Spiral bevel gear system dynamics modeling method based on bidirectional fluid-solid coupling

Abstract

The invention relates to a spiral bevel gear system dynamics modeling method based on bidirectional fluid-solid coupling, and belongs to the technical field of aviation transmission, and the method comprises the following steps: S1, calculating the radial deformation and deformation speed of an elastic ring through an analytical method; s2, solving a transient control equation of oil film pressure by taking the radial deformation and the deformation speed of the elastic ring calculated in the step S1 as input to obtain ERSFD internal and external oil film pressure distribution; obtaining a rigidity coefficient and a damping coefficient of the oil film through numerical integration; s3, establishing a kinetic model of the spiral bevel gear transmission system by adopting a lumped parameter method, and deducing a differential equation of the gear system; and S4, through the ERSFD oil film dynamic characteristics calculated in the S2, internal excitation and external excitation are comprehensively considered, an ERSFD-spiral bevel gear system coupling dynamic response result is obtained, the modeling method considers the influence of the elastic ring boss structure characteristics and the complex coupling relation oil film-elastic ring current-solid coupling effect, and the accuracy and calculation efficiency of the model are improved to the maximum extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of aviation transmission, and relates to a method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling, and in particular to a method for dynamic modeling of a spiral bevel gear system with an elastic ring squeeze film damper and based on bidirectional fluid-solid coupling. Background Art

[0002] As a core component in the field of aviation transmission, spiral bevel gears play a vital role in the transmission systems of helicopters, aircraft and their engine accessories due to their excellent load-bearing capacity, lightweight design, smooth transmission performance and superior lubrication characteristics. They are particularly good at handling power transmission between intersecting shafts. However, with the rapid advancement of aviation technology, engine performance indicators such as speed, thrust and operating intensity continue to rise, and the working environment and structural complexity increase, which directly leads to increasingly severe vibration challenges faced by aviation components and a significant increase in the risk of vibration failure. This situation urgently requires us to deeply optimize the vibration control strategy of the gear rotor system, especially in the frequency modulation vibration reduction design.

[0003] Squeeze film damper (SFD) is a traditional vibration reduction device used to reduce vibration and mechanical parts. Its advantages are simple structure, high reliability and significant cost-effectiveness. However, when faced with high eccentricity and large vortex radius conditions, the highly nonlinear characteristics of the oil film may aggravate the vibration of the system, thus limiting the widespread application of SFD. For this reason, the elastic ring squeeze film damper (ERSFD) came into being. It not only inherits the traditional advantages of SFD, but also effectively alleviates the nonlinear problem of the oil film through design improvements. However, faced with the time-varying loads and complex working conditions experienced by aviation bevel gears, the vibration reduction effect of ERSFD is still not stable enough, and sometimes even causes instability of the gear rotor system.

[0004] In-depth exploration of the mechanical properties of ERSFD requires accurate solution of the dynamic characteristics of the oil film. Previous studies have mostly used the "short bearing" or "long bearing" theory for approximate analysis. Although these methods have advantages in calculation speed, they are based on idealized assumptions (such as infinitely short or infinitely long) and ignore the limitations of the elastic ring boss structure, making it difficult to directly apply the results to engineering practice. On the other hand, although the finite element model can fully consider the geometric details of the elastic ring and the boundary conditions of the oil film, its huge amount of calculation, low solution efficiency, and the complex coupling relationship between the oil film gap and deformation and oil film pressure bring great challenges to its integration into the analysis of dynamic gear rotor systems.

[0005] Therefore, it is urgent to develop a more accurate and efficient calculation method that can not only ensure the calculation accuracy, but also overcome the shortcomings of the existing methods in terms of calculation efficiency and applicability, so as to provide solid technical support for the application of ERSFD in aviation bevel gear transmission systems. Summary of the invention

[0006] In view of this, in order to solve the problems of large calculation amount, low solution efficiency and poor applicability in the above-mentioned finite element model analysis of the mechanical properties of the spiral bevel gear system with an elastic ring squeeze film damper, the present invention provides a dynamic modeling method of the spiral bevel gear system based on bidirectional fluid-solid coupling, which fully considers the structural characteristics of the elastic ring, the complex coupling relationship between the oil film gap and deformation, and the oil film pressure, and derives the deformation equation of the elastic ring and the oil film pressure control equation to solve the variable boundary elastic fluid-solid coupling problem of the oil film-gear system.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling comprises the following steps:

