A reduced order model for nonlinear dynamics of mistuned bladed disks with shroud friction contacts

A new reduced order modeling technique for nonlinear vibration analysis of mistuned bladed disks with shrouds is presented. It has been shown in the literature that the loss of cyclic symmetry properties which is known as mistuning could considerably increase the response level, localize the vibration around few number of blades and finally bring high cyclic fatigue. The developed reduction technique employs two component mode synthesis methods, namely, the Craig-Bampton (CB) method followed by a modal synthesis based on loaded interface modeshapes (Benfield and Hruda). In the new formulation the fundamental sector is divided into blade and disk components. The CB method is applied to the blade, where nodes lying on shroud contact surfaces and blade-disk interfaces are retained as master nodes, while modal reductions is performed on the disk sector with loaded interfaces. The use of loaded interface component modes allows removing the blade-disk interface nodes from the set of master nodes retained in the reduced model. The result is a much more reduced order model with no need to apply any secondary reduction. In the paper it is shown that the reduced order model of the mistuned bladed disk can be obtained with only single-sector calculation, so that the full finite element model of the entire bladed disk is not necessary. Furthermore, with the described approach it is possible to introduce the blade frequency mistuning directly into the reduced model. In this way, reduction is performed only once in case of multiple analyses, necessary for statistical characterization of the nonlinear response of the system. The nonlinear forced response is computed using the harmonic balance method (HBM) and alternating frequency/time domain (AFT) approach. Friction contacts are introduced into the FE model using a 3D contact element. Numerical simulations revealed the accuracy, efficiency and reliability of the new developed technique for nonlinear vibration analysis of mistuned bladed disks with shroud friction contacts.