Effect of resonant frequency variation on the ultrasonically assisted deep drawing process: numerical and experimental study

Abstract

This paper focuses on the system frequency variation effect on the ultrasonically assisted deep drawing (UADD) process, based on experimental and numerical approaches. A special ultrasonic die is precisely designed and fabricated to improve draw-ability and reduce the forming force. The longitudinal resonance frequency of the vibratory system is established as 20 kHz prior to forming load application on the system. Consequently, a three-dimensional finite element model of the deformation process is developed. The output of this simulation shows good agreement with the experimental test results. The UADD test with 5 μm amplitude demonstrated 5.6% decrease in maximum average force and 12.2% increase in the drawing ratio when compared with the conventional deep drawing (CDD). In addition, the resonant frequency variation effect on the forming force is revealed during the experimental tests. Since the excitation frequency is tuned out with the natural frequency of the system at the beginning of the test, no forming force reduction was observed at this stage. To further investigate this effect, two complementary steps are implemented in this work. In the first phase, the natural frequency of the system is determined by numerical modal analysis and reshaping the blank at various deformation stages. Consequently, forced vibrations with frequencies very close to the natural frequencies, calculated from the first phase, are applied to the system in the second phase, to simulate the forming process. Based on the validated numerical model, the forming force, friction force, and material flow stress distributions are disclosed for UADD in various excitation frequencies.