# Rib Design for Improving the Local Stiffness of Gearbox Housing for Agricultural Electric Vehicles
## 1 Introduction  
The development of eco-friendly vehicles through the electrification of powertrains is becoming an active area of research, and the demand for the development of such electric vehicles has been increasing in the agricultural machinery industry [1]. At the same time, new ergonomic designs are being highlighted as a way to improve the working environment, and studies are being actively conducted to evaluate and reduce noise and vibration generated from agricultural machines [2]. However, because the noise problem of electric vehicles is quite different from that of conventional engine driven vehicles, the existing sound design method can no longer be used [3]. The noise of electric vehicle powertrains includes high frequency factors and pure tones, and these are more annoying to the operator [4]. The powertrain of a typical electric vehicle consists of an electric motor, a single-speed reduction gearbox, and a differential [5]. For electric motors, because they operate at a relatively high rotation speed and low torque compared to internal combustion engines, the motors are generally manufactured by integration with a reduction gearbox. The main sources of noise in electric vehicle powertrains are electromagnetic excitation, inverter switching, and gear wine [6]. Especially in the high frequency range, gear wine dominantly affects sound quality. The excitation force caused by the transmission error of the gear mesh is transmitted through the shaft and the bearing, and this vibrates the housing. Therefore, this study aims to reducevibration by improving the stiffness of the gearbox housing through rib design and finally solve the problem of radiated noise in agricultural electric vehicle powertrains. [PERSON] et al. [6] experimentally investigated the sound quality of electric vehicle powertrains and redesigned the shape of the gearbox housing to improve it. Topology optimization was conducted with an objective function, the aim of which was to reduce the sound pressure level generated by gear wine in the frequency range of interest, and data were compared to assess the changes in sound quality. However, topology optimization is a technique that is generally used in the conceptual design phase; the shape that appears after optimization is often difficult to use in actual manufacturing. Therefore, in order to manufacture an actual housing, additional process steps are necessary, such as a parameter study using several cases designed in consideration of manufacturability. Rib design is one of the ways to improve the stiffness of the housing, but the existing methods are problematic in that these techniques are dependent on experience and assumptions. [PERSON] et al. [7] analyzed the dynamic behavior by designing ribs on a relatively simple shell. They observed the natural frequency variation with the change in height, thickness, and width of the triangular rib. In order to improve the dynamic behavior, most studies aim to increase the first natural frequency for a resonance avoidance design. However, as mentioned above, the noise of electric vehicles has a high frequency characteristic, so the resonance avoidance design is limited. [PERSON] and [PERSON] [8] improved the stiffness of the chassis mount to reduce vibration transmitted from the engine and suspension within the vehicle. They evaluated the body attachment stiffness of the mount using an impact hammer test with a set target level and compared the results after shape modification. In the case of noise transmitted through a structure, the stiffness of the component on a vibration transfer path acts as the main factor. Hence, most studies that have evaluated the stiffness of a local point have been conducted with components such as a mount. A study evaluating local stiffness to reduce radiated noise was conducted by [PERSON] et al. [9]. They evaluated the local stiffness on the housing surface to find and reinforce the parts that were relatively weak and contributed to the radiated noise and vibration in the transmission.