A bidirectional fluid-structure coupling calculation method for a gas hydrostatic radial bearing with a pressure equalization cavity

Abstract

The invention discloses a bidirectional fluid-solid coupling calculation method for a gas hydrostatic radial bearing containing a pressure equalizing cavity, comprising the following steps: a first step, establishing an air film thickness equation for the gas hydrostatic radial bearing; a second step, based on the gas lubrication theory, calculating the gas mass flow rate at the inlet of a small hole, the gas mass flow rate at the outlet of the pressure equalizing cavity and the change of the gas mass flow rate in the cavity; establishing a flow balance equation according to the mass conservation equation; a third step, establishing an air film flow field control equation, using an alternating direction implicit format method to discretize the air film flow field control equation, and numerically solving the air film pressure through the Thomas algorithm; integrating the pressure of the entire air film surface to obtain the air film bearing capacity; a fourth step, establishing a 5-degree-of-freedom spindle force equation containing a rotation speed, and solving it through the Runge-Kutta method; a fifth step, solving the steady-state flow field control equation to obtain the air film support force; updating the spindle position by solving the spindle force equation, thereby updating the air film thickness, air film pressure and air film support force.

Description

Technical Field

[0001] The invention belongs to the technical field of gas hydrostatic bearing dynamics simulation, and in particular relates to a bidirectional fluid-solid coupling calculation method for a gas hydrostatic radial bearing containing a pressure equalizing cavity. Background Art

[0002] Gas bearings have the advantages of high speed, low friction, no pollution, high precision, and long life, and are widely used in various ultra-precision processing equipment and measurement equipment. Gas bearings can generally be divided into gas hydrodynamic bearings, gas static pressure bearings, and hydrodynamic and static pressure hybrid bearings. Hydrodynamic bearings have greater wear during the start-up and shutdown process, and the design, calculation, and processing of hydrodynamic and static pressure hybrid bearings are relatively complex, so static pressure bearings are more widely used, and are increasingly used in the ultra-precision processing of high-precision and cutting-edge parts such as large-scale integrated circuit manufacturing, laser nuclear fusion mirrors, large-aperture astronomical radio telescopes, and aspheric optical devices.

[0003] Although gas hydrostatic bearings have many advantages, they also have disadvantages such as low bearing capacity, poor dynamic stability, and demanding manufacturing precision. Generally, the bearing capacity is improved by opening a pressure equalization cavity. The existence of the pressure equalization cavity will change the flow rate inside the bearing, which must be considered. The gas hydrostatic bearing system is a typical bidirectional fluid-solid coupling system. The change in the thickness of the gas film will affect the gas film pressure, which in turn affects the bearing capacity of the gas film, thereby affecting the force on the spindle. The change in the force on the spindle will change its spatial position, which in turn affects the thickness of the gas film. In transient state, this bidirectional fluid-solid coupling is always in progress. At present, when analyzing the dynamic performance of gas hydrostatic bearings, most of them directly bring the gas film support force into the spindle force equation, ignoring the influence of the spindle movement on the gas film flow field. The perturbation method can consider the fluid-solid coupling effect, but this method uses a linear assumption that the spindle is slightly perturbed at the equilibrium position, and the stability of the bearing system can be obtained with a small amount of calculation. However, gas hydrostatic bearings have strong nonlinearity. When the bearing vibrates greatly, this method will produce errors that are difficult to estimate. In addition, various existing commercial software such as FLUENT also have fluid-structure interaction modules, but they are highly encapsulated and users cannot access their program codes. They also cannot consider the swing of the spindle and the various forces it causes.

[0004] Based on the fact that the spindle has five degrees of freedom in space (its axial degree of freedom will be restricted), the movement of the spindle in two directions, the swing and rotation speed in two directions, and the unbalanced mass force and gyroscopic force caused by the rotation speed are taken into account. The air film thickness equation, the air film flow field control equation, the flow balance equation and the spindle force equation are coupled, and the bidirectional fluid-solid coupling calculation of the gas hydrostatic radial bearing with a pressure equalizing cavity is realized by numerically solving the coupling equations. This is of great significance for the accurate analysis of the dynamic performance of the gas hydrostatic bearing. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problem and to provide a method for bidirectional fluid-solid coupling calculation of a gas hydrostatic radial bearing with a pressure equalizing cavity, which takes into account the influence of the flow field and the solid field on each other at each moment, implements coupling from the mechanical essence, and realizes bidirectional fluid-solid coupling calculation of a gas hydrostatic radial bearing with a pressure equalizing cavity.

