Estimation Of Deflection Research Articles

Deflection Estimation of Bending Beam Structures Using Fiber Bragg Grating Strain Sensors

This paper uses strains measured by fiber Bragg grating (FBG) sensors to estimate the static or dynamic deflection curve of bending beam structures. The deflection estimation method is only based upon the geometric equations of a beam structure without knowing the material information. At each cross section of a beam structure, two FBG strain sensors are installed, and the curvature at the cross section can be estimated by using the two measured strains from the geometric equation. Then the curvature function is assumed as a polynomial function and the coefficients can be estimated using least squares method. Finally, the deflection curve is estimated by integrating the curvature function twice. For dynamic deflection estimation, since only the geometric equations are used, and at each time step, the geometric equations can be also used for a dynamic system. Therefore, at each time step, the deflection can be estimated using the proposed method and the dynamic deflection can be finally obtained. The method is verified by the simulations of a continuous beam under static loads and experimental tests of a simply supported beam under various static loads. A simply support beam under moving loads is also simulated to verify the method for dynamic deformation estimation. All the numerical and test results show that the method can estimate the static and dynamic deflection curve of beam structures with a high accuracy.

An Electrothermally Actuated VO2-Based MEMS Using Self-Sensing Feedback Control

A self-sensing approach is used to accurately control the large displacements observed in VO 2 -based microelectromechanical systems actuators. The device is operated electrothermally using integrated resistive heaters. The coupling of the abrupt electrical and mechanical changes in VO 2 films across its phase transition allow for the estimation of the device's deflection by monitoring the film's resistance. Furthermore, the typical hysteretic behavior observed in VO 2 films is significantly reduced in the present device and the need for optical testing equipment is eliminated. The displacement-resistance relationship is modeled by a memoryless Boltzmann function consisting of four parameters, which are optimized to fit the experimental data with an average error of 1.1 μm throughout the complete actuation range of 95 μm. The estimated deflection is used as feedback to achieve closed-loop micropositioning control of the device, which is designed from the system dynamics obtained experimentally. Closed-loop sinusoidal and step reference response experiments are performed in order to show the effectiveness of the self-sensing feedback technique used. In the closed-loop sinusoidal frequency response, a cutoff frequency of 43 Hz is observed with a maximum actual deflection error of 0.19 dB up to the phase margin frequency of 30 Hz. In the step response, an average actual displacement steady-state error of ±1.15 μm is obtained with response times ranging from 5 to 12 ms.

On-line Deflection Estimation of X-axis Beam on Positioning Machine

For high-precision devices, one of the most important factors that influence their positioning accuracy is the deflection in the mechanical structures. The finite-element method (FEM) is the most common method used to investigate deflections. However, it has such a high computational complexity that it cannot be used in real-time deflection correction applications. In this paper, to improve the accuracy of a positioning machine, an online deflection estimation method that has high accuracy and low computational complexity is proposed. First, by analyzing the mechanical characteristics of the beam, the effect of the positioning head on the beam is represented by four forces located at their contact points and a deflection estimation model is developed. Then, the uncertain parameters of this estimation model are identified by the use of the deflection values obtained from the FEM analysis. The final mathematical model is seen to result in deflection values that are very close to the values obtained by FEM analysis. The applicability of this novel method is discussed and algorithms are proposed that extend the approach to other general gantry structures. Finally, the approach is successfully verified under three typical cases indicating its advantages, w.r.t. estimation accuracy and decreased computational complexity.

