Method for predicting bearing capacity of radial foil gas bearing

Abstract

The invention discloses a method for predicting the bearing capacity of a radial foil gas bearing, and belongs to the technical field of mechanical lubrication. According to the method for predicting the bearing capacity of the radial foil gas bearing, the rigidity non-uniformity characteristic of a foil structure in the length direction can be considered. According to the method, commercial finite element software Ansys Workbench and a finite element numerical calculation method of a bearing clearance process are combined, the bearing capacity can be accurately predicted, and meanwhile economical efficiency is achieved.

Description

Technical Field

[0001] This invention relates to the field of mechanical lubrication technology, specifically to a method for predicting the load-bearing capacity of a radial dynamic pressure foil gas bearing. Background Technology

[0002] Foil gas bearings are self-acting hydrodynamic gas bearings that utilize elastic supports. Because they use gas as the lubricating medium and achieve contactless operation through the hydrodynamic film formed by the high-speed rotation of the rotor, they offer advantages such as low frictional power consumption, high speed adaptability, and being oil-free. These advantages have made them key support components in many high-end equipment such as aircraft air compressors, hydrogen fuel cell air compressors, and high-speed centrifugal blowers.

[0003] The load-bearing capacity of radial foil gas bearings directly affects the load-bearing safety and operational stability of the entire machine. Accurate prediction of this capacity is of great significance for optimizing bearing structural parameters, improving overall machine performance, and upgrading and iterating equipment.

[0004] Predicting the load-carrying capacity of foil gas bearings mainly involves two steps: solving for the flow field pressure and solving for the foil deformation. These two steps involve gas-solid coupling problems. Currently, a common prediction method is to use commercial simulation software to couple the solution of the gas flow field pressure and the foil deformation under its action. However, this method often requires a significant amount of computation time and computing resources.

[0005] Another approach is to select a physical model that describes the foil structure and use the finite element method to iteratively solve the Reynolds equation for gas lubrication and the deformation of the foil. This method can predict the bearing capacity relatively quickly, but the accuracy of the results needs improvement because the physical models of the foil structure used by most scholars or practitioners are not accurate enough to describe the deformation characteristics of the foil in the length direction. Chinese patent application number "2021109863143" entitled "A Method for Predicting the Load Capacity of a Thrust Dynamic Pressure Gas Bearing" discloses a method for predicting the load capacity of a thrust dynamic pressure gas bearing. Its formula for calculating the stiffness of the corrugated foil is based on the premise that the stiffness of the corrugated foil is the same in the length direction. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for predicting the load-carrying capacity of radial foil gas bearings.

[0007] To achieve the above objectives, the present invention provides a method for predicting the load-bearing capacity of a radial foil gas bearing, comprising the following steps:

[0008] The steps include: S1: Based on the foil structure parameters, use either SolidWorks or SpaceClaim software to model and draw dividing lines on the top foil;

[0009] S2: In the Static Structural module of Ansys Workbench, configure the materials (top foil and corrugated foil are GH145, bearing housing is a rigid body), set the contact (Lagrange / Augmented Lagrange method, friction coefficient 0.05-0.2), generate the MultiZone mesh, create naming selection for the split line nodes, apply nodal forces (multi-load steps) and constraints, and run the example to generate the file.rst file;

[0010] S3: Read the nodal displacements of file.rst using Python (PyDPF-Core, PyMAPDL) and calculate the stiffness distribution along the length of the foil using formulas;

[0011] S4: Fit the stiffness distribution of the overall foil structure;

[0012] S5: Set the parameters for the operation of the foil bearing and output the stiffness matrix of the foil structure;

[0013] S6: The steady-state Reynolds equation of the radial foil bearing is solved using the finite element method. The stiffness matrix K is obtained by fitting the stiffness and used to solve the deformation equation. The iterative equations are coupled with the pressure of the bearing clearance and the deformation of the foil until the air film thickness converges. The load-bearing capacity and friction torque are then calculated.

[0014] Furthermore, the number of substeps in the Lagrange method is ≥40, the applied load is a nodal force that is large in the middle and small at both ends and fitted by a quadratic function, and the permeability tolerance of the augmented Lagrange method is 0.0001-0.001 and the normal stiffness factor is 1.0-1.3.

[0015] Furthermore, the stiffness calculation formula in step 3 is as follows: where represents the load difference of the node under two load steps, represents the displacement difference of the node under two load steps, L is the length of the foil, and s is the pitch of the corrugated foil.

[0016] Furthermore, the Reynolds equation in step 5 is: Where x represents the bearing axial direction, z represents the circumferential direction, p represents the gas film pressure, h represents the gas film thickness, Λ represents the number of bearings, μ represents the gas viscosity, ω represents the rotor speed, l represents the reference length, p0 represents the ambient air pressure, and h0 represents the reference gas film thickness.

