INFLUENCE OF GEAR ECCENTRICITY ON THE CHARACTERISTICS OF NOISE SPECTRUM–FREQUENCY MODULATION AND SIDEBANDS OF MESH FREQUENCY

摘要

The influence of gear eccentricity is normally considered that it is not so important for gear transmissions. However gear eccentricity causes large delay motion, and tooth meshing noise is subjected to two kinds of modulations; frequency modulation and amplitude modulation. That is one of sources of beat noise and sideband noise of mesh frequency. The purpose of this research is to clarify the influence of gear eccentricity on the characteristics of noise spectrum using transmission error analysis. In this paper, relations between frequency modulation and sidebands of mesh frequency are investigated. Large waviness in transmission error due to gear eccentricity is the prime cause of modulation. Large waviness causes a phase variation in time of mesh frequency. Regarding mesh frequency as a carrier, it can be said that the phase variation modulates the carrier frequency. The phase variation is calculated by the approximate formula of transmission error with gear eccentricity obtained by the authors. By assuming that the carrier is purely sinusoidal, the modulated spectrum is calculated theoretically. The obtained spectral components are known as sidebands. Sideband spectrum consists of infinite number of components, whose amplitudes are calculated by Bessel functions of the first kind. Since modulation index is very small in the case of gear eccentricity, it is enough that only Bessel functions of zero, the first plus and minus, and the second plus and minus orders are considered. Although the spectrum is generally symmetric about carrier frequency, it sometimes becomes asymmetric according to the gear ratio.