[0009] S1. Calculate the radial deformation and deformation speed of the elastic ring of the elastic ring squeeze film damper by analytical method;

[0010] S2, taking the radial deformation and deformation speed of the elastic ring calculated in step S1 as input, solving the oil film pressure by using the Reynolds equation, discretizing the control equation by using the central finite difference method, solving the transient control equation of the oil film pressure, and obtaining the oil film pressure distribution inside and outside ERSFD; after solving the oil film pressure control equation to obtain the oil film pressure, the radial elastic restoring force and circumferential damping force of the oil film are obtained by numerical integration, and then the stiffness coefficient and damping coefficient of the oil film are obtained;

[0011] S3. Using the lumped parameter method and based on the principles of Newtonian mechanics, a dynamic model of the spiral bevel gear transmission system is established. A spring-damper system is used to simulate gear meshing, the mass of the transmission shaft is simplified to the center of the gear, and the differential equation of the gear system is derived.

[0012] S4. The ERSFD oil film dynamic characteristics calculated in step S2 are used as the input of the dynamic model of the spiral bevel gear system, taking into account the time-varying meshing stiffness excitation, the time-varying transmission error excitation, the internal excitation of the tooth side clearance, and the external excitation of the speed and torque, to obtain the ERSFD-spiral bevel gear system coupled dynamic response result.

[0013] Furthermore, when the elastic ring is deformed by force in step S1, δ iis the displacement of the i-th boss. Assume that the elastic ring is still an arc segment after deformation. R and R′ are the outer surface radii before and after deformation, respectively. The arc segment passes through two fixed points (Rsinγ, Rcosγ) and (0, R+δ i ), then the center distance of the elastic ring segment before and after deformation is:

[0014]

[0015] According to the geometric relationship, the deformation of the elastic ring at any angle α is:

[0016]

[0017] Calculation of the deformation velocity of an elastic ring by forward difference method

[0018]

[0019] Furthermore, in step S2, it is assumed that the oil film is an isovistoric incompressible fluid and the fluid viscosity and density are constant. The polar coordinate control equation applicable to the inner and outer oil films of ERSFD is:

[0020]

[0021] Where R is the radius of the lower surface of the oil film.

[0022] In the ERSFD cross section, wall-1 represents the outer ring surface of the bearing, which serves as the external boundary of the structure; wall-2 represents the inner convex surface of the elastic ring, and wall-2 and wall-1 together define the internal oil film area of ​​ERSFD; wall-3 represents the outer convex surface of the elastic ring; wall-4 represents the inner ring surface of the bearing seat, and wall-3 and wall-4 together form the external oil film area of ​​ERSFD. 1 and R 2 is the radius of wall-1 and wall-2, R 3 and R 4 is the radius of wall-3 and wall-4, e is the eccentricity;

[0023] set up and are the translational velocity components of the journal along the X-axis and Y-axis directions, respectively. Since the movement of the journal is restricted to a two-dimensional plane, that is, only translational movement along the X-axis and Y-axis directions is allowed, and no rotation or other complex movement is involved, the velocity components of the visual wall-1 along the X-axis and Y-axis will usually also be and r represents the radial deformation of the elastic ring, t is the time, is the deformation speed of the elastic ring in the radial direction, Ω is the precession angular velocity, h 1 is the inner oil film thickness, h 2 is the outer oil film thickness;

[0024] The inner oil film thickness function is:

[0025]

[0026] The control equation of the inner oil film is obtained as follows:

[0027]

[0028] Similarly, for the outer oil film, since the bearing seat is fixed, the elastic ring only has a deformation velocity in the radial direction, and the control equation of the outer oil film is:

[0029]

[0030] in is the deformation speed of the elastic ring,

[0031] After solving the oil film pressure control equation to obtain the oil film pressure, the radial elastic restoring force F of the oil film is obtained by numerical integration: or and circumferential damping force F ot

[0032]

[0033] Then the oil film force along the X-axis and Y-axis is:

[0034] F ox =-F or cosβ+F ot sinβ

[0035] F oy =-F or sinβ+F ot cosβ (10)

[0036] The oil film stiffness coefficient and oil film damping coefficient are:

[0037]

[0038] The negative sign in the above formula indicates that the radial force and circumferential force of the oil film are in opposite directions to the eccentricity e and the precession velocity eΩ respectively.

