## Mathematical Analysis of Clutch Thermal Energy during Automatic Shifting Coupled with Input Torque Truncation

*SAE paper #2020-01-0967, 2020 SAE World Congress, Detroit, MI*,

*2020*.

A step-ratio automatic transmission alters torque paths for gearshifting through engagement and disengagement of clutches. It enables torque sources to run efficiently while meeting driver demand. Yet, clutch thermal energy during gearshifting is one of the contributors to the overall fuel loss. In order to optimize drivetrain control strategy, including the frequency of shifts, it is important to understand the cost of shift itself. In a power-on upshift, clutch thermal energy is primarily dissipated during inertia phase. The interaction between multiple clutches, coupled with input torque truncation, makes the decomposition of overall energy loss less obvious. This paper systematically presents the mathematical analysis of clutch thermal energy during the inertia phase of a typical single-transition gear shift. In practice, a quicker shift is generally favored, partly because the amount of energy loss is considered smaller. However, the analysis reveals that there is a critical input torque truncation level, as a function of transmission output torque, where a shorter shift actually results in a larger energy penalty. Numerical simulations of gearshifting as well as vehicle testing are conducted to examine clutch thermal energy characteristics above and below the critical input torque truncation level.