**2.2. The test rig evolution**

**1.3. Goals of the chapter**

FE: external excitation on blades.

102 Contact and Fracture Mechanics

[39], and recounts its latest improvements.

**Figure 3b**) and justifies all modeling choices.

(conforming and nonconforming surfaces both).

knowledge, will be explored.

**2. Experimental evidence**

damper designer/tester.

The main purpose of this chapter is to present the latest advances made by the AERMEC lab to improve the fidelity of damper modeling and to rigorously assess processes needed for

**Figure 2.** (a) Example of tuning of contact parameters in the full stick regime: two sets of contact parameters (one from Section 3 and one with a simplified assumption) leading to the "same" FRF. (b) Resulting FRFs (excitation level out of the tuning range) produced by the two sets of contact parameters from **Figure 1a**. CF: centrifugal force on the damper,

In detail, Section 2 briefly describes the Piezo Damper Rig (see **Figure 3a**), first presented in

Section 3 with reference to Section 1.1, defines a numerical damper model (also represented in

Section 3.2 uses the experimental evidence gathered on the above-mentioned rig to estimate all contact parameters necessary to represent a curved-flat damper between a set of platforms

In Section 4, the adequacy of the chosen contact model is discussed on the basis of an experimental campaign on numerous damper samples. Furthermore, the role of rotation of nonconforming contacts, a topic which has never been addressed in this context to the author's

The chapter conclusion (Section 5) includes a series of warning and recommendation for the

The majority of the rigs developed to test underplatform dampers see a bladed system (equipped with dampers) excited at resonance [8, 35]. Often, the FRF of the system is used as

reliable predictions/estimation of contact parameters (see **Figure 2**).

The key features of the test rig described above remain unchanged since its first version [39], however several subsequent improvements have been performed (see **Figure 4** for a graphical representation). In detail, the tripod and the structure hosting the force sensors have been redesigned to increase the overall stiffness of the rig [18]. This had a positive impact over the frequency operating range which increased from [≈5–80] Hz to [≈5–160 Hz]. In [40] each platform has been redesigned into two parts: a "fixed" part connected to the rest of the test rig (the left platform to the actuators, the right one to the force sensors) and a second part, termed here "insert" in contact with the damper. This configuration has several advantages: (i) the "insert" can be substituted to test different platform angles, (ii) the contact is localized along the damper axis by means of 4 mm wide protrusions present on both platform inserts which ensure high contact pressures even with moderate deadweights on the damper.

Lastly, the new platform inserts and dampers have been machined with cube-like protrusions oriented with one of the faces perpendicular to the contact line. Each contact line (left and right) is equipped with two cubes (one on the damper and one on the corresponding platform).

This allows for the direct measurement of the tangential relative motion at the contact (as shown in **Figure 3d**): this constitutes a true improvement in the test rig capabilities since it allows, as described in Section 3, for the estimation of the tangential contact stiffness values.

Modeling Friction for Turbomachinery Applications: Tuning Techniques and Adequacy…

http://dx.doi.org/10.5772/intechopen.72676

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Each experimental nominal condition is defined by: damper configuration (i.e. shape, platform angles, etc.), centrifugal load on the damper, excitation frequency, amplitude and direc-

The analysis of the damper performance under each nominal experimental condition is operated through the cross-comparison of a series of quantities (whose graphical representation can be found in **Figure 3b**–**d**) organized into diagrams (summarized in **Table 1**, shown in **Figures 5** and **6** and further commented in Section 3.2). Both contact forces and damper/ platform kinematics are taken into account for the purpose of uncovering the cross-relations existing between them and to estimate contact parameters. It should be noted that some of these quantities are directly measured (e.g. tangential and normal forces at the nonconforming contact TR and NR and all damper displacements), while other quantities are derived (e.g. tangential and normal forces at the conforming contact TL and NL are obtained through the damper equilibrium by neglecting inertia forces at frequencies where this is correct, as shown

**2.3. Measurement protocol**

**Figure 4.** Piezo Damper Rig evolution.

tion of motion.

**Figure 3.** (a) Piezo Damper Rig scheme and relevant quantities. (b) Piezo Damper Rig numerical model. (c) Measured and derived contact forces. (d) Laser positioning to obtain relevant kinematical quantities.


1 Damper rotation is here obtained as described in, that is, with reference to **Figure 3d**, *β<sup>D</sup>* = (*wD <sup>A</sup>*<sup>0</sup> − *wD AR A*<sup>0</sup> *AR*. 2 This example is carried out in case of IP motion, a similar diagram can be obtained in case of OOP motion by plotting the horizontal force component HR against the corresponding horizontal platform relative displacement uLP − uRP.

**Table 1.** Essentials in damper diagrams.

This allows for the direct measurement of the tangential relative motion at the contact (as shown in **Figure 3d**): this constitutes a true improvement in the test rig capabilities since it allows, as described in Section 3, for the estimation of the tangential contact stiffness values.
