Identification of Dominant Source of Vibration in Geared Rotors Using Full-Spectrum Analysis

Torque transfer through gears causes vibration and often leads to irritating tonal noise called gear whine due to micron-level deviations from conjugate gear profile. These profile deviations due to manufacturing as well as tweaked deviations to minimize gear edge contact are quantified in terms of static transmission error (STE). A vast literature is available on STE as the source of vibration and noise at the gear mesh frequency. Another dynamic effect in a loaded geared rotor due to shaft deflection, gear mesh stiffness, gear run-out errors and gear mesh misalignments along the line of action along with STE constitutes the dynamic transmission error (DTE). In this work, a novel gear vibration system model for the low-torque transmission applications with the asymmetric STE assumed in orthogonal transverse directions at the pitch point is presented for identifying dominant source of vibration in geared rotors. In order to avoid nonlinearities due to transverse and torsional vibration couple, the shaft is assumed to be rigid in torsion under low torque. To further reduce complexities in solving resulting EoM, rotor shafts are mounted on rigid supports and gear mesh misalignments have been ignored. The equations of motion are derived with Lagrange dynamics. System model response is calculated by solving EoM in time domain using the RK method. The resulting time domain response is converted into frequency domain using the full spectrum to analyse it. The full-spectrum response splits the response spectrum into backward and forward whirl amplitudes of dominant dynamic effects within the system. With full-spectrum and orbit plots, the gear mesh vibration is analysed by generating response with different shaft speeds and by varying the key gear mesh parameters by loading gear pair with nominal torque to identify the dominant source.