A vibration analysis method, system and device for a gas turbine tie rod rotor wheel disc

Abstract

The application discloses a gas turbine pull rod rotor wheel disc vibration analysis method, system and device, relates to the technical field of gas turbines, and comprises the following steps: constructing a three-dimensional finite element dynamics equation of a rotating component; considering rough contact characteristics of a contact interface, combining a micro contact mechanics model of the contact interface and a rough consolidated interface contact mechanics model based on a statistical theory, and deducing contact stiffness of adjacent contact units; considering stress strengthening effects, iteratively calculating a stress stiffening matrix and a contact stiffness matrix; considering local contact nonlinearity of a center pull rod end surface tooth structure, constructing an end surface tooth contact model considering collision separation; and adopting a degree of freedom reduction method to solve vibration response of the three-dimensional finite element dynamics equation; and the method can greatly retain geometric characteristics, contact surface characteristics and load actions of an original model without simplifying the pull rod rotor by establishing a vibration analysis model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gas turbines, in particular to a gas turbine tie rod rotor wheel disc vibration analysis method, system and device. BACKGROUND

[0002] For the rotor system of the gas turbine multi-disc tie rod structure, due to the existence of a large number of contact surfaces between the discs, the dynamic model becomes very complex. The stiffness characteristics between these contact surfaces will affect the running state of the rotor, and are one of the important factors affecting the dynamic characteristics of the rotor. The stiffness of the contact surface is determined by the size of the pre-tightening force of the tie rod, so determining the contact model and its parameters under different pre-tightening force states is a complex problem faced in dynamic modeling and simulation analysis.

[0003] Current research mainly uses simplified models, which need to simplify the geometric structure of the tie rod rotor to a large extent, so it is difficult to deeply study these problems. In addition, the center tie rod rotor of the heavy-duty gas turbine may cause some special failure forms due to its special structure and operating environment, such as uneven distribution of pre-tightening force, poor contact of the disc contact surface, and even separation. These problems will introduce nonlinearity to the rotor, which may cause the vibration of the rotor to intensify. For the combined center tie rod rotor connected by Hirth teeth, in the ideal state, each pair of Hirth teeth uniformly bears the pre-tightening force to ensure that the contact surface maintains a good contact state, and the contact surface pressure in this state is called "saturation pressure".

[0004] However, the simplified model used in the past for vibration analysis of the multi-disc tie rod rotor of the gas turbine has greatly simplified the geometric structure of the tie rod rotor, but in actual process, the contact surface of the disc hirth tooth may be in poor contact or separation due to certain conditions, at this time, nonlinearity will be introduced to the rotor, which may cause the vibration of the rotor to intensify, and the simplified model cannot deeply analyze such problems. SUMMARY

[0005] In view of the problem in the prior art that the geometric structure of the tie rod rotor is greatly simplified and the poor contact or separation of the contact surface of the disc hirth tooth due to certain conditions cannot be deeply analyzed, the present application provides a gas turbine tie rod rotor wheel disc vibration analysis method, system and device, which establishes a vibration analysis model of the gas turbine tie rod rotor wheel disc with a full three-dimensional multi-scale contact interface, without simplifying the tie rod rotor, and can greatly retain the geometric characteristics, contact surface characteristics and load action of the original model, thereby solving the problem existing in the prior art.

[0006] A gas turbine tie rod rotor wheel disc vibration analysis method, comprising the following steps:

[0007] The three-dimensional finite element dynamic equation of the gas turbine tie rod rotor wheel disc containing a stress stiffening matrix and a contact stiffness matrix is constructed.

[0008] The rough surface of the rotor wheel disc is regarded as a surface formed by a series of micro-convex bodies with different heights on a smooth surface; according to an elastic-plastic contact model, the deformation stage of a single micro-convex body is divided into an elastic stage, an elastic-plastic stage and a plastic stage, and the normal contact load of each stage is calculated; the normal contact loads of all the micro-convex bodies participating in the contact are integrated to obtain a function relationship between a contact variable and a contact surface distance; the current contact stiffness matrix is determined according to the function relationship between the contact variable and the contact surface distance;

[0009] The displacement field and the corresponding stress field are obtained through static analysis according to the current contact stiffness matrix, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; after multiple iteration updates, until the residual error of the contact stiffness matrix of the adjacent two iterations is less than the set tolerance, the final contact stiffness matrix and the stress stiffening matrix are output;

[0010] The vibration response of the gas turbine tie rod rotor wheel disc is obtained by introducing the final contact stiffness matrix and the stress stiffening matrix into the three-dimensional finite element dynamic equation and then analyzing and solving the three-dimensional finite element dynamic equation.

[0011] Further, the three-dimensional finite element dynamic equation of the gas turbine tie rod rotor wheel disc containing a stress stiffening matrix and a contact stiffness matrix is constructed, and is expressed as:

[0012] ;

[0013] Wherein represents a mass matrix; is a rotating speed; is a Coriolis force matrix; represents a bearing damping matrix; represents a structural stiffness matrix; represents a rotating softening matrix; represents a linear load force vector calculated from a pre-tightening force; represents a centrifugal load vector; represents a stiffness matrix of a bearing, is a displacement vector, is a velocity vector, is an acceleration vector.

[0014] Further, according to an elastic-plastic contact model, the deformation stage of a single micro-convex body 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:

[0015] The normal contact load of the elastic stage is expressed as:

[0016] ;

[0017] The normal contact load of the elastic-plastic stage is represented as:

[0018] ;

[0019] ;

[0020] The normal contact load of the fully plastic stage is represented as:

[0021] ;

[0022] wherein represents the critical deformation of the micro asperity, ; represents the contact deformation of a single micro asperity; represents the equivalent elastic modulus of the contact interface; represents the approximate radius of curvature of the micro asperity tip; represents the contact microhardness; represents the hardness coefficient, which is related to the Poisson's ratio of the material;

[0023] The normal contact load of all the micro asperities involved in the contact is integrated to obtain the function relationship between the contact variable and the distance from the contact surface, which is:

[0024] ;

[0025] wherein, ;

[0026] ;

[0027] ;

[0028] ;

[0029] wherein represents the dimensionless Gaussian distribution, ; , and represent the parameters of the surface roughness, specifically the number of micro asperities per unit area, the average radius of the micro asperities, and the standard deviation of the micro asperity height, respectively.

