**1. Introduction**

High cycle fatigue failure is a primary concern among operators and suppliers of turbo engines because of their suddenness [1].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

They are caused by the large response levels at resonance. Since turbine blades do not benefit significantly from material hysteresis and aerodynamic damping, the only option is to add external sources of damping, for example, in the form of dry friction devices [2, 3] such as the underplatform damper. Underplatform dampers, available in several shapes (cylindrical, curved-flat and wedge-like), are small metallic objects placed on the underside of two adjacent blades. As shown in **Figure 1a**, the centrifugal force (CF) provides the necessary precompression and the resonant-induced blade vibration triggers the damper-platform relative motion and therefore friction dissipation. Dampers are extensively used in turbine designs because they are easy to manufacture, install and substitute, while relatively inexpensive.

**1.1. A quick critical review of contact modeling in the turbomachinery field**

(kn, k<sup>t</sup>

In the technical literature, the problem of modeling periodical contact forces at friction contacts is still ongoing [5] and has been addressed by several authors, leading to different contact models and techniques. Some authors adopt a Dynamic Lagrangian method to solve on the contact patch [6, 7], that is, the contact constraints are taken into account in their non-regularized form without additional compliance. Other authors, for example, [4, 8] apply a contact element to each meshed node belonging to the contact area, introducing normal and tangential stiffnesses and a Coulomb friction law. This last method is preferred here, as its calibration parameters

Modeling Friction for Turbomachinery Applications: Tuning Techniques and Adequacy…

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 and μ), however difficult to determine, represent a physical measurable property.<sup>1</sup> The contact elements typically used in turbomachinery belong to the "spring-slider" family, a class of displacement-dependent contact models which neglect features like viscous forces along the normal direction and friction's velocity-dependence. These features, while relevant in other fields, are not typically considered in turbomachinery applications. These models belong to the larger family of heuristic models, as opposed to microscale "realistic" models where asperities and surface roughness are modeled using stochastic distributions [9].

These interactions can be geometrically divided in the normal and the tangential directions. A unilateral contact law is often considered in the normal direction (with or without normal contact stiffness) and frictional law for the tangential contact. The spring-slider elements have undergone an evolution, starting from 1D tangential motion without normal compliance [2] up to a fully coupled 3D motion [10], passing through a 1D element with normal compliance (2D motion) [11]. This last element has been adopted by many authors because of its simplicity and versatility. In fact, it can be applied to represent 1D in-plane relative motion (a quite common occurrence if the first bending modes of the blades are considered), or, with a simple

Modeling conforming (i.e. flat-on-flat) or nonconforming (e.g. cylinder-on-flat) surfaces requires a different strategy. Nevertheless, the same standard macroslip contact element pre-

Conforming contact surfaces are typically discretized into contact points (or nodes in FE terms) and each one is assigned a standard macroslip element, either with uncoupled 2D inplane motion [8, 13, 14] or with a coupled one [15]. This choice allows to account for the presence of "microslip", first theorized by Cattaneo in 1938 [16], and later explored by Mindlin [17]. Modeling microslip is particularly relevant in those cases where high normal loads prevent actual slipping of the complete interface: in that case the gradual loss of stiffness that forecomes gross slip and the consequent dissipation does have an impact on the system

Nonconforming contacts are, in most cases, represented using one of the standard macroslip contact elements described above. Recently, a novel contact element, fit to take into account microslip as well as the nonlinearity in the normal direction typical of nonconforming con-

Furthermore, Herzog et al. [7] have shown that Dynamic Lagrangians may incur in convergence problems for penalty parameters lower than 107 N/m, thus highlighting a possible limitation of their use in case of "softer" contact interfaces.

upgrade [12], to give a simplified representation of 2D in-plane motion.<sup>2</sup>

sented in [11] can be applied (as it is done in this Chapter, see also **Figure 1b**).

response, while it becomes negligible if the gross slip regime is reached [18].

Where the 2D tangential motion is albeit considered as the combination of two uncoupled 1D motions.

tacts, has been proposed [18].

1

2

Whenever a damper is added to the bladed system, its dynamic response is modified into two fundamental ways:


An additional complication is posed by the nonlinearity introduced by friction: it is well known that the non-linear dynamic response of bladed systems (both in frequency and maximum amplitude) is tightly coupled to the motion of the damper and its contact states (stick-slip-separation).

Accounting for the presence of friction is not an easy task. The presence of friction-induced nonlinearities makes solving the equilibrium equations a challenging task, therefore standard FE codes are not suited to the purpose: a complex hierarchy of techniques has been developed, a thorough review can be found in [4]. Furthermore, modeling friction entails:


**Figure 1.** (a) Sketch representing curved-flat underplatform dampers mounted on a turbine disk. (b) Example of standard macroslip contact element used to represent conforming and nonconforming contacts.