[0006] In order to solve the above technical problems, the technical solution of the present invention is: a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalizing cavity, comprising the following steps:

[0007] S1. Establish the air film thickness equation of the gas hydrostatic radial bearing, taking into account the movement of the main shaft in two directions and the swing in two directions;

[0008] S2. Based on the gas lubrication theory, calculate the gas mass flow rate at the orifice inlet, the gas mass flow rate at the pressure equalization chamber outlet, and the change in the gas mass flow rate in the chamber; according to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the change in the chamber flow rate, and establish the flow balance equation;

[0009] S3. Establish the air film flow field control equation, which is a second-order nonlinear partial differential equation. In view of the shortcomings of poor stability of the explicit method and poor convergence of the implicit method in numerical solution, the alternating direction implicit format method is used to discretize the air film flow field control equation, and a periodic tridiagonal equation group and a general tridiagonal equation group are obtained. The generalized Thomas algorithm and the traditional Thomas algorithm are used to solve the air film pressure, and the pressure of the entire air film surface is integrated to obtain the air film bearing capacity.

[0010] S4, taking into account the air film force, gravity, unbalanced mass force and gyroscopic force, the 5-DOF main axis force equation with rotation speed is established, which is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients, and is solved by the Runge-Kutta method;

[0011] S5. Given the initial displacement of the main shaft in two directions, the initial swing in two directions and the rotation speed, solve the steady-state flow field control equation to obtain the air film support force; update the main shaft position by solving the main shaft force equation, thereby updating the air film thickness, air film pressure and air film support force; repeat the iteration until the set time step is met; due to the continuous air intake of the hydrostatic bearing, the flow balance equation must also be met in each time step.

[0012] Furthermore, the step S1 specifically takes the position of the maximum air film thickness of the bearing as the reference origin of the circumferential angle coordinates of the bearing, and the air film thickness equation can be obtained from the geometric relationship, and the equation includes the movement and swing of the main shaft.

[0013] Furthermore, the step S2 includes the following sub-steps:

[0014] S21, obtaining the gas mass flow rate at the orifice inlet according to the Laval nozzle model;

[0015] S22, obtaining the gas mass flow rate at the outlet of the pressure equalizing chamber according to the flow speed of the gas in the x and z directions;

[0016] S23, expressing the gas density in the pressure equalizing chamber with pressure, calculating the gas mass in the chamber according to the volume of the pressure equalizing chamber, and differentiating the gas mass with respect to time to obtain the change in the gas mass flow rate in the chamber;

[0017] S24. According to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the changing flow rate in the cavity, and the flow balance equation is established.

[0018] Furthermore, the step S3 also includes the following sub-steps:

[0019] S31, establish the air film flow field control equation and expand it; assume that the derivative with respect to θ is unknown, assume that the derivative with respect to ξ is a known value at the time point n, obtain a periodic tridiagonal equation group, and use the generalized Thomas algorithm to solve and obtain the air film pressure;

[0020] S32. Assume that the derivative with respect to ξ is unknown, and assume that the derivative with respect to θ is a known value at time point n+1, and obtain a general tridiagonal system of equations. Use the traditional Thomas algorithm to solve and obtain the air film pressure.

[0021] Furthermore, the step S4 includes the following sub-steps:

[0022] S41. According to Newton's laws of motion, the force equation of the 5-DOF spindle including the rotation speed is obtained, which is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients;

[0023] S42. The equation is reduced to a first-order ordinary differential equation group, and the Runge-Kutta method is used to numerically solve it to obtain the position of the principal axis at the next moment, thereby obtaining the corresponding new air film thickness.

