A Fluid-Structure Interaction Computational Model of an Elastic Ring Squeeze Film Damper

Abstract

The invention discloses a fluid-solid coupling calculation model of an elastic ring type squeeze film damper, which uses the Reynolds equation as the oil film control differential equation of the oil film, thereby simplifying the three-dimensional fluid mechanics model of the oil film into a two-dimensional model, reducing the number of degrees of freedom of the ERSFD fluid-solid coupling model, compressing the calculation scale, and significantly saving calculation time. In addition, the deflection curve differential equation of the beam is used to describe the structural deformation of the elastic ring, simplifying the three-dimensional structural mechanics model into a one-dimensional model, and according to the working state of the elastic ring, the boundary condition of the elastic ring segment is set to a simply supported type, eliminating the contact iteration process between the boss-bearing seat and the boss-bearing outer ring, which provides a basis for further improving the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of elastic ring type squeeze film dampers, and in particular relates to a fluid-solid coupling calculation model of an elastic ring type squeeze film damper. Background Art

[0002] The elastic ring squeeze film damper (ERSFD) achieves vibration reduction through the coupling effect of the elastic ring and the oil film. The overall structure of the elastic ring is a short cylindrical ring, and evenly distributed bosses are processed on the inner and outer surfaces of the cylindrical ring. In engineering applications, the number of bosses on the inner and outer surfaces of the elastic ring is equal, and the inner and outer bosses are in a staggered distribution structure. The elastic ring of ERSFD is installed between the bearing seat and the bearing. Due to the presence of the boss and the sealing device at the end of the elastic ring, multiple segmented oil film cavities are formed on the inner and outer ring surfaces of the elastic ring. The oil supply device provides lubricating oil of a certain pressure and flow rate to the oil film cavity, forming an elastic ring squeeze film damper.

[0003] Engineering applications have shown that a well-designed ERSFD can have a very significant vibration suppression effect. Russia has done relatively well in this regard, and ERSFD has important applications in many types of Russian aircraft engines.

[0004] At present, the construction of the structural mechanics model of the elastic ring mainly relies on the finite element method, and the construction of the fluid mechanics model of the oil film mainly relies on various flow models proposed in the fluid mechanics theory, among which the k-ε model is the main one.

[0005] As described above, the vibration reduction mechanism of ERSFD, ERSFD itself produces damping effect through the fluid-solid coupling of oil film and elastic ring. So far, the fluid-solid coupling mechanism of ERSFD has not been fully understood, which restricts the improvement of design level. Understanding the fluid-solid coupling mechanism of ERSFD is inseparable from the mechanical model of ERSFD. Summary of the invention

[0006] In order to solve at least one of the above technical problems, the present disclosure aims to construct a fluid-solid coupling calculation model of an elastic ring squeeze film damper with high calculation efficiency and short calculation time.

[0007] In order to achieve the purpose of this disclosure, the technical solutions adopted by this disclosure are as follows:

[0008] A fluid-solid coupling calculation model of an elastic ring squeeze film damper includes:

[0009] Ignore the change of pressure along the radial gap direction of the oil film, simplify the three-dimensional model of the fluid in the fluid domain into a two-dimensional model; use the Reynolds equation to establish the oil film control differential equation between the oil film pressure and the oil film thickness in the fluid domain;

[0010] The three-dimensional structural model of each segment of the elastic ring in the solid domain is converted into a one-dimensional beam model, and the deformation control equation of the elastic ring corresponding to the elastic ring segment is established according to the deflection curve differential equation;

[0011] Determine the boundary condition equation of the oil film pressure according to the circumferential boundary condition and the axial boundary condition;

[0012] The calculation model is formed according to the oil film control differential equation, the elastic ring deformation control equation and the boundary condition equation.

[0013] Optionally, the oil film control differential equation between the oil film pressure and the oil film thickness includes a control differential equation between the inner oil film pressure and the inner oil film thickness, and a control differential equation between the outer oil film pressure and the outer oil film thickness; wherein,

[0014] The governing differential equation between the inner oil film pressure and the inner oil film thickness is:

[0015]

[0016] In the formula, R i represents the radius of the oil film in the middle layer, p i (θ,z,t) represents the internal oil film pressure, h i (θ, z, t) is the inner oil film thickness, r(θ, z, t) is the deformation function of the elastic ring, Ω represents the angular velocity of the journal vortex, μ represents the viscosity of the oil, θ and z represent the circumferential and axial coordinates respectively, and t represents time;

[0017] The governing differential equation between the outer oil film pressure and the outer oil film thickness is:

[0018]

[0019] In the formula, p e (θ,z,t) represents the pressure of the outer oil film, h e (θ,z,t) is the thickness of the outer oil film, R e Represents the radius of the outer oil film in the middle layer.

