Abstract
As a type of spatial transmission mechanism, noncircular bevel gears (NBGs) can transfer power and motion between two intersecting axes with variable transmission following a suitable program of motion. Utilizing the spherical triangle theorem and meshing principle, parametric equations are established in the spherical polar coordinate system for the driving and driven gears, for the pitch curves, and for the addendum and dedendum curves of a NBG for a given transmission ratio and axis angle. A formulation of the tooth profile of a NBG is deduced using an analytic method. Three-dimensional models of the 3- and 4-lobed NBGs are derived in verifying this method.
Highlights
With noncircular bevel gears (NBGs), power and motion can be transferred between two intersecting axes with a variable transmission executed by a suitable program of motion
The point N2 is the trail of the tooth profile, which is below the pitch curve
The following summarizes the results obtained: (1) The equations that determine the pitch curve of the NBGs were obtained for any order and in any configuration during their pure rolling motion for a given transmission ratio and axis
Summary
With noncircular bevel gears (NBGs), power and motion can be transferred between two intersecting axes with a variable transmission executed by a suitable program of motion. Many scholars have studied the tooth shape, pitch curve, and machining method of NBGs. Because of its variable transmission ratio, Wang and collaborators[4,5] applied noncircular gears to a limited-slip differential and were granted patents for the device. The varying-coefficient-profile-shift-modification method is used to avoid undercutting, ensuring the root part of the tooth face does not participate during meshing They further presented a design method for NBGs having a concave pitch curve described in the spherical polar coordinate system[17] and proposed a method to determine whether a gear is continuously driven based on the coincidence degree defined by the engagement angle[18]. The tooth profiles can be derived from the Willis theorem.[19] The concave pitch curve of NGBs can be processed by the bevel gear milling cutter, so the deduced tooth profile equation is universal. The point N2 is the trail of the tooth profile, which is below the pitch curve
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