Method for analyzing dynamic characteristics of sealing structure based on perturbation method

Abstract

The invention discloses a method for analyzing dynamic characteristics of a sealing structure based on a perturbation method, and relates to the technical field of sealing structure dynamics. The method comprises the following steps: firstly, establishing a sealing structure model, determining a three-dimensional fluid continuity equation and a momentum equation based on an overall flow theory and a perturbation method, taking a rotor eccentricity as a perturbation amount, decoupling the three-dimensional gap circulation in time and space, decomposing the eccentric vortex motion of the three-dimensional gap circulation into steady-state zero-order concentric vortex motion and transient first-order eccentric vortex motion, and finally obtaining the three-dimensional gap circulation. Solving a zero-order linear three-dimensional gap circulation fluid control equation set and a first-order linear three-dimensional gap circulation fluid control equation set to obtain three-dimensional gap circulation flow field distribution, performing pressure field integration on a contact surface of the rotor and the three-dimensional gap fluid, and simulating and obtaining hydrodynamic force bearing capacity borne by the rotor during vortex motion by using a sealing structure model to obtain hydrodynamic force bearing capacity of the rotor during vortex motion. The rigidity coefficient and the damping coefficient of the sealing structure model are obtained, the flowing condition of clearance circulation is truly restored, and the dynamic characteristic parameters of the sealing structure are accurately obtained.

Description

Technical Field

[0001] The 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 in the pump seal gap generates unevenly distributed pressure and velocity along the axial and circumferential directions, which is the dynamic characteristic of the seal structure. For the rotor system, this characteristic directly affects the critical speed and motion stability of the system, and has become an important part of evaluating the safety of the pump.

[0003] Considering that all the forces acting on the sealing structure are nonlinear forces, and there is currently a lack of a relatively reliable calculation method for the seal gap flow field, seal dynamic stiffness and damping, which seriously restricts the development of the wet critical speed analysis of the pump rotor. Therefore, it is urgent to propose a seal structure dynamic characteristics analysis method based on the perturbation method to accurately characterize the flow field results of the three-dimensional small gap circulation in the sealing structure, solve the characteristic coefficients such as dynamic pressure, bearing capacity, stiffness and damping of the three-dimensional small gap flow field, and provide an effective reference for the dynamic analysis of the sealing structure. Summary of the invention

[0004] The present invention aims to solve the above-mentioned problem 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, which provides 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: According to 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, and 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, and 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, perform linear approximation on the nonlinear terms in the steady-state zero-order concentric vortex and the transient first-order eccentric vortex, determine 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, combine the boundary conditions of the sealing structure model during concentric vortex and eccentric vortex, calculate 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, obtain the zero-order flow field result and the first-order flow field result 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;

[0009] 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, so as to obtain the radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity of the rotor surface after the rotor moves eccentrically;

[0010] Step 4, characterize the stiffness coefficient and damping coefficient based on the first-order linear three-dimensional gap circulation fluid control equation group, 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, and 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, the eccentricity is 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 overall flow theory as follows:

[0013]

[0014] Wherein, t is time; x is the annular coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the integral 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 integral flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the integral 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 integral flow theory; is the wall shear stress of the stator inner wall in the yz plane;

[0018] The circumferential momentum equation is:

[0019]

[0020] In the formula, 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 a steady-state zero-order concentric vortex and a transient first-order eccentric vortex, and obtain the zero-order perturbation equation group and the 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 friction coefficient of the stator wall, c1, c2, c3 are all Moody experimental constants, μ is the dynamic viscosity, e is 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 of the three-dimensional gap circulation in the sealing structure model are:

[0029]

[0030] in,

[0031]

[0032] In the formula, u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equation group of three-dimensional gap circulation.

[0033] Preferably, in step 2, when the rotor and stator in the sealing structure model swirl concentrically during the concentric swirl, the thickness h of the three-dimensional gap fluid does not change in the circumferential and axial directions, and the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model is 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 is performed on formula (9), and we get:

[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, so that the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equations, and the zero-order linear three-dimensional gap circulation fluid control equations are obtained.

