# Vibroacoustic Optimization Study for the Volute Casing of a Centrifugal Fan
## 4 **Volute Vibroacoustic Model, FEM Validation, and Simulation**
### Volute Vibration Simulation and Validation  
The finite element analysis method is one of the important methods to obtain the vibrations of the structure surface. In this study, N \(\times\) Nastran, the commercial software made by the Siemens Company, was used to calculate the modal and vibration response of the volute. The finite element model (FEM) of the volute was selected by using a high-quality surface quadrilateral mesh, as shown in Figure 9. The thickness of the volute panel is relatively small (up to six mm), and the shell63 element is selected for the FEM, as the shell63 element has both bending and membrane capabilities, and can suffer from both plane and normal loads. The volute FEM with a total of 46,182 shell63 element grids was divided into three main sections according to the different thickness properties. The front panel thickness (FT) and the back panel thickness (BF) were set to six mm, and the volute side panel thickness was set to five mm (ST). In addition, the model material was steel, the density \(\rho\) = 7800 kg/m\({}^{3}\), the elastic modulus = 2.06e11 pa, and Poisson's ratio \(v\) = 0.3. The volute casing was fixed to a supporting stand by 10 fastening bolts at the casing front. The volute panel rear (near the motor) was connected by four fixed bolts, and the three translational degrees of freedom of the nodes at the bolts were restricted to zero. The panel thickness distribution and the degree of freedom constraints on the volutes are shown in Figure 9.  
To validate the one-way fluid-solid coupling, vibration analysis was performed, and the results were compared with those of experimental vibrational analysis. The LMS Test Lab test system was used to complete the vibrational test of the fan casing. To eliminate the vibrational disturbances on the volute originating from the imported pipe and outlet throttle flow, elastic connections were used in two positions: at the connection between the transition section of an inlet and the volute, and between the volute outlet and the throttle valve. The flexible installation should meet the requirements of GJB4058-2000 (The Noise and Vibration Measurement Method of Ship Equipment) [28]. There is some major equipment required for this test, such as an LMS SC310W signal analyzer, a B&K 4513 accelerometer, and a B&K 4514 accelerometer. The background noise is ignored because of the lower value compared to the actual value of the fan. One hand of the accelerometer is fixed on the volute by bonding, and the other hand is directly connected to the data processing and analysis notebook by the data line. The arrangement of the vibration sensor is shown in Figure 10. There are 16 vibration measurement locations on the casing surface. The first five measuring points are arranged near the border between the back panel of the volute and the side panel of the volute. The first measuring point is located near the tongue, and the second through fifth measuring points, #2-5, are respectively arranged at the positions of 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\). The sixth to ninth measuring points, which are located at the edge of the plate between the back panel of the volute and the motor along with the  
Figure 9: The finite element model (FEM) of the volute. connecting plate in the circumferential direction, are arranged at an interval of 90 degrees. At the front panel of the solute, with a 90-degree interval in the direction of a counterclockwise rotation layout, are measuring points 10 to 12. The vibration measuring point of the solute side panel is in the middle of the axial width of the volume arranging measuring points 13 to 15. Measuring point 13 is defined as the starting point; measuring points 14 and 15 are also arranged in the side volute at an interval of 140 degrees; and the measuring point 16 is at the outlet of the volute side panel. The vibration test and the dynamic pressure test of the volute are carried out at the same time, and the data are, respectively, collected in different control computers.