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$Measuring Spray Droplet Size from Agricultural Nozzles Using Laser Diffraction$

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Theoretical Model for a Pneumatic Nozzle-Cylindrical Flapper System.

Peimin Xu¹, Kazuaki Inaba¹, Toshiharu Kagawa²

¹Department of Transdisciplinary Science and Engineering, Institute of Science Tokyo, Tokyo 152-8550, Japan.

|October 29, 2025

Summary

This study optimizes a nozzle-flapper system to precisely measure and compensate for shaft displacement in air bearings, crucial for high-yield semiconductor manufacturing. The enhanced model ensures shaft stability under processing forces, improving production efficiency.

Keywords:

high-speed rotation spindle with aerostatic bearings machining nozzle flapper pneumatic

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Area of Science:

Mechanical Engineering
Aerospace Engineering
Manufacturing Technology

Background:

Air bearings increase semiconductor production speed but face challenges with shaft displacement due to non-contact support.
Engineering requirements mandate limiting lateral shaft deflection to within 30 μm under transverse forces.
Previous research validated a nozzle-flapper system for measuring shaft displacement up to 20,000 rpm and compensating for a 5 N external force.

Purpose of the Study:

To analyze and optimize the system characteristics of a cylindrical nozzle-flapper mechanism for enhanced shaft displacement control.
To develop an optimized theoretical model for cylindrical nozzle-flapper configurations based on geometric airflow analysis.
To experimentally validate the proposed theoretical model for improved air bearing performance in semiconductor manufacturing.

Main Methods:

Modeling the geometric space of a cylindrical nozzle-flapper.
Proposing an airflow hypothesis based on the specific geometry.
Integrating the hypothesis into a standard nozzle-flapper theoretical model to create an optimized method for cylindrical configurations.
Conducting experimental validation of the developed theoretical model.

Main Results:

An optimized theoretical model for cylindrical nozzle-flapper systems was developed.
The model accurately reflects the system characteristics influenced by the unique geometry.
Experimental results confirmed the effectiveness of the proposed model in addressing shaft displacement challenges.

Conclusions:

The optimized theoretical model provides a robust solution for controlling shaft displacement in air bearing systems.
This advancement is critical for enhancing precision and yield in semiconductor manufacturing.
The study successfully validated a refined approach for nozzle-flapper displacement sensing and compensation.