Robinette, D. and Wehrwein, D., "Automatic Transmission Gear Ratio Optimization and Monte Carlo Simulation of Fuel Consumption with Parasitic Loss Uncertainty," SAE Int. J. Commer. Veh. 8(1):45-62, 2015, doi:10.4271/2015-01-1145.
This investigation utilizes energy analysis and statistical methods to optimize step gear automatic transmissions gear selection for fuel consumption. A full factorial matrix of simulations using energy analysis was performed to determine the optimal number of gears and gear ratios that provide the best fuel consumption performance for a particular vehicle - engine application. The full factorial matrix setup as a design of experiment (DOE) was applied to five vehicle applications, each with two engines to examine the potential differences that variations in road load and engine characteristics might have on optimal transmission gearing selection. The transmission gearing options considered in the DOE were number of gears, launch gear ratio and top gear ratio. Final drive ratio was also included due to its global influence on vehicle performance and powertrain operating speeds and torque. An enterprise approach for vehicle fleet balancing of fuel consumption objectives based upon selection of automatic transmission gearing strategy is presented. Monte Carlo simulations for the influence of parasitic loss uncertainty for the automatic transmissions selected from the generalized DOE were conducted to determine the range of fuel consumption that might be realized in production. Specifically, the focus of uncertainty analysis was on automatic transmission parasitic loss variation that might be encountered due to manufacturing and assembly. The overall findings of the investigation show that the optimal number of transmission gears begins to plateau above 8 speeds and reaches a minimum at 10 speeds, but gearing selection is highly dependent on vehicle and engine application. Automatic transmission gearing parameter selection was unaffected by the variation introduced by the Monte Carlo simulations, but did show fuel consumption performance to vary upwards of 9 g CO2/km depending on applications and to have a direct impact on powertrain operating parameters.