Linear Variable Differential Transformer Research Articles

Understanding the dynamic properties of trees using the motions constructed from multi-beam flash light detection and ranging measurements.

Measuring the three-dimensional motion of trees at every position remains challenging as it requires dynamic measurement technology with sufficient spatial and temporal resolution. Consequently, this study explores the use of a novel multi-beam flash light detection and ranging (LiDAR) sensor to tackle such a sensing barrier. A framework is proposed to record tree vibrations, to construct the motions of tree skeletons from the point-cloud frames recorded by the LiDAR sensor and to derive the dynamic properties of trees. The feasibility of the framework is justified through measurement on a Ficus microcarpa under pull-and-release tests. The relative differences for the first two modal frequencies between the LiDAR and linear variable differential transformer measurements in the displacement Fourier spectra are 0.1% and 2.5%, respectively. The framework is further adopted to study the dynamic response of different trees subjected to typhoons, including a Liquidambar formosana, three Araucaria heterophylla trees, a Sterculia lanceolata, a Celtis sinensis, a Tabebuia chrysantha and a Cinnamomum camphora. Results suggest that broadleaved trees might exhibit vibration in a wide frequency band, whereas the coniferous trees could follow a distinct dominant frequency.

Experimental Study on the Coupling Mechanism of Sensors under a Strong Electromagnetic Pulse.

This paper presents a study on the electromagnetic effects of a main fuel control system under the action of a strong electromagnetic pulse. It assesses the electromagnetic sensitivity of a speed sensor and a linear variable differential transformer (LVDT) sensor. This assessment focuses on the control system’s electromagnetic effects and the sensors’ coupling signals. The effects and signals were determined using radiation and pulse current injection tests. Analysis of the signal at the system power port shows that it is the same as those for the two test methods. Based on analysis of the working mechanism and terminal signals of the sensors, the electromagnetic sensitivity of the system is different under the different electromagnetic pulse conditions. The electromagnetic sensitivity characteristics of the sensors were verified, and the electromagnetic effects of the main fuel regulation control system were analyzed. Meanwhile, the degree of sensor coupling mechanism caused by the electromagnetic coupling effects of the main fuel regulation control system under strong electromagnetic pulses were studied. These findings have clear practical implications for electromagnetic pulse protection of aero-engine control systems.

Central fixation element type and length affect glenoid baseplate micromotion in reverse shoulder arthroplasty.

Reverse shoulder arthroplasty (RSA) is commonly used to treat patients with rotator cuff tear arthropathy. Loosening of the glenoid component remains one of the principal modes of failure and represents a significant complication that requires revision surgery. This study assessed the effects of various factors on glenoid baseplate micromotion for primary fixation of RSA. A half-fractional factorial design of experiment was used to assess 4 factors: central element type (central peg or screw), central cortical engagement according to length (13.5 or 23.5 mm), anterior-posterior peripheral screw type (nonlocking or locking), and cancellous bone surrogate density (160 or 400 kg/m3, 10 or 25 PCF). Glenoid baseplates were implanted into high- or low-density Sawbones rigid polyurethane foam blocks and cyclically loaded at 60° for 1000 cycles (500-N compressive force range) using a custom-designed loading apparatus. Micromotion at the 4 peripheral screw positions was recorded using linear variable differential transformers. Central peg fixation generated 358% greater micromotion at all peripheral screw positions compared with central screw fixation (P<.001). Baseplates with short central elements that lacked cortical bone engagement generated 328% greater micromotion than those with long central elements (P=.001). No significant effects were observed when varying anterior-posterior peripheral screw type or bone surrogate density. There were significant interactions between central element type and length (P<.001). A central screw and a long central element that engaged cortical bone reduced RSA baseplate micromotion. These findings serve to inform surgical decision making regarding baseplate fixation elements to minimize the risk of glenoid loosening and, thus, the need for revision surgery.

