## 2 Theoretical Analysis  
Schematic diagram of the hydraulic hybrid vehicle with a series connection is shown in Figure 1. There are four pump/motors installed in the investigated hydraulic hybrid vehicle, because there are four wheels and each wheel is driven independently. There is another pump to connect the engine, high-pressure accumulator, and the four pump/motors, which is used to transform the mechanical energy generated by the engine to the hydraulic energy and transmit it to the four wheels through the flow of hydraulic oil. Meanwhile, the low-pressure accumulator was used to form a complete hydraulic oil circuit. The four directional valves are used to control flow direction of the hydraulic oil, which can work in the forward or backward conduction status. The four clutches are used to connect the four pump/motors and the four wheels, which are used to transmit the energies between the four pump/motors and the four wheels. When the vehicle is in the normal running process, the engine is taken as the original power supply of whole vehicle, and four pump/motors work in the condition of hydraulic motor. The mechanical energy generated by the engine is transformed to the hydraulic energy of the hydraulic oil, and the four directional valves work in the forward conduction status, by which the hydraulic oil is delivered to the four pump/motors and the hydraulic energy is transferred to four wheels. For the mechanism of energy transfer, it included two processes. Firstly, during the braking process, the wheels are considered as the power supply and the four pump/motors work in the condition of the pump, and the four directional valves work in the backward conduction status. The mechanical energies of four wheels are transferred to the hydraulic energies in the four pump/motors and those four are laid in the high-pressure accumulator. Secondly, when the vehicle starts again or accelerates, the stored hydraulic energies in the high-pressure accumulator can be released to auxiliary drive the four wheels and the four directional valves work in the forward conduction status again, which can obtain the aim of energy recovery in the hydraulic hybrid vehicle. The anti-lock braking (ABS) system is usually fixed between the wheel and the pump/motor to improve the driving safety, which has no influence to operation of the energy recovery system in Figure 1. However, the energy recovery rate will be decreased, because the ABS system uses some braking energy and this energy can't be regenerated. Furthermore, the additional tare mass on the hydraulic hybrid vehicle has complicated effect to the energy recovery rate. The larger the additional tare mass is, the higher capacity of the pump/motor and the bigger volume of the accumulator will be. For the same speed, the hydraulic hybrid vehicle with additional tare mass indicates more braking energy can be recovered in the braking process and more energy is required when the vehicle starts again or accelerates. Thus, to a certain extent, the energy recovery rate is not affected when the additional tare mass is small. When the energy recovery exceeds capacity of the selected accumulator along with increase of the additional tare mass, the excessive energy is not reused and the energy recovery rate will decrease. Figure 1: Schematic diagram of the hydraulic hybrid vehicle with a series connection. The hydraulic accumulator is the critical component of the regenerative braking system, and its properties are the major influencing factors for the energy recovery rate [25; 26]. As the major energy conversion component, gas in the hydraulic accumulator changes along with the temperature during the energy conversion process. Therefore, the heat dissipation loss should be taken into account when energy recovery rate of the accumulator is calculated. The heat dissipation loss is mainly influenced by air polytropic exponent \(n\), which can be calculated by Equation (1) [27].