Park, J., "The Unified Relationship between Torque and Gear Ratio and Its Application in Multi-Step Automatic Transmissions," SAE Technical Paper 2016-01-1098, 2016, doi:10.4271/2016-01-1098.
The market demands for CO2 reduction and fuel economy have led to a variety of new gear set concepts of automatic transmissions with 4 planetary gear sets and 6 shift elements in recent years. Understanding the relationship between the torque of clutch and brake and gear ratio in the design stage is very important to assess new gear set concepts and to set up the control strategy for enhancing shift quality and to reduce the heat generation of clutch and brake.In this paper, a new systematic approach is used to unify the relationship between torque and gear ratio during the gear shift for all multi-step planetary automatic transmissions. This study describes the unified concept model with a lumped inertia regardless of the specific transmission layout and derives the principal unified relationship equations using torque and energy analysis, which prove that the sum of brake torque is always gear ratio -1 in every in-gear. Based on the unified relationship equations, the relationship among the required torques of shift elements is illustrated in 20 operating combinations of 6 shift elements.Furthermore, this study shows that the torque of shift element is a function of the ratio of input speed change to slip speed change of shift element during the inertia phase of the shift process and the energy loss of shift element during the gear shift is a function of gear shift time and gear ratios before and after shifting.