Showing papers on "Deflection (engineering) published in 2006"

Development of liquid-environment frequency modulation atomic force microscope with low noise deflection sensor for cantilevers of various dimensions

Abstract: We have developed a liquid-environment frequency modulation atomic force microscope (FM-AFM) with a low noise deflection sensor for a wide range of cantilevers with different dimensions. A simple yet accurate equation describing the theoretical limit of the optical beam deflection method in air and liquid is presented. Based on the equation, we have designed a low noise deflection sensor. Replaceable microscope objective lenses are utilized for providing a high magnification optical view (resolution: <3μm) as well as for focusing a laser beam (laser spot size: ∼10μm). Even for a broad range of cantilevers with lengths from 35to125μm, the sensor provides deflection noise densities of less than 11fm∕Hz in air and 16fm∕Hz in water. In particular, a cantilever with a length of 50μm gives the minimum deflection noise density of 5.7fm∕Hz in air and 7.3fm∕Hz in water. True atomic resolution of the developed FM-AFM is demonstrated by imaging mica in water.

An experimental, analytical and numerical study of the static behavior of steel beams reinforced by pultruded CFRP strips

Abstract: The paper presents the results of an experimental and numerical programme to characterize the static behaviour of steel beams reinforcement by pultruded carbon fibre reinforced polymer (CFRP) strips. Traditional H shaped steel beams with different CFRP reinforcement geometries bonded to the tension flanges using different epoxy adhesives were tested under three points bending configuration. Beams were not naturally or artificially corroded or notched but they were in good conditions before testing. The mid-span deflection and the strain along the whole CFRP lamina were recorded as function of the applied loading. The main objective of the experimental programme was the evaluation of the force transfer mechanism, the increment of the beam load carrying capacity and the bending stiffness. It allowed also to validate different analytical and numerical models for the static analysis of reinforced beams. In particular, a finite element model validated against the experimental data is presented.

Concrete Beams Strengthened with Prestressed Near Surface Mounted CFRP

Abstract: Retrofitting concrete structures with fiber reinforced polymer (FRP) has today grown to be a widely used method throughout most parts of the world. The main reason for this is that it is possible to obtain a good strengthening effect with a relatively small work effort. It is also possible to carry out strengthening work without changing the appearance or dimensions of the structure. Nevertheless, when strengthening a structure with external FRP, it is often not possible to make full use of the FRP. The reason for this depends mainly on the fact that a strain distribution exists over the section due to dead load or other loads that cannot be removed during strengthening. This implies that steel yielding in the reinforcement may already be occurring in the service limit state or that compressive failure in the concrete is occurring. By prestressing, a higher utilization of the FRP material is made possible. It is extremely important to ensure that, if external prestressing is used, the force is properly transferred to the structure. Most of the research conducted with prestressing carbon fiber reinforced polymer (CFRP) for strengthening has been on surface bonded laminates. However, this paper presents research on prestressed CFRP quadratic rods bonded in sawed grooves in the concrete cover. This method has proven to be an advantageous means of bonding CFRP to concrete, and in comparison to surface bonded laminates, the shear and normal stress between the CFRP and the concrete are more efficiently transferred to the structure. In the presented test, no mechanical device has been used to maintain the prestress during testing, which means that the adhesive must transfer all shear stresses to the concrete. Fifteen beams with a length of 4 m have been tested. The tests show that the prestressed beams exhibited a higher first-crack load as well as a higher steel-yielding load as compared to nonprestressed strengthened beams. The ultimate load at failure was also higher, as compared to nonprestressed beams, but in relation not as large as for the cracking and yielding. In addition, the beams strengthened with prestressed FRP had a smaller midpoint deflection. All strengthened beams failed due to fiber rupture of the FRP.

