# Process Parameters Optimization of Thin-Wall Machining for Wire Arc Additive Manufactured Parts
## 5 Optimization Strategy  
The proposed approach allows for identifying the dynamics of the tool-workpiece system during the whole machining cycle and could be coupled with any optimization strategy to achieve different goals, computing an optimized machining cycle. Two main dynamic phenomena could arise in machining thin-walled components: forced vibrations and chatter vibrations. Both the effects are minimized by increasing the stiffness of the system or reducing the MRR (i.e., depth of cut). The first approach is hard to follow since workpiece shape and tooling system are generally fixed. The second one affects the productivity of the process. Therefore, optimization strategies are generally based on the selection of spindle speed [23], which governs the frequency content of the cutting forces and thus could reduce vibration levels, without affecting productivity or altering system layout. However, the selection of spindle speed has conflicting  
Figure 8: Workpiece driving point frequency response functions (FRFs): (**a**) experimental setup (**b**) comparison with numerical FRF. Figure 9: Compliance at the tip of the blade moving from the trailing to the leading edge. requirements for forced and chatter vibrations. Indeed, to reduce forced vibrations, the spindle speed should be far from the resonance frequencies of the system, hence reducing the relative tool-workpiece displacements during the cycle. On the contrary, for chatter avoidance, the optimal spindle speeds excite the resonance frequency of the dominant mode [24]. According to these considerations, the machining cycle optimization strategy should be tailored for the specific application. In this work, two simple optimization strategies were applied, with the aim of showing the potential applications of the proposed approach. * Strategy A: ensuring chatter-free machining by selecting a spindle speed, exciting the resonance of the dominant mode
* Strategy B: minimizing forced vibrations by selecting spindle speeds far from the resonances of the systems  
Both the strategies were applied to the test case, starting from the dynamic behavior of the system at the cutting point computed by the proposed technique, presented in the previous section. For strategy A, the dominant mode of the system was identified in the different steps of the machining cycle and a single optimized spindle speed was selected, ensuring the excitation of the dominant mode with one of the tooth pass frequency (\(\mathrm{f_{tp}}\)) harmonics. The procedure is exemplified in Figure 10, where FRFs of system during the machining cycle at the trailing edge are presented. The figure shows the dominant mode of the system around 1300 Hz. A single spindle speed equal to 5580 rpm (\(\mathrm{f_{tp}}=186\) Hz) was selected to ensure the system to work close to the dominant mode resonance frequency with one of the \(\mathrm{f_{tp}}\) harmonics (7 th). For strategy B, machining parameters were selected to minimize the relative displacement of the tool-workpiece under the effect of cutting force (i.e., force vibrations). These vibrations were assessed by computing the system compliance at the \(\mathrm{f_{tp}}\) and harmonics (till 12 th). The harmonics were weighted based on the results of a preliminary analysis in which cutting forces were simulated in the finishing cutting conditions (i.e., radial depth of cut (_ae_) 0.2 mm, axial depth of cut (_ap_) 0.5 mm).Fast Fourier Transform (FFTs) of the cutting force and weights adopted are presented in Figure 11. This approach allows for identifying the relative displacement of the tool and workpiece in the case of stable cutting (i.e., without chatter) and, based on this information, selecting the optimal speed in a defined range (in this case, 140 to 235 m/min). The interesting advantage of such approach is not considering a cutting force model and the consequently need of cutting force  
Figure 10: Optimization strategy A applied to the airfoil.