Linear Variable Differential Transformer Research Articles

Experimental Examination of Additively Manufactured Patterns on Structural Nuclear Materials for Digital Image Correlation Strain Measurements

Abstract Background There are a limited number of commercially available sensors for monitoring the deformation of materials in-situ during harsh environment applications, such as those found in the nuclear and aerospace industries. Such sensing devices, including weldable strain gauges, extensometers, and linear variable differential transformers, can be destructive to material surfaces being investigated and typically require relatively large surface areas to attach (> 10 mm in length). Digital image correlation (DIC) is a viable, non-contact alternative to in-situ strain deformation. However, it often requires implementing artificial patterns using splattering techniques, which are difficult to reproduce. Objective Additive manufacturing capabilities offer consistent patterns using programmable fabrication methods. Methods In this work, a variety of small-scale periodic patterns with different geometries were printed directly on structural nuclear materials (i.e., stainless steel and aluminum tensile specimens) using an aerosol jet printer (AJP). Unlike other additive manufacturing techniques, AJP offers the advantage of materials selection. DIC was used to track and correlate strain to alternative measurement methods during cyclic loading, and tensile tests (up to 1100 µɛ) at room temperature. Results The results confirmed AJP has better control of pattern parameters for small fields of view and facilitate the ability of DIC algorithms to adequately process patterns with periodicity. More specifically, the printed 100 μm spaced dot and 150 μm spaced line patterns provided accurate measurements with a maximum error of less than 2% and 4% on aluminum samples when compared to an extensometer and commercially available strain gauges. Conclusion Our results highlight a new pattern fabrication technique that is form factor friendly for digital image correlation in nuclear applications.

An Analytical Model for the Initial Stiffness of Bearing Connections with Slotted Holes

In steel structures, cover plate joints are mainly used with normal round holes, but slotted holes, where the slot is oriented perpendicular to the direction of the bearing force, make it possible to release displacements in selected directions and thus better control the complex state of stresses in the connected plates. This study investigates the initial stiffness of a cover plate with a single slotted hole. The aim of this paper is to propose an analytical model that predicts the initial stiffness of slotted holes with respect to experimental results obtained on a panel of different geometries. This approach makes it possible to evaluate the effects of the end distances on the bending of the plate compared to the bearing under the bolt. A large panel of geometries is tested to quantify the experimental value of initial stiffness using Digital Image Correlation (DIC) technique compared to Linear Variable Differential Transformer (LVDT) sensors. To evaluate the initial stiffness, a method of processing experimental data is developed that allows a reproducible determination of stiffnesses. An analytical model is then proposed based on the improvement of existing models available in the literature. It is validated for different specimen geometries considering the contribution to the initial stiffness due to bending, shearing and support of the steel plate under the bolt. The comparisons show that the proposed analytical model can predict the initial stiffness of different geometries of tested specimens with slotted holes.

Displacement sensing based on microscopic vision with high resolution and large measuring range

AbstractMicroimage strain sensing (MISS) is a novel piston‐type sensor based on microscopic vision. In this study, optical disc slice is used as information carriers to improve MISS. There are multiple pits on the surface of an optical disc. By using machine vision algorithms, the pits can be converted into digital information, making them scales for recording displacements. By this means, we proposed a sensing method that combines high resolution, wide range, and strong robustness. The study measured displacement under different conditions. To address inevitable factors such as pixel drift, and manufacturing errors, corresponding compensation methods were provided. The results show that the measurements closely match those of the linear variable differential transformer, with a resolution of up to 20 nm and a range approaching the sensor size. Despite the sensor's dependence on machine vision, it demonstrates strong resistance to environmental factors such as brightness and angle. Combining compensation methods for pixel drift, and manufacturing errors, this sensor can be well‐applied in various working conditions.

Effect of aging on the mechanical properties of woven fabric-reinforced calcined diatomite substituted cement-based composites

The mechanical characteristics of polyester and flax woven fabric-reinforced, diatomite-substituted, cement-based composites have been examined at different ages within the scope of this study. The use of calcined diatomite in combination with a cement-based matrix aims to improve the mechanical performance within the composite as well as reduce carbon emissions. The consistency of cement-based and diatomite-substituted matrices with water-to-binder proportions of 0.28 and 0.45 was maintained at a fixed flow diameter of 235 mm with the adjusted use of a superplasticizer. The stress–strain graphs of the composites were obtained using an axial tensile testing machine and Linear Variable Differential Transformers (LVDT). The tensile strength, ductility, toughness development, and multi-crack performance of WFRC were obtained as a function of fabric type and aging. The effects of aging on tensile properties are discussed separately for each fabric type. Polyester woven fabric-reinforced composites were found to be superior to flax WFRC in terms of several mechanical properties at all ages. The substitution of diatomite further improved the tensile performance of the polyester woven fabric-reinforced composites. The fabric-matrix interface densification role of diatomite was determined by SEM/EDS line analysis. Evidence of a pozzolanic reaction between portlandite and diatomite was obtained through microstructure studies. Carbon emission analysis revealed that equivalent CO2 emissions could be reduced using diatomite in woven fabric reinforced composites. However, diatomite substitution caused a cost increasing effect.