[0030] Further, the displacement field and the corresponding stress field are obtained according to the current contact stiffness matrix for static analysis, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; after multiple iteration updates, until the residual error of the contact stiffness matrix between adjacent two iterations is less than a set tolerance, the final contact stiffness matrix and the stress stiffening matrix are output, and the method specifically comprises the following steps:

[0031] Let the initial stress stiffening matrix be zero, and the current contact stress is obtained, and the calculation process is as follows:

[0032] ;

[0033] ;

[0034] Wherein and represent the contact force of the end face tooth contact surface; represents the pre-tightening force; represents the tangential force converted from the torque; represents the sliding friction coefficient; φ represents the pressure angle of the end face tooth, ;

[0035] According to the current contact stress, the current contact stiffness matrix is calculated through the finite element formula of the contact stiffness matrix;

[0036] The current contact stiffness matrix and the stress stiffening matrix are substituted into the dynamic equation, and the displacement vector is obtained by solving without considering the time term;

[0037] The contact pressure is calculated according to the displacement vector, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; the stress stiffening matrix is calculated through the finite element calculation formula; the finite element calculation formula of the stress stiffening matrix is , wherein is related to the Cauchy stress; represents a geometric matrix, which describes the influence of the geometric state on the strain when the unit deforms;

[0038] After multiple iteration updates, the residual error of the contact stiffness matrix between adjacent time steps is judged: ; if the residual error is less than the tolerance tol , the final calculated contact stiffness matrix and stress stiffening matrix are output; the tolerance tol is defined as:

[0039] .

[0040] Further, the finite element formula of the contact stiffness matrix is represented as: ; wherein shape functions of the contact element, contact matrix of adjacent contact elements; the contact matrix of adjacent contact elements is expressed as:

[0041] ;

[0042] wherein, and respectively represent normal contact stiffness and tangential contact stiffness of the element;

[0043] In the natural coordinate system, the shape function of the contact element is expressed as:

[0044] ,

[0045] wherein,

[0046] ;

[0047] wherein and represent natural coordinates of the contact element.

[0048] Further, the method further comprises, before introducing the final contact stiffness matrix and the stress stiffening matrix into the three-dimensional finite element dynamics equation, constructing a face gear contact model considering collision separation by considering the normal pressure and the tangential pressure of the unit area of the contact surface of the center pull rod face gear structure and the normal displacement and the tangential displacement of the nodes of the end gear surface contact surface; and obtaining the contact pressure of the face gear under different contact states according to the face gear contact model.

[0049] Further, after introducing the final contact stiffness matrix and the stress stiffening matrix into the three-dimensional finite element dynamics equation, the vibration response of the gas turbine pull rod rotor disc is analyzed by using the degree of freedom reduction method, and the method comprises the following steps:

[0050] Under the action of periodic excitation, the displacement vector in the dynamics equation is expressed in the form of finite order Fourier according to the harmonic balance method;

[0051] The finite order Fourier form of the displacement vector is substituted into the dynamics equation to calculate the multi-order harmonic vector expression form of the nonlinear force and the linear force;

[0052] The Newton-Raphson iteration method is used to solve the steady-state solution of the multi-order harmonic vector expression form of the nonlinear force and the linear force; the sampling degree of freedom reduction method is used to ignore the damping term, the time-varying term and the load term on the right end in the dynamic equation; the fixed interface modal synthesis method is used to obtain the reduced equation of the system degree of freedom according to the main modal matrix, the reduced modal matrix, the modal coordinate and the reserved node displacement vector; the reduced modal matrix is obtained according to the stiffness matrix of the divided dependent displacement vector and the stiffness matrix of the bearing node displacement and the contact surface node displacement vector causing the contact failure; the main modal matrix is composed of the reserved first k order modal vectors after the constraint bearing node displacement and the contact surface node displacement causing the contact failure;

[0053] According to the equation after modal reduction, the vibration response of the tie rod rotor wheel disc is analyzed.

[0054] The application also includes a gas turbine tie rod rotor wheel disc vibration analysis system, comprising:

[0055] The construction module is used to construct the three-dimensional finite element dynamic equation of the gas turbine tie rod rotor wheel disc containing the stress stiffening matrix and the contact stiffness matrix;

[0056] The contact stiffness matrix calculation module is used to regard the rough surface of the rotor wheel disc as a series of different height micro convex bodies formed on the smooth surface; according to the elastic-plastic contact model, the deformation stage of a single micro convex body 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 the micro convex bodies participating in the contact is integrated to obtain the functional relationship between the contact variable and the contact surface distance; the current contact stiffness matrix is determined according to the functional relationship between the contact variable and the contact surface distance;

[0057] The update module is used to obtain the displacement field and the corresponding stress field through the static force analysis according to the current contact stiffness matrix, and update the contact stiffness matrix and the stress stiffening matrix through the displacement field and the corresponding stress field; after multiple iteration updates, until the contact stiffness matrix residual error of adjacent two iterations is less than the set tolerance, the final contact stiffness matrix and the stress stiffening matrix are output;

[0058] The analysis module is used to analyze and solve the three-dimensional finite element dynamic equation after introducing the final contact stiffness matrix and the stress stiffening matrix into the three-dimensional finite element dynamic equation, and obtain the vibration response of the gas turbine tie rod rotor wheel disc.

