Robinette, D., "A Two Degree of Freedom, Lumped Inertia Model for Automatic Transmission Clutch-to-Clutch Shift Dynamics," SAE Int. J. Passeng. Cars - Mech. Syst. 7(3):1163-1174, 2014, doi:10.4271/2014-01-1782.
This paper presents a methodology to represent automatic transmission clutch-to-clutch shift dynamics with a two degree of freedom, lumped inertia model. The method of reducing the automatic transmission to a lumped, two inertia model as a function of shift and input shaft acceleration is detailed using a full kinematic representation of the automatic transmission. For a given clutch-to-clutch shift maneuver there are two dependent equations that utilize the two lumped inertias and represent the response of the transmission system from input to output shaft. Applicability of the method is shown for planetary automatic and layshaft dual clutch transmissions. Typical clutch-to-clutch shift maneuvers are illustrated with the two inertia model for power on upshifts and downshifts. The simplification of automatic transmission shift dynamics using this method enables rapid synthesis of a given transmission powerflow for estimation of shift quality potential, required clutching torques, inertia phase engine torque intervention and output torque through all phases of a shift event.