关键词: 包络法, 面齿轮, 齿廓, 齿轮根切, 最小二乘法

Abstract:

In order to effectively machine an orthogonal face gear, the geometrical design of tooth profile and the undercut condition for the gear are investigated via the enveloping method. In the investigation, first, a coordinates is established to describe the enveloping process of the gear, and the generation of the gear as well as the tooth-angle equation is studied. Next, the equations describing both the tooth profile and the transitional surface are presented. Then, the geometrical design of the tooth profile is simulated by using Matlab software. Moreover, the undercut of the face gear is analyzed and the corresponding undercut conditions are obtained. According to the calculated datum of undercut and the corresponding statistical results obtained via the least square method, an approximate engineering equation of undercut is deduced. The feasibilities of the theoretical calculation and the proposed approximate equation are finally verified by the practical machining of a face gear.

Key words: enveloping method, face gear, tooth profile, gear undercut, least square method