[0059] The application also includes a gas turbine tie rod rotor wheel disc vibration analysis computer equipment, comprising a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to realize the steps of the gas turbine tie rod rotor wheel disc vibration analysis method.

[0060] The application further comprises a readable storage medium storing a computer program, the computer program comprising program instructions for executing the steps of the vibration analysis method of the gas turbine tie rod rotor wheel disc.

[0061] The application provides a vibration analysis method of a gas turbine tie rod rotor wheel disc, which has the following beneficial effects:

[0062] The application constructs a vibration analysis model of a full three-dimensional multi-scale contact interface, does not need to simplify the tie rod rotor, greatly retains the geometric characteristics, contact surface characteristics and load action of the original model, significantly improves the accuracy of analysis, deduces the contact stiffness of adjacent contact units through a micro contact mechanics model, can accurately simulate the elastic-plastic deformation (elastic, elastic-plastic and plastic stages) of a rough surface, and thus more truly reflects the actual contact state, iteratively updates the contact stiffness matrix and stress stiffening matrix until the residual error is less than a set tolerance, ensures the convergence and reliability of the calculation results, and effectively solves the nonlinear problem caused by the pre-tightening force, the method considers the complex contact state between multiple contact surfaces, establishes a vibration analysis model of a full three-dimensional multi-scale contact interface of a gas turbine wheel disc based on the elastic-plastic contact theory and a high-fidelity finite element method, does not need to simplify the tie rod rotor, and can greatly retain the geometric characteristics, contact surface characteristics and load action of the original model. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 FIG. 1 is a schematic diagram of a rough surface contact model of an end face tooth contact in an embodiment of the application;

[0064] Figure 2 FIG. 4 is a schematic diagram of the relationship between the normal contact stiffness and the contact pressure of different contact surfaces in an embodiment of the application;

[0065] Figure 3 FIG. 6 is a schematic diagram of the iteration process of calculating the contact stiffness matrix in an embodiment of the application;

[0066] Figure 4 FIG. 8 is a schematic diagram of a center tie rod end face tooth structure considering local contact nonlinearity in an embodiment of the application;

[0067] Figure 5 FIG. 11 is a schematic diagram of a multi-disc center tie rod rotor experimental system of a Hirth tooth structure in an embodiment of the application;

[0068] Figure 6 FIG. 14 is a schematic diagram of the surface profile curve of the contact surface of the experimental tie rod rotor in an embodiment of the application;

[0069] Figure 7 FIG. 17 is a schematic diagram of the comparison of the first three order free vibration frequencies under different pre-tightening forces in an embodiment of the application.Figure 7 (a) in FIG. 1 is a schematic diagram of the comparison between the experimental value and the calculated value, Figure 7 (b) in FIG. 1 is a schematic diagram of the relative error between the experimental value and the calculated value;

[0070] Figure 8 FIG. 1 is a flow chart of a vibration analysis method of a wheel disc of a gas turbine tie rod rotor according to an embodiment of the present application.

[0071] Explanation of reference signs:

[0072] 11-main wheel disc, 12-first test disc, 13-second test disc, 14-central tie rod, 15-nut, 21-knock hammer, 31-acceleration sensor, 32-dynamic data acquisition instrument, 33-data analysis computer, 41-strain gauge, 42-strain gauge, 51-hanging rope; C#1-contact between the nut 15 and the first test disc 12, C#2-end surface tooth contact between the first test disc 12 and the main wheel disc 11, C#3-end surface tooth contact between the second test disc 13 and the main wheel disc 11. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments.

[0074] The present application provides a vibration analysis method of a wheel disc of a gas turbine tie rod rotor. For the vibration response analysis problem of a multi-stage wheel disc of a gas turbine, the complex contact state between the contact surfaces of the gas turbine tie rod rotor is considered. Based on the elastic-plastic contact theory and the high-fidelity finite element method, a vibration analysis model of the wheel disc of the gas turbine tie rod rotor with a full three-dimensional multi-scale contact interface is established. The original model can be greatly retained in terms of geometric characteristics, contact surface characteristics and load action without simplifying the tie rod rotor. The correctness of the method is proved by experimental research, as shown in FIG. 1. Figure 8 The method specifically includes the following steps:

[0075] S1, a three-dimensional finite element dynamics equation of a rotating component (a wheel disc of a gas turbine tie rod rotor) is constructed. For a rotating coordinate system with a rotating shaft as the Z axis and a rotating speed of Ω, the coordinate conversion relationship of a point P in the rotating coordinate system and the fixed coordinate system can be written as:

[0076] (1)

[0077] wherein 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, and its expression is as follows:

[0078] (2).

[0079] The dynamic equation of the rotor-bearing system in the rotating coordinate system is:

[0080] (3)

[0081] wherein denotes a mass matrix; denotes a Coriolis force matrix; denotes a bearing damping matrix; denotes a structural stiffness matrix; denotes a rotational softening matrix; denotes a linear load force vector calculated from the pre-tightening force; denotes a centrifugal load vector; denotes a stiffness matrix of the bearing, and its expression is as follows:

[0082] (4)

[0083] (5)

[0084] In the formula:

[0085] and

[0086] In the central tie-rod rotor-bearing system, each stage of the wheel disc is positioned and transmits torque through the end face teeth, forming multiple contact surfaces. In order to simulate the connection relationship in the three-dimensional finite element, the zero-thickness surface element is used to calculate the contact stiffness between two contact surfaces. The Goodman zero-thickness element is used in the present application, and the two adjacent nodes of the Goodman zero-thickness element are one-to-one corresponding, e t1 , e t2 and e n respectively represent the tangential and normal directions of the contact surface, and the potential energy of the element is:

[0087] (6)

[0088] wherein denotes an element contact stiffness coefficient matrix per unit area, denotes an element displacement per unit area, and S e denotes a contact element area. The finite element formula of the contact stiffness matrix can be derived from the potential energy of the contact element:

[0089] (7)

[0090] wherein denotes a shape function of the contact element, The contact matrix representing the adjacent contact elements, the contact matrix expression is as follows, wherein and respectively represent the unit normal contact stiffness and the tangential contact stiffness.

