COMPUTERIZED ANALYSIS OF MESHING AND CONTACT OF GEAR REAL TOOTH SURFACES

The authors propose a technique for computerized simulation and tangen cy of gears provided with real tooth surfaces. The deviations of real tooth surfaces from the theoretical ones are caused by the distortion of surfaces during the heat treatment and lapping. The main ideas of t he proposed technique are as follows: (i) The gear real tooth surface is represented by a sum of two vector functions that determine the the oretical tooth surface and the deviations of the real surface from the theoretical one, respectively. (ii) Both vector functions mentioned a bove are represented in terms of the same Gaussian surface coordinates (the Gaussian coordinates of the theoretical surface). (iii) The devi ations of the real surface are initially determined numerically using the data of surface coordinate measurements. The analytical representa tion of the vector function of deviations is based on the interpolatio n of a numerically given vector function by a bi-cubic spline. The int erpolation provides a relatively high precision because it is accompli shed for the surface of small deviations but not for the whole real su rface. (iv) The computerized simulation of meshing and tangency of gea rs with real tooth surfaces is based on the algorithm that describes t he conditions of continuous tangency of real tooth surfaces. The propo sed approach is illustrated with application to the hypoid gear drive with real tooth surfaces. The data of surface deviations have been det ermined experimentally at the Nissan Motor Co.