[0039] Furthermore, in order to accurately analyze the dynamic behavior of the oil film, the oil film is equally divided along the circumferential direction and the axial direction. In order to solve the transient change of the oil film pressure, the deformation r of the elastic ring and its deformation velocity are calculated. As key parameters, they are substituted into the control equation of the oil film; dimensionless parameters Z = z / L, X = x / c, Y = y / c, H = h / c, P = p / p are introduced 0 , p 0 =2μR / c and

[0040] Di.j (P i.j ) l -A i.j (P i+1,j ) l -B i.j (P i-1,j ) l -C i.j (P i,j+1 ) l -C i.j (P i,j-1 ) l =-(F i.j ) l (13)

[0041] In the formula

[0042] D i.j =A i.j +B i.j +2C i.j ,

[0043]

[0044] Further, the dynamic model of the spiral bevel gear transmission system in step S3 is a dynamic model of the gears, the transmission shaft, the elastic support and the bearing.

[0045] Further, in the dynamic model of the spiral bevel gear system in step S3, K is the stiffness coefficient, C is the damping coefficient, T is the torque, and the subscripts 1 and 2 represent the driving wheel and the driven wheel respectively; the system differential equation group is:

[0046]

[0047] Where, T 1 (t), T 2 (t) are the driving and load torques on the driving wheel and the driven wheel respectively, J 1 , J 2 The moment of inertia of the driving and driven wheels, m ij , C ij , K ij (i=1,2;j=x,y,z) are the equivalent mass, equivalent stiffness and equivalent damping of the driving and driven wheels along each translation direction respectively. is the acceleration in each direction, is the speed in each direction, F oy and F oz are the oil film forces in the translational direction of the driving wheel;

[0048] Normal dynamic meshing force F n and its normal force F along each coordinate axis x 、Fy 、F z They are

[0049]

[0050] In the formula, C m are the average meshing damping of the gear pair, α n is the normal pressure angle, δ is the pitch cone angle, β m is the midpoint helix angle, K(t) is the time-varying meshing stiffness, and its form is:

[0051] K(t)=K m +K v cos(Ω h t+Φ) (16)

[0052] In the formula, K m is the average meshing stiffness, K v is the first-order harmonic variable, Ω h is the gear meshing frequency, Φ is the initial phase. n is the relative displacement between the driving and driven wheels along the normal direction of the instantaneous meshing point,

[0053] λ n =a 1 (X 1 -X 2 )+a 2 (Y 1 -Y 2 )+a 3 (Z 1 -Z 2 )+a 3 (θ 1 -θ 2 )-e n (t) (17)

[0054] Where e n (t) is the static transmission error of the gear pair, a 1 = -cosα n sinβ m sinδ 2 -sinα n cosδ 2 ; a 2 =

[0055] -sinα n sinδ 2 +cosα n sinβ m cosδ 2 ; a 3 =cosα n cosβm .

[0056] Furthermore, step S4 synchronously solves the oil film control equation and the bevel gear dynamics equation, which can accurately capture and calculate the instantaneous oil film dynamic characteristic parameters of the bevel gear system during operation and the overall dynamic response of the system.

[0057] The beneficial effects of the present invention are:

[0058] 1. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling disclosed in the present invention takes into account the complex coupling relationship between the structural characteristics of the elastic ring boss, the oil film gap and deformation, and the oil film pressure, and the influence of the oil film-elastic ring fluid-solid coupling during the ERSFD modeling process, thereby maximizing the accuracy and computational efficiency of the model.

[0059] 2. The dynamic modeling method of the spiral bevel gear system based on bidirectional fluid-solid coupling disclosed in the present invention fully considers the oil film dynamic characteristics such as oil film force, oil film stiffness, oil film damping, etc. when coupling and solving the ERSFD and the spiral bevel gear system, and constructs the mapping relationship between the journal displacement and the oil film force, avoiding the shortcomings of the traditional simplified processing of the long and short bearing assumptions.

