# Augmented Reality Visualization of Modal Analysis Using the Finite Element Method
## 2 Materials and Methods  
Pumps generate energy thanks to the fluid flow, and the impeller inside makes the greatest impact on the pump performance. The impeller is used for energy transfer (Figure 3a). The correct impeller design enables the pump to deliver the desired properties, while also decreasing the operating costs. For this reason, it is necessary to optimize the design variables that affect the impeller performance. The aluminum impellers used in this study are widely used in the industry and are known for their strength, corrosion resistance and excellent heat resistance. Impeller failure is frequently encountered as a result of fatigue. Resonance is an undesirable situation on an impeller. To avoid impeller resonance, an optimum design is important. Therefore, determining the modal analysis, which is the first step of the dynamic analysis before designing impellers, is of great importance. This study aims to obtain the mode shapes of an aluminum impeller by modal analysis. The first six natural frequencies are obtained through modal analysis. Knowing the natural frequencies is important for determining the region where resonance may occur in the system. The deformation on the first six mode shapes is examined after determining the natural frequencies. The geometric model is designed on Computer Aided Design (CAD) software. For the design of the geometric model, a computer-aided design program Solidworks 2019 is used. The material properties, mesh and boundary condition steps are determined before obtaining the simulations results. On the CAD software, the value of the size to be calculated in an element is found by interpolation, using the values in the nodes. In the finite element method, the unknown and required values are the values in the nodes. Using a variance principle, a set of equations is obtained for the values of the size field at the nodes. This impeller is made of 6061 aluminum alloy, and 51,422 nodes and 32,265 meshes are used in the model design (Figure 3b). The hole passing through the middle part is fixed as a boundary condition (Figure 3c). The finite element analysis workflow steps are followed in this study (Figure 4a).  
The representation of this set of equations in matrix form is a simple finite element equation Equation (1). F is the force vector, the applied load, in global coordinates [N]. u is the displacement vector, the nodal deformation [m or mm]. K is the element stiffness matrix.  
\[\text{[K]}\times\text{[u]}=\text{[F]} \tag{1}\]  
Finite Element Analysis (FEA) software packages regularly use heat maps and shape deformation to visualize the outcomes of a given situation. Despite being an effective way to demonstrate the effect on a 3D object, in the case where a physical object exists (such as when refining a design or analyzing an existing system), it can be difficult to correlate the FEA simulation-provided visual information with the physical part.  
The CAD model and FEA simulation results are combined on 3 dsMax 2020 software (Figure 4b). The combined data is imported as an Fbx. file on Unity Hub. Unity Vuforia Model Target is used to create an Android package kit (APK) file. An Android package can be installed on a mobile phone or tablet. The AR android program, which is designed to  
Figure 4: (**a**) Finite element analysis workflow; (**b**) Data visualization and Augmented Reality workflow.  
Figure 3: (**a**) Impeller; (**b**) The mathematical mesh finite element model; (**c**) The boundary condition.  
operate when the camera of a mobile phone or tablet sees the real product, recognizes the real product and fits the 3D analysis result on the real product. In this way, the FEA result is provided so as to be displayed on the real product. Moreover, engineers can see the analysis result on the real product in the real environment with the naked eye. Accordingly, the analysis results can be seen in the real environment.