Predicting the variability of the dynamics of bolted joints using polynomial chaos expansion

Friction and contact occurring in bolted joints can lead to highly nonlinear dynamics. Moreover, joints are prone to high sample-to-sample variability as well as low test-to-test repeatability. Notably, experimental work is increasingly highlighting the most influential sources of uncertainties. Nevertheless, randomness due to some uncertainties, such as surface imperfections, cannot be completely eliminated. Others, such as the actual applied bolt load, can be laborious to control. In this work, we aim to computationally predict the variability of numerical models of joints given such uncertainties. We perform the dynamic analysis using the Multi-Harmonic Balance Method (MHBM) to compute the forced, periodic response of the system. For probabilistic surrogate modeling, we use Polynomial Chaos Expansion (PCE). We show that PCE can be successful in studying the impact of ISO tolerances and uncertain bolt loads in the practical case where only a few numerical samples can be generated. We also show that an empirical error metric is unreliable and a validation error metric must be used. In addition, we assess using PCE to propagate uncertainties due to mesoscale imperfections, and highlight that unsuccessful PCE models indicate sensitive structural designs.