Electromechanical Impedance Response of a Cracked Timoshenko Beam

Typically, the Electromechanical Impedance (EMI) technique does not use an analytical model for basic damage identification. However, an accurate model is necessary for getting more information about any damage. In this paper, an EMI model is presented for predicting the electromechanical impedance of a cracked beam structure quantitatively. A coupled system of a cracked Timoshenko beam with a pair of PZT patches bonded on the top and bottom surfaces has been considered, where the bonding layers are assumed as a Kelvin-Voigt material. The shear lag model is introduced to describe the load transfer between the PZT patches and the beam structure. The beam crack is simulated as a massless torsional spring; the dynamic equations of the coupled system are derived, which include the crack information and the inertial forces of both PZT patches and adhesive layers. According to the boundary conditions and continuity conditions, the analytical expression of the admittance of PZT patch is obtained. In the case study, the influences of crack and the inertial forces of PZT patches are analyzed. The results show that: (1) the inertial forces affects significantly in high frequency band; and (2) the use of appropriate frequency range can improve the accuracy of damage identification

Finite Element Analysis of Beam with Smart Materials

Impedance-based structural health-monitoring techniques are developed by utilizing a number of smart material technologies and represent a new non-destructive evaluation (NDE) method. The basic concept of this approach is monitoring the variations in mechanical impedance of the structure resulted by the presence of damage. Since it is very difficult to measure the structural mechanical-impedance, the new impedance methods utilize the electromechanical coupling properties of piezoelectric materials. The impedance-based structural health monitoring is done by using piezoelectric patches which are bonded to the host structure that act as both sensors and actuators on the system. When a PZT comes under a change in environment, it produces an electric charge. Conversely when an electric field is applied the PZT undergoes a mechanical strain. A sinusoidal voltage is used for the excitation of the PZT patch. As the patch is surface bonded to the host structure, the structure deforms along with it and gives a local dynamic response to the vibration. That response is then transmitted back from the PZT patch as an electrical response. The electrical response is then analysed where damage is shown as a phase shift or magnitude change in the impedance. In this project finite element simulation of the interaction between a PZT patch and a structure utilizing the electromechanical impedance (EMI) technique is studied. Simulation of the host structure with a piezoelectric patch at a high frequency range (up to 1000 kHz) using ANSYS version 13, was successfully performed. Advantages over the traditional FEA based impedance model and the impedance based analytical models include higher accuracy, direct acquisition of electrical admittance/impedance. This study proves that the FEM could emerge as an excellent alternative to structural health monitoring by visual inspection method

Geometric Nonlinear Finite Element and Genetic Algorithm Based Vibration Energy Harvesting from Functionally Graded Nonprismatic Piezolaminated Beams

Energy harvesting technology has the ability to create autonomous, self-powered systems which do not rely on the conventional battery for their operation. The term energy harvesting is the process of converting the ambient energy surrounding a system into some useful electrical energy using certain materials. Among several energy conversion techniques, the conversion of ambient vibration energy to electrical energy using piezoelectric materials has great deal of importance which encompasses electromechanical coupling between mechanical and electrical domains. The energy harvesting systems are designed by incorporating the piezoelectric materials in the host structure located in vibration rich environment. The work presented in this dissertation focuses on upgrading the concept of energy harvesting in order to engender more power than conventional energy harvesting designs. The present work deals with first the finite element (FE) formulation for coupled thermo-electro-mechanical analysis of vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated cantilever beam. A two noded beam element with two degrees of freedom (DOF) at each node has been used in the FE formulation. The FG material (i.e. non-homogeneity) in the axial direction has been considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) have been modelled using the Euler-Bernoulli beam theory and Hamilton‘s principle is used to solve the governing equation of motion. The simultaneous variation of tapers (both width and height in length directions) is incorporated in the mathematical formulation. The FE formulation developed in the present work has been compared with the analytical solutions subjected to mechanical, electrical, thermal and thermo-electro-mechanical loading. Results obtained from the present work shows that the axially FG nonprismatic beam generates more output power than the conventional energy harvesting systems. Further, the work has been focussed towards the nonlinear vibration energy harvesting from an axially FG non-prismatic piezolaminated cantilever beam. Geometric nonlinear based FE formulation using Newmark method in conjunction with Newton-Raphson method has been formulated to solve the obtained governing equation. Moreover, a real code GA based constrained optimization technique has also been proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of the beam and voltage of the PZT sensor. It is observed that more output power can be obtained based on the present optimization formulation within the allowable limits of stress and voltage than that of selection of design variables by trial and error in FE modelling

Bi-stable buckled energy harvesters actuated via torque arms.

