Visualization of phase differences between tooth helix deviations using graph theory

The purpose of this study is to create eye-friendly network images representing manufacturing error of gears which cause vibration and noise during operation. Especially, this paper proposes a visualization method of phase differences between tooth helix deviations. Firstly, the tooth helix deviations of a gear were measured. Then, the DC components in the measured deviation data were eliminated, and a Gaussian filter with a suitable wavelength diminished the roughness components in the measured deviation data for extracting shape deviation components. Furthermore, correlation coefficients were derived by calculating the inner product between the deviation data of all teeth for acquisition of the phase differences. Then, a network image of the phase differences between the tooth helix deviations was generated by regarding each tooth and correlation coefficient as a vertex and edge based on the graph theory. The helix deviation network image of a ground helical gear, whose tooth number was 15, was shown in this paper. The created network image showed that the manufactured gear had three classes related to the phase. Eight consecutive teeth constituted one of the three classes and five consecutive teeth on the opposite side were belonging to the other class. The two classes had negative correlation, and the third class existed between the first two classes. This means that the measured gear had a possibility of out-of-plane vibration. The method we have developed will allow for the simple evaluation of gears.