Detection of asymmetric transmission error in geared rotor system through transverse vibration analysis using full spectrum

Abstract

Transmission error (TE) in geared rotors is a predominant source of inherent excitation at the pitch point of the gear meshing. In this paper, a transverse vibration analysis is presented to study the effect of TE on geared rotors. Due to asymmetry in the TE, it is expected to have both forward and backward whirls excited during rotor whirling, which could be used for its detection. This aspect has been envisioned first time in the present work. To capture this, an approach of orienting the line of action of a gear-pair along oblique plane is considered and the mathematical modeling has been performed of a simple spur gear-pair connecting two parallel shafts at its mid-span with an asymmetric TE. To capture the forward and backward whirls, equations of motion are converted into a complex form that facilitates obtaining response in full spectrum. The response of system model with assumed transmission error and gear-pair parameters has been obtained through a numerical simulation, which shows distinctly the forward and backward whirls due to the TE. Through a simple test rig experimentation, a similar behaviour was observed in transverse vibrations of geared rotors in the full spectrum, which validate the proposed model.