# Development of Transmission Systems for Parallel Hybrid Electric Vehicles
## 2 Materials and Methods
### Parallel Hybrid Transmission Design
#### 2.2.4 Torque-Coupled-Type Transmission  
The aforementioned discussion examined the constraint of the TC-PIM. In this study, we select the spur gear for the TC-PIM. The flowing section discusses the design torque-coupled-type transmission based on speed-torque. The TC-PIM in this study uses the spur gear train to design and analyze the parallel hybrid transmission system. Spur gears are widely used in power transmission mechanisms. It is a simple mechanism that is used to transfer mechanical power. In spur gear-type transmission, a gear set comprises drive and driven gears. These gears have different dimensions and, thus, it can adjust torque and rotation speed. The relationship between the torque value and rotation speed value for drive and driven gears can be expressed using Equations (15) and (16). The term \(\frac{r_{dn}}{r_{d}}\) also represents the gear ratio. Figure 4a shows the basic driveline architecture for TC-PIM. In this architecture, the engine and motor are always connected with the TC-PIM, which indicates that each power unit cannot only provide power for the traction vehicle. To ensure that all of the driving modes can work, clutches or brakes must be installed in the driveline architecture. For the ICE mode and the smooth integration of mechanical power in the hybrid mode, a clutch must be installed between the EM and TC-PIM. To reduce the engine pumping loss, the clutch that is installed between the engine and TC-PIM is necessary. Figure 4b shows the suitable clutches that were added in the driveline architecture for the TC-type parallel hybrid powertrain. A brake should not be installed in driveline, as the TC-PIM is one-degree-of-freedom mechanism. When the brake is installed in the driveline, it locks up all shafts; thus, the transfer of mechanical power to the TW becomes difficult. In the parallel hybrid mode, the gearbox can be installed at three positions. To determine the position for the installation of the gearbox, the relationship between the speed-torque characteristic of power units and the constraints of the TC-PIM must be determined [18]. The TC-PIM would restrict  
Figure 4: **(a) Basic driveline architecture for the torque-coupled-type PIM (TC-PIM). (b) Clutches added driveline architecture for TC-PIM. **  
the angular speed when power is integrated. The speed relationship with power units and the TC-PIM can be expressed using Equation (17), as follows:  
\[\eta_{speed}=\frac{k_{1}\omega_{E-max}}{k_{2}\omega_{ICE-max}} \tag{17}\]  
If \(\eta_{speed}\ll 1\), the gearbox or single gear must be installed between the engine and TC-PIM to ensure that the engine delivers complete power (GB1). If \(\eta_{speed}\gg 1\), the gearbox or single gear can be installed between the EM and TC-PIM to ensure that the EM delivers complete power (GB2). If \(\eta_{speed}\cong 1\), only the gearbox must be installed behind the TC-PIM and, thus, it can simplify system complexity (GB3). Therefore, the proper placement of gearbox for this primary simulation is behind TC-PIM. Hybrid vehicles have three driving modes, namely EV mode, ICE mode, and hybrid power mode. To satisfy all of the driving modes for satisfactory performance, the gear ratio design must consider the requirements of each driving mode. Equation (17) can be used to calculate \(\eta_{speed}\), which influences the gearbox location. Therefore, the first step in designing the gear ratio is to determine the \(k_{1}\) and \(k_{2}\) of the TC-PIM. To ensure that all of the power units can provide power within an adequate speed range. The relationship between \(k_{1}\) and \(k_{2}\), and power units with a capable speed can be obtained using the following Equation (18):  
\[\omega_{3-Pmax}=\frac{\omega_{2-Pmax}}{k_{2}}=\frac{\omega_{1-Pmax}}{k_{1}} \tag{18}\]  
\(\omega_{1-Pmax}\) and \(\omega_{2-Pmax}\) are compared to determine which term has a smaller value. The smaller term is determined for \(k=1\) and, thus, the theoretical value of \(k\) for another term can be obtained.