Vibrational energy harvesters (VEH) are one way to generate electricity. Though the energy quantities are not enough to run desktop computers, they can power remote devices such as temperature, pressure, and accelerometer sensors or power biological implants. New versions of the Bluetooth protocol can even be used with VEH technology to send wireless data. An important aspect of VEH devices is the power output, operating frequency, and bandwidth. This dissertation investigates a novel method of actuating the primary buckled energy harvesting structure using torque arms as a force amplification mechanism. Buckled structures can exhibit snap-through and has the potential to broaden the operating frequency for the VEH. Macro and MEMS size prototypes are fabricated and evaluated via a custom made shaker table. The effect of compliance arms, which pin the center beam with piezoelectric strips, are also evaluated along with damping ratios. ANSYS models evaluating generated power are created for use in future optimization studies. Lastly, high energy orbitals (HEO) are observed in the devices. Results show that buckling lowers and broadens the output power of the new devices. Reverse sweeps drastically increase the operating frequency during snap-through. Rectangular compliance arms made of poly-lactic acid (PLA) generated the most power of all compliance arms tested. HEO performance can be induced by perturbing the system while maintaining the same input force which increases power output

Dynamic Analysis, Identification and Control Studies of Aero-Engine Model Rotor-Bearing Systems

Aero-engines have high speed rotors carrying multi-stage turbine and compressor discs. Such systems need continuous monitoring during the operating regime. These rotors are mounted on ball bearings supported with squeeze film dampers and connected to stator casings. The motions of bearings and rotor are influenced by each other and therefore such a system requires structural dynamic studies. These rotors involve several nonlinear factors including contact forces, varying compliance vibration of ball bearing, nonlinear oil-film force of squeeze film damper etc Solving such nonlinear dynamic problems using the traditional transfer matrix method, modal synthesis approach, finite element method or impedance coupling technique is therefore a challenging task. Present work focuses on modelling of rotors using ball bearing nonlinearities along with nonlinear secondary transient excitations using finite element modelling. In order to validate the finite element model, preliminary dynamic analysis is carried out using linear spring-damper bearing elements. Results are illustrated both for LP rotor model and twin-spool rotor. Initially, the natural frequencies obtained from the computer program based on Timoshenko beam elements are validated with ANSYS results. Further, the results are also validated with those obtained from impact hammer tests on a scaled dual disk rotor-bearing system. To utilize this finite element model, the time and frequency-domain response studies are conducted with double-row ball bearing forces, rub-impact forces, Muszynska’s gas transients along with squeeze-film forces. In all the cases, differences from simple rotor supported by single-row ball bearings with only unbalance excitations have been reported. Using the fundamental frequency and its amplitude, an inverse modelling approach is applied to predict the parameters of rotor bearing system such as increased bearing clearance, changes in disc unbalances and the centralizing spring constants in squeeze-film damper. In this regard, a trained model of 3-layer perceptron neural network model is employed. In the second study, changes in dynamic response due to waviness and race-way defects in ball-bearings are first studied using modified contact force relations. Using this data, type of bearing fault is estimated from the statistical parameters of the time-domain signal by training an unsupervised Kohenen’s neural network model. Here, the simulated data is collected from the rotor over an operating speed range. In the third study, the additional stiffness of rotor due to rub-impact forces is identified from optimization modelling. Such identification of rotor stiffening effect using finite element modelling is a new concept. Two types of control studies are proposed to minimize the amplitudes of rotor during the critical operating conditions. Semi active electromagnetic damper design helps in reducing vibration amplitudes of the LP rotor over a frequency range of interest. Here, the damper comprises of an electro-magnet and a spring. The required current and spring stiffness are identified from the basic relations and the results of control are illustrated with a two-disc LP rotor model. In active controller design, an electromagnetic actuator model is employed. The nominal gap maintained between the rotor and actuator coils is used in computing the actuator force. A proportional derivative (PD) control strategy is used to estimate the required forces. A neural network based alternate control scheme also proposed to compute the required actuator forces. In overall, the work focussed on the dynamic analysis of dual disc rotor model subjected to parametric nonlinear bearing loads under the action of various external forces and some controller design aspects applicable to this rotor

Stress analysis, dielectric, piezoelectric, and ferroelectric properties of PZT thick films. Fabrication of a 50MHz Tm-pMUT annular array