[0020] Alternatively, the governing differential equation between oil film pressure and oil film thickness is:

[0021] Inner oil film thickness h i (θ,z,t) is obtained by the following function:

[0022]

[0023] represents the initial design clearance of the inner oil film section, r(θ,t) is the elastic deformation of the elastic ring, x(t) and y(t) represent the displacement of the rotor journal in the radial plane along the two coordinate axes, and Ω is the vortex angular velocity of the rotor journal;

[0024] External oil film thickness h e (θ,z,t) is obtained by the following function:

[0025]

[0026] Represents the initial design gap of the outer oil film.

[0027] Optionally, the elastic deformation r(θ,t) of the elastic ring is obtained by the following function:

[0028]

[0029] It describes the spatial form of the elastic ring deformation in cylindrical coordinates, which is obtained by the elastic ring deformation control equation corresponding to the elastic ring segment. Represents the temporal shape function of the elastic ring segment.

[0030] Optionally, the displacements x(t) and y(t) of the rotor journal in the radial plane along the two coordinate axis directions are obtained by the following functions:

[0031] x(t)=A r cos(Ωt)

[0032] y(t)=A r sin(Ωt)

[0033] In the formula, A r Represents the complex amplitude of the vibration, containing both magnitude and phase information.

[0034] Optionally, the elastic ring deformation control equation corresponding to the elastic ring segment is:

[0035]

[0036] Where η is the local coordinate along the tangent direction of the elastic ring segment, is the spatial morphology function of the elastic ring segment in the local coordinates, M(η) is the bending moment at the elastic ring segment η, E is the elastic modulus of the elastic ring segment, and I is the section moment of inertia of the elastic ring segment.

[0037] Optionally, the left truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is:

[0038]

[0039]

[0040] In the formula, F R is the support reaction force at the right end boss of the elastic ring segment, M(η) is the bending moment at the elastic ring segment η, η is the local coordinate along the tangent direction of the elastic ring segment, L is the length of the elastic ring segment, i represents the segment mark in the length direction after the elastic ring type squeeze film damper is expanded, is the internal oil film force concentration on the ring segment on the left side of the middle boss of the elastic ring segment, is the internal oil film force concentration on the ring segment located on the right side of the middle boss, q o (η) represents the external oil film force concentration of the current elastic ring segment, and τ is the auxiliary integral variable;

[0041] The right truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is:

[0042]

[0043]

[0044] In the formula, F L is the support reaction force at the left end boss of the elastic ring segment, M(η) is the bending moment at the elastic ring segment η, η is the local coordinate along the tangent direction of the elastic ring segment, L is the length of the elastic ring segment, i represents the segment mark in the length direction after the elastic ring type squeeze film damper is expanded, is the internal oil film force concentration on the ring segment on the left side of the middle boss of the elastic ring segment, is the internal oil film force concentration on the ring segment located on the right side of the middle boss, q o (η) represents the external oil film force intensity of the current elastic ring segment, and τ is the auxiliary integral variable.

[0045] Optionally, and q o (η) is obtained by the following formula,

[0046] Solve for the support reaction force F R and F L hour;

[0047] q(η)dη≈∑F k (θ,z,t)

[0048] In the formula, q represents and q o (η), F k (θ,z,t) represents the concentrated force on the kth grid area on the ring segment;

[0049] When solving the bending moment M(η), the following approximate relationship is obtained:

[0050] q(τ)dτ≈∑F k(θ,z,t)

[0051] In the formula, q represents and q o (τ).

[0052] Optionally, the concentrated force on the mesh area on the ring segment is calculated by the following formula:

[0053]

[0054] In the formula, θ and z represent the circumferential and axial coordinates respectively, t represents time, R represents the corresponding oil film radius, when calculating the outer oil film, it is the radius of the outer oil film in the middle layer, when calculating the inner oil film, it is the radius of the inner oil film in the middle layer, Represents the arithmetic mean of the pressure values ​​of the four vertices of the grid.

[0055]

[0056] Where, j represents the segment mark in the width direction after the elastic ring squeeze film damper is expanded, i represents the segment mark in the length direction after the ring squeeze film is expanded, and p i,j (θ,z,t) is obtained through the boundary condition equations.

