Abstract: There are many kinds of characteristic curves that characterize involute helical gears. The most well-known are involute and helix with clear geometrical definition. In fact, there are other characteristic curves with outstanding engineering value such as profile of path of contact and contact line on the tooth surface. However, the addition of characteristic lines brings two problems. One is that the complex equations of the characteristic curves are not related to each other and lack mathematical unity. The other is that except for involute and helix, other characteristic curves have no measuring method, which results in a lack of measurability. According to the characteristics of involute gear transmission, the characteristic curves on the tooth surface are mapped to the meshing plane. It is found that each characteristic curves on the tooth surface has its corresponding 2-D straight line in the meshing plane. Based on this, a straight-line model is established to uniformly express various characteristic curves on the tooth surface. On basis of the 3-D deviation measurement data of the gear and the unified model of the characteristic curves, the extraction method of the deviations of various characteristic curves is proposed, which is applied to the measurement practice. By comparing with the profile deviation and helix deviation measured by the general gear measuring instrument, the effectiveness and practicability of the unified model of the characteristic curves and the extraction method of the deviations of the characteristic curves are proved, and the measurability of the complex characteristic curves on the tooth surface is solved. Meanwhile, the unified model of the gear characteristic curves also has important application value in the traceability of gear process error and the prediction of transmission performance.

Key words: gear, gear characteristic curve, gear deviation, gear measurement, characterization of gear 3D deviation