Influence of co-firing process condition on low temperature co-fired ceramics membrane deflection

Purpose – The paper aims to present the influence of the co-firing process conditions of low temperature co-fired ceramics (LTCC) on the deformation of thin LTCC membranes. Design/methodology/approach – The statistical design of the experiment methodology was used in the frame of these investigations to reduce the time and costs of the experiments and to ensure easier interpretation of the obtained results. Moreover, this conception permits the rough estimation of the membrane deflection fired at optimal process conditions. Findings – The applied design of the experiment methodology allowed the researchers to find the optimal co-firing process conditions and to estimate the membrane deflection at the optimal process conditions. The estimation fits well with the results of real measurement that was conducted to confirm the estimation precision. Research limitations/implications – The experiment was conducted for only one type of LTCC, DP951. The precision of the design of the experiment optimization and estimation of the response at optimal conditions depend on the described object. Therefore, the findings of this paper do not have to be generally true for other LTCC tapes, and if other LTCC tapes deformation should be investigated, then similar analysis shall be conducted for them. Practical implications – The deformation of LTCC membranes affects the sensitivity and repeatability of LTCC acceleration and pressure sensors. Hence, the decrease of membrane deflection increases the usability of LTCC in such applications. Originality/value – This paper presents simple optimization of co-firing process conditions of LTCC devices using statistical design of the experiment.

Estimation of flexible needle deflection in layered soft tissues with different elastic moduli.

The estimation of needle deflection when the needle interacts with biological tissue is challenging in needle steering. Most previous studies have used homogeneous tissue models to estimate the deflection of a needle. However, biological tissue typically has a layered structure with variable mechanical properties and geometric features. In this study, we propose a needle deflection model with a double-layered elastic medium. Each layer possesses distinct mechanical properties, which result in inconsistent degrees of friction force on the needle surface, needle-cutting force, and forces caused by the stiffness of the elastic medium. The model uses the Rayleigh-Ritz method to analytically estimate the needle deflection. To validate the model, needle steering experiments were performed using double-layered tissue phantoms and porcine tissues. The experimental results revealed that changes in reaction force at the needle base occurred when the needle passed through the boundary between the two layers. The mean absolute error between the estimated and measured needle tip trajectory was 0.88±0.30mm for the double-layered tissue phantom and 1.85±0.73mm for the porcine tissue. These results are comparable with previous studies of homogeneous tissue. The proposed model could improve needle steering in biological tissues, which consist of multiple layers.

BEHAVIOR OF LATERALLY LOADED PILES IN COHESIVE SOILS

Pile foundations are often required to resist lateral loading. Lateral loads come from a variety of sources including wind, earthquakes, waves, and ship impacts. So, it is important to know the lateral load resistance capacity of pile foundation. This requires estimation of ultimate loads based on which safe working loads will be assessed and also estimation of pile deflections to ensure that serviceability aspects are accounted in the design Several methods are available for predicting the ultimate lateral resistance to piles in clay soil. However, these methods often produce significantly different ultimate resistance values. This makes it difficult for practicing engineers to effectively select the appropriate method when designing laterally loaded piles in clay soil. In this paper, lateral load behavior of single piles in clay soil was studied, for different L/D ratio by changing the diameter and length of pile. The analysis was carried out by considering free head pile. The influence of soil type, effect of pile length and pile diameter on the pile response was observed and the results obtained by IS2911Part1 (sec2) were compared with the Broms method. Also deflection and lateral load were calculated for a typical pile for various L/D ratio and their results were presented

SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects

In this paper, reinforced concrete beams subjected to blast and impact loads are examined. Two single degree of freedom models are proposed to predict the response of the beam. The first model (denoted as “energy model”) is developed from the law of energy balance and assumes that the deformed shape of the beam is represented by its first vibration mode. In the second model (named “dynamic model”), the dynamic behavior of the beam is simulated by a spring-mass oscillator. In both formulations, the strain rate dependencies of the constitutive properties of the beams are considered by varying the parameters of the models at each time step of the computation according to the values of the strain rates of the materials (i.e. concrete and reinforcing steels). The efficiency of each model is evaluated by comparing the theoretical results with experimental data found in literature. The comparison shows that the energy model gives a good estimation of the maximum deflection of the beam at collapse, defined as the attainment of the ultimate strain in concrete. On the other hand, the dynamic model generally provides a smaller value of the maximum displacement. However, both approaches yield reliable results, even though they are based on some approximations. Being also very simple to implement, they may serve as an useful tool in practical applications.

