The aim of this research is to investigate different types of air bearings for a large number of crashes using real operational parameters from the.

**Table of contents**

- Original Articles
- Comparison between grooved and plane aerostatic thrust bearings: static performance
- Advantages of Air Bearings | Machine Design
- A-65x PIglide HB: Hemispherical Air Bearing

Save to Library. Create Alert. Share This Paper. Figures and Tables from this paper. Figures and Tables. Citations Publications citing this paper. Performance characteristics of rectangular aerostatic thrust bearing by conformal mapping Shang-Han Gao , Sheng-Long Nong. References Publications referenced by this paper. Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice -type restrictor on its performance Yuntang Li , Han Ding. As mentioned above, a single air bearing can be modeled as a sliding spring which has only nonzero stiffness in the normal direction which represents the effect of the finite area of pressurized air.

### Original Articles

The air bearing system can be modeled as a combination of distributed sliding springs, and each one of them represents a single air bearing, which indicates three single air bearings in the air bearing system in Figure 5. As shown in Figure 6 , two air bearing systems in the ultra-precision positioning dual-stage system are modeled as two sets of multiple distributed sliding springs, which represent as blue spring in this figure. In this way, the established air bearing model can reflect the tilt characteristics of actual air bearing system and can be used in the dynamic modeling of ultra-precision positioning dual stage.

Figure 6. Dynamic model of the ultra-precision positioning dual stage. In the ultra-precision positioning dual stage, the 12 air bearings of the air-foot can be simplified as 12 distributed sliding springs mentioned above, to ensure the fine stage floats on the granite base with no horizontal friction and high vertical stiffness. The 16 air bearings in the coarse air bearing system can also be simplified as 16 distributed sliding springs to support the linear motor slider in the x and y directions.

The influence of vibration caused by excitation of the air bearing system and mechanical structure dominates the performance of the ultra-precision positioning dual stage. Because these effects are within the ultra-precision positioning dual stage, the stage needs to be divided into a finite number of components.

This number has to be relatively small so as to come up with a low dimensional description of the ultra-precision positioning dual stage. On one hand, this number should be as small as possible in order to keep track of the basic mechanisms causing the dynamic behavior of the ultra-precision positioning dual stage; on the other hand, this number should be large enough to be able to describe all the relevant phenomena with sufficient details.

In order to be able to describe the aforementioned effects, the ultra-precision positioning dual stage is split up into four components or bodies. Body 1 contains the granite base and the linear motor stator of the x direction. Body 2 contains only the linear motor slider of the x direction or the linear motor stator of the y direction. Body 3 contains the linear motor slider of the y direction, the planar motor, and the table of the fine stage.

Body 4 contains only the air-foot of the fine stage. The dynamic model of the ultra-precision positioning dual stage is shown in Figure 6. The blue springs represent air bearings, and the black springs fixed at both ends reflect the structural flexibility. The vibration differential equations are derived according to the Newton—Euler method. The resulting equations are in the matrix form. Clearly, the stiffness matrix K q , t is not diagonal, which means the stiffness of air bearings is coupled with other structural stiffness. The rigid body masses are calculated based on the shape and size of corresponding components.

The structural spring stiffness is obtained through the finite element analysis of the corresponding components in the fine stage. In order to obtain the spring stiffness of air bearings, the following procedures are proposed:.

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According to the structural properties of the coarse air bearing system and air-foot, we establish a 3D flow model of the air bearing, set proper boundary conditions and properties of the fluid, select the appropriate solver for iterative calculation, and use computational fluid dynamics CFD software Fluent to obtain numerical solutions of the gas pressure distribution.

Obtain the load capability of each air bearing. The load capability can be calculated by integrating the pressure in the lubricating film area. The air bearing in the air-foot is a ring bearing, the load capacity of which can be calculated as follows. The air bearing in the coarse air bearing system is a rectangular bearing, and its load capacity can be calculated as follows.

Calculate the air bearing stiffness. According to the above steps, the load capacity W can be calculated when the gas film thickness is h 0.