[0091] (8)

[0092] In the natural coordinate system, the shape function of the contact element can be expressed as:

[0093] (9)

[0094] (10)

[0095] wherein and represent the natural coordinates of the contact element.

[0096] S2, considering the rough contact characteristics of the contact interface, combining the micro contact mechanics model of the contact interface and the rough consolidated interface contact mechanics model based on statistical theory, the contact stiffness of the adjacent contact elements is derived.

[0097] At the micro scale, the rough surface can be regarded as a surface formed by a series of micro convex bodies of different heights on the smooth surface, and the height distribution of the micro convex body can be considered to satisfy the Gaussian distribution. See Figure 1 In order to consider the rough surface contact model of uniform, random and isotropic end face tooth contact. The top of the micro convex body is approximated as a sphere with a radius of curvature R n , and the height z s represents the distance between the vertex of the micro convex body and the mean line of the micro convex body height. Under the action of the normal load on the rough surface, the contact deformation of a single micro convex body is:

[0098] (11)

[0099] wherein represents the distance between the mean line of the rough surface height and the rigid plane, represents the distance between the mean line of the rough surface height and the mean line of the micro convex body height.

[0100] According to the elastic-plastic contact model, the deformation of a single micro convex body is considered, and the deformation stage is divided into elastic stage, elastic-plastic stage and plastic stage, and the normal contact load of each stage can be obtained.

[0101] The normal contact load of the elastic stage is:

[0102] (12)

[0103] The normal contact load in the elastic-plastic stage is:

[0104] (13)

[0105] (14)

[0106] The normal contact load in the fully plastic stage is:

[0107] (15)

[0108] wherein represents the critical deformation of the micro asperity, ; represents the equivalent elastic modulus of the contact interface / Pa; represents the contact microhardness / Pa; represents the hardness coefficient, which is related to the Poisson's ratio of the material . .

[0109] The integral of the normal contact load of all micro asperities participating in the contact can obtain the function relationship between the contact variable and the distance of the contact surface:

[0110] (16)

[0111] (17)

[0112] (18)

[0113] (19)

[0114] (20)

[0115] wherein represents the dimensionless Gaussian distribution, s represents the distance between the vertex of the micro asperity and the average line of the height of the micro asperity, ; , and represent the parameters of the surface roughness, which are specifically the number of micro asperities per unit area, the average radius of the micro asperities, and the standard deviation of the height of the micro asperities, respectively.

[0116] For the surface with the contact surface topography of s ( x ), the calculation method of the parameters of the surface roughness is as follows:

[0117] (21)

[0118] (22)

[0119] (twenty three)

[0120] in , , , , This represents the length of the contact surface; on the element contact surface, it is assumed that the local roughness parameters and the overall roughness parameters of the contact surface follow the same statistical distribution law. The element normal contact stiffness can be expressed as the derivative of the contact pressure with respect to the dimensionless distance:

[0121] (twenty four)

[0122] Tangential contact stiffness is calculated by the following formula:

[0123] (25).

[0124] Figure 2 The figure shows the curves of contact stiffness versus contact pressure under different surface roughness parameters. Figure 2 It is known that under the same contact pressure, the surface normal contact stiffness decreases with increasing surface roughness. Furthermore, the normal contact stiffness increases with increasing contact pressure, and on smoother surfaces, the rate of increase in normal contact stiffness with contact pressure is faster. However, the normal contact stiffness cannot increase indefinitely with increasing contact pressure; there are certain limitations. According to the microscopic contact mechanics model of the contact interface, when... h =0, meaning that when the surface contact pressure causes the interfacial micro-protrusions to undergo complete deformation, the contribution of the micro-protrusions to the normal contact stiffness is zero. At this point, the contact stiffness is already very large. To avoid numerical calculation problems, we assume that the normal contact stiffness does not change with further increases in contact pressure, such as... Figure 2 As shown by the horizontal line in the image.

[0125] S3. Considering the stress hardening effect, iteratively calculate the stress stiffening matrix and the contact stiffness matrix.

[0126] In tie rod rotors, stress hardening is a crucial consideration in preloaded structural analysis, as the natural frequency may become sensitive to local stresses due to this effect. For instance, a structure under axial tension exhibits increased resistance to bending deformation, while resistance to bending decreases under axial compression. Treating the tie rod preload as an external force factor in preloaded structural analysis, this effect is considered in finite element analysis using the auxiliary stiffness matrix of the stress stiffening matrix. Therefore, the stress stiffening matrix resulting from the preload should also be included in the system dynamics equations. K σThe finite element formulation of the unit stress stiffening matrix is

[0127] (26)

[0128] where is related to the Cauchy stress; denotes the geometry matrix, which describes the influence of the geometric state on the strain when the unit deforms.

[0129] The unit contact stiffness matrix and the stress stiffening matrix are extrapolated to the global structure and substituted into the system dynamics equation to obtain

[0130] (27)

[0131] If the contact pressure of the contact surface is obtained in advance, the contact stiffness matrix of the contact surface can be calculated in theory. When the pre-tightening force of the two ends of the face gear connection section is determined, the contact pressure of the Hirth gear can be calculated approximately by the following two formulas:

[0132] (28)

[0133] (29)

[0134] where and denote the contact force of the face gear contact surface; denotes the pre-tightening force; denotes the tangential force converted from the torque; denotes the sliding friction coefficient; φ denotes the pressure angle of the face gear, .

[0135] However, in most examples, the contact pressure of the contact surface is difficult to obtain in advance, so it is necessary to obtain the contact stiffness matrix by iteration. Considering the effect of the pre-tightening force on the center rod rotor, the implicit relationship of the stiffness matrix can be expressed as

[0136] (30)

[0137] where and denote the total stiffness matrix of the current iteration step and the last iteration step, respectively.

