*3.4. Operating Deflection Shape*

According to the method presented in [35], an ODS of the tool in the burnishing process of C45 with a force of 90 N and without vibration assistance was performed to analyze the tool rigidity. A frequency of 32 Hz was selected as it had a noticeable displacement and an acceptable background noise. Figure 15 presents the ODS. Figure 15a is a lateral view and depicts the movement in the vertical direction. Red lines correspond to extreme positions and blue lines correspond to the mean position. A rotatory movement around the center of the tool is clearly noticeable, with an amplitude at the extremes of around 0.6 μm. Figure 15b presents the plant view. A translation movement in the burnishing feed direction of about 0.5 μm amplitude is also noticeable. In order to determine the movement in the axis of the tool direction, a zoom around the zero-point was performed (Figure 15c) and a displacement of about 0.9 μm was detected.

The methodology proposed in this paper (joining vibratory analysis with AE) allows one to extend the range of frequencies up to several hundred kHz. This approach is suitable for any machine-tool-part setup with different rigidities, configurations, and designs. Therefore, this may be used in the near future to characterize tools used in ultrasonic vibration-assisted machining operations such as those presented in [36]. Unfortunately, this methodology does not allow one to quantify the amplitude of the vibration in the AE range.

**Figure 14.** AE spectra corresponding to different VABB: (**a**) C45 steel with 90 N; (**b**) C45 steel with 270 N; (**c**) GJL250 cast iron with 90 N.

**Figure 15.** *Cont.*

**Figure 15.** ODS of the tool at 32 Hz: (**a**) lateral view; (**b**) plant view; (**c**) zoom of lateral view.

#### **4. Conclusions**

The conclusions of this paper are clustered according to the test through which they were obtained.

#### **Impact tests**

No natural frequencies higher than 2 kHz were noted (about 5% of 40 kHz, the vibration assisting frequency); consequently, the high frequency that appeared in the process was only that of the tool.

The structural behavior of the tool was affected by the contact between tool and specimen but was not affected by their contact force value.

#### **Vibration measurements**

The material of the workpieces, the vibration assistance, the burnishing force, and the feed movement did not affect the frequency spectra measured.

Spectrum lines appeared in the frequency range 800–1400 Hz during the burnishing process at the rear point and in the lathe bed with much lower amplitudes than those considered to be standard for a new machine, in accordance with the operation deflection shape results.

The vibration levels measured in the tool axis had higher amplitudes than those corresponding to the other directions, due to the burnishing force.

The amplitudes of the signals measured in the rear of the tool were slightly higher than those measured at the frontal part.
