A Reduction Technique for the Calculation of the Forced Response of Bladed Disks in Presence of Contact Mistuning At Blade Root Joints

The effect of differences in nominally equal sectors of a bladed disk (mistuning) is a well-known problem for designers since the forced response may show localized amplification of the blade response with respect to a cyclically symmetric (tuned) configuration. In order to perform a large number of simulations in a reasonable amount of time to characterize the highest blade response, corresponding to the worst mistuning pattern, reduction techniques have been developed where mistuning is introduced directly in Reduced Order Models (ROM) obtained from very large finite element (FE) models. Typically, mistuning is introduced in the ROM in terms of natural frequency perturbations of the blade; nevertheless, a better insight is required to correlate mistuning to a specific source (geometrical, material, contact mistuning). In this paper, a reduction technique is presented to take into account mistuning due to the contact uncertainties at the blade root joint, which can be caused by design tolerances, manufacturing process, assembly procedures, wear. The technique takes its basis from the Craig-Bampton Component Mode Synthesis applied to the uncoupled blade and disk sector, which is typically included in most of the FE software for an easy implementation in standard industrial practice. The set of master degrees of freedom at the random contacts are purposely reduced using an optimal local modal basis based on the Gram-Schmidt Interface technique developed by the authors. Experimental evidence of actual uncertain contacts obtained during joint pre-loading is used to find an appropriate base to represent typical contact patterns.