A dynamic characteristics analysis method of sealing structure based on perturbation method

Abstract

The present invention discloses a method for analyzing the dynamic characteristics of a sealing structure based on a perturbation method, and relates to the technical field of sealing structure dynamics. The present invention first establishes a sealing structure model, determines its three-dimensional fluid continuity equation and momentum equation based on overall flow theory and the perturbation method, uses the rotor eccentricity as a perturbation, decouples the three-dimensional gap circulation in time and space, decomposes the eccentric vortex of the three-dimensional gap circulation into a steady-state zero-order concentric vortex and a transient first-order eccentric vortex, solves the zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group, obtains the three-dimensional gap circulation flow field distribution, and performs a pressure field integration on the contact surface between the rotor and the three-dimensional gap fluid. The sealing structure model is used to simulate and obtain the hydrodynamic bearing capacity of the rotor during vortex motion, and the stiffness coefficient and damping coefficient of the sealing structure model are obtained. This truly restores the flow conditions of the gap circulation and achieves accurate acquisition of the dynamic characteristic parameters of the sealing structure.

Description

Technical Field

[0001] The present invention relates to the technical field of sealing structure dynamics, and in particular to a sealing structure dynamic characteristic analysis method based on a perturbation method. Background Art

[0002] Driven by the eccentric shaft, the fluid within the pump seal gap generates unevenly distributed pressure and velocity along the axial and circumferential directions, representing the dynamic characteristics of the seal structure. For rotor systems, this characteristic directly impacts the system's critical speed and motion stability, and has become a crucial component in assessing pump safety.

[0003] Considering that all forces acting on sealing structures are nonlinear, and the current lack of a relatively reliable method for calculating the seal gap flow field, seal dynamic stiffness, and damping, this severely restricts the analysis of wet critical speeds of pump rotors. Therefore, it is urgent to propose a perturbation-based dynamic characteristic analysis method for sealing structures. This method can accurately characterize the flow field results of the three-dimensional small gap annular flow within the sealing structure and solve the characteristic coefficients such as dynamic pressure, bearing capacity, stiffness, and damping of the three-dimensional small gap flow field, providing an effective reference for the dynamic analysis of sealing structures. Summary of the Invention

[0004] The present invention aims to solve the above problems and proposes a method for analyzing the dynamic characteristics of a sealing structure based on the perturbation method. By constructing a sealing structure model to restore the three-dimensional gap circulation flow field in the real sealing structure, the dynamic characteristics of the sealing structure are analyzed, and the dynamic characteristic parameters of the sealing structure such as the stiffness coefficient and damping coefficient of the sealing structure are accurately obtained, providing a basis for the analysis of the wet critical speed of the pump rotor.

[0005] The present invention specifically adopts the following technical solutions:

[0006] A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method comprises the following steps:

[0007] Step 1: Based on the actual sealing structure, a sealing structure model consisting of a stator, a rotor, and a three-dimensional gap circulation is established in a three-dimensional rectangular coordinate system. The three-dimensional fluid continuity equation and momentum equation of the sealing structure model are determined based on the overall flow theory and the perturbation method. The rotor eccentricity is used as the perturbation quantity, the three-dimensional gap circulation is decoupled in time and space, and the eccentric vortex of the three-dimensional gap circulation is decomposed into a steady-state zero-order concentric vortex and a transient first-order eccentric vortex.

[0008] Step 2, performing linear approximation on the nonlinear terms in the steady-state zero-order concentric vortex and the transient first-order eccentric vortex, determining the zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group, combining the boundary conditions of the sealing structure model during concentric vortex and eccentric vortex, calculating the zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group, obtaining the zero-order flow field result and the first-order flow field result of the three-dimensional gap circulation, obtaining the flow field distribution of the three-dimensional gap circulation, and obtaining the flow velocity field and pressure field of the three-dimensional gap circulation;

[0009] Step 3: Based on the flow field distribution of the three-dimensional gap annular flow, the pressure field of the three-dimensional gap annular flow is integrated on the contact surface between the rotor of the sealing structure model and the three-dimensional gap fluid to obtain the radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity on the rotor surface after the rotor undergoes eccentric motion;

[0010] Step 4: Characterize the stiffness coefficient and damping coefficient based on the first-order linear three-dimensional gap circulation fluid control equations, use the sealing structure model to simulate the rotor vortex process, and introduce vortex momentum Δx and Δy near the vortex position according to the simulated bearing capacity of the three-dimensional gap circulation in the sealing structure model at different vortex positions. Use the sealing structure model to simulate the rotor vortex process, obtain the bearing capacity of the three-dimensional gap circulation in the sealing structure model after the action of the vortex momentum, and determine the stiffness coefficient and damping coefficient of the sealing structure model.

[0011] Preferably, the sealing structure model consists of a stator, a rotor and a gap fluid, wherein the rotor rotates counterclockwise in the stator and is eccentrically arranged with an eccentricity of e. The gap fluid is filled into the gap between the stator and the rotor through the fluid inlet to form a three-dimensional gap circulation. The structural parameters and boundary conditions of the sealing structure model are set, and the sealing structure model is placed in a three-dimensional rectangular coordinate system. The stator axis at the gap fluid inflow end of the sealing structure model is located at the origin of the three-dimensional rectangular coordinate system. The stator radial direction is the y-axis direction, the stator axial direction is the z-axis direction, and the x-axis direction is perpendicular to the y-axis direction and the z-axis direction, respectively.

