Torsional Resonance Mode Research Articles

Damping Torsional Interharmonic Effects of Large Drives

Current source thyristor converters are the most widespread technology for large drives, and today still a suitable choice for supplying high-power variable speed drives because of excellent reliability records. The integer and noninteger harmonics generated by line-commutated converters cause pulsating torque harmonics on the motor and on the grid side of the converter. Intersections of harmonic excitation frequencies with torsional natural frequencies of mechanical drive trains (motor-driven load or generator train) cannot always be avoided in the operating-speed range of the motor. Continuously generated harmonic torque excitations could have a critical impact on the torsional behavior of the entire train. It is therefore mandatory to perform torsional analyses during the design stage of large drives, as specified in API 617 [1] to avoid torsional interaction issues. In multiunit plants, more sophisticated analyses have to be performed, considering the fully coupled electrical and mechanical system. The risk for operational problems increases with increasing percentage of converter loads (converter power relative to the short circuit level of the grid). Some oil and gas production sites, e.g., offshore platforms, are based on island or island-like power systems. To mitigate the risk of torsional issues with increasing percentage of converter loads in weak power systems, new devices for damping torsional resonance modes have been developed and successfully tested. The effect of torsional mode damping will be explained by coupled electromechanical simulations and by measurement results from applying an integrated torsional mode damper (TMD) to a 30 MW gas compression train. The TMD does not require changes to the mechanical or electrical system design and can be designed as a retrofit control system extension for variable speed drives from different manufacturers.

Ultrasensitive detection of lateral atomic-scale interactions on graphite (0001) via bimodal dynamic force measurements

Enhanced sensitivity to lateral forces on the nominally flat and inert (0001) surface of graphite is demonstrated via room-temperature dynamic force microscopy using simultaneous excitation and FM detection of the lowest flexural and torsional cantilever resonance modes. The site-independent long-range tip-sample interaction causes no significant lateral force variations except near atomic steps but unprecedented sensitivity to short-range forces is achieved on flat terraces in the attractive range. Two-dimensional bimodal force vs distance maps confirm the stronger distance dependence of the torsional frequency shift compared to the flexural resonance shift. This agrees with model calculations based on theoretical expressions. The lateral force gradient is extracted from the measured torsional shift, and a lateral force variation in at most $\ifmmode\pm\else\textpm\fi{}20\text{ }\text{pN}$ is obtained by integrating this gradient parallel to the surface. A further integration reveals a potential-energy variation in the attractive force range of only 3 meV.

Pulsating Torques in PWM Multi-Megawatt Drives for Torsional Analysis of Large Shafts

This paper presents new, simple, and linear mathematical relationships to predict pulsating torque frequencies in industrial multi-megawatt pulse width-modulated (PWM) drives. The proposed relationships provide direct definition of possible drive operating points where the torsional resonance modes of the mechanical shaft assembly might be excited. The calculation accuracy of natural frequencies and the induction motor slip have been taken into account in the definition of a critical excitation band. Variable switching frequency PWM strategies have also been analyzed. Pulsating torque frequencies of complex load-commutated-inverter configurations have been proposed as complementary results. Several tests have been performed on an integrated-motor-compressor system operating at high-speed (3.3 kV, 6 MW at 10 000 r/min). Intensive simulation results of a higher power PWM drive for compressor applications are shown to validate the suggested approach. This paper is a key tool for electrical engineers involved in the design of multi-megawatt drive systems such as in liquefied natural gas compression and transportation, mining, or cements.

Flexural-torsional resonance mode of a chip cantilever system: Applications to nanomachining

Cantilever vibration modes beyond the first harmonic of the standard flexural vibration mode were intensely explored in atomic force microscopy (AFM) during the past years. One example for this development is the usage of the torsional resonance mode. Further, the lateral bending mode was investigated and applied in AFM imaging and measurement. Here, the authors report on an extraordinary resonance mode of a cantilever chip system. In this mode the cantilever performs flexural as well as torsional movements. The mode was investigated in detail by scanning laser-Doppler vibrometry. It was found that there exists an intermediate stripelike region between the cantilever and the chip, which significantly contributes to the mechanical vibrations. In addition simulations using the finite-element method were performed to explore possible natural modes of the chip cantilever system. Nanomachining was performed on samples in a highly efficient manner with help of the above described resonance mode. The atomic force microscope could be specialized for material processing tasks on the micro- and nanometer scales utilizing this resonance mode.