[0046] Preferably, in step 2, during the eccentric vortex motion, 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 simple harmonic vortex;

[0050] 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. The vortex frequency is taken as the dominant response, and only the first-order harmonic in the series expansion is considered, so that each first-order flow field physical quantity is 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] In the formula, 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 annular first-order flow velocity; u 1c is the cosine coefficient of the annular first-order velocity;

[0053] Substitute formula (14) into the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equation group of the three-dimensional gap circulation into 6 nonlinear equations, which are:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, 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 axial velocity sinusoidal coefficient, expressed in forward difference format;

[0061] The nonlinear terms in each nonlinear equation are linearized, so that the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equation group, and the first-order linear three-dimensional gap circulation fluid control equation group is obtained.

[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 equation group 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 circulation in the sealing structure model are calculated using the first-order linear three-dimensional gap circulation fluid control equations to determine the first-order velocity field and first-order pressure field of the three-dimensional gap circulation.

[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] In the formula, 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, among which k xxis the stiffness coefficient in the x direction, k xy and k yx are the 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, among which 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 the mass influence coefficients, among which, 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 vortex 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 speed 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 fluid control equations:

[0073]

[0074] The sealing structure model is used to simulate the rotor vortex process. 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 specific speed are obtained by using the differential method.

[0075] The eddy momentum Δx and Δy are introduced near the rotor eddy position, and the eddy momentum Δx and Δy are set. 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:

[0076]

[0077] In the formula, 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. The fluid control equations are used to characterize the sealing water dynamic load when the rotor vortexes in an arbitrary elliptical trajectory at different vortex speeds, breaking the limitations of the traditional rotor center vortex and improving 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 a steady-state zero-order concentric vortex and a transient first-order eccentric vortex by introducing the eccentricity e as the perturbation quantity, thereby obtaining a zero-order perturbation equation group and a first-order perturbation equation group 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 equation group 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, and can be widely used in 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 It is a 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 is further described below in conjunction with 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: According to 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 is composed of a stator, a rotor and a gap fluid. Figure 1 As shown, the rotor rotates counterclockwise in the stator and is eccentrically set, the eccentricity is 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 inlet 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, 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, and the polar coordinate system is used to determine the position coordinates in the longitudinal section of the sealing structure model, with the section 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] The three-dimensional fluid continuity equation and momentum equation of the sealing structure model are determined based on the overall flow theory and perturbation method. The rotor eccentricity is used as the perturbation quantity, 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] Wherein, t is time; x is the annular coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the integral 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 integral flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the integral 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 integral flow theory; is the wall shear stress of the stator inner wall in the yz plane.

[0096] The circumferential momentum equation is:

[0097]

[0098] In the formula, 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 friction coefficient of the stator wall, c1, c2, c3 are all Moody experimental constants, μ is the dynamic viscosity, e is 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 of the three-dimensional gap circulation in the sealing structure model are:

[0108]

[0109] in,

[0110]

[0111] In the formula, u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equation group of three-dimensional gap circulation.

[0112] Step 2, use numerical methods such as finite element method, bisection method, finite difference method, simple harmonic vortex hypothesis, etc. to linearly approximate the nonlinear terms in the steady-state zero-order concentric vortex and transient first-order eccentric vortex, derive the zero-order linear three-dimensional gap circulation fluid control equations and the first-order linear three-dimensional gap circulation fluid control equations, combine 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, obtain the zero-order flow field results and the 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 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 the concentric swirl, and the thickness h of the three-dimensional gap fluid does not change in the circumferential θ direction and the axial z direction. Then, the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model is 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] In the formula, F1 and F2 are intermediate parameters used for simplification.