Linear Variable Differential Transformer Signal Conditioning Circuit Based on Phase-Locked Loop

Linear Variable Differential Transformer Signal Conditioning Circuit Based on Phase-Locked Loop

Effects of the addition of short straight steel fibers on the strength and strains of high-strength concrete during compression

The article presents the effect of the addition of short straight steel fibers on the behavior of high-strength concrete (HSC) under compression (σ–ε curves). Deformations of cylindrical samples were measured simultaneously with the use of linear variable differential transformers (LVDT), strain gauges and the method of digital image correlation (DIC). The study showed that as the content of short straight steel fibers increases, both the composite compressive strength (fc) and strains (ε0), which correspond to the stress equal to the compressive strength, increase as well. To a lesser extent, the effect of short straight fibers on the descending part of the σ–ε curve was observed. An increase in the density and toughness ratio of the compressive strength of high-strength concrete with fibers compared to concrete without fibers was also observed. Moreover, compressive strength of the composite was estimated using the ultrasonic method. Based on the obtained results, a statistical analysis and an estimation of parameters fc and ε0 were carried out, and an analytical model was proposed to describe σ–ε relationship for HSC reinforced with short straight fibers under compressive loading. The results obtained for compressed fiber-reinforced concrete were compared with data available in literature.

Effect of variations in concrete quality on the crack width in rigid pavement

Cracks pose a significant issue in rigid pavement, leading to substantial damage. The manual mixing and casting of road pavement concrete underscore the importance of concrete quality as a critical parameter. This study investigates crack behavior by varying concrete quality. Loading is performed statically using line loads, shedding light on the impact of concrete quality on crack development. The concrete to be used has a quality fc' of 15 MPa, 25 MPa, and 35 MPa. The fine aggregate used in this study was Lumajang black sand, while the coarse aggregate used was machine crushed stone, and Portland Composite Cement (PCC) was used in all concrete mixes. The reinforcing steel used had a quality fy of 480 MPa, with a reinforcement ratio of ρ=0.010, which was converted to 5-D16 reinforcement. The subgrade density used to support the specimens had a CBR value of 10 %. Specimen dimensions were 2×0.6×0.2 m for length, width, and thickness. Pavement plates, 30 cm thick, were placed on leveled subgrade soil in a steel box set to achieve a 6 % CBR reading. Hydraulic jacks, monitored by a load cell, applied monotonic static loading with 2 kN intervals, reaching a maximum load of 200 kN. Steel tension and plate settlement were measured using a tension sensor and Linear Variable Differential Transformer (LVDT), respectively. A data logger recorded readings, and crack widths were captured by a digital microscope with 0.01 mm accuracy. Experimental results show that low concrete compressive strength values result in larger crack widths, and vice versa. Cracks also occur at earlier loading of concrete quality fc' 15 MPa. In addition, experiments show that the reinforcement stress value has a significant influence on crack width in specimens with low concrete quality

Procedure for Determining the Upper Bound on Absolute Error for LVDT Sensors

This paper presents the procedure for determining the upper bound on absolute error (UBAE) for linear variable differential transformer (LVDT) sensors without inter-winding capacitance. This procedure is based on the results of a parametric identification of the sensor, from which the coefficient values of the corresponding transfer function are obtained. The UBAE is then determined by a simulation experiment using dedicated computational software. The error value and the shape of the input signal, which is constrained in magnitude, are determined. The calculations and additional validation of the procedure presented in this article are carried out using the MathCad 5.0 program. As the basis for the proposed procedure, we review issues related to the modelling of LVDT sensors without inter-winding capacitance. The solutions presented here can be used to determine the UBAE, which can then be used to assess the accuracy of these types of sensor and their mutual comparability in terms of dynamic accuracy.

