Torsional Resonance Mode Research Articles

Modeling the Converse Magnetoelectric Effect in the Low-Frequency Range.

This article is devoted to the theory of the converse magnetoelectric (CME) effect for the longitudinal, bending, longitudinal-shear, and torsional resonance modes and its quasi-static regime. In contrast to the direct ME effect (DME), these issues have not been studied in sufficient detail in the literature. However, in a number of cases, in particular in the study of low-frequency ME antennas, the results obtained are of interest. Detailed calculations with examples were carried out for the longitudinal mode on the symmetric and asymmetric structures based on Metglas/PZT (LN); the bending mode was considered for the asymmetric free structure and structure with rigidly fixed left-end Metglas/PZT (LN); the longitudinal-shear and torsional modes were investigated for the symmetric and asymmetric free structures based on Metglas/GaAs. For the identification of the torsion mode, it was suggested to perform an experiment on the ME structure based on Metglas/bimorphic LN. All calculation results are presented in the form of graphs for the CME coefficients.

Micropillared Surface to Enhance the Sensitivity of a Love-Wave Sensor

Surface-acoustic-wave (SAW) sensors have undergone outstanding developments during the last decades. However, for biosensing applications, they struggle to compete with optical sensing technologies. In this work, we present a Love-wave-based sensing platform that leverages the use of the local resonances of micropillars fabricated on the surface of the guiding layer. We demonstrate numerically and experimentally that the Love-wave interaction with the micropillars produces sharp attenuation dips in the transmission spectrum. These dips are associated with the excitations of flexural and torsional resonance modes of the pillars. We utilize these modes to achieve higher detection sensitivity of temperature variation and mass loading using sugar and microbeads concentrations in aqueous solutions. Integrating a lattice of micropillars into SAW-based devices offers a strong potential for detecting low particles concentrations.

Measurement of frequency-dependent shear properties of highly compliant materials using Kibble’s method

We present a method to determine the frequency-dependent properties of highly-compliant materials by measuring the response of rod-like specimens subjected to an applied torque. Kibble’s method, which utilizes a velocity measurement and two electrical measurements, is used to calculate the applied torque on the specimen as a function of frequency. Shear modulus and loss factor in shear are determined by fitting mechanical models to transfer functions between the applied torque and torsional response of the sample. We demonstrate this technique on a prototype apparatus using different polymer materials and specimen geometry. Estimates of the shear modulus and loss factor in shear are determined over a range of frequencies that include the first six torsional resonant modes. These material properties are compared with data obtained using a commercial Dynamic Material Analyzer wherein the samples are excited in a bending mode.

Modeling, calculation, and analysis of torsional vibration characteristics of the hydrodynamic transmission system in engineering vehicle

According to the typical working conditions of a loader and considering the complexity of the working conditions, the hydrodynamic transmission powertrain system was modeled in this study. Because the hydrodynamic torque converter is a flexible fluid transmission component in the transmission system, this study proposes and establishes equivalent variable damping and equivalent variable stiffness models of the hydrodynamic torque converter. Based on this, a torsional vibration simulation model of the loader with variable damping and stiffness is proposed, and the frequencies and amplitudes of the torsional resonance modes of the transmission system varying with engine speed and hydrodynamic torque converter speed ratio are obtained. It is determined that the variable stiffness of the hydrodynamic torque converter has little effect on the natural frequency of the vehicle, and taking variable damping and stiffness as input, the natural frequency and resonance points of the transmission system can be calculated more accurately. The simulation modeling and calculation approach are experimentally verified, and the simulation results are valid and closer to the real resonance.

Optical Fiber Spool Acoustic Wave Resonances Employing a Mach-Zehnder Interferometer in Vacuum Chamber

Abstract The longitudinal, flexural, and torsional modes of acoustical resonances are presented for a long and small thickness cylindrical fiber spool. The fiber spool is built using a monomode optical fiber tightly wound in a helix form around a cylindrical Styropor. The acoustical resonance values are obtained using a Mach Zehnder interferometer with the fiber spool in the long (2 km) arm and a small linewidth laser. To reduce spurious signals, the interferometer was placed inside a vacuum chamber. The measured and theoretical results reasonably agree up to the first fifteen resonant longitudinal modes and for the first five flexural and torsional resonant modes, with a span from 10 Hz up to 200 Hz.

