Linear Variable Differential Transducers Research Articles

Monitoring local fiber volume fraction in preform lap joints using Hall‐effect sensors

AbstractThis article describes the use of Hall‐effect sensors for monitoring local values of the fiber volume fraction in vacuum‐assisted resin transfer molding. Nonintrusive sensors mounted on the vacuum bag enable monitoring at a large number of points, under molding inserts and around geometrical features. Magnets can be mounted on the outer face of nonmetallic moulds. Low‐cost sensors can be discarded if damaged and the signal is unaffected by ambient conditions. The technique is demonstrated for lap‐jointed preforms made from two different reinforcements. All results presented in the article are validated using linear variable differential transducers. Although preform thickness is higher at superimposed lap joints, the fiber volume fraction is significantly larger in the joints. Interlaid continuous plies lead to a more reproducible behavior. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers

Expanding implementation of an on-line measurement system of topsoil compaction in loamy sand, loam, silt loam and silt soils

A previously developed model for on-line prediction of soil compaction indicated as bulk density (BD), was limited in use for a sandy loam field. This study was undertaken to investigate the possibility of modifying this model for new soil textures, namely loamy sand, loam, silt loam and silt soils. Using the on-line measurement system of BD, measurements were carried out in four fields with different average textures of loam, sandy loam and silt loam and silt loam/silt fields. The on-line measurement system used consisted of a subsoiler, whom draught ( D) was measured with a single shear beam load cell and depth ( d) was measured with a wheel gauge consisted of a swinging arm metal wheel equipped with a linear variable differential transducer (LVDT). The soil gravimetric moisture content (MC) was measured with the oven drying method. The on-line measured BD was compared with measured BD with Kopecki rings (core sampling method) (736 samples), to validate the potential use of this sensor in the new studied soil textures. Results showed that the BD model can be used for on-line measurement of soil compaction for the selected textures. It was found that the correction factor ( M) of this model was mainly sensitive to variable MC, and slightly sensitive to clay content. The M at field scale varied between 0.994 (silt loam/silt soil with an average MC of 0.279 kg kg −1) and 1.171 (loam soil with an average MC of 0.105 kg kg −1). At almost the same texture, M varied between 1.171 for an average MC of 0.105 kg kg −1 and 1.122 for an average MC of 0.186 kg kg −1, which proves the domination of MC effect on M. The multiple linear regression (MLR) analysis (analysis of variance (ANOVA)) performed between MC and clay and M retained MC as M predictor ( P < 0.001, R 2 = 0.86). This MLR resulted in similar prediction accuracy of compacted zones as compared to the linear regression model between MC and M. In a variable texture field, the corrected BD model resulted in remarkable spatial similarity of BD between the corrected on-line and core sampling method. Therefore, it can be concluded that the BD model with the new M can be used for on-line measurement of soil compaction in loamy sand, sandy loam, loam, silt loam, and silt soils at different MC, bearing in mind that the difference in clay content is minimal (83–175 g kg −1).

A Linear Variable Differential Capacitive Transducer for Sensing Planar Angles

A linear variable differential capacitive transducer for the measurement of planar angles (from 0deg to 360deg) is presented in this paper. The sensor part of the transducer is made of parallel plates of standard and easy-to-fabricate shapes, and the signal-conditioning electronics are realized, employing a couple of simple relaxation oscillators. The output of the transducer is only dictated by a pair of dc reference voltages, and hence, high accuracy and linearity over the entire range (from 0deg to 360deg) are easily obtained by the use of precision dc reference voltages. Detailed analysis indicates that the sensitivity of the transducer is minimal for variations in different parameters. Experimental results obtained on a prototype transducer that has been built and tested establish the efficacy of the proposed transducer. The worst-case error of the prototype transducer is found to be less than 0.1%.

