In turbomachinery, direct contacts between bladed disks and surrounding casings occur through a variety of mechanisms that may lead to severe damages. These mechanisms still remain unclear and understanding their origins is a new challenge. On that subject, the present work deals with a new full 3D strategy in order to provide meaningful insights to designers. It involves reduced computational costs and a robust contact methodology able to account for high relative displacements at the contact interface. The first aspect of the problem is addressed through the reduction of the structures using the Craig-Bampton approach. The second one is treated with the use of spline concepts in order to smooth the contact surface and thus, avoid numerical issues. Accordingly, one set of interface nodes belonging to the area where contact is anticipated is defined for each structure. The contact constraints are enforced through a surface spline attached to the interface nodes of the casing. The respective contact forces are calculated using the Lagrange multiplier framework within an explicit time-marching procedure. Accuracy and computational costs are controlled by the size of the reduced-order models. The capabilities of this very versatile strategy encompass a wide range of finite element meshes and interaction problems that may occur in fan, turbine or compressor sections. First results show complex behaviors with coupling between the different modes of the structures and sensitivity to the friction coefficient.