Method and device for predicting load capacity of high-speed aerostatic bearing, electronic equipment and storage medium

Abstract

The application is suitable for the technical field of gas bearing, and provides a load capacity prediction method and device of high-speed static pressure gas bearing and electronic equipment, which comprises the following steps: establishing a dimensionless Reynolds equation of the high-speed static pressure gas bearing; discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation; setting an initial iteration load capacity and a deflection angle, and iteratively calculating the fully implicit difference equation by using different bearing parameters to obtain a relationship diagram of bearing parameters and load capacity; and predicting the load capacity under target bearing parameters according to the relationship diagram. Since the method changes the bearing parameters, analyzes the distribution diagram of the load capacity and the bearing parameters under different rotating speeds, and predicts the load capacity of the high-speed static pressure gas bearing according to the distribution diagram, the method avoids a large amount of repetitive work caused by the fact that the analyzed load capacity data cannot be used, and effectively improves the efficiency of the load capacity prediction of the high-speed static pressure gas bearing.

Description

Technical Field

[0001] The present invention relates to gas bearing technology, and in particular to a method, device and electronic equipment for predicting the bearing capacity of a high-speed static pressure gas bearing. Background Art

[0002] In the development of turbine expansion machinery, it is very important to solve the lubrication problem of high-speed bearings. The lubricating medium of liquid-lubricated bearings is very low in compressibility and can produce great load-bearing capacity and rigidity. Therefore, liquid-lubricated bearings have been widely used in industrial production for a long time. However, the lubricating medium of liquid-lubricated bearings has a very high viscosity, which will generate large friction power consumption and heat at high speeds, making them unsuitable for high-speed applications. Gas bearings use gases as lubricating media with low viscosity, small temperature changes, clean and pollution-free, radiation-resistant, and good compressibility. These many characteristics of gas give bearings the advantages of low power consumption, long life, and high precision. They have absolute application advantages in the fields of high-speed bearings, low-friction and low-power bearings, high-precision bearings, and bearings under special working conditions.

[0003] According to the mechanism of gas film generation, gas bearings can be divided into static pressure gas bearings, dynamic pressure gas bearings, dynamic and static mixed pressure gas bearings and gas pressure film bearings. Among them, small hole throttling static pressure gas bearings are the most studied and applied.

[0004] However, most current research on gas bearings focuses on low-speed hydrostatic gas bearings. Existing technologies for calculating the load capacity of small-bore throttle hydrostatic gas bearings primarily employ finite element and finite difference methods. These methods calculate the load capacity by varying a single bearing parameter, replacing the exact solution with an approximate solution. While these methods can yield load capacity, they involve significant repetitive work, particularly as previously analyzed bearing load capacity data cannot be utilized, consuming significant manpower and resources. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, device and electronic equipment for predicting the load-bearing capacity of a high-speed static pressure gas bearing, aiming to solve the technical problem of low efficiency in predicting the load-bearing capacity of a high-speed static pressure gas bearing in the prior art.

[0006] In a first aspect, the present invention provides a method for predicting the load-bearing capacity of a high-speed static pressure gas bearing, which is applied to electronic equipment, comprising:

[0007] Establish the dimensionless Reynolds equation for high-speed hydrostatic gas bearings;

[0008] Discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation;

[0009] The iterative initial load capacity and deflection angle are set, and the fully implicit difference equation is iteratively calculated using different bearing parameters to obtain a relationship diagram between the bearing parameters and the load capacity;

[0010] Based on the relationship diagram, the load-bearing capacity under the target bearing parameters is predicted.

[0011] Preferably, the step of establishing the dimensionless Reynolds equation for the high-speed static pressure gas bearing comprises:

[0012] Combining the theory of fluid dynamic lubrication, the Reynolds equation of the high-speed hydrostatic gas bearing is established;

[0013] The Reynolds equation is non-dimensionalized to obtain the dimensionless Reynolds equation.

[0014] Preferably, the step of discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation comprises:

[0015] The dimensionless Reynolds equation is discretized using a finite difference method to obtain a nonlinear equation;

[0016] The nonlinear equation is linearized by the Newton-Raphson method to obtain a fully implicit difference equation.

[0017] Preferably, the bearing parameters include shaft diameter, and the steps of setting the iterative initial load capacity and deflection angle, iteratively calculating the fully implicit difference equation using different bearing parameters, and obtaining a relationship diagram between the bearing parameters and the load capacity include:

[0018] Setting an iterative initial bearing capacity and a deflection angle, changing the shaft diameter, and calculating the bearing capacity when the shaft diameter is different;

[0019] According to the bearing capacity under different shaft diameters, the relationship between the bearing capacity and the shaft diameter is analyzed.

