**6.2 Damping of turbine blades**

Another application is the vibration damping of turbine blades. Here the excitation comes from high static and dynamic loads. Static loads are due to centrifugal forces and thermal strains while fluctuating gas forces are the cause of dynamic excitation which can lead to High Cycle Fatigue (HCF) failures. As the material damping is extremely low, any further damping provided to the structure is desireable. Coupling devices like underplatform dampers, lacing wires and tip shrouds are common in turbomachinery applications [19, 20]. The effectiveness of these damping concepts is limited to the relative vibrations of neighbouring blades and therefore they are often only efficient for specific engine speeds and mode shapes. Furthermore, the aerodynamics of the blades is influenced by these coupling devices.

In the following, the damping of turbine blades by shunted piezoceramics is studied with a bladed disc model (BLISC), depicted in Figure 14, which has been introduced by Hohl [8]. Each

**Figure 14.** Photography and sketch of the BLISC test rig with attached piezoceramics.

blade is equipped with a MACRO FIBER COMPOSITE piezoceramics M2814 P1 from MARCO company for vibration damping.

#### *6.2.1 Optimizing the location of the piezoceramics*

18 Will-be-set-by-IN-TECH

with the same capacitance ratios as in the simulations reported in Figure 11. It can be seen that the maximum reduction for each shunt is achieved for the perfectly tuned shunts (*L* ≈ *L*opt respectively *η* ≈ 1). In these cases, all shunts - including the passive *LR* shunt - are capable to suppress the squealing totally, as predicted by the simulations. The differences in the maximum reduction can be explained by different strength of the squealing. Naturally, a weak squealing delimits the maximum possible reduction compared to a strong squealing. From the inductance ratio *L*/*L*opt, the frequency ratio between the electrical eigenfrequency and the squealing frequency can be re-calculated. Defining the state 'silent' and 'squealing' by an arbitrary threshold of 12 dB SPL-reduction, the brake is stabilized in a range of Δ*f* = 40Hz for the passive *LR* shunt. With actice *LRC*-shunts, the stabilized range covers Δ*f* = 212Hz with *δ* = −0.66 and Δ*f* = 950Hz with *δ* = −0.88. These results show a good accordance with the simulation results in Figure 11. However, some influences like the heating up of the piezoceramics lead to a reduction of the piezoelectric effect so that the performance at the end

Another application is the vibration damping of turbine blades. Here the excitation comes from high static and dynamic loads. Static loads are due to centrifugal forces and thermal strains while fluctuating gas forces are the cause of dynamic excitation which can lead to High Cycle Fatigue (HCF) failures. As the material damping is extremely low, any further damping provided to the structure is desireable. Coupling devices like underplatform dampers, lacing wires and tip shrouds are common in turbomachinery applications [19, 20]. The effectiveness of these damping concepts is limited to the relative vibrations of neighbouring blades and therefore they are often only efficient for specific engine speeds and mode shapes.

Furthermore, the aerodynamics of the blades is influenced by these coupling devices.

**Figure 14.** Photography and sketch of the BLISC test rig with attached piezoceramics.

In the following, the damping of turbine blades by shunted piezoceramics is studied with a bladed disc model (BLISC), depicted in Figure 14, which has been introduced by Hohl [8]. Each

*r*

*α*

of each measurement is slightly lower than in the beginning.

**6.2 Damping of turbine blades**

The intention of this study was to optimize the placement of the piezoceramics within the structure. As the geometry is too complex for an analytical description, it is modeled by Finite Elements in Ansys using 3-D 20-Node structural solid elements (solid186) and a 3-D 20-node coupled-flied solid (solid226) for the piezoelectric material. Subsequently a modal reduction is performed. The location of every piezoceramics is described by the radius *r* and the orientation *α*, which have to be optimized, with the generalized coupling coefficient *K* taken as a measure of the coupling. This factor can be calculated by the system' eigenfrequencies with isolated and short circuit electrodes of the piezoceramics, which are both determined within the FE program. Generally, the coupling with the individual eigenforms of the system differ from each other. In Figure 15 the coupling coefficients for the first bending and first torsion mode of the blades are given versus *α* and *r*. For the bending mode, the piezoceramics should

**Figure 15.** Generalized coupling coefficient *K* for the first bending and torsion modes versus the location of the piezoceramics.

be placed close to the clamped ending of the blade at *r* = 90mm, which is approximately the radius of the disc. This can be explained by the bending moment, which is maximized at this position. The bending moment reduces to zero at the free end of the blade, therefore also the coupling reduces in that direction. The dependency with the orientation *α* is nearly symmetric: the coupling is maximal when the piezoceramics is facing in radial direction (*α* = 0◦ or *α* = 180◦) and minimal for *α* = 90◦. The resulting maximum coupling is *K* ≈ 3.5%.

For the torsion mode, the optimal radius is similar, yet slightly larger than for the bending mode. However, the orientation is oppositional to the bending case: the best coupling results for *α* = 45◦, while it is nearly zero for *α* = 0◦ and *α* = 90◦. The maximum coupling with the torsion mode is *K* ≈ 2.25% and thus smaller than for the bending.

Therefore, for the overall optimal location a trade-off is necessary, and the piezoceramics is placed with *r* = 97.5mm and *α* = 22.5◦. In this case the coupling with both the bending and torsion mode is about *K* = 2%.

#### *6.2.2 Measurements*

Finally, measurements are conducted with the BLISC test rig. The system is excited harmonically by additional piezoceramics placed at the back side at identical positions as the shunted ones at the front side. One single passive *LR* network is connected to all piezoceramics simultaneously, and the electrical eigenfrequency and the damping ratio are set to the optimal values according to the previous sections. Figure 16 shows the measurement as well as the simulation results for isolated electrodes and optimal *LR*-shunting. Generally, the

**Figure 16.** Simulated and measured frequency response of the BLISC model for isolated electrodes and *LR*-shunting.

simulation results are in very good agreement with the measured ones. The damping effect of the shunted piezoceramics is clearly visible.
