Optimization-Based Quantification of Residual Traction Uncertainty in Friction-Damped Turbine Blades

Abstract This study advances the prediction of vibration response variability arising from the nonuniqueness of static friction forces (residual traction uncertainty) in turbine blades coupled by frictional interfaces. Utilizing a nonlinear mode-based method, uncertainty is first quantified on amplitude-dependent modal parameters and then forward propagated to the vibration response to obtain frequency response bounds via interval analysis. For the first time, the uncertainty quantification is systematically demonstrated on a state-of-the-art model with a newly developed optimization-based framework. To address the computational demands of the optimization problem, two variants are proposed: (1) performing three optimizations that are independent from the forcing pattern and response location, or (2) conducting six optimizations that enable a full characterization but are valid only for a specific forcing pattern and response location. The former yields a slightly more conservative upper bound of frequency responses, but is limited to the backbone curve computation, significantly reducing the overall computational effort. The effectiveness of the proposed approach is demonstrated using a high-fidelity model of turbine blades coupled by an asymmetric underplatform damper. During the uncertainty quantification phase, the bounds of amplitude-dependent modal parameters, systematically determined through optimization, are validated by comparison with results from multiple Harmonic Balance simulations using manually assigned residual tractions. In the uncertainty propagation phase, the frequency response bounds are shown to successfully capture the full range of vibration response variability, up to the onset of 1:1 internal resonance between the first two modes at higher amplitudes.