Design of Experiment (DOE) for Vibration Horns Using Modal Analysis to Improve Resonant Frequency in the Simple Shear Extrusion Process

Document Type : Research Paper

Author

Mechanical Engineering Department, University of Birjand, Birjand, Iran

Abstract

In most studies conducted to transmit ultrasonic vibrations to the target workpiece, vibration concentrators (horns) are employed, whose design, simulation (modal analysis), and manufacturing is critical. The use of vibration horns in the simple shear extrusion process, aimed at reducing the forming force, has been investigated both through simulation and experimentally. The effects of input parameters of the concentrators, including element type (cylindrical, conical, and exponential) and geometric dimensions, on the output parameter of resonant frequency have been examined. Design of experiments (DOE) based on the response surface methodology (RSM) and the Box-Behnken design was employed to precisely investigate and analyze the effects of each input parameter and their interactions on the resonant frequency. The design of experiments for the concentrators was conducted using Minitab software version 2019, while the process simulation was performed through modal analysis in Abaqus/Explicit software. The results indicated that to optimize the input parameters and achieve the maximum resonant frequency, the optimal element type across all three vibration zones is exponential. Furthermore, the vibration zone diameter and transducer connection zone diameter were found to have minimal impact and were eliminated. A comparison of the resonant frequency of the vibrating horn from modal analysis simulation with experimental vibration test values showed an error of less than 2%, indicating the high accuracy of the process. After obtaining the optimal horn parameters, the combined process of simple shear extrusion with the vibrating horn was simulated. Subsequently, a comparison and validation of the finite element simulation results for the forming force with the experimental values were carried out. The results from the experimental tests and the simulation of the combined simple shear extrusion process with the vibrating horn showed an error margin of 9%, confirming the efficacy of the new process.

Keywords

References

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Iranian Journal of Materials Forming
Volume 13, Issue 1
January 2026
Pages 71-82

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