Ian Howard

The Dynamic Modeling of Multiple Pairs of Spur Gears in Mesh, Including Friction and Geometrical Errors

This article presents a dynamic model of three shafts and two pair of gears in mesh, with 26 degrees of freedom, including the effects of variable tooth stiffness, pitch and profile errors, friction, and a localized tooth crack on one of the gears. The article also details howgeometrical errors in teeth can be included in a model. The model incorporates the effects of variations in torsional mesh stiffness in gear teeth by using a common formula to describe stiffness that occurs as the gears mesh together. The comparison between the presence and absence of geometrical errors in teeth was made by using Matlab and Simulink models, which were developed from the equations of motion. The effects of pitch and profile errors on the resultant input pinion angular velocity coherent-signal of the input pinions average are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results.

Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations

A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented in this paper. The new contributions for modelling the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretization, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations and orthonormalized global matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously by other researchers. There are also benefits to presenting the numerical techniques proposed in this paper. First, the proposed numerical techniques can be used for applications in many different geometrical models, including micro-electro-mechanical system power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can result in a very practical design, which avoids direct contact with piezoelectric material because of its brittle nature. Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating single voltage, we introduce the new electromechanical discretization, consisting of the mechanical and electrical discretized elements. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions of the displacement, velocity, voltage, current and power, including optimal power harvesting. The normalized numerical strain node and eigenmode shapes are also further formulated using numerical discretization. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under a resistive shunt circuit show good agreement with the experimental studies.

Analytical techniques for broadband multielectromechanical piezoelectric bimorph beams with multifrequency power harvesting

This paper presents the multifrequency responses of multielectromechanical piezoelectric bimorph beams using a novel analytical model based on the closed-form boundary value method reduced from the strong form of Hamiltonians principle. The reduced constitutive multielectromechanical dynamic equations for the multiple bimorph beams connected in series, parallel, and mixed series-parallel connections can be further formulated using Laplace transformation to give new formulas for power harvesting multifrequency response functions. The parametric case studies based on the change in geometrical structures of the multiple bimorphs with and without tip masses are discussed to analyze the trend of multifrequency power harvesting optimization under resistive load. Nyquist responses based on varying geometrical structures and load resistances were used to analyze the multifrequency power amplitudes in the complex domain. Overall, the trend of system response using multiple tiers consisting of multiple bimorphs was found to significantly widen the multifrequency band followed by increasing the power amplitudes.

Analytical modeling of self-powered electromechanical piezoelectric bimorph beams with multidirectional excitation

Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment, vehicles, aircraft, piping systems, fluid flow, and even external movement of the human body. A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology. The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions, simultaneously or singularly. This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonians principle and space- and time-dependent eigenfunction series which were further formulated using orthonormalization. The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions (FRFs). The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.

A vibration cavitation sensitivity parameter based on spectral and statistical methods

Octave band analysis and PCA used on RMS velocity to obtain key indicators.Mahalanobis distance is used to set thresholds since data is normally distributed.Pump health separated into no cavitation, incipient, and fully formed condition.Method works on a range of types and sizes of centrifugal pumps. Cavitation is one of the main problems reducing the longevity of centrifugal pumps in industry today. If the pump operation is unable to maintain operating conditions around the best efficiency point, it can be subject to conditions that may lead to vaporisation or flashing in the pipes upstream of the pump. The implosion of these vapour bubbles in the impeller or volute causes damaging effects to the pump. A new method of vibration cavitation detection is proposed in this paper, based on adaptive octave band analysis, principal component analysis and statistical metrics. Full scale industrial pump efficiency testing data was used to determine the initial cavitation parameters for the analysis. The method was then tested using vibration measured from a number of industry pumps used in the water industry. Results were compared to knowledge known about the state of the pump, and the classification of the pump according to ISO 10816.

Electromechanical Piezoelectric Power Harvester Frequency Response Modeling Using Closed-Form Boundary Value Methods

The conversion of mechanical vibration to electrical energy has shown great promise for extending battery life of smart sensor wireless devices for various engineering applications. This paper presents novel analytical models of a piezoelectric bimorph, using the closed-form boundary value (CFBV) method, for predicting the electromechanical power harvester frequency response. The derivations of the coupled electromechanical dynamic response of the transverse-longitudinal (CEDRTL) form based on the CFBV method were developed using the reduced strong form method of the Hamiltonian principle. The equations from CEDRTL can be reduced to give the coupled electromechanical dynamic response of the transverse (CEDRT) form. The electromechanical frequency response functions with variable load resistance were also given in detail using Laplace transformation. The two theoretical studies are compared together and validated with an experimental study. For some cases, when the load resistance approached open circuit, the difference between CEDRTL and CEDRT tended to be more pronounced. Conversely, the CEDRTL and CEDRT models tended to overlap when the load resistance approached short circuit. Nyquist plots are used to demonstrate the shifting frequency and amplitude changes due to variable resistance. Overall, the experimental and CEDRTL model results were very close to each other.

