ANALYSIS OF THE VIBRATORY EXCITATION OF GEAR SYSTEMS .2. TOOTH ERROR REPRESENTATIONS, APPROXIMATIONS, AND APPLICATION

The second part of a theory is presented for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces. The first part of the theory [J. Acoust. Soc. Am. 63, 1409–1430 (1978)] provides expressions for the Fourier-series coefficients of the vibratory excitation, which was shown to be described by the static transmission errors of all pairs of meshing gears in a system. The present paper provides expressions for these Fourier-series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth-face measurements. Detailed results are given for rectangular tooth-face contact regions using two-dimensional Legendre polynomial expansions of local tooth-pair stiffnesses and stiffness-weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters, thereby permitting independent assessment of the effects of gear design parameters on the vibratory excitation. The theory is applicable to both helical and spur gears and is illustrated using measurements of tooth-spacing errors and tooth profiles obtained from a pair of spur gears. © 1979 Acoustical Society of America