Abstract 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. Introduction The automatic transmission market for over 6 speed has been increased to perform a proper engine speed control for CO2 reduction and better fuel economy in recent years. To provide more gear steps, a variety of new gear set concepts with 4 planetary gear sets and 6 shift elements are utilized. The torques and slip speeds of shift elements are very important to assess new gear set concepts, however recent trends take the level of complexity of gear and clutch system up a notch in automatic transmissions. The studies which deal with the relationship between the torque of clutch and brake and gear ratio has been done with a specific layout in 4 or 5 speed automatic transmissions. For this reason, the previous studies can’t be applicable to a variety of new gear set for current automatic transmission with 6 and more gear steps. This paper uses a new system approach applicable to all automatic transmissions with planetary gear sets regardless of how to connect rotational elements among planetary gears and surrounding 3 elements, which is input, output and transmission case. Therefore, the unified relationship equations from this study can be used to illustrate the torque and speed characteristics in in-gear state as well as during the gear shift for the current and future transmissions. The Unified Relationship Equations The Unified Model Figure 1 shows 6-speed and 8-speed transmission layout with planetary gear sets. As shown in Figure 1, Even though those have the same 6 speed, there are differences in the use of single pinion planetary gears, double pinion planetary gears, clutches, brakes, internal connecting between rotational elements in planetary gears and external connecting between a rotational element in planetary gears and input, output and transmission case. Figure 1. Schematic diagrams of 6HP26(ZF) and U660E(Toyota)The Unified Relationship between Torque and Gear Ratio and Its Application in Multi-Step Automatic Transmissions2016-01-1098 Published 04/05/2016 Jongsool Park Hyundai Motor Company CITATION: 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. Copyright © 2016 SAE InternationalDownloaded from SAE International by University of British Columbia, Monday, August 20, 2018These differences are being bigger as a number of gear steps are growing. Therefore the system approach with a specific layout causes the r