On the influence of radial displacements and bending strains on the large deflections of impulsively loaded circular plates

This work considers the validity of the assumption that the influence of radial displacements and bending strains can be ignored when constructing closed form analytical solutions for the large displacement response of impulsively loaded circular plates. Three successive energy based analyses are presented. The first analysis considers only membrane strains, but includes radial displacements in addition to transverse displacements. It is shown that the inclusion of radial displacements alters the plastic strain distribution but does not alter the integral of the total energy dissipated due to plastic strain, and consequently, does not affect the final central deflection estimate. This result provides a rigorous justification for the assumption that radial displacements can be ignored. However, though neglectable, the radial displacements are not negligible and must be included in order to obtain realistic strain distributions. Thereafter, a model is presented that considers the interaction of bending and membrane strains. It is shown that at large displacements the membrane strains suppress the effect of bending strains. This result supports the assumption that bending strains can be ignored at large deflections. Furthermore, it provides an estimate for the displacement range in which the interaction between bending and membrane effects is significant and should not be ignored. Lastly, the non-monotonic nature of the strain history is considered and shown to have a small effect.

Needle deflection estimation: prostate brachytherapy phantom experiments

The performance of a fusion-based needle deflection estimation method was experimentally evaluated using prostate brachytherapy phantoms. The accuracy of the needle deflection estimation was determined. The robustness of the approach with variations in needle insertion speed and soft tissue biomechanical properties was investigated. A needle deflection estimation method was developed to determine the amount of needle bending during insertion into deformable tissue by combining a kinematic deflection model with measurements taken from two electromagnetic trackers placed at the tip and the base of the needle. Experimental verification of this method for use in prostate brachytherapy needle insertion procedures was performed. A total of 21 beveled tip, 18 ga, 200 mm needles were manually inserted at various speeds through a template and toward different targets distributed within 3 soft tissue mimicking polyvinyl chloride prostate phantoms of varying stiffness. The tracked positions of both the needle tip and base were recorded, and Kalman filters were applied to fuse the sensory information. The estimation results were validated using ground truth obtained from fluoroscopy images. The manual insertion speed ranged from 8 to 34 mm/s, needle deflection ranged from 5 to 8 mm at an insertion depth of 76 mm, and the elastic modulus of the soft tissue ranged from 50 to 150 kPa. The accuracy and robustness of the estimation method were verified within these ranges. When compared to purely model-based estimation, we observed a reduction in needle tip position estimation error by [Formula: see text] % (mean [Formula: see text] SD) and the cumulative deflection error by [Formula: see text] %. Fusion of electromagnetic sensors demonstrated significant improvement in estimating needle deflection compared to model-based methods. The method has potential clinical applicability in the guidance of needle placement medical interventions, particularly prostate brachytherapy.

A New Loss and Deviation Model for Axial Compressor Inlet Guide Vanes

This paper describes a new universal algebraic model for the estimation of flow deflection and losses in axial compressor inlet guide vane devices. The model deals with nominal flow and far-off-design operating conditions in connection with large stagger angle adjustments. The first part of the model considers deflection and losses in 2D cascades, taking into account the main cascade geometry parameters and operating conditions, such as Mach number and stagger adjustment. The second part of the model deals with additional deviation and losses due to secondary flow caused by the end wall viscous effects and by the trailing vortices. The model is developed for NACA65 airfoils, NACA63-A4K6 airfoils, and airfoils having an NACA65 thickness distribution on a circular-arc camber line. It is suitable for application in 1D or 2D through-flow calculations for design and analysis cases. The development of the method is based on systematic computational fluid dynamics (CFD) flow calculations for various cascade geometries and operating parameters. The comparison of correlation results with experimental data for several test cases shows good agreement.