PZT films up to 35 μm thick were fabricated, using a composite sol gel route combining a PZT powder and a PZT sol. The maximum temperature for the process was 710°C. A demonstration of single layer and multilayer structures was given to show the flexibility of this technology. With Stoney’s Equation, studies of the in-situ film stress development as a function of the film thickness and density was effectuated. It helped to understand that the internal forces increase considerably with the film thickness and density. This study yields to set up experimental conditions in which a crack free surface finish of a 28μm thick film revealed the adaptability of the spin coating technique to fabricate thick films. The wet etching technology revealed the possibility of a great adaptability to pattern and shape innovative devices such as bars 10 μm wide of 21μm PZT thick film. The results open the way to a wide range of new industrial application requiring small features and/or multilayer PZT thick film with embedded electrodes. The single element and annular array devices have been shown to resonate at approximately 60MHz in air and 50 MHz in water. Three types of the composite thick film – 2C+4S, 2C+5S and 2C+6S – were used to fabricate the Tm-pMUT devices. In each case the most effective poling was obtained by maintaining the poling field of 8.4V/μm during cooling from the poling temperature (200ºC) to ‘freeze’ poled domains in place. This ‘freezing’ was required to prevent the tensile stresses within the film from reorienting the domains at high temperatures when the poling field is removed. Increasing values of thickness mode coupling coefficient (kt) were observed with increasing levels of sol infiltration (decreasing density). Such behaviour is thought to be due to non linear effects on the piezoelectric coefficient (e33) at high levels of porosity. For very dense thick film material a kt of 0.47 was observed which is comparable to that observed for the bulk material

Partial delamination detection and quantification in composite laminates using Laser Doppler Vibrometer

Vibration based structural health monitoring techniques are widely used for detection and quantification of delamination in composite structures. In this work, non-contact vibration measurement technique namely Laser Doppler Vibrometer (LDV) is used for damage characterization of partial delamination in composite beams. The modal information such as natural frequencies and mode shapes of composite beam are obtained using LDV and validated with finite element models for comparison with the obtained experimental results. Mode shape based damage detection algorithms namely, fractal dimension approach is used for quantification of delamination in composite beams. In the present work, a modified generalized fractal dimension technique is proposed to locate delamination of different sizes and shapes in the composite beam. Different types of partial delamination like C-type, I-type in composite beam specimens were fabricated and experimentally studied usingLDV. The modified fractal dimension technique was then applied to the mode shapes results of the various partial delamination to quantify the damage. In addition, multiple delamination were introduced in composite plates and experiments were carried out using LDV. Modified fractal dimension technique was then applied to quantify the delamination in composite laminates

Rotordynamic Analysis and Feasibility Study of a Disk Spin Test Facility for Rotor Health Monitoring

Recently, National Aeronautics and Space Administration (NASA) initiated a program to achieve the significant improvement in aviation safety. One of the technical challenges is the design and development of accelerated experiments that mimic critical damage cases encountered in engine components. The Nondestructive Evaluation (NDE) Group at the NASA Glenn Research Center (GRC) is currently addressing the goal concerning propulsion health management and the development of propulsion system specific technologies intended to detect potential failures prior to catastrophe. For this goal the unique disk spin simulation system was assembled at NASA GRC, which allows testing of rotors with the spinning speeds up to 10K RPM, and at the elevated temperature environment reaching 540 C (1000 F). It is anticipated that the facility can be employed for detection of Low Cycle Fatigue disk cracking and further High Cycle Fatigue blade vibration. The controlled crack growth studies at room and elevated temperatures can be conducted on the turbine wheels, and various NDE techniques can be integrated and assessed as in-situ damage monitoring tools. Critical rotating parts in advanced gas turbine engines such as turbine disks frequently operate at high temperature and stress for long periods of time. The integrity of these parts must be proven by non-destructive evaluation (NDE) during various machining steps ranging from forging blank to finished shape, and also during the systematic overhaul inspections. Conventional NDE methods, however, have unacceptable limits. Some of these techniques are time-consuming and inconvenient for service aircraft testing. Almost all of these techniques require that the vicinity of the damage is known in advance. These experimental techniques can provide only local information and no indication of the structural strength at a component and/or system level. The shortcomings of currently available NDE methods lead to the requirement of new damage detection techniques that can provide global information on the rotating components/system, and, in addition, they do not require direct human access to the operating system. During this period of research considerable effort was directed towards the further development of experimental facility and development of the vibration-based crack detection methodology for rotating disks and shafts. A collection of papers and reports were written to describe the results of this work. The attached captures that effort and represents the research output during the grant period