# Geometric Design of a Face Gear Drive with Low Sliding Ratio
## 1 Introduction  
Face gear drive is a meshing transmission mechanism composed of cylindrical gear and bevel gear. Compared with the traditional spiral bevel gear transmission, it has the advantages of smaller volume, lighter weight, higher load-bearing capacity, better component force, which can meet the development requirements of future aviation equipment [1]. At present, the face gear drive has been successfully applied to the military [2, 3] and civil industries [4], and the application scope and occasions will be broader. However, during the meshing process, there is relatively larger sliding friction between tooth surfaces, which will affect the operational life [5, 6]. Therefore, it is necessary to develop a face gear drive with a low sliding ratio. In view of the advantages of face gear transmission, many new face gear drives have been continuously reported. [PERSON] et al. [7] studied a design and analysis method for face gear drive with an involutte helical involutte pinion. Combining the characteristics of the worm drive, a larger gear ratio face gear drive was developed, which is composed of conical or cylindrical worms [8]. They also investigated a new geometry different from the existing one by application of asymmetric proles and double-crowned pinion of the drive [9]. This face gear drive can reduce the stresses and transmission errors. [PERSON] et al. [10] presented a geometric design method for face gear with helix angle, shaft angle, and axle offset. [PERSON] et al. [11, 12] implemented the meshing theory of curve-face gear pair, which can achieve compound motion with much compact structure, better transmission efficiency, and load-bearing capacity than gear-linkage mechanism. For improving the performance and reducing the weight of noncircular gear transmission systems, [PERSON] et al. [13] provided a novel spatial noncircular gear set comprising a cylinder gear and an eccentric face gear. [PERSON] et al. [14] put forward a curved tooth surface gear, which has the characteristics of relatively simple technology, compact structure, low cost, high coincidence, stabletransmission, and high load-bearing capacity than those of the general face gear drive. In addition, [PERSON] [15] introduced a novel face gear drive with a conical involute pinion. [PERSON] and [PERSON] [16] disclosed the tooth geometry of face gear drive with offset axes. Thus far, the tooth profile design of the face gear drive with a low sliding ratio is rare, whereas the design of the cylindrical gear drive has been previously considered. [PERSON] and [PERSON] [17] reported a parametric tooth profile of spur gear drive with a low sliding ratio. [PERSON] [18] advanced an asymmetric gear drive, which has a low sliding ratio. [PERSON] et al. [19] improved the cycloid gear drive, and the sliding ratio is lower than that of involute gear. By controlling the relative curvature of the conjugate tooth profiles, [PERSON] et al. [20] presented a design method for plane meshing tooth profiles, which can also be used as the design of gear drive with a low sliding ratio. [PERSON] et al. [21] presented a pure rolling cylindrical helical gear drive with variable helix angles. [PERSON] et al. [22] implemented the deviation function (DF) method for the design of the conjugated tooth profiles, which can be used for designing the low sliding ratio gear drive. It is a more effective method to realize the design of a low-sliding plane meshing tooth profile by editing the meshing path, for example, the path combined with a straight line and a curve [23], and a specific arc path [24]. Additionally, [PERSON] et al. [25; 26] completed the design of the low sliding ratio tooth profile, which is based on the approximate range of the given sliding ratio. As the sliding ratio is related to the operational life of the system, a low sliding ratio of the cylindrical gear drive has been developed. However, the sliding ratio has rarely been used as the design purpose to develop a novel face gear drive.