Harmonic Balance Method to Analyze the Steady-State Response of a Controlled Mass-Damper-Spring Model

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA), were applied to suppress the undesired oscillations of the harmonically-excited car. 2D and 3D graphical plots are included based upon the equations resulting from the harmonic balance method. Moreover, a numerical simulation was established using the fourth order Rung–Kutta technique in order to confirm the overall controlled behavior of the studied model.

High-rate (20 Hz) single-frequency GPS/GALILEO variometric approach for real-time structural health monitoring and rapid risk assessment

Real-time monitoring and the rapid risk assessment of the engineering structures after a natural event is crucial to prevent further disasters. Global Navigation Satellite System (GNSS) relative positioning and Precise Point Positioning (PPP) have been widely used in determining the seismic waveform and structural displacement. On the other hand, variometric approach (VA) is a future-promising method in capturing the real-time dynamic motions. VA technique has been broadly used in real-time co-seismic displacement retrieval so far. However, the usability of the high-rate single-frequency (SF) variometric approach in real-time structural health monitoring has not been investigated in the literature, yet. This paper examines the ability of the SF-VA based on 20 Hz GPS-only and GPS/GALILEO observations to capture high-frequency dynamic displacement and time difference displacement. The dynamic harmonic motions with various frequency and amplitude values were created using a single-axis shake table. In addition to that 1995 Kobe earthquake’s ground motion was also tested on the shake table to evaluate the performance of SF-VA for GNSS seismology applications. Displacement time and frequency series of SF-VA were compared with a series of Linear Variable Differential Transformer (LVDT) sensor installed to the shake-table. The comparisons show that SF-VA can effectively capture the harmonic motions’ vibrational frequencies and displacement amplitudes. The observed amplitudes of the displacement of harmonic movements are slightly different from the LVDT values at the order of millimeters. Thus, it is found that the SF-VA approach is a powerful and reliable tool in real-time structural health monitoring and rapid risk assessment.

Linear-Range Extension for Linear Variable Differential Transformer Using Hyperbolic Sine Function.

In this paper, a circuit technique to extend the measuring range of a linear variable differential transformer (LVDT) is proposed. The transfer characteristic of the LVDT contains the odd function form of the cubic polynomial. Therefore, the measuring range of a commercial LVDT is linear in a narrow range compared to its physical dimensions. The wide measuring range of the LVDT requires a large structure of the LVDT, which increases the scale and the cost of the measurement system. The measuring range of the LVDT can be linearly extended to the maximum of the stroke range using the proposed technique. The realization of the proposed technique is based on the use of the hyperbolic sine (sinh) function of the electronic circuit building block, named the class AB bipolar amplifier. The class AB bipolar amplifier can be obtained by the current feedback operational amplifier (CFOA). The circuit of the proposed technique requires two CFOAs and an operational transconductance amplifier (OTA) as the active devices and all devices used in the proposed technique to synthesize the sinh function are commercially available. The proposed technique exhibits an ability to compensate for the nonlinear characteristic of the LVDT without digital components. The proposed technique is attractive in terms of its simple circuit configuration, small size, and low cost. The linear range extension of the LVDT used in this paper is significantly increased with a maximum error of about 18.3 μm of 6.2 mm at the full stroke range or the full-scale percentage error of about 0.295%. The results indicate that the proposed technique provides excellent performance to extend the measuring range of the LVDT without modifying the LVDT structure.

One-Year Push-Off specimens using cocktail and polymeric fibres at elevated temperatures

Shear failure is generally considered to be among most of the critical topics in reinforced concrete structures due to specific features that shear failure possesses, including no warning signs and brittle nature, especially after exposed to elevated temperature. The push-off model is adopted to investigate the shear performance at the current study using different types of fibres. Two mixes have been tested herein, i.e., one mix contains 4 kg/m3 of polymeric fibres whereas the other mix contains cocktail fibres, i.e., 2 kg/m3 of polymeric fibres and 40 kg/m3 of steel fibres simultaneously. Test setup is designed to measure the deformations occurred at the shear surface plane using means of Linear Variable Differential Transformers (LVDTs), fixed horizontally and vertically on both faces of the specimen. Thus, two different deformations are investigated: vertical displacement considered as “crack slip” and horizontal displacement considered as “crack width”. Each concrete mix is investigated by exposing the related specimens to one of the five different maximum temperatures adopted. Results showed that, at ambient temperature, shear capacity is significantly increased by the virtue of using cocktail fibres, while insignificant increase is noticed using polymetric fibres only. However, significant decrease is noticed when elevated temperatures are included for both mixes.

