# Optimization of the Housing Shape Design for
## 1 Introduction  
With increasing interest in reducing greenhouse gases and fine dust, the development and dissemination of eco-friendly vehicles is expanding. In the agricultural machinery industry, the demand for the development of electric vehicles is increasing as a result of the electrification of power transmission systems [1]. The electric motor of an electric vehicle is operated at a relatively high rotational speed and low torque compared to the engine of an internal combustion locomotive. Therefore, to adjust the driving speed of the electric vehicle to the internal combustion locomotive, a speed-reducing gearbox is required [2]. For a conventional engine-driven vehicle, the engine is the main noise source; however, for an electric vehicle, there is no engine noise, but the gear noise owing to the driving of the electric motor is the main noise source [3]. The noise of the motor and gearbox generated during driving shows relatively high-frequency characteristics compared to that of the engine noise. Depending on therotational speed, specific pure tone noise occurs at the torque ripple frequency of the electric motor and gear mesh frequencies of the gearbox. The pure tone generated in the wide frequency band coincides with the natural frequency of the system, which can cause resonance and enhance noise [4]. Pure tone acts as a hissing noise in the high-frequency region and booming noise in the low-frequency region. The higher the frequency of noise, the greater the discomfort to the operator [5]. Therefore, to improve the working environment of the operators, noise reduction in agricultural electric vehicles should be studied. [PERSON] et al. [6] measured radiated noise using a microphone to analyze the noise characteristics of an electric powertrain and measured the vibration using an accelerometer on a bearing block. The noise and vibration were analyzed by classifying electromagnetic noise, inverter noise, and gear whine noise; the high-speed gear whine noise dominates the sound quality at high speed. As a result of evaluating the sound quality through experiments, the electric powertrain exhibited a high-frequency characteristic, and produced more discomfort than that by the conventional engine. As described above, to reduce noise in an electric vehicle, a process of analyzing structure-borne noise caused by gear mesh excitation force generated in the gearbox is required. [PERSON] et al. [7] produced a simple experimental model consisting of two-speed gear trains to analyze the noise characteristics of the gearbox and compared the noise levels of the first and second gear trains. A rotational acceleration sensor and a microphone were used to measure the structure-borne noise due to gear excitation. The analysis of the noise according to the order component of the first and second gear meshes confirmed that the first gear mesh was dominant in the noise level by operating at a relatively high speed. [PERSON] et al. [8] conducted a study on the optimization of the stiffener to reduce the noise and vibration of the gearbox housing and revealed a correlation between the vibration reduction design and noise reduction design. In addition, to minimize the structure-borne noise of the gearbox housing, the vibration energy of the mode existing in the frequency domain of interest was reduced; this method was most effective when the stiffener was positioned between the bearing and housing fixing. [PERSON] et al. [9] experimentally measured the load at the bearing position to realize the dynamic load acting on the gearbox and verified it by comparing it with the simulation model. The natural frequency of the housing increased by modifying the shape of the housing through a topology optimization technique. [PERSON] et al. [10] optimized the dynamic performance of sawing machine gearbox using topology optimization. The internal components were modeled as point masses to reduce the computational burden. The natural frequencies were used as the output design variables.