[0060] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0062] Figure 1 This is a flow chart of a method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to the present invention;

[0063] Figure 2 It is a schematic diagram of elastic ring deformation in a method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling of the present invention;

[0064] Figure 3 It is a schematic cross-sectional view of ERSFD in a method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling of the present invention;

[0065] Figure 4 It is a schematic diagram of the fluid calculation domain in a method for dynamics modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling of the present invention;

[0066] Figure 5 A dynamic model diagram of a spiral bevel gear system with ERSFD in a dynamic modeling method of a spiral bevel gear system based on bidirectional fluid-solid coupling of the present invention;

[0067] Figure 6 The present invention provides a flow chart of fluid-solid coupling calculation in a method for dynamics modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling. DETAILED DESCRIPTION

[0068] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0069] like Figure 1-Figure 6 A method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling is shown, which specifically includes the following steps:

[0070] S1. Calculate the radial deformation and deformation speed of the elastic ring by analytical method.

[0071] Reference Figure 2 When the elastic ring of the elastic ring type squeeze film damper is deformed by force, δ i is the displacement of the i-th boss. Assume that the elastic ring is still an arc segment after deformation. R and R′ are the outer surface radii before and after deformation, respectively. The arc segment passes through two fixed points (Rsinγ, Rcosγ) and (0, R+δ i ), then the center distance of the elastic ring segment before and after deformation is:

[0072]

[0073] According to the geometric relationship, the deformation of the elastic ring at any angle α is:

[0074]

[0075] The deformation velocity of the elastic ring is calculated by the forward difference method:

[0076]

[0077] S2. The radial deformation and deformation speed of the elastic ring calculated in step S1 are used as input, the Reynolds equation is used to solve the oil film pressure, the control equation is discretized by the central finite difference method, the transient control equation of the oil film pressure is solved, and the oil film pressure distribution inside and outside ERSFD is obtained; after the oil film pressure is obtained by solving the oil film pressure control equation, the radial elastic restoring force and circumferential damping force of the oil film are obtained by numerical integration, and then the stiffness coefficient and damping coefficient of the oil film are obtained.

[0078] Assuming that the oil film is an isovistoric incompressible fluid and the fluid viscosity and density are constant, the polar coordinate control equations for the inner and outer oil films of ERSFD are:

[0079]

[0080] Where R is the radius of the lower surface of the oil film.

[0081] Reference Figure 3 , the schematic diagram of the ERSFD cross-section structure shows in detail the positional relationship of its various components. In the ERSFD cross-section, wall-1 represents the outer ring surface of the bearing, which serves as the external boundary of the structure; wall-2 represents the inner convex surface of the elastic ring, and wall-2 and wall-1 together define the internal oil film area of ​​ERSFD; then, wall-3 represents the outer convex surface of the elastic ring, and wall-4 represents the inner ring surface of the bearing seat, and wall-3 and wall-4 together form the external oil film area of ​​ERSFD, R 1 and R 2 is the radius of wall-1 and wall-2, R 3 and R 4 is the radius of wall-3 and wall-4, and e is the eccentricity.

[0082] set up and are the translational velocity components of the journal along the X-axis and Y-axis directions, respectively. Since the movement of the journal is restricted to a two-dimensional plane, that is, only translational movement along the X-axis and Y-axis directions is allowed, and no rotation or other complex movement is involved, the velocity components of wall-1 (usually regarded as the lower surface of the oil film, fixed to or closely following the movement of the journal) along the X-axis and Y-axis will also be and r represents the radial deformation of the elastic ring, t is the time, is the deformation speed of the elastic ring in the radial direction, Ω is the precession angular velocity, h 1 is the inner oil film thickness, h 2 is the outer oil film thickness;

[0083] The inner oil film thickness function is:

[0084]

[0085] The control equation of the inner oil film is obtained as follows:

[0086]

[0087] Similarly, for the outer oil film, since the bearing seat is fixed, the elastic ring only has a deformation velocity in the radial direction, and the control equation of the outer oil film is:

[0088]

[0089] in is the deformation speed of the elastic ring;

[0090] Reference Figure 4 In the θ-z plane expansion diagram, the oil film is equally divided along the circumferential direction and the axial direction in order to accurately analyze the dynamic behavior of the oil film. In order to solve the transient change of the oil film pressure, the deformation r of the elastic ring and its deformation speed are calculated. As key parameters, they are substituted into the control equation of the oil film; dimensionless parameters Z = z / L, X = x / c, Y = y / c, H = h / c, P = p / p are introduced 0 , p 0 =2μR / c and

