# Study on the Design of the Fear Pair and Flow Characteristics of Circular-Arc Gear Pumps
## 1 Introduction  
With the continuous iteration of technology, the hydraulic system has higher requirements for hydraulic pumps. First, with the development of the aerospace field, there is a high demand for a high power-to-weight ratio [1]. As the flow rate depends on the displacement and rotation speed, under the premise of fixed displacement, the higher the rotation speed is, the greater the flow rate. Therefore, the method of reducing the displacement and increasing the rotation speed can improve the power-to-weight ratio. Second, because of the development of the electrical era, hydraulic pumps should also be able to work at high speed to adapt to high-speed motors [2]. Therefore, high-speed, high-pressure, miniaturized hydraulic pumps have become a development trend. Thus, gear pumps are more suited for higher speeds, often as main and fuel pumps for aircraft engines [3]. However, traditional gear pumps have some inevitable problems due to their structural characteristics, such as oil trapping, cavitation, and flow pulsation. These problems restrict the high-speed development of gear pumps. [PERSON], [PERSON] attempted to studymultiple tooth profiles and produced an involute-cycloid composite tooth profile. The gear pump has a relatively large displacement but is still prone to oil trapping [4]. Circular-arc gear pumps are structurally designed to eliminate oil trapping and thus minimize flow pulsations [5]. [PERSON] studied a microsegment tooth profile, which is oil-free and has a relatively high maximum working pressure, and the tooth profile is a circular gear [6]. Therefore, this gear pump has good development prospects. However, it possesses stringent design requirements for its gear pairs, and suboptimal design will still have adverse effects, such as flow pulsation. Hence, studying the mechanism of flow characteristics and designing gear pairs based on this theory are highly important. Many studies have been conducted on circular-arc gear pumps at home and abroad. Rexroth showcased a silent pump at the 2011 Hannover exhibition in Germany, which has low noise and low flow pulsation. The gear pump features a double-arc tooth profile [7]. [PERSON] developed an algorithm for comparing the performance of spur and helical gear pairs, revealing that the helical gear pump produced less noise [8]. [PERSON] designed a circular helical gear that has higher volumetric efficiency and lower noise than spur gears of the same size [9]. [PERSON] revealed the fundamental flow characteristics through theoretical analysis and utilized an algorithm to mitigate flow pulsations [10]. [PERSON] addressed the equation of a rack gear pair and then estimated the approximate displacement of the pump via a specific formula [11]. [PERSON] focused on a gear pair with an involute transition curve to investigate how tooth profile parameters affect performance [12]. [PERSON] et al. [13] proposed a numerical method to calculate the sine curve, and the results show that the circular gear pump with a spur gear still has large flow pulsation. [PERSON] studied the vibration and dynamics of a circular-arc helical gear pump through simulation [14]. [PERSON] derived the axial force formula for the circular-arc helical gear pump and used it to analyze its impact on leakage [15]. [PERSON] used a hydraulic motor as the object and established a prediction model using neural networks, which can be used as a reference for modeling and prediction for other aspects [16]. [PERSON] discussed various simulation methods for the simulation analysis of gear pumps [17]. [PERSON] has developed a visualization method that provides new ideas for the study and analysis of the flow field in gear pumps [18]. Most of the research objects mentioned above are circular-arc gear pumps with involute curves as transition curves, but some studies have shown that gear pumps with sinusoidal curves as transition curves have better performance.