Walter Sextro

Frequency tuning of piezoelectric energy harvesters by magnetic force

A piezoelectric energy harvester is an electromechanical device that converts ambient mechanical vibration into electric power. Most existing vibration energy harvesting devices operate effectively at a single frequency only, dictated by the design of the device. This frequency must match the frequency of the host structure vibration. However, real world structural vibrations rarely have a specific constant frequency. Therefore, piezoelectric harvesters that generate usable power across a range of exciting frequencies are required to make this technology commercially viable. Currently known harvester tuning techniques have many limitations, in particular they miss the ability to work during harvester operation and most often cannot perform a precise tuning. This paper describes the design and testing of a vibration energy harvester with tunable resonance frequency, wherein the tuning is accomplished by changing the attraction force between two permanent magnets by adjusting the distance between the magnets. This tuning technique allows the natural frequency to be manipulated before and during operation of the harvester. Furthermore the paper presents a physical description of the frequency tuning effect. The experimental results achieved with a piezoelectric bimorph fit the calculated results very well. The calculation and experimental results show that using this tuning technique the natural frequency of the harvester can be varied efficiently within a wide range: in the test setup, the natural frequency of the piezoelectric bimorph could be increased by more than 70%.

Vibration Damping by Friction Forces -Theory and Applications

In this paper, we deal with the vibrational behavior of mechanical structures interconnected by contacts with friction. The focus is set on the utilization of friction forces that are generated in the contact interfaces with the objective to increase damping and to reduce vibration amplitudes in order to prevent structures from failures owing to high resonance stresses. We present a comparison and classification of different contact models that are most commonly used, including the derivation of a three-dimensional contact model under consideration of rough surfaces. We give different solution methods for problems with non-linear friction elements. The effectiveness of friction damping devices is pointed out by a single-degree-of-freedom friction oscillator, beam-like structures with frictional interfaces and different underplatform dampers in turbo-machinery applications. It can be shown that in many practical applications friction damping devices provide a remarkable decrease of vibration amplitudes.

The Calculation of the Forced Response of Shrouded Blades with Friction Contacts and Its Experimental Verification

Shrouds with a frictional interface are used to reduce the dynamic stresses in turbine blades. Due to dry friction energy is dissipated, which can be used to decrease vibration amplitudes and, hence, to increase the life time of turbine blades.The spatial motion of the blades results in a spatial motion of the contact planes. Due to the non-linearity of the problem, the contact planes are discretized. For each contact area, the developed contact model is used to calculate the corresponding tangential and normal contact forces. This contact model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffnesses in normal and tangential direction and dry friction. Due to the roughness of the contact planes the normal contact forces and the contact stiffnesses in normal and tangential direction are nonlinear dependent on the relative displacements in the normal direction. This effect is verified by experiments.An experiment with one shrouded blade and two non-Hertzian contacts is used to verify the developed contact model and the calculation method. The comparison between measured and calculated frequency response functions for bending and torsional vibrations of the blade show a very good agreement.A bladed disk assembly with shrouds is investigated and optimized with respect to the vibration amplitudes and alternating stresses. Varying the normal contact force best damping effects are obtained. Separation of the contacts leads to an increase of the alternating stresses and, thus, has to be avoided.Copyright

Asymmetrical Underplatform Dampers in Gas Turbine Bladings: Theory and Application

During operation, the rotating blades of a gas turbine are subjected to centrifugal forces as well as fluctuating gas forces, resulting in blade vibrations. In addition to material damping, aerodynamical and blade root damping, underplatform dampers are widely used to increase the amount of damping and to decrease blade vibration amplitudes. The friction forces generated by the relative displacements between the underplatform damper and the blade platforms provide a significant amount of energy dissipation. In practice, a number of different underplatform damper designs are applied. Basically, these are wedge dampers with flat contact areas, cylindrical dampers with curved surfaces or asymmetrical dampers with both flat contact surfaces on one side and curved contact surfaces on the other. The latter damper type combines the advantages of both the wedge and the cylindrical damper by preventing the damper from pure rolling on the one hand as it has been observed for cylindrical dampers and on the other hand, avoiding a diverged plane area contact in case of a wedge damper, causing a damper lift-off. This paper will focus on the investigation of cylindrical and asymmetrical underplatform dampers. A comparison between measurements of rotating assemblies in Siemens PG gas turbines (V84.2, V64.3A and V94.3A(2)) under test and real operating conditions with cylindrical and asymmetrical underplatform dampers and the predictions of the developed theoretical model are presented. Special attention is paid to the frequency shift due to the application of an underplatform damper, since in particular for stationary gas turbines, in addition to the amplitude reduction, the accurate prediction of the resonance frequency is of major interest.Copyright

Optimization of Interblade Friction Damper Design

The vibration amplitudes of bladed disk assemblies can be reduced significantly by means of friction damping devices such as shrouds, damping wires and interblade friction dampers. In practice, interblade friction dampers are applied in rotating arrangements with various geometries showing curved or flat surfaces like so-called wedge-shaped dampers. This paper is focusing on a computation method to predict the dynamical behaviour of turbine blades with friction dampers including both, curved and wedge-shaped dampers with Hertzian and non-Hertzian contact conditions, respectively. The presented computation method uses a 3D contact model to calculate the contact forces, including normal and tangential stiffnesses, roughness and microslip effects. The relative displacements in the contact area can be expressed by means of 6 DOF of the blade platforms and 6 rigid body DOF of the damper including translational and rotational displacements. The relative displacement of the friction damper with respect to the adjacent blades can be derived from the contact kinematics of the blade-damper-blade system and the equations of motion of the friction damper. Thus, the model can be applied to investigate spatial motions of the bladed disk assembly including bending and torsional vibrations. A comparison of different friction damper designs with respect to an optimal damper geometry and damper mass is presented. The advantages and disadvantages of each design will be discussed. Experimental results are shown to validate the developed computation method.Copyright

