Determination of periodic response limits among multiple solutions for mechanical systems with wedge dampers

Wedge dampers are commonly used to utilize the frictional behavior in many engineering fields such as vehicle dynamics and turbo-machinery. However, the presence of non- unique contact forces in the damper interfaces creates an uncertainty that provides different dynamic response amplitudes even for the same input parameters. The maximum limits of the variability range always take the core attention in most of the damper design processes. In this paper, determination of an upper and a lower boundary among multiple steady-state solutions is presented by using a numerical approach. The method is specifically suitable for the mechanical systems with wedge dampers modeled by macro-slip frictional contact elements in the joint interfaces. In the approach proposed, a criterion that determines the periodic response boundaries according to the limit tangential force values is utilized. The method is demonstrated by illustrating several case studies on a lumped parameter system which represents a turbo-machinery application with a symmetric wedge damper pressed against two vibrating adjacent blades. A point-to-point 1D friction model with varying normal force is used in both contact sides. A parametric investigation on the variability range and response limits is performed for different damper configurations. Harmonic Balance Method with Newton’s iteration scheme is used in the numerical solution of the governing equations. The results show that a large variability exists for damper geometries where a strong coupling is present between tangential and normal contact forces. The method proposed successfully captures the limits of the variability range in all cases.