A New Method of Constructing Tooth Surface for Logarithmic Spiral Bevel Gear

Abstract

For a new type of bevel gear—logarithmic spiral bevel gear, establish its tooth direction curves and the mathematical model of tooth surface equation. With CAD software platform which can intuitive understanding of complex curves and combined with conical logarithmic spiral parameter equation build the logarithmic spiral on cone surface. Then array logarithmic spiral to make them evenly distributed in the cone surface, without any interference and to meet the strength distribution on both ends of circular truncated cone equally. Use two logarithmic spirals from different starpoint as tooth direction curves of lift and right tooth surface. Finally, use space geometric knowledge to build tooth surface equation by tooth direction curves and tooth profile curves.

Dynamic Contact Emulate Analysis of Logarithmic Spiral Bevel Gear with ANSYS/LS-DYNA

“…The size of tooth profile face for gear small end and big end isn't equal, that is, the angle between left and right involutes of tooth profile face for gear small end and big isn't equal. In the determination process of location for left and right involutes, according to the size of tooth thickness and cogging width for the standard gear pitch circle is equal, the angle value of share of tooth thickness is equal to the angle value of share of cogging [2]. 360 。 /2Z can calculate the angle value between two conical logarithmic spirals, which on left and right tooth surface of tooth.…”

A New Method of Constructing Tooth Surface for Logarithmic Spiral Bevel Gear

“…The vector equation of conical logarithmic spiral is equation (1), m = sinαcotβ , c b = e , α -half cone angle, β -helix angle, c -integral constant, φ -conical logarithmic spiral turn angle. Among α , β and b are constants, only φ is a parametric variable.…”

“…Helix angle on each point of conical log-spiral line is constant , and the conical logarithmic spiral line itself meets the uniform distribution from the small end to big end of the cone, so at the pitch cone cogging and tooth thickness are equal itself meets the non-backlash meshing. Each contact points of a pair meshing logarithmic spiral bevel gear is stressed steadily and is in the same size, while tooth surface of logarithmic spiral bevel gear is the surface formed by the motion that a involute is along the conical logarithmic spiral line [1].…”