Quasi-distributed optical fibre extensometers for continuous embedding into concrete:design and realization

This paper reports on the design and realization of a new optical fibre sensor for continuousmeasurement of concrete strain over very long distances.We propose a composite-made wave-like sensor body that enables continuous bondingbetween optical fibre and concrete. Finite element analysis shows that the stiffnessof the optical fibre can be adapted to that of the concrete, reducing the strainconcentrations and the need for a theoretical calibration factor. Moreover, unlike the bodyof traditional I-shaped sensors, a wave-like sensor body enables a symmetricalresponse in tensile and compressive loadings whatever the contact conditions may be.We have realized optical fibre extensometers based on this technique and on alow-coherence interferometry method for the measurements. Despite its wave-shape, theproposed sensor body does not introduce any losses or strain that would result from fibremicrobending. The process of realization is adapted to distributed sensors and sensors witha very long gauge length. Furthermore, several sensors were multiplexed, demonstrating theability to perform quasi-distributed measurements. Once embedded into concrete cylinders,the optical fibre sensors were tested under compressive and tensile loading, and comparedwith traditional sensors. The allocation of one of the multiplexed sensors as a dummygauge provides self-compensation for thermal effects and ambient fluctuations.As a result, and without any calibration factor, optical sensor measurementsperfectly agreed with external linear variable differential transducer measurements.

Design of an expert measurement system for close-range photogrammetric applications

Digital photogrammetric systems have been used to solve various measurement problems in industrial applications for many years. Industrial line-scan video cameras have been widely used in these systems and in machine vision applications. This paper addresses the use of a digital photogrammetric expert measurement system for deformation measurements on the surface of concrete materials. The system consists of two industrial cameras having fixed-focus lenses. Because the accuracy of the photogrammetrically derived object data mostly depends on the camera calibration, the system had to be calibrated first. A 3-D wooden object was specially designed and constructed for that purpose. A measurement process of 17 steps was carried out to determine the displacements on the surface of the samples. Linear variable differential transducers were also used to measure the deformations in a conventional way. Data obtained from the two sets of measurements confirmed the system's reliability and allowed us to monitor surface behavior of the concrete samples under loading.

Development of on-line measurement system of bulk density based on on-line measured draught, depth and soil moisture content

On-line measurement of soil compaction is needed for site specific tillage management. The soil bulk density ( ρ) indicating soil compaction was measured on-line by means of a developed compaction sensor system that comprised several sensors for on-line measurement of the draught ( D) of a soil cutting tool (subsoiler), the soil cutting depth ( d) and the soil moisture content ( w ). The subsoiler D was measured with a single shear beam load cell, whereas d was measured with a wheel gauge that consisted of a swinging arm metal wheel and a linear variable differential transducer (LVDT). The soil w was measured with a near infrared fibre-type spectrophotometer sensor. These on-line three measured parameters were used to calculate ρ, by utilising a hybrid numerical–statistical mathematical model developed in a previous study. Punctual kriging was performed using the variogram estimation and spatial prediction with error (VESPER) 1.6 software to develop the field maps of ρ, soil w , subsoiler d and D, based on 10 m × 10 m grid. To verify the on-line measured ρ map, this map was compared with the map measured by the conventional core sampling method. The spherical semivariogram models, providing the best fit for all properties was used for kriging of different maps. Maps developed showed that no clear correlation could be detected between different parameters measured and subsoiler D. However, the D value was smaller at shallow penetration d, whereas large D coincided with large ρ values at few positions in the field. Maps of ρ measured with the core sampling and on-line methods were similar, with correlation coefficient ( r) and the standard error values of 0.75 and 0.054 Mg m −3, respectively. On-line measured ρ exhibited larger errors at very dry zones. The normal distribution of the ρ error between the two different measurement methods showed that about 72% of the errors were less than 0.05 Mg m −3 in absolute values. However, the overall mean error of on-line measured ρ was of a small value of 2.3%, which ensures the method accuracy for on-line measurement of ρ. Measurement under very dry conditions should be minimised, because it can lead to a relatively large error, and hence, compacted zones at dry zones cannot be detected correctly.

Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration

This paper compares results from dynamic live load tests using the non-contact laser Doppler vibrometer (LDV) system with those from two types of contact sensors. Bridge girder deflections and vibrations are simultaneously measured using a linear variable differential transducer (LVDT)-cable system (deflection) and geophone sensors (velocity), both attached to the girders, and the LDV, equipped with displacement and velocity signal decoders. Live load tests are performed on a 3-span continuous unit of the 9-span Doremus Avenue Bridge Replacement Project using 5-axle trucks of known weight and configuration. The Doremus Avenue Bridge is a composite steel slab-on-girder construction. Bridge response is compared for two of the 10 girders. Overall, the LDV measurements of deflection and velocity compare very well with those recorded by the contact sensors and may be used as an alternative to the two systems. Other advantages and disadvantages are also highlighted.

Time-Temperature and Time-Aggregate Gradation Superposition in Asphalt Mixes

ABSTRACT This study was devoted to evaluate the effect of aggregate gradation, temperature, and type of asphalt cement on the permanent deformation of Hot-Mix Asphalt (HMA). An experimental program was conducted to characterize the viscoelastic deformation response of asphalt mixture using the static creep test. The specimen was exposed to a constant vertical stress of 100 KPa and the vertical deformation of the specimen was monitored through linear variable differential transducers (LVDTs). All tests were conducted within a temperature-controlled chamber to keep the temperature constant throughout the test. Time-temperature and time-aggregate gradation shift factors for each evaluated type of HMA were estimated using plots of log time versus log creep compliance. If the deformations under reference temperature or reference gradation are known, those under given temperature or any given gradation can be obtained using shift factor. Also, viscoelastic models were developed to represent the deformation behavior of HMA under constant stress. The collected data was analyzed to study the effects of aggregate gradation, testing temperature, and asphalt consistency on creep behavior. The effect of temperature variation on creep behavior was found to be more significant at low temperatures and long loading time than those at high temperatures and short loading time. Moreover, aggregate gradation found to has a significant effect on creep behavior, the lowest creep deformation was for HMA prepared using ASTM upper limit gradation. While HMA prepared using ASTM mid-limits aggregate gradation was the least affected by temperature variation.

Shear Behavior of Full-Scale Post-Tensioned Prestressed Concrete Bridge Girders

Test data on shear behavior of full-scale posttensioned prestressed concrete girders (PPCGs) is very limited. Therefore, this study aimed to experimentally explore the shear behavior of PPCGs. Large-scale PPCGs were designed, fabricated, and tested on 1.2 m deep x 10.6 m long PPCGs with medium-high and high-strength concretes. The girders were tested to failure while deflections, steel stirrup strains, cracking pattern, and average strains in the web were monitored. The stirrup strains showed a sudden increase immediately after cracking and continue to grow as the load increases. To measure the average strains in 3 directions, triangular grids of linear variable differential transducers (LVDTs) were also placed at the shear regions of the girders. These LVDTs enable measurement of average strains in the vertical, longitudinal, and diagonal directions even after the diagonal cracking has occurred. Shear strains, principal strains, and principal directions were calculated from these measured average strains. It was found that the angle of principal strain direction decreases as the applied load increases and that it approaches ~23-25 deg at ultimate load.

Time-Temperature and Time-Aggregate Gradation Superposition in Asphalt Mixes

ABSTRACT This study was devoted to evaluate the effect of aggregate gradation, temperature, and type of asphalt cement on the permanent deformation of Hot-Mix Asphalt (HMA). An experimental program was conducted to characterize the viscoelastic deformation response of asphalt mixture using the static creep test. The specimen was exposed to a constant vertical stress of 100 KPa and the vertical deformation of the specimen was monitored through linear variable differential transducers (LVDTs). All tests were conducted within a temperature-controlled chamber to keep the temperature constant throughout the test. Time-temperature and time-aggregate gradation shift factors for each evaluated type of HMA were estimated using plots of log time versus log creep compliance. If the deformations under reference temperature or reference gradation are known, those under given temperature or any given gradation can be obtained using shift factor. Also, viscoelastic models were developed to represent the deformation behavior of HMA under constant stress. The collected data was analyzed to study the effects of aggregate gradation, testing temperature, and asphalt consistency on creep behavior. The effect of temperature variation on creep behavior was found to be more significant at low temperatures and long loading time than those at high temperatures and short loading time. Moreover, aggregate gradation found to has a significant effect on creep behavior, the lowest creep deformation was for HMA prepared using ASTM upper limit gradation. While HMA prepared using ASTM mid-limits aggregate gradation was the least affected by temperature variation.