[0024] Furthermore, the step S5 includes the following sub-steps:

[0025] S51, input bearing parameters and environmental values, give the initial displacement of the main shaft in two directions, the initial swing and speed in two directions, obtain the initial air film thickness, solve the steady-state flow field control equation to obtain the air film pressure, and then integrate to obtain the air film support force. Obtain the pressure of each equalizing cavity by iteratively solving the steady-state flow balance equation;

[0026] S52, updating the spindle position by solving the spindle force equation, thereby updating the air film thickness, air film pressure and air film support force. In this process, the transient flow balance equation must also be satisfied, thereby obtaining the pressure of the equalizing chamber at each moment;

[0027] S53, repeat the iteration until the set time step is met. Then, bidirectional fluid-solid coupling can be realized, and the flow field and solid field parameters at each moment can be obtained.

[0028] The beneficial effects of the present invention are as follows: the bidirectional fluid-solid coupling calculation method of the gas hydrostatic radial bearing with a pressure equalizing cavity provided by the present invention couples a variety of control equations, takes into account the five degrees of freedom of the main shaft and the unbalanced mass force and gyroscopic force caused by the rotation speed, etc. A bidirectional fluid-solid coupling calculation method of the gas hydrostatic radial bearing with a pressure equalizing cavity is established, which provides support for accurately analyzing the dynamic characteristics of the bearing in the entire domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalizing cavity according to the present invention;

[0030] Figure 2 It is a coordinate system setting diagram of the present invention;

[0031] Figure 3 It is the air film grid division diagram of the present invention;

[0032] Figure 4 It is a diagram of the support mode of the main shaft system of the present invention;

[0033] Figure 5 is a steady-state gas film thickness distribution diagram of the present invention;

[0034] Figure 6 It is the steady-state air film pressure distribution diagram of the present invention;

[0035] Figure 7 It is the air film thickness distribution diagram after 600 iterations of the present invention;

[0036] Figure 8 It is the air film pressure distribution diagram after 600 iterations of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

[0038] like Figures 1 to 8 As shown, the present invention provides a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalizing cavity, comprising the following steps:

[0039] S1. Establish the air film thickness equation of the gas hydrostatic radial bearing, taking into account the movement of the main shaft in two directions and the swing in two directions.

[0040] Step S1 specifically uses the position of the maximum air film thickness of the bearing as the reference origin of the circumferential angle coordinates of the bearing, and the air film thickness equation can be obtained from the geometric relationship, and the equation includes the movement and swing of the main shaft.

[0041] like Figure 2The coordinate system is established as shown, considering the displacement and angular swing in the two directions of the main axis. The film thickness equation is established and dimensionless processing is performed:

[0042]

[0043] Among them: H=h / c, ε=e / c, θ=x / R, ξ=z / R.

[0044] Where: h is the thickness of the air film, c is the air film gap, x and z are the coordinates in two directions, φ and ψ are the swings in two directions, L and R are the bearing length and radius, θ a is the deflection angle.

[0045] S2. Based on the gas lubrication theory, calculate the gas mass flow rate at the small hole inlet, the gas mass flow rate at the pressure equalization chamber outlet and the change in gas mass flow rate in the chamber; according to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the change in the chamber flow rate, and establish the flow balance equation.

[0046] Step S2 includes the following sub-steps:

[0047] S21. Obtain the gas mass flow rate at the small hole inlet according to the Laval nozzle model.

[0048] Since the throttle hole is short, the time required for the gas to flow through is very short, and the heat cannot be exchanged in time, which can be considered as an adiabatic process. The gas mass flow rate flowing into the bearing through the throttle hole is:

[0049]

[0050] In the formula, A 0 is the cross-sectional area of ​​the throttle hole, φ=0.8 is the flow coefficient, p s is the gas supply pressure, ρ a is the gas density, p a is the standard atmospheric pressure. ψ is the flow function, specifically:

[0051]

[0052] Where k is the adiabatic index, β is the pressure ratio, and p is d is the gas pressure in the pressure equalizing chamber after the throttle hole, is the critical pressure ratio.

[0053] S22. Obtain the gas mass flow rate at the outlet of the pressure equalizing chamber according to the flow velocity of the gas in the x and z directions.

[0054] By performing a second integration of the gas flow velocity in the x and z directions, the gas mass flow rate out of the pressure equalization chamber can be obtained as:

[0055]

[0056] Where η is the gas viscosity adiabatic index, p is the pressure, ω is the spindle speed, and b is the length of the square pressure equalization chamber.

