# Tribological Analysis of Several Coatings under Flood and Cryogenic Cooling Conditions
## 2 Materials and Experimental Set-Up
### Determination of Contact Conditions in Machining of Ti-6 Al-4V Alloy
#### 2.3.2 Determination of the Normal Force Acting in the Pins  
Figure 5 shows the procedure used for determining the normal force to be applied into the pins in the tribological tests. The first step of this procedure consists of gathering the forces, CCR and the tool-chip contact lengths generated by the orthogonal cutting tests of Ti-6 Al-4V alloy using cemented carbide tools. Based on the measured cutting (\(F_{c}\)) and thrust (\(F_{t}\)) forces, the normal force (\(F_{n\gamma}\)) to the tool rake face was calculated using the forces diagram for orthogonal cutting, shown in many publications [47; 48]. Then, the average contact pressure (\(P_{n\gamma}\)) between the tool and the chip is calculated by dividing the normal force by the tool-chip contact area. The next step consists of calculating the normal force necessary to be applied to the pins (\(F_{n,pin}\)) to reach a contact pressure at the pin-workpiece interface (\(P_{pub}\)) equal to the contact pressure calculated in the cutting tests (\(P_{n\gamma}\)). Determination of the Contact Pressure in Machining of Ti-6 Al-4V Alloy  
Data from orthogonal cutting tests conducted by [PERSON] et al. [50] were used in the procedure described above to calculate the normal forces acting on the pins during the tribological tests. This data are presented in Table 3, corresponding to two tests conducted  
Figure 4: Chip compression ratio (CCR) in the orthogonal cutting of Ti-6 Al-4V alloy using uncoated cemented carbide tools [49]. Figure 5: Flowchart of the procedure to determine the normal force to be applied to the pins. for two cutting speeds, keeping the other cutting regime parameters constant. The force diagram shown in Figure 6 was used to calculate the normal force applied to the tool rake face, \(F_{n\gamma}\), using the measured cutting and thrust forces and the equations derived from this figure (Equations (4)-(6)) [48]. Then, the contact pressure was calculated by dividing the normal force \(F_{n\gamma}\) by the tool-chip contact area (Equation (8)). This area is the product of the contact length \(l_{c}\) (Equation (7), taken from [48]) multiplied by the width of cut \(b\). \[R=\sqrt{F_{\varepsilon}^{2}+F_{t}^{2}} \tag{4}\]  
\[F_{n\gamma}=R\cdot\sin[\frac{\gamma}{4}+(\phi-\gamma)] \tag{5}\]  
\[\phi=\tan^{-1}(\frac{\cos\gamma}{\zeta-\sin\gamma}) \tag{6}\]  
\[l_{c}=h\cdot\zeta^{1.5} \tag{7}\]  
\[P_{n\gamma}=\frac{F_{n\gamma}}{l_{c}b} \tag{8}\]  
Under the cutting conditions listed in Table 3, the average contact pressure during the orthogonal cutting of the Ti-6 Al-4V alloy for the selected cutting conditions is 1188 MPa. Therefore, a reference contact pressure of 1000 MPa is used in the tribological tests. Initially, two analytical models of the pin-on-bar test were developed using the Hertz theory for both elastic and elastoplastic contact. However, these models considered only the indentation in a static contact between two spheres, so the sliding was neglected, which does not exactly represent the physical phenomenon occurring in the pin-on-bar test. Therefore, an inverse approach consisting of conducting numerical simulations of the pin-on-bar tests was applied by varying the normal force until the contact pressure at the pin-workpiece interface (\(P_{\text{pub}}\)) was equal to the pressure calculated from the cutting tests (\(P_{n\gamma}\)). A model of the pin-on-bar test was developed and simulated using the Abaqus FEA (implicit) software (Abaqus, 2022). This model is shown in Figure 7, where the pin comprises uncoated cemented carbide with a radius of 6 mm sliding over a flat workpiece made of Ti-6 Al-4V, with a rectangular shape of 10 mm length and 4 mm height. The workpiece was fixed at its bottom side and the pin was allowed to slide over the top surface of the workpiece in the X-direction at a constant speed (the sliding speed). Amongst the sliding speeds shown in Figure 4, five of them were used in the simulations of pin-on-bar: 10, 20, 40, 60 and 80 m/min.