Topology optimization of large ultrasonic tools for uniform vibration using density model

Abstract

The uniform vibration of vibrating tools for ultrasonic welding is important for industrial applications but the design requires considerable know-how due to the nature of the wave phenomena. Topology optimization is a structural optimization technique that achieves the desired objective by controlling the material distribution in the design region including voids. In this study, we propose an objective function that maximizes the amplitude of a specific target point in phase with the input. A uniform vibration is obtained by maximizing the point with the smallest amplitude among multiple target points. Optimization is performed using a commonly used density model, resulting in a vibration distribution with an aligned phase on the output surface. In addition, we perform an eigenvalue analysis of the structure by isosurface extraction to study the frequency error and the deterioration in the uniformity of the assumed vibration mode.