# A Novel Finite Element Method Approach in the Modelling of Edge Trimming of CFRP Laminates
## 5 Results and Discussion
### Fibre Orientation of 90\({}^{\circ}\)  
An observation of the vertical forces obtained reveals that these initially undergo a steep rise due to the effect of the spring back that pushes the cutting tool in the normal direction to the machined surface. This steep rise slope occurs because of the cutting tool being initially pushed with the characteristic high rigidity of laminates that are loaded parallel to the fibre. After this sharp rise, there is a decrease in the slope of this curve until it reaches a significant drop attributable to two factors. The first factor that causes this drop is that the contribution of forces produced by the spring back phenomenon in the vertical component decreases appreciably with the advance of the cutting tool tooth. The second factor is that the cutting forces generated during the machining process are added in the negative component of the vertical axis. Horizontal force steady rises because of the horizontal contributions given during the simulation of the spring back and cutting forces. The horizontal cutting forces are primarily increased because of the increase in chip thickness as the tool rotates. Subsequently, the forces coming from the spring back increase their contribution in the horizontal axis while the cutting force contribution becomes less relevant with the advance of the cutter  
Figure 18: Representation of the average machining foces simulated with a fibre orientation of 45\({}^{\circ}\): (**a**) \(F_{X}\) and \(F_{Y}\) (**b**) \(F_{T}\) and \(F_{N}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Tool Edge Radius** & **Average \(F_{X}(N)\)** & **Average \(F_{Y}(N)\)** & **Average \(F_{T}(N)\)** & **Average \(F_{N}(N)\)** \\ \hline
10 \(\upmu\)m & 126.13 (\(-\%\)) & 130.89 (\(-\%\)) & 23.  
tooth. Figure 19 visualises the global machining forces collected for the cutting tool edge radius of 10 \(\upmu\)m, 20 \(\upmu\)m, 40 \(\upmu\)m, and 50 \(\upmu\)m, which is the subject of the above statements. Regarding the forces measured in the tooth of the cutting tool \(F_{N}\) and \(F_{T}\), they reach a stable level of force over which they fluctuate. Different reasons explain this trend for both investigated forces. In the case of \(F_{N}\), this force is obtained as a consequence of the spring back phenomenon. Initially, a rapid force increase is observed because the penetration stiffness is high when the tool pushes the laminate in a direction parallel to the fibre. As the tool advances, the relative machining angle decreases in a range from 90\({}^{\circ}\) to 30\({}^{\circ}\), softening the workpiece/cutting tool contact and substantially reducing the contact  
Figure 19: \(F_{X}\) and \(F_{Y}\) forces simulated in laminates with a fibre orientation of 90\({}^{\circ}\) and tool edge radius of (**a**) 10 \(\upmu\)m, (**b**) 20 \(\upmu\)m, (**c**) 40 \(\upmu\)m, and (**d**) 50 \(\upmu\)m.  
stiffness. The level of force previously obtained is maintained due to the deeper penetration of the cutting tool tooth (with an increase in chip thickness), however this is compensated by the contact stiffness reduction when the cutting tool tooth advances. An identical mechanism occurs with the tangential forces \(F_{T}\), where the cutting forces decrease with relative cutting angles lower than 90\({}^{\circ}\). However, in this analysis, this factor is compensated by the larger amount of material removed when the simulation goes ahead. As seen in Figure 20, the reached force levels of \(F_{N}\) are significantly higher than those of \(F_{T}\) because each pass of the tool tooth has a small depth-of-cut. Figure 20: \(F_{T}\) and \(F_{N}\) forces simulated in laminates with a fibre orientation of 90\({}^{\circ}\) and a tool edge radius of (**a**) 10 \(\upmu\)m, (**b**) 20 \(\upmu\)m, (**c**) 40 \(\upmu\)m, and (**d**) 50 \(\upmu\)m.  
The average forces simulated in this investigation highlight several assertions. The machining forces tend to experience a linear incremental increase produced by the effect of the cutting tool wear.