Analysis of coupled lateral-torsional vibration response of a geared shaft rotor system with and without gyroscopic effect

Abstract

A torsional gear dynamic model and a coupled lateral-torsional geared shaft rotor dynamic model are developed considering the time-varying mesh stiffness, backlash, and static transmission error excitation. The torsional dynamic transmission error responses gained from the torsional gear dynamic model and coupled lateral-torsional geared shaft rotor dynamic model are compared. The natural frequencies and mode shapes of the geared shaft rotor system are given and the frequency whirling behaviors are analyzed based on the Campbell diagram. The influences of gyroscopic effects of rotating shafts and meshing gear rotors on the lateral-torsional vibration responses of the geared shaft rotor system are talked about and some conclusions are drawn. (1) The coupled lateral-torsional geared shaft rotor dynamic model could reflect the jump phenomenon of dynamic responses near the critical speed of the gear pair as well as the pure torsional gear dynamic model and it can give more vibration features caused by geared shaft and bearings than the torsional gear dynamic model. (2) When the gear pair is set in the midpoint of the shaft, the influences of the gyroscopic effects on the gear pair’s lateral vibration responses are light and only can be observed near the high critical speeds. However, when the displacements from the gear body to the bearings are not the same, the influences of the gyroscopic effects on the lateral and torsional vibration responses are obvious and can be located both near the low critical speeds and the high critical speeds corresponding to the forward and backward whirling frequency. (3) The influences of the gyroscopic effects on the lateral and torsional vibration responses of the pinion are more obvious than those on the vibration responses of the gear. In addition, relative to the torsional vibration, the lateral vibration of the gear pair is more easily affected by the gyroscopic effect.

Dynamic behaviour of three-dimensional planetary geared rotor systems

“…Mode shapes in rotor systems can either be uncoupled with no interaction between the lateral, axial and torsional vibration of the system, or coupled where these modes can interact. A simple cyclically symmetric rotor system can be considered as uncoupled [58], but the presence of a gearbox in the system can lead to lateral, torsional and axial mode interaction [42,[45][46][47]49]. To quantify the impact of a planetary gearbox on the coupling behaviour of the global modes of the geared rotor system, a modal energy approach is used where the modal energy of the gearbox for each mode is compared to the total modal energy in the system.…”

“…The coupled dynamic behaviour of geared rotor systems with gyroscopic effects has also been studied in great detail with a focus on the coupling effects of the gearbox due to its torsional, axial and lateral stiffness. Lateral-torsional coupling in spur geared rotors and lateral-torsional-axial coupling in helical geared rotors were shown by many studies [40][41][42][43][44][45][46][47][48][49]. Among these studies, the finite element method has become a popular tool for the dynamic analyses [41,42,44,45,48,49].…”

“…Lateral-torsional coupling in spur geared rotors and lateral-torsional-axial coupling in helical geared rotors were shown by many studies [40][41][42][43][44][45][46][47][48][49]. Among these studies, the finite element method has become a popular tool for the dynamic analyses [41,42,44,45,48,49]. Although the dynamic behaviours of spur and helical geared rotor systems are well understood today, less research has been carried out to understand the dynamic behaviour of planetary geared rotor systems [50][51][52][53][54][55][56][57] .…”

Vibration Response Analysis of a Gear-rotor-bearing System Considering Steady-state Temperature

“…Chen et al [23] analyzed the dynamic response of the herringbone rotor-bearing system. Hu [24] compared the difference of the dynamic response between the torsional gear dynamics model and the gear-rotor-bearing model coupled with lateral torsion and analyzed the effect of the gyroscopic effect on the lateral-torsional vibration of the gear-rotor-bearing system.…”

A New Model for Studying Nonlinear Vibration Behaviors of Gear-Bearing System

“…Tristan E. and Robert P. [19] confirmed the anisotropy of bearing stiffness through experiment results and finite-element/contact mechanics combined method; additionally, the bearing stiffness was found to be load-dependent and could have impact on gear mode. Zehua H., Jinyuan T. and Siyu C. [20] brought the comprehensive bearing stiffness model into a lateral-torsional coupled gear transmission system to study the influence of gyroscopic effect on the vibration behaviors of the system. Recently, Guanghui L., Jun H. and Robert P. [21] investigated the influence of time-varying rolling element bearing stiffness on the system vibration very carefully; strong nonlinear vibration behaviors caused by fluctuation of bearing stiffness over ball pass cycle was observed and theoretical explanation based on perturbation for the system instability caused by the mesh and bearing stiffness excitations was given.…”