The roles of toughness and cohesive strength on crack deflection at interfaces

Abstract: In order to design composites and laminated materials, it is necessary to understand the issues that govern crack deflection and crack penetration at interfaces. Historically, models of crack deflection have been developed using either a strength-based or an energy-based fracture criterion. However, in general, crack propagation depends on both strength and toughness. Therefore, in this paper, crack deflection has been studied using a cohesive-zone model which incorporates both strength and toughness parameters simultaneously. Under appropriate limiting conditions, this model reproduces earlier results that were based on either strength or energy considerations alone. However, the general model reveals a number of interesting results. Of particular note is the apparent absence of any lower bound for the ratio of the substrate to interface toughness to guarantee crack penetration. It appears that, no matter how tough an interface is, crack deflection can always be induced if the strength of the interface is low enough compared to the strength of the substrate. This may be of significance for biological applications where brittle organic matrices can be bonded by relatively tough organic layers. Conversely, it appears that there is a lower bound for the ratio of the substrate strength to interfacial strength, below which penetration is guaranteed no matter how brittle the interface. Finally, it is noted that the effect of modulus mismatch on crack deflection is very sensitive to the mixed-mode failure criterion for the interface, particularly if the cracked layer is much stiffer than the substrate.

Wide-angle, low-voltage electro-optic beam deflection based on space-charge-controlled mode of electrical conduction in KTa1−xNbxO3

Abstract: An electro-optic beam deflector with unprecedented performance is demonstrated. A full deflection angle of 250mrad (=14.3°) has been achieved by applying only ±250V to a 0.5-mm-thick KTa1−xNbxO3 crystal with a short interaction length of 5.0mm. The operating principle is investigated and the origin of the deflection phenomenon is attributed to a nonuniform electric field induced by space-charge-controlled electrical conduction in the crystal.

The impulsive response of sandwich beams: Analytical and numerical investigation of regimes of behaviour

Abstract: An analytical model is developed to classify the impulsive response of sandwich beams based on the relative time-scales of core compression and the bending/stretching response of the sandwich beam. It is shown that an overlap in time scales leads to a coupled response and to the possibility of an enhanced shock resistance. Four regimes of behaviour are defined: decoupled responses with the sandwich core densifying partially or completely, and coupled responses with partial or full core densification. These regimes are marked on maps with axes chosen from the sandwich beam transverse core strength, the sandwich beam aspect ratio and the level of blast impulse. In addition to predicting the time-scales involved in the response of the sandwich beam, the analytical model is used to estimate the back face deflection, the degree of core compression and the magnitude of the support reactions. The predictions of the analytical model are compared with finite element (FE) simulations of impulsively loaded sandwich beams comprising an anisotropic foam core and elastic, ideally plastic face-sheets. The analytical and numerical predictions are in good agreement up to the end of core compression. However, the analytical model under-predicts the peak back face deflection and over-predicts the support reactions, especially for sandwich beams with high strength cores. The FE calculations are employed to construct design charts to select the optimum transverse core strength that either minimises the back face deflections or support reactions for a given sandwich beam aspect ratio or blast impulse. Typically, the value of the transverse core strength that minimises the back face deflection also minimises the support reactions. However, the optimal core strength depends on the level of blast impulse, with higher strength cores required for greater blasts.

Wireless power supply system for multiple electronic devices e.g. sensors, actuators has at least one field reinforcement or deflection unit that is brought into magnetic field such that resonance is adjusted

Abstract: An MF oscillator drives a primary winding to produce a magnetic field for wireless power supply to devices connected to a secondary winding. At least one field reinforcement or deflection unit (4) is brought into the magnetic field at a desired angle of inclination such that the field reinforcement or deflection unit is adjusted in resonance by the magnetic field. An auxiliary field produced over the resulting high resonance current increases a field range and the available field strength.

On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires

Abstract: Nanomechanical bending behavior and elastic modulus of silver nanowires (65–140nm∅) suspended across silicon microchannels were investigated using digital pulsed force mode (DPFM) atomic force microscopy through coincident imaging and force profiling. Deflection profiles analyzed off-line demonstrate the role of bending nanowire shape and symmetry in experimentally determining boundary conditions, eliminating the need to rely on isolated midpoint bending measurements and the usual assumptions for supported-end behavior. Elastic moduli for as-prepared silver nanowires ranged from 80.4±5.3to96.4±12.8GPa, which met or exceeded the literature values for bulk silver. The calculated moduli were based on classic modeling, both with one-dimensional analytical solutions and three-dimensional finite element analysis. Modeling results indicate that the classic models are accurate as long as the boundary conditions are not arbitrarily assumed but directly confirmed by data analysis. DPFM also facilitated the experime...