[0057] Optionally, the boundary condition equations include an inner oil film pressure equation, an outer oil film pressure equation and an end oil film pressure equation; wherein,

[0058] The internal oil film pressure equation is:

[0059]

[0060] It indicates the central angular position of the qth inner oil film segment in the circumferential direction, the superscript i represents the inner oil film, and the subscript q represents the number of the oil film segment; represents the circumferential oil film width of the qth inner oil film segment, measured in angle; n i Indicates the number of inner oil film segments with positive oil film pressure;

[0061] The external oil film pressure equation is:

[0062]

[0063] It indicates the central angular position of the qth outer oil film segment in the circumferential direction, and the superscript e represents the outer oil film; It represents the circumferential oil film width of the qth outer oil film segment, expressed as an angle; n e Indicates the number of external oil film segments with positive oil film pressure;

[0064] The end oil film pressure equation is:

[0065]

[0066] p0 represents the oil supply pressure, θ represents the circumferential coordinate, and z0 represents the axial width of the elastic ring.

[0067] The present invention extracts the main mechanical characteristics of the elastic ring and oil film of ERSFD, ignores the secondary characteristics, and makes full use of the theories of structural mechanics and fluid mechanics to simplify the three-dimensional structural model of the solid domain in the traditional method into a one-dimensional structural model, and simplifies the three-dimensional model of the fluid in the fluid domain into a two-dimensional model. Therefore, while ensuring the calculation accuracy, the number of degrees of freedom of the ERSFD fluid-solid coupling model is greatly reduced, the calculation scale is compressed, and the calculation time can be significantly saved. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The accompanying drawings illustrate exemplary embodiments of the present disclosure and together with the description serve to explain the principles of the present disclosure. These drawings are included to provide a further understanding of the present disclosure and are incorporated in and constitute a part of this specification.

[0069] Figure 1 is a schematic structural diagram of an elastic ring type squeeze film damper in the present disclosure;

[0070] Figure 2 It is a schematic diagram of a fluid-solid coupling calculation model for establishing an elastic ring type squeeze film damper in the present disclosure;

[0071] Figure 3 It is the simplified geometry and meshing of a single elastic ring segment in the present disclosure;

[0072] Figure 4 It is the simplified geometric structure and mesh division of a single elastic ring segment after it is unfolded into a plane in the present disclosure;

[0073] Figure 5 It is the principle of calculating the concentrated force of each grid area on a single elastic ring segment in the present disclosure;

[0074] Figure 6 is the equivalent beam model of a single elastic ring segment in the present disclosure. DETAILED DESCRIPTION

[0075] The present disclosure is further described in detail below in conjunction with the accompanying drawings and implementations. It is understood that the specific implementations described herein are only used to explain the relevant content, rather than to limit the present disclosure. It should also be noted that, for ease of description, only the parts related to the present disclosure are shown in the accompanying drawings.

[0076] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in the present disclosure may be combined with each other. The present disclosure will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0077] See also Figure 2 As shown, a fluid-solid coupling calculation model of an elastic ring squeeze film damper includes:

[0078] Ignore the change of pressure along the radial gap direction of the oil film, simplify the three-dimensional model of the fluid in the fluid domain into a two-dimensional model; use the Reynolds equation to establish the oil film control differential equation between the oil film pressure and the oil film thickness in the fluid domain, assuming that the elastic ring is not deformed or giving an estimated oil film thickness; when assuming that the elastic ring is not deformed, the oil film thickness is the original thickness of the oil film, and the oil film thickness value estimated according to the approximate initial thickness and compression thickness of the elastic ring is 0.35mm, 0.4mm, 0.45mm or other thicknesses. The squeezed oil film can have one or more layers of ring structure, and the fluid-solid coupling performance of each layer of the oil film can be calculated by the calculation method disclosed in the present invention.

[0079] In this application, a layer of ring is used as an example. According to the structural characteristics and working characteristics of ERSFD used in engineering, the following three main assumptions are proposed: (a) the flow of the oil film is laminar; (b) the lubricating oil is a Newtonian fluid; (c) the influence of the curvature of the oil film is ignored. On this basis, the oil film control differential equation of the inner oil film of ERSFD can be obtained by using the microelement analysis method and ignoring the influence of small quantities. The elastic ring deformation control equation between the oil film pressure and the oil film thickness includes: the control differential equation between the inner oil film pressure and the inner oil film thickness, and the control differential equation between the outer oil film pressure and the outer oil film thickness;

[0080] The governing differential equations between the internal oil film pressure and the internal oil film thickness include:

[0081]

[0082] In the formula, R i represents the radius of the oil film in the middle layer, p i (θ,z,t) represents the internal oil film pressure, h i (θ, z, t) is the inner oil film thickness, r(θ, z, t) is the deformation function of the elastic ring, Ω represents the angular velocity of the journal vortex, μ represents the viscosity of the oil, θ and z represent the circumferential and axial coordinates respectively, and t represents time;

[0083] The quantitative relationship between the outer oil film pressure and the outer oil film thickness is:

[0084]

[0085] In the formula, p e (θ,z,t) represents the pressure of the outer oil film, h e (θ,z,t) is the thickness of the outer oil film, R e Represents the radius of the outer oil film in the middle layer.

