Cylindrical gear transmission is one of the most widely used transmission methods in gear mechanism. At present, it has three forms: straight cylindrical gear, helical cylindrical gear and herringbone cylindrical gear. Because of the structural reasons, the cylindrical gear has some disadvantages. In this paper, a new type of cylindrical gear arc tooth cylindrical gear is proposed. Its main feature is that the teeth on the cylinder are arc-shaped. The tooth profile of arc tooth cylindrical gear is the same as that of ordinary cylindrical gear, which can be either involute or arc curve. The arc tooth cylindrical gear has the advantages of good meshing performance, large overlapping coefficient, mutual offset of axial force, high transmission efficiency, large bending strength and good contact strength of tooth surface. Arc tooth cylindrical gear has superior transmission characteristics, which can replace straight tooth, helical tooth and herringbone tooth cylindrical gear in most application environments. At the same time, it has the characteristics of stable transmission, low transmission noise, high efficiency, long service life, low use and installation requirements, and has a broad application prospect. However, because the structure parameters and transmission characteristics of spiral bevel gears are not clear, the application of spiral bevel gears is restricted.
In the aspect of gear meshing mechanism, many scholars have carried out extensive research on it and put forward a complete set of gear meshing theory. In this paper, the meshing mechanism of theis analyzed by the differential geometry theory, and the meshing characteristics of the spiral are revealed, including the tooth surface equation, conjugate tooth surface, tooth surface meshing line, tooth surface contact line of gear pair transmission, etc.
The involute arc tooth cylindrical gear has excellent transmission characteristics, but it has not been applied at present. One of the reasons is that the structural parameters of the involute arc tooth cylindrical gear are not clear.
The main characteristics of the arc tooth cylindrical gear proposed in this paper are as follows: the tooth line is a part of the arc, the tooth profile is involute, the circumferential tooth thickness of the tooth is equal, and its shape is shown in Figure 1. In Figure 2, the most important difference between the geometric parameters of the spiral gear and the straight gear is that there is more arc radius value RT of the tooth line, which must be greater than half of the thickness of the gear, or it can be considered that the arc radius value RT →∞ of the straight gear. The circumferential tooth thickness at each point of the pitch circle section of the arc gear tooth is the same, that is, St = SC, and the circumferential groove width is the same, that is, Pt = PC.