Elsevier

Precision Engineering

Volume 67, January 2021, Pages 14-23
Precision Engineering

Theoretical modeling and experimental study of pressure fields of inclined airflow film

https://doi.org/10.1016/j.precisioneng.2020.09.014Get rights and content

Abstract

Air flotation rails are widely used in semiconductor production lines to produce an airflow film for handling components such as liquid crystal glass substrates. During transportation, the glass substrate deforms with a large curvature, which inclines the airflow film between each hole in the rail and substrate. This study theoretically and experimentally investigated the pressure field of an inclined airflow film. First, the radial velocity distribution of the inclined airflow film was derived, and a theoretical model of the radial velocity-dominated pressure distribution was developed that considered the inclination angle and central height of the film. Then, experiments were performed to measure the pressure fields of inclined airflow films with different inclination angles and central heights, and the results showed good agreement with the theoretical results. When the central height of the airflow film was fixed, the asymmetry of the pressure field increased as the inclination angle of the airflow film increased. On the other hand, when the inclination angle of the airflow film was fixed, the asymmetry of the pressure field decreased as the central height of the airflow film increased. Thus, considering the inclination angle of the velocity distribution can better embody the asymmetry of the pressure field of the inclined airflow film. These findings serve as important theoretical and experimental references for monitoring the deformation of airflow films.

Introduction

In recent years, air flotation rails have been successfully applied in semiconductor production lines to transport large liquid crystal glass substrates [[1], [2], [3]]. For the transportation process, a glass substrate is usually suspended 0.10–0.30 mm above the rails, from which air is blown out of orifices to form an airflow film [[4], [5], [6], [7]]. The combined action of the weight of the glass substrate and pressure field of the airflow film causes the glass substrate to deform with a large curvature, which makes the airflow film between each hole in the rail and the substrate inclined instead of parallel. Thus, the glass substrate can be regarded as suspended on a number of inclined airflow films. Therefore, research on inclined airflow films is very important for understanding the flotation of the glass substrate and designing the air flotation rails.

Many researchers have previously studied the flow field characteristics of inclined airflow films. Gans et al. studied the inclined airflow film between axisymmetric nonparallel plates and found that the inclined airflow film can reduce the central pressure and eliminate the overpressure when the operating parameters of conical bearings are optimized [8]. Prata et al. investigated the pressure distribution along the valve reed for an airflow film flowing through inclined disks in the laminar state and numerically analyzed the pressure field when the irregular domain was transformed to a regular domain [9]. Deschamps et al. studied parallel and inclined airflow films flowing in the turbulent state, and their experimental results showed that different ratios between the diameters of the frontal disk and feeding orifice varied the pressure distribution [10]. Baghani et al. numerically studied the inclined airflow film in a conical microchannel heat sink and showed that increasing the convergence angle of channels reduced the temperature gradient along the bottom wall of the heat sink, which improved its thermal performance [11]. Tsubone et al. investigated the flow characteristics of a wire non-parallel plate-type electrohydrodynamic (EHD) air pump and found a nonlinear relationship between the pressure generation and air velocity [12]. Takeda theoretically and experimentally studied the squeeze air film formed between non-parallel plates and found that a steady airflow occurred because of the asymmetry of the pressure distribution, which is useful for the design of a squeeze film bearing with a noncontact air seal effect [13].

However, there have been almost no reports on the experimental pressure field of an inclined airflow film, and the difference between the velocity distributions of airflow films formed between inclined disks and between parallel disks has rarely been considered, despite its fundamental importance. In this study, the flow field characteristics of the airflow film between inclined disks were studied theoretically and experimentally. First, the unique radial velocity distribution of an inclined airflow film was derived to develop a theoretical model of the radial velocity-dominated pressure distribution considering the inclination angle and central height of the film. Then, experiments were performed to measure the pressure fields of inclined airflow films with different inclination angles and central heights for comparison with the theoretical results. When the central height of the airflow film was fixed, the asymmetry of the pressure field increased with the inclination angle of the airflow film. On the other hand, when the inclination angle of the airflow film was fixed, the asymmetry of the pressure field decreased as the central height of the air film increased. This study showed that considering the inclination angle of the velocity distribution can better reflect the asymmetry of the pressure field of an inclined airflow film. The findings of this study afford important theoretical and experimental references for monitoring the deformation of an airflow film.

Section snippets

Theoretical modeling

Fig. 1 shows the schematic of the airflow film formed by inclined disks including an upper disk and a lower disk. The upper disk is inclined, forming an inclination angle α with the lower disk, while the lower disk is supplied with air. The flow field of the inclined airflow film is described in terms of a cylindrical coordinate system (?? ?? ??), thus, h1 is the minimum height of the inclined airflow film, and h2 is the maximum height of the inclined airflow film. Noting that the inclined

Experimental methods

A 2D pressure field was generated on the working surface of an inclined airflow film unit, as shown in Fig. 5. Fig. 6 depicts the platform used to measure this 2D pressure field comprising a fixed bracket, movable bracket, drive device, precision measurement plane, and peripheral measurement circuit. The unit was pre-tensioned with a spring at its top and fixed in the movable bracket with its working surface inclined to the measurement surface. Three pins in the movable bracket ensured that the

Validation of the model

To validate the model, the air supply flow rate was set to 2.59 g/min, the central height of the inclined airflow film hc was set to 0.25 mm, and the inclination angle α was set to 0.004 rad (i.e., h2h1 = 0.2 mm). Fig. 7(a) shows the 2D pressure field obtained with the theoretical model in Section 2, and Fig. 7(b) shows the 2D pressure field measured with the experimental apparatus in Section 3. The airflow film between the inclined disks clearly formed an asymmetric pressure field with the

Conclusions and future work

In this study, the pressure field of an inclined airflow film between inclined disks was theoretically and experimentally investigated. The findings are summarized as follows:

  • 1)

    A unique radial velocity distribution of an inclined airflow film was derived and used to develop a theoretical model of the radial velocity-dominated pressure distribution that considers the inclination angle and the central height of the film.

  • 2)

    The 2D pressure field of an inclined airflow film was measured, and the

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

There are no conflicts to declare.

Acknowledgements

This study was supported by Shenzhen Science and Technology Plan (No. JCYJ20170816172938761), National Natural Science Foundation of China (Nos. U1613203 and 51975514), and Fundamental Research Funds for the Central Universities (No. 51221004).

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