[0086] And the inner oil film thickness h in formula (1) i (θ,z,t) satisfies the quantitative relationship between the deformation of the elastic ring and the thickness of the inner oil film:

[0087] For the inner and outer oil films, there is a definite quantitative relationship between the oil film thickness and the oil film pressure distribution. The thickness of the inner and outer oil films of ERSFD is closely related to the initial design clearance of the oil film segment, the displacement of the rotor journal and the deformation of the elastic ring. Assume that the thickness of the inner oil film is represented by h(θ,z,t), which is a function of the spatial position and time of the oil film.

[0088] h i (θ,z,t)=c i 0+r(θ,z,t)-x(θ,z,t)cos(Ωt)-y(θ,z,t)sin(Ωt) (3)

[0089] In the formula, h i (θ,z,t) is the inner oil film thickness, represents the initial design gap of the inner oil film section, which is a constant. r(θ,z,t) is the elastic deformation of the elastic ring. x(θ,z,t) and y(θ,z,t) represent the displacement of the rotor journal in the radial plane along the two coordinate axes, respectively. Ω is the vortex angular velocity of the rotor journal. Considering that the axial dimension of the elastic ring is small, the change of its elastic deformation along the axial direction is ignored. r(θ,z,t) degenerates into a function of θ and t, that is, it becomes r(θ,t). In subsequent studies, the finite element method is planned to be used to establish the dynamic model of the rotor system. The displacement of the rotor journal is the displacement value of the rotor node where ERSFD is located. Since ERSFD only affects the rotor at one node in the rotor system modeling, x(θ,z,t) and y(θ,z,t) degenerate into a function of t, that is, they become x(t) and y(t), respectively. Therefore, equation (3) can be re-expressed in a more concise form, that is,

[0090]

[0091] For the outer oil film, its thickness is only directly related to the deformation of the elastic ring. Let the thickness of the outer oil film be h e (θ,z,t) represents,

[0092]

[0093] In the formula, h e (θ,z,t) is the thickness of the outer oil film, Represents the initial design gap of the external oil film, which is also a constant.

[0094] Similarly, since r(θ,z,t) degenerates into a function of θ and t, that is, it becomes r(θ,t), equation (6) can be simplified as:

[0095]

[0096] The determination of the deformation function r(θ, t) of the elastic ring is the key to establishing the ERSFD fluid-structure interaction model. Furthermore, it is crucial to determine the deformation mechanism of the elastic ring and describe it quantitatively with mathematical functions. As discussed in the previous section, the deformation of the elastic ring is a function of the angular position θ and time t, that is, the deformation of the elastic ring is a function of both space and time dimensions.

[0097] The deformation of the elastic ring is caused by the oil film pressure, and the oil film pressure is constantly fluctuating. In essence, the deformation of the elastic ring is a vibration problem of the elastic body.

[0098] According to the theory of continuum mechanics, the vibration of an elastic body can be separated in space and time. Based on this conclusion, the deformation of an elastic ring can be expressed as follows:

[0099]

[0100] In the formula, It describes the spatial form of the elastic ring deformation in cylindrical coordinates, which is obtained by the elastic ring deformation control equation corresponding to the elastic ring segment. Represents the temporal shape function of the elastic ring segment.

[0101] To obtain r(θ,t), it is necessary to analyze the governing equations for the deformation of the elastic ring in the solid domain.