Quantifying supercritical CO2 dilation of poly(vinylidene fluoride) and poly(vinylidene fluoride‐co‐hexafluoro‐propylene) utilizing a linear variable differential transducer: plasticization and melting behavior

AbstractMelting behavior of semicrystalline poly(vinylidene fluoride) (PVDF) and poly(vinylidene fluoride‐co‐hexafluoropropylene) is investigated as a function of supercritical CO2 pressure using a Linear Variable Displacement Transformer (LVDT). The melting temperature (Tm) of both polymers is lowered due to supercritical CO2 plasticization. For PVDF, the maximum lowering of Tm (ΔTm/n=23°C) occurs between 483 and 552 bar. The corresponding value for the copolymer is Δ Tm = 26°C at 552 bar. At higher pressures, hydrostatic effects override plasticization and Tm increases for both polymers. By comparing Tm in N2, a noninteracting gas, the opposing effects of plasticization and hydrostatic pressure on Tm are explored.

Forming Shaped/Molded Structures by Integrating Meltblowing and Robotic Technologies

A novel system is described that forms three-dimensional (3D) molded nonwoven structures through proper integration of a laboratory scale meltblown unit with a small die and a six-axis robot. The 3D fiberweb structures can be formed by deposition of fibers from the die of the meltblown unit, which is manipulated by the robot, on any desired 3D mold. The mold rotational and surface speeds can be controlled by an additional external axis. The die is connected by two flexible hoses to the melt extruder of the meltblown unit and a hot air supply system. This system directly sprays fibers onto a 3D mannequin mold to produce structures from polypropylene polymers. With varying degrees of success. several robot manipulation algorithms of fiber deposition on the mold are developed to accurately control the basis weight uniformity the fiberwebs. A rule-based control algorithm using a linear variable differential transducer to map the mold contour results in the greatest fiberweb basis weight uniformity.

A Novel Experimental Device for Measurement of Agglomerative Crystallization Forces

A novel experimental apparatus has been developed which enables the estimation of agglomeration forces between two crystals. The set-up consists of an inverted optical microscope, fitted with an adapted stage on which two micromanipulators are employed to hold a pair of micropipettes. The two crystals in close proximity within the supersaturated solution are then allowed to agglomerate over a fixed time period. The force necessary to break the agglomerate (e.g., the adhesion force between two agglomerated crystals) is measured by using two linear variable differential transducers, one of which detects the movement of the moving manipulator and the other one the fiexion of a calibrated fiexible blade. The geometry of crystal surfaces at the contact points and the dynamic development of the bond are captured on video camera and characterized using an image analysis technique. The experimental apparatus has been designed to allow control of supersaturation, orientation of crystal faces, distance between crystals, relative movement of crystals and contact time. Agglomerate adhesion forces ranging from 1 to 9×10 4 N per m 2 of contact area were measured for agglomerates of potash alum in aqueous supersaturated solutions. Several measurements were performed at varying levels of supersaturation. The experimental results show that the agglomeration force per unit contact area increases with increasing supersaturation. This evidence constitutes a fundamental validation of the experimental finding that crystal agglomerates become more difficult to disrupt at high supersaturation. The experimental results were used in combination with theoretical expressions for mechanical stresses on suspended particles in an agitated system to estimate the size of fragments to be expected in a crystallizer as a function of particle size and agitation conditions. These estimates proved to be within the range of values of fragment sizes measured in agitated suspensions of agglomerated crystals.

