Basic Theory on Tooth Contact and Dynamic Loads of Gears. A Path of Contact of a Gear Pair Having Modified Involute Helicoids for One Member.

Abstract

When a gear pair which has tooth surfaces (elastic) modified slightly and convexly from involute helicoids for one member and the conjugate surfaces (rigid) of the involute helicoids for the other is given, the path of contact with its contact normals of the gear pair is obtained as algebraic functions of angle of rotation expressed by two parameters, the deviation of the tangent plane from that at the corresponding point of contact without modification and the inclination angle of the path of contact on the plane of action, which are determined by measuring the single flank error and the helix form deviation. Fundamental requirements for multiple tooth pair contact of the gear pair are clarified and the path of contact with its contact normals under load are calculated, which is expressed through the deviation of the tangent plane at a point of contact under load from that at the corresponding point of contact without modification under no load. The path of contact under load is discontinuous generally at the point where the region of mesh changes. The actual contact ratio of the gear pair which depend on load is also calculated along the path of contact.