[0138] Reference Figure 3 is made to the iteration process of obtaining the contact stiffness matrix. First, the displacement and force boundary conditions are given, and when n= 0, the stress stiffening matrix is set to zero, the contact pressure is calculated by equation (28) and equation (29), and then the initial contact stiffness matrix is calculated by equation (7) to equation (25). Considering static analysis, ignoring the time term of equation (27), solving the finite element equation to obtain the displacement vector, calculating the contact stress, repeating the calculation process of equation (7) to equation (25), updating the contact stiffness matrix, and calculating the stress stiffening matrix by equation (26). Judge the convergence condition, that is, the residual of the contact stiffness matrix calculated in the adjacent two steps (defined as: ) is less than the tolerance. If it is greater than the tolerance tol , repeat the above process, otherwise stop iteration and output the contact stiffness matrix and stress stiffening matrix calculated in the current step. During the iteration process, the tolerance tol is defined as:

[0139] (31)

[0140] S4, considering the local contact nonlinearity of the center pull rod face gear structure, a face gear contact model considering collision separation is constructed.

[0141] Figure 4 The center pull rod face gear structure considering local contact nonlinearity is shown, under the action of gravity and unbalanced force, the adjacent disc contact face gear occurs relative motion, and obvious contact nonlinearity phenomenon occurs, which can be simplified as two components of parallel face gear and vertical face gear.

[0142] The normal pressure and tangential pressure per unit area under different contact states are represented as:

[0143] (32)

[0144] (33)

[0145] Wherein and represent the normal pressure and tangential pressure per unit area of the contact surface in the initial state, and represent the node normal displacement of the left and right face gear contact surfaces, and represent the node tangential displacement of the left and right face gear contact surfaces.

[0146] S5, the degree of freedom reduction method is used to solve the vibration response of the above dynamic equation to obtain the displacement response.

[0147] For the dynamic equation of the structure containing linear force and nonlinear force, it can be uniformly expressed in the form of partial differential equation:

[0148] (34)

[0149] Under periodic excitation, the displacement vector u( t ) in the above equation can be expressed in the form of finite order Fourier series according to the harmonic balance method:

[0150] (35)

[0151] where, represents the static displacement component, Nh represents the total harmonic order, and represents the coefficient vector of the i th cosine harmonic and the sine harmonic.

[0152] Substitute equation (35) into equation (34), calculate the multi-harmonic vector expression form of the nonlinear force and the linear force, and rearrange the form of the left and right sides of the equation, then equation (35) can be rearranged as follows:

[0153] (36)

[0154] where R(U) represents the residual matrix, represents the multi-harmonic vector of the nonlinear force, represents the Fourier coefficient vector of the system response, represents the multi-harmonic vector of the linear force, U represents the harmonic term coefficient vector of the node displacement, , is composed of the mass matrix, the damping matrix and the stiffness matrix.

[0155] The Newton-Raphson iteration method is used to solve the steady-state solution, and the iteration process is as follows:

[0156] (37)

[0157] where k represents the current iteration step.

[0158] Modeling with a three-dimensional model will make the degrees of freedom of the system become huge, and directly solving the dynamic equation will become difficult, so it is necessary to carry out degree reduction. The fixed interface modal synthesis method is used to retain part of the degrees of freedom of the disc contact surface and the bearing. Ignoring the damping term, the time-varying term and the load term on the right side in equation (34), we have:

[0159] (38)

[0160] The main modal matrix is composed of the first k order modal vectors after the constraint bearing node displacement and the contact surface node displacement that causes poor contact, and the reduced modal matrix is .

[0161] According to the fixed interface modal synthesis method, the reduction equation of system degrees of freedom can be expressed as:

[0162] (39)

[0163] wherein is a transformation matrix, is a coordinate vector of the system, is a modal coordinate, is a reserved node displacement vector.

[0164] According to the fixed interface modal synthesis method, the reduction modal matrix can be expressed as:

[0165] (40)

[0166] (41)

[0167] wherein represents a stiffness matrix of the matrix K which is divided into dependent displacement vectors, represents a stiffness matrix of the matrix K which is composed of bearing node displacement vectors and contact surface node displacement vectors causing poor contact, represents a coupling stiffness matrix between dependent displacement vectors and bearing node displacement vectors and contact surface node displacement vectors causing poor contact, represents a coupling stiffness matrix between bearing node displacement vectors and contact surface node displacement vectors causing poor contact and dependent displacement vectors.

[0168] After modal reduction, equation (36) can be rewritten as:

[0169] (42)

[0170] In the formula: .

[0171] Figure 5 An experimental system of a multi-disc center pull rod rotor with Hirth tooth structure is provided for verifying a pull rod rotor disc vibration analysis method based on a rough surface contact model, and the system comprises:

[0172] The pull rod rotor body 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 body system 1 includes a main wheel disc 11, a first test disc 12, a second test disc 13, a central pull rod 14 and a nut 15; the excitation system 2 includes a knocking hammer 21; the data acquisition and analysis system 3 includes an acceleration sensor 31, a dynamic data acquisition instrument 32 and a data analysis computer 33; the strain measurement system 4 includes a strain gauge 41 and a strain gage 42; and the support system 5 includes a hanging rope 51.

[0173] The pull rod rotor body system is fastened by the central pull rod 14 penetrating axially to the second test disc 13, the main wheel disc 11, the first test disc 12 and the nut 15. For the convenience of describing the contact state of the test pull rod rotor, the contact surface between the nut 15 and the first test disc 12 is denoted as NF, the contact surface between the first test disc 12 and the nut 15 is denoted as SF, the end surface tooth surface of the first test disc 12 is denoted as H1F, the end surface tooth surface of the left side of the main wheel disc 11 is denoted as H2F, the end surface tooth surface of the right side of the main wheel disc 11 is denoted as H3F, and the end surface tooth surface of the second test disc 13 is denoted as H4F. The test pull rod rotor has a total of three pairs of contact surfaces, which are the contact between the nut 15 and the first test disc 12 (C#1: NF-SF), the end surface tooth contact between the first test disc 12 and the main wheel disc 11 (C#2: H1F-H2F), and the end surface tooth contact between the second test disc 13 and the main wheel disc 11 (C#3: H4F-H3F).