Development and Performance of Interlayer Stress-Absorbing Composite in Asphalt Concrete Overlays

An interlayer stress-absorbing composite (ISAC) was developed and evaluated for the purpose of effectively alleviating or mitigating the problem of reflection cracking in an asphalt concrete (AC) overlay. ISAC materials and performance properties were carefully selected through comprehensive theoretical studies and laboratory evaluation programs. The ISAC system consists of a low-stiffness geotextile as the bottom layer, a viscoelastic membrane layer as the core, and a very high stiffness geotextile for the upper layer. In order to evaluate the effectiveness of the ISAC layer to control reflective cracking, a laboratory pavement section with an AC overlay placed on a jointed portland cement concrete slab was constructed and tested in an environmental chamber. A mechanical device was used to simulate thermal strain in the slab, and the joint was opened and closed at an extremely slow rate. The testing was conducted at −1.1°C, and strain in the overlay was monitored using a sensitive linear variable differential transducer device. The force required to pull and push the slab was monitored using a load cell placed between the slab and a hydraulic ram. Performance of ISAC was evaluated by comparing the cycles to failure of an ISAC-treated overlay with the performance of a control section without ISAC and of test sections containing two commercially available products. The base isolation properties of the ISAC system were demonstrated in the laboratory evaluation studies, which indicated that the ISAC system vastly outperformed the control section and the sections with the two commercial products tested. Several years of field performance testing have show that the ISAC system is highly effective for mitigating reflective cracking in AC overlays used on both airport and highway pavement systems.

Simple Performance Test for Fatigue Cracking and Validation with WesTrack Mixtures

Viscoelastic characterization of asphalt concrete in indirect tensile (IDT) testing and development of a simple performance test for fatigue cracking are described. A 50-mm gauge length was adopted to measure the horizontal and vertical deformations with surface-mounted linear variable differential transducers on an IDT specimen with a 100- or 150-mm diameter and 38-mm thickness. The effect of a concentrated load under loading strips on vertical displacement within the 50-mm gauge length was evaluated by the digital image correlation method, a noncontact, full-field displacement and strain measurement technique. The theory of viscoelasticity was used to develop analytical solutions for creep compliance and center strain from displacements measured on the specimen surface. These solutions were verified by three-dimensional finite element viscoelastic analysis. IDT creep and strength tests were performed on fine and coarse mixtures from WesTrack with various asphalt contents and air void contents, and various parameters determined from the analysis of these data were compared with the known fatigue performance of these mixtures from the WesTrack testing facility. The fracture energy obtained from viscoelastic analysis of the IDT strength test at 20°C correlated highly with the field performance of these mixtures at WesTrack.

Contributing factors of mandibular deformation during mouth opening

Objectives: A decrease in mandibular arch width during forced opening has been documented. However, the contributing factors of mandibular deformations are still unclear. This study investigated the mandibular deformation during mouth opening, and searched for contributing factors related to this phenomenon. Methods: Sixty-two dental students volunteered for this study. A linear variable differential transducer (LVDT) was cemented on the mandibular first molars to record mandibular deformation during mouth opening. Proposed factors including geometric factors of the mandible such as lower gonial angle, mandibular length, symphyseal width and height were measured from cephalometric analysis. Densitometric analysis was performed to detect symphyseal area and bone density. Results: The changes in width between the mandibular first molars ranged from 20 to 437 μm, which was negatively correlated to the symphyseal width, area, and bone density. Where the lower gonial angle had a positive influence, the arch width changed during mouth opening. A multifactorial model showed a significant correlation between the set of predictor variables (symphyseal area, bone density, and mandibular length) and mandibular deformation. Conclusions: Mandibular arch width narrowed during forced opening. Subjects with smaller symphysis, lower bone density and longer mandible tend to have larger arch width changes.

Kinetics and Spatial Distribution of Leaf Elongation of Wheat (Triticum aestivum L.) under Saline Soil Conditions

