Teeth geometry and contact pressure calculation of external cycloidal gears

Abstract

Cycloidal (also called epicyclical or convex-concave) gears are used less often than common involute gears, which are very easy to manufacture and can be modified by corrections to the gear profile. Cycloidal gears are very sensitive to the proper axial distance between the pinion and the gear. The main advantage of convex-concave gears is the lowering of the contact pressure due to teeth flanks meshing and also the lowering of the slide ratios compared to involute gears. The calculation of the selected geometrical parameters and the contact pressure between the teeth flanks of the cycloidal gearing is described in the presented article.

Comparison of Selected Parameters of a Planetary Gearbox with Involute and Convex–Concave Teeth Flank Profiles

“…The determination of the geometric parameters of the gears' teeth flanks is based on the equations evaluated using the shape of the path of contact. The general path of contact starting at point A and ending at the point E of this type of gearing is presented in Figure 1 [45].…”

“…The determination of the geometric parameters of the gears' teeth flanks is based on the equations evaluated using the shape of the path of contact. The general path of contact starting at point A and ending at the point E of this type of gearing is presented in Figure 1 [45]. The arcs of the path of contact are circular arcs defined by their radii rAC for the part of the contact path defined using the arc AC and rCE for the part of the contact path defined by the arc CE.…”

“…The x and y coordinates of the teeth flank curves are defined in the coordination systems with the origin at the points O 1 or O 2 for each coordinate system, respectively. The division of the contact path into parts divided into circular arcs AC and CE requires the division of all geometric and other gear pair parameters to analogous parts, which is defined according to the corresponding parts of the contact path curve [45].…”

“…The Hertzian contact pressures at the tooth flanks of the pinion-gear contact point were calculated according the equation [45]:…”