On Bending Characteristics of Skis in Use

Measuring ski deflection while skiing allows the characterization of essential aspects of the complex interplay between the skier's performance and the interaction of the ski with the snow. This provides an opportunity to optimize skis with regard to skiers’ skills and athletic ability, thus improving skiing performance. To establish an analysis system, we developed, characterized and tested a system capable of measuring ski deflection while skiing. Using competition-type slalom skis, we applied 30 strain gauge sensors - 15 on each ski. The strain gauges sampled data at 65Hz and the readings were translated into deflection estimates. This was done by validating the system using a specialized bending machine equipped with a laser sensor system to accurately track the changes in ski shape with increasing applied force. We sampled strain gauge data while the bending apparatus deformed the ski. The RMS error of our ski-shape estimates relative to laser-measured data was 11mm. In on slope tests, the center of mass (CoM) position and speed of a skier were acquired using a highly accurate differential Global Navigation Satellite System (dGNSS) at 50Hz and a pendulum model. From this data we estimated the CoM turn radii of carved turns. During the ski tests, the bending radii along the ski over time were obtained from strain gauge data and analyzed for each carved turn. We observed smaller radii relative to the path radii at the tip of a ski. We further analyzed the correlation between ski turn radius from deflection measurements and the CoM turn radius. The RMS error between radii calculated from deflection measurements and CoM radii obtained with a high resolution dGNSS was on average 1.26m, with the smallest error being 0.78m. We tested our system on a hard-snow slope and a soft-snow slope. Our system has manageable technological complexity and is potentially suitable as a training tool or for use in ski-fitting for skiers of various skill levels.

Analytical Qualification of Heliborne TDEM Equipments Subjected to Static, Shock and Vibration Loadings

In geophysical survey system, a Time Domain Electro-Magnetic (TDEM) technique is used to detect the presence of uranium in the earth crust. For heliborne survey, certain equipments, such as power converter and data acquisition system are installed on a helicopter. The power converter is responsible for the generation of high current pulses to feed the transmitter for setting up the required electromagnetic field. The power converter consists of a free running inverter, which sits over a DC-DC converter. Data acquisition system acquires data from various sensors for further processing and interpretation. Data acquisition system consists of a highly vibration sensitive onboard computer (IDAN boxes) rigidly mounted over a plate inside the data acquisition system enclosure. Since the power converter and data acquisition system are installed on the floor inside the surveying helicopter, it is mandatory to qualify these equipments for vibration & shock as per MIL standard before onboard installation. To evaluate the structural integrity of power converter and data acquisition system under various loading conditions of vibration and shock, a preliminary estimation of stresses and deflections was made by hand calculations and then, finite element analysis has been performed to optimize the design. Modal analysis has been performed to estimate the natural frequencies of power converter. Since the natural frequencies of the power converter were within the disturbing frequency range (i.e., 10 to 84 Hz), thickness of converter base plate and inverter base plate has been increased to avoid resonance. Since the data acquisition system consists of a highly vibration sensitive onboard computer, it has been proposed to mount it on isolators to minimize the vibration. To evaluate the structural integrity of data acquisition system under various loading conditions, finite element analysis has been performed. This paper presents the methodology adopted for design and analysis of the equipments for the specified input of vibration and shock.

A Numerical Study of the Flexural Behavior of Concrete Beams Reinforced with AFRP Bars

In this study, analytical and numerical investigations were extensively conducted to evaluate the flexural behavior of concrete beams reinforced with aramid fiber-reinforced polymer (AFRP) rebars. The AFRP-reinforced concrete beams were analyzed using the separated finite element method containing different elements for concrete and reinforcement. In addition, this study used two different effective moment of inertia expressions to estimate the load-deflection responses and the service-load deflections of the beams. The service-load deflections of the AFRP-reinforced concrete beams obtained from the finite element analysis were in close agreement with those from the effective moment of inertia expressions. The numerical ultimate moments also correlated well with the analytical values of concrete stress-strain models. Numerical analyses, which hardly predict the sudden reduction in the flexural rigidity of FRP-reinforced concrete beams due to the crushing of cover concrete, were shown to provide somewhat conservative deflection estimates.

