# A Novel Finite Element Method Approach in the Modelling of Edge Trimming of CFRP Laminates
## 5 Results and Discussion  
The cutting mechanism notably varies with tool wear, as shown in Figure 8. A new tool cut the laminate shearing small chips away. In order to model this problem, the fibre and matrix fracture mechanism should be included in the model to achieve a good quality in the numerical results. However, this configuration was not studied in this manuscript because this matter is out of the scope of this research. A worn tool edge radius considerably reduces its effectiveness to cut fibres. As a result, the tool edge removes the material due to the high rubbing forces with the laminate, as shown in Figure 8. The increment of tool/workpiece contact area increases abruptly the ploughing forces and sub-surface damage. The proposed FE model takes into account this phenomenon and check how the cutting forces increase because of the tool wear. These results can be employed in a real test to check the tool wear, analysing the machining forces. Therefore, the inserts can be replaced before the worn edges induce excessive laminate damage. The simulations focus on the study of the action of the tool teeth on the material. Therefore, the simulation time selected was the time it takes for one of the tool teeth to be in contact with the laminate. A feed rate (\(f_{r}\)) of 1200 mm/min, spindle speed (\(w\)) of 6000 rpm, and a radial depth of cut of 2 mm were modelled in this research. Five cutting edges, with a radius of 10 \(\upmu\)m, 20 \(\upmu\)m, 30 \(\upmu\)m, 40 \(\upmu\)m, and 50 \(\upmu\)m, were investigated to assess the tool wear influence on the machining forces. Four distinct machining forces were analysed \(F_{X}\), \(F_{Y}\), \(F_{T}\), and \(F_{N}\), which are represented in Figure 9. \(F_{X}\) and \(F_{Y}\) denotes the horizontal and vertical forces, respectively. These variables allow us to analyse the machining forces experienced by the cutting tool in the spindle axis. In the case of \(F_{T}\) and \(F_{N}\), they are the tangent and normal forces to the cutting tool edge trajectory, respectively. Henceforth, \(F_{T}\) is named tangent force and \(F_{N}\) corresponds to the normal force for the purpose of clarity. These variables reliably represent the forces that the tool tooth undergoes during the machining process. In the above figure, \(\theta\) represents the angle between the line that connects the tip and the rotational centre of the cutter and the horizontal axis. Variables \(w\), \(f_{r}\), and \(R\) denote the cutting speed, feed rate, and radius of the cutting tool, respectively. \(V_{t}\) is the tangent velocity of the tip of the cutting tooth in contact with the laminate. Finally, \(\beta\) and \(\alpha\) correspond to the angles that indicate the orientation of \(V_{t}\) and the coordinate system to analyse \(F_{t}\) and \(F_{n}\) with respect to the global coordinate system, respectively. To transfer the machining forces obtained in the global coordinates \(F_{x}\) and \(F_{y}\) to the relative coordinates \(F_{t}\) and \(F_{n}\), it is necessary to develop a vector base change. For this purpose, the angle that forms the tangent velocity at the tool tip (\(V_{t}\)) with the horizontal axis of the coordinate system (\(\beta\)) is calculated. The angle between the two vector bases (\(\alpha\)) is established then to transfer the forces obtained in the global coordinate system to  
Figure 8: Representation of the characteristic edge trimming cutting mechanisms using a (a) new tool and (b) worn tool. the new coordinate axes. The relevant equations to complete the change of vector base are set out below.