# Development of Transmission Systems for Parallel Hybrid Electric Vehicles
## 3 Results
### Extra-Urban Driving Cycle  
The EUDC is designed to represent more aggressive, high-speed driving conditions, as shown in Figure 12a. The maximum speed of the EUDC is 120 km/h, starting from the still phase. In this driving condition, the functions of an idle start in the EV mode and power assist for high power demand are enabled. Figure 12b shows the simulation results of the following EUDC with different \(k_{2}\) values and the same overall gear ratio. Figure 12c shows the engine on-off state. Figure 12c shows that the engine is always on under the EUDC, excluding the start-from-still phase and the brake-to-still phase. Figure 12d shows that the EM is also on in the 316-336 th second regions, excluding the start-from-still and brake-to-still phase. Table 6 shows fuel consumption under the EUDC with different \(k_{2}\) values. The optimal results are obtained for \(k_{2}=1.6\), wherein fuel consumption improves by 1.5%, because the vehicle can be driven for a longer duration in the EV mode and the required torque can be provided in the hybrid mode. The detailed effects of \(k_{2}\) values are discussed in the following discussions. Figure 11: (**a**) Driving mode control logic. (**b**) Gear shifting control logic. Figure 13a shows the different motor statuses, which indicate that a larger \(k_{2}\) value drives the motor for a longer duration in the EV mode. Figure 13b shows the motor torque that is provided under the EUDC. The motor provides a positive torque under the EUDC, which indicates that the motor works as a traction motor. Engage and disengage clutches when shifting the gear or when changing the driving mode generate negative impulse. Figure 13c shows that the motor provides a torque in the power-assist region, and a smaller of \(k_{2}\) value provides more torque, whereas a larger \(k_{2}\) provides less torque from the motor side before TC-PIM. The torque that is provided by the motor increases after the 325 th second due to gear shifting, as shown in Figure 13d. Table 7 shows that the torque provided by the motor after the TC-PIM is larger for \(k_{2}=1.6\); thus, higher \(k_{2}\) values exhibit superior power-assist ability. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(k_{2}\) = 1 & \(k_{2}\) = 1.2 & \(k_{2}\) = 1.4912 & \(k_{2}\) = 1.6 \\ \hline EV gear ratio & 19.92 & 14.06 & 13.36 & 12.45 \\ EV overall ratio & & 19.92 & & \\ Fuel consumption (km/L) & 16.9 & 16.98 & 17.12 & 17.15 \\ \hline \end{tabular}
\end{table} 
Table 6: Fuel consumption under extra-urban driving cycle (EUDC). Figure 12: (**a**) Standard extra-urban driving cycle (EUDC) driving cycle. (**b**) Simulation follow driving cycle. (**c**) Status of engine. (**d**) State of motor (\(k_{2}=1\)). Figure 14a presents the reason why larger \(k_{2}\) values cause a longer driving time in the EV mode. Due to the EV gear ratio and \(k_{2}\) being different, the required speed and TW speed are different when the speed of the drive shaft placed before the gearbox is more than 3000 rpm. For a larger \(k_{2}\) value, the vehicle can operate the motor in the higher speed region and drive the vehicle with higher speed in the EV mode. Therefore, the vehicle can drive for a longer duration in the EV mode. Figure 14b shows why the motor provides torque before the TC-PIM. Larger \(k_{2}\) values can provide lower torque to reach the load demand because of the fixed load and fixed gear ratio. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(k_{2}\) = 1 & \(k_{2}\) = 1.6 \\ \hline Torque (Nm) & 14.85 & 10.07 \\ Torque after TC-PIM (Nm) & 14.85 & 16.112 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulated torque convert values. Figure 13: (**a**) Comparison of motor status. (**b**) Comparison of motor torque. (**c**) Comparison of motor torque at power-assist region. (**d**) Gear position. Figure 15a-d present the operation points of the engine under the EUDC.