## 1 Introduction
### Meshing, Boundary Conditions and Load Settings  
In this paper--based on the Hypermesh software--the honeycomb-core material in the processing path of the disc-cutter was locally refined and sharpened. The honeycomb core was is meshed with C3D8T eight-node thermal coupling hexahedron, and the disc-cutter uses C3D10 MT ten-node thermal coupling second-order tetrahedron meshing. The divided honeycomb core is imported into ABAQUS. Since the calculation of cutting heat is considered, an explicit temperature-displacement algorithm is selected. Before the model is submitted to the calculation, carefully check the setting of nonlinear parameters that may lead to nonconvergence or difficult convergence, Such as material settings, contact settings, etc.  
During the simulation, the disk cutter and the honeycomb core must be subjected to load and boundary condition constraints according to the actual working conditions. Since the stiffness of the disc-cutter is much greater than that of the honeycomb core, the cutter is used as a rigid body during the simulation. In terms of boundary constraints, due to the poor local strength of the honeycomb core, it is not possible to use the traditional method of holding. In actual working conditions, the part is  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Density** & **Elastic** & **Poisson’s** & **Thermal Expansion** & **Thermal** & **Specific Heat** \\  & **\(\rho\) (kg/m\({}^{3}\))** & **Modulus** & **Ratio** & **Coefficient** & **Conductivity** & **Capacity** \\  & **E/Gpa** & **\(\sigma\)** & **10\({}^{-6}\)/C** & **W/(m\({}^{-5}\)C)** & **J/(kg\({}^{-5}\)C)** \\ \hline W18 Cr4 V high speed steel & 7800 & 210 & 0.3 & 4.5 & 24 & 420 \\ Nomex honeycomb core & 1334 & 2.01 & 0.25 & 4 & 0.123 & 1300 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Tool and honeycomb material properties [16; 17].  
held by vacuum suction through adhesive tape on the bottom surface of the part. In the simulation model, it is assumed that the part is held firmly. All joints on the bottom of the part are fully fixed.  
The disc-cutter has three directions of motion synthesis relative to the honeycomb material, which are the feed movement, rotary movement of the cutter along its cutting trajectory and the vibration of the cutter along its axis. Velocity/angular velocity was adopted in ABAQUS The disc-cutter defines the feed velocity (vf) along the x-axis and the rotary motion along the z-axis, while applying a reciprocating ultrasonic wave up and down to the periodic amplitude function of the Fourier series in the z-axis direction of the disc-cutter vibration. Set the initial temperature of parts, disc-cutter and environment to room temperature. The simulation model of Nomex honeycomb core with ultrasonic vibration of disc-cutter is shown in Figure 3.  
In the direction of the z-axis of the tool, the vibration equation of any node of the disc-cutter during rotary-vibration-cutting is:  
\[z_{i}=A\sin(2\pi ft) \tag{2}\]  
where \(A\) is the amplitude (\(\mu\)m); \(f\) is the frequency (Hz).  
The periodic amplitude function in the formula is expressed by Fourier series, and loaded in ABAQUS in the form of Figure 4, the expression is:  
\[a=A_{0}+\sum_{n=1}^{N}\left[A_{n}\cos n\omega(t-t_{0})+B_{n}\sin n\omega(t-t_{ 0})\right] \tag{3}\]  
where \(A_{0}\) is the initial amplitude (\(\mu\)m); \(\omega\) is the circular frequency (rad/s); \(A_{n}\) is the coefficient of the \(cos\) function; \(B_{n}\) is the coefficient of the \(sin\) function.  
Figure 4: Schematic diagram of the rotary vibration amplitude loading of disc-cutter.  
Figure 3: Nomex simulation model of ultrasonic vibration cutting of disk cutter.