Design and Application of a Miniature Pneumatic Bellows Loading Device for In-Situ Tensile Testing inside the Scanning Electron Microscope

A miniature pneumatic bellows device was designed for in-situ testing inside the scanning electron microscope. The device uses a pneumatic actuator to load the specimen and displacement is directly monitored with a linear variable differential transformer sensor. Its application allowed the direct monitoring of microstructural and defect evolution in materials at the micro scale. The data produced by this testing device, in combination with measurements from micro digital image correlation, were successfully used to model the crystal plasticity of a martensitic/bainitic steel at the microstructural length scale.

Hydraulic characteristics of gypseous sand soil using modeled oedometer cell

The current study investigates the permeability of the sand soil using a modified Odometer cell with a constant head connected to a data logger and computer software. The soil sample is taken from the Al-Jameah district in Al-Najaf city, Iraq. The soil is classified as “SP” according to the unified soil classification system, with a gypsum content of 29%. A modified Oedometer with computerized water volume change is adopted. The samples are disturbed and remolded into the Odometer cell with different densities of 90% and 95% of the maximum Proctor dry density and initially dry. Each of the specific density samples is subjected to three different water heads: 80, 100, and 120 cm. The first head (80cm) is applied to the initially dry soil up to a saturated and steady state. While the other heads are subjected after the completion of the first one. The results of the modification are verified with the results in the literature and it is more flexible and accurate due to the digital recording of the data by the Linear Variable Differential Transformer (LVDT). The results of the water volume change versus time and the coefficient of permeability state that the dry condition (first head) of the specimen is the longest duration of the test for both 90% and 95% density in the change from dry to saturated and then to steady condition. For a 95% density longer than the 90% as expected, but after completing the saturation by the first head, there are method results of the 90% and 95% density, and this may be attributed to the higher water head and/or the effect of the gypsum dissolution.

Development of a Creep Mechanical Frame Setting Based on Arcan Test

Abstract Structural adhesive bonding has several advantages compared to other assembly techniques such as welding and riveting. Yet, creep is an important long-term phenomenon that needs to be considered for the design of such joints. To investigate this aspect, experimental investigations are needed at the scale of the adhesive layer. At such a scale, Arcan setting presents several advantages compared to other existing tests (analysis of different loads, limited edge effects) and was thus chosen for the development of an experimental approach aiming at providing creep characterization of adhesive layers. A mechanically operated testing machine was thus developed and is presented herein. To measure local strains of the adhesive layer, two linear variable differential transformer sensors are fixed on a support placed on the beaks of the Arcan sample according to two directions: normal and tangential to the bonded surface. The developed system (mechanical system and strain measurement) proved to be successful in investigating the creep behavior of adhesive layers while varying several parameters (load levels, type of load, temperature, adhesive thickness).

A novel monitoring system for fatigue crack length of compact tensile specimen in liquid lead-bismuth eutectic

Fatigue strength of the structural materials of lead-cooled fast reactors (LFRs) and accelerator-driven systems (ADS) may be degraded in liquid metal (Lead or lead-bismuth eutectic (LBE)) environments. The fatigue crack growth (FCG) data of structural materials in liquid LBE are necessary for damage tolerance design, safety assessment and life management of key equipment. A novel monitoring system for fatigue crack length was designed on the compliance method and the monitor technology of crack opening displacement (COD) of CT specimens by the linear variable differential transformers (LVDT) system. It can be used to predict the crack length by monitoring the COD of CT specimens in harsh high-temperature liquid LBE using a LVDT system. The prediction accuracy of this system was verified by FCG experiments in room temperature air and liquid LBE at 150, 250 and 350 °C. The first results obtained in the FCG test for T91 steel in liquid LBE at 350 °C are presented.

Development and applications of the quasi‐dynamic triaxial apparatus for deep rocks

AbstractThe mechanical behaviors of deep rocks have always posed a challenge for the implementation and safe operation of major underground engineering projects. To this end, this study modified the existing mainstream rock mechanics instruments equipped with a dynamic disturbance loading system and developed a second‐generation TFD‐2000/D triaxial instrument. The first‐generation device is equipped with an independent disturbance system and an advanced EDC‐580 all‐digital servo controller, which can apply disturbing load independently, implement the function of cyclic disturbance, and combine dynamic and static disturbances. The instrument was found to be reliable for use in analyzing the damage process of rocks in the disturbance test of marbles. The second‐generation instrument tackles three limitations of the first‐generation instrument: (i) it upgrades the strain measurement system and uses extensometers with linear variable differential transformers to accurately measure deformation; (ii) it uses the self‐balanced chamber to replace the Hoek–Franklin triaxial cell and auto‐balancing triaxial pressure chamber; and (iii) the loading rod is independently equipped with an EDC‐580 all‐digital servo controller, which measures precise loads. The experimental findings confirmed that the second‐generation instrument can be used for rock mechanics testing under cyclic disturbance loading, the disturbance–stress relaxation cycle, and the creep–fatigue cycle. In this sense, the second‐generation instrument can be a useful addition to deep rock mechanical instruments and provide a valuable reference.

