Vibration of High-Speed Compliant Gear Pairs

This study analytically investigates the vibration of high-speed, compliant gear pairs using a model consisting of coupled, spinning, elastic rings. The gears are elastically coupled by a space-fixed, discrete stiffness element that represents the contacting gear teeth. Hamilton’s principle is used to derive the nonlinear governing equations of motion and boundary conditions. These equations are linearized for small vibrations about the steady equilibrium due to rotation. The equations are cast in operator form, which exemplifies their gyroscopic system structure. The eigenvalue problem is discretized using Galerkin’s method. The natural frequencies and vibration modes for an example aerospace gear pair are numerically calculated for a wide-range of rotation speeds. The system coupling leads to multiple eigenvalue veering regions as the gear rotation speed varies. Highly coupled vibration modes that have meaningful deflection in the discrete mesh stiffness occur within a set frequency band. The vibration modes within this band have distinct nodal diameter components that evolve with rotation speed.

Wind Turbine Blade Damage Detection Using Various Machine Learning Algorithms

Wind turbine blades undergo high operational loads, experience variable environmental conditions, and are susceptible to failures due to defects, fatigue, and weather induced damage. These large-scale composite structures are essentially enclosed acoustic cavities and currently have limited, if any, structural health monitoring in practice. A novel acoustics-based structural sensing and health monitoring technique is developed, requiring efficient algorithms for operational damage detection of cavity structures. This paper describes a systematic approach used in the identification of a competent machine learning algorithm as well as a set of statistical features for acoustics-based damage detection of enclosed cavities, such as wind turbine blades. Logistic regression (LR) and support vector machine (SVM) methods are identified and used with optimal feature selection for decision making using binary classification. A laboratory-scale wind turbine with hollow composite blades was built for damage detection studies. This test rig allows for testing of stationary or rotating blades (each fit with an internally located speaker and microphone), of which time and frequency domain information can be collected to establish baseline characteristics. The test rig can then be used to observe any deviations from the baseline characteristics. An external microphone attached to the tower will also be utilized to monitor blade damage while blades are internally ensonified by wireless speakers. An initial test campaign with healthy and damaged blade specimens is carried out to arrive at certain conclusions on the detectability and feature extraction capabilities required for damage detection.

Tailoring Plate Thickness of a Helmholtz Resonator for Improved Sound Attenuation

A Helmholtz resonator with flexible plate attenuates noise in exhaust ducts, and the transmission loss function quantifies the amount of filtered noise at a desired frequency. In this work the transmission loss is maximized (optimized) by allowing the resonator end plate thickness to vary for two cases: 1) a non-optimized baseline resonator, and 2) a resonator with a uniform flexible endplate that was previously optimized for transmission loss and resonator size. To accomplish this, receptance coupling techniques were used to couple a finite element model of a varying thickness resonator end plate to a mass-spring-damper model of the vibrating air mass in the resonator. Sequential quadratic programming was employed to complete a gradient based optimization search. By allowing the end plate thickness to vary, the transmission loss of the non-optimized baseline resonator was improved significantly, 28 percent. However, the transmission loss of the previously optimized resonator for transmission loss and resonator size showed minimal improvement.

FEM-BEM Modeling and Experimental Verification of the Vibro-Acoustic Behaviour of a Section of Aircraft Fuselage

The aerodynamics of an aircraft in flight impose significant stresses upon the structure. Specifically, the mechanics of fluid flow are highly turbulent and, the layer around the aircraft, is referred to the turbulent boundary layer (TBL). The TBL incites a gradient of pressure fluctuations across the fuselage skin resulting in its vibration, and in turn, the generation of noise inside the passenger cabin. The investigation herein proposes a hybrid FEM-BEM modeling technique to predict the aforementioned vibro-acoustic response and an experimental methodology to verify the results (following ASTM and ANSI international testing standards). The described expectations required construction of an acoustic facility consisting of a reverberation chamber and a semi-anechoic room, the development of DAQ software using LabVIEW, an assembly of DAQ hardware using National Instruments products, and the post-processing of test data using Microsoft Excel. The principal quantity of interest is transmission loss (though insertion loss, absorption and other metrics are also calculated). Two panels (0.04in (40thou) and 0.09in (90thou) in thickness) were simulated and tested (0.01in = 1thou). The calculated error of the proposed methodology is within a maximum of 5dB, with an average of 1dB. Ongoing work is investigating complex constructions and the use of damping materials.