[0174] The knocking hammer 21 is connected to the dynamic data acquisition instrument 32 through a wire, and records the knocking force signal in the experiment, and processes and analyzes the knocking force signal in the subsequent. The acceleration sensor 31 is installed on the first test disc 12 and connected to the dynamic data acquisition instrument 32 through a wire, and the dynamic data acquisition instrument 32 is connected to the data analysis computer 33, which completes the data acquisition, transmission, processing and analysis tasks in the experiment. The strain gage 42 is pasted on the shaft of the first test disc 12 and connected to the strain gauge 41 through a wire, and the strain is read in the experiment to estimate the pretightening force of the pull rod. The hanging rope 51 is installed to the outer ends of the first test disc 12 and the second test disc 13 to support the pull rod rotor body system.

[0175] In the experiment, the torque wrench is used to apply clamping force to the rotor assembly, which generates tension in the pull rod and generates compression force on the shaft. According to the basic principles of mechanics, the tension and compression force are equal, and then the strain gauge is pasted on the test disc shaft to read the strain and estimate the pre-tightening force of the pull rod. When the pre-tightening force is loaded, the corresponding strain value is read by the strain gauge in turn and recorded. In order to ensure the reliability of the measurement results, the experiment should be repeated, and the strain gauge is pasted on the same position after each experiment. The surface roughness parameters of the experimental rotor are obtained by using the surface profilometer to test the surface profile curve of the contact surface of the experimental pull rod rotor. Among them, 3 regions are randomly selected on each tooth surface, and the surface roughness parameters are calculated according to the profile curve, and then the average value of multiple measurement results is taken. Then, the force hammer is used to knock the rotor assembly, and the response signal collected by the acceleration sensor is input into the data acquisition and analysis system for recording and processing. In the post-processing, the natural frequency of the rotor is identified by the response curve to realize the measurement of the natural frequency of the rotor.

[0176] The experimental verification method provided by the application is to study the influence of the pre-tightening force of the pull rod and the roughness of the contact surface on the natural frequency of the free vibration of the rotor assembly, compare the experimental measurement results with the numerical model calculation results, and verify the accuracy of the method.

[0177] Embodiment:

[0178] The pull rod rotor wheel disc vibration analysis method and the Hirth tooth structure multi-disc center pull rod rotor experimental system provided by the application are used to perform numerical calculation on the Hirth tooth structure multi-disc center pull rod rotor model in the experimental system, and experimental measurement is performed. The experimental measurement results are compared with the numerical model calculation results, and the accuracy of the method is verified.

[0179] The strain gauge used in the experiment is SDY2102 dynamic and static strain gauge, the resolution is 1 μe , and the measurement range is 0~±19999 μe ; the type of the knocking hammer is LC-04A; the broadband resolution of the accelerometer is 0.005 m s 2 rms In the frequency range of 1~4000Hz, the measurement uncertainty of the acceleration amplitude is ±5%, and the type is 356A24; the data collected by the acceleration sensor is input into the data acquisition system for recording and processing, and the sampling rate is 10kHz. In the post-processing, the natural frequency of the rotor is identified by the response curve.

[0180] ​The axial pre-tightening force is applied by a torque wrench, and the torque is directly read from the torque wrench. The torque value is increased from 10Nm, and 10Nm, 20Nm, 30Nm, 40Nm and 50Nm are taken respectively. When the pre-tightening force is loaded, the corresponding strain value is read by the strain gauge in turn and recorded. In order to ensure the reliability of the measurement results, 5 experiments are repeated, and the strain gauge is re-pasted at the same position after each experiment, and the experiment process is repeated. After removing the abnormal data in the 5 groups of experimental data, the measurement results of the remaining 3 experiments show a close consistency in the axial strain of the shaft, and no extreme value appears, therefore, the average value of the 3 data is taken as the final result. The relationship between the torque and the pre-tightening force is calculated by the measured axial strain and the three-dimensional finite element result, and the results shown in Table 1 are obtained.

[0181] Table 1 Torque and pre-tightening force

[0182]

[0183] The surface profile curve of the contact surface of the experimental pull rod rotor is obtained by using a surface profiler, as shown in the accompanying drawings. Figure 6 Among them, 3 regions of each tooth surface are randomly selected for measurement 3 times, the roughness parameters of the surface are calculated according to the profile curve, and then the average value of multiple measurement results is taken, and the calculation results are shown in Table 2.

[0184] Table 2 Surface roughness parameters of the experimental rotor

[0185]

[0186] The material parameters of each component of the experimental pull rod rotor are shown in Table 3.

[0187] Table 3 Material parameters of each component of the experimental pull rod rotor

[0188]

[0189] Figure 7 The comparison between the rotor frequency measured by the knocking experiment and the result calculated by the numerical model is shown in the accompanying drawings. As can be seen from the drawings, the frequency of each order increases with the increase of the pre-tightening force, the experimental test result is close to the numerical model calculation result, and the absolute value of the relative error is less than 5%, which verifies the effectiveness of the method.

[0190] The present application provides a pull rod rotor disc vibration analysis method based on a rough surface contact model for the vibration analysis problem of a rotor system of a gas turbine multi-disc pull rod structure, considers the complex contact state between multiple contact surfaces, establishes a full three-dimensional multi-scale contact interface vibration analysis model of a gas turbine disc based on an elastic-plastic contact theory and a high-fidelity finite element method, does not need to simplify the pull rod rotor, and can greatly retain the geometric characteristics, contact surface characteristics and load action of the original model.