[0057] S23. Express the gas density in the pressure equalizing chamber with pressure, calculate the gas mass in the chamber according to the volume of the pressure equalizing chamber, and obtain the change in the gas mass flow rate in the chamber by differentiating the gas mass with respect to time.

[0058] In transient state, the gas mass in the pressure equalization chamber will change, and the change amount is:

[0059]

[0060] In the formula, h d is the height of the pressure equalization chamber, A d is the cross-sectional area of ​​the pressure equalization chamber, n is the time step, and t is the time.

[0061] S24. According to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the changing flow rate in the cavity, and the flow balance equation is established.

[0062] Gas hydrostatic bearings require a continuous supply of gas. The gas flows in from the throttle hole and flows out from the boundary of the pressure equalizing chamber, so the law of conservation of mass must be satisfied. In steady state, without considering the time term, the flow balance equation is that the flow rate flowing into the throttle hole is equal to the flow rate flowing out of the pressure equalizing chamber. In transient state, the gas flowing in should be equal to the gas flowing out plus the gas changed inside the pressure equalizing chamber. Then at each throttle hole, the steady-state and transient flow balance equations are:

[0063] qin-qout=0 (6)

[0064] qin-qout-dq=0 (7)

[0065] S3. Establish the air film flow field control equation, which is a second-order nonlinear partial differential equation. In view of the shortcomings of poor stability of the explicit method and poor convergence of the implicit method in numerical solution, the alternating direction implicit format method is used to discretize the air film flow field control equation, and the periodic tridiagonal equation group and the general tridiagonal equation group are obtained. The generalized Thomas algorithm and the traditional Thomas algorithm are used to solve the air film pressure, and the pressure of the entire air film surface is integrated to obtain the air film bearing capacity.

[0066] The air film flow field control equation is established and dimensionless processing is performed to obtain:

[0067]

[0068] Where: f = P 2 , T=ωt

[0069] Removing the time term from the above equation will give the steady-state air film flow field control equation. If the initial air film thickness is known, the steady-state air film pressure can be obtained by solving the steady-state equation in combination with the steady-state flow balance equation. The above equation is expanded and discretized, and the time term is solved using the alternating direction implicit format method. The air film pressure at different times can be obtained by numerical solution.

[0070] Step S3 also includes the following sub-steps:

[0071] S31. Establish the air film flow field control equation and expand it; assume that the derivative with respect to θ is unknown, and assume that the derivative with respect to ξ is a known value at time point n, and obtain a periodic tridiagonal equation group, and use the generalized Thomas algorithm and solve to obtain the air film pressure.

[0072] S32. Assume that the derivative with respect to ξ is unknown, and assume that the derivative with respect to θ is a known value at time point n+1, and obtain a general tridiagonal system of equations. Use the traditional Thomas algorithm to solve and obtain the air film pressure.

[0073] Specifically: according to Figure 3 Divide the air film grid. At the beginning, assume that the air film pressure at time point n is known. In the first stage of the iteration cycle, at time point n+1, the derivative with respect to θ is unknown, and the derivative with respect to ξ is the known value at time point n; in the second stage of the iteration cycle, at time point n+2, the derivative with respect to ξ is unknown, and the derivative with respect to θ is the known value at time point n+1. When the iteration cycle is completed, the time point n+2 is regarded as the new time point n and the next iteration cycle is started, and this is repeated. This paper takes the steady state as time point n and starts the calculation:

[0074] From time n to n+1, the derivative with respect to θ is unknown, and the derivative with respect to ξ is the known value at time point n, then the transient air film flow field control equation is:

[0075]

[0076] Among them, the thickness of the air film at time n+1 can be obtained by solving the main axis force equation. So the unknown quantity in the above formula is f n +1 i+1,j , f n+1 i,j , f n+1 i-1,j .

[0077] Combine similar terms in the above formula and write it in matrix form:

[0078]

[0079] Among them, A1, B1, C1, b1 are coefficients of known values ​​in equation (9). The above equation is a periodic tridiagonal equation system, which can be solved row by row using the generalized Thomas algorithm to obtain the air film pressure at time n+1.