In-Plane-Sense Magnetometer Based on Torsional MEMS With Vertically-Interlaced Combs via Self-Alignment Technique

We present a MEMS magnetometer based on the Faraday electromagnetic induction principle that works in the torsional resonance mode to sense in-plane magnetic fields. As for the device design and fabrication, a self-alignment technique is introduced to realize vertically-interlaced combs used for electrostatic driving for a torsional frame structure. In order to directly acquire relatively pure resonance characteristics of devices, an electromagnetic detection means with differential outputs is proposed to suppress the parasitic feed-through effect existing in the normal electrostatic-detection. Based on magnetic response tests, the proposed device has the measured sensitivity of 491 mV/mT with the non-linearity of 0.40% and the resolution of 6 μT under atmospheric pressure. Featured with the quasi-zero power consumption (75 nW), the measurement bandwidth without mechanical bandwidth limits, and the wide dynamic range (98 dB), this in-plane-sense device constituting as an essential for a 3-axis MEMS magnetometer has wide application prospects in automotive and portable electronics.

A resonant microcantilever sensor for in-plane multi-axis magnetic field measurements

A novel magnetic field sensor is developed based on the microcantilever resonator to realize the parameter measurements of in-plane multi-axis magnetic field under different vibration modes. The working equations of the resonant sensor are established to calculate the strength and direction angle of measured magnetic field based on different resonances. The strength components of magnetic field along x-axis and y -axis are independently measured by the proposed resonant sensor under flexural and torsional resonant modes, respectively. The corresponding outputs of the sensor are linearly related to the magnetic field strength components. The finite element simulations are performed not only to prove the capability of the sensor to measure magnetic field under different modes, but also indicate the mode coupling of microcantilever resonator existed in the measurement. Thus, the coupling compensation method is proposed by amending ouput voltage of the sensor through experiments. The experimental results at atmospheric pressure show that the compensated accuracies of in-plane magnetic field are 3.06% (strength) and 1.59% (angle), and the measuring sensitivities are 98.79 µV mT−1 along x-axis and 92.46 µV mT−1 along y -axis, respectively.

Three-Dimensional Atomic Force Microscopy for Sidewall Imaging Using Torsional Resonance Mode.

This article presents an atomic force microscopy (AFM) technique for true three-dimensional (3D) characterization. The cantilever probe with flared tip was used in a home-made 3D-AFM system. The cantilever was driven by two shaking piezoceramics and oscillated around its vertical or torsional resonance frequency. The vertical resonance mode was used for upper surface imaging, and the torsional resonance mode was used for sidewall detecting. The 3D-AFM was applied to measure standard gratings with the height of 100 nm and 200 nm. The experiment results showed that the presented 3D-AFM technique was able to detect the small defect features on the steep sidewall and to reconstruct the 3D topography of the measured structure.

Use of CFD to predict trapped gas excitation as source of vibration and noise in screw compressors

This paper investigates the source of noise in oil free screw compressors mounted on highway trucks and driven by a power take-off (PTO) transmission system. Trapped gas at the discharge side is suggested as possible source of the excitation of low frequency torsional resonance in these compressors that can lead to noise and vibration. Measurements and lumped mass torsional models have shown low frequency torsional resonance in the drive train of these compressors when they are mounted on trucks. This results in high torque peak at the compressor input shaft and in part to pulsating noise inside the machine. The severity of the torque peak depends on the amplitude of the input torque fluctuation from the drive (electric motor or truck engine). This in turn depends on the prop-shaft angle. However, the source of the excitation of this low torsional resonance inside the machine is unknown. Using CFD with mesh motion at every 1° rotation of the rotors, it is shown that the absence of a pressure equalizing chamber at the discharge can lead to trapped gas creation, which can lead to over-compression, over-heating of the rotors, and to high pressure pulsations at the discharge. Over-compression can lead to shock wave generation at the discharge plenum and the pulsation in pressure can lead to noise generation. In addition, if the frequency of the pressure pulsation in the low frequency range coincides with the first torsional frequency of the drive train the first torsional resonance mode can be excited.

Dynamic nano-triboelectrification using torsional resonance mode atomic force microscopy.