Elastic-Plastic Contact Between Rough Surfaces: Proposal for a Wear or Running-In Model

Abstract: A semi-analytical thermo-elastic-plastic contact model has been recently developed and presented in a companion paper. The main advantage of this approach over the classical finite element method (FEM) is the treatment of transient problems with the use of fine meshing and the possibility of studying the effect of a surface defect on the surface deflection as well as on subsurface stress state. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and a von Mises criterion is now used, which improves the plasticity loop. This improvement in the numerical algorithm increases the computing speed significantly and shows a much better convergence and accuracy. The contact model is validated through a comparison with the FEM results of Kogut and Etsion (2002, J. Appl. Mech., 69, pp. 657–662) which correspond to the axisymmetric contact between an elastic-perfectly plastic sphere and a rigid flat. A model for wear prediction based on the material removal during cyclic loading is then proposed. Results are presented, first, for initially smooth surfaces and, second, for rough surfaces. The effects of surface shear stress and hardening law are underlined.

Bump-type foil bearing structural stiffness : Experiments and predictions

Abstract: Gas foil bearings (FB) satisfy many of the requirements noted for novel oil-free turbomachinery. However, FB design remains largely empirical, in spite of successful commercial applications. The mechanical structural characteristics of foil bearings, namely stiffness and damping, have been largely ignored in the archival literature. Four commercial bump-type foil bearings were acquired to measure their load capacity under conditions of no shaft rotation. The test bearings contain a single Teflon-coated foil supported on 25 bumps. The nominal radial clearance is 0.036mm for a 38mm journal. A simple test setup was assembled to measure the FB deflections resulting from static loads. The tests were conducted with three shafts of increasing diameter to induce a degree of preload into the FB structure. Static measurements show nonlinear FB deflections, varying with the orientation of the load relative to the foil spot weld. Loading and unloading tests evidence hysteresis. The FB structural stiffness increases as the bumps-foil radial deflection increases (hardening effect). The assembly preload results in notable stiffness changes, in particular for small radial loads. A simple analytical model assembles individual bump stiffnesses and renders predictions for the FB structural stiffness as a function of the bump geometry and material, dry-friction coefficient, load orientation, clearance and preload. The model predicts well the test data, including the hardening effect. The uncertainty in the actual clearance (gap) upon assembly of a shaft into a FB affects most of the predictions.

Fiber deflection probe for small hole metrology

Abstract: This paper presents the development of a new probing method for coordinate measuring machines (CMM) to inspect the diameter and form of small holes. The technique, referred to as fiber deflection probing (FDP), can be used for holes of approximately 100 μm nominal diameter. The expanded uncertainty obtained using this method is 0.07 μm (k = 2) on diameter. The probing system consists of a transversely illuminated fiber (with a ball mounted on the end) whose shadows are imaged using a camera. We can infer the deflection of the probe from the motion of the image seen by the camera, and we infer the position of the measured surface by adding the fiber deflection along x- and y-directions to the machine scale readings. The advantage of this technique is the large aspect ratio attainable (5 mm deep for a 100 μm diameter hole). Also, by utilizing the fiber as a cylindrical lens, we obtain sharp crisp images of the fiber position, thus enabling high resolution for measured probe deflection. Another potential advantage of the probe is that it exerts an exceptionally low force (ranging from a few micronewtons down to hundreds of nanonewtons). Furthermore, the probe is relatively robust, capable of surviving more than 1 mm over-travel, and the probe should be inexpensive to replace if it is broken. In this paper, we describe the measurement principle and provide an analysis of the imaging process. Subsequently, we discuss data obtained from characterization and validation experiments. Finally, we demonstrate the utility of this technique for small hole metrology by measuring the internal geometry of a 129 μm diameter fiber ferrule and conclude with an uncertainty budget.