[0012] Preferably, in step 1, the three-dimensional fluid continuity equation of the sealing structure model is determined based on the integral flow theory as follows:

[0013]

[0014] Where t is time; x is the circumferential coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the bulk flow theory, h = h(z, θ, t), θ is the rotation angle of the three-dimensional gap annular flow along the circumferential direction; u is the annular flow velocity of the three-dimensional gap annular flow under the bulk flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the bulk flow theory;

[0015] The momentum equation includes an axial momentum equation and a circumferential momentum equation, wherein the axial momentum equation is:

[0016]

[0017] Where p is the radial pressure of the three-dimensional gap annular flow under the bulk flow theory; is the wall shear stress of the stator inner wall in the yz plane;

[0018] The circumferential momentum equation is:

[0019]

[0020] Where, is the hoop shear stress on the rotor surface;

[0021] Based on the perturbation method, the rotor eccentricity e is taken as the perturbation quantity, and the velocity and pressure in the sealing structure model are expressed as:

[0022]

[0023] Where h0 is the local thickness of the zero-order fluid; h1 is the local thickness of the first-order fluid; u0 is the zero-order component of the annular velocity of the three-dimensional gap annular flow, u1 is the first-order component of the annular velocity of the three-dimensional gap annular flow; w0 is the zero-order component of the axial velocity of the three-dimensional gap annular flow, w1 is the first-order component of the axial velocity of the three-dimensional gap annular flow; p0 is the zero-order component of the radial pressure of the three-dimensional gap annular flow, p1 is the first-order component of the radial pressure of the three-dimensional gap annular flow; ε is the dimensionless perturbation small eccentricity, R is the stator radius, r is the rotor radius;

[0024] Decouple the three-dimensional gap circulation in time and space, substitute formula (4) into formula (1) to formula (3), decompose the eccentric vortex of the three-dimensional gap circulation into steady-state zero-order concentric vortex and transient first-order eccentric vortex, and obtain the zero-order perturbation equation group and first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model;

[0025] The zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are:

[0026]

[0027] Where ω is the rotor speed; f s0 is the zero-order friction coefficient of the stator wall, f s is the stator wall friction coefficient, c1, c2, c3 are Moody's experimental constants, μ is the dynamic viscosity, e s is the friction coefficient of the stator wall; f r0 is the zero-order friction coefficient of the rotor wall, f ris the friction coefficient of the rotor wall, e r is the friction coefficient of the rotor wall;

[0028] The first-order perturbation equations for the three-dimensional gap circulation in the sealing structure model are:

[0029]

[0030] in,

[0031]

[0032] Where u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equations of three-dimensional gap circulation.

[0033] Preferably, in step 2, when the rotor and stator in the sealing structure model swirl concentrically during concentric swirl, the three-dimensional gap fluid thickness h does not change in both the circumferential and axial directions, and the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are simplified to:

[0034]

[0035] The third nonlinear equation in the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model shown in formula (8) is simplified to:

[0036]

[0037] in,

[0038]

[0039] In the formula, F1 and F2 are intermediate parameters used for simplification;

[0040] Taylor expansion of formula (9) yields:

[0041]

[0042] in,

[0043]

[0044] Where u0 0 Expand position points for Taylor;

[0045] Then, the nonlinear terms in formula (5) and formula (11) are linearized, thereby converting the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model into a linear equation system, and obtaining the zero-order linear three-dimensional gap circulation fluid control equation system.

[0046] Preferably, in step 2, during the eccentric vortex process, the stator center O of the sealing structure model coincides with the rotor axis O1 in static state, and the stator center O vortexes around the rotor axis O1 in dynamic state;

[0047] When the rotor axis O1 vortexes around the stator center O, the vortex trajectory of the rotor axis is:

[0048]

[0049] Where x(t) is the displacement of the rotor axis in the x direction; y (t) is the displacement of the rotor axis in the y direction; r o is the vortex radius; Ω is the vortex speed; t is the time; is the phase angle of the simple harmonic vortex;

[0050] According to the vortex trajectory of the rotor axis, the simple harmonic vortex hypothesis is used to eliminate the time dependence of the first-order flow field physical quantities in the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model. The vortex frequency is taken as the dominant response, and only the first-order harmonic in the series expansion is considered, so that the first-order flow field physical quantities are expressed in a simple harmonic form. The first-order pressure field and first-order velocity field of the three-dimensional gap circulation in the sealing structure model are obtained as follows:

[0051]

[0052] Where p 1s is the sine coefficient of the first-order pressure field; p 1c is the cosine coefficient of the first-order pressure field; w 1s is the sinusoidal coefficient of the first-order axial velocity; w 1c is the cosine coefficient of the first-order axial velocity; u 1s is the sinusoidal coefficient of the first-order annular flow velocity; u 1c is the cosine coefficient of the annular first-order velocity;

[0053] Substitute formula (14) into the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equations of the three-dimensional gap circulation into six nonlinear equations, namely:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Where, is the speed of the rotor axis in the x direction; is the speed of the rotor axis in the y direction; is the axial derivative of the first-order axial velocity cosine coefficient, expressed in forward difference format; is the axial derivative of the first-order sine coefficient of the axial velocity, expressed in forward difference format;

[0061] The nonlinear terms in each nonlinear equation are linearized, thereby converting the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model into a linear equation system, and obtaining the first-order linear three-dimensional gap circulation fluid control equation system.

