# Statistical Analysis of Cutting Force and Vibration in Turning X5 CrNi18-10 Steel
## 3 Results
### Vibration Analysis  
The vibrational data were collected through the electronic setup; as mentioned in the experimental setup, the data were saved in \"[dot] csv\" format with order time (ms). The selected range of the accelerometer has a full-scale \(\pm\)2 g, a sensitivity of 16,384 LSB/g, and a sampling data rate of 1 kHz. Acceleration in the X direction (AccX) (m/s\({}^{2}\)) is tangential acceleration, acceleration in the Y direction (AccY) (m/s\({}^{2}\)) is radial acceleration, the acceleration in the Z direction is axial, and it was kept at zero intentionally because of the movement of the tool in the Z direction. The active vibration consists of the X and Y components. After the collection of data, Origin Pro 2024b academic licensed software was used to process the data and analyze the signals during the machining process. The raw or unfiltered data from the sensor, where the vibrational signals in are terms of acceleration in the X direction and acceleration in the Y direction, were computed, and the magnitude was taken. Figure 6 represents the magnitude of the tangential and radial acceleration. The active vibration (AVb) is the sum of the tangential and radial acceleration, as mentioned in Equation (2). The data were separated according to the surface to calculate the relation between the vibration and the machining parameters. EX in Figures 6 and 7 means the experiment number. The change in feed values is defined by three colors: dark blue, where the value of the feed is 0.08 mm/rev, pink, with a feed rate of 0.16 mm/rev, and sky blue, with a feed rate of 0.24 mm/rev. The cutting speed in Figures 6 and 7 is also represented by three  
\begin{table}
\begin{tabular}{c c c c} \hline
**No. ** & **Depth of Cut (a\({}_{\text{p}}\))** & **Cutting Speed (V\({}_{\text{c}}\))** & **Feed Rate (\(f\))** \\  & **mm** & **m/min** & **mm/rev** \\ \hline
1 & 0.5 & 150 & 0.08 \\
2 & 0.5 & 150 & 0.16 \\
3 & 0.5 & 150 & 0.24 \\
4 & 0.5 & 200 & 0.08 \\
5 & 0.5 & 200 & 0.16 \\
6 & 0.5 & 200 & 0.24 \\
7 & 0.5 & 300 & 0.08 \\
8 & 0.5 & 300 & 0.16 \\
9 & 0.5 & 300 & 0.24 \\colors, dark grey with V\({}_{\rm c}\)--150 m/min, Light grey with V\({}_{\rm c}\)--200 m/min, and orange with V\({}_{\rm c}\)--300 m/min. These colors help to visualize the effect of the machining parameters on the vibration and cutting forces. It can be visualized from Figure 6 that the total no. of experiments was eighteen, and active vibration RMS is computed for each experiment. The horizontal axis represents the time in seconds. Figure 6 displays the depth of cut on the top, the cutting speed below it, and the feed rate used for each experiment. Figure 6 can be used to analyze the effect of vibration in each experiment with a change in parameter. It can be analyzed from Figure 6 that, during each  
Figure 6: The magnitude of active vibration with time for each experiment. Figure 7: Magnitude of active force with time for each experiment with changes in machining parameters. the value of the active vibration RMS is low, high, or medium. The vibration analysis represents that with an increase in the feed rate, the vibration during the machining process also increases. It can be concluded from Figure 6 that, with a lower feed rate (_f_)--0.08 mm/rev, V\({}_{\text{c}}\)--200 m/min and 300 m/min, and a\({}_{\text{p}}\)--0.5 mm and 1 mm, less vibration can be achieved in the turning of X5 CrNi18-10. The lowest value of the active vibration RMS can be seen in EX13 with DOC (a\({}_{\text{p}}\))--1 mm, V\({}_{\text{c}}\)--200 m/min, and _f_--0.08 mm/rev, but the signal peaks are high in that period; however, in EX4, with DOC (a\({}_{\text{p}}\))--0.5 mm, V\({}_{\text{c}}\)--200 m/min, and _f_--0.08 mm/rev, there are better results with a low active vibration RMS value and low peaks. The highest value of the active vibration RMS can be seen in EX11 with DOC (a\({}_{\text{p}}\))--1 mm, V\({}_{\text{c}}\)--150 m/min, and _f_--0.16.