The Mathematical Model of Spiral Bevel Gears - A Review

The spiral bevel gear (SBG), with its high contact ratio, high strength and smooth driving, is widely used to transmit dynamic power in various mechanical products, including vehicles, mining machinery, aerospace engineering, and helicopters [1] to [4]. Typical SBGs are shown in Figs. 1a and b. The SBG has been a subject of research for almost a century, and there is a significant amount of literature on the mathematical model of SBGs. The tooth surface of an SBG is a complicated curved surface with a kinematic performance directly bonded to the special cutting process [5]. The mathematical model has significantly contributed to the Computer-Aided Design and Manufacturing (CAD/CAM) of SBGs, because the mathematical model of SBG can be constructed to determine the processing method [6] and [7], to calculate machine-tool settings [8] to [11], to optimize tooth surface topography [12] to [15], to build models of Finite Element Analysis (FEA) [16] to [18], Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) [19] to [21], and to develop new SBG types, as shown in Fig. 2. Therefore, the study of the mathematical model construction significantly influences the technological development of the SBG. The most popular method of manufacturing SBGs is that used by Gleason, Oerlikon, and Klingeinberg. The basic structural forms of special machines include the traditional cradle-type hypoid and computer numerical control (CNC) hypoid generators. The typical feature and manufacturing principle of these special machines are to cut the workpiece using a rotating cutter head. To analyse the process of manufacturing SBGs, the mathematical model of the tooth surface can be considered to be a spatial trajectory of the cutter blade [22].