[0091] D i.j (P i.j ) l -A i.j (P i+1,j ) l -B i.j (P i-1,j ) l -C i.j (P i,j+1 ) l -C i.j (P i,j-1 ) l =-(F i.j ) l (9)

[0092] In the formula

[0093] D i.j =A i.j +B i.j +2C i.j ,

[0094]

[0095] After solving the oil film pressure control equation to obtain the oil film pressure, the radial elastic restoring force F of the oil film is obtained by numerical integration: or and circumferential damping force F ot

[0096]

[0097] Then the oil film force along the X-axis and Y-axis is:

[0098] F ox =-F or cosβ+F ot sinβ

[0099] F oy =-F or sinβ+F ot cosβ (11)

[0100] The oil film stiffness coefficient and oil film damping coefficient are:

[0101]

[0102] The negative sign in the above formula indicates that the radial force and circumferential force of the oil film are in opposite directions to the eccentricity e and the precession velocity eΩ respectively.

[0103] S3. Using the concentrated parameter method and based on the principles of Newtonian mechanics, a dynamic model of the spiral bevel gear transmission system is established. A spring-damper system is used to simulate gear meshing, the mass of the transmission shaft is simplified to the center of the gear, and the differential equation of the gear system is derived. The dynamic model of the spiral bevel gear transmission system is a dynamic model of the gears, transmission shafts, elastic supports and bearings.

[0104] Reference Figure 5 The dynamic model of the spiral bevel gear system is shown in the figure. K is the stiffness coefficient, C is the damping coefficient, T is the torque, and the subscripts 1 and 2 represent the driving wheel and the driven wheel respectively. The system differential equations are:

[0105]

[0106] Where, T 1 (t), T 2 (t) are the driving and load torques on the driving wheel and the driven wheel respectively, J 1 , J 2 The moment of inertia of the driving and driven wheels, m ij , C i , K ij (i=1,2;j=x,y,z) are the equivalent mass, equivalent stiffness and equivalent damping of the driving and driven wheels along each translation direction respectively. is the acceleration in each direction, is the speed in each direction, F oy and F oz are the oil film forces in the translational direction of the driving wheel;

[0107] Normal dynamic meshing force F n and its normal force F along each coordinate axis x 、Fy 、F z They are

[0108]

[0109] In the formula, C m are the average meshing damping of the gear pair, α n is the normal pressure angle, δ is the pitch cone angle, β m is the midpoint helix angle, K(t) is the time-varying meshing stiffness, and its form is:

[0110] K(t)=K m +K v cos(Ω h t+φ) (16)

[0111] In the formula, K m is the average meshing stiffness, K v is the first-order harmonic variable, Ω h is the gear meshing frequency, φ is the initial phase. n is the relative displacement between the driving and driven wheels along the normal direction of the instantaneous meshing point,

[0112] λ n =a 1 (X 1 -X 2 )+a 2 (Y 1 -Y 2 )+a 3 (Z 1 -Z 2 )+a 3 (θ 1 -θ 2 )-e n (t) (17)

[0113] Where e n (t) is the static transmission error of the gear pair, a 1 = -cosα n sinβ m sinδ 2 -sinα n cosδ 2 ; a 2 =-sinα n sinδ 2 +cosα n sinβ m cosδ 2 ; a 3 =cosα n cosβ m .

[0114] S4. The ERSFD oil film dynamic characteristics calculated by S2 are used as the input of the dynamic model of the spiral bevel gear system, and the coupled dynamic response results of the ERSFD-spiral bevel gear system are obtained by comprehensively considering the internal excitations such as time-varying meshing stiffness excitation, time-varying transmission error excitation and tooth side clearance and the external excitations such as speed and torque.

[0115] By solving the oil film control equation and the bevel gear dynamics equation simultaneously, the instantaneous oil film dynamic characteristic parameters of the bevel gear system during operation and the overall dynamic response of the system can be accurately captured and calculated. The core of this process is to achieve data exchange between the fluid domain (oil film) and the solid domain (bevel gear and journal), that is, fluid-solid coupling analysis.