Servo kontrollü maliyet etkin bir aktif kuvvet duyargası tasarımı ve denenmesi

In this work, the computerized control of a hydraulic system with analog characteristics is examined, and within this scope, a novel force sensor is designed. The system consists of two main structures: an analog subsystem comprising a four-way servo valve, hydraulic piston, servo amplifier, and the designed force sensor, and a digitizing subsystem responsible for comparison and control, composed of a desktop computer. Throughout this work, a cost-effective force sensor was designed by integrating a compression spring, guides, a support frame and a linear variable differential transformer (LVDT). In this integrated system, the force applied at a specific magnitude and frequency from an external force measurement and feedback unit is converted into electrical signals by horizontal motion of the LVDT core. These electrical signals from the force sensor are digitized and fed back to the computer and data acquisition card. The digitized data transferred to the software developed in this study continuously compare with the reference data, enabling position-dependent force control. Experiments conducted with the force sensor placed between two hydraulic pistons controlled by a servo valve revealed that it caused the pistons to move right and left, providing the desired control of the system with the reference force input. The system was observed to operate much more stably, especially for high-frequency signal inputs.

Experimental and numerical study on fire-induced collapse of double-span steel portal frames

This paper introduces experimental and numerical investigations on the fire-induced collapse behavior of double-span steel portal frames. A natural fire test was conducted on a 16 m × 6 m portal frame, and a localized collapse occurred. Thermal and displacement responses of the test frame were measured and analyzed. It was found that the steel members inside the fire compartment experienced similar temperature-time curves, which reached 1000 °C in 15 min. The heated column experienced upward expansion and downward contraction, while the side columns were pushed outside and pulled inside during the fire test. The measuring accuracy and practicability of the thermocouple, microwave radar, inclinometer, and linear variable differential transformer (LDVT) in real fire measurements were compared and evaluated. Numerical models were established in FDS and ABAQUS to simulate the thermal and structural response of the test frame and validated against experimental results, respectively. Parametric analysis was conducted on the validated numerical models with various combinations of heating conditions, heating rates, load ratios, and base stiffness. The collapse temperature of the burning frame was 1.2 and 1.1 times the temperature when the displacements of the heated side column reached their peak values along the span and height directions, respectively.

Research on the application of laser camera to support LVDT in geotechnical laboratory work

Laboratory tests are essential for analyzing the behavior of geotechnical materials and models. Two of the most common methods for measuring displacement in laboratory tests are Dial indicator and Linear variable differential transformer (LVDT). However, using these equipments has some limitations, such as measuring only discrete points, and Dial indicators require surfaces to be measured must have a certain hardness. This feature is a significant limitation because geomaterials are not usually rigid masses. To overcome these limitations, the authors studied using laser cameras to support the LVDTs and the Dial indicators. Laser cameras offer high sampling rates, but their accuracy needs to be carefully investigated as they are mainly used to measure large distances. In this paper, we show how to investigate the accuracy of laser cameras with reliable, intuitive observations, reviewing recent studies on using laser cameras in laboratory tests. Experiments, including their advantages, limitations and potential applications: The potential application of laser cameras to measure distances can be evaluated instead of LVDT. We also discuss the challenges and future directions of using laser cameras in laboratory testing. The results showed that laser cameras could improve the accuracy and efficiency of laboratory tests and may become a preferred method for displacement measurement in the future.

Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon

This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator(SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.