The stiffness of an air bearing can be obtained as follows. There are three specifications of air bearings in the ultra-precision positioning dual stage: 12 air bearings in the air-foot, 8 vertical air bearings, and the 8 horizontal air bearings in the coarse air bearing system. Each type of the spring has the same stiffness. The damp effect of aerostatic bearing is squeezed-film damping mainly, and its damping can be calculated by the following equation.

## Comparison between grooved and plane aerostatic thrust bearings: static performance

The damping ratio of a vertical air bearing and a horizontal air bearing in the coarse air bearing system can be identified as 0. The damping ratio of an air bearing in the air-foot can be identified as 0. The ultra-precision positioning dual stage modeled by four bodies is represented by a 24th-order dynamic model. This dynamic model can be used for analysis in the simulation software package Simulink, by transforming it into C-code and using the so-called s-functions defined in Simulink. Besides time-domain analysis, frequency-domain analysis can also be performed.

To confirm the validity of the simulation result, a series of experiments of the ultra-precision positioning dual stage are conducted. The standard drop hammer tests on specimens have been carried out. The locations of the excitation point and sensor arrangement are shown in Figure 7.

In the drop hammer test, the hammer equipped with a rubber head is used, and an acceleration sensor CA-YD and CA-YD is placed at the test position to obtain the vibration responses. Figure 7. Location of excitation points and measurement points. Seven groups of experiments are performed, each group for four times, and average data values are taken. The excitation point and measurement point for each experiment are shown in Table 1. Using modal test and analysis software LMS to collect excitation signals and response signals, with a sampling resolution of 0.

The experimental results for tests 1—7 are shown in Figure 8. Table 1. Locations of excitation points and sensors for each experiment.

## Advantages of Air Bearings | Machine Design

In test 1 and test 2, the excitation point is located on the stator of the y direction linear motor, and the measurement points are located on the stator and slider of the y direction linear motor, respectively. The direction of excitation and measurement are in the z direction. In test 3 and test 4, the excitation point is located on the slider of the y direction linear motor; the measurement points are located on the stator and slider of the y direction linear motor, respectively; and the direction of excitation and measurement are the same as those in test 1 and test 2.

The excitation and measurement points of the four tests are interchangeable; therefore, the common peak frequencies of the two frequency response functions in both tests are adopted. According to the position and direction of the excitation points, the frequencies corresponding to the vibration mode for rotation around x-axis and y-axis and translational motion along z-axis of coarse stage are relatively easy to be represented in tests 1—4. The frequencies corresponding to the vibration mode for rotation around x-axis and z-axis of coarse stage are relatively easy to be excited in test 5.

The frequencies corresponding to the vibration mode for rotation around y-axis and z-axis of coarse stage are relatively easy to be excited in test 6. The frequencies corresponding to the vibration mode for rotation around x-axis and y-axis of fine stage are relatively easy to be excited in test 7.

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Comparison of simulation results and experimental results is shown in Table 2. Table 2. Simulation and experimental modal of the ultra-precision positioning dual stage. Figure 9. Figure In this article, a novel dynamic modeling method for air bearing is proposed, which can simultaneously reveal the moving direction dynamics, and the tilt characteristics of bearings. The proposed method models a signal air bearing as a sliding spring with force direction determined by stator and location by the slider and models a system of air bearings as a combination of distributed sliding springs.

And each spring has only nonzero stiffness along the normal axis which represents the effect of the finite area of pressurized air. An ultra-precision positioning dual stage which contains multiple air bearings is presented, and the system structure and bearing distribution are also introduced.

The proposed dynamic modeling method has been applied successfully for an ultra-precision positioning dual stage which contains multiple air bearings. An analytic dynamic model of an ultra-precision positioning dual stage with air bearings is established. Model parameters of the dynamic model are obtained through the finite element analysis. Experimental results demonstrate that the proposed modeling method for air bearings is accurate and effective.

The proposed dynamic model can quantitatively describe the ultra-precision positioning dual stage accurately and can be successfully used for controller design or dynamic optimization in the future. Skip to main content. Advances in Mechanical Engineering.

## A-65x PIglide HB: Hemispherical Air Bearing

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