## 1 Introduction  
As an emerging renewable energy source, the proton exchange membrane (PEM) fuel cell system has great potential in various vehicles and distributed energy systems [1]. In the last three decades, fuel cell technology has made great progress in commercialization. The output power of the PEM fuel cell has been increased steadily, the majority of which are in the range of 60-100 kW, but the cost and durability are still big challenges [2]. On the one hand, a large amount of research on fuel cells has been performed to improve the performance and durability of the stack [3]. On the other hand, developing a simple and efficient Balance of Plant (BOP) subsystem can also increase the life of the fuel cell. BOP mainly includes the anode hydrogen supply, cathode air supply, and thermal management systems [4]. With the increase in the output power and the use of the metal bipolar plate, the operating pressure of the PEM fuel cell system has gradually increased to 200-300 kPa. In these systems, which have a large output power and high operating pressure, the hydrogen recirculating scheme is preferred for the anode hydrogen supply subsystem. Generally, there are three anode hydrogen supply configurations applied in the PEM fuel cell system: dead-end design, flowing through the structure, and hydrogen recirculation. Compared to the dead-end design or flowing through the structure, the configuration with hydrogen recirculation has advantages such as high power density, low hydrogen consumption, and robust reliability [5]. The hydrogen pump is an important component of the anode hydrogen supply configuration with hydrogen recirculation, the performance of which has a significant impact on the performance of the fuel cell system [6]. A performance map of the hydrogen pump is always needed in the design of a fuel cell system [7]. It is also very important for the realization of the control strategies during the operation of the fuel cell system [8; 9]. The performance map of the hydrogen pump is dependent on the specific type of pumps. There are three kinds of pumps used for hydrogen recirculation in the PEM fuel cell systems: electrochemical pump, ejector, and mechanical pump [10]. The electrochemical hydrogen pump dissociates hydrogen into electron and hydrogen ion by using DC voltage. This kind of hydrogen pump has advantages such as small power consumption and low noise [11]. The ejector utilizes the pressure difference between the hydrogen tank and the fuel cell stack as the driving force, which has the advantages of no moving parts, low maintenance cost, and relatively high efficiency [12]. However, the design and control methods of the ejector are complicated because of difficulty in adapting to variable working conditions of fuel cell systems [13]. The mechanical pump increases the hydrogen pressure at the outlet of the fuel cell stack to recirculate it to the inlet, which is driven with a motor powered by the fuel cell system itself. Due to the advantages including multi-phase delivery, easy control, and excellent characteristics in off-design operating conditions, the mechanical pump is widely used in the fuel cell system, especially for automotive applications. Regarding energy efficiency, the system efficiencies of three types of pumps were investigated by [PERSON] et al. [10]. The system efficiency of the ejector is highest because of the low parasitic power while, the system of the mechanical compressor has the lowest efficiency. Hence, low system efficiency is the disadvantage of the mechanical compressor. It means that a mechanical hydrogen pump with high performance is in urgent need to be developed. The mechanical pump is the general name of a group of pumps, which can be divided into several types according to the structures of the key components, such as the regenerative pump, claw pump, scroll pump, and Roots pump.