Integrated topology and shape optimization of the five-spoke steel wheel to improve the natural frequency

A wheel is a vehicle component that has an important role in supporting ground reaction forces and, at the same time, transmitting the driving force from the engine to the tire. This paper presents an integrated topology and shape optimization to determine the optimal steel wheel with enhanced natural frequency. First, topology optimization was conducted with a solid-shell finite element (FE) model to maximize the first rim-mode frequency while satisfying a rotational inertia constraint. Based on the topology optimization results, a surface-based initial design was constructed to precisely consider structural and manufacturability concerns at the second design stage. Shape optimization was then performed to maximize both the rim-mode and spoke-mode frequency. Finally, the prototype of the steel wheel was manufactured to be experimentally validated in terms of natural frequencies and road booming noises. Experimental results showed that the prototype achieved a substantial increase in the first rim-mode frequency from 164 (that of conventional steel wheel) to 262 Hz, thereby accomplishing a maximum 2.2 dB decrease in the range of road booming noise. Such enhanced noise and vibration are critical factors in the ride comport at low-speed driving.