Design of Novel Longitudinally-Torsionally Coupled Ultrasonic Bezier Horns for Machining Advanced Hard and Brittle Materials

Purpose Utilization of advanced hard and brittle materials in engineering applications has led to the need of non-conventional machining techniques such as rotary ultrasonic machining (RUM) to achieve high dimensional accuracy and low machining defects (delamination, burr and cracks formation, etc.). RUM performance greatly depends on vibration amplitude at tool end which is achieved through appropriate ultrasonic horn design. Longitudinal-torsional coupled (LTC) vibrations, generated by incorporating helical slots in horn design, improve ultrasonic machining quality of hard and brittle materials. In present investigative work, modified ultrasonic horns were designed and analyzed for RUM by producing helical slots in quadratic and cubic Bezier horn profiles to achieve high amplitude ratio (T-A/L-A) within safe stress limits. Methods Modal and harmonic analyses were performed to investigate the influence of depth (D-s), width (W-s), angle (theta(s)) and location (L-sp) of helical slots on the modal frequencies, vibration amplitudes, torsional to longitudinal amplitude ratio and stresses in ultrasonic LTC Bezier horns using FEM. Modified ultrasonic horns were tested for three different materials: steel, aluminum, and titanium after validation with available literature. Results Presently designed horns were found to attain high amplitude ratio and low stresses as compared to the commercial step LTC horn for same end diameters and length. Different stresses (shear, von Mises, radial, tangential and axial) were also computed and plotted along horn axial length for optimum designs and were found well below the endurance limit. Conclusions For the same end conditions and length, cubic Bezier LTC ultrasonic horn is preferable to its quadratic counterpart due to 19.91% higher amplitude ratio. However, stresses are 24.78% less in quadratic Bezier LTC ultrasonic horn. The amplitude ratio attained by both types of LTC Bezier horns was found to be significantly greater than that in the commercial LTC step horn, with additional advantage of low stresses. Achievement of high amplitude ratio will help in reduced cutting force and improved surface quality of advanced hard and brittle materials as compared to standard LTC horn design.