[0191] The application designs a multi-disc center pull rod rotor experimental system with Hirth tooth structure, and carries out experimental research on the natural frequency, compares the experimental results with the calculation results of the method in the application, so as to prove the high precision and accuracy of the model and method in the application, and further verify the applicability of the method in the application to actual engineering problems.

[0192] The multi-disc center pull rod rotor experimental system with Hirth tooth structure designed in the application carries out experimental verification on the vibration analysis method, realizes the organic combination of method modeling, simulation calculation and experimental verification, constructs a complete technical closed loop, and has certain academic value and engineering application value.

[0193] Based on the above inventive concept, the application further provides a gas turbine pull rod rotor wheel disc vibration analysis system, which comprises:

[0194] The construction module is used for constructing a three-dimensional finite element dynamics equation of the gas turbine pull rod rotor wheel disc containing a stress stiffening matrix and a contact stiffness matrix.

[0195] The contact stiffness matrix calculation module is used for regarding the rough surface of the rotor wheel disc as a surface formed by a series of micro-convex bodies with different heights on the smooth surface; according to an elastic-plastic contact model, the deformation stage of a single micro-convex body is divided into an elastic stage, an elastic-plastic stage and a plastic stage, and the normal contact load of each stage is calculated; the normal contact loads of all the micro-convex bodies participating in the contact are integrated to obtain a functional relationship between a contact variable and a contact surface distance; and the current contact stiffness matrix is determined according to the functional relationship between the contact variable and the contact surface distance.

[0196] The update module is used for obtaining a displacement field and a corresponding stress field through static force analysis according to the current contact stiffness matrix, updating the contact stiffness matrix and the stress stiffening matrix through the displacement field and the corresponding stress field, and updating through multiple iterations until the residual error of the contact stiffness matrix of two adjacent iterations is less than a set tolerance, and finally outputting the final contact stiffness matrix and the stress stiffening matrix.

[0197] The analysis module is used for analyzing and solving the three-dimensional finite element dynamics equation after the final contact stiffness matrix and the stress stiffening matrix are introduced into the three-dimensional finite element dynamics equation, and obtaining the vibration response of the gas turbine pull rod rotor wheel disc.

[0198] The application further comprises a gas turbine pull rod rotor wheel disc vibration analysis computer device, which comprises a memory, a processor and a computer program stored in the memory, and the processor realizes the steps of the gas turbine pull rod rotor wheel disc vibration analysis method when executing the computer program.

[0199] The application also comprises a readable storage medium, which stores a computer program, the computer program comprises program instructions, and the program instructions are executed by a processor to execute the steps of the vibration analysis method of the gas turbine tie rod rotor wheel disc.

[0200] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can make equivalent replacements or changes to the technical scheme and the inventive concept of the present application within the technical scope disclosed by the present application, which should be covered by the protection scope of the present application.

Claims

1. A method of gas turbine tie-rod rotor disc vibration analysis, characterised in that, The method comprises the following steps: The three-dimensional finite element dynamics equation of the gas turbine pull rod rotor wheel disc containing the stress stiffening matrix and the contact stiffness matrix is constructed; The rough surface of the rotor wheel disc is regarded as a surface formed by a series of micro-convex bodies with different heights on a smooth surface; according to an elastic-plastic contact model, the deformation stage of a single micro-convex body is divided into an elastic stage, an elastic-plastic stage and a plastic stage, and the normal contact load of each stage is calculated; the normal contact loads of all the micro-convex bodies participating in the contact are integrated to obtain a functional relationship between the contact variable and the distance of the contact surface; The current contact stiffness matrix is determined according to the functional relationship between the contact variable and the distance of the contact surface; The displacement field and the corresponding stress field are obtained through static analysis according to the current contact stiffness matrix, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; After multiple iterative updates, until the residual error of the contact stiffness matrix of the adjacent two iterations is less than the set tolerance, the final contact stiffness matrix and the stress stiffening matrix are outputted; The vibration response of the gas turbine pull rod rotor wheel disc is obtained by introducing the final contact stiffness matrix and the stress stiffening matrix into the three-dimensional finite element dynamics equation and then analyzing and solving the three-dimensional finite element dynamics equation.

2. A method of vibration analysis of a gas turbine tie-rod rotor disc as claimed in claim 1, wherein, The three-dimensional finite element dynamics equation of the gas turbine pull rod rotor wheel disc containing the stress stiffening matrix and the contact stiffness matrix is constructed, and is expressed as: ； wherein denotes a mass matrix; is a rotational speed; is a Coriolis matrix; denotes a bearing damping matrix; denotes a structural stiffness matrix; denotes a rotational softening matrix; denotes a linear load force vector calculated from the preload force; denotes a centrifugal load vector; denotes a stiffness matrix of the bearing, is a displacement vector, is a velocity vector, is an acceleration vector.

3. A method of vibration analysis of a gas turbine tie-rod rotor disk as set forth in claim 1, wherein According to the elastic-plastic contact model, the deformation stage of a single micro-convex body 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 of the elastic stage is expressed as: ； The normal contact load of the elastic-plastic stage is expressed as: ； ； The normal contact load of the plastic stage is expressed as: ； wherein represents the critical deformation of the micro asperity, ; represents the contact deformation of a single micro asperity; represents the equivalent elastic modulus of the contact interface; represents the approximate radius of curvature of the micro asperity tip; represents the contact microhardness; represents the hardness coefficient, which is related to the Poisson's ratio of the material; The normal contact loads of all the micro-convex bodies participating in the contact are integrated to obtain a functional relationship between the contact variable and the distance of the contact surface, and the functional relationship is: ； wherein ; ； ； ； wherein represents a dimensionless Gaussian distribution, ; , and represent parameters of surface roughness, specifically the number of microconvex bodies per unit area, the average radius of the microconvex bodies, and the standard deviation of the microconvex body height, respectively.

