The gear ratio and electric motor sizing are two fundamental parameters in the design of propulsion systems for Battery Electric Vehicles (BEVs), simultaneously influencing the motor operating regime, energy consumption, regenerative braking energy recovery, driving range, and the utilization level of the propulsion system capabilities. In modern architectures based on Permanent Magnet Synchronous Motors (PMSMs) and single-stage reduction gearboxes, the gear ratio establishes the relationship between the traction requirements at the wheels and the operating points of the electric machine, while PMSM sizing determines the motor loading level and the positioning of these operating points on the efficiency map. Consequently, an uncoordinated selection of these two parameters may lead either to operation predominantly within partial-load regions, with limited utilization of high-efficiency areas, or to operating conditions that are infeasible from a design and implementation perspective.

In the scientific literature, the optimization of BEV propulsion systems is frequently performed using objective functions based on energy consumption, driving range, dynamic performance, or total powertrain losses. Although numerous studies employ electric motor efficiency maps for result interpretation, the actual distribution of operating points across these maps is rarely used as an explicit optimization parameter. Furthermore, gear ratio optimization and PMSM sizing are often addressed separately, while their combined influence on both traction and generator operating modes remains only partially investigated.

Based on these observations, this study proposes a methodological framework referred to as the Efficiency Map Utilization Framework (EMUF) for the co-optimization of PMSM sizing and gear ratio selection in battery electric vehicles. The proposed methodology aims to quantify how different combinations of electric motor scaling factors and gear ratios influence the distribution of operating points on the efficiency map, energy consumption, regenerative braking energy recovery, and vehicle driving range. To this end, PMSM sizing is introduced through a scaling factor applied to the motor torque and current capabilities, enabling the evaluation of multiple motor configurations without modifying the vehicle longitudinal dynamics parameters.

To characterize the utilization level of the efficiency map, a set of four indicators is introduced within the EMUF framework. The first indicator, the Energy-based High-Efficiency Utilization Ratio (EHUR), quantifies the proportion of traction energy delivered within high-efficiency operating regions. The second indicator, the Energy-weighted Map Efficiency (EME), represents the energy-weighted average efficiency of the electric propulsion system throughout the driving cycle. The third indicator, the Operating Point Concentration Index (OPCI), characterizes the degree of concentration of operating points in the vicinity of the maximum-efficiency region. For generator-mode analysis, the Energy High-Efficiency Regeneration Ratio (EHRR) is introduced to quantify the proportion of regenerative braking energy recovered within the high-efficiency regions of the efficiency map.

The proposed methodology includes verification of the physical constraints of the propulsion system for each analyzed combination of motor scaling factor and gear ratio. The maximum PMSM speed, torque, power, and current limits are evaluated, together with compliance with the maximum torque–speed characteristic provided by the electromagnetic motor model. To quantify infeasible operating conditions, an indicator termed the Feasibility Violation Factor (FVF) is employed, and configurations exceeding the system design constraints are excluded from the selection process. In addition, operating-range utilization metrics are determined, including the utilization levels of the maximum motor speed, maximum torque, and maximum available power.

For each analyzed configuration, the traction energy drawn from the battery, the energy recovered through regenerative braking, the net battery energy consumption, the specific energy consumption, the estimated driving range, and the values of the EHUR, EME, OPCI, and EHRR indicators are determined. Subsequently, the correlations between the EMUF indicators and the overall vehicle energy performance metrics are investigated in order to assess the capability of these indicators to simultaneously identify the optimal PMSM size and the optimal gear ratio without relying exclusively on objective functions based on final energy consumption.