Basic Theory on Tooth Contact and Dynamic Loads of Gears. 6th Report. Path of Contact of A Gear Pair having Modified Involute Helicoids for One Member under Load.

Abstract

When a gear pair which has tooth surfaces (elastic) modified slightIy and convexly from involute holicoids for one member and the conjugate surfaces (rigid) of the involute hellcolds for the other is given, the path of contact and the inclination angles of the contact normals of the gear pair under load are obtaind as functions of angle of rotation. They are expressed through the deviation of the tangent plane at a point of contact under h)ad from that at the corresponding point of contact under no load. To calculate the deviation of tangent plane in the region of multiple tooth pair mesh, the equivalent tooth load is introduced, which transmits the same torque that the multiple tooth pairs carry at the same time. The diviation of tangent plane under load is a periodical function of angular pitch of the gear pair and is continuos but non-differentiable generally at the point where the number of tooth meshing at the same time changes. The starting and ending points of mesh of a tooth pair and the actual contact ratio which depend on load are also calculated.