Long-term lateral deflection of precast, prestressed concrete spandrel beams

Slender precast concrete spandrels are used to increase cost effectiveness of precast concrete parking structures. They reduce the number of column lines in building floor plans and the number of elements to transport and erect. However, these spandrels can be prone to larger deflections, as the increased slenderness can reduce sectional stiffness. Design of these structures should also consider vertical and lateral deflections because of the eccentric loading transferred from the deck double-tee beams. In this paper, the authors provide realistic estimates of long-term deflections for the next generation of spandrels. They also examine the sensitivity of long-term deflection to parameters such as spandrel type, span length, creep and load eccentricity. The results of their numerical study included the finding that long-term lateral deflections are less than corresponding lateral deflections.

Precise Photogrammetric Reconstruction Using Model-Based Image Fitting for 3D Beam Deformation Monitoring

Periodic structural health monitoring of infrastructure systems is important to avoid economic losses and human casualties. Traditionally, deformation monitoring has been done through surveying techniques. Recently, with the increased availability of inexpensive off-the-shelf cameras, photogrammetry has become a viable noncontact alternative for complete three-dimensional reconstruction of the object or surface of interest. This paper aims at combining two methodologies of photogrammetric reconstruction—image-matching-based reconstruction and model-based image fitting—to achieve submillimeter precision for the estimation of both vertical deflections and horizontal displacements. The proposed methodology was tested with data collected using a photogrammetric system at a structures laboratory where a concrete beam was subjected to different loading conditions by a hydraulic actuator. The experimental results showed that the photogrammetric system was capable of monitoring both static and dynamic deformations. The methodology used exhibited a high level of automation and the final results yielded a root-mean-square error (RMSE) of half a millimeter.

Fusion of Electromagnetic Trackers to Improve Needle Deflection Estimation: Simulation Study

We present a needle deflection estimation method to anticipate needle bending during insertion into deformable tissue. Using limited additional sensory information, our approach reduces the estimation error caused by uncertainties inherent in the conventional needle deflection estimation methods. We use Kalman filters to combine a kinematic needle deflection model with the position measurements of the base and the tip of the needle taken by electromagnetic (EM) trackers. One EM tracker is installed on the needle base and estimates the needle tip position indirectly using the kinematic needle deflection model. Another EM tracker is installed on the needle tip and estimates the needle tip position through direct, but noisy measurements. Kalman filters are then employed to fuse these two estimates in real time and provide a reliable estimate of the needle tip position, with reduced variance in the estimation error. We implemented this method to compensate for needle deflection during simulated needle insertions and performed sensitivity analysis for various conditions. At an insertion depth of 150mm, we observed needle tip estimation error reductions in the range of 28% (from 1.8 to 1.3mm) to 74% (from 4.8 to 1.2mm), which demonstrates the effectiveness of our method, offering a clinically practical solution.

Revised approach to assessing traffic speed deflectometer data and field validation of deflection bowl predictions

This study presents a revised approach to conceptualising and analysing data from the traffic speed deflectometer (TSD) which enables full deflection bowl predictions. The approach was successfully applied to TSD surface velocity measurements collected at seven test sites as part of recent Australian trials. More than 1500 deflection bowls produced from the TSD data were validated against approximately 600 40- and 50-kN falling weight deflectometer (FWD) deflection bowl profiles. Overall, the results showed a clear correlation between the shape and magnitude of deflection bowls predicted by both methods. Estimates of maximum deflection (d 0) and structural curvature index (SCI300) from both methods were also compared, showing a strong correlation. The results suggest that the TSD device has significant potential to be used to collect measurements of pavement deflection bowls at highway speeds which are comparable with FWD deflection bowl measurements.