[0020] Preferably, the bearing parameters include bearing clearance, and the steps of setting the iterative initial load capacity and deflection angle, iteratively calculating the fully implicit difference equation using different bearing parameters, and obtaining a relationship diagram between the bearing parameters and the load capacity include:

[0021] Setting an iterative initial load capacity and a deflection angle, changing the bearing clearance, and calculating the load capacity when the bearing clearance has different values;

[0022] According to the load-bearing capacity under different bearing clearances, the relationship between the load-bearing capacity and the bearing clearance is analyzed.

[0023] Preferably, the bearing parameters include a small hole diameter, and the steps of setting the iterative initial bearing capacity and the deflection angle, iteratively calculating the fully implicit difference equation using different bearing parameters, and obtaining a relationship diagram between the bearing parameters and the bearing capacity include:

[0024] Setting the iterative initial bearing capacity and the deflection angle, changing the diameter of the small hole, and calculating the bearing capacity when the small hole diameter is different;

[0025] According to the bearing capacity under different small hole diameters, the relationship between the bearing capacity and the small hole diameter is analyzed.

[0026] Preferably, the method further comprises:

[0027] According to the relationship diagram, predict the bearing parameters corresponding to the maximum bearing capacity as the optimal bearing parameters;

[0028] Bearing parameters for bearing design are selected from the optimal bearing parameters.

[0029] In a second aspect, the present invention provides a device for predicting the load-bearing capacity of a high-speed static pressure gas bearing, comprising:

[0030] Dimensionless equation building module, used to establish the dimensionless Reynolds equation for high-speed static pressure gas bearings;

[0031] A discretization module, used for discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation;

[0032] An iterative calculation module is used to set an iterative initial load capacity and a deflection angle, and iteratively calculate the fully implicit difference equation using different bearing parameters to obtain a relationship diagram between the bearing parameters and the load capacity;

[0033] The prediction module is used to predict the bearing capacity under the target bearing parameters according to the relationship diagram.

[0034] In a third aspect, the present invention further provides an electronic device, comprising:

[0035] processor; and

[0036] A memory in communication with the processor; wherein,

[0037] The memory stores readable instructions, and when the readable instructions are executed by the processor, the method according to the first aspect is implemented.

[0038] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the method of the first aspect when executed.

[0039] In the method and device for predicting the load-bearing capacity of a high-speed static pressure gas bearing and the electronic equipment provided by the present invention, after establishing the dimensionless Reynolds equation of the high-speed static pressure gas bearing, the dimensionless Reynolds equation is discretized to obtain a fully implicit difference equation, and then by changing the bearing parameters and analyzing the distribution diagram of the load-bearing capacity and the bearing parameters at different speeds, the load-bearing capacity of the high-speed static pressure gas bearing is predicted according to the distribution diagram, thereby avoiding a large amount of repetitive work caused by the inability to utilize the load-bearing capacity data that has been analyzed, and effectively improving the efficiency of the load-bearing capacity prediction of the high-speed static pressure gas bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flowchart of the implementation of the method for predicting the load-bearing capacity of a high-speed static pressure gas bearing shown in the first embodiment.

[0041] Figure 2 This is a schematic diagram showing the relationship between the bearing capacity and the shaft diameter at different rotational speeds in the method for predicting the bearing capacity of a high-speed static pressure gas bearing according to the first embodiment.

[0042] Figure 3 This is a schematic diagram of the relationship between the bearing capacity and the bearing clearance at different rotational speeds in the method for predicting the bearing capacity of a high-speed static pressure gas bearing according to the first embodiment.

[0043] Figure 4 This is a schematic diagram showing the relationship between the bearing capacity and the small hole diameter at different rotational speeds in the method for predicting the bearing capacity of a high-speed static pressure gas bearing according to the first embodiment.

[0044] Figure 5 This is a schematic diagram showing the relationship between the bearing capacity and the eccentricity at different rotational speeds in the method for predicting the bearing capacity of a high-speed static pressure gas bearing according to the first embodiment.

[0045] Figure 6 This is a schematic diagram showing the relationship between the bearing capacity and the gas supply parameters at different rotational speeds in the method for predicting the bearing capacity of a high-speed static pressure gas bearing according to the first embodiment.