Amplitude and frequency modulation torsional resonance mode atomic force microscopy of a mineral surface

Scanning probe imaging in a shear force mode allows for the characterization of in-plane surface properties. In a standard AFM, shear force imaging can be realized by the torsional resonance mode. In order to investigate the imaging conditions on mineral surfaces, a torsional resonance mode atomic force microscope was operated in amplitude (AM) and frequency modulation (FM) feedback. Freshly cleaved chlorite was investigated, which showed brucite-like and talc-like surface areas. In constant amplitude FM mode, a slight variation in energy dissipation was observed between both surfaces. Amplitude and frequency vs. distance curves revealed that the tip was in repulsive contact with the specimen during imaging.

TORSIONAL RESONANCE MODE ATOMIC FORCE MICROSCOPY OF A PROTEIN–DNA COMPLEX

Precise mapping of protein-binding sites on DNA is an important application of atomic force microscope (AFM) imaging. For a reliable measurement of distances on curved DNA molecules, an image-processing algorithm is required, which extracts the DNA contour from topographic AFM data. To this end we implemented an image analysis method providing an efficient way to obtain the contour together with a physical map of single and multiple protein-binding sites. This method relies on a calculation of the height profile along the DNA fragment, allowing one to determine the DNA length and the relative position of the binding site occupied by a protein. As a first test, complexes of the LexA repressor protein from the Escherichia coli SOS system and DNA fragments containing a specific LexA binding site (recA operator) were imaged by the torsional resonance mode (TR mode) and analyzed using the specialized algorithm. A topographic height of less than 0.5 nm of the DNA molecules indicates repulsive imaging conditions.

Frequency modulated torsional resonance mode atomic force microscopy on polymers

In-plane mechanics of polymers can be probed by integrating frequency modulation and torsional resonance mode atomic force microscopy. We investigated a thin film of polystyrene-block-polybutadiene diblock copolymer. To gain more insight into image contrast formation, we examined displacement curves on polystyrene homopolymer surfaces of different molecular weights focusing on energy dissipation and frequency shift. Data suggest that the transition from a highly motile surface layer to the bulk material depends on the molecular weight of the polymer. This, in turn, indicates that the tip is slightly oscillating within the sample surface during imaging.

Frequency modulation torsional resonance mode AFM on chlorite (001)

In this paper, we discuss torsional resonance mode atomic force microscopy in frequency modulation (FM-TR-AFM) under ambient conditions. Freshly cleaved chlorite (001) exhibiting brucite-like and mica-like surface areas was investigated in constant amplitude operation in order to visualize topography and frictional properties. The measurements in frequency modulation allow the characterization of dissipative effects due to changes in the lateral forces between tip and sample.

Torsional Resonance Risk Management in Islanded Industrial Power Systems Supplying Large VFDs

This paper describes a design study for the power system for an industrial plant with islanded gas turbine generators (GTGs) and large variable frequency drives (VFDs). Examples discussed are based on the authors' experience of liquefied natural gas plants where VFDs are used as compressor drivers. The shaft of a GTG has mechanical torsional resonant modes which may be excited by the inter-harmonic currents produced by the VFDs. At the power levels considered, up to 90 MW for each compressor, the VFD converters should be arranged to give suitable harmonic and inter- harmonic characteristics. This paper describes real case studies and compares three LCI (load commutated inverter) VFD arrangements. Their advantages and limitations are analyzed; this highlights features that are different for each design for both the normal harmonics as well as for the inter-harmonics. It is shown that in islanded operation the GTGs cannot provide any electrical damping to the torsional vibration which implies that strict inter- harmonic limits should be applied in the design. PSCAD-EMTDC time domain simulation results are used to confirm the analysis and justify the considerations that are important in the design exercise.

Response of a laterally vibrating nanotip to surface forces

The torsional eigenmodes of atomic force microscope (AFM) cantilevers are highly sensitive toward in-plane material properties of the sample. We studied the effect of viscosity and lateral contact stiffness on the detuning, amplitude, and phase response numerically. To verify the theoretical considerations, a torsion mode AFM was operated in frequency modulation. During approach and retract cycles, we observed a negative detuning of the torsional resonant frequency close to the sample surface depending on the tilt angle between the tip and the sample. Thus, the tilt has a significant effect on the imaging process in torsional resonance mode.

Integrated cantilever sensors with a torsional resonance mode for ultraresoluble on-the-spot bio/chemical detection

Torsion-mode resonance is built in an integrated cantilever sensor for ultraresoluble detection of specifically bio/chemical mass adsorption. The superior mass resolution of the torsion-mode cantilever to a conventional bending-mode one is verified by energy-dissipation analysis and Q-factor simulation. With integrated transverse piezoresistance for frequency-shift signal readout and Lorentz force for resonance excitation, the torsion-mode sensor is optimally designed for high sensitivity. The microfabricated torsion-mode sensor is measured with a high close-loop Q factor in air. By Allan-variance analysis for the measured frequency stability, 23fg resolution is obtained for the torsion-mode sensor, which is much improved compared to the 313fg for the conventional flexure-mode sensor. The torsional sensor is used to recognize biotin-avidin specific combination, resulting in 443Hz frequency shift for 50μM streptavidin solution.