Analytical determination of characteristic frequencies and equivalent circuit parameters of a piezoelectric bimorph

Piezoelectric structures are nowadays used in many different applications. A better understanding of the influence of material properties and geometrical design on the performance of these structures helps to develop piezoelectric structures specifically designed for their application. Different equivalent circuits have been introduced in the literature to investigate the behaviour of piezoelectric transducers. The model parameters are usually determined from measurements covering the characteristic frequencies of the piezoelectric transducer. This article introduces an analytical technique for calculating the mechanical and electrical equivalent system parameters and characteristic frequencies based on material properties and geometry for a cantilever bimorph structure. The model is validated by measurements using a cantilever bimorph and fits the experimental results better than previous models. The model gives a full set of piezoelectric transducer parameters and is therefore well suited for further theoretical investigations of piezoelectric transducers for different applications. The results also show that even small manufacturing tolerances have a considerable effect on the system parameters and characteristic frequencies. This might lead to intolerable deviations, especially in dynamic applications and should be avoided by careful design and production.

PEM fuel cell prognostics using particle filter with model parameter adaptation

Application of prognostics and health management (PHM) in the field of Proton Exchange Membrane (PEM) fuel cells is emerging as an important tool in increasing the reliability and availability of these systems. Though a lot of work is currently being conducted to develop PHM systems for fuel cells, various challenges have been encountered including the self-healing effect after characterization as well as accelerated degradation due to dynamic loading, all which make RUL predictions a difficult task. In this study, a prognostic approach based on adaptive particle filter algorithm is proposed. The novelty of the proposed method lies in the introduction of a self-healing factor after each characterization and the adaption of the degradation model parameters to fit to the changing degradation trend. An ensemble of five different state models based on weighted mean is then developed. The results show that the method is effective in estimating the remaining useful life of PEM fuel cells, with majority of the predictions falling within 5% error. The method was employed in the IEEE 2014 PHM Data Challenge and led to our team emerging the winner of the RUL category of the challenge.

Optimization of the Contact Geometry Between Turbine Blades and Underplatform Dampers With Respect to Friction Damping

The blades of rotating compressor or turbine disks are subjected to fluctuating fluid forces that cause blade vibrations. To avoid high resonance stresses, in many applications additional damping is introduced into the bladed disk assembly by means of friction damping devices such as underplatform dampers. These are mounted between adjacent turbine blades and pressed onto the platforms due to centrifugal forces to dissipate energy by the generated friction forces due to relative motions between the damper and the neighboring blades. In real turbomachinery applications, the rotating blades are subjected to spatial vibrations caused by a complex blade geometry and distributed excitation forces acting on the airfoil. Therefore, a spatial model is presented including an appropriate spatial contact model to predict the generalized contact forces acting between the damper and the blades accurately. Six degrees of freedom are considered for each contact between the damper and the respective neighboring blades. Roughness effects are considered that determine the real contact area with respect to the nominal contact area. Different spatial blade vibration modes are investigated with regard to the friction damping that is provided by the underplatform damper. To gain the maximum damping effect, the damper mass is optimized at different working conditions of the assembly like the excitation amplitudes and the engine order. Furthermore, the influence of the contact geometry upon the damping potential is investigated in detail including the damper as well as the blade platform geometry. In practice, different damper geometries are in operation. Studies will be presented that prove the capability of the developed model to compare the effectiveness of different damper and blade platform geometries. Asymmetric platform angles leading to different contact conditions at the left and right damper contact, respectively, are studied in detail to improve the damping effect.Copyright

On Nonlinear Forced Vibration of Shrouded Turbine Blades

Numerical predictions of the forced vibration of a disk assembly including frictional effects between the shrouds are presented concerning engineering needs for the blade design process. Assuming a tuned disk assembly, numerical static, free, and then forced vibration analyses of a shrouded turbine blade measured in the spin pit are performed systematically. For the excitation forces of an air jet evaluated from the fairly linear behavior of the experimental blade resonance peaks, the reliability of the proposed approach is validated through the very close agreement of the computed and measured resonant peaks. These resonant peaks demonstrate either a fairly linear behavior or a nonlinear one like the jump effect of blade resonance amplitudes, or elastic impacts between the shrouds. Also, the damping performance for different contact configurations between the shrouds is numerically analyzed. These numerical results indicate that the shrouds generate higher frictional damping for small angles (0-30 deg) between the circumferential direction and the normal vector to the contact surface.

Improving the bond quality of copper wire bonds using a friction model approach

In order to increase mechanical strength, heat dissipation and ampacity and to decrease failure through fatigue fracture, wedge copper wire bonding is being introduced as a standard interconnection method for mass production. To achieve the same process stability when using copper wire instead of aluminum wire a profound understanding of the bonding process is needed. Due to the higher hardness of copper compared to aluminum wire it is more difficult to approach the surfaces of wire and substrate to a level where van der Waals forces are able to arise between atoms. Also, enough friction energy referred to the total contact area has to be generated to activate the surfaces. Therefore, a friction model is used to simulate the joining process. This model calculates the resulting energy of partial areas in the contact surface and provides information about the adhesion process of each area. The focus here is on the arising of micro joints in the contact area depending on the location in the contact and time. To validate the model, different touchdown forces are used to vary the initial contact areas of wire and substrate. Additionally, a piezoelectric tri-axial force sensor is built up to identify the known phases of pre-deforming, cleaning, adhering and diffusing for the real bonding process to map with the model. Test substrates as DBC and copper plate are used to show the different formations of a wedge bond connection due to hardness and reaction propensity. The experiments were done by using 500 μm copper wire and a standard V-groove tool.