[0017] This invention provides a method for predicting the load-carrying capacity of radial foil gas bearings, which has the following advantages: The above-mentioned method for predicting the load-carrying capacity of radially dynamic pressure foil gas bearings can be used to estimate the load-carrying capacity of bearings under various foil structures. The foil stiffness curve obtained by this method describes the deformation of the bearing in the length direction well, combining accuracy and economy. Several improvements and modifications can be made without departing from the technical principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for predicting the load-carrying capacity of a radial foil gas bearing;

[0019] Figure 2 This is a schematic diagram of a corrugated foil radial foil gas bearing structure;

[0020] Figure 3 This is a simulation model diagram of a radial foil gas bearing foil of a wave-shaped foil type;

[0021] Figure 4 This is a diagram showing the insertion and naming selection process;

[0022] Figure 5 This is a screenshot showing the effect of inserting a name selection;

[0023] Figure 6 This is a schematic diagram of a simulation model of a single corrugated foil structure;

[0024] Figure 7 This is a simulation result diagram of a single corrugated foil structure. Detailed Implementation

[0025] A method for predicting the load-carrying capacity of a radial foil gas bearing includes the following steps:

[0026] S1. Three-dimensional modeling based on foil structure parameters;

[0027] S2. Create a static structure module in Ansys Workbench, configure material properties in the project properties, import the model described in S1 into the geometry, mesh, create contact surfaces, create naming selections, and set loads and constraints, etc., and run the calculation example.

[0028] S3. Extract the deformation of the foil structure under different loads from the simulation result file obtained in S2, and calculate the stiffness distribution of the foil structure in the length direction.

[0029] S4. Fit the stiffness distribution of the wave foil structure;

[0030] S5. Set the operating parameters of the foil bearing and output the stiffness matrix of the overall foil structure;

[0031] S6. Use the foil stiffness matrix obtained in S5 to solve the Reynolds equation in the coupled gas lubrication form until it meets the accuracy requirements, and calculate the bearing capacity and friction torque, etc.

[0032] In this example, the load-carrying capacity of the corrugated foil radial gas bearing is predicted, such as... Figure 2 The diagram shown is a schematic of a corrugated radial foil gas bearing structure, which includes a top foil 1, a corrugated foil 2, and a bearing housing 3.

[0033] S1 specifically involves modeling the foil using 3D software such as SolidWorks based on its structural parameters.

[0034] Preferably, the top foil 1, the corrugated foil 2, and the bearing seat 3 are unfolded circumferentially, as shown below. Figure 3 The diagram shows a simulation model of a radial foil gas bearing foil of a corrugated foil type. A dividing line 11 is drawn on the top foil 1, located on the upper surface of the top foil. The circumferential direction of the dividing line 11 corresponds to the position where the top foil and the corrugated foil are tangent, which is also the highest point of the corrugations 21. The dividing line is used as the positioning for load application in the AnsysWorkbench software simulation analysis.

[0035] Preferably, the model's coordinate system is established at a specific point on the model, such as the wavy foil of the top foil or the endpoint of the constraint end of the top foil. The direction of one axis of the coordinate system is the same as the direction of the applied load force, and the direction of the load force is perpendicular to the top foil in its natural state and points towards the bearing seat.

[0036] If you are using SolidWorks for modeling, you can convert the model into Step format;

[0037] S2 specifically refers to:

[0038] In S2.1, create a static structure module in Ansys Workbench and configure the material used for the foil in the engineering data. In this example, the material is GH145 with a density of 8.25 g / cm3, isotropic elasticity, Poisson's ratio of 0.29, and Young's modulus of 2.14 × 1011 Pa. Import the model obtained in S1 into the geometry.

[0039] S2.2 Enter the static structure module and configure materials for each structure in the geometric structure. Since the deformation of the bearing housing is very small compared to the deformation of the foil structure, it is preferable to set the bearing housing as a rigid body, and the material can be stainless steel, etc.

[0040] S2.3 In the connection, a contact area is created between each structure. Preferably, the bottom of the corrugated foil 2 is used as the contact surface for the contact between the corrugated foil 2 and the bearing seat 3, and the surface of the bearing seat 3 is used as the target surface. The lower surface of the top foil is used as the target surface for the contact between the top foil 1 and the corrugated foil 2, and the arch of the corrugated foil 2 is used as the contact surface. The contact surface type is friction.

[0041] Furthermore, the formula for the contact surface is to use the Lagrange method or the augmented Lagrange method. When using the augmented Lagrange method, the permeability tolerance is adopted as a factor with a value between 0.0001 and 0.001, and the normal stiffness is adopted as a factor with a value between 1.0 and 1.3.

