## 4 EHA Power Matching
### Power Matching Comparative Analysis  
Based on the above analysis, we can draw the power curve of the motor and the power demand of the actuator in the same chart by dividing the torque of the motor by the hydraulic reduction ratio and multiplying the speed of the motor by the hydraulic reduction ratio. the EHA power matching is such that the selected motor power must meet the power requirements of the actuator at every point, as shown in Figure 12(a). First, we can easily choose a motor with the same peak power as the actuator. Then in order to meet the stalled load requirement, \(k_{h}\) can be set to \(T_{\rm{max}}/F_{\rm{Imax}}\). However, a constant \(k_{h}\) is not easy to ensure that the motor can exceed the power demand of the actuator at every point, as the M1 curve illustrated in Figure 12(b). the rotational speed of the chosen motor cannot meet the requirement of no-load velocity of the actuator. It is assumed that, due to the design of the motor, the motor speed is limited to this maximum speed, so in order to achieve power matching, \(k_{h}\) can be only increased. Simultaneously, for the sake satisfying the stalled requirements, the maximum output torque of the motor must be increased. In order not to increase the thermal load, more copper needs to be added to the motor windings to increase the current. the reason for further explanation is that the motor output torque can be increased by increasing the current. Under the current is increased, the thermal load will increase if the winding resistance is not reduced. Therefore, it is necessary to reduce the winding resistance by increasing the winding cross-sectional area. Eventually this will lead to increase motor power and size as well as volume, as M2 curve shown in Figure 12(b). the motor is one of the massive segments in EHA, so a method that allows a smaller motor to be utilized is required. a variable displacement pump is a desirable choice, because \(k_{h}\) is variable and the smallest size motor can be adopted to match the power requirements of the actuator at each point. Assuming that the EHA system has no losses, the motor power to be selected for the power matching of the fixed displacement EHA must be greater than the power required by the actuator (load), and leave a certain margin, as shown in Figure 14. Therefore, it is disadvantageous from the perspective of improving the power density of the system. For variable displacement EHA power matching, under low speed and high load conditions, \(k_{h}\) is reduced to meet the demand of large load, that is, decreasing the pump displacement, so that the power curve of the motor envelopes the high load power requirements of the actuator as shown in Figure 14(a). good power matching can be not only achieved in this operating  
Figure 13: Actuator power requirement and motor power output curves. condition, but also reducing the displacement is beneficial to lower the output torque of the motor leading to reducing the copper loss of the motor; under high-speed and low load working conditions, \(k_{h}\) is increased to meet the requirements of high-speed load, that is, increasing the displacement of the pump, so that the power curve of the motor envelopes the power requirements of the actuator in high-speed conditions as indicated in Figure 15b. Therefore, the variable displacement EHA can dynamically adjust the power matching. It is only necessarily equal to the power requirements of the actuator, which is conducive to improving the power density of the system. In order to make the motor meet the load requirements, when EHA-FPVM is used, \(k_{h}\) is a fixed value, which can be taken as \(T_{\text{max}}/F_{\text{max}}\) to meet the power requirements of the stalled load, that is, the theoretically required motor power is at least equal to load power. The maximum output power of the motor is selected to be the maximum power of the load.