Shape Optimisation for Friction Dampers with Stress Constraint

Friction dampers are classically used in turbomachinery for bladed disks to control the levels of vibrations at resonance and limit the risk of fatigue failure. It consists of small metal components located under the platforms of the blades, which dissipates the vibratory energy through friction when a relative displacement between the blades and the damper appears. It is well known that the shape of such component has a strong influence on the damping properties and should be designed with a particular attention. With the arrival of additive manufacturing, new dedicated shapes for these dampers can be considered, determined with specific numerical methods as topological optimisation (TO). However, the presence of the contact nonlinearity challenges the use of traditional TO methods to minimise the vibration levels at resonance. In this work, the topology of the damper is parametrized with the Moving Morphable Components (MMC) framework, and optimised based on meta-modelling techniques: here kriging coupled with the Efficient Global Optimisation (EGO) algorithm. The level of vibration at resonance are computed based on the harmonic balanced method augmented with a constraint to aim directly for the resonant solution. It corresponds to the objective function to be minimised. Additionally, a mechanical constraint based on static stress analysis is also considered to propose reliable damper designs. Results demonstrate the efficiency of the method and show that dampers geometries that meet the engineers’ requirements can be identified.