Enhancement of punching strength in GFRP reinforced single footings by means of handmade GFRP shear bands

In the present study, four set of full scale specimens have been cast to investigate the effects of handmade GFRP shear bands on punching behavior of single footings. To do so, the specimens’ reinforcement was designed so that the punching failure governed. Besides, two types of concrete mixture, i.e. normal concrete (NC) and self-compacting lightweight concrete (SCLC) were used. Five Linear Variable Differential Transformer (LVDT) sensors have been installed on each specimen to record settlement as well as deflections. Moreover, the amounts of strain of bars and shear bands, caused by loading, at the edge of baseplate and two-way shear critical section have been recorded by installing strain gauges. The results show that the use of GFRP shear bands results in the increase of cracking resistance, maximum tolerable deflection, and recorded peak loads. In addition, it led to an increase of failure time which could warn occupants before complete failure.

Wireless SmartVision system for synchronized displacement monitoring of railroad bridges

AbstractThe deflection of railroad bridges under in‐service loads is an important indicator of the structure's health. Over the past decade, an increasing number of studies have demonstrated the efficacy of using vision‐based approaches for displacement tracking of civil infrastructure. These studies have relied primarily on external processing of manually recorded videos of a structure's motion to estimate displacements. To date, vision‐based techniques applied to long‐term structural health monitoring have yet to be proven effective as an alternative to the traditional displacement measurement methods, such as linear variable differential transformers. This paper proposes a wireless SmartVision system (WSVS) that uses edge computing to directly output bridge displacements that can be sent to the end user. The system estimates displacements using both target‐free and target‐based approaches. A synchronized sensing framework is developed for multipoint displacement estimation using several wireless vision‐based nodes for full‐scale displacement‐based modal analysis of structures. Pose estimation using an AprilTag, a fiducial marker, is employed with a modified algorithm for improved displacement tracking of targets installed on a bridge, yielding subpixel accuracy. The robustness of the results in field conditions is enhanced by linking a tracking quality factor to each timestamp to handle vision‐related uncertainties. To meet the need for precise error metrics evaluation, an inexpensive cyber‐physical setup using a synthetic testing environment is also developed in this study. Following laboratory validation, field tests on a cable‐stayed pedestrian bridge were performed to demonstrate the efficacy of the proposed WSVS.

Accurate structural displacement monitoring by data fusion of a consumer-grade camera and accelerometers

The displacement responses of bridge structures are critical both for structural health monitoring and structural safety evaluation. Using vision-based sensors to measure structural displacement responses is an effective method and has attracted considerable attention owing to its advantages of achieving non-contact, time-saving, and full-field measurements. However, there are several obstacles, including the limited frame rate, insufficient accuracy in large-scale measurements, and camera instability, which prevent the application of vision-based sensors. To overcome the shortcomings and improve the accuracies of the vision-based sensors, a displacement monitoring system combined with a consumer-grade camera and accelerometers was developed. Accelerometers attached to the target structures were used to reconstruct the dynamic displacement for data fusion with the vision-based displacement, while an accelerometer attached to the camera was used for camera vibration cancellation. Dynamic loading tests on a self–anchored suspension model bridge were conducted and results of the proposed system, the linear variable differential transformers, and a conventional vision-based system were compared. Field tests on a steel–concrete composite continuous beam bridge and a cable-stayed railway bridge were conducted, and the potential of the proposed system for use in real structures was validated.

