The geometric features of elliptical arc tooth line cylindrical gears are shown in Figure 1. The tooth surface is divided into convex and concave tooth surfaces. The middle section of the gear tooth is an involute tooth profile, and any tooth profile parallel to the middle section is an involute. Taking the middle section as a reference, the other sections only rotate by one position angle relative to it, as shown in Figure 2 (a).
The tooth line of a cylindrical gear with an elliptical arc is a part of the elliptical arc and is symmetrical about the middle section. It should be noted that its special elliptical arc tooth line form is caused by its machining method. Figure 2 (b) shows the unfolded view of the elliptical arc tooth line cylindrical surface on the indexing cylindrical surface. Among them, the major axis of the elliptical arc tooth line is 2a, the minor axis is 2b, and b=a cos α，α It refers to the reference circle pressure angle of elliptical spiral bevel cylindrical gear. On the unfolded surface of the indexing cylinder, the end tooth thickness St and the end tooth groove width Pt of the elliptical arc tooth line cylindrical gear are equal; The tooth thickness Sc and tooth groove width Pc at any section of an elliptical arc tooth line cylindrical gear parallel to the end section are equal. Along the direction of the tooth line, the tooth thickness and groove width at any cross-section are equal, and are half of the tooth pitch P, i.e. Pt=Pc=Sc=St=P/2; At the same time, the pressure angle of the tooth profile at each radial section is equal to that at the degree circle.
This type of elliptical arc tooth cylindrical gear has an ideal arc tooth shape and has meshing characteristics of full tooth width line contact. During the transmission process of elliptical arc tooth line cylindrical gears, changes in the machining cutter radius, tooth width, and number of revolutions may cause changes in their speed fluctuation coefficient, thereby affecting the transmission stability of elliptical arc tooth line cylindrical gears.