steady-state solution for the multi-order harmonic vector expression of nonlinear force and linear force; a sampling degree of freedom reduction method is used to ignore the damping term, time-varying term and load term on the right side in the dynamic equation; a fixed interface modal synthesis method is used to obtain a reduced equation for the system's degrees of freedom based on a main modal matrix, a reduced modal matrix, modal coordinates and retained node displacement vectors; wherein the reduced modal matrix is ​​obtained based on a stiffness matrix divided into slave displacement vectors and a stiffness matrix of bearing node displacements and contact surface node displacement vectors that produce poor contact; the main modal matrix is ​​composed of the retained first k-order modal vectors after constraining the bearing node displacements and the contact surface node displacements that produce poor contact; The vibration response of the pull-rod rotor disc is analyzed based on the equation after modal reduction.

8. A gas turbine pull rod rotor disc vibration analysis system, characterized in that: include: A construction module for constructing the three-dimensional finite element dynamic equations of the gas turbine pull rod rotor disc including the stress stiffening matrix and the contact stiffness matrix; The contact stiffness matrix calculation module treats the rough surface of the rotor disc as a surface formed by a series of asperities of varying heights on a smooth surface. Based on the elastic-plastic contact model, the deformation phase of a single asperity is divided into the elastic phase, the elastic-plastic phase, and the plastic phase, and the normal contact load is calculated for each phase. The normal contact load of all contacting asperities is integrated to obtain the functional relationship between the contact variable and the distance between the contact surfaces. Determine the current contact stiffness matrix based on the functional relationship between the contact variable and the contact surface distance; An update module is used to perform static analysis based on the current contact stiffness matrix to obtain the displacement field and the corresponding stress field, and to update the contact stiffness matrix and the stress stiffening matrix through the displacement field and the corresponding stress field; After multiple iterations, the contact stiffness matrix residuals between two adjacent iterations are less than the set tolerance, and the final contact stiffness matrix and stress stiffening matrix are output; The analysis module is used to analyze and solve the three-dimensional finite element dynamic equations by introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equations to obtain the vibration response of the gas turbine pull rod rotor wheel.

9. A computer device for analyzing vibration of a gas turbine pull rod rotor disc, characterized in that: include: A memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, the steps of the gas turbine pull rod rotor disk vibration analysis method according to any one of claims 1 to 7 are implemented.

10. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the gas turbine tie rod rotor disk vibration analysis method according to any one of claims 1 to 7.

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