4. The method of claim 1, wherein, The displacement field and the corresponding stress field are obtained through static analysis according to the current contact stiffness matrix, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; After multiple iterative updates, until the residual error of the contact stiffness matrix of the adjacent two iterations is less than the set tolerance, the final contact stiffness matrix and the stress stiffening matrix are outputted, and the method comprises the following steps: Let the initial stress stiffening matrix be zero, and the current contact stress is obtained, and the calculation process is as follows: ； ； wherein and denotes the contact force of the face tooth contact surface; denotes the pretension; denotes the tangential force converted from the torque; denotes the sliding friction coefficient; According to the current contact stress, the current contact stiffness matrix is calculated through the finite element formula of the contact stiffness matrix; denotes the pressure angle of the face tooth, ; The current contact stiffness matrix and the stress stiffening matrix are substituted into the dynamics equation, and the displacement vector is obtained by solving the equation without considering the time term. In the natural coordinate system, the shape function of the contact element is expressed as: The contact pressure is calculated according to the displacement vector, and the contact stiffness matrix and the stress stiffening matrix are updated through the displacement field and the corresponding stress field; the stress stiffening matrix is calculated through a finite element calculation formula; the finite element calculation formula of the stress stiffening matrix is wherein is related to the Cauchy stress; denotes a geometric matrix, and describes the influence of the geometric state on the strain when the unit is deformed. After several iterations of updating, the residual of the contact stiffness matrix between adjacent time steps is determined: If the residual is less than a tolerance wherein, , then output the final calculated contact stiffness matrix and stress stiffening matrix; the tolerance Further comprising, before the final contact stiffness matrix and the stress stiffening matrix are introduced into the three-dimensional finite element dynamics equation, constructing an end face tooth contact model considering collision separation by considering the normal pressure and the tangential pressure of the unit area of the contact surface of the central pull rod end face tooth structure and the normal displacement and the tangential displacement of the nodes of the end tooth surface contact surface; and obtaining the contact pressure of the end face tooth under different contact states according to the end face tooth contact model. is defined as: 。 5. A method of vibration analysis of a gas turbine tie-rod rotor disc as claimed in claim 4, wherein, The contact stiffness matrix finite element formulation is expressed as: ; where Nc represents the shape function of the contact element, Kc represents the contact matrix of the adjacent contact element; the contact matrix of the adjacent contact element is expressed as: ； wherein, and respectively denote the unit normal contact stiffness and the tangential contact stiffness; ​ ， ​ ； wherein and denote the natural coordinates of the contact elements.

6. A method of vibration analysis of a gas turbine tie-rod rotor disc as claimed in claim 5, wherein, ​ 7. The method of claim 1, wherein The vibration response of the gas turbine tie rod rotor wheel disc is analyzed by introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation, specifically including the following steps: Under the action of periodic excitation, the displacement vector in the dynamic equation is expressed as a finite order Fourier form according to the harmonic balance method; The finite order Fourier form of the displacement vector is substituted into the dynamic equation to calculate the multi-order harmonic vector expression form of the nonlinear force and the linear force; The Newton-Raphson iteration method is used to solve the steady-state solution of the multi-order harmonic vector expression form of the nonlinear force and the linear force; the damping term, the time-varying term and the load term on the right side of the dynamic equation are ignored by using the sampling degree of freedom reduction method; the fixed interface modal synthesis method is used to obtain the reduced equation of the system degree of freedom according to the main modal matrix, the reduced modal matrix, the modal coordinates and the reserved node displacement vector; wherein the reduced modal matrix is obtained according to the stiffness matrix of the slave displacement vector, the stiffness matrix of the bearing node displacement and the contact surface node displacement vector causing contact failure; the main modal matrix is composed of the reserved first k order modal vectors after the constraint bearing node displacement and the contact surface node displacement causing contact failure; The vibration response of the tie rod rotor wheel disc is analyzed according to the modal reduced equation.

8. A gas turbine tie-rod rotor disk vibration analysis system characterized by, It includes: A construction module is used to construct a three-dimensional finite element dynamic equation of a gas turbine tie rod rotor wheel disc containing a stress stiffening matrix and a contact stiffness matrix; A contact stiffness matrix calculation module is used to regard the rough surface of the rotor wheel disc as a series of micro-convex bodies of different heights formed on a smooth surface; according to the elastic-plastic contact model, the deformation stage of a single micro-convex body is divided into an elastic stage, an elastic-plastic stage and a plastic stage, and the normal contact load of each stage is calculated; the normal contact loads of all micro-convex bodies participating in contact are integrated to obtain the functional relationship between the contact variable and the contact surface distance; The current contact stiffness matrix is determined according to the functional relationship between the contact variable and the contact surface distance; An update module is used to update the contact stiffness matrix and the stress stiffening matrix according to the displacement field and the corresponding stress field obtained by static analysis of the current contact stiffness matrix; After multiple iterations and updates, until the residual error of the contact stiffness matrix of the adjacent two iterations is less than the set tolerance, the final contact stiffness matrix and stress stiffening matrix are output; An analysis module is used to analyze and solve the three-dimensional finite element dynamic equation by introducing the final contact stiffness matrix and stress stiffening matrix into the three-dimensional finite element dynamic equation, and obtain the vibration response of the gas turbine tie rod rotor wheel disc.

9. A gas turbine tie-rod rotor disk vibration analysis computer device, characterized by, It includes: A memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to realize the steps of the vibration analysis method of the gas turbine tie rod rotor wheel disc according to any one of claims 1-7.

10. A readable storage medium, characterized by, The readable storage medium stores a computer program, and the computer program includes program instructions, which are executed by the processor to perform the steps of the vibration analysis method of the gas turbine tie rod rotor wheel disc according to any one of claims 1-7.

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