[0102] The three-dimensional structural model of each segment of the elastic ring in the solid domain is converted into a one-dimensional beam model, and the elastic ring deformation control equation corresponding to the elastic ring segment is established according to the deflection curve differential equation. The specific analysis method is:

[0103] See also Figures 3 to 6 As shown in the figure, the elastic ring is a segmented structure along the circumferential direction (θ direction), and each segment is separated from the adjacent two segments by a boss. In engineering practice, the number of elastic ring segments is relatively large. In addition, there is usually a gap or transition fit between the boss and the bearing seat and the outer ring of the bearing. Therefore, each ring segment can be equivalent to a beam, and the constraint form of the beam at the end point is a simply supported type. This equivalence has a high degree of similarity both in geometry and boundary conditions. Based on this, the geometric shape of the elastic ring in space can be described by the differential equation of the deflection curve of the beam. For the convenience of expression, refer to Figure 1As shown in the figure, a local plane coordinate system o′-ηξ is established at the elastic ring segment under study, where o′η is along the length direction of the elastic ring segment, o′ξ is perpendicular to o′η, and the coordinate origin o′ is located at the midpoint of the neutral layer of the elastic ring. The difference between o′-ηξ and the global coordinate system O-rθz is only a rotation transformation around the global coordinate system Oz axis, and the rotation angle is the center position angle of the elastic ring segment. In this way, the elastic ring deformation control equation corresponding to the elastic ring segment in the local coordinate system o′-ηξ is:

[0104]

[0105] Where η is the local coordinate along the tangent direction of the elastic ring segment, is the spatial morphology function of the elastic ring segment under the local coordinates, M(η) is the bending moment of the elastic ring segment, which is a function of the local coordinates η of the elastic ring segment, E is the elastic modulus of the elastic ring segment, I(η) is the section inertia moment of the ring segment, the elastic ring segment studied here is a uniform cross-section structure, so I(η) is a constant, which can be abbreviated as I, and then, formula (9) can be abbreviated as

[0106]

[0107] The bending moment M(η) exerted on the elastic ring segment in formula (10) can be determined by integrating the internal and external oil film pressures exerted on the elastic ring segment.

[0108] First, it is necessary to determine the bending moment at each location of the elastic ring segment, so that the deflection at each location of the elastic ring segment can be further calculated. To this end, the force analysis of the entire ring segment is first performed to determine the support reaction force at the boss. According to the equilibrium equation of the plane force system, the support reaction force F at the two bosses of the elastic ring segment can be obtained. L and F R .

[0109] The left truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is:

[0110]

[0111] In the formula, F R is the support reaction force at the right end boss of the elastic ring segment, η is the local coordinate along the tangent direction of the elastic ring segment, and L is the length of the elastic ring segment.

[0112] After obtaining the support reaction force at the outer boss of the elastic ring segment, the next step is to determine the bending moment M (η) at each location of the elastic ring segment using the truncation method;

[0113]

[0114] In the formula, is the internal oil film force concentration on the ring segment on the left side of the middle boss of the elastic ring segment, is the internal oil film force concentration on the ring segment located on the right side of the middle boss, q o (η) represents the external oil film force intensity of the current elastic ring segment, and τ is the auxiliary integral variable.

[0115] The right truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is:

[0116]

[0117] In the formula, F L is the support reaction force at the left end boss of the elastic ring segment, η is the local coordinate along the tangent direction of the elastic ring segment, and L is the length of the elastic ring segment.

[0118] After obtaining the support reaction force at the outer boss of the elastic ring segment, the next step is to determine the bending moment M (η) at each location of the elastic ring segment using the truncation method;

[0119]

[0120] q o (η), and q o (τ) is obtained by the following formula;

[0121] See also Figure 5 , Figure 6 As shown, the concentrated force on the kth grid area on the ring segment can be expressed as;

[0122]

[0123] In the formula, F k (θ,z,t) represents the concentrated force on the kth grid area on the ring segment, θ and z represent the circumferential and axial coordinates respectively, t represents time, and R represents the corresponding oil film radius. When calculating the outer oil film, R i , when calculating the inner oil film, R e ,and Represents the arithmetic mean of the pressure values ​​of the four vertices of the grid, that is,

[0124]

[0125] i represents the segmentation mark in the length direction after the annular squeeze oil film is expanded; j represents the segmentation mark in the width direction after the annular squeeze oil film is expanded.

[0126] The numerical integration method is used to solve the support reaction force F R and F L When , there is the following approximate relationship:

[0127] q(η)dη≈∑F k (θ,z,t)

[0128] In the formula, q represents and q o (η), the summation sign indicates that the concentrated forces on all grids in the same axial direction are summed.

[0129] Similarly, when the numerical integration method is used to solve the bending moment M(η), the following approximate relationship is obtained:

[0130] q(τ)dτ≈∑F k (θ,z,t)

[0131] In the formula, q represents and q o (τ).