Computational FEA Model of A Coupled Piezoelectric Sensor and Plate Structure for Energy Harvesting

his paper presents a mathematical model of a piezo-plate energy-harvesting scheme. An analytical method is used to generate a finite element model of the coupled piezoelectric sensor element using Love-Kirchhoff’s plate theory. Constitutive equations for a single layer plate element are formulated. The polarisation of the piezoelectric sensor bounded on the upper plate structure is due to ambient vibration exerted on the structure. Forced vibration of the smart structure will create strain energy within the crystalline structure of the piezoelectric material. The resulting electric field generated by the sensor element was mO’Delled using a linear thickness interpolation function and the meshed plate elements were mO’Delled using four-node rectangular elements with three degrees of freedom for each node. The structural eigenmodes and dynamic response of the coupled piezo- plate system were solved by using modal analysis and Newmark-β integration methods respectively. The analysis is demonstrated with both dynamic displacement and electric voltage responses to an applied step force. Further mO’Delling of the smart structure is aimed at maximising the power generation capability.

Effect of shunted piezoelectric control for tuning piezoelectric power harvesting system responses – Analytical techniques

This paper presents new analytical modelling of shunt circuit control responses for tuning electromechanical piezoelectric vibration power harvesting structures with proof mass offset. For this combination, the dynamic closed-form boundary value equations reduced from strong form variational principles were developed using the extended Hamiltonian principle to formulate the new coupled orthonormalized electromechanical power harvesting equations showing combinations of the mechanical system (dynamical behaviour of piezoelectric structure), electromechanical system (electrical piezoelectric response) and electrical system (tuning and harvesting circuits). The reduced equations can be further formulated to give the complete forms of new electromechanical multi-mode frequency response functions and the time waveform of the standard AC–DC circuit interface. The proposed technique can demonstrate self-adaptive harvesting response capabilities for tuning the frequency band and the power amplitude of the harvesting devices. The self-adaptive tuning strategies are demonstrated by modelling the shunt circuit behaviour of the piezoelectric control layer in order to optimize the harvesting piezoelectric layer during operation under input base excitation. In such situations, with proper tuning parameters the system performance can be substantially improved. Moreover, the validation of the closed-form technique is also provided by developing the Ritz method-based weak form analytical approach giving similar results. Finally, the parametric analytical studies have been explored to identify direct and relevant contributions for vibration power harvesting behaviours.

A Review of Machinery Diagnostics and Prognostics Implemented on a Centrifugal Pump

Centrifugal pumps are a widely used machine found in industries such as water, sewerage, oil, and gas. As a result, it is vital that these pumps are monitored, diagnosed, maintained, or replaced prior to the pump failing to reduce downtime, material, and labour costs. Most companies employ a run-to-fail method or a time-based maintenance strategy to service their pumps, instead of condition based maintenance or a predictive maintenance strategy. This paper reviews the state of art in diagnostics and prognostics pertaining to centrifugal pumps. Attention is given to detailing the methods of application, detection of fault modes and results used by researchers in the main areas of diagnostics and prognostics.

Assessing the reliability of system modules used in multiple life cycles

This paper presents a reliability assessment model for maintenance and reliability engineers to determine the reusability potential of system modules based on their operating lives and, the pre-determined lifecycle of the parent product. In the first phase, the paper considers the time-to-failure of system modules to determine their overall operating life under normal operating conditions. Then, it determines the maximum number of lifecycles of the modules under consideration, which is a function of the modules’ total functional life and the product lifecycle. The functional potential of the modules is then discussed with reference to the probability of their failure. The study employs Weibull analysis for carrying out this analysis. The methodology was validated by using lifecycle data from a consumer product. The findings show that some of the components/modules of the product have a remarkable amount of residual life, which can be utilized by reusing these components in the next generation of the product. The results demonstrate the effectiveness and practicality of this multiple-use strategy. The study provides more perspectives to future research in the field of reliability, and decision-making on maintenance management and value recovery through multiple uses of system modules.