# Statistical Analysis of Cutting Force and Vibration in Turning X5 CrNi18-10 Steel
###### Abstract  
X5 CrNi18-10 is a corrosion-resistant steel that has become popular in the automotive, marine, food, nuclear, and other industries. Chromium alloyed in the X5 CrNi18-10 increases the material's toughness, which influences the cutting phenomena such as the cutting force and vibration. It is necessary to investigate the effect of the machining parameters on the X5 CrNi18-10 turning, particularly the feed, which has significant effects on the cutting phenomena. The objective of this research is to investigate the correlation between the feed and cutting phenomena to improve the product quality, reduce machining disruptions, and optimize the parameters for a low cutting speed and vibration. Statistical analysis has shown promise in identifying the impact of variables using correlation analysis and estimated marginal means plots. This study highlights the findings of the Pearson's correlation analysis between the feed, active cutting force, and active vibration as well as the estimated marginal means plots between the machining parameters and cutting phenomena. The results indicate that there is a strong correlation between the feed and active cutting force with a coefficient of correlation of 0.688, as well as the feed and active vibration with a coefficient of correlation of 0.697. The estimated marginal means plots indicate that as the cutting speed increases, the value of the active vibration and the active force decreases. cutting force analysis; vibration analysis; turning process; X5 CrNi18-10 steel; statistical analysis; machining dynamics; regression analysis +
Footnote †: journal: Applied sciences  
0000-0001-5000-0000-0000-0000-0000-0000-0000-00  
force is very important to understand the machinability of the material, especially when the material possesses properties like toughness. The cutting force can be divided into three components, as shown in Figure 1: the cutting force (\(\overset{\rightarrow}{F_{\text{c}}}\)), which is tangential, the feed force (\(\overset{\rightarrow}{F_{\text{f}}}\)), which is axial, and the radial force (\(\overset{\rightarrow}{F_{\text{r}}}\)), which is also radial. However, the effective force that is responsible for the main cutting force is called the active force (\(\overset{\rightarrow}{F_{\text{a}}}\)), which is the sum of various components of the cutting and feed forces. The passive force is the radial force, which is irrelevant because the workpiece and tool remain stationary in the direction of force. The active force (\(\overset{\rightarrow}{F_{\text{a}}}\)) or (\(\overset{\rightarrow}{AF}\)) in turning operation is noted by Equation (1). \[\overset{\rightarrow}{F_{\text{a}}}=\sqrt{F_{\text{c}}^{2}+F_{\text{f}}^{2}} \tag{1}\]  
A larger cutting force generates a poor surface finish and extensive surface damage during high-speed turning [9]. Understanding cutting phenomena also requires the study of the vibration induced by the cutting force components. These vibrations have an impact on common machining processes, including turning, milling, and drilling. In an investigation, it was found that the variations in cutting force components and vibration have a direct impact on the flank wear [10]. It was concluded that vibration is a common concern in turning processes, affecting machining results, particularly tool wear [11]. Machining vibrations, often known as chatter, have several effects on the quality characteristics of the final machined product. Like the cutting force, the induced vibration can also be divided into three components: tangential (\(V_{\text{t}}\)), axial (\(V_{\text{a}}\)), and radial (\(V_{r}\)) vibrations; however, the effective vibration, which is responsible for affecting the quality parameters, is tangential and radial. The effective vibration (\(V_{\text{e}}\)) or (\(AV_{\text{b}}\)) can be defined by Equation (2), as follows. The effective vibration is the sum of tangential (\(V_{\text{t}}\)) and radial (\(V_{r}\)).