[0042] Furthermore, after the bearing housing is set as a rigid body, the bottom of the bearing housing is fixed by a geometric shape - the ground;

[0043] S2.4 Insertion method at the grid: Use MultiZone grid division method for top foil and corrugated foil. Adjust the edge size of top foil and corrugated foil. The grid size of top foil and corrugated foil is ≤0.75mm in the length direction and ≤0.3mm in the circumferential direction. Industry practitioners can adjust the grid size of foil structure according to actual needs so that the corrugation 21 has an equal fraction in the circumferential direction ≥10 and the top foil and corrugated foil have an equal fraction in the length direction ≥40, and generate the grid.

[0044] S2.5 such as Figure 4 The diagram showing the insertion of a naming selection operation illustrates how, after meshing, a naming selection is inserted at the model location. After selecting each node along the dividing line 11 described in S1, click on the geometry. The naming selection is used for subsequent load application, as shown below. Figure 5 The image shown is the result after selecting the name option;

[0045] S2.5.1 Similar to the operation in S2.5, create named selections for both ends of all dividing lines 11;

[0046] S2.6 Preferably, in the analysis settings, the number of steps is set, automatic time step selection is turned off, and when the Lagrange method is used as the contact algorithm, the number of substeps is set to at least 40; if the augmented Lagrange method is used, a smaller number of substeps can be selected.

[0047] In S2.7, insert nodal forces at the dividing lines in the static structure. In the menu for dividing loads by nodes, select "No". Use the naming option from S2.5. In this example, the load application direction is the z-axis of the model, and the length direction of the foil is the y-axis. Input the actual load on the simulated foil structure in the z-direction:

[0048] Similarly, insert nodal forces in the static structure, select the naming option described in S2.5, and enter the nodal load formula in the z-direction: In the formula, L is the length of the foil, y1 and y2 are the y coordinates of the two ends in the length direction, time is the increase of the load with time, and dy is the distance between the nodes.

[0049] A total load is applied through this nodal force. The load is fitted by a quadratic function along the length of the foil, with a large load in the middle and a small load at both ends. Multiple forces are applied to all corrugations 21 through multiple load steps. The stiffness is obtained by the relationship between the load and the displacement calculated afterward.

[0050] S2.8 Preferably, constraints are set according to the actual structure of the bearing. In this example, the top foil 1 and the wave foil 2 are fixed at one end in the circumferential direction.

[0051] S2.9 Run the example. Optionally, insert directional deformation at the solution before running the example, selecting the direction of the load force.

[0052] S3 specifically refers to:

[0053] S3.1 After the example calculation is completed, click Save in the Ansys Workbench interface and confirm the location of the example result file. The example result file is usually named: file.rst. Its path can be found in the Static Structure module, click Analysis Settings in Static Structure, and find the Solver File directory in Analysis Data Management in the menu.

[0054] S3.2 After finding the path, preferably, code is written using the Python programming language to read the displacements of all nodes at the dividing lines. In this example, the coordinates of dividing line 11 in S1 are read, PyDPF-Core is used to read the numbers of all nodes on the dividing line and arrange them in order of coordinates, and then PyMAPDL is used to retrieve the displacement results of the nodes on dividing line 11 under each load step according to the node numbers;

[0055] S3.3 uses the displacement results from S3.2 and calculates the stiffness distribution of all nodes along the length direction of the dividing line 11 using the following formula:

[0056] In the formula, This represents the load difference at the node under two load steps. This represents the displacement difference of the node under two load steps, where L is the length of the foil and s is the pitch of the corrugated foil.

[0057] S4 specifically refers to:

[0058] Preferably, after obtaining the nodal stiffness distribution along the length direction of all the dividing lines 11 described in S3, the functional relationship of the foil stiffness along the length direction on the dividing lines 11 is obtained by function fitting and used as the stiffness function of the wave foil along the length direction.

[0059] S5 specifically refers to:

[0060] S5.1 Set the bearing operating parameters, such as rotor speed, eccentricity, and gas parameters. Based on the mesh division of the bearing bearing area, construct the stiffness matrix of the top foil using shell elements. The stiffness matrix of the wave foil is constructed using the stiffness function of the wave foil along its length direction as described in S4. Finally, the overall foil stiffness matrix is ​​constructed:

[0061]

[0062] S5.2 Constructing the deformation equations for the foil structure:

[0063] Where K is the stiffness matrix of the foil, P is the nodal deformation matrix of the foil under air film pressure, and P is the pressure matrix of the nodal.