[0080] From time n+1 to n+2, the derivative with respect to ξ is unknown, and the derivative with respect to θ is the known value at time point n+1, then the transient air film flow field control equation is:

[0081]

[0082] Among them, the thickness of the air film at time n+2 can be obtained by solving the main axis force equation. So the unknown quantity in the above formula is f n +2 i,j+1 , f n+2 i,j , f n+2 i,j-1 .

[0083] Combine similar terms in the above formula and write it in matrix form:

[0084]

[0085] Among them, C2, D2, E2, b2 are coefficients of known values ​​in equation (11). The above equation is a general tridiagonal equation system, and the traditional Thomas algorithm can be used to solve it column by column to obtain the air film pressure at time n+2.

[0086] After obtaining the air film pressure, the air film support forces in the x and y directions can be obtained by integrating them over the entire air film surface:

[0087]

[0088] S4. Taking the air film force, gravity, unbalanced mass force and gyroscopic force into consideration, the 5-DOF main axis force equation including rotation speed is established. This equation is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients, which is solved by the Runge-Kutta method.

[0089] Step S4 includes the following sub-steps:

[0090] S41. According to Newton's laws of motion, the force equation of the 5-DOF spindle including the rotation speed is obtained, which is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients.

[0091] S42. The equation is reduced to a first-order ordinary differential equation group, and the Runge-Kutta method is used to numerically solve it to obtain the position of the principal axis at the next moment, thereby obtaining the corresponding new air film thickness.

[0092] The support method of the spindle system is as follows Figure 4 As shown in the figure, the force equation of the main axis is obtained from Newton's second law and the momentum theorem:

[0093]

[0094] Where M is the main shaft mass, e x , e y , e z are the unbalanced masses in three directions, J x , J y , J z are the moments of inertia in three directions, W Ax and W Bx are the air film support forces of the left and right bearings in the x direction, W Ay and W By They are the air film supporting forces of the left and right bearings in the y direction respectively.

[0095] The above equation is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients, which needs to be reduced to a first-order ordinary differential equation system and numerically solved using the Runge-Kutta method to obtain the position of the principal axis at the next moment, thereby obtaining the corresponding new air film thickness.

[0096] S5. Given the initial displacement of the main shaft in two directions, the initial swing in two directions and the rotation speed, solve the steady-state flow field control equation to obtain the air film support force; update the main shaft position by solving the main shaft force equation, thereby updating the air film thickness, air film pressure and air film support force; repeat the iteration until the set time step is met; due to the continuous air intake of the hydrostatic bearing, the flow balance equation must also be met in each time step.

[0097] According to the above theory, the corresponding calculation program is programmed to numerically solve various control equations and perform bidirectional fluid-solid coupling calculation. Step S5 includes the following sub-steps:

[0098] S51, input bearing parameters and environmental values, give the initial displacement of the main shaft in two directions, the initial swing and speed in two directions, obtain the initial air film thickness, solve the steady-state flow field control equation to obtain the air film pressure, and then integrate to obtain the air film support force. The pressure of each equalizing cavity is obtained by iteratively solving the steady-state flow balance equation.

[0099] S52, updating the spindle position by solving the spindle force equation, thereby updating the air film thickness, air film pressure and air film support force. In this process, the transient flow balance equation must also be satisfied, thereby obtaining the pressure of the equalizing chamber at each moment.

[0100] S53, repeat the iteration until the set time step is met. Then, bidirectional fluid-solid coupling can be realized, and the flow field and solid field parameters at each moment can be obtained.

[0101] Follow the above steps to perform self-programming calculations. Figure 5 and Figure 6is the film thickness and pressure distribution in steady state, Figure 7 and Figure 8 The film thickness and pressure distribution after 600 time steps of bidirectional fluid-structure interaction iterations.

