Modeling and fitting of an ultrasonic straight-blade cutting system

Abstract

Ultrasonic straight-blade tool is one type of effective tool for processing Nomex composites. As a system part, the ultrasonic tool, directly contacting the workpiece and providing the vibration, is an important acoustic element alongside the cutter. And the resonant frequency of ultrasonic processing systems, a key parameter of the vibration performance, is greatly influenced by the straight-blade tool changes when connected to the ultrasonic system. In the present paper, a mathematical model for calculating the resonant frequency was established for the ultrasonic straight-blade tools with variable cross-sectional areas. The relationship between the parameters of the straight-blade tool and the resonant frequency, as well as between the force and the vibration of the ultrasonic system, were presented and utilized to calculate the system resonant frequency change and the corrected horn value to hold the frequency. To solve the vibration equations, they were refined by fitting a trigonometric function combination. The errors of the vibration equations and the fitting were analyzed, showing the applicable scope of the vibration equations. According to the model and the common ultrasonic straight-blade tool sizes, four tools were manufactured for verification experiments. Results showed that the presented model could be well matched with the actual value.