One-year push-off specimens using cocktail and polymeric fibres at elevated temperatures

Purpose This study aims to test push-off specimens at elevated temperatures. This research work is part of the author’s PhD work. The author has published several of the significant findings that were remarkably cited in short time. This research is a continuation of that work, yet it has new findings as well. The author hopes this to be accepted and published.Design/methodology/approachThe approach that was used herein is widely used in the field i.e., the push-off specimen testing. The author has used this approach to investigate the shear performance of concrete exposed to elevated temperatures. In addition, the author has used means of Linear Variable Differential Transformers (LVDTs) to record the displacements of the loading.FindingsResults showed that, at ambient temperature, shear capacity is significantly increased by the virtue of using cocktail fibres, while insignificant increase is noticed using polymeric fibres only. However, significant decrease is noticed when elevated temperatures are included for both mixes.Originality/valueMany of the research findings here were accepted as New Scientific Results in my PhD Thesis. The novelty is remarkable and was appreciated by the committee.

Effects of asymmetric tooth profile on single-tooth stiffness of polymer gears

Abstract As a result of polymer materials development and the use of additive manufacturing technologies, gear wheels made of polymer materials are becoming widespread in many areas of the industry. In recent years, determining the dynamic behavior of polymer gears has gained significant importance because it is desired to carry more loads and operate at higher speeds. Since it is one of the most critical factors affecting dynamic behavior, tooth stiffness should also be determined. In this study, the single-tooth stiffness (STS) of polymer gears with symmetrical and asymmetrical profile was measured experimentally with a unique test setup. Force was applied to three different points on the tooth, and the resulting deflection was measured with the help of linear variable differential transformer and a high-speed camera. Using the obtained deflection values, STS of the polymer tooth was calculated depending on the pressure angle. The experimental results are also compared with the finite element model created, and it is found that the results are matched well. As a result of the study, it is determined that the drive-side pressure angle of the polymer gear increased from 20° to 32°, and the tooth stiffness increased by approximately 10.8%.

Field programmable gate array implementation of an intelligent soft calibration technique for linear variable differential transformers

Background: Displacement is often used as an indirect indicator for monitoring multiple parameters, i.e. force, velocity, acceleration, and weight, making it an important variable for the measurement and control of processes. Sensors such as Linear Variable Differential Transformers (LVDTs) play a primary role in the design of any displacement measuring instrument. Calibration of an instrument is carried out to produce accurate results from the measuring instrument. Methods: The objective of this study is to calibrate the output of LVDT by designing a signal conditioning circuit so as to extend the linearity range of the sensor to 100% of the full scale input range, and also allows the measurement technique to adapt to variations in the physical parameters of the LVDT, the supply frequency, and the temperature. An optimized neural network is trained to produce linear and adaptive output from the raw data obtained from LVDT. Optimization is achieved by choosing the best neural network algorithm, number of hidden layers and transfer function of neurons which produce the least mean square error. The optimized neural network algorithm is implemented on a Field Programmable Gate Array (FPGA) chip for testing and validation in real life. Results: Experimental results show that the proposed technique was able to extend the linearity of LVDT and make the output adaptive for variations in physical parameters of LVDT, supply frequency and temperature. Conclusions: Accurate measurement of displacement is essential in many process applications, and a good calibration technique is required to produce accurate measurement. The presented calibration technique using optimized neural network algorithms has produced reliable measurements as desired.

Exploring deep carbonate reservoir samples: Anisotropy and correlation of static and dynamic Young’s moduli