Understanding the mechanism of charge generation, distribution, and transfer between surfaces is very important for energy harvesting applications based on triboelectric effect. Here, we demonstrate dynamic nanotriboelectrification with torsional resonance (TR) mode atomic force microscopy (AFM). Experiments on rubbing the sample surface using TR mode for the generation of triboelectric charges and in-situ characterization of the charge distribution using scanning Kelvin probe microcopy (SKPM) were performed. This method allows the tip to perform lateral oscillation and maintains the tip-sample interaction in the attractive region to ensure high efficiency of the charge generation during the rubbing process. The measured efficiency of generating triboelectric charges can achieve ~10.53 times higher than conventional static/contact mode in the triboelectrification experiments. In addition to the charge generation, local discharging experiments were also performed. This work would provide a new method to generate patterned charges and also be helpful in understanding the mechanism of nanotriboelectrification.

High-sensitivity imaging with lateral resonance mode atomic force microscopy.

In the operation of a dynamic mode atomic force microscope, a micro-fabricated rectangular cantilever is typically oscillated at or near its mechanical resonance frequency. Lateral bending resonances of cantilevers are rarely used because the resonances are not expected to be detected by the beam-deflection method. In this work, we found that micro-cantilevers with a large tip produced an out-of-plane displacement in lateral resonance (LR), which could be detected with the beam-deflection method. Finite-element analysis indicated that the presence of a large tip is the major source of the out-of-plane coupling for the LR. We also imaged a heterogeneous sample by operating a cantilever in LR, torsional resonance, and tapping modes. LR mode yielded a small deformation and noise level in the height maps as well as a high contrast and small noise level in the phase maps. LR mode also had a resonance frequency that was orders of magnitude higher than that of tapping mode. Operation with LR mode may have the benefits of high-speed scanning, high-sensitivity imaging, and mapping of in-plane mechanical properties of the sample surface. In general, LR mode may become a powerful new atomic force microscopy technique for characterizing sample materials.

Design Rules for Temperature Compensated Degenerately n-Type-Doped Silicon MEMS Resonators

The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from $2.4 \times 10^{17}$ to $7.5 \times 10^{19}~{\rm cm}^{-3}$ . Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lame/square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of $\sim 150$ ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below $7.5 \times 10^{19}~{\rm cm}^{-3}$ . However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond $10^{20}~{\rm cm}^{-3}$ . [2015-0018]

Determining elastic moduli of concrete using resonance

The elastic moduli of rods of material can be determined by resonance techniques. The torsional, longitudinal, and transverse resonance modes for a rod of known mass and length can be measured experimentally. These resonance frequencies are related to the elastic properties of the material, hence, by measuring these quantities the strength of the material can be determined. Preliminary tests as proof of principle are conducted with metallic rods. Data and experimental techniques for determining the elastic moduli for concrete using this procedure will be presented.

Shape effect of torsional resonance mode AFM cantilevers operated in fluids

Nanoscale resolution, high scanning rate, and non-destructive measurement are highly desirable attributes for imagining living cells in fluids. Torsional resonance (TR) mode is a promising approach that can satisfy these requirements. In this study, we have fabricated scanning probes with suitable cantilever designs for use in TR mode in fluids, using computer simulation as an aid in the design and fabrication iterations. Several geometrical parameters of cantilevers were considered and simulated for mechanical properties and dynamic characteristics, and selected designs were fabricated for performance evaluation. The influences of design parameters on scan performance were investigated by statistical analysis. Based on this approach, we designed and fabricated optimal cantilevers that can be operated in TR mode in water with high quality (Q) factor (∼60), high resonance frequency (∼240 kHz), and low spring constant (∼0.14 N m−1). Overall, O-shape cantilevers have demonstrated superior Q factors to typical rectangular shape, A-shape and V-shape designs.

Torsional resonance mode atomic force microscopy in liquid with Lorentz force actuation

In this work, we present a design based on Lorentz force induction to excite pure torsional resonances of different types of cantilevers in air as well as in water. To demonstrate the atomic force microscopy imaging capability, the phase-modulation torsional resonance mode is employed to resolve fine features of purple membranes in a buffer solution. Most importantly, force-versus-distance curves using a relatively stiff cantilever can clearly detect the characteristic oscillatory profiles of hydration layers at a water–mica interface, indicating the high force sensitivity of the torsional mode. The high resonance frequencies and high quality-factors for the torsional mode may be of great potential for high-speed and high-sensitivity imaging in aqueous environment.

