Passive control of vibration of thin-walled gears: advanced modelling of ring dampers

Vibrations on gears are mainly induced by the gear mesh contact. Resonance conditions of the gear may occur during service if the mesh frequency is close to the natural frequencies of the system at the designed speed of the shaft. Since detuning is not always possible in gears, the response level must be reduced by increasing the damping of the system. In this paper, a passive approach based on the application of a ring damper to reduce the vibration level is presented. The ring damper is placed in a groove underneath the outer rim of the gear. The contact is guaranteed by the preload due to the elasticity of the ring damper itself and above all by the centrifugal force that presses the damper against the groove during rotation. The relative motion of the two components at the contact interface dissipates energy by friction, and hence damping is generated. The vibration amplitude is reduced by optimizing the material and geometrical properties of the ring damper. One of the most important parameters in the determination of the amount of damping due to friction phenomena is the static normal load at the contact, which depends on the mass, the shape, and the material of the ring damper. A numerical method is presented, which couples the static and dynamic equilibrium equations of the assembly. The core of the proposed method is the contact element that takes into account local stick-slip-lift off of the contact and determines the contact forces in terms of static and dynamic loads, which are then used to solve the coupled static and dynamic equilibrium. Since the ring damper has a cut that breaks its continuous circular shape in order to be fitted on the groove, the hypothesis of cyclic symmetry for the gear/ring-damper assembly fails. As a consequence, an appropriate reduced-order modeling is presented to allow the forced response calculations. The algorithm is applied to a dummy bevel gear and to a ring damper having a flat punch contact area. The forced response calculations are performed to highlight the nonlinear interaction between the gear and damper by varying the parameters that mainly affect the amount and distribution of the contact forces and therefore the response level.