Three-dimensional dynamic deflections and natural frequencies of a stiff footbridge based on measurements of collocated sensors

SUMMARY A redundant system of collocated geodetic sensors and an accelerometer were used to measure the displacements of a stiff, 40-m-long footbridge excited by essentially vertical synchronized jumps. A main output of the measurements was that excitations produced vertical deflections (of the order of several mm), lateral deflections with an amplitude about half that of the vertical, an effect known for various bridges, and also smaller-scale longitudinal deflections, probably induced by the vertical ones. This combination of deflections in three axes is not an artifact of measuring errors, or of limitations of specific instruments, and do not reflect random effects, for they have been observed in different experiments by different sensors (Global Navigation Satellite System-GNSS, i.e., Global Positioning System-GPS plus the Russian Global Navigation Satellite System-GLONASS), robotic total stations-RTS (or robotic theodolite), and an accelerometer, and were tested through control of the measurement errors from time series reflecting no bridge oscillations. In all cases, sensors provided similar estimates of deflections and of deflection-derived dominant frequencies, which were found equal to those derived from the accelerometer. The proposed instrumentation and methodology seem suitable to control deflections of bridges in cases that visibility of satellites is poor or is disrupted by vehicle circulation. Measurement-based modeling of bridges described might be useful for understanding the structural behavior of bridges under several types of dynamic loads and can contribute to the displacement-based design of structures. Copyright © 2013 John Wiley & Sons, Ltd.

Force-Sensor-Based Estimation of Needle Tip Deflection in Brachytherapy

A virtual sensor is developed for the online estimation of needle tip deflection during permanent interstitial brachytherapy needle insertion. Permanent interstitial brachytherapy is an effective, minimally invasive, and patient friendly cancer treatment procedure. The deflection of the needles used in the procedure, however, undermines the treatment efficiency and, therefore, needs to be minimized. Any feedback control technique to minimize the needle deflection will require feedback of this quantity, which is not easy to provide. The proposed virtual sensor for needle deflection incorporates a force/torque sensor, mounted at the base of the needle that always remains outside the patient. The measured forces/torques are used by a mathematical model, developed based on mechanical needle properties. The resulting estimation of tip deflection in real time during needle insertion is the main contribution of this paper. The proposed approach solely relies on the measured forces and torques without a need for any other invasive/noninvasive sensing devices. A few mechanical models have been introduced previously regarding the way the forces are composed along the needle during insertion; we will compare our model to those approaches in terms of accuracy. In order to conduct experiments to verify the deflection model, a custom-built, 2-DOF robotic system for needle insertion is developed and discussed. This system is a prototype of an intelligent, hand-held surgical assistant tool that incorporates the virtual sensor proposed in this paper.

Empirical Equation of Wire Sag Model for Semiconductor Packaging With Numerical and Experimental Verification

For the semiconductor packaging industry, the issue of wire sag has not been touched upon because only one single layer of wire bond is constructed along the perimeter of the chip system. Over-sag deflections may not cause any problems. However, driven by the demands for smaller and faster advanced microelectronic devices, modern 3-D and multichip modules have become the solution of choice in delivering higher integration and more multifunctional products to meet consumer needs. For 3-D and multichip packaging, excessive wire sag can lead to wires touching against the lower layer, causing a short-circuit and failure of chip functionality. Therefore, gaining knowledge of wire bond sag theory becomes extremely important for advanced packaging. We propose an empirical model to predict the sag stiffness of a wire bond. The sag stiffness of a wire bond is defined to represent its resistance to the sag drag force occurring during the encapsulation process by the molding flow. A higher sag stiffness of a wire bond gives the premise of less sag deflection, thereby avoiding short-circuiting and/or double wire crosstalk due to the closeness of the top-layer to the bottom-layer wire bonds. The theory of sag regarding semiconductor wire bonding has not been documented, to our knowledge, in the literature. Therefore, to deal with this issue, this paper will primarily focus on the theoretical and numerical analysis of sag deflection of a wire bond. A set of sag experiments is conducted to verify the validity of the sag model hypothesis outlined in the earlier paper. Subsequently, an empirical sag model could be put forward to predict the sag stiffness of a wire bond if the corresponding bond spans, bond heights, and material properties are known. The engineered design of a wire bond can be improved through the use of this sag equation. By making use of the proposed sag model, one can attain not only a first-order estimation of the sag deflection but also omit the tedious procedures of numerical analysis.