[0116] The calculation process of fluid-structure interaction of ERSFD-spiral bevel gear system is as follows: Figure 6 As shown, the specific process is as follows:

[0117] Initialization phase: Set initial conditions for the calculation process, including the initial displacement of the journal and the initial estimated values ​​of the oil film dynamic characteristic parameters, which are usually set to 0 or reasonable assumptions based on prior knowledge.

[0118] Solid domain solution: The bevel gear dynamics equation is used for solution. This equation takes into account internal excitations such as time-varying meshing stiffness excitation, time-varying transmission error excitation, and tooth side clearance, as well as external excitations such as speed and torque, so as to obtain the displacement data of the solid domain (mainly the journal) at the current time step.

[0119] Fluid domain input: Substitute the journal displacement calculated in the previous step as the input condition into the ERSFD control equation. The ERSFD control equation describes the dynamic behavior of the oil film between the journal and the gear or bearing surface, including the oil film pressure distribution, oil film thickness change, etc.

[0120] Fluid domain solution: By solving the ERSFD control equation, the key dynamic characteristic parameters of the oil film, such as oil film force, oil film stiffness and oil film damping, are obtained. These parameters reflect the feedback effect of the oil film on the journal movement.

[0121] Data feedback and iteration: The calculated parameters such as oil film force are re-substituted into the bevel gear dynamics equation as new external loads or boundary conditions for the next round of iterative calculation. This process is repeated until the convergence conditions are met.

[0122] Result output: Through multiple iterative calculations, the dynamic response of the entire ERSFD-spiral bevel gear system at different time points is obtained, including the displacement, velocity, acceleration of the journal and the dynamic characteristic parameters of the oil film, thereby fully revealing the dynamic behavior characteristics of the system.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling, characterized in that: The following steps are involved: S1. Calculate the radial deformation and deformation speed of the elastic ring of the elastic ring squeeze film damper by analytical method; S2, taking the radial deformation and deformation speed of the elastic ring calculated in step S1 as input, solving the oil film pressure by using the Reynolds equation, discretizing the control equation by using the central finite difference method, solving the transient control equation of the oil film pressure, and obtaining the oil film pressure distribution inside and outside ERSFD; after solving the oil film pressure control equation to obtain the oil film pressure, the radial elastic restoring force and circumferential damping force of the oil film are obtained by numerical integration, and then the stiffness coefficient and damping coefficient of the oil film are obtained; S3. Using the lumped parameter method and based on the principles of Newtonian mechanics, a dynamic model of the spiral bevel gear transmission system is established. A spring-damper system is used to simulate gear meshing, the mass of the transmission shaft is simplified to the center of the gear, and the differential equation of the gear system is derived. S4. The ERSFD oil film dynamic characteristics calculated in step S2 are used as the input of the dynamic model of the spiral bevel gear system, taking into account the time-varying meshing stiffness excitation, the time-varying transmission error excitation, the internal excitation of the tooth side clearance, and the external excitation of the speed and torque, to obtain the ERSFD-spiral bevel gear system coupled dynamic response result.

2. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 1, characterized in that: When the elastic ring is deformed by force in step S1, δ i is the displacement of the ith boss. Assuming that the elastic ring is still an arc segment after deformation, R and R ′ are the outer surface radii before and after deformation, respectively. The arc segment passes through two fixed points (Rsinγ, Rcosγ) and (0, R+δ i ), then the center distance of the elastic ring segment before and after deformation is: According to the geometric relationship, the deformation of the elastic ring at any angle α is: Calculation of the deformation velocity of an elastic ring by forward difference method 3. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 1, characterized in that: In step S2, it is assumed that the oil film is an isovistoric incompressible fluid and the fluid viscosity and density are constant. The polar coordinate control equation applicable to the inner and outer oil films of ERSFD is: Where R is the radius of the lower surface of the oil film; In the ERSFD cross section, wall-1 represents the outer ring surface of the bearing, which serves as the external boundary of the structure; wall-2 represents the inner convex surface of the elastic ring, and wall-2 and wall-1 together define the internal oil film area of ​​ERSFD; wall-3 represents the outer convex surface of the elastic ring; wall-4 represents the inner ring surface of the bearing seat, and wall-3 and wall-4 together form the external oil film area of ​​ERSFD; R1 and R2 are the radii of wall-1 and wall-2, R3 and R4 are the radii of wall-3 and wall-4, and e is the eccentricity; set up and are the translational velocity components of the journal along the X-axis and Y-axis directions, respectively. Since the movement of the journal is restricted to a two-dimensional plane, that is, only translational movement along the X-axis and Y-axis directions is allowed, and no rotation or other complex movement is involved, the velocity components of the visual wall-1 along the X-axis and Y-axis will usually also be and r represents the radial deformation of the elastic ring, t is the time, is the deformation speed of the elastic ring in the radial direction, Ω is the precession angular velocity, h1 is the inner oil film thickness, and h2 is the outer oil film thickness; The inner oil film thickness function is: The control equation of the inner oil film is obtained as follows: Similarly, for the outer oil film, since the bearing seat is fixed, the elastic ring only has a deformation velocity in the radial direction, and the control equation of the outer oil film is: in is the deformation speed of the elastic ring, After solving the oil film pressure control equation to obtain the oil film pressure, the radial elastic restoring force F of the oil film is obtained by numerical integration: or and circumferential damping force F ot Then the oil film force along the X-axis and Y-axis is: F ox =-F or cosβ+F ot sinβ F oy =-F or sinβ+F ot cosβ (10) The oil film stiffness coefficient and oil film damping coefficient are: The negative sign in the above formula indicates that the radial force and circumferential force of the oil film are in opposite directions to the eccentricity e and the precession velocity eΩ respectively.

4. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 3, characterized in that: In order to accurately analyze the dynamic behavior of the oil film, the oil film is divided equally along the circumferential direction and the axial direction. In order to solve the transient change of the oil film pressure, the deformation r of the elastic ring and its deformation speed are calculated. As key parameters, they are substituted into the control equation of the oil film; the dimensionless parameters Z = z / L, X = x / c, Y = y / c, H = h / c, P = p / p0, p0 = 2μR / c and D i.j (P i.j ) l -A i.j (P i+1,j ) l -B i.j (P i-1,j ) l -C i.j (P i,j+1 ) l -C i.j (P i,j-1 ) l =-(F i.j ) l (13) In the formula 5. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 1, characterized in that: The dynamic model of the spiral bevel gear transmission system in step S3 is a dynamic model of the gears, the transmission shaft, the elastic support and the bearing.

6. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 5, characterized in that: In the dynamic model of the spiral bevel gear system in step S3, K is the stiffness coefficient, C is the damping coefficient, T is the torque, and the subscripts 1 and 2 represent the driving wheel and the driven wheel respectively; the system differential equation group is: Where, T1(t) and T2(t) are the driving and load torques on the driving and driven wheels, respectively; J1 and J2 are the moments of inertia of the driving and driven wheels, respectively; m ij , C ij , K ij (i=1,2;j=x,y,z) are the equivalent mass, equivalent stiffness and equivalent damping of the driving and driven wheels along each translation direction respectively. is the acceleration in each direction, is the speed in each direction, F oy and F oz are the oil film forces in the translational direction of the driving wheel; Normal dynamic meshing force F n and its normal force F along each coordinate axis x 、F y 、F z They are In the formula, C m are the average meshing damping of the gear pair, α n is the normal pressure angle, δ is the pitch cone angle, β m is the midpoint helix angle, K(t) is the time-varying meshing stiffness, and its form is: K(t)=K m +K v cos(Ω h t+Φ) (16) In the formula, K m is the average meshing stiffness, K v is the first-order harmonic variable, Ω h is the gear meshing frequency, Φ is the initial phase; λ n is the relative displacement between the driving and driven wheels along the normal direction of the instantaneous meshing point, <h2 style=";text-align:left;direction:ltr">λ<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> = a1(X1-X2)+a2(Y1-Y2)+a3(Z1-Z2)+a3(θ1-θ2)-e<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> (t) (17) Where e n (t) is the static transmission error of the gear pair, a1=-cosα n sinβ m sinδ2-sinα n cosδ2; a2 = -sinα n sinδ2+cosα n sinβ m cosδ2;a3=cosα n cosβ m .

7. The method for dynamic modeling of a spiral bevel gear system based on bidirectional fluid-solid coupling according to claim 1, characterized in that: Step S4 synchronously solves the oil film control equation and the bevel gear dynamics equation, which can accurately capture and calculate the instantaneous oil film dynamic characteristic parameters of the bevel gear system during operation and the overall dynamic response of the system.

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