In total, 14 limestone samples, drilled in the vertical and horizontal directions from a depth &gt;3 km, are analyzed to understand the correlation between static (operating at in-situ strain levels) and dynamic (at a sound wave strain level) Young’s moduli, [Formula: see text] and [Formula: see text], and also to investigate their directional dependence. Young’s moduli are measured simultaneously under a confining pressure of 30 MPa to a differential axial stress of 50 MPa using a triaxial frame with linear variable differential transformers: two axial and one radial calibrated with a standard aluminum slug. Static and dynamic moduli decrease with increasing porosity whereas the static moduli are typically less than the dynamic moduli. The static measurements exhibit significant hysteresis indicating a nonlinear (irreversible) regime, whereas the dynamic moduli, measured with low-strain amplitude, indicate a linear (reversible) regime. The static Poisson’s ratio increases with porosity, but the dynamic ratio remains unchanged over the whole range of porosity, which seems to not be sensitive enough to the heterogeneity in the pore structure. The induced microfractures, naturally developed under tensile stress after these deep samples were brought to the surface, are imaged in computer microtomography (micro-CT) scan experiments. The mineralogical composition is determined as higher than 95% calcite CaCO3and mapped out using quantitative evaluation of minerals by scanning electron microscopy. Elastic anisotropy is observed with increasing porosity, where the ratio [Formula: see text]/[Formula: see text] increases for the vertical but decreases for the horizontal samples. Likewise, a permeability anisotropy also is observed as porosity increases, where the ratio of the vertical to horizontal permeability [Formula: see text]/[Formula: see text] is higher than one, indicating a preferred vertical structure for fluid flow. Two linear correlations between [Formula: see text] and [Formula: see text] are developed for the studied calcite samples, and for samples composed of up to 30% dolomite CaMg(CO3)2reported in the literature.

Dowels effectiveness investigation between ultra high performance fiber reinforced concrete and reinforced concrete

In the present study, the performance of Reinforced Concrete (RC) beams which were strengthened with Ultra High Performance Fiber Reinforced Concrete (UHPFRC) and dowels at the interface was investigated. RC beams with a length of 2.2 m strengthened with UHPFRC layers at the tensile side. Before the application of the layers, the interface between RC and UHPFRC was roughened. During the testing, the interface slips between UHPFRC and RC were recorded using Linear Variable Differential Transformers (LVDTs). The beams were tested under four-point flexural test. The results of the present study indicated that the dowels at the interface reduce the slips at the interface, delay the formation of cracks and result in higher load carrying capacity.

Challenges and perspectives for integral bridges in the UK: PLEXUS small-scale experiments

This study focuses on the investigation of the factors that have limited, so far, the development of a consistent design and assessment approach for integral bridges (IBs). This paper presents a review of previous research and current design practices for IBs, followed by an overview of monitoring studies in the laboratory and in the field. As part of the UK Collaboratorium for Research on Infrastructure and Cities–Priming Laboratory EXperiments on Infrastructure and Urban Systems experimental campaign, a small-scale 1 g physical experiment is described. The test aimed to simulate the soil–structure interaction arising from seasonal expansion and contraction of the bridge deck and assess the performance of different monitoring techniques. Pressure cells were used to measure the lateral stresses behind the abutment wall, particle image velocimetry was employed to monitor the soil behaviour behind the abutment and linear variable differential transformers were used to monitor the backfill surface movements. By combining the data from these instruments, a preliminary assessment of the soil–structure interaction behaviour of the idealised integral abutment under seasonal thermal loading has been obtained. These monitoring methods and the associated understanding of IB behaviour gained from the tests provide definitive evidence for the development of monitoring systems for larger-scale physical tests and field monitoring systems for IBs.

Low-Cost Linearity Range Enhancement for Linear Variable Differential Transformer

This research proposes a low-cost and low-complexity technique to enhance the linearity range of linear variable differential transformer (LVDT) using logarithmic approximation and summing/subtracting operation. The proposed technique utilizes the feedforward approach and thus encounters no divide-by-zero behavior from inverse functions. The nonlinearity of LVDT can be counteracted by simply manipulating the parameters of the canceller circuit. Besides, the proposed technique can be applied to various LVDT nonlinearity types. The proposed linear enhancing circuit consists of operational amplifiers and a small number of passive elements. The nonlinearity cancellation could be further enhanced using a temperature-compensation circuit. Simulations were carried out using two different LVDT nonlinearity types: LVDT#1 and #2. The simulation results showed that the linearity enhancing circuit effectively enhances the LVDT linearity range, with the linearity errors of 0.51% and 1.83%, respectively. To validate, experiments were undertaken with the identical LVDT nonlinearity types using a circuit prototype, and the measured linearity errors are around 2.5% and 5.5%, respectively. The simulation and experimental results are agreeable with the theory, indicating that the proposed technique enhances the linearity range.

