Optimization of piezoelectric cantilever energy harvesters including non-linear effects

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations

A geometric parameter study of piezoelectric coverage on a rectangular cantilever energy harvester

This paper proposes a versatile model for optimizing the performance of a rectangular cantilever beam piezoelectric energy harvester used to convert ambient vibrations into electrical energy. The developed model accounts for geometric changes to the natural frequencies, mode shapes and damping in the structure. This is achieved through the combination of finite element modelling and a distributed parameter electromechanical model, including load resistor and charging capacitor models. The model has the potential for use in investigating the influence of numerous geometric changes on harvester performance, and incorporates a model for accounting for changes in damping as the geometry changes. The model is used to investigate the effects of substrate and piezoelectric layer length, and piezoelectric layer thickness on the performance of a microscale device. Findings from a parameter study indicate the existence of an optimum sample length due to increased mechanical damping for longer beams and improved power output using thicker piezoelectric layers. In practice, harvester design is normally based around a fixed operating frequency for a particular application, and improved performance is often achieved by operating at or near resonance. To achieve unbiased comparisons between different harvester designs, parameter studies are performed by changing multiple parameters simultaneously with the natural frequency held fixed. Performance enhancements were observed using shorter piezoelectric layers as compared to the conventional design, in which the piezoelectric layer and substrate are of equal length

Variation propagation control in mechanical assembly of cylindrical components

AbstractVariation propagation control is one of the procedures used to improve product quality in the manufacturing assembly process. The quality of a product assembly depends on the product type and the optimization criteria employed in the assembly. This paper presents two assembly procedures of component stacks by controlling variation propagation. The procedures considered are: (i) straight-build assembly by minimizing the distances from the centres of components to table axis; (ii) parallelism-build assembly by minimizing the angular errors between actual and nominal planes. Simulation results are presented for the assembly of four cylindrical components. The results indicate that the variation can be reduced significantly by using these procedures, compared to that without minimization. The results also indicate that the variation not only greatly relies on the assembly procedures, but also on the number of available orientations at the assembly stage. The radial variation increases with the stage for the straight-build assembly, while the angular error decreases with the stage for the parallelism-build assembly. The assembly quality for the two assembly procedures can be improved by increasing the number of orientations. The variation decreases exponentially and monotonically with the number of orientations. The information obtained is useful for manufacturing processes and the assembly modeling

Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼60%∼60%, it is found that three ring modes of vibration (1θ,2θ1θ,2θ and 3θ3θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2θ2θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping

Review and comparison of different support loss models for micro-electro-mechanical systems resonators undergoing in-plane vibration

International audienceSeveral approaches for calculating support loss in micro-electro-mechanical system resonators undergoing in-plane vibration are reviewed. In each of them, the support is approximated as a semi-infinite domain. The first approach is analytical and models the support as a semi-infinite thin plate. This is compared with two different finite element approaches that introduce artificial boundaries to their finite domain. In order to absorb outgoing waves and model the infinite support, a perfectly matched layer method and the use of infinite elements are considered. Simple test cases are studied and the results for the support losses predicted by the different methods are compared. It is shown that each of the methods yields similar trends. Using the developed analytical model, a parametric study is performed on the support losses of a ring-based resonator. General strategies for improving the quality factor by reducing support losses are provided

Vibration analysis of a MEMS ring-based rate sensor by the ray tracing method

International audienceIn this paper a wave approach, known as the ray tracing method, is used to analyse the vibration performance of a Micro-Electro-Mechanical Systems (MEMS) ring-based rate sensor. This approach uses propagation and transmission of elastic waves, and fully exploits the presence of cyclic symmetry to determine the vibrating response. Sensor sensitivity is highly degraded by the presence of damping. Support loss is one of the important sources of damping in MEMS resonators and takes account of the energy dissipated through the supporting structure. Using classic wave theory in a two-dimensional thin plate, analytical expressions are obtained for substrate displacements due to shear and normal stresses being applied to its edge, and these displacements are used to determine the support loss. Numerical results for the natural frequencies and mode shapes of a MEMS ring-based rate sensor are provided and it is shown that they are in very good agreement with a finite element analysis. The corresponding support losses are also presented

Up to 30 mW of broadly tunable CW green-to-orange light, based on sum frequency mixing of Cr4+:forsterite and Nd:YVO4 lasers

Efficient generation of continuous-wave (CW) tunable light in the yellow region is reported. The method is based on sum-frequency mixing of a tunable Cr4+:forsterite laser with a Nd:YVO4 laser. A periodically poled lithium niobate crystal was placed intra-cavity in a Nd:YVO4 laser, and the Cr4+ :forsterite laser was single-passed through the non-linear media. With this setup, it was possible to generate up to 3 mW of yellow light smoothly tunable from 573 to 587 nm. This is the highest output demonstrated to date for a tunable diode pumped solid-state CW laser in this wavelength region. The ways to improve the efficiency further are discussed. (c) 2005 Elsevier B.V. All rights reserved.</p

Low-loss GaInNAs saturable Bragg reflector for mode-locking of a femtosecond Cr/sup 4+/:forsterite-laser

A GaInNAs saturable Bragg reflector is used to mode-lock a Cr/sup 4+/ : forsterite solid-state laser. This low-loss saturable absorber mediates the generation of tunable femtosecond pulses having durations as short as 62 fs in the 1300-nm spectral region