Coupling of cantilever lateral bending and torsion in torsional resonance and lateral excitation modes of atomic force microscopy

Torsional resonance (TR) mode and lateral excitation (LE) mode of atomic force microscopy (AFM) have been increasingly used in atomic and nanoscale surface imaging. In TR and LE modes, it is the changes of the cantilever dynamic characteristics caused by tip-sample interaction that reveal surface properties. For quantitative explanation of measured results, researchers have established dynamic models of TR and LE modes in which the AFM cantilever was modeled as a shaft in pure torsional vibration. However, the cantilever in TR and LE modes actually undergoes both torsion and lateral bending since due to lateral tip-sample interaction, not only a torque but also a lateral force are exerted on the cantilever. In this paper, a dynamic analysis is performed for TR and LE modes with the coupling between the cantilever torsion and lateral bending taken into account. Analytical solutions of cantilever responses are obtained considering linear viscoelastic tip-sample interaction. Through parametric analyses, we demonstrate that in TR and LE modes, the pure torsional approximation can provide accurate cantilever responses if the lateral tip-sample interaction is relatively weak compared to the cantilever torsional (or lateral bending) stiffness. Otherwise, lateral bending of the cantilever has to be considered in any endeavors for quantitative extraction of surface properties. The differences between the two modes due to the different excitation mechanisms are also discussed.

Simulation of dynamic modes of atomic force microscopy using a 3D finite element model

In dynamic atomic force microscopy (AFM), a cantilever is used to extract surface properties by observing the changes of its dynamic characteristics due to the tip–sample interaction. Analytical/numerical models that can accurately simulate the surface-coupled dynamics of the cantilever are essential for quantitative/qualitative understanding/explanation of measured results. In this paper, a comprehensive finite element model is developed for numerical simulation of free and surface-coupled dynamics of tip–cantilever system in dynamic modes of AFM. Representing the cantilever by three-dimensional beam elements, this model can simulate all the cantilever dynamic modes within a framework of the standard finite element method. Formulations reflecting the exact excitation mechanisms are derived for tapping mode (TM), torsional resonance (TR) mode, and lateral excitation (LE) mode. Under tip–sample interaction, the location/geometry of the tip and the tilting of the cantilever to the sample surface become important and can be easily addressed in this model. With the application of this finite element model, in TM, we show that phase shift of cantilever response and interaction force sensitively depend on in-plane mechanical properties but it is not true for cantilever vibration amplitude. The excitation of higher-order modes of vertical bending is observed in our simulation and its influence on data acquisition and interpretation is discussed. In TR and LE modes, torsion and lateral bending of the cantilever are coupled. We investigate how the torsion and lateral bending contribute to the twist of the cantilever and demonstrate that the lateral bending contribution can be ignored only if the lateral interaction is relatively weak compared to the cantilever stiffness of lateral bending. Tip eccentricity, if any, strongly affects amplitude and phase of cantilever responses and therefore cannot be ignored in TR and LE modes. The differences of TR and LE modes due to their different excitation mechanisms are also discussed. The presented model is capable of accurately simulating the cantilever dynamics under complex tip–sample interaction and might be used for quantitative extraction of surface properties.

AFM studies of environmental effects on nanomechanical properties and cellular structure of human hair

Characterization of cellular structure and physical and mechanical properties of hair are essential to develop better cosmetic products and advance biological and cosmetic science. Although the morphology of the cellular structure of human hair has been traditionally investigated using scanning electron microscopy and transmission electron microscopy, these techniques provide limited capability to in situ study of the physical and mechanical properties of human hair in various environments. Atomic force microscopy (AFM) overcomes these problems and can be used for characterization in ambient conditions without requiring specific sample preparations and surface treatment. In this study, film thickness, adhesive forces and effective Young's modulus of various hair surfaces were measured at different environments (humidity and temperature) using force calibration plot technique with an AFM. Torsional resonance mode phase contrast images were also taken in order to characterize the morphology and cellular structure changes of human hair at different humidity. The correlation between the nanomechanical properties and the cellular structure of hair is discussed.