On Vibration Suppression and Energy Dissipation Using Tuned Mass Particle Damper

Particle damping has the promising potential for attenuating the unwanted vibrations in harsh environment. However, the damping performance of the conventional particle damper (PD) may be ineffective, especially when the acceleration of the particle damper is less than gravitational acceleration (1g). In order to improve the damping performance of the traditional PD, the tuned mass particle damper (TMPD) which utilizes the advantages of both the tuned mass damper and particle damper is investigated in this paper. The TMPD can act as the tuned mass damper to not only absorb the vibration of the primary structure but also amplify the motions of the particles in the enclosure, which will significantly enhance the particle damping effect. To analyze the damping effect of the TMPD, a new coupling method to integrate the TMPD into the continuous host structure is first developed. The 3D discrete element method is then adopted to accurately describe and analyze the motion of particles in the enclosure. Furthermore, the analysis is validated by correlating the numerical and experimental results. With the new method as basis, detailed numerical studies are further carried out to verify the damping effectiveness of the TMPD compared with conventional PD under various excitation levels. The results demonstrate that the TMPD can significantly improve the damping effect of the conventional PD on suppressing the vibration of the primary structure under both the low and high excitation levels.

Modelling and Experimental Comparison of Fluid Structure Coupling for Thin Sheet Metal Tanks Using Statistical Energy Analysis

Acoustic response of flat surfaces in contact with a fluid volume is of some interest for the design of automotive fuel tanks, fluid containers and underwater applications [1]. As this response can be related to the surface vibration response in the linear domain, the effect of fluid structure coupling on the vibration response of the structure is studied in this paper. Advances in the computational abilities have increased the focus of analysis-led approaches in the design of thin sheet metal tanks. Conventional finite element (FE) based approaches are useful at low frequencies but are highly sensitive to geometrical details and local effects at higher frequencies. With changing input parameters, finite element approaches could prove to be computationally expensive during the initial design phase of such structures. Statistical Energy Analysis (SEA) is an energy based approach and was used to study the fluid structure coupling effect on the vibration characteristics of a simple rectangular parallelepiped thin sheet metal tank. A thin steel tank (thickness/min. characteristic dimension <0.01) was excited by a broad band uniform power spectral density white noise signal and the spatial and frequency averaged acceleration responses were compared. Some parameters like the damping loss factor and the excitation force were calculated from the experimental measurements and used as input for SEA simulations. Coupling loss factors were calculated from tests and the trend lines were found to be in agreement with the theoretical calculations. The SEA simulation model results were compared with the conventional FE based approach for reference. Variance studies were used to compute the envelope for the SEA simulation response for a 90% confidence interval. The SEA and the test results comparison was quantified by a correlation coefficient which indicated a moderately strong correlation (>0.5) between the SEA and experimental results.

