# Optimization of the Housing Shape Design for
## 4 Radiated Noise Reduction Using Topology Optimization
### New Design Areas for Optimization  
The operating conditions with high response levels for each excitation component were confirmed from the ERP analysis results. After the ODS was predicted under these conditions, the ESE was analyzed for the mode causing the relevant deflection, and the location had the greatest influence on the deflection. This location was determined as the weak areas against noise and vibration for reinforcement. The original shape of the gearbox housing before optimization is shown in Figure 11.  
Figure 10: Results of the equivalent radiated power analysis. (**a**): Clockwise rotation of the input shaft; (**b**): Counterclockwise rotation of the input shaft. When the input shaft rotated in the CW direction, the ERP value peaked at 3500 rpm for the first harmonic component and at 2636 rpm for the second harmonic component. The GMF can be calculated according to Equation (1) using the order of the harmonic components and the rotational speed. The GMF of the first harmonic component is 817 Hz at 3500 rpm, and the GMF of the second harmonic component is 1230 Hz at 2636 rpm. Comparing these excitation frequencies with the natural frequencies of the gearbox, the closest mode frequencies were 813 and 1238 Hz, respectively. Figure 12 shows the ODS under operating conditions with high ERP values for CW driving, and Figure 13 shows the ESE of the mode shape causing the relevant deflection. Figure 11: Original shape of the gearbox housing. Figure 12: Operating deflection shape (ODS) for clockwise drive. (**a**): ODS excited by gear mesh stage 1-first harmonic at 3500 rpm; (**b**): ODS excited by gear mesh stage 1-second harmonic at 2636 rpm. When the input shaft rotated in the CCW direction, the ERP value peaked at 3788 rpm for the first harmonic component and at 2724 rpm for the second harmonic component. The GMF of the first harmonic component is 884 Hz at 3788 rpm, and the GMF of the second harmonic component is 1271 Hz at 2724 rpm. Comparing these excitation frequencies with the natural frequencies of the gearbox, the closest mode frequencies were 885 and 1280 Hz, respectively. Figure 14 shows the ODS under operating conditions with high ERP values for CCW driving, and Figure 15 shows the ESE of the mode shape causing the relevant deflection. Figure 14: _Cont._  
Figure 13: Elastic strain energy (ESE) for clockwise drive. (**a**): ESE of mode shape at 813 Hz; (**b**): ESE of mode shape at 1237 Hz. From the ESE analysis results, the location that had the greatest influence on the large deflection of the ODS was the points at which the ESE showed a large value. As this location was confirmed to be weak areas against noise and vibration, reinforcement was required. The reinforcing design for the housing was performed to reduce the deflection by increasing the stiffness of the weak areas against noise and vibration and to reduce the radiated noise owing to the structural vibration of the gearbox housing. The new design area for optimizing the shape design was modeled, as shown in Figure 16.  
Figure 14: Operating deflection shape for counterclockwise drive. (**a**): ODS excited by gear mesh stage 1-first harmonic at 3788 rpm; (**b**): ODS excited by gear mesh stage 1-second harmonic at 2724 rpm. Figure 15: Elastic strain energy for counterclockwise drive. (**a**): ESE of mode shape at 885 Hz; (**b**): ESE of mode shape at 1280 Hz. Figures 18 and 19 show the changes in the ERP values before and after performing shape design optimization through topology optimization. Most of the maximum ERP values were reduced under all operating conditions. When the input speed of the gearbox was rated at 2650 rpm, the ERP value decreased by approximately 9.7 dB for the first harmonic and 4.2 dB for the second harmonic in the first-stage gear mesh for CW driving. The ERP value decreased by approximately 2.7 dB for the first harmonic and 5.7 dB for the second harmonic in the first-stage gear mesh for CCW driving.