ABSTRACT
Meshing gears are common parts found in machinery, and they generate vibration which is transmitted to the support structure of the gearbox [1,2]. To suppress this vibration, Sutton et. al. [3] used three magnetostrictive actuators clamped to a support strut of a helicopter gearbox to attenuate the vibration transmitted to the receiving structure. Barrett et. al [4] used piezoelectric actuators incorporating flexible casing effects for the active control of rotating machinery. Variation of gear meshing stiffness is considered to be the most probable source of gear vibration as discussed by Dalpiaz and Meneghetti [5]. They also proposed a simple stiffness function which consists of two half-sinusoids of different amplitudes and duration superimposed on a constant term. In the paper written by Umezawa et. al. [6 ], seven stiffness functions were discussed and it can be seen that healthy gears show a variation of meshing stiffness. In this paper, three specially configured sensors are used to measure the rotational acceleration of a meshing gear, and this is used to determine the required control force to cancel the gear vibration at source. Three actuators positioned on the gear are used to generate secondary forces to suppress the vibration. The equation used to analyse the behaviours of meshing gears is derived from a pair of meshing gears by introducing the relative displacement between meshing teeth [7]. A stiffness variation function is incorporated into the model to simulate the vibration generated by the meshing gears. This appears in the model as a parametric excitation function. In order to cancel the gear vibration, secondary forces are generated by three actuators positioned on the gear. An equivalent secondary force is calculated using a linearised equation for a pair of meshing gears derived from the simple model. It is shown that the secondary force required for the actuators to suppress the gear vibration is related to the meshing stiffness modulation index. This is a key result that determines the actuator requirements for any pair of meshing gears.
