CVT Modeling and Simulation: An Optimization Framework for Design and Performance

Bashar Alzuwayer, Clemson University


A Continuously Variable Transmission (CVT) has the potential of increasing the overall powertrain efficiency, and reducing fuel consumption and greenhouse emissions. Based on CVT performance metrics and with the use of a physics-based model, this study focuses on developing a structured CVT design optimization framework. This approach can be used to define the CVT design configuration during early product development stages. Dynamics of a CVT under load are governed primarily by the friction characteristics between the belt and the pulley. The flexibility of the pulley sheaves, the material, and design parameters such as sheave angle also play a part. Therefore, creating realistic models that are numerically efficient and general enough to allow for design optimization are crucial and are addressed in this dissertation. CVT pulleys subjected to high-friction torque exhibit elastic deformations that influence the system dynamics and efficiency. Thus, a sheave deformation model based on representing the CVT sheave as a non-uniform elastically restrained Euler-Bernoulli beam, and solved by the Assumed Modes Method, is developed. The model can consider different CVT sheave structure details, such as the material properties, sheave angle, sheave surface profile, and sheave supporting system. This model is integrated into the CVT model and compared with the deformation models provided in literature. Because the CVT might exhibit different loading conditions and friction regimes, this dissertation investigates different friction models and their influence on the dynamics of the system. These models include Coulomb, Stribeck, and LuGre friction models, where each model has the ability to describe different frictional regime and/or regimes. These friction models are used to analyze the CVT dynamics and to generate the performance maps such as the clamping force ratio, efficiency, and the frictional torque, under different operating conditions. Examination of the results revealed that the CVT dynamics are primarily dominated by the Coulomb friction regime, while the viscous friction regime dominates in limited operating conditions. Using the developed deformation model, the influence of different CVT structural properties on the CVT performance is investigated. Therefore, a multi-objective optimization problem was formulated to search for the optimal sheave structure design that minimizes the clamping force and the slip. Based on the Pareto front principle, different suboptimal design configurations were identified. Two design configurations were selected and analyzed based on their performance. Furthermore, the selected designs were implemented in a low-order vehicle model to investigate the performance of the CVT design configurations under different driving cycles. The results of low-order vehicle/powertrain implementation, generated performance maps, and analysis of the optimized CVT design configurations were all in agreement, and a reduction in the required clamping force was achieved. In summary, this framework provides a systematic procedure toward optimizing the CVT performance through developing and integrating a general sheave deformation model into a state-of-the-art CVT dynamics model that can help in adopting advanced optimization methods in a numerically efficient approach.