[0102] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A bidirectional fluid-structure coupling calculation method for a gas hydrostatic radial bearing with a pressure equalization cavity. It is characterized in that The following steps are involved: S1. Establish the air film thickness equation of the gas hydrostatic radial bearing, taking into account the movement of the main shaft in two directions and the swing in two directions; S2. Based on the gas lubrication theory, calculate the gas mass flow rate at the orifice inlet, the gas mass flow rate at the pressure equalization chamber outlet, and the change in the gas mass flow rate in the chamber; according to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the change in the chamber flow rate, and establish the flow balance equation; S3, establishing the air film flow field control equation, which is a second-order nonlinear partial differential equation; In view of the shortcomings of poor stability of explicit method and poor convergence of implicit method in numerical solution, the alternating direction implicit format method is used to discretize the air film flow field control equations, and the periodic tridiagonal equations and general tridiagonal equations are obtained; the generalized Thomas algorithm and the traditional Thomas algorithm are used to solve the air film pressure, and the pressure of the entire air film surface is integrated to obtain the air film bearing capacity; S4, taking into account the air film force, gravity, unbalanced mass force and gyroscopic force, the 5-DOF main axis force equation with rotation speed is established, which is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients, and is solved by the Runge-Kutta method; S5. Given the initial displacement of the main shaft in two directions, the initial swing in two directions and the rotation speed, solve the steady-state flow field control equation to obtain the air film support force; update the main shaft position by solving the main shaft force equation, thereby updating the air film thickness, air film pressure and air film support force; repeat the iteration until the set time step is met; due to the continuous air intake of the hydrostatic bearing, the flow balance equation must also be met in each time step.

2. According to claim 1, a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalization cavity, Features: The step S1 specifically uses the position of the maximum air film thickness of the bearing as the reference origin of the circumferential angle coordinates of the bearing, and the air film thickness equation can be obtained from the geometric relationship, and the equation includes the movement and swing of the main shaft.

3. According to the bidirectional fluid-solid coupling calculation method of a gas static pressure radial bearing with a pressure equalization cavity as described in claim 1, It is characterized in that The step S2 comprises the following sub-steps: S21, obtaining the gas mass flow rate at the orifice inlet according to the Laval nozzle model; S22, obtaining the gas mass flow rate at the outlet of the pressure equalizing chamber according to the flow speed of the gas in the x and z directions; S23, expressing the gas density in the pressure equalizing chamber with pressure, calculating the gas mass in the chamber according to the volume of the pressure equalizing chamber, and differentiating the gas mass with respect to time to obtain the change in the gas mass flow rate in the chamber; S24. According to the mass conservation equation, the inlet flow rate is equal to the outlet flow rate plus the changing flow rate in the cavity, and the flow balance equation is established.

4. According to the bidirectional fluid-solid coupling calculation method of a gas static pressure radial bearing with a pressure equalization cavity as described in claim 1, It is characterized in that The step S3 also includes the following sub-steps: S31, establish the air film flow field control equation and expand it; assume that the derivative with respect to θ is unknown, assume that the derivative with respect to ξ is a known value at the time point n, obtain a periodic tridiagonal equation group, and use the generalized Thomas algorithm to solve and obtain the air film pressure; S32. Assume that the derivative with respect to ξ is unknown, and assume that the derivative with respect to θ is a known value at time point n+1, and obtain a general tridiagonal system of equations. Use the traditional Thomas algorithm to solve and obtain the air film pressure.

5. According to claim 1, a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalization cavity, Features: The step S4 comprises the following sub-steps: S41. According to Newton's laws of motion, the force equation of the 5-DOF spindle including the rotation speed is obtained, which is a second-order non-homogeneous linear ordinary differential equation system with constant coefficients; S42. The equation is reduced to a first-order ordinary differential equation group, and the Runge-Kutta method is used to numerically solve it to obtain the position of the principal axis at the next moment, thereby obtaining the corresponding new air film thickness.

6. According to claim 1, a bidirectional fluid-solid coupling calculation method for a gas static pressure radial bearing with a pressure equalization cavity, Features: The step S5 comprises the following sub-steps: S51, input bearing parameters and environmental values, give the initial displacement of the main shaft in two directions, the initial swing and rotation speed in two directions, obtain the initial air film thickness, solve the steady-state flow field control equation to obtain the air film pressure, and then integrate to obtain the air film support force; obtain the pressure of each equalizing cavity by iteratively solving the steady-state flow balance equation; S52, updating the main axis position by solving the main axis force equation, thereby updating the air film thickness, air film pressure and air film support force; in this process, the transient flow balance equation must also be satisfied, thereby obtaining the pressure of the equalizing chamber at each moment; S53, repeat the iterations until the set time step is met; then bidirectional fluid-solid coupling can be realized, and the flow field and solid field parameters at each moment can be obtained.

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