[0132] After determining the concentrated force on each grid at time t, the concentrated force on each grid of the elastic ring segment is translated to the middle section of the elastic ring segment along the axial direction. According to the force translation theorem, it is necessary to add a bending moment to the middle section of the elastic ring segment after the force translation. However, considering that the bending section stiffness of the elastic ring segment on the circumferential section is much greater than its value on the axial section, the deformation caused by the additional bending moment can be ignored. Only the bending deformation of the elastic ring segment caused by the concentrated force obtained after the translation is considered. At this time, the deformation problem of the elastic ring is transformed into a classic beam bending problem.

[0133] The elastic ring deformation control equation corresponding to the elastic ring segment is solved by the difference method, the deformation equation of the elastic ring segment's spatial morphology function in the local coordinate system is discretized, and a set of equations for solving the elastic ring segment's spatial morphology is established. The equations are solved by the Gaussian elimination method to obtain the elastic ring segment's spatial deformation.

[0134] The difference format is:

[0135]

[0136] In the formula, is the spatial deformation of each node of the elastic ring segment at the current time t, n is the number of discrete points, M k is the bending moment of each node of the elastic ring segment. Equation (17) is a linear algebraic equation system consisting of n-2 differential equations. Combined with two boundary conditions, the Gaussian elimination method is used to solve the linear algebraic equation system to obtain the spatial deformation of each node of the elastic ring segment at the current time t.

[0137] Obtain Can be converted to

[0138] Assuming that the position angle of the center of the elastic ring segment currently being studied in the global coordinate system is θ0, then the following relationship exists:

[0139] θ=η / R m +θ0 (18)

[0140] Formula (18) is the conversion formula between global coordinates and local coordinates, where Rm represents the radius of the circle where the neutral layer of the elastic ring segment is located.

[0141] In formula (8), It describes the time form of the vibration of each cross section of the elastic ring. The deformation of the elastic ring is caused by the vortex of the journal, which causes the internal oil film to generate pressure. The pressure is transmitted to the elastic ring, causing the deformation of the elastic ring segment. Therefore, the pulsation frequency of the pressure is equal to the vortex frequency of the journal, that is, the pulsation frequency is the journal vortex frequency Ω. The elastic ring generates forced vibration due to pressure pulsation. According to the linear vibration theory, the forced vibration frequency of each cross section of the elastic ring segment is also Ω. The form of the elastic ring vibration is similar to that of the continuum vibration, which is a simple harmonic function form. At the same time, considering that the actual deformation of the elastic ring will not have negative deformation, there is

[0142]

[0143] At this point, the deformation function r(θ, t) of the elastic ring segment is determined. Next, the deformation of the elastic ring segment caused by the journal vortex is determined.

[0144] For most rotor systems, under normal operating conditions, the steady-state response caused by unbalanced excitation is the most prominent. At this time, the steady-state response is in the same frequency as the unbalanced excitation force, but there is a certain lag in phase, and the lag angle is determined by the inherent properties of the system. Therefore, the vibration frequency of the rotor journal is dominated by the rotation frequency, so it can be assumed that the function form of the rotor journal vortex is

[0145] x(t)=A r cos(Ωt) (20)

[0146] y(t)=A r sin(Ωt) (21)

[0147] In the formula, x(t) and y(t) represent the vibration of the journal along the two radial directions, A r Represents the complex amplitude of the vibration, containing both magnitude and phase information.

[0148] Next, the boundary condition equations of the oil film pressure are determined based on the circumferential boundary conditions and the axial boundary conditions. They are mainly used to solve the pressure value in the elastic annular squeeze oil film, which is an indispensable part of the ERSFD fluid-solid coupling model. The boundary condition equations include the inner oil film pressure equation, the outer oil film pressure equation, and the end oil film pressure equation.

[0149] The boss on the elastic ring makes the oil film in ERSFD exist in the form of segments between the elastic ring-journal and the elastic ring-support. When calculating, it is necessary to model each segment separately and determine its circumferential boundary conditions in segments. According to the working principle of ERSFD, there is no oil film or the oil film is very thin at the boss, so the pressure of the oil film at the boss is considered to be zero, which is equivalent to giving the circumferential boundary conditions of the pressure distribution of the oil film segment between the two bosses. The inner oil film pressure equation for the inner oil film is:

[0150]

[0151] In formula (22), It indicates the central angular position of the qth inner oil film segment in the circumferential direction, the superscript i represents the inner oil film, and the subscript q represents the number of the oil film segment; represents the circumferential oil film width of the qth inner oil film segment, measured in angle; n i It indicates the number of inner oil film segments with positive oil film pressure. It is generally believed that in ERSFD, only the oil film within the π angle range has load-bearing capacity (when the entire circumference is filled with oil). i The value is half of the total number of inner oil film segments.