[0120] Taylor expansion is performed on formula (9), and we get:

[0121]

[0122] in,

[0123]

[0124] Where u0 0 Expand the position points 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] When setting the boundary conditions of the sealing structure model during concentric vortex motion, including the inlet flow velocity and outlet static pressure of the sealing structure model, the zero-order flow field result of the three-dimensional gap circulation in the sealing structure model is calculated using the zero-order linear three-dimensional gap circulation fluid control equation group, and the zero-order flow velocity field and zero-order pressure field of the three-dimensional gap circulation are determined. In this embodiment, the inlet flow velocity of the sealing structure model is set to 5m / s and the outlet static pressure is set to 0Pa. The input parameters for the zero-order linear three-dimensional gap circulation fluid control equation group are shown in Table 1.

[0127] Table 1 Input parameters of zero-order linear three-dimensional gap annular flow fluid 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, and the stator center O vortexes around the rotor axis O1 in dynamic state. The vortex trajectory of the rotor axis is:

[0131]

[0132] In the formula, 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 rotation speed is the dominant response, so 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 set to simple harmonic form, and the simple harmonic form is used to represent the physical quantities of the first-order flow field, and 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] In the formula, 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 annular first-order flow velocity; u 1c is the cosine coefficient of the annular first-order flow velocity.

[0136] Substitute formula (14) into the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equation group of the three-dimensional gap circulation into 6 nonlinear equations, which are:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] In the formula, 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; It 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 first-order perturbation equations of the three-dimensional gap circulation 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 circulation fluid control equation group are shown in Table 2. The first-order linear three-dimensional gap circulation fluid control equation group is used to calculate the first-order flow field results of the three-dimensional gap circulation in the sealing structure model, and determine the first-order velocity field and first-order pressure field of the three-dimensional gap circulation.

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

[0147]

[0148] The nonlinear terms in each nonlinear equation are linearized, so that the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equation group, and the first-order linear three-dimensional gap circulation fluid control equation group is obtained.

[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, integrate the pressure field of the three-dimensional gap circulation 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 moves eccentrically, the bearing force on the three-dimensional gap fluid of the sealing structure model is:

[0152]

[0153] in,

[0154]

[0155]

[0156] In the formula, 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, among which k xx is the stiffness coefficient in the x direction, k xy and k yx are the 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, among which 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 the mass influence coefficients, among which, 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 vortex 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 duration of the simulation cycle is preset to 3.6s. The simulation cycle is divided into time intervals of 0.1s to obtain the vortex position and vortex speed of the rotor at different vortex moments. In this embodiment, R is set w =0.005m, Ω=100rad / s=5π / 9, use 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 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, determine the velocity field (i.e., the axial velocity field and circumferential velocity field of the three-dimensional gap circulation) and pressure field of the three-dimensional gap circulation during the vortex process, and obtain the bearing capacity of the three-dimensional gap circulation at each moment in the preset simulation period, and 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 the tangential hydrodynamic bearing capacity F Y , respectively, the radial hydrodynamic bearing capacity F on the rotor wall is obtained X and the 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 equation group, 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, and 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, they are 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 fluid 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 at different whirl moments, steps 1 to 3 are used to perform simulation using the sealing structure model to obtain the stiffness coefficient and damping coefficient of the sealing structure model at a specific position and a specific speed.

[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 simulated, and the stiffness coefficient and damping coefficient of the sealing structure model during the rotor eddy after the action of eddy momentum are:

[0163]

[0164] In the formula, 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 according to the analytical expression between the seal hydrodynamic bearing capacity and the stiffness matrix and the damping matrix, and solves the characteristic coefficients such as the flow field dynamic pressure, bearing capacity, stiffness and damping of the three-dimensional gap circulation by adopting a semi-analytical method, thereby realizing the accurate acquisition of the dynamic characteristics of the sealing structure, and providing a basis for the dynamic analysis of small gap sealed pumps such as nuclear pumps / 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 protection scope of the present invention.