[0046] Figure 7 The second embodiment shows a structural block diagram of a device for predicting the load-bearing capacity of a high-speed static pressure gas bearing. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0048] The following describes the specific implementation of the present invention in detail with reference to specific embodiments:

[0049] Example 1:

[0050] Figure 1 This is a flowchart illustrating the implementation of the method for predicting the load-bearing capacity of a high-speed static-pressure gas bearing, as shown in Example 1. The method for predicting the load-bearing capacity of a high-speed static-pressure gas bearing, as shown in Example 1, is applicable to electronic devices, wherein a processor is provided in the electronic device to predict the load-bearing capacity under target bearing parameters. For ease of illustration, only the portions relevant to this embodiment of the present invention are shown, and the details are as follows:

[0051] Step S110, establishing a dimensionless Reynolds equation for a high-speed static pressure gas bearing;

[0052] Step S120, discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation;

[0053] Step S130, setting the iterative initial load capacity and deflection angle, using different bearing parameters to iteratively calculate the fully implicit difference equation, and obtaining a relationship diagram between the bearing parameters and the load capacity;

[0054] Step S140: predicting the bearing capacity under the target bearing parameters according to the relationship diagram.

[0055] In high-speed static pressure gas bearings, the working gas can be hydrogen, air or helium.

[0056] Combining the theory of fluid dynamic lubrication, the Reynolds equation for high-speed hydrostatic gas bearings is established. The dimensionless Reynolds equation is obtained by non-dimensionalizing the Reynolds equation. The dimensionless Reynolds equation is as follows:

[0057]

[0058] Where θ and λ are the dimensionless coordinates along the circumferential and axial directions of the bearing, respectively; H is the dimensionless gas film thickness; P is the dimensionless gas film pressure; T is the dimensionless time; Λ is called the bearing number or compressibility coefficient; Q is the dimensionless gas mass flow factor introduced by the throttle hole; δk is the introduced Kronecker symbol, δk = 1 at the throttle hole and δk = 0 at the non-throttle hole.

[0059] The Reynolds equation is the core theory of fluid dynamic lubrication. It is obtained based on the continuity equation and the NS equation by making the following assumptions:

[0060] (1) Ignore the effects of body forces, mainly including gravity, magnetic force, etc.;

[0061] (2) No-slip boundary condition of the solid wall—that is, the fluid does not slip on the solid interface;

[0062] (3) Since the thickness of the air film is very small, the air film pressure does not change in the direction of the air film thickness, that is,

[0063] (4) Since the thickness of the air film gap is very small compared to the curvature radius of the rotor surface, the influence of the rotor curvature radius on the shape and velocity direction of the fluid film can be ignored, so the circumference of the shaft and the inner wall of the bearing sleeve can be imagined as an unfolded plane.

[0064] (5) The flow is laminar;

[0065] (6) Compared with friction, inertial force can be neglected;

[0066] (7) The viscosity and density of air remain unchanged in the direction of the air film thickness.

[0067] By making the Reynolds equation dimensionless, the accuracy of calculation can be improved and the application can be facilitated.

[0068] Because the dimensionless Reynolds equation is a second-order partial differential equation, it is necessary to discretize the dimensionless Reynolds equation to obtain a nonlinear equation, and then linearize the nonlinear equation through the Newton-Raphson method to obtain a fully implicit difference equation, so as to replace the analytical solution with a numerical solution.

[0069] The finite difference method can be used to discretize the dimensionless Reynolds equation. The finite difference method is a numerical solution method. Its basic idea is to first mesh the domain of the problem, and then, at the mesh nodes, use appropriate numerical differentiation formulas to replace the differential quotients in the well-defined problem with difference quotients, thereby discretizing the original problem into a difference format and then obtaining a numerical solution.

[0070] In order to obtain the bearing capacity, it is necessary to know the pressure distribution and deflection angle. The solution is to iterate the fully implicit difference equation. The corresponding pressure and deflection angle when the iteration converges are the required values. The conditions for iterative convergence when calculating the pressure distribution are as follows:

[0071]

[0072] When calculating the convergence of the deflection angle θ0, given that the direction of the external load is vertically downward, the resultant force should be consistent with the direction of the external load, and the load angle The calculation can take α0<10 -3 (radians) as the convergence criterion. Follow the steps below to find the deflection angle using Newton's method:

[0073] Any Find the resultant force F x , F y and load angle

[0074] Might as well take Same calculation

[0075] For the iterative process The selection is based on the following Newton iteration formula:

[0076]

[0077] Finally, the finite difference format of the dimensionless Reynolds equation is iterated and the corresponding pressure at convergence is the required pressure. The solution of the bearing capacity is obtained by integrating the pressure, as follows:

[0078]

[0079]

[0080]

[0081] From the above, it can be seen that by setting the iterative initial load capacity and deflection angle, the fully implicit difference equation is iteratively calculated using different bearing parameters to obtain the relationship diagram between the bearing parameters and the load capacity. Based on the relationship diagram, the load capacity under the target bearing parameters is predicted.