[0062] Preferably, the boundary conditions of the sealing structure model during concentric vortex motion are set, and the zero-order flow field results of the three-dimensional gap circulation in the sealing structure model are calculated using the zero-order linear three-dimensional gap circulation fluid control equations to determine the zero-order flow velocity field and zero-order pressure field of the three-dimensional gap circulation;

[0063] The boundary conditions of the sealing structure model during eccentric vortex motion are set, and the first-order flow field results of the three-dimensional gap annular flow in the sealing structure model are calculated using the first-order linear three-dimensional gap annular flow fluid control equations, and the first-order velocity field and first-order pressure field of the three-dimensional gap annular flow are determined.

[0064] The zero-order flow field results and the first-order flow field results of the three-dimensional gap circulation are integrated according to Equations (4) and (14) to obtain the real flow field results of the three-dimensional gap circulation in the sealing structure model, and determine the velocity field and pressure field of the three-dimensional gap circulation.

[0065] Preferably, in step 3, after the rotor undergoes eccentric motion, the bearing force exerted on the three-dimensional gap fluid of the sealing structure model is:

[0066]

[0067] in,

[0068]

[0069]

[0070] Where, F X is the radial hydrodynamic bearing capacity of the rotor wall, F Y k is the tangential hydrodynamic bearing capacity of the rotor wall; xx 、k xy 、k yx 、k yy are stiffness coefficients, where k xxis the stiffness coefficient in the x direction, k xy and k yx are cross stiffness coefficients, k yy is the stiffness coefficient in the y direction; X is the position of the rotor vortex around the axis in the x direction, and Y is the position of the rotor vortex around the axis in the y direction; c xx 、c xy 、c yx 、c yy are the damping coefficients, where c xx is the damping coefficient in the x direction, c xy and c yx are cross damping coefficients, c yy is the damping coefficient in the y direction; is the vortex velocity of the rotor around the axis in the x direction, is the vortex velocity of the rotor around the axis in the y direction; m xx 、m xy 、m yx 、m yy are all mass influence coefficients, where m xx is the mass influence coefficient in the x direction, m xy and m yx are the coupling quality influence coefficients, m yy is the mass influence coefficient in the y direction; is the eddy acceleration of the rotor around the axis in the x direction, is the eddy acceleration of the rotor around the axis in the y direction; L is the axial length of the seal;

[0071] The sealing structure model is used to simulate the vortex process of the rotor in the stator, and the vortex position and vortex velocity of the rotor at different vortex moments are obtained. The zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group in step 2 are used to calculate the zero-order flow field results and the first-order flow field results of the three-dimensional gap circulation in the sealing structure model, and the velocity field and pressure field of the three-dimensional gap circulation during the vortex process are determined. The bearing capacity of the three-dimensional gap circulation at each moment within the preset simulation period is obtained, and the hydrodynamic bearing capacity of the rotor surface is obtained. The radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity of the rotor wall during the vortex process are determined by fitting.

[0072] Preferably, in step 4, since the stiffness coefficient and the damping coefficient in the first-order linear three-dimensional gap annular flow fluid control equation group are non-constants, the rotor motion state parameters X, Y, The stiffness coefficient and damping coefficient of the sealing structure model are characterized as follows based on the first-order linear three-dimensional gap annular flow control equations:

[0073]

[0074] The rotor vortex process is simulated using a sealing structure model. During the vortex process, the stiffness coefficient and damping coefficient of the sealing structure model change with the motion state of the rotor. The stiffness coefficient and damping coefficient of the sealing structure model at a specific position and speed are obtained using the difference method.

[0075] The eddy momentum Δx and Δy are introduced near the rotor eddy position. The eddy momentum Δx and Δy are set, and the rotor eddy process is simulated using the sealing structure model. The bearing capacity of the three-dimensional gap annular flow in the sealing structure model at different eddy positions after the eddy momentum is simulated, and the stiffness coefficient and damping coefficient of the sealing structure model during the rotor eddy after the eddy momentum are calculated as follows:

[0076]

[0077] Where, is the rotor's vortex velocity in the x direction; is the vortex velocity of the rotor in the y direction.

[0078] The present invention has the following beneficial effects:

[0079] (1) The present invention proposes a method for analyzing the dynamic characteristics of a sealing structure based on the perturbation method, which fully considers the axial, circumferential and radial flows of the three-dimensional gap circulation in the sealing structure, and effectively averages the radial flow of the three-dimensional gap circulation by using the overall flow theory. Based on the fluid control equations, the sealing water dynamic load on the rotor when it vortexes in an arbitrary elliptical trajectory at different vortex speeds is characterized, which breaks the limitations of the traditional rotor center vortex and improves the accuracy of obtaining the dynamic characteristic coefficients of the sealing structure.

[0080] (2) The present invention proposes a method for analyzing the dynamic characteristics of a sealing structure based on the perturbation method. The perturbation method is used to decompose the fluid control equations into steady-state zero-order concentric vortex and transient first-order eccentric vortex by introducing the eccentricity e as the perturbation quantity, thereby obtaining the zero-order perturbation equations and the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model. The three-dimensional gap circulation is decoupled in time and space, reducing the solution complexity of the three-dimensional gap circulation flow field control equations and improving the solution efficiency of the three-dimensional gap circulation flow field.

[0081] (3) The present invention proposes a method for analyzing the dynamic characteristics of a sealing structure based on the perturbation method, and specifically discloses a method for characterizing the stiffness coefficient and damping coefficient of a sealing structure, thereby achieving accurate acquisition of the dynamic characteristics of the sealing structure. The method can be widely applied to the dynamic analysis of most sealing structures with small gaps. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1Schematic diagram of the sealing structure model of the present invention; in the figure, (a) is the cross section of the sealing structure model, and (b) is the longitudinal section of the sealing structure model.

