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The use of advanced brittle composites in engineering systems has necessitated robotic rotary ultrasonic machining to attain high precision with minimal machining defects such as delamination, burrs, and cracks. Longitudinal-torsional coupled (LTC) vibrations are created by introducing helical slots to a horn's profile to enhance the quality of ultrasonic machining. In this investigative research, modified ultrasonic horns were designed for a giant magnetostrictive transducer by generating helical slots in catenoidal and cubic polynomial profiles to attain a high amplitude ratio (TA/LA) and low stress concentrations. Novel ultrasonic horns with a giant magnetostrictive transducer were modelled to compute impedances and harmonic excitation responses. A structural dynamic analysis was conducted to investigate the effect of the location, width, depth and angle of helical slots on the Eigenfrequencies, torsional vibration amplitude, longitudinal vibration amplitude, stresses and amplitude ratio in novel LTC ultrasonic horns for different materials using the finite element method (FEM) based on the block Lanczos and full-solution methods. The newly designed horns achieved a higher amplitude ratio and lower stresses in comparison to the Bezier and industrial stepped LTC horns with the same length, end diameters and operating conditions. The novel cubic polynomial LTC ultrasonic horn was found superior to its catenoidal counterpart as a result of an 8.45% higher amplitude ratio. However, the catenoidal LTC ultrasonic horn exhibited 1.87% lower stress levels. The position of the helical slots was found to have the most significant influence on the vibration characteristics of LTC ultrasonic horns followed by the width, depth and angle. This high amplitude ratio will contribute to the improved vibration characteristics that will help realize good surface morphology when machining advanced materials.

Nomex honeycomb composite (NHC) has been increasingly used in the automotive, aerospace and defence applications due to its excellent thermal and mechanical properties. Its complex cellular hexagonal thin-walled configuration along with heterogeneous, soft and brittle nature pose substantial processing defects such as burr formation, tearing of walls, surface roughness, dimensional inaccuracy and low machining quality during conventional machining (CM). These surface defects have a substantial influence on the operating life and functional performance of its sandwiched structural members. Hybrid ultrasonic vibration assisted machining (HUSVAM) technology has been introduced to overcome such limitations. For an in depth research on HUSVAM of NHC using ultrasonic toothed disc cutter (UTDC), three dimensional finite element model was developed and experimental validation was carried out. The numerical simulation and experimental results were found to be in good agreement with one another. The influence of various machining parameters including the ultrasonic tool vibration amplitude (UTVA), feed rate (FR), depth of cut (DoC) and spindle angular speed (SAS) on NHC cutting forces, chip formation and surface quality was investigated using both HUSVAM and CM techniques. Furthermore, stresses, deformation and forces near tool-workpiece interaction along with the surface topography and morphologies were also analysed and compared for various operating conditions. A reduction in the cutting forces was found with the increase of SAS and UTVA (up to 65.47 % and 65.74 %, respectively). Although, the cutting forces were observed to increase by increasing the DoC and FR (up to 159.45 % and 126.33 %, respectively). DoC has a greater impact on the cutting forces among all machining parameters according to 4 levels, 4 factors (L 16 ) orthogonal experiments based on Taguchi method. The results show that the chip formation and machining quality of NHC core can be improved with HUSVAM technique using UTDC. HUSVAM also reduced the cutting forces (up to 73 %) compared to CM. The ultrasonic toothed disc cutter generated large number of burr with very short length, no tearing defects and no uncut fibers as observed from scanning electron microscopy of NHC hexagonal cell structure, walls and triple points. A burr formation of less than 10 % was realized during HUSVAM of NHC cores for F x ≤3N, while it was found up to 20 % if F x >3N, compared to at least 40 % during CM. The finite element model developed can be used to investigate the influence of HUSVAM on modern difficult to machine materials for enhanced surface quality., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)