Phase and amplitude patterns in DySEM mappings of vibrating microstructures

We use a dynamic scanning electron microscope (DySEM) to analyze the movement of oscillating micromechanical structures. A dynamic secondary electron (SE) signal is recorded and correlated to the oscillatory excitation of scanning force microscope (SFM) cantilever by means of lock-in amplifiers. We show, how the relative phase of the oscillations modulate the resulting real part and phase pictures of the DySEM mapping. This can be used to obtain information about the underlying oscillatory dynamics. We apply the theory to the case of a cantilever in oscillation, driven at different flexural and torsional resonance modes. This is an extension of a recent work (Schröter et al 2012 Nanotechnology 23 435501), where we reported on a general methodology to distinguish nonlinear features caused by the imaging process from those caused by cantilever motion.

Torsional resonance mode magnetic force microscopy: enabling higher lateral resolution magnetic imaging without topography-related effects

We present experimental work that reveals the benefits of performing magnetic force microscopy measurements employing the torsional resonance mode of cantilever oscillation. This approach provides two clear advantages: the ability of performing magnetic imaging without topography-related interference and the significant lateral resolution improvement (approximately 15%). We believe that this work demonstrates a significant improvement to a versatile magnetic imaging technique widely used in academia and in industry.

Systematic study of the dolomite (104) surface by bimodal dynamic force microscopy in ultra-high vacuum

We have investigated the morphology and structure of dolomite MgCa(CO3)2(104) surfaces by bimodal dynamic force microscopy with flexural and torsional resonance modes in ultra-high vacuum at room temperature. We found that the surface slowly decomposes by degassing CO2 in a vacuum and becomes covered by amorphous clusters, presumably MgO and CaO. By choosing an optimal sample preparation procedure (i.e. cleaving in a vacuum and mild annealing for stabilizing clusters for a short time), atomically clean surfaces were obtained. The complex tip–sample interaction, arising from carbonate groups and Mg and Ca atoms of the surface, induces a large variety of atomic-scale imaging features.

Torsional and Lateral Resonant Modes of Cantilevers as Biosensors: Alternatives to Bending Modes

We show here novel cantilever designs that express torsional and lateral modes exhibit excellent mass-change sensitivity to molecular self-assembly on gold (75-135 fg/Hz) which is superior to that of widely investigated bending modes. Lead zirconate titanate (PZT) millimeter-sized cantilevers were designed with two types of anchor asymmetry that induced expression of either torsional or lateral modes in the 0-80 kHz frequency range. Experiments and supporting calculations show that anchor asymmetry enables resonant mode impedance-coupling. The sensitive torsional and lateral modes enabled measurement of self-assembled monolayer formation rate at picomolar levels. The anchor design principle was extended to microcantilevers via finite element simulations, which caused both 97% sensitivity improvement relative to conventional designs, as well as new nonclassical resonant mode shapes.

A General Approach of Damping Torsional Resonance Modes in Multimegawatt Applications

In large-drive applications, load-commutated inverters (LCIs) are one of the most used technologies mainly because of their excellent reliability records. However, LCIs are known to generate interharmonics. They can interact with the mechanical system at torsional natural frequencies of the rotating train, on both the inverter and rectifier sides in weakly connected power systems, such as offshore oil and gas platforms. These interactions can lead to accelerated shaft fatigue, lifetime reduction, gear damage, and system blackouts. On the other hand, pulsewidth-modulated (PWM) voltage-source inverters (VSIs) are known to produce less torque ripple compared to LCIs. Consequently, VSIs are supposed to be less subject to exciting torsional resonances in mechanical shaft systems. Even with reduced torque ripple, mechanical failures have been consistently reported due to motor air-gap torques supplied by PWM drives. This paper is focused on solving torsional vibration issues. Due to system uncertainties, these issues cannot be excluded in the design phase of LCIs and VSIs for high-power applications. With regard to LCIs, the dc-link inductance is used as an integrated energy-storage unit. Motor and generator interactions are therefore decoupled. Excited eigenmodes on the grid side are damped with the rectifier; the inverter is driving the variable-speed motor. This approach is also successfully applied to damping resonance modes in the motor side. Simulation and selected experimental results on a 30-MW LCI system are provided to validate the proposed design approach. As for VSIs, a more general approach of damping or controlling excited shafts is proposed. This method is successfully applied using the dc-link capacitor as an integrated energy-storage source. This approach is used to optimize the design of new systems; otherwise, it is used to improve the performance of existing systems with minor modifications.