# Design of an Angled Single-Excitation Elliptical Vibration System

## TL;DR

This paper presents a new angled vibration system for machining that improves elliptical motion control through theoretical and experimental analysis.

## Contribution

A novel angled single-excitation elliptical vibration system is designed and validated with theoretical and experimental methods.

## Key findings

- Resonant frequency and phase difference decrease with increasing included angle.
- Transverse amplitude increases while longitudinal amplitude decreases with larger angles.
- Experimental results align well with theoretical calculations for elliptical trajectories and resonant frequencies.

## Abstract

An angled single-excitation elliptical vibration system for ultrasonic-assisted machining was developed in this paper, which was composed of a giant magnetostrictive transducer and an angled horn. Based on the continuous boundary conditions between the components, the frequency equation of the angled vibration system was derived, and the resonant frequencies of vibration systems with different angles were theoretically calculated. The finite element method was employed to investigate the impact of varying angles on the resonant frequency, elliptical trajectory, phase difference, and output amplitude of the vibration systems. The electrical impedance of the vibration system and the longitudinal and transverse vibration amplitudes at the end face of the horn were tested experimentally. The results show that the resonant frequency and phase difference in the vibration system decreased, the transverse amplitude of the output elliptical trajectory increased, and the longitudinal amplitude decreased with the increase in the included angle. The elliptical trajectories obtained from the test were generally consistent with the calculated results, and the calculated values of the resonant frequencies of the three angled vibration systems were in good agreement with the experimental test values.