Research On Measurement For Single Noncircular Gear

For the noncircular characteristic of the noncircular gear pitch, each tooth shape of the noncircular gear is different, so the transmission performance of noncircular gears can’t be obtained by simply studying the meshing of a pair of tooth profiles as cylindrical gears. Furthermore, there is not any general theory which can be used to measure and evaluate the accuracy grade of noncircular gears, which restricted their application. Based on the current research of noncircular gears, comparing with evaluation method of cylindrical gears, a universally applicable measurement and evaluation method is presented to measure noncircular gears in this dissertation.A method to obtain noncircular gears’ tooth profile equation is introduced on the basis of the discrete points of noncircular gears’ tooth profile. According to pitch curves of a noncircular gear, the data points of tooth profile can be calculated by use of the medium conjugate method; and the data points and normal directions on tooth profile can be calculated by use of the numerical method. These points can be dealt with the cubic spline and B spline interpolation function, and then by contrasting the spline interpolation function with the theoretical tooth profile, a spline interpolation curve, which closely approximates theoretical tooth profile, can be chosed out, and thus a universally applicable expression of noncircular gears is to be established.Since the measurement of involute cylindrical gears is clear, this dissertation presents feasible measurement indexes related to a single gear, mainly including single-tooth and multi-tooth errors. With different indexes, different measurement programs can be formulated, and then it is easy to analyze the errors and assess the accuracy rating. During the measurement process, all the related mathematical algorithms involved are deduced and detailed algorithm analysis are presented, which provide theoretical foundations for the measurement. The measurement of tooth profile errors of single-tooth and tooth pitch errors of multi-tooth is analysed detailedly. Taking the eccentric gear for example, the effectiveness is verified theoretically. The simulation experiment is conducted with Vericut software, which proves how the pitch and profile errors of gears are influenced by the machining tool.