The cutting performance of an ultrasonic machining machine (USM) depends primarily on the ability of the design of the acoustic horn (also known as concentrator or tool holder). A horn is a waveguide-focusing device with a cross-sectional area that decreases from the transducer end to the toe end. It amplifies the input amplitude of vibrations so that at the output end the amplitude is sufficiently large for machining. In the present work, a finite element method (FEM) design procedure has been developed for the design of a horn for rotary ultrasonic machining (RUM). The double conical horn shape has taken as a domain with a hole at the tip for the cooling purpose. The analysis of the various stress components in the horn domain has been studied. The stresses at the middle of the horn are found to be maximum but it is within the allowable stress of the horn material due to the sudden change in the area of the horn. The stresses on the horn for various frequencies are also studied and concluded that at resonance condition the stress is minimum.
This paper presents a 2D dynamics infinite element method (DIEM) for modeling the multiple-hole membrane for vibration analysis. A new concept involving converting the DIEM into a super element that can adjust the hole size and free and fixed boundary conditions around the hole is also proposed. The special element, embedded with an elastic membrane, is formulated on the basis of the conventional finite element method (FEM) by using the similarity mass/stiffness property of isoparametric elements and Craig-Bampton matrix reduction procedures. A DIEM-FE coupling scheme is also developed and self-programmed into the software MATLAB to conduct the vibration analysis of a membrane with multiple holes. The DIEM-FE approach is validated to study the vibration of the rectangular membranes by using the corresponding analytical solutions and the solutions obtained using the conventional FEM. The DIEM-FE is then applied to analyze imbedded L-shaped and circular opening problems. The effects of varying hole diameters and the free or fixed boundary condition along the hole are also examined. Finally, the last example shows that to perform vibration analysis of the multiple-hole membrane, only one DIEM mass/stiffness matrix must be calculated for all holes with an identical circular shape. Overall, this study provides a flexibility and efficient scheme for analyzing a wide variety of membrane vibration problems. The number of degrees of freedom and the corresponding PC memory storage are substantially reduced through the computation.
The Finite Element Method Using MATLAB - Kwon And Bang.pdf
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