Switch-Mode Continuously Variable Transmission: Modeling and Optimization

Abstract

Hybrid vehicles are an important step toward reducing global petroleum consumption and greenhouse gas emissions. Flywheel energy storage in a hybrid vehicle combines high energy density and high power density, yet requires a highly efficient continuously variable transmission with a wide operating range. This paper presents a novel solution to coupling a high-speed flywheel to the drive train of a vehicle, the switch-mode continuously variable transmission (CVT). The switch-mode CVT, the mechanical analog of a boost converter from power electronics, utilizes a rapidly switching clutch to transmit energy from a flywheel to a spring, which applies a torque to the drive train. By varying the duty ratio of the clutch, the average output torque is controlled. This paper examines the feasibility of this concept by formulating a mathematical model of the switch-mode CVT, which is then placed in state-space form. The state-space formulation is leveraged to analyze the system stability and perform simple optimization of the switch time and damping rate of the spring over the first switching period. The results of this work are that a stable equilibrium does exist when the speed of the output shaft is zero, but the system will not reach and stay at a desired torque if this condition is not met, but requires continuous switching between the two states. An optimal switching time and damping ratio were found for the given parameters, where the lowest error occurred with low values of damping ratio. This work builds a foundation for future work in increasing the complexity of the model and the optimization method.