[0152] Similarly, for the outer oil film section, the outer oil film pressure equation is:

[0153]

[0154] In formula (23), It indicates the central angular position of the qth outer oil film segment in the circumferential direction, and the superscript e represents the outer oil film; It represents the circumferential oil film width of the qth outer oil film segment, expressed as an angle; n e It represents the number of external oil film segments with positive oil film pressure, and its value is half of the number of external oil film segments.

[0155] For the axial boundary conditions, the pressure of the oil film segment at the end position is the oil supply pressure p0, and the end oil film pressure equation is:

[0156]

[0157] p0 represents the oil supply pressure, θ represents the circumferential coordinate, and z0 represents the axial width of the elastic ring.

[0158] Forming a calculation model based on the above-mentioned oil film control differential equation, elastic ring deformation control equation and boundary condition equation can compress the calculation scale and significantly save calculation time.

[0159] So far, a complete and efficient fluid-solid coupling model of ERSFD has been established, and its efficiency is reflected in two aspects: First, the Reynolds equation is used as the control differential equation of the oil film, thereby simplifying the three-dimensional fluid mechanics model of the oil film into a two-dimensional model, reducing the number of degrees of freedom of the ERSFD fluid-solid coupling model, compressing the calculation scale, and significantly saving calculation time. Second, the deflection curve differential equation of the beam is used to describe the structural deformation of the elastic ring, simplifying the three-dimensional structural mechanics model into a one-dimensional model, and according to the working state of the elastic ring, the boundary conditions of the elastic ring segment are set as simply supported, eliminating the contact iteration process between the boss-bearing seat and the boss-bearing outer ring, which provides a basis for further improving the calculation efficiency.

[0160] In the description of this specification, the description with reference to the terms "one embodiment / method", "some embodiments / methods", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment / method or example are included in at least one embodiment / method or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment / method or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments / methods or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments / methods or examples described in this specification and the features of the different embodiments / methods or examples, unless they are contradictory.

[0161] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0162] Those skilled in the art should understand that the above embodiments are only for the purpose of clearly illustrating the present disclosure, and are not intended to limit the scope of the present disclosure. For those skilled in the art, other changes or modifications may be made based on the above disclosure, and these changes or modifications are still within the scope of the present disclosure.

Claims

1. A fluid-solid coupling calculation model for an elastic ring squeeze film damper, characterized in that: include: Ignore the change of pressure along the radial gap direction of the oil film, simplify the three-dimensional model of the fluid in the fluid domain into a two-dimensional model; use the Reynolds equation to establish the oil film control differential equation between the oil film pressure and the oil film thickness in the fluid domain; The three-dimensional structural model of each segment of the elastic ring in the solid domain is converted into a one-dimensional beam model, and the deformation control equation of the elastic ring corresponding to the elastic ring segment is established according to the deflection curve differential equation; Determine the boundary condition equation of the oil film pressure according to the circumferential boundary condition and the axial boundary condition; A calculation model is formed according to the oil film control differential equation, the elastic ring deformation control equation and the boundary condition equation; The oil film control differential equation between the oil film pressure and the oil film thickness includes the control differential equation between the inner oil film pressure and the inner oil film thickness, and the control differential equation between the outer oil film pressure and the outer oil film thickness; wherein, The governing differential equation between the inner oil film pressure and the inner oil film thickness is: In the formula, R i represents the radius of the oil film in the middle layer, p i (θ,z,t) represents the internal oil film pressure, h i (θ, z, t) is the inner oil film thickness, r(θ, z, t) is the deformation function of the elastic ring, Ω represents the angular velocity of the journal vortex, μ represents the viscosity of the oil, θ and z represent the circumferential and axial coordinates respectively, and t represents time; The governing differential equation between the outer oil film pressure and the outer oil film thickness is: In the formula, p e (θ,z,t) represents the pressure of the outer oil film, h e (θ,z,t) is the thickness of the outer oil film, R e represents the radius of the outer oil film in the middle layer; The elastic ring deformation control equation corresponding to the elastic ring segment is: Where η is the local coordinate along the tangent direction of the elastic ring segment, is the spatial morphology function of the elastic ring segment in the local coordinates, M(η) is the bending moment at the elastic ring segment η, E is the elastic modulus of the elastic ring segment, and I is the section moment of inertia of the elastic ring segment; The left truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is: In the formula, F R is the support reaction force at the right end boss of the elastic ring segment, M(η) is the bending moment at the elastic ring segment η, η is the local coordinate along the tangent direction of the elastic ring segment, L is the length of the elastic ring segment, i represents the segment mark in the length direction after the elastic ring type squeeze film damper is expanded, is the internal oil film force concentration on the ring segment on the left side of the middle boss of the elastic ring segment, is the internal oil film force concentration on the ring segment located on the right side of the middle boss, q o (η) represents the external oil film force concentration of the current elastic ring segment, and τ is the auxiliary integral variable; The right truncation method is used to obtain the cross-sectional bending moment at each location of the elastic ring. The specific formula is: In the formula, F L is the support reaction force at the left end boss of the elastic ring segment, M(η) is the bending moment at the elastic ring segment η, η is the local coordinate along the tangent direction of the elastic ring segment, L is the length of the elastic ring segment, i represents the segment mark in the length direction after the elastic ring type squeeze film damper is expanded, is the internal oil film force concentration on the ring segment on the left side of the middle boss of the elastic ring segment, is the internal oil film force concentration on the ring segment located on the right side of the middle boss, q o (η) represents the external oil film force concentration of the current elastic ring segment, and τ is the auxiliary integral variable; The boundary condition equations include the inner oil film pressure equation, the outer oil film pressure equation and the end oil film pressure equation; among them, The internal oil film pressure equation is: It indicates the central angular position of the qth inner oil film segment in the circumferential direction, the superscript i represents the inner oil film, and the subscript q represents the number of the oil film segment; represents the circumferential oil film width of the qth inner oil film segment, measured in angle; n i Indicates the number of inner oil film segments with positive oil film pressure; The external oil film pressure equation is: It indicates the central angular position of the qth outer oil film segment in the circumferential direction, and the superscript e represents the outer oil film; It represents the circumferential oil film width of the qth outer oil film segment, expressed as an angle; n e Indicates the number of external oil film segments with positive oil film pressure; The end oil film pressure equation is: p0 represents the oil supply pressure, θ represents the circumferential coordinate, and z0 represents the axial width of the elastic ring.

