# Process Parameters Optimization of Thin-Wall Machining for Wire Arc Additive Manufactured Parts
## 4 Thin-Walled Dynamics Prediction  
Thin wall dynamics can be proficiently estimated using finite element analysis. To increase modelling reliability and to reduce the computational effort, shell elements were considered. Moreover, considering the application of the proposed technique to the WAAM process, the deposition path can be used to automatically generate the shell FE mesh. Each point of the NC code generated to create the deposition toolpath can be used to become a node of the FE model, where only the properties and thickness of the shell elements shall be adjusted to create a realistic model. This enables a fast and automatic mesh and model creation starting from the simple G-code of the deposition process (see Figure 5). To take the material removal into account, the FE model must be continuously updated, according to the tool position along to the CAM generated toolpath. For this reason, a general algorithm was developed to modify the nodal thicknesses, according to the tool engagement obtained by a post-processing of the G-code (Figure 6).  
Figure 4: (**a**) Roughing cycle, (**b**) finished part.  
Figure 5: (**a**) Traditional shell element representation, (**b**) 3D element representation, showing the nodal thickness.  
For each node of the FE model, the corresponding block of the G-code is determined, computed as the minimum distance between the tooltip and the node considered. The nodal thickness is then updated considering the intersection of the tooltip geometry (a ball nose mill for the considered test case) with the external surface of the machined component (Figure 7). The predicted frequency response (FR) of the machined part can thus be easily obtained, performing a numerical frequency response analysis. For the test case considered, a modal frequency response was preferred. A unit force was applied to the node closest to the tooltip position (obtained by G-code), directed normal to the surface. Linear behavior was assumed, and dynamic compliance in the other direction was neglected. This allows for obtaining a good description of thin wall dynamics in a wide frequency range using a limited number of excitation frequencies, notably reducing the computational effort: a FR analysis took about 3 s on a PC using a commercial FE solver (MSC Nastran 2014.1, Swedish Hexagon AB, Newport Beach, CA, USA). The accuracy of the FE model was tested after the roughing machining phase, considering the FE model, updated according to the aforementioned algorithm (Figure 8). The following mechanical characteristics were considered: elastic modulus: 200 GPa, density: 7850 kg/m\({}^{3}\), Poisson's ratio: 0.31, structural damping: 0.005. According to the results in Figure 1, the proposed approach allows for predicting the changing of workpiece dynamics along the toolpath, taking the material removal into account at the same time.  
Figure 6: Roughing cycle toolpath post-processing.  
Figure 7: Finite element (FE) model updating phase: (**a**) FE model (**b**) tooltip position.  
Simulated workpiece FRFs can be then composed, according with the orientation of the tool (lead and tilt angle) with the tooltip FRFs (experimentally determined), to obtain the dynamics of the system (tool + workpiece), changing with respect to the cutting point (see Figure 9). Combination of tool-workpiece compliance was used in the optimization strategy.