Mathematical Modeling of the Longitudinal Motion of a Vehicle with a Continuously Variable Transmission

The Continuously Variable Transmission (CVT) is a widely adopted transmission system. The operation of a CVT is simple, but successfully foretelling the longitudinal motion of a vehicle that utilizes this transmission is sophisticated. As a result, different vehicles taking part in BAJA-SAE competitions were developed using various strategies to model the vehicle’s longitudinal dynamics and CVT operation. This article aims to provide a tool for obtaining a quantitative estimate of the longitudinal performance of a CVT equipped vehicle and for the selection of an optimal drive-train gear ratio for such a vehicle. To this end, this article proposes a novel, relatively simple, and reasonably accurate mathematical approach for modeling the longitudinal motion of a vehicle utilizing a CVT, which was developed by a novel integration of existing vehicle dynamics concepts. The proposed technique splits the longitudinal motion into three distinct phases - low ratio acceleration, shifting, and over-run - and uses mathematical modeling to simulate each stage. The low ratio acceleration and over-run stages were modeled using an iterative approach based on Newton’s equations of motion, taking into account engine torque and aerodynamic drag variation. On the other hand, the shifting stage was modeled using a differential equation that governs the vehicle’s motion during the said stage. The technique was made more ‘realistic’, another novel aspect, by taking into account the effect of rotating masses. The proposed approach’s potency was validated through experimental validation studies on BAJA-SAE All-Terrain Vehicles (ATVs). It is concluded that the proposed modeling technique largely simplifies the motion simulation task while giving a relatively accurate estimate of the vehicle’s actual longitudinal performance. An All-Terrain Vehicle for the BAJA SAE collegiate competitions forms this cornerstone of this article.