[0083] Figure 2 Schematic diagram of the finite difference format of the present invention.

[0084] Figure 3 It is a schematic diagram of the eccentric vortex process of the rotor in the sealing structure model of the present invention. DETAILED DESCRIPTION

[0085] The specific implementation of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0086] A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method comprises the following steps:

[0087] Step 1: Based on the actual sealing structure, a sealing structure model consisting of a stator, a rotor and a three-dimensional gap circulation is established in a three-dimensional rectangular coordinate system.

[0088] In this embodiment, the sealing structure model consists of a stator, a rotor and a gap fluid, such as Figure 1 As shown, the rotor rotates counterclockwise in the stator and is eccentrically set with an eccentricity of e. The gap fluid is filled into the gap between the stator and the rotor through the fluid inlet to form a three-dimensional gap circulation. The structural parameters and boundary conditions of the sealing structure model are set, and the sealing structure model is placed in a three-dimensional rectangular coordinate system. The stator axis at the gap fluid inflow end of the sealing structure model is located at the origin of the three-dimensional rectangular coordinate system. The stator radial direction is the y-axis direction, the stator axial direction is the z-axis direction, and the x-axis direction is perpendicular to the y-axis direction and the z-axis direction, respectively, that is, the x-axis direction corresponds to the circumferential direction, the y-axis direction corresponds to the radial direction, and the z-axis direction corresponds to the axial direction. The polar coordinate system is used to determine the position coordinates in the longitudinal section of the sealing structure model, with the center of the longitudinal section of the sealing structure model as the pole, the y-axis as the polar axis, and the rotor rotation direction as the positive direction.

[0089] Based on the overall flow theory and perturbation method, the three-dimensional fluid continuity equation and momentum equation of the sealing structure model are determined. The rotor eccentricity is used as the perturbation, and the three-dimensional gap circulation is decoupled in time and space. The eccentric vortex of the three-dimensional gap circulation is decomposed into a steady-state zero-order concentric vortex and a transient first-order eccentric vortex.

[0090] The three-dimensional fluid continuity equation of the sealing structure model determined based on the overall flow theory is:

[0091]

[0092] Where t is time; x is the circumferential coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the bulk flow theory, h = h(z,θ,t), θ is the rotation angle of the three-dimensional gap annular flow along the circumferential direction; u is the annular flow velocity of the three-dimensional gap annular flow under the bulk flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the bulk flow theory.

[0093] The momentum equation includes an axial momentum equation and a circumferential momentum equation, wherein the axial momentum equation is:

[0094]

[0095] Where p is the radial pressure of the three-dimensional gap annular flow under the bulk flow theory; is the wall shear stress of the stator inner wall in the yz plane.

[0096] The circumferential momentum equation is:

[0097]

[0098] Where, is the hoop shear stress on the rotor surface.

[0099] Since the radial physical quantities of the three-dimensional gap annular flow have been averaged in the radial direction based on the overall flow theory, there is no radial momentum equation.

[0100] Based on the perturbation method, the rotor eccentricity e is taken as the perturbation quantity, and the velocity and pressure in the sealing structure model are expressed as:

[0101]

[0102] Where h0 is the local thickness of the zero-order fluid; h1 is the local thickness of the first-order fluid; u0 is the zero-order component of the annular velocity of the three-dimensional gap annular flow, u1 is the first-order component of the annular velocity of the three-dimensional gap annular flow; w0 is the zero-order component of the axial velocity of the three-dimensional gap annular flow, w1 is the first-order component of the axial velocity of the three-dimensional gap annular flow; p0 is the zero-order component of the radial pressure of the three-dimensional gap annular flow, p1 is the first-order component of the radial pressure of the three-dimensional gap annular flow; ε is the dimensionless perturbation small eccentricity, R is the stator radius and r is the rotor radius.

[0103] The three-dimensional gap circulation is decoupled in time and space, and formula (4) is substituted into formulas (1) to (3). The eccentric vortex of the three-dimensional gap circulation is decomposed into a steady-state zero-order concentric vortex and a transient first-order eccentric vortex, and the zero-order perturbation equation group and the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model are obtained.

[0104] The zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are:

[0105]

[0106] Where ω is the rotor speed; f s0 is the zero-order friction coefficient of the stator wall, f s is the stator wall friction coefficient, c1, c2, c3 are Moody's experimental constants, μ is the dynamic viscosity, e s is the friction coefficient of the stator wall; f r0 is the zero-order friction coefficient of the rotor wall, f r is the friction coefficient of the rotor wall, e r is the friction coefficient of the rotor wall.

[0107] The first-order perturbation equations for the three-dimensional gap circulation in the sealing structure model are:

[0108]

[0109] in,

[0110]

[0111] Where u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equations of three-dimensional gap circulation.

[0112] Step 2. Use numerical methods such as the finite element method, bisection method, finite difference method, and simple harmonic vortex hypothesis to linearly approximate the nonlinear terms in the steady-state zero-order concentric vortex and transient first-order eccentric vortex to derive the zero-order linear three-dimensional gap circulation fluid control equations and the first-order linear three-dimensional gap circulation fluid control equations. Combined with the boundary conditions of the sealing structure model during concentric vortex and eccentric vortex, numerically solve the zero-order linear three-dimensional gap circulation fluid control equations and the first-order linear three-dimensional gap circulation fluid control equations to obtain the zero-order flow field results and first-order flow field results of the three-dimensional gap circulation, obtain the flow field distribution of the three-dimensional gap circulation, and obtain the flow velocity field and pressure field of the three-dimensional gap circulation.

