## 3 Design of the Mechanical Power Circulation Test Rig
### Hydraulic Control System Design for Torque-Applying Device  
The section is based on previous research by [PERSON] et al. [11]. The test rig applies torque in a closed-loop through a separate torque-applying device, which consists of a planetary gearbox and a hydraulic control system, as shown in Figure 10. The hydraulic control system consists of a controller, a directional control valve, two relief valves, four linear actuators,  
Figure 8: Layout of auxiliary gearbox #2. Figure 7: Layout of auxiliary gearbox #1. Figure 9: Layout of torque application gearbox. a hydraulic pump, an electric motor, and oil pressure lines. The directional control valve applies torque in the normal/reverse direction (A mode/B mode) to the torque arms of the planetary gearbox, by changing the direction of flow supplied from the hydraulic pump. A two-way valve is used. Two relief valves are installed between the directional control valve and hydraulic pump, which control the pressure of the entire hydraulic control system. Figure 10: Hydraulic circuit for controlling actuators [11]. The controller controls the movement of the four actuators by controlling the directional control valve, relief valve, and electric motor. It can switch between A and B modes by controlling the directional control valve and can vary the magnitude of the torque applied to the system by controlling the proportional pressure control-type relief valve. Furthermore, the electric motor can be stopped after the desired torque is applied to the torque-applying device, and the pressure of the actuators is maintained by the pilot-operated check valve. In this study, the switch control and on/off control were used to control a directional control valve and an electric motor, respectively. Additionally, a PID (Proportional Integral Derivative) controller was used to regulate a proportional pressure control-type relief valve. The parametric values of the PID controller were obtained by a trial-and-error method. Figure 11 shows a block diagram of the feedback control system to control the torque of the test rig. A controller input of 50.2 kN-m was set as the reference target torque, and the hydraulic actuators were operated until the target torque was reached using the feedback signal from a torque meter. Four actuators were used in the torque-applying device. If only two actuators were used (one each at the left and right lower sides of torque-applying device), the torque could not have been controlled accurately when applying it to the planetary gearbox due to the difference between the areas of the actuator rods arising from the same operating pressures of the actuators. Thus, radial loads other than the torque act on the planetary gearbox. However, if four actuators are used, torque can be controlled accurately when it is applied to the planetary gearbox because the actuators are operated at the same pressure. Thus, loads other than torque do not act on the planetary gearbox. The ring gear torque, \(T_{load}\), which is applied by the hydraulic control system, is expressed as the product of the input torque, \(T_{in}\), of the sun gear and the gear ratio (\(i=Z_{r}/Z_{s}\)) of the planetary gearbox, and the force \(F_{load}\) acting on the actuator is calculated from radius \(l_{2}\) and safety factor \(s\) of the torque-applying device. The pressure required by the system can be derived from the force acting on the actuators and their cross-sectional areas. These relationships are expressed in Equations (1)-(5). The torque-applying device changes the linear motion, \(x_{\text{p}}\), of the actuator to rotational motion, \(\theta\). Therefore, there are mechanical limits to the torque-applying device. Equation (6) shows the rotational angle of the planetary gearbox depending on the change of stroke of the actuator. The structure and specifications of the torque-applying device are shown in Figure 12 and Table 2, respectively.