The authors propose a technique for computerized simulation and tangency 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 the proposed technique are as follows: (i) The gear real tooth surface is represented by a sum of two vector functions that determine the theoretical tooth surface and the deviations of the real surface from the theoretical one, respectively. (ii) Both vector functions mentioned above are represented in terms of the same Gaussian surface coordinates (the Gaussian coordinates of the theoretical surface). (iii) The deviations of the real surface are initially determined numerically using the data of surface coordinate measurements. The analytical representation of the vector function of deviations is based on the interpolation of a numerically given vector function by a bi-cubic spline. The interpolation provides a relatively high precision because it is accomplished for the surface of small deviations but not for the whole real surface. (iv) The computerized simulation of meshing and tangency of gears with real tooth surfaces is based on the algorithm that describes the conditions of continuous tangency of real tooth surfaces. The proposed approach is illustrated with application to the hypoid gear drive with real tooth surfaces. The data of surface deviations have been determined experimentally at the Nissan Motor Co.

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

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In the AGMA standard for the scoring resistance evaluation of gears, flash temperature is used as an index indicating the risk of scoring. The flash temperature is expressed as the sum of flash rise of temperature and initial temperature. In this research, the initial temperatures are measured for various gear sets in running by thermocouples which are mounted just beneath the working surface of pinion. The effects of gear dimensions, rotating speed, and lubrication conditions on the initial temperature are clarified. An experimental formula is proposed for estimating the initial temperature, which depends on the temperature of oil inlet, the frictional power loss, and the running conditions such as rotating speed, contact position, and the oil supply rate. The estimated initial temperatures are in good agreement with the measured values. The proposed method is available for the scoring resistance evaluation of the vehicle transmissions.

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