Blade Root Joint Modelling and Analysis of Effects of Their Geometry Variability on the Nonlinear Forced Response of Tuned and Mistuned Bladed Disks

One of the major sources of the damping of the forced vibration for bladed disk structures is the micro-slip motion at the contact interfaces of blade-disk joints. In this paper, the modelling strategies of nonlinear contact interactions at blade roots are examined using high-fidelity modelling of bladed disk assemblies and the nonlinear contact interactions at blade-disk contact patches. The analysis is performed in the frequency domain using multiharmonic harmonic balance method and analytically formulated node-to-node contact elements modelling frictional and gap nonlinear interactions.

The effect of the number, location and distribution of nonlinear contact elements are analyzed using cyclically symmetric bladed disks. The possibility of using the number of the contact elements noticeably smaller than the total number of nodes in the finite element mesh created at the contact interface for the high-fidelity bladed disk model is demonstrated.

For the analysis of mistuned bladed disks, the number of nonlinear elements is large due to the necessity of modelling of the contact interfaces for each blade individually.  In practical calculations, this number is restricted by high computational expense and computational time. The optimal modelling strategy is proposed for the analysis of the nonlinear forced response of mistuned bladed disks.

The geometric shapes of blade roots and corresponding slots in disks cannot be manufactured perfectly and there is inevitable root joint geometry variability within the manufacture tolerances. Based on these tolerances, the extreme cases of the geometry variation are defined and the assessment of the possible effects of the root geometry variation on the nonlinear forced response are performed based on a set of these extreme cases.