###### Abstract  
Maching of Nomex honeycomb composite (NHC) structures is of critical importance in manufacturing parts to the specifications required in the aerospace industry. However, the special characteristics of the Nomex honeycomb structure, including its composite nature and complex geometry, require a specific machining approach to avoid cutting defects and ensure optimal surface quality. To overcome this problem, this research suggests the adoption of RUM technology, which involves the application of ultrasonic vibrations following the axis of revolution of the UCK cutting tool. To achieve this objective, a three-dimensional finite element numerical model of Nomex honeycomb structure machining is developed with the Abaqus/Explicit software, 2017 version. Based on this model, this research examines the impact of vibration amplitude on the machinability of this kind of structure, including cutting force components, stress and strain distribution, and surface quality as well as the size of the chips. In conclusion, the results highlight that the use of ultrasonic vibrations results in an important reduction in the components of the cutting force by up to 42%, improves the quality of the surface, and decreases the size of the chips. modeling finite elements (EF); NHC core; RUM technology; UCK cutting tool; surface quality; stress and strain distribution; chip size +
Footnote †: journal: _Algorithms_  
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materials, including titanium and aluminum alloys [11; 12]. For example, [PERSON] et al. [13] conducted a study to optimize the dimensions of an ultrasonic disc tool with the aim of evaluating the influence of its geometric properties on its energy density and stiffness. Their results demonstrated a significant correlation between the processing efficiency of the NHC structure and geometric parameters such as cutting angle. The study carried out by [PERSON] et al. [14] shows the benefits of integrating rotary ultrasonic machining (RUM) into the milling process of aluminum honeycomb structures. Their study established that the use of this technology resulted in the reduction of the cutting force, which helped to mitigate the plastic deformation of the walls of the structure. In general, the machining of Nomex honeycomb structures is often carried out using an experimental approach, with direct involvement of the machine tool. In this regard, [PERSON] et al. [15] compared the cutting forces generated during the milling of Nomex honeycomb composites (NHCs), using conventional and ultrasonic machining. Their results demonstrated that ultrasonic vibration machining induced a notable reduction in cutting forces. In the same way, [PERSON] et al. [16] carried out a comparative study of the quality machined surface of the Nomex honeycomb structure using rotary ultrasonic milling (RUM) technology and conventional milling. Their findings demonstrated a notable reduction in the formation of defects on surfaces generated by ultrasonic vibration-assisted machining. In this perspective, [PERSON] et al. [17] proposed the use of a disc milling cutter with vibration conditions combining longitudinal torsion for the machining of Nomex honeycomb composites (NHCs). Their research found that adding torsional vibrations to longitudinal vibrations not only increased the instantaneous cutting speed of the cutting disc but also promoted material breakage. These improvements result in shorter burrs, reduced burr rates, and less tearing. Due to the rapid movement of the cutting tool and the difficulty in accessing the interface between the cutting tool and the structure to be machined, the experimental process fails to adequately follow the cutting process and the formation of shavings. Therefore, numerical modeling presents itself as a valuable tool for monitoring chip formation and analyzing in detail the machinability characteristics of the structure.