Energy Harvesting From Torsional Vibrations Using a Nonlinear Oscillator

Harvesting ambient energy in a variety of systems and applications is a relatively recent trend, often referred to as Energy Harvesting. This can be typically achieved by harvesting energy (that would otherwise get wasted) through a physical process aiming to convert energy amounts to useful electrical energy. The harvested energy can be thermal, solar, wind, wave or kinetic energy, with the last class mainly referring to harvesting energy from vibrating components or structures. More often these oscillations are error states from the systems’ ideal function and through harvesting this potentially wasted energy could be reclaimed and become useful. Regardless of the generally low power output of the devices designed to harvest energy from vibrations, their use remains an attractive concept, which is mostly attributed to the growing use of modern electronic devices that exploit the low power requirements of semi-conductors. Energy Harvesting applications are often met in situations where a network of essential electronic devices, such as sensors in Structural Health Monitoring or bio-implantable devices, becomes hardly accessible. Harvesting ambient vibrations to power up these devices offers the option to utilize wireless sensors rendering these systems autonomous. Typical cases of systems, where ambient vibrations are ubiquitous are met in automotive and aerospace applications. Besides their potentially adverse impact, the energy carried by vibrating parts could be harvested, such that wireless sensors are powered. In this paper, a concept for harvesting torsional vibrations is proposed, based on a concept that employs magnetic levitation to establish a nonlinear Energy Harvester. Experience has shown that linear harvesters require resonant response to operate, often leading to low performance of the device when the excitation frequency deviates from resonance conditions. This is why harvesters with essential nonlinearity are preferred, since they are able to demonstrate high response levels over wider frequency regions. Herein, the conducted study aims to demonstrate the functionality of this concept for torsional systems. A mathematical model of the coupled nonlinear electromechanical system is established, seeking preliminary estimates of the harvested power. The compelling attribute of this system lies in the dependency of its linear natural frequency on the excitation frequency, which is found to cause multiple response peaks in the corresponding frequency spectra. Moreover, the selection of the static equilibrium of the levitating magnet is found to greatly influence the system’s response.

Polynomial Chaos Expansion Sensitivity Analysis for Electromechanical Impedance of Plate

Piezoelectric wafer active sensors (PWAS) have been the widely used in impedance based damage detection applications. A most important matter in impedance method is applied voltage to PWAS and measuring current in PWAS. In this paper, for modeling of impedance based structural health monitoring, a 3D spectral finite element method (SFEM) is developed for plate structure with PWAS. Because of high frequency application of impedance method, high degree of freedom (DOF) is needed for modeling of impedance of PWAS attached on the plate. Uncertainty of plate and PWAS parameters could be effect on the natural frequencies of structure. So, impedance signal of modeling would be different based on uncertainty parameters. Polynomial chaos expansion (PC) is a probabilistic method consisting in the projection of the model output on a basis of orthogonal stochastic polynomials in the random inputs. In this paper, PCE is used for sensitivity analysis of the electromechanical impedance of plate structure with PWAS.

Surface Error and Stability Chart of Beam-Type Workpiece in Milling Processes

In milling processes, the intermittent cutting force may lead to harmful vibrations. These vibrations are classified into two groups. One of them is the self excited vibration which comes from the loss of stability due to the regeneration effect and these vibrations lead to unacceptable chatter marks. The other one is the forced vibration which can lead to high Surface Location Error (SLE) in case of resonant spindle speeds. In this paper, the dynamics of the beam-type workpiece is considered which is modelled by means of Finite Element Analysis (FEA). Both the forced vibration and the stability properties are predicted along the tool path. The surface properties are computed on the stable regions of the stability chart which presents the chatter-free (stable) parameter domain as a function of the spindle speed and the tool path. The theoretical results are compared to the measured SLE and surface roughness.

The Influence of Modal Geometrical Imperfections on the Nonlinear Vibrations of a Thin-Walled Circular Cylindrical Shell

This work investigates the influence of several modal geometric imperfections on the nonlinear vibration of simply-supported transversally excited cylindrical shells. The Donnell nonlinear shallow shell theory is used to study the nonlinear vibrations of the shell. A general expression for the transversal displacement is obtained by a perturbation procedure which identifies all modes that couple with the linear modes through the quadratic and cubic nonlinearities. The imperfection shape is described by the same modal expansion. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Substituting the obtained modal expansions into the equations of motions and applying the standard Galerkin method, a discrete system in time domain is obtained. Several numerical strategies are used to study the nonlinear behavior of the imperfect shell. Special attention is given to the influence of the form of the initial geometric imperfections on the natural frequencies, frequency-amplitude relation, resonance curves and bifurcations of simply-supported transversally excited cylindrical shells.