Basic Theory on Tooth Contact and Dynamic Loads of Gears. 1st Report. New Tooth Geometry.

Abstract

In the present tooth geometries, rotational motion of a gear pair with variation of angular velocities caused by errors and deflection cannot be analyzed because the ratio of angular velocities is always given as a premise. In the present models of dynamic load, rotational motion of a gear pair is not sufficiently approximated because the fundamental requirement for contact is neglected ; thus the calculated results are not reliable. To solve these problems, a new theory on tooth contact and dynamic loads is presented in this series of papers. This first paper introduces a new tooth geometry that can deal with rotational motion of gears with errors and deflection. Namely, the two axes and their common perpendicular determine the static coordinate systems in which a point of contact and its common contact normal are arbitrarily given and described as functions of angle of rotation by using the instantaneous planes of action that include the common contact normal and are parallel to each axis, and the ratio of angular velocities at each point of contact is obtained from the fundamental requirement for contact. When the points of contact and their common contact normals are transformed to the coordinate systems rotating with each gear at the obtained ratio of angular velocities which varies with the rotation of gears, a pair of tooth profiles is obtained.