[0113] In step 2, the rotor and stator in the sealing structure model swirl concentrically during concentric swirl, and the three-dimensional gap fluid thickness h does not change along the circumferential θ direction and the axial z direction. The zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are simplified to:

[0114]

[0115] The third nonlinear equation in the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model shown in formula (8) is simplified to:

[0116]

[0117] in,

[0118]

[0119] Where F1 and F2 are intermediate parameters used for simplification.

[0120] Taylor expansion of formula (9) yields:

[0121]

[0122] in,

[0123]

[0124] Where u0 0 Expand position point for Taylor.

[0125] In this embodiment, the central finite difference method is used to linearize the nonlinear terms in formula (5) and formula (11). The finite difference format is as follows: Figure 2 As shown, the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equation group, and the zero-order linear three-dimensional gap circulation fluid control equation group is obtained.

[0126] The boundary conditions of the sealing structure model during concentric vortex motion are set, including the inlet flow velocity and outlet static pressure of the sealing structure model. The zero-order flow field results of the three-dimensional gap annular flow in the sealing structure model are calculated using the zero-order linear three-dimensional gap annular flow fluid control equations, and the zero-order flow velocity field and zero-order pressure field of the three-dimensional gap annular flow are determined. In this embodiment, the inlet flow velocity of the sealing structure model is set to 5 m / s and the outlet static pressure is set to 0 Pa. The input parameters for the zero-order linear three-dimensional gap annular flow fluid control equations are shown in Table 1.

[0127] Table 1 Input parameters of the zero-order linear three-dimensional gap annular flow control equations

[0128]

[0129]

[0130] The eccentric vortex process is as follows Figure 3 As shown in the figure, the stator center O of the sealing structure model coincides with the rotor axis O1 in static state. In dynamic state, the stator center O vortexes around the rotor axis O1. The vortex trajectory of the rotor axis is:

[0131]

[0132] Where, x(t) is the displacement of the rotor axis in the x direction; y (t) is the displacement of the rotor axis in the y direction; r o is the vortex radius; Ω is the vortex speed; t is the time; is the phase angle of the simple harmonic vortex.

[0133] According to the vortex trajectory of the rotor axis, the simple harmonic vortex hypothesis is used to eliminate the dependence of the first-order flow field physical quantities in the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model on time, and the frequency of the rotational speed dominates the response. Therefore, the first-order pressure field and velocity field of the three-dimensional gap circulation only consider the first-order harmonic in the series expansion, that is, the first-order physical quantities of the three-dimensional gap circulation flow field are all set to simple harmonic form, and the simple harmonic form is used to express the physical quantities of the first-order flow field. The first-order pressure field and first-order velocity field of the three-dimensional gap circulation in the sealing structure model are obtained as follows:

[0134]

[0135] Where p 1s is the sine coefficient of the first-order pressure field; p 1c is the cosine coefficient of the first-order pressure field; w 1s is the sinusoidal coefficient of the first-order axial velocity; w 1c is the cosine coefficient of the first-order axial velocity; u 1s is the sinusoidal coefficient of the first-order annular flow velocity; u 1c is the cosine coefficient of the annular first-order flow velocity.

[0136] Substitute formula (14) into the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equations of the three-dimensional gap circulation into six nonlinear equations, namely:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] Where, is the speed of the rotor axis in the x direction; is the speed of the rotor axis in the y direction; is the axial derivative of the first-order axial velocity cosine coefficient, expressed in forward difference format; is the axial derivative of the first-order sine coefficient of the axial flow velocity, expressed in forward difference format.

[0144] Similarly, according to the nonlinear term linearization method of the zero-order linear three-dimensional gap circulation fluid control equations, based on Taylor expansion and finite difference method, the six nonlinear equations in the three-dimensional gap circulation first-order perturbation equations are transformed into a large linear matrix to obtain the first-order linear three-dimensional gap circulation fluid control equations.

[0145] The boundary conditions of the sealing structure model during eccentric vortex motion are set, and the input parameters for the first-order linear three-dimensional gap annular flow fluid control equations are shown in Table 2. The first-order linear three-dimensional gap annular flow fluid control equations are used to calculate the first-order flow field results of the three-dimensional gap annular flow in the sealing structure model, and determine the first-order velocity field and first-order pressure field of the three-dimensional gap annular flow.

[0146] Table 2 Input parameters of the first-order linear three-dimensional gap annular flow control equations

[0147]

[0148] The nonlinear terms in each nonlinear equation are linearized, thereby converting the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model into a linear equation system, and obtaining the first-order linear three-dimensional gap circulation fluid control equation system.

[0149] The zero-order flow field results and the first-order flow field results of the three-dimensional gap circulation are integrated according to Equations (4) and (14) to obtain the real flow field results of the three-dimensional gap circulation in the sealing structure model, and determine the velocity field and pressure field of the three-dimensional gap circulation.

[0150] Step 3: Based on the flow field distribution of the three-dimensional gap circulation, the pressure field of the three-dimensional gap circulation is integrated on the contact surface between the rotor of the sealing structure model and the three-dimensional gap fluid to obtain the radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity on the rotor surface after the rotor undergoes eccentric motion.