2. The fluid-solid coupling calculation model of the elastic ring squeeze film damper according to claim 1, characterized in that: The governing differential equation between oil film pressure and oil film thickness is: Inner oil film thickness h i (θ,z,t) is obtained by the following function: represents the initial design clearance of the inner oil film section, r(θ,t) is the elastic deformation of the elastic ring, x(t) and y(t) represent the displacement of the rotor journal in the radial plane along the two coordinate axes, and Ω is the vortex angular velocity of the rotor journal; External oil film thickness h e (θ,z,t) is obtained by the following function: Represents the initial design gap of the outer oil film.

3. The fluid-solid coupling calculation model of the elastic ring squeeze film damper according to claim 2, characterized in that: The elastic deformation r(θ,t) of the elastic ring is obtained by the following function: It describes the spatial form of the elastic ring deformation in cylindrical coordinates, which is obtained by the elastic ring deformation control equation corresponding to the elastic ring segment. Represents the temporal shape function of the elastic ring segment.

4. The fluid-solid coupling calculation model of the elastic ring squeeze film damper according to claim 2, characterized in that: The displacements x(t) and y(t) of the rotor journal in the radial plane along the two coordinate axes are obtained by the following functions: x(t)=A r cos(Ωt) y(t)=A r sin(Ωt) In the formula, A r Represents the complex amplitude of the vibration, containing both magnitude and phase information.

5. The fluid-solid coupling calculation model of the elastic ring squeeze film damper according to claim 1, characterized in that: and q o (η) is obtained by the following formula, Solve for the support reaction force F R and F L hour; q(η)dη≈∑F k (θ,z,t) In the formula, q represents and q o (η), F k (θ,z,t) represents the concentrated force on the kth grid area on the ring segment; When solving the bending moment M(η), the following approximate relationship is obtained: q(τ)dτ≈F k (θ,z,t) In the formula, q represents and q o (τ).

6. The fluid-solid coupling calculation model of the elastic ring squeeze film damper according to claim 5, characterized in that: The concentrated force on the mesh area of ​​the ring segment is calculated using the following formula: In the formula, θ and z represent the circumferential and axial coordinates respectively, t represents time, R represents the corresponding oil film radius, when calculating the outer oil film, it is the radius of the outer oil film in the middle layer, when calculating the inner oil film, it is the radius of the inner oil film in the middle layer, Represents the arithmetic mean of the pressure values ​​of the four vertices of the grid. Where, j represents the segment mark in the width direction after the elastic ring squeeze film damper is expanded, i represents the segment mark in the length direction after the ring squeeze film is expanded, and p i,j (θ,z,t) is obtained through the boundary condition equations.

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