[0064] S6 specifically refers to:

[0065] S6.1 Solving the Reynolds equations for gas lubrication using the finite element method: Where x represents the axial direction of the bearing, z represents the circumferential direction of the bearing, p represents the film pressure, and h represents the film thickness. For the number of bearings, Let be the gas viscosity, l be the reference length of the bearing (generally taken as the bearing diameter), and w be the rotor operating speed. The ambient air pressure at which the bearing operates. The reference gas film thickness for the bearing is used in this equation to solve for the nodal pressure of a radial foil gas bearing. In the initial calculation, the gas film thickness is determined by the bearing... The clearance and rotor eccentricity are used to determine this.

[0066] S6.2 The deformation of the node is calculated by using the foil structure deformation equation obtained in S5 to obtain the nodal air pressure obtained in S6.1.

[0067] S6.3 The initial air film thickness plus the foil deformation is used as the updated air film thickness. Used to solve for pressure in the next cycle, repeat S6.1 and S6.2 until the foil deformation meets the accuracy requirements. When the difference in foil deformation between two adjacent iterations is 1e-7 meters, it can be considered that the foil deformation and film pressure have converged.

[0068] S6.4 The solved air pressure is used to calculate the bearing's load-carrying capacity and friction torque.

[0069] S4 to S6 were performed in Matlab;

[0070] Figure 6 This is a schematic diagram of a simulation model of a single-corrugated foil structure. This invention uses a single-corrugated foil structure to compare with a traditional linear spring model to calculate the difference in foil deformation. The foil structure uses foils with a thickness of 0.1mm, made of GH145 material. The radius of curvature of the inner ring at the corrugated foil arch is 1.5mm, the pitch is 5mm, the height of the corrugated foil is 0.5mm, and the length of the foil is 10mm. The coefficient of friction between the top foil and the corrugated foil is set to 0.05, and the coefficient of friction between the corrugated foil and the bearing seat is set to 0.1. The foil structure is simulated using the methods described in S1 to S4. To compare with a traditional linear spring, S(2.8) does not constrain the foil structure; both ends of the corrugated foil are free.

[0071] When using the load settings in S2.7, with time=10s, the total load is 10N, and the result is as follows. Figure 7 The simulation results of the single corrugated foil structure show that the calculation results using the traditional linear spring model underestimate the deformation at both ends of the foil structure. The deformation calculated using Ansys is more in line with reality. The fluid-structure interaction simulation combined with the foil stiffness calculation method described in this invention can achieve better accuracy.

Claims

1. A method for predicting the load-carrying capacity of a radial foil gas bearing, characterized in that, Includes the following steps: S1: Based on the foil structure parameters, use either SolidWorks or SpaceClaim software to model and draw the dividing lines on the top foil; S2: In the Static Structural module of Ansys Workbench, configure the materials (top foil and corrugated foil are GH145, bearing housing is a rigid body), set the contact (Lagrange / Augmented Lagrange method, friction coefficient 0.05-0.2), generate the MultiZone mesh, create naming selection for the split line nodes, apply nodal forces (multi-load steps) and constraints, and run the example to generate the file.rst file; S3: Read the nodal displacements of file.rst using Python (PyDPF-Core, PyMAPDL) and calculate the stiffness distribution along the length of the foil using formulas; S4: Fitting the stiffness distribution of the wave foil structure; S5: Set the parameters for the operation of the foil bearing and output the stiffness matrix of the overall foil structure; S6: The steady-state Reynolds equation for the radial foil bearing is solved using the finite element method. The stiffness matrix K is obtained by fitting the stiffness and then used to solve the deformation equation. The pressure of the bearing clearance and the deformation of the foil are coupled in an iterative equation until the gas film thickness converges, and the load-bearing capacity and friction torque are calculated.

2. The method according to claim 1, characterized in that, In step 2, the number of substeps of the Lagrange method is ≥40, the applied load is a nodal force that is large in the middle and small at both ends and fitted by a quadratic function, and the permeability tolerance of the augmented Lagrange method is 0.0001-0.001 and the normal stiffness factor is 1.0-1.

3.

3. The method according to claim 1, characterized in that, The stiffness calculation formula in step 3 is as follows: In the formula, This represents the load difference at the node under two load steps. This represents the displacement difference of the node under two load steps, where L is the length of the foil and s is the pitch of the corrugated foil.

4. The method according to claim 1, characterized in that, The Reynolds equation in step 5 is: , where x represents the bearing axial direction, z represents the circumferential direction, p represents the gas film pressure, h represents the gas film thickness, Λ represents the number of bearings, μ represents the gas viscosity, ω represents the rotor speed, l represents the reference length, p0 represents the ambient air pressure, and h0 represents the reference gas film thickness.

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