## 3 Results
### Verification of Ultrasonic Vibration-Assisted Cutting Simulation Model  
In order to verify the accuracy of the finite element model, the simulation scheme in Table 3 was used to conduct cutting experiments on honeycomb-core materials, and the simulation resulted of cutting force were compared with the experimental results. The ultrasonic vibration cutting experiment of the Nomex honeycomb-core composite material was carried out on the advanced ultrasonic processing machine US-50 produced by the Austrian GFM company. The measurement of the cutting force in the experiment was performed by the Kistler9257B dynamic force measurement system. In the test, the data acquisition frequency was 4000 Hz, the Nomex honeycomb-core material used in the test was NRH-3-48, and the sample size was 100 mm \(\times\) 80 mm \(\times\) 60 mm. The cutting force measurement principle is shown in Figure 9. The basic principle is that the voltage analog signal of the cutting force in three directions is first measured by the Kistler9275B three-way dynamometer, and then the signal is collected by the quasi-static charge amplifier, data acquisition card and chassis. Then, it is converted into numeric signals by data-acquisition virtual instrument software for data storage and analysis by the computer, and finally the average value of the collected cutting force signals is used as the cutting force during the processing. During the experiment, each group of process parameters are tested twice, and the average value is taken to ensure the reliability of the experimental data. The specific processing environment is shown in Figure 10.  
Figure 10: Overview of experimental devices. Figure 9: Cutting-force measurement principle. During the experiment, the spindle speed was 1500 r/min and the feed rate was 4500 mm/min. There were 8 groups of experiments, 4 groups of cutting width experiments and 4 groups of cutting depth experiments. As shown in Figure 11, the surface topography of ae = 5 mm was obviously better than that of \(a_{e}\) = 10 mm. There were a large number of burrs on the surface when the constant was 10 mm, in addition to a large number of burrs; the regular hexagon on the surface also had serious distortion. It could be seen, with the increase of cutting depth \(a_{p}\), the surface morphology of honey comb core material became better. When \(a_{p}\) = 40 mm the surface of the material had almost no burrs, and the surface hexagon was regular. Figure 11: _Cont._  
Based on the change curve of the cutting force under different machining parameters obtained by actual cutting experiments, the simulation data of the vibration cutting of the disc-cutter was compared and analyzed. The experimental data were obtained by the three-dimensional dynamometer. The simulation data were obtained by the reaction force of the tool reference point in the ABAQUS software. In the verification data, two sets of cutting data were selected, as shown in Figure 12. Among them, under the conditions of feed speed \(v_{f}\) = 4000 mm/min, cutting depth \(a_{p}\) = 10 mm, spindle speed \(n\) = 1500 r/min and amplitude \(\mu\) = 30 \(\upmu\)m, Figure 12a shows the cutting width \(a_{e}\) versus cutting force \(F_{y}\) With the increase of the cutting width, the experimental value of the rotary-vibration-cutting force component of the disc-cutter increased linearly. This was mainly because the increase of the cutting width will increase the contact area between the tool and the workpiece surface. Thus, the cutting force increased. Under the conditions of feed speed \(v_{f}\) = 4000 mm/min, cutting depth \(a_{e}\) = 10 mm, spindle speed \(n\) = 1500 r/min and amplitude \(\mu\) = 30 \(\upmu\)m, Figure 12b showed the effect of cutting depth \(a_{p}\) on cutting force \(F_{y}\) The regular curve, with the increase of the cutting depth, the cutting force tends to increase, but the increase of the entire cutting force was also gentler. Because the disc-cutter did not made the contact area between the tool and the workpiece surface increase during the cutting process.