# Statistical Analysis of Cutting Force and Vibration in Turning X5 CrNi18-10 Steel
## 4 Discussion  
We need to understand the correlation between the machining parameters, particularly the feed and its effect on cutting phenomena (cutting force and vibration), which affects the quality of the machined products in terms of the surface integrity shape. The research demonstrates the computed active vibration RMS, the active force RMS, and the correlation analysis between the variables. The active vibration RMS results are presented in Table 4 and Figure 6. The results highlight that changes in the machining parameters, feed, depth of cut, and cutting speed, influence the vibration peaks and RMS value. The low feed rate, _f_--0.08 mm/rev, with different cutting speeds and depths of cut, as shown in Figure 6, suggests favorable results. To achieve better results, DOC--0.5 mm is suggested. The cutting speed also influences the value of the active vibration RMS; as the cutting speed is increased, the AV\({}_{\text{b}}\) RMS value decreases, i.e., vibration impacts during machining can be reduced at a higher speed. EX13, with V\({}_{\text{c}}\)--200 m/min, _f_--0.08 mm/rev, and DOC--1 mm, has less vibration magnitude during the whole experiment; however, the vibration peaks are high in comparison to EX1, EX4, and EX7 with the same feed. As the feed rate is increased, the magnitude of vibration increases. To achieve less vibration during the turning of X5 CrNi18-10, the feed should be kept low, the cutting speed should be high, and the depth of cut should be low. The active cutting force results are presented in Table 4 and Figure 6; the cutting force analysis also suggests similar results. It is visualized in Figure 6 that increasing the feed rate results in higher cutting forces, which impacts the shape deformation, poor surface finish, and tool wear. It is recommended to keep a low feed rate to achieve better quality products. EX7, with V\({}_{\text{c}}\)--300 m/min, _f_--0.08 mm/rev, and DOC--0.5 mm, shows the lowest active cutting force value of 122.57 N during the whole experiment. In EX12, the highest magnitude of AF RMS was observed for V\({}_{\text{c}}\)--150 m/min, _f_--0.24 mm/rev, and DOC--1 mm; to achieve better results, these parameters should not be considered. To have less impact of the cutting forces on the quality of the product, the feed should be kept low, with a low depth of cut and cutting speed. The standard deviation results between the cutting force and vibration data suggest that the amount of variability in each dataset is the same. EX3, 5, 8, and 17 show that the values of both the force and vibration are closer, suggesting consistency during each test. The correlation analysis between the feed and AV\({}_{\text{b}}\) RMS suggests that there is a 69.7% correlation between the variables. The correlation analysis between the feed and AF RMS suggests that there is a 68.8% correlation between the variables. There is a 99% probability that a real relationship exists between each variable, and it is not random. The ANOVA results for the feed and AF RMS show a significant _p_-value of 0.002, which is less than 0.05, suggesting that the model is highly significant. Similarly, the ANOVA results for the feed and AV\({}_{\text{b}}\) RMS show a significant _p_-value of 0.001, which also suggests that the model is highly significant, and a real relationship exists between the variables. The main effects plot analysis between three machining parameters and AV\({}_{\text{b}}\) RMS and AF RMS shows that the increase in the feed rate influences the vibration, which can also be observed in the correlation results. With the increase in DOC, the active vibration magnitude also increases. However, the cutting speed has different effects; to lower the vibration, the cutting speed must be kept high. The increase in the feed rate also influences the active cutting force, which is also noticeable in the correlation results. When the depth of cut increases, the AF RMS also increases, which can be understood by the material removal rate.