Ivanovic, V. and Tseng, H., "Bond Graph Based Approach for Modeling of Automatic Transmission Dynamics," SAE Int. J. Engines 10(4):2017, doi:10.4271/2017-01-1143.
This paper describes a method for modeling the dynamics of planetary automatic transmissions by using bond graphs. Bond graph models for the most relevant planetary gear sets (single, double and stepped pinion and Ravigneaux) are summarized and used as building blocks to construct the "device-mapping" bond graphs of complete planetary transmissions. Examples used include the legendary Ford Model T transmission and state-of-the-art six- and ten-speed transmissions. A systematic procedure of deriving mathematical models based on the constructed bond graph models is described which can be applied to any clutch application combination. It is illustrated how device-mapping bond graph models can be converted into conceptual torque-path bond graphs for better insight on the analysis of transmission shift events. Lastly, the effect of system rotational inertias on shift dynamics is discussed for practical concerns.