Biomechanical study of extramedullary and intramedullary fixation in the treatment of unstable intertrochanteric reversed-tilt fractures of the femur.

BackgroundTo investigate the efficacy of the 135° hip screw, 95° intramedullary hip screw (IMHS) and 95° hip screw in the treatment of intertrochanteric reverse dip fracture of the femur.MethodsWe retrospectively analyzed 125 matched pairs of human femurs (median age 64 years) which were osteotomized at a 33° angle in the left femur and extended downward from the minor trochanter to simulate a reverse oblique intertrochanteric fracture. The right femur served as a control. The left femur (n=4) was implanted with a 135° hip screw, 95° hip screw, or IMHS. A strain detector was placed distal to the fracture site to monitor fragment strain. The lateral displacement of the proximal femur was measured by a linear variable differential transformer. An Instron tester measured stiffness, strain, and lateral displacement at 25° adduction, and 90° adduction with vertical loads on the femoral head. A 2 cm gap was then formed at the fracture site to simulate comminution and the mechanical test was repeated.ResultsBefore the formation of the gap, there was no significant difference in stiffness among different bone structures (P>0.05), but after the formation of the gap, the stiffness of all the adduction structures decreased (P=0.03), and the difference in adduction was statistically significant (135° hip screw: 46.6%±3%; 95° hip screw: 22.9%±2%; IMHS: 53.7%±7.8%; P<0.05). Similar results were found for the abduction and buckling positions. There was no significant difference in the lateral displacement of the gap before (P=0.92) and after (P=0.26), but a significant difference in the failure load was found (135° hip screw: 1,222±560 N; 95° hip screw: 2,566±283 N; IMHS: 4,644±518 N; P=0.02).ConclusionsThere was no statistically significant difference in stiffness among different structures (P>0.05). However, in the presence of gaps, IMHS bone implant structures are much stiffer than 135° and 95° structures and have a greater destructive load.

Development of a portable Universal Testing Machine (UTM) compatible with 3D laser-confocal microscope for thin materials

The tensile test always delivers an in-depth understanding of true stress-strain relationship. However, it is not easy for the researchers to understand and evaluate the tensile properties of micro-specimens. This paper presents a research work aiming at the design and manufacturing of a small universal test machine (UTM) for measuring the mechanical properties of the miniaturised samples. The newly developed machine is sensitive to small loads and permits to obtain the stress-strain curves for thin materials. This portable UTM consists of a stepper motor, a load cell, a linear variable differential transformer (LVDT), a load cell amplifier and a data acquisition system. Copper based small and thin (50 μm) tensile test samples were tested on this machine at room temperature, and the calculated results were compared with the test results derived from a commercial UTM (METEX - 1 kN) to justify the validation of the developed apparatus. The obtained mechanical properties are in good agreement with the values obtained from a commercial UTM. To confirm the possibility of in-situ micro-observation, the surface roughness analysis has been conducted on the developed apparatus for pure copper foils under 3D laser-confocal microscope. Finally, it is concluded that this kind of testing apparatus could be manufactured within a manageable budget.

Design and initial validation of micro image strain sensing system based on digital microscope-camera

Strain response is one of the most widely used methods for structural health monitoring because of its high accuracy in static and dynamic measurement. Although several sensing technologies have been developed for strain measurement, they need specialized equipment such as fiber Bragg grating interrogator, which is costly and cumbersome for general structures, especially for small infrastructures. Therefore, a micro image strain sensing (MISS) method was improved based on our previous preliminary study. The novelty of MISS sensor is that digital microscope camera is adopted instead of the combination of smartphone and microscope for long-term monitoring. Moreover, the micro image strain sensing system was developed on the basis of improved speeded-up robust features (SURF) algorithm. Experimental results showed that the strain measured by the micro image strain sensing system is consistent with that measured by the linear variable differential transformer, indicating that the system is stable and robust. This system has the advantages of low cost, high accuracy, and easy to operate. It does not need interrogators and can be used to measure strain quickly even for non-professionals. The proposed micro image strain sensing method will serve as a promising strain measuring alternative in the field of structural health monitoring.