Leaf development of wheat largely determines the rate of plant growth in the early growth stages and is most sensitive to salinity. The objectives were to investigate the shoot growth, area of leaves, and kinetics of leaf elongation of wheat seedlings (Triticum aestivum L.) grown in illitic‐chloritic silt loam with four salinity levels from 0 to 120 mM NaCl in growth chambers. Shoot fresh mass (FM) and leaf area were measured at days 12 and 18 after sowing. Instantaneous measurements of the leaf elongation rate (LER) of leaves 3, 4, and 5 of the main stem were carried out by using linear variable differential transducers (LVDT). Spatial distribution of relative elemental growth rate (REGR) and the length of the leaf elongation zone were determined by measuring displacement rates with a pricking method. Shoot FM per plant linearly decreased with increasing salinity levels. Leaf area under saline conditions was significantly correlated to the shoot FM during vegetative stages, indicating that leaf growth most sensitively responds to salinity. Salinity delayed leaf emergence and affected leaf growth longitudinally and laterally. Reduction in the final length of leaves 3, 4, and 5 was mainly a result of a decrease in their LER. The decreased LER under saline conditions was more pronounced during the steady growth phase and during the light period compared to later stages and to the dark period, respectively. Salinity affected the LER more severely with increasing leaf number, probably as a result of the longer exposure to salinity and longer elongation zones for higher leaf numbers. The reduction in LER resulted from decreasing the REGR but did not result from shortening the length of the leaf elongation zone during the linear phase of leaf growth.

Design and Construction of a Quantitative Uniaxial Straining Stage For The Environmental SEM

Abstract The environmental scanning electron microscope (or Environmental SEM) is a powerful tool in the materials science laboratory. The large sample chamber and ability to operate in a very poor vacuum (&amp;gt;5Torr) makes it an ideal device for a wide variety of in-situ studies. A three point bending stage has been used in the ElectroScan E3 environmental SEM at the University of Michigan for over four years. The stage is extremely flexible and can be used to view samples in both planar and transverse views. It also allows for quantitative recording of the stress and strain exerted on the sample via a load cell and a linear variable differential transducer. The output s of the load cell are acquired into an Apple Macintosh computer via a National Instruments analog-to-digital acquisition card. To extend the capability of EMAL's in-situ tensile testing laboratory, a uniaxial tensile stage has been constructed in collaboration with the Department of Mechanical Engineering and Applied Mechanics.

Measurement of strain and axial contraction of an FRP tube under large rotation

Abstraet-Large strain measurement and axial contraction of a fiber-reinforced plastic (FRP) tube under biaxial loading were investigated theoretically and experimentally. The equation for calculating strains from strain gage measurements for the case of large deformation and large rotation was derived based on the analysis of kinematics of deformation. Axial contraction of a tube could be predicted as a function of stresses, a twist angle and an initial elastic modulus of the axial direction. To demonstrate applicability of the equations, the tests of a cross-ply carbon/epoxy composite tube were conducted under uniaxial and tension/torsion biaxial loading up to failure. The signal of a linear variable differential transformer (LVDT) and angular displacement transducer (ADT) of a testing machine could be adopted in strain measurement of the biaxial test for fairly large deformation. The prediction of axial contraction of a CFRP tube agreed well with the LVDT result of the testing machine.

Fatigue behavior of the equine third metacarpus: Mechanical property analysis

This is the first in a series of experiments to study the fatigue properties of equine cannon (third metacarpal) bone specimens from Thoroughbred racehorses. Monotonic and fatigue tests to failure were performed in four-point bending on diaphyseal specimens in a 37 degrees C saline bath to answer three initial questions. (a) Will a linear variable differential transducer yield the same elastic modulus as strain gauges? (b) Will fatigue results depend on whether the periosteal or endosteal side of the beam is in tension? (c) Are there regional variations in the monotonic and fatigue properties of the cannon bone midshaft? Eighteen left-right pairs of specimens from six horses were used. One beam of each pair was fitted with strain gauges. Fatigue tests were conducted on 24 specimens under load control at 2 Hz; an initial range of 0-10,000 microstrain was used so as to produce failure in a reasonable period of time. There were no left-right differences in the fatigue or monotonic properties, and the presence of a gauge had no effect on modulus measured by a linear variable differential transducer. However, gauge-measured moduli were about 1 GPa less than transducer-measured values. Fatigue life was independent of which side of the beam was in tension, and there were significant variations in mechanical properties around the cortex. The lateral region was stiffer than the dorsal region but the latter had a longer fatigue life. The fixed cylindrical supports used in this experiment eventually produced slight wear grooves, causing artifactual stiffening at the end of the load cycle in some specimens. A second experiment using roller supports confirmed the reason for this stiffening. It also showed that fatigue life was shorter when roller supports were used but regional differences were similar.