# Optimization of the Housing Shape Design for
## 5 Conclusions  
This study aimed to reduce the structural vibration of the gearbox housing owing to the gear mesh excitation force and resulting radiated noise. The whole procedure of this study focused on the objectivity and reliability for reducing the radiated noise in agricultural electric vehicle gearbox. The noise and vibration of the gearbox were measured and analyzed by considering the load characteristics of the gearbox for agricultural electric vehicles. A FE model, which was validated through an experimental modal analysis, was used, and the internal machine elements were modeled. This process is suitable for optimization because it provides accurate bearing reaction force even if the shape of the housing changes. Numerical analysis on the noise was performed using the validated FE model, and the shape of the gearbox housing was optimized using topology optimization technique. Since the value of the equivalent radiated power in the frequency range of interest was used as the output variable for the topology optimization, results were obtained regardless of the measurement location. In conclusion, the shape design process, which was previously dependent on experience, was performed through an objective and reliable process. The main conclusions from this study are as follows. Figure 19: Equivalent radiated power comparison for counterclockwise drive. (**a**): ERP excited by gear mesh stage 1—first harmonic; (**b**) ERP excited by gear mesh stage 1—second harmonic. * The white noise of the gearbox represents the pure tone characteristics occurring at a specific frequency, and this frequency is determined by the rotational speed of the input shaft. Therefore, to analyze the noise and vibration considering these characteristics, an order analysis test was performed to analyze the data according to the rotational speed of the input shaft. To reduce the radiated noise owing to the structural vibration of the gearbox housing, the contribution level was evaluated by comparing the GMF component with the overall noise level according to the rotational speed. As a result, the first and second harmonic components of the first stage of the gear train were evaluated as the main noise sources. * Through the EMA, the dynamic characteristics of the actual housing were identified, and the FE model was updated and validated based on this result. In the model update process, the material properties of the gearbox housing and the contact method between the housings were set as variables. The natural frequency of the improved model and the actual model showed an error of approximately 2.8%. For the mode shape, the FE model was validated by comparing the MAC value. The internal machine elements, such as the gears, shafts, and bearings, were modeled in a substructure using a reduced-order modeling technique and were connected to the housing. * To optimize the shape design of the gearbox housing for reducing radiated noise, the design areas were modeled by analyzing the weak areas against noise and vibration. ERP analysis was performed according to the rotational direction of the input shaft and gear excitation force. The new design areas were determined through the ODS analysis under the operating conditions where the ERP value was high and the ESE analysis in the mode causing the relevant deflection. To optimize the shape design, a topology optimization technique was used to determine the optimum material distribution in the design areas, and the minimization of the ERP value was set as the objective function. After optimization, the maximum ERP value decreased under all operating conditions; however, the weight of the housing increased by approximately 12%. 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.