# Theoretical Model for a Pneumatic Nozzle–Cylindrical Flapper System

## TL;DR

This paper presents a theoretical model for a pneumatic nozzle–cylindrical flapper system to improve air bearing performance in semiconductor manufacturing.

## Contribution

A novel theoretical model for cylindrical nozzle–flapper systems is proposed and experimentally validated.

## Key findings

- A geometric model of the cylindrical nozzle–flapper system was developed.
- An airflow hypothesis was integrated into the theoretical model for cylindrical configurations.
- Experimental validation confirmed the effectiveness of the proposed model.

## Abstract

To increase semiconductor production yield and meet the growing global demand, air bearings offering higher processing speeds and reduced friction losses have been proposed as an ideal solution. However, due to the non-contact support characteristic of air bearings, challenges such as shaft displacement caused by processing resistance inevitably arise. As an engineering requirement, the shaft must restrict lateral deflection to within 30 μm under transverse force. In our previous research, a compensation system using a nozzle–flapper mechanism as a displacement sensor was proposed to address shaft displacement. The effectiveness of the nozzle–flapper system in measuring shaft displacement was validated at rotational speeds up to 20,000 rpm. Furthermore, the compensation system’s ability to maintain the shaft’s initial position under a 5 N external force was verified in related collaborative research. In this study, building upon prior work, we further analyze the system characteristics of the cylindrical nozzle–flapper. This includes modeling the geometric space formed by the specific shape of the cylindrical flapper and nozzle and proposing an airflow hypothesis based on this geometry. The hypothesis is incorporated into the theoretical model of a standard nozzle–flapper system, resulting in an optimized theoretical method applicable to cylindrical configurations. Experimental results validating the effectiveness of the proposed model are also presented.