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

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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.