Rack-mounted air deflector

Abstract: One or more air deflection assemblies are used to redirect air emitted by computers in a rack-based computer system. These air deflection assemblies may be used to redirect air emerging horizontally out of the back sides of computers into a vertically-oriented exhaust plenum. This can eliminate the need for exhaust fans to draw heated air through the exhaust plenums and out of the rack.

Microplates-based rheometer for a single living cell

Abstract: We developed a new versatile micron-scale rheometer allowing us to measure the creep or the relaxation function (time analysis), as well as to determine the dynamical complex modulus (frequency analysis) of a single living cell. In this setup, a microscopic sample can be stretched or compressed uniaxially between two parallel microplates: one rigid, the other flexible. The flexible microplate is used as a nanonewton force sensor of calibrated stiffness, the force being simply proportional to the plate deflection. An original design of the microplates allows us to achieve an efficient feedback control of either strain or stress applied to the cell. Controlling the flexible plate deflection with a typical precision of less than 200nm, we are able to apply stresses ranging from a few pascals to thousands of pascals with a precision better than 2%. The control of the flexible plate deflexion is achieved by direct imaging of the plate tip on a photosensitive detector mounted on the phototube of an inverted mic...

Prediction of workpiece elastic deflections under cutting forces in turning

Abstract: One of the problems faced in turning processes is the elastic deformation of the workpiece due to the cutting forces resulting in the actual depth of cut being different than the desirable one. In this paper, a cutting mechanism is described suggesting that the above problem results in an over-dimensioned part. Consequently, the problem of determining the workpiece elastic deflection is addressed from two different points of view. The first approach is based on solving the analytical equations of the elastic line, in discretized segments of the workpiece, by considering a stored modal energy formulation due to the cutting forces. Given the mechanical properties of the workpiece material, the geometry of the final part and the cutting force values, this numerical method can predict the elastic deflection. The whole approach is implemented through a Microsoft Excel © workbook. The second approach involves the use of artificial neural networks (ANNs) in order to develop a model that can predict the dimensional deviation of the final part by correlating the cutting parameters and certain workpiece geometrical characteristics with the deviations of the depth of cut. These deviations are calculated with reference to final diameter values measured with precision micrometers or on a CMM. The verification of the numerical method and the development of the ANN model were based on data gathered from turning experiments conducted on a CNC lathe. The results support the proposed cutting mechanism. The numerical method qualitatively agrees with the experimental data while the ANN model is accurate and consistent in its predictions.

Active integration of tool deflection effects in end milling. Part 1. Prediction of milled surfaces

Abstract: Tools deflection that occurs during machining, and especially when flexible tools such as end mills are used, can result in dimensional errors on workpieces. The study presented here is part one of a two-part paper: it deals with the estimation of cutting forces and the prediction of milled surface. The second part will focus on a methodology that allows to optimize the production rate by compensating the deflection and meeting the part tolerance. Cutting force models have been and are still the subject of a lot of research. The model used is based on Kline and Devor's [5]: a polynomial approximation whose coefficients are obtained by least square methodology is used for the calculation of cutting forces. The machined surface (two axis machining) is determined using the contact point methodology and some experimental tests are done to validate the models.

Long-Term Behavior of Timber–Concrete Composite Beams. II: Numerical Analysis and Simplified Evaluation

Abstract: This second part of two companion papers investigates the contribution of different rheological phenomena and thermohygrometric variations on long-term behavior of timber–concrete composite beams (TCCs) in outdoor conditions. The numerical algorithm presented and validated against two experimental tests in the first part is employed with this aim. Such a model fully considers all rheological phenomena and, therefore, leads to rigorous solutions. Effects on the beam response include the creep and mechanosorptive creep of both timber and connection, along with concrete creep and shrinkage, and may markedly increase the elastic deflection due to live load. The inelastic strains due to yearly and daily variations of environmental conditions (temperature and relative humidity) produce an important fluctuation of the deflection. A simplified method, which is suitable for practical design of TCCs under long-term loading, is at last proposed. The effects of load, concrete shrinkage, and inelastic strains due to environmental variations are evaluated one by one using approximate formulas and are then superimposed. Creep and mechanosorptive creep are taken into account by adopting modified elastic moduli. The reliability of the proposed method is checked by way of some comparisons with numerical results. The applicability for the case of TCCs in heated indoor conditions is also discussed.