[0082] Specifically, bearing parameters include shaft diameter, bearing clearance, small hole diameter, and eccentricity. When analyzing the relationship between load capacity and bearing parameters, the initial load capacity and deflection angle are pre-set. Then, the shaft diameter, bearing clearance, small hole diameter, and eccentricity are varied. The load capacity is calculated for different values ​​of these bearing parameters, thereby obtaining the relationship between the load capacity and the bearing parameters.

[0083] For example, taking the rotation speed of 100,000 rpm and 120,000 rpm as an example, changing the shaft diameter from 16mm to 45mm, the corresponding relationship between the shaft diameter and the load-bearing capacity at different speeds is obtained as follows: Figure 2 .

[0084] For example, taking the speed of 100,000 rpm and 120,000 rpm as an example, changing the bearing clearance from 0.02mm to 0.05mm, the corresponding relationship between the bearing clearance and the load-bearing capacity at different speeds is obtained as follows: Figure 3 .

[0085] For example, taking the rotation speed of 100,000 rpm and 120,000 rpm as an example, changing the small hole diameter from 0.25mm to 0.4mm, the corresponding relationship between the small hole diameter and the bearing capacity at different rotation speeds is obtained as follows: Figure 4 .

[0086] For example, taking the rotation speed of 100,000 rpm and 120,000 rpm as an example, changing the eccentricity from 0.2 to 0.35, the corresponding relationship between the eccentricity and the bearing capacity at different rotation speeds is obtained as follows: Figure 5 .

[0087] Taking the speed of 100,000 rpm, 120,000 rpm and 140,000 rpm as an example, the different bearing parameters are combined into one air supply parameter. The air supply parameter is shown in the following formula. The air supply pressure and the number of holes remain unchanged, the small hole diameter is changed from 0.25mm to 0.4mm, and the bearing clearance is changed from 0.02mm to 0.05mm. Figure 6 This is a diagram showing the relationship between the load-bearing capacity and the air supply parameters at different speeds.

[0088]

[0089] Where n is the number of air supply holes on a circumference, d is the diameter of the small hole or air supply hole, μ is the gas viscosity, Ps is the air supply pressure, Cr is the radial clearance of the bearing, is the gas constant, T0 is the gas supply temperature, and g is the acceleration due to gravity.

[0090] Optionally, after obtaining the relationship diagram between bearing parameters and load-bearing capacity, the bearing parameters corresponding to the maximum load-bearing capacity are predicted according to the relationship diagram as the optimal bearing parameters, and then the bearing parameters used for bearing design are selected from the optimal bearing parameters, thereby optimizing the bearing parameters to obtain the maximum load-bearing capacity, greatly improving the load-bearing performance of the gas bearing.

[0091] Example 2:

[0092] like Figure 7 As shown, the second embodiment of the present invention provides a device for predicting the load-bearing capacity of a high-speed static-pressure gas bearing. The device can perform all or part of the steps of any of the above-mentioned methods for predicting the load-bearing capacity of a high-speed static-pressure gas bearing. The device includes:

[0093] Dimensionless equation establishment module 1, used to establish the dimensionless Reynolds equation for high-speed static pressure gas bearings;

[0094] Discrete module 2, used to discretize the dimensionless Reynolds equation to obtain the fully implicit difference equation;

[0095] Iterative calculation module 3 is used to set the iterative initial load capacity and deflection angle, use different bearing parameters to iteratively calculate the fully implicit difference equation, and obtain the relationship diagram between bearing parameters and load capacity;

[0096] The prediction module 4 is used to predict the bearing capacity under the target bearing parameters according to the relationship diagram.

