Modeling and fitting of an ultrasonic straight-blade cutting system
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ORIGINAL ARTICLE
Modeling and fitting of an ultrasonic straight-blade cutting system Ke Ma 1 & Jianfu Zhang 1,2 & Pingfa Feng 1,2,3 & Dingwen Yu 1 & Zhijun Wu 1 Received: 24 April 2020 / Accepted: 19 October 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
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. Keywords Ultrasonic straight-blade tool . Vibration model . Resonant design . Error analysis
1 Introduction The Nomex honeycomb composites have been widely applied in the aviation, aerospace, defense, and automotive field due to their low density, high specific strength, high specific stiffness, and good thermal insulation [1–3]. However, Nomex honeycomb composite has poor processability because of its special properties, such as anisotropy, brittleness, and easy deformation. Nomex honeycomb composite processing defects caused during the conventional processing techniques, such as high-speed milling, greatly affected its application. In traditional milling, the high-speed rotating tools smash the Nomex honeycomb composites, causing problems such as * Jianfu Zhang [email protected] 1
Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
2
State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
3
Division of Advanced Manufacturing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
cell collapse, large dust high tool wear, and low surface quality, whereas Nomex honeycomb composite ultrasonic processing provides an ideal processing effect [4, 5]. The ultrasonic straight-bl
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