Aiming at the problem of low stiffness of aerostatic bearing, according to the principle of gas-solid coupling, this paper designs a kind of aerostatic thrust bearing with elastic equalizing pressure groove (EEPG) and investigates the effect of elastic equalizing pressure groove (EEPG) on the stiffness of aerostatic bearing. According to the physical model of the bearing, one deduces the deformation control equation of the elastic equalizing pressure groove and the control equation of gas lubrication, using finite difference method to derive the control equations and coupling calculation. The bearing capacity and stiffness of aerostatic bearing with EEPG in different gas film clearance are obtained. The calculation results show that the stiffness increased by 59%. The results of numerical calculation and experimental results have good consistency, proving the gas-solid coupling method can improve the bearing stiffness.
Aerostatic bearings are widely used in the field of high speed and high accuracy due to their good performance [
At present, there are two methods to improve the stiffness of aerostatic bearings: one way is the change of geometric structure of aerostatic bearing, increasing the supply pressure, increasing the throttle hole quantity, decreasing throttle hole diameter, and setting the equalizing pressure groove and a throttling cavity with different shapes on the aerostatic bearing surface to obtain a high stiffness [
Through the above analysis, it can be seen that the gas film clearance is an important factor that affects the stiffness of aerostatic bearing. In this paper, the gas-solid coupling method is proposed to enhance the stiffness of aerostatic bearing with EEPG, and the gas film clearance can be changed dynamically through the deformation of EEPG. The mathematical model of the gas-solid coupling of EEPG is derived. The numerical simulation and experimental results show that the EEPG can improve the stiffness of aerostatic bearing.
This section mainly introduces the two-dimensional physical model and its working principle. This new type of bearing consists of two parts: the bearing body and the elastic thin plate. The elastic thin plate is connected with the bearing body through vacuum brazing, and the EEPG is mainly obtained by the deflection deformation of elastic thin plate in this paper. The new bearing structure is shown in Figure
Schematic diagram of physical model.
Figure
Deformation and working state of EEPG.
Manufacture process
Working state
The bearing is working, the elastic thin plate is affected by the pressure difference between the supply pressure and the gas film pressure, and thin elastic deformation is generated, thus forming an EEPG. The gas film clearance is small, with gas film pressure distribution near the supply pressure, and the pressure difference of thin plate is small, so the basic elastic thin plate is not deformed. Elastic equalizing pressure groove depth of aerostatic bearing is substantially equal to the initial processing produce. At this time, the working state is equal to the working state of the aerostatic bearing of the REPG (rigid equalizing pressure groove). The gas film clearance increases to a certain range, the gas film pressure is less than the supply pressure. The elastic thin plate pressure difference increases, resulting in deformation of thin plate, but less than the depth of the initial equalizing pressure groove. At the moment, the depth of the EEPG is equal to initial elastic equalizing pressure groove minus the deformation of the thin plate. The gas film clearance increases to limit clearance, with distribution of film pressure close to standard atmospheric pressure. At the same time, the elastic thin plate is only affected by the supply pressure, the EEPG disappears, and the equalizing pressure effect disappears. Figure
It is worth noting that the gas supply pressure at work should be greater than processing pressure (
According to the assumption of small deflection bending theory of thin plate [
The stress component is obtained by (
That is,
Taking a parallelepiped element from the elastic thin plate, each edge length is
By the same argument, on the cross section which is perpendicular to the
The equilibrium equation of thin plate is
From (
The calculation model of this paper is a circle, so formula (
The general form of the Reynolds equation is shown in
The ideal gas state equation is shown in
In low speed state, there is negligible relative sliding speed. Because the static gas bearing is calculated in this paper, the pressure does not change with time, and the time-term is equal to 0. Therefore, the right side of (
The mass flow rate of the bearing is equal to the mass flow of the outlet bearing.
Here,
Given the boundary conditions and the simultaneous equations (
The calculation formula of bearing stiffness is as follows:
The calculation formula of stiffness is obtained:
The EEPG generates deflection deformation in the range of
The pressure
The governing equations (
4-order finite difference scheme in polar coordinates.
The calculation process of this paper is the coupling process of the deformation control equation and the gas lubrication governing equation of EEPG. The flow chart of gas-solid coupling is shown in Figure
Flow chart of gas-solid coupling.
Build the aerostatic bearing stiffness test rig, as shown in Figure
Bearing stiffness test rig. (
According to the calculation method of the previous section, the calculation parameters of gas bearing, as shown in Table
Bearing parameters.
Parameter | Value |
---|---|
|
|
|
1.12 |
|
0.4 |
|
0.25 |
|
30 |
|
15 |
|
25 |
|
0.3 |
|
|
|
1.4 |
|
29.27 |
|
300 |
|
0.5 |
|
0.1 |
Diagram of (i) coupling deformation of EEPG and (ii) pressure distribution.
In order to compare the performance of the aerostatic bearing with EEPG, this paper calculated the performance of aerostatic bearing with REPG in the same performance parameters. Calculation parameters are also shown in Table
Pressure distribution of aerostatic bearing with REPG.
According to the calculation results of model 1 and model 2, the numerical performance curves of the 2 kinds of aerostatic bearings can be obtained, as shown in Figure
Performance comparison curves of two kinds of aerostatic bearing with different pressure equalizing grooves.
Bearing capacity curve
Stiffness curve
Mass flow curve
It can be seen from Figure
When the gas film clearance is from 6
When the gas film clearance is more than 16
As shown in Figure
It can be seen from Figure
According to the above analysis, it is found that the performance of aerostatic thrust bearing with EEPG is better than that of the aerostatic bearing with REPG.
Figure
Tested aerostatic bearings.
The experimental results are shown in Figure
Experimental results.
Bearing capacity curve
Stiffness curve
In this paper, the bearing characteristics of aerostatic bearing with EEPG are studied by numerical calculation and experiment. Through the research, we can draw the following conclusions. In this paper, the use of gas-solid coupling adaptive mode of aerostatic bearing is feasible in theory and practice. The stiffness of aerostatic thrust bearing with EEPG is increased by 40% than that of the aerostatic bearing with REPG. The structure and location of the EEPG have a great influence on the performance of the bearing, so how to optimize the design warrants further research.
The authors declare that they have no conflicts of interest.
The authors would like to acknowledge that the project was supported by the National Natural Science Foundation of China (51375384), China Postdoctoral Fund (2016M602937XB), and Xi’an Technological University gas lubrication research and innovation team construction project.