Claims

1. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method, characterized in that: The following steps are involved: Step 1: According to 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, and 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, and 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, perform linear approximation on the nonlinear terms in the steady-state zero-order concentric vortex and the transient first-order eccentric vortex, determine 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, combine the boundary conditions of the sealing structure model during concentric vortex and eccentric vortex, calculate 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, obtain the zero-order flow field result and the first-order flow field result 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; 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, so as to obtain the radial hydrodynamic bearing capacity and tangential hydrodynamic bearing capacity of the rotor surface after the rotor moves eccentrically; Step 4, characterize the stiffness coefficient and damping coefficient based on the first-order linear three-dimensional gap circulation fluid control equation group, 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, and 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 method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in claim 1, characterized in that: 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, the eccentricity is 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 method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in 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: Wherein, t is time; x is the annular coordinate, z is the axial coordinate; ρ is the fluid density; h is the thickness of the three-dimensional gap annular flow under the integral 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 integral flow theory; w is the axial flow velocity of the three-dimensional gap annular flow under the integral 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 integral flow theory; is the wall shear stress of the stator inner wall in the yz plane; The circumferential momentum equation is: In the formula, 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 a steady-state zero-order concentric vortex and a transient first-order eccentric vortex, and obtain the zero-order perturbation equation group and the 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 friction coefficient of the stator wall, c1, c2, c3 are all Moody experimental constants, μ is the dynamic viscosity, e is 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 of the three-dimensional gap circulation in the sealing structure model are: in, In the formula, u a 、u b 、u c 、u d They are all intermediate calculation quantities of the first-order perturbation equation group of three-dimensional gap circulation.

4. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in claim 3, characterized in that: In step 2, the rotor and stator in the sealing structure model swirl concentrically during the concentric swirl, and the thickness h of the three-dimensional gap fluid does not change in the circumferential and axial directions. Then, the zero-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model is 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 is performed on formula (9), and we get: in, Where u0 0 Expand position points for Taylor; Then, the nonlinear terms in formula (5) and formula (11) are linearized, so that the zero-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equations, and the zero-order linear three-dimensional gap circulation fluid control equations are obtained.

5. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in claim 4, characterized in that: In step 2, during the eccentric vortex motion, 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 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. The vortex frequency is taken as the dominant response, and only the first-order harmonic in the series expansion is considered, so that each first-order flow field physical quantity is 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: In the formula, 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 annular first-order flow velocity; u 1c is the cosine coefficient of the annular first-order velocity; Substitute formula (14) into the first-order perturbation equation group of the three-dimensional gap circulation in the sealing structure model, thereby transforming the first-order perturbation equation group of the three-dimensional gap circulation into 6 nonlinear equations, which are: ① ② ③ ④ ⑤ ⑥ In the formula, 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 axial velocity sinusoidal coefficient, expressed in forward difference format; The nonlinear terms in each nonlinear equation are linearized, so that the first-order perturbation equations of the three-dimensional gap circulation in the sealing structure model are transformed into a linear equation group, and the first-order linear three-dimensional gap circulation fluid control equation group is obtained.

6. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in 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 circulation in the sealing structure model are calculated using the zero-order linear three-dimensional gap circulation fluid control equations, and the zero-order velocity field and zero-order pressure field of the three-dimensional gap circulation 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 circulation in the sealing structure model are calculated using the first-order linear three-dimensional gap circulation fluid control equations to determine the first-order velocity field and first-order pressure field of the three-dimensional gap circulation. 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 as claimed in claim 6, characterized in that: In step 3, after the rotor moves eccentrically, the bearing force on the three-dimensional gap fluid of the sealing structure model is: in, In the formula, 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, among which k xx is the stiffness coefficient in the x direction, k xy and k yx are the 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, among which 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 the mass influence coefficients, among which, 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 vortex 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 speed 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. A method for analyzing dynamic characteristics of a sealing structure based on a perturbation method as claimed in claim 7, characterized in that: In step 4, since the stiffness coefficient and 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 fluid control equations: The sealing structure model is used to simulate the rotor vortex process. 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 specific speed are obtained by using the differential method. The eddy momentum Δx and Δy are introduced near the rotor eddy position, and the eddy momentum Δx and Δy are set. 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: In the formula, 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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