[0151] In this embodiment, after the rotor undergoes eccentric motion, the bearing force on the three-dimensional gap fluid of the sealing structure model is:

[0152]

[0153] in,

[0154]

[0155]

[0156] Where, F X is the radial hydrodynamic bearing capacity of the rotor wall, F Yk is the tangential hydrodynamic bearing capacity of the rotor wall; xx 、k xy 、k yx 、k yy are stiffness coefficients, where k xx is the stiffness coefficient in the x direction, k xy and k yx are cross stiffness coefficients, k yy is the stiffness coefficient in the y direction; X is the position of the rotor vortex around the axis in the x direction, and Y is the position of the rotor vortex around the axis in the y direction; c xx 、c xy 、c yx 、c yy are the damping coefficients, where c xx is the damping coefficient in the x direction, c xy and c yx are cross damping coefficients, c yy is the damping coefficient in the y direction; is the vortex velocity of the rotor around the axis in the x direction, Y is the vortex velocity of the rotor around the axis in the y direction; m xx 、m xy 、m yx 、m yy are all mass influence coefficients, where m xx is the mass influence coefficient in the x direction, m xy and m yx are the coupling quality influence coefficients, m yy is the mass influence coefficient in the y direction; is the eddy acceleration of the rotor around the axis in the x direction, is the eddy acceleration of the rotor around the axis in the y direction; L is the axial length of the seal.

[0157] The sealing structure model is used to simulate the vortex process of the rotor in the stator. The total simulation cycle is preset to 3.6s, and the vortex position and vortex speed of the rotor at different vortex moments are obtained. In this embodiment, R is set to w =0.005m, Ω=100rad / s=5π / 9, use the zero-order linear three-dimensional gap annular flow fluid control equations and the first-order linear three-dimensional gap annular flow fluid control equations in step 2 to calculate the zero-order flow field results and the first-order flow field results of the three-dimensional gap annular flow in the sealing structure model, determine the velocity field (i.e., the axial velocity field and circumferential velocity field of the three-dimensional gap annular flow) and pressure field of the three-dimensional gap annular flow during the vortex process, and obtain the bearing capacity of the three-dimensional gap annular flow at each moment in the preset simulation period to obtain the hydrodynamic bearing capacity of the rotor surface, and then determine the radial hydrodynamic bearing capacity F of the rotor wall during the vortex process based on the radial basis function method. Xand tangential hydrodynamic bearing capacity F Y , respectively, the radial hydrodynamic bearing capacity F on the rotor wall is obtained X and tangential hydrodynamic bearing capacity F Y About X, Y, Explicit surface expression of .

[0158] Step 4: Characterize the stiffness coefficient and damping coefficient based on the first-order linear three-dimensional gap circulation fluid control equations, use the sealing structure model to simulate the rotor vortex process, and introduce vortex momentum Δx and Δy near the vortex position according to the simulated bearing capacity of the three-dimensional gap circulation in the sealing structure model at different vortex positions. Use the sealing structure model to simulate the rotor vortex process, obtain the bearing capacity of the three-dimensional gap circulation in the sealing structure model after the action of the vortex momentum, and determine the stiffness coefficient and damping coefficient of the sealing structure model.

[0159] For nonlinear problems, since the stiffness coefficient and damping coefficient in the first-order linear three-dimensional gap annular flow control equations are non-constant, the rotor motion state parameters X, Y, The stiffness coefficient and damping coefficient of the sealing structure model are characterized as follows based on the first-order linear three-dimensional gap annular flow control equations:

[0160]

[0161] The sealing structure model is used to simulate the rotor whirl process. During the whirl process, the stiffness coefficient and damping coefficient of the sealing structure model change with the motion state of the rotor. When the rotor is at different whirl positions or different whirl moments, steps 1 to 3 are used to simulate the sealing structure model to obtain the stiffness coefficient and damping coefficient of the sealing structure model at specific positions and specific speeds.

[0162] Small eddy momentum Δx and Δy are introduced near the rotor eddy position, and the rotor eddy process is simulated using the sealing structure model. The bearing capacity of the three-dimensional gap annular flow in the sealing structure model at different eddy positions after the action of small eddy momentum is obtained. The stiffness coefficient and damping coefficient of the sealing structure model during the rotor eddy after the action of eddy momentum are:

[0163]

[0164] Where, is the rotor's vortex velocity in the x direction; is the vortex velocity of the rotor in the y direction.

[0165] In summary, the method of the present invention inverts the stiffness coefficient and damping coefficient of the sealing structure based on the analytical expression between the seal hydrodynamic bearing capacity and the stiffness matrix and the damping matrix. By adopting a semi-analytical method to solve the characteristic coefficients such as the flow field dynamic pressure, bearing capacity, stiffness and damping of the three-dimensional gap annular flow, the dynamic characteristics of the sealing structure are accurately obtained, which provides a basis for the dynamic analysis of small-gap sealed pumps such as nuclear pumps and water pumps.

[0166] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the dynamic characteristics of a sealing structure based on a perturbation method, characterized in that: The following steps are involved: Step 1: Based on the actual sealing structure, a sealing structure model consisting of a stator, a rotor, and a three-dimensional gap circulation is established in a three-dimensional rectangular coordinate system. The three-dimensional fluid continuity equation and momentum equation of the sealing structure model are determined based on the overall flow theory and the perturbation method. The rotor eccentricity is used as the perturbation quantity, the three-dimensional gap circulation is decoupled in time and space, and the eccentric vortex of the three-dimensional gap circulation is decomposed into a steady-state zero-order concentric vortex and a transient first-order eccentric vortex. Step 2, performing linear approximation on the nonlinear terms in the steady-state zero-order concentric vortex and the transient first-order eccentric vortex, determining the zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group, combining the boundary conditions of the sealing structure model during concentric vortex and eccentric vortex, calculating the zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group, obtaining the zero-order flow field result and the first-order flow field result of the three-dimensional gap circulation, obtaining the flow field distribution of the three-dimensional gap circulation, and obtaining the flow velocity field and pressure field of the three-dimensional gap circulation; Step 3: Based on the flow field distribution of the three-dimensional gap annular flow, the pressure field of the three-dimensional gap annular flow is integrated on the contact surface between the rotor of the sealing structure model and the three-dimensional gap fluid to obtain the radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity on the rotor surface after the rotor undergoes eccentric motion; Step 4: Characterize the stiffness coefficient and damping coefficient based on the first-order linear three-dimensional gap circulation fluid control equations, use the sealing structure model to simulate the rotor vortex process, and introduce vortex momentum Δx and Δy near the vortex position according to the simulated bearing capacity of the three-dimensional gap circulation in the sealing structure model at different vortex positions. Use the sealing structure model to simulate the rotor vortex process, obtain the bearing capacity of the three-dimensional gap circulation in the sealing structure model after the action of the vortex momentum, and determine the stiffness coefficient and damping coefficient of the sealing structure model.

