Multi-objective gear ratio and shifting pattern optimization of multi-speed transmissions for electric vehicles considering variable transmission efficiency

In the development of electric vehicles, multi-speed transmissions have become an alternative to conventional single-speed transmissions. The superior design of multi-speed transmissions requires simultaneous optimization of the gear ratios and shifting patterns. The transmission efficiency of multi-speed structures is inevitably lower than that of single-speed structures; this disadvantage should be considered in the design optimization for multi-speed transmissions. Typically, the transmission efficiency varies depending on the torque, speed, and drive gear, and it has a direct effect on the optimal transmission design. Based on the variable transmission efficiency analysis, the design objectives representing energy efficiency and dynamic performance were defined as the quantified functions. To consider the trade-off between these two objectives, a multi-objective optimization process was implemented, and the surrogate models were utilized for effective optimization. To verify the importance of a variable transmission efficiency, the gear ratios and shifting patterns were optimized by considering a variable and constant transmission efficiencies. The comparison of optimal design solutions and objective-function values clearly highlights the necessity of considering a variable transmission efficiency, and the energy efficiency and dynamic performance could be improved to maximums of 12.1% and 10.7%, respectively, compared to those of the electric vehicle with a single-speed transmission.