[0097] Example 3:

[0098] A third embodiment of the present invention provides an electronic device capable of executing all or part of the steps of any of the above-mentioned methods for predicting the load-bearing capacity of a high-speed static pressure gas bearing. The electronic device includes:

[0099] processor; and

[0100] a memory communicatively connected to the processor; wherein,

[0101] The memory stores instructions that can be executed by the at least one processor. The instructions are executed by the at least one processor to enable the at least one processor to perform the method as described in any of the above exemplary embodiments, which will not be elaborated here.

[0102] In this embodiment, a storage medium is also provided. The storage medium is a computer-readable storage medium, such as a temporary or non-temporary computer-readable storage medium containing instructions. The storage medium, for example, includes a memory containing instructions. The instructions can be executed by a processor of a server system to implement the load capacity prediction method for a high-speed static pressure gas bearing.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the load-bearing capacity of a high-speed static pressure gas bearing, applied to electronic equipment, characterized in that: The method comprises: Establish the dimensionless Reynolds equation for high-speed hydrostatic gas bearings; Discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation; The iterative initial load capacity and deflection angle are set, and the fully implicit difference equation is iteratively calculated using different bearing parameters to obtain a relationship diagram between the bearing parameters and the load capacity; According to the relationship diagram, the load-bearing capacity under the target bearing parameters is predicted; wherein: The step of discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation comprises: The dimensionless Reynolds equation is discretized using a finite difference method to obtain a nonlinear equation; The nonlinear equation is linearized by the Newton-Raphson method to obtain a fully implicit difference equation.

2. The method according to claim 1, wherein The steps of establishing the dimensionless Reynolds equation for a high-speed static pressure gas bearing include: Combining the theory of fluid dynamic lubrication, the Reynolds equation of the high-speed hydrostatic gas bearing is established; The Reynolds equation is non-dimensionalized to obtain the dimensionless Reynolds equation.

3. The method according to claim 1, wherein The bearing parameters include shaft diameter, the setting of iterative initial load capacity and deflection angle, and the iterative calculation of the fully implicit difference equation using different bearing parameters to obtain a relationship diagram between bearing parameters and load capacity. The steps include: Setting an iterative initial bearing capacity and a deflection angle, changing the shaft diameter, and calculating the bearing capacity when the shaft diameter is different; According to the bearing capacity under different shaft diameters, the relationship between the bearing capacity and the shaft diameter is analyzed.

4. The method according to claim 1, wherein The bearing parameters include bearing clearance, the setting of iterative initial load capacity and deflection angle, and the iterative calculation of the fully implicit difference equation using different bearing parameters to obtain a relationship diagram between bearing parameters and load capacity. The steps include: Setting an iterative initial load capacity and a deflection angle, changing the bearing clearance, and calculating the load capacity when the bearing clearance has different values; According to the load-bearing capacity under different bearing clearances, the relationship between the load-bearing capacity and the bearing clearance is analyzed.

5. The method according to claim 1, wherein The bearing parameters include the small hole diameter, the setting of the iterative initial load capacity and the deflection angle, and the iterative calculation of the fully implicit difference equation using different bearing parameters to obtain a relationship diagram between the bearing parameters and the load capacity. The steps include: Setting the iterative initial bearing capacity and the deflection angle, changing the diameter of the small hole, and calculating the bearing capacity when the small hole diameter is different; According to the bearing capacity under different small hole diameters, the relationship between the bearing capacity and the small hole diameter is analyzed.

6. The method according to claim 1, wherein The method further comprises: According to the relationship diagram, predict the bearing parameters corresponding to the maximum bearing capacity as the optimal bearing parameters; Bearing parameters for bearing design are selected from the optimal bearing parameters.

7. A device for predicting the load-bearing capacity of a high-speed static-pressure gas bearing using the method for predicting the load-bearing capacity of a high-speed static-pressure gas bearing according to claim 1, characterized in that: The device comprises: Dimensionless equation building module, used to establish the dimensionless Reynolds equation for high-speed static pressure gas bearings; A discretization module, used for discretizing the dimensionless Reynolds equation to obtain a fully implicit difference equation; An iterative calculation module is used to set an iterative initial load capacity and a deflection angle, and iteratively calculate the fully implicit difference equation using different bearing parameters to obtain a relationship diagram between the bearing parameters and the load capacity; The prediction module is used to predict the bearing capacity under the target bearing parameters according to the relationship diagram.

8. An electronic device, characterized in that: The electronic device comprises: processor; and A memory in communication with the processor; wherein, The memory stores readable instructions, and when the readable instructions are executed by the processor, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the method according to any one of claims 1 to 6 when executed.

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