2. A sealing structure dynamic characteristics analysis method based on perturbation method according to claim 1, characterized in that: The sealing structure model consists of a stator, a rotor and a gap fluid, wherein the rotor rotates counterclockwise inside the stator and is eccentrically arranged with an eccentricity of e. The gap fluid is filled into the gap between the stator and the rotor through a fluid inlet to form a three-dimensional gap circulation. The structural parameters and boundary conditions of the sealing structure model are set, and the sealing structure model is placed in a three-dimensional rectangular coordinate system. The stator axis at the gap fluid inflow end of the sealing structure model is located at the origin of the three-dimensional rectangular coordinate system. The stator radial direction is the y-axis direction, the stator axial direction is the z-axis direction, and the x-axis direction is perpendicular to the y-axis direction and the z-axis direction, respectively.

3. A sealing structure dynamic characteristics analysis method based on perturbation method according to claim 2, characterized in that: In step 1, the three-dimensional fluid continuity equation of the sealing structure model is determined based on the overall flow theory as follows: Where t is time; x is the circumferential coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the bulk flow theory, h = h(z, θ, t), θ is the rotation angle of the three-dimensional gap annular flow along the circumferential direction; u is the annular flow velocity of the three-dimensional gap annular flow under the bulk flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the bulk flow theory; The momentum equation includes an axial momentum equation and a circumferential momentum equation, wherein the axial momentum equation is: Where p is the radial pressure of the three-dimensional gap annular flow under the bulk flow theory; is the wall shear stress of the stator inner wall in the yz plane; The circumferential momentum equation is: Where, is the hoop shear stress on the rotor surface; Based on the perturbation method, the rotor eccentricity e is taken as the perturbation quantity, and the velocity and pressure in the sealing structure model are expressed as: Where h0 is the local thickness of the zero-order fluid; h1 is the local thickness of the first-order fluid; u0 is the zero-order component of the annular velocity of the three-dimensional gap annular flow, u1 is the first-order component of the annular velocity of the three-dimensional gap annular flow; w0 is the zero-order component of the axial velocity of the three-dimensional gap annular flow, w1 is the first-order component of the axial velocity of the three-dimensional gap annular flow; p0 is the zero-order component of the radial pressure of the three-dimensional gap annular flow, p1 is the first-order component of the radial pressure of the three-dimensional gap annular flow; ε is the dimensionless perturbation small eccentricity, R is the stator radius, r is the rotor radius; Decouple the three-dimensional gap circulation in time and space, substitute formula (4) into formula (1) to formula (3), decompose the eccentric vortex of the three-dimensional gap circulation into steady-state zero-order concentric vortex and transient first-order eccentric vortex, and obtain the zero-order perturbation equation group and first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model; The zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are: Where ω is the rotor speed; f s0 is the zero-order friction coefficient of the stator wall, f s is the stator wall friction coefficient, c1, c2, c3 are Moody's experimental constants, μ is the dynamic viscosity, e s is the friction coefficient of the stator wall; f r0 is the zero-order friction coefficient of the rotor wall, f r is the friction coefficient of the rotor wall, e r is the friction coefficient of the rotor wall; The first-order perturbation equations for the three-dimensional gap circulation in the sealing structure model are: in, Where u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equations of three-dimensional gap circulation.

4. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method according to claim 3, characterized in that: In step 2, the rotor and stator in the sealing structure model swirl concentrically during concentric swirl, and the three-dimensional gap fluid thickness h does not change in the circumferential and axial directions. The zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are simplified to: The third nonlinear equation in the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model shown in formula (8) is simplified to: in, In the formula, F1 and F2 are intermediate parameters used for simplification; Taylor expansion of formula (9) yields: in, Where u0 0 Expand position points for Taylor; Then, the nonlinear terms in formula (5) and formula (11) are linearized, thereby converting the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model into a linear equation system, and obtaining the zero-order linear three-dimensional gap circulation fluid control equation system.