Pile Behavior Due to Excavation-Induced Soil Movement in Clay. I: Stable Wall

Abstract: A series of centrifuge model tests has been conducted to investigate the behavior of a single pile subjected to excavation-induced soil movements behind a stable retaining wall in clay. The results reveal that after the completion of soil excavation, the wall and the soil continue to move and such movement induces further bending moment and deflection on an adjacent pile. For a pile located within 3 m behind the wall where the soil experiences large shear strain (>2%) due to stress relief as a result of the excavation, the induced pile bending moment and deflection reach their maximum values sometime after soil excavation and thereafter decrease slightly with time. For a pile located 3 m beyond the wall, the induced pile bending moment and deflection continue to increase slightly with time after excavation until the end of the test. A numerical model developed at the National University of Singapore is used to back-analyze the centrifuge test data. The method gives a reasonably good prediction of the induced bending moment and deflection on a pile located at 3 m or beyond the wall. For a pile located at 1 m behind the wall where the soil experiences large shear strain (>2%) due to stress relief resulting from the excavation, the calculated pile response is in good agreement with the measured data if the correct soil shear strength obtained from postexcavation is used in the analysis. However, if the original soil shear strength prior to excavation is used in the analysis, this leads to an overestimation of the maximum bending moment of about 25%. The practical implications of the findings are also discussed in this paper.

Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate

Abstract: The quadrilateral area co-ordinate method is used to formulate a new quadrilateral element for Mindlin–Reissner plate bending problem. Firstly, an independent shear field is assumed based on the locking-free Timoshenko's beam formulae; secondly, a fourth-order deflection field is assumed by introducing some generalized conforming conditions; thirdly, the rotation field is determined by the strain–displacement relations. Furthermore, a hybrid post-processing procedure is suggested to improve the stress/internal force solutions. Following this procedure, a new 4-node, 12-dof quadrilateral element, named AC-MQ4, is successfully constructed. Since all formulations are expressed by the area co-ordinates, element AC-MQ4 presents some different, but beneficial characters when compared with other usual models. Numerical examples show the new element is free of shear locking, insensitive to mesh distortion, and possesses excellent accuracy in the analysis of both thick and thin plates. It has also been demonstrated that the area co-ordinate method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. Copyright © 2005 John Wiley & Sons, Ltd.

Active integration of tool deflection effects in end milling. Part 2. Compensation of tool deflection

Abstract: This study presents a compensation method in milling machining in order to take into account tool deflection during tool-path generation. Tool deflection that occurs during machining, and especially when flexible tools such as end mills are used, can result in dimensional errors on workpieces. The study presented here is part two of a two-part paper. In part one the cutting force models and the surface prediction method have been presented. Here the focus is on tool deflection effects' integration during the generation of the tool path. A strategy is proposed that modifies the nominal tool trajectory, compensates for the machining errors due to tool deflection, without degrading the production performance and the machined accuracy. The methodology allows optimization of the tool path trajectory in order to achieved a specified tolerance. Some experimental results are presented.

Force-Deflection Spectroscopy: A New Method to Determine the Young's Modulus of Nanofilaments

Abstract: We demonstrate the determination of Young's modulus of nanowires or nanotubes via a new approach, that is, force-deflection spectroscopy (FDS). An atomic force microscope is used to measure force versus deflection (F-D) curves of nanofilaments that bridge a trench patterned in a Si substrate. The FD data are then fit to the Euler-Bernoulli equation to determine Young's modulus. Our approach provides a generic platform from which to study the mechanical and piezoelectric properties of a variety of materials at the nanoscale level. Young's modulus measurements on ZnS (wurtzite) nanowires are presented to demonstrate this technique. We find that the Young's modulus for rectangular cross section ZnS nanobelts is 52 +/- 7.0 GPa, about 30% smaller than that reported for the bulk.