Dynamic analysis of torsional resonance mode of atomic force microscopy and its application to in-plane surface property extraction

In the torsional resonance (TR) mode of atomic force microscopy (AFM), the changes in the torsion-related dynamic characteristics of a tip–cantilever system due to in-plane (lateral) tip–sample interaction are used for surface property imaging. This paper investigates the fundamental dynamics of a tip–cantilever system when it is operated in TR mode, with or without tip–sample interaction. With the actual location of the tip on the cantilever taken into consideration, modal analysis is carried out to obtain the cantilever TR frequencies/mode shapes under linear elastic tip–sample interaction. The relations of lateral contact stiffness and viscosity to torsional amplitude/phase shift are established. A comprehensive understanding on the effects of lateral contact stiffness and viscosity, driving frequency, and tip location on the cantilever torsional amplitude/phase shift is achieved by parametric analysis. The basic methodology to extract in-plane surface properties in TR mode is described. This work will help in advancing the development and applications of the techniques and instruments using TR mode of AFM.

Morphological, nanomechanical and cellular structural characterization of human hair and conditioner distribution using torsional resonance mode with an atomic force microscope

Characterization of the cellular structure and chemical and physical properties of hair are essential to develop better cosmetic products and advance the biological and cosmetic sciences. Although the morphology of the fine cellular structure of human hair has traditionally been investigated using scanning electron microscopy and transmission electron microscopy, atomic force microscopy can be used for characterization in ambient conditions without requiring specific sample preparations and surface treatment. In this study, the tapping and torsional resonance modes in an atomic force microscope are compared for measurements of stiffness and viscoelastic properties. The materials were mapped using amplitude and phase angle imaging. The torsional resonance mode showed advantages in resolving the in-plane (lateral) heterogeneity of materials. This mode was used for investigating and characterizing the fine cellular structure of human hair. Various cellular structures (such as the cortex and the cuticle) of human hair and fine sublamellar structures of the cuticle, such as the A-layer, the exocuticle, the endocuticle and the cell membrane complex were easily identified. The distribution and thickness of conditioner on the treated hair surface affects the tribological properties of hair. The thickness of the conditioner was estimated using force distance measurements with an atomic force microscope.

Dynamic lateral force microscopy with true atomic resolution

We present frequency modulation dynamic lateral force microscopy with true atomic resolution. Torsional resonance mode of a commercially available rectangular cantilever was used to detect interaction lateral force gradients caused between the tip and the sample surface. A slight negative frequency shift of the torsional resonance frequency was observed before contact to the silicon surface. Individual adatoms in a unit cell of the Si(111)-7×7 reconstructed surface were imaged with the constant frequency shift mode. Two sets of the neighboring corner adatoms and one set of the center adatoms on the dithering direction of the tip were connected on the image. This method has a great potential to observe friction between single atoms.

Quantitative extraction of in-plane surface properties using torsional resonance mode of atomic force microscopy

In the torsional resonance mode of atomic force microscopy (AFM), torsional amplitude and phase shift have been used for in-plane surface property imaging. However, no quantitative relation between torsional amplitude/phase shift and surface properties has yet been established. This paper studies how lateral contact stiffness and viscosity affect the torsional vibration of the cantilever in AFM. A basic methodology to extract in-plane surface properties is described and its effectiveness is demonstrated by quantitatively extracting the lateral contact stiffnesses and viscosities of two different materials: Si(100) and epoxy.

Characterization of microcantilevers solely by frequency response acquisition

A method is presented to determine the geometry of tipless microcantilevers by measuring the resonance frequencies of at least one of their bending, lateral and torsional resonance modes, and having knowledge of the beam's elastic modulus, Poisson's ratio and density. Once the geometry is known, the beam's stiffness and mass can be calculated. Measurement of multiple modes allows for multiple estimates of cantilever geometry. Multiple data points from the experimental results show that this approach yields dimensional values accurate to roughly 2.5% as compared to SEM-determined length, width and thickness. Stiffness values determined with this new technique are roughly 4.7% and 6.5% less than two existing characterization methods (i.e., Sader's method and Euler–Bernoulli beam theory predictions), and roughly 16% greater than Hutter and Bechhoefer's stiffness determination method.

A surface topography-independent friction measurement technique using torsionalresonance mode in an AFM

The recently introduced torsional resonance mode (TR mode) technique has been appliedfor friction force measurements at the micro/nanoscale. In this technique, an atomic forcemicroscope (AFM) with a vibrating cantilever tip in torsional mode is used, andthe contact torsional vibration amplitude of the tip motion (TR amplitude) ismonitored at a contact resonance frequency under constant normal load. In thispaper, the TR mode friction force images are compared to the friction force imagesacquired by conventional contact mode friction force microscopy on three samples:a self-assembled monolayer (SAM) with two phase structure, a silicon ruler, and a metalevaporated (ME) tape. The results from those samples show that the TR mode frictionforce images are much less affected by the surface topography and are almostindependent of the scanning direction of the tip, whereas this is not the case forthe contact mode friction force measurements. Mechanisms responsible for theseobservations are also discussed in the paper. In order to predict coefficient of frictionas a function of the change in the TR amplitude, an energy balance model isproposed.