5. The method for analyzing dynamic characteristics of a sealing structure based on perturbation method according to claim 4, characterized in that: In step 2, during the eccentric vortex process, the stator center O of the sealing structure model coincides with the rotor axis O1 in static state, and the stator center O vortexes around the rotor axis O1 in dynamic state; When the rotor axis O1 vortexes around the stator center O, the vortex trajectory of the rotor axis is: Where x(t) is the displacement of the rotor axis in the x direction; y (t) is the displacement of the rotor axis in the y direction; r o is the vortex radius; Ω is the vortex speed; t is the time; is the phase angle of the simple harmonic vortex; According to the vortex trajectory of the rotor axis, the simple harmonic vortex hypothesis is used to eliminate the time dependence of the first-order flow field physical quantities in the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model. The vortex frequency is taken as the dominant response, and only the first-order harmonic in the series expansion is considered, so that the first-order flow field physical quantities are expressed in a simple harmonic form. The first-order pressure field and first-order velocity field of the three-dimensional gap circulation in the sealing structure model are obtained as follows: Where p 1s is the sine coefficient of the first-order pressure field; p 1c is the cosine coefficient of the first-order pressure field; w 1s is the sinusoidal coefficient of the first-order axial velocity; w 1c is the cosine coefficient of the first-order axial velocity; u 1s is the sinusoidal coefficient of the first-order annular flow velocity; u 1c is the cosine coefficient of the annular first-order velocity; Substitute formula (14) into the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equations of the three-dimensional gap circulation into six nonlinear equations, namely: ① ② ③ ④ ⑤ ⑥ Where, is the speed of the rotor axis in the x direction; is the speed of the rotor axis in the y direction; is the axial derivative of the first-order axial velocity cosine coefficient, expressed in forward difference format; is the axial derivative of the first-order sine coefficient of the axial velocity, expressed in forward difference format; The nonlinear terms in each nonlinear equation are linearized, thereby converting the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model into a linear equation system, and obtaining the first-order linear three-dimensional gap circulation fluid control equation system.

6. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method according to claim 5, characterized in that: The boundary conditions of the sealing structure model during concentric vortex motion are set, and the zero-order flow field results of the three-dimensional gap annular flow in the sealing structure model are calculated using the zero-order linear three-dimensional gap annular flow fluid control equations, and the zero-order flow velocity field and zero-order pressure field of the three-dimensional gap annular flow are determined; The boundary conditions of the sealing structure model during eccentric vortex motion are set, and the first-order flow field results of the three-dimensional gap annular flow in the sealing structure model are calculated using the first-order linear three-dimensional gap annular flow fluid control equations, and the first-order velocity field and first-order pressure field of the three-dimensional gap annular flow are determined. The zero-order flow field results and the first-order flow field results of the three-dimensional gap circulation are integrated according to Equations (4) and (14) to obtain the real flow field results of the three-dimensional gap circulation in the sealing structure model, and determine the velocity field and pressure field of the three-dimensional gap circulation.

7. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method according to claim 6, characterized in that: In step 3, after the rotor undergoes eccentric motion, the bearing force on the three-dimensional gap fluid of the sealing structure model is: in, Where, F X is the radial hydrodynamic bearing capacity of the rotor wall, F Y k is the tangential hydrodynamic bearing capacity of the rotor wall; xx 、k xy 、k yx 、k yy are stiffness coefficients, where k xx is the stiffness coefficient in the x direction, k xy and k yx are cross stiffness coefficients, k yy is the stiffness coefficient in the y direction; X is the position of the rotor vortex around the axis in the x direction, and Y is the position of the rotor vortex around the axis in the y direction; c xx 、c xy 、c yx 、c yy are the damping coefficients, where c xx is the damping coefficient in the x direction, c xy and c yx are cross damping coefficients, c yy is the damping coefficient in the y direction; is the vortex velocity of the rotor around the axis in the x direction, is the vortex velocity of the rotor around the axis in the y direction; m xx 、m xy 、m yx 、m yy are all mass influence coefficients, where m xx is the mass influence coefficient in the x direction, m xy and m yx are the coupling quality influence coefficients, m yy is the mass influence coefficient in the y direction; is the eddy acceleration of the rotor around the axis in the x direction, is the eddy acceleration of the rotor around the axis in the y direction; L is the axial length of the seal; The sealing structure model is used to simulate the vortex process of the rotor in the stator, and the vortex position and vortex velocity of the rotor at different vortex moments are obtained. The zero-order linear three-dimensional gap circulation fluid control equation group and the first-order linear three-dimensional gap circulation fluid control equation group in step 2 are used to calculate the zero-order flow field results and the first-order flow field results of the three-dimensional gap circulation in the sealing structure model, and the velocity field and pressure field of the three-dimensional gap circulation during the vortex process are determined. The bearing capacity of the three-dimensional gap circulation at each moment within the preset simulation period is obtained, and the hydrodynamic bearing capacity of the rotor surface is obtained. The radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity of the rotor wall during the vortex process are determined by fitting.

8. The method for analyzing dynamic characteristics of a sealing structure based on perturbation method according to claim 7, characterized in that: In the step 4, since the stiffness coefficient and the damping coefficient in the first-order linear three-dimensional gap annular flow control equation are non-constant, the rotor motion state parameters X, Y, The stiffness coefficient and damping coefficient of the sealing structure model are characterized as follows based on the first-order linear three-dimensional gap annular flow control equations: The rotor vortex process is simulated using a sealing structure model. During the vortex process, the stiffness coefficient and damping coefficient of the sealing structure model change with the motion state of the rotor. The stiffness coefficient and damping coefficient of the sealing structure model at a specific position and speed are obtained using the difference method. The eddy momentum Δx and Δy are introduced near the rotor eddy position. The eddy momentum Δx and Δy are set, and the rotor eddy process is simulated using the sealing structure model. The bearing capacity of the three-dimensional gap annular flow in the sealing structure model at different eddy positions after the eddy momentum is simulated, and the stiffness coefficient and damping coefficient of the sealing structure model during the rotor eddy after the eddy momentum are calculated as follows: Where, is the rotor's vortex velocity in the x direction; is the vortex velocity of the rotor in the y direction.

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