Basic Theory on Tooth Contact and Dynamic Loads of Gears : 5th Report, Path of Contact of A Gear Pair having Modified Involute Helicoids for One Member

Abstract

When a gear pair which has involute helicoids for one member and their conjugate surfaces for the other is given, equations of the path of contact with the contact normals are presented algebraically by using the inclination angle of the path of contact to the plane of rotation on the plane of action as a parameter. In the gear pair, when the involute helicoids are slightly and smoothly modified, equations of the path of contact with the contact normals between the modified ones and the mating conjugate surfaces are expressed analytically by the deviation of the tangent plane from that at the corresponding point of contact without modification, so that they are determined by measuring the single flank error which corresponds to the deviation of the tangent plane and the helix form deviation which indicates the inclination angle of the path of contact. Fundamental requirements for multiple tooth pair mesh in the gear pair with modified involute helicoids are analyzed and clarified, which say that the deviations of the tangent planes and the radii of the base circles at the points of contact in the region of multiple tooth pair mesh must be equal. According to the requirements, the gear pair with the modified involute helicoids has no region of multiple tooth pair mesh under no load.