Complete stress-strain analysis of masonry prisms under compressive loading-unloading cycles through digital image correlation

This paper presents the findings of an experimental study focused on the behaviour of masonry structures subjected to uniaxial loading-unloading compression. The study's primary objective is to examine the impact of joint mortar on the failure mode and the development of permanent strains using the digital image correlation technique (DIC). Masonry prisms were constructed using two types of fired bricks and five different mortars, each with varying cement and lime contents. The prisms were instrumented with a linear variable differential transformer (LVDT) for displacement measurements and prepared for image processing using DIC. The prisms were then subjected to compression testing until failure to capture their complete behaviour. The experimental results obtained through DIC and LVDT measurements showed good agreement. The DIC technique proved its effectiveness in providing comprehensive strain evaluations of the brick prisms, enabling a detailed stress-strain analysis at a full-scale level. Furthermore, the study revealed that prisms with lower cement content exhibited a more ductile behaviour in the post-peak region, with strain localisation observed at the joint mortar interface.To validate DIC's reliability in characterising masonry's cyclic behaviour, the results obtained from analytical modelling were compared with those derived from DIC. This comparison aimed to confirm the accuracy and consistency of DIC measurements. Overall, this study contributes to our understanding of masonry behaviour under compression and highlights the capabilities of DIC in capturing strain patterns and providing valuable insights into the influence of joint mortar on the structural response of masonry elements.

Development and Application of Linear Variable Differential Transformer (LVDT) Sensors for the Structural Health Monitoring of an Urban Railway Bridge in Vietnam

Measuring the structure's displacement plays a very important role in ensuring the safe operation of railway bridges in general and urban railway bridges in particular. In Vietnam, traditional methods using high-precision mechanical gauges have been used to measure the displacement of railway bridges. However, these methods need a lot of effort in installation and traffic control during implementation. These methods are based on the static principle: The test loads are placed on the bridge structure, and then the structure's displacement is observed. The safety assessment and analysis results are guaranteed by multiplying the dynamic coefficients, leading to some assessments that may not be close to the actual exploitation of the bridge structure. Therefore, the current study presents a new solution for measuring the displacement of railway bridge structures. This method uses Linear Variable Differential Transformer (LVDT) sensors to record the continuous displacement of the structure during the time the train passes over the bridge. Through field measurements combined with a finite element analysis model, the research focuses on developing and applying LVDT sensors in urban railway bridge structure health monitoring. At the same time, the potential of developing this method in Vietnam in the future is evaluated.

Thermally induced shear displacement of sand-concrete interface under different stress levels

Energy geostructures are modern technologies developed to exploit shallow geothermal energy. Their installation has recently increased rapidly throughout the world. Their use is devoted to the heating and cooling of buildings, and their operation can induce thermal cycles at the soil-structure interface in the range of 5–40 °C [1]. In addition, their activation would produce thermally-induced stress and strain in structure. Over the last few decades, several full-scale tests have been performed to study the geotechnical aspects of energy piles [2,3]. The main results show that the thermal operations may slightly influence the mechanical performance of the energy pile by increasing the additional thermal compressive stresses and changing the pile axial strain. Numerical studies [4,5] concluded that the temperature increment can lead to thermal expansion of the pile, causing its uplift and the generation of negative shear forces at the pile–soil interface near the pile head. Considering that the thermal operation of energy geostructures leads to temperature change along the piles as well as in the neighbouring soil due to the heat exchange phenomenon, many researchers have investigated the temperature effects on the behaviour of soil and soil–structure interface [6,7,8,9]. Others investigated thermally induced soil deformation using modified triaxial or oedometric apparatuses allowing temperature control [10,11,12]. These results show expansive deformation of coarse-grained soils upon heating and contractive deformation upon cooling for all relative densities. A modified geothermal direct shear box (MGSB) developed at Gustave Eiffel University [13] was used to investigate the effects of temperature cycles on soil–concrete interface. The preliminary results showed that the sand expands upon heating and contract upon cooling. An accumulated contraction and shear displacement were observed after each thermal cycle. However, these preliminary results should be carefully re-analysed since the device was not fully calibrated under various thermo-mechanical loads.
 In this study, the MGSB was utilized after its calibration [13], to investigate the thermally induced vertical and lateral displacements of sand–structure interface. It consists of two half-shear boxes with dimensions of 200 mm x 200 mm x 80 mm. A Peltier module was used to heat and cool water connected to a pipe embedded in the concrete plate, which was used to simulate the pile surface. Normal and shear stresses were applied to represent the geostatic stress of soil and pile load, respectively. Four linear variable differential transformers (LVDTs) were placed in contact with the lower and the upper boxes of the device to measure the shear displacement. One LVDT was placed at the top of the box to measure the vertical displacement of soil. To prevent heat losses, the system was insulated using an insulating foam. Two series of test were performed. The four tests of the first series were conducted on dense (D) sand and the three tests of the second series were on loose (L) sand, with relative densities of about 90% and 30%, respectively. For each density, three normal stress levels were tested: 25, 50 and 100 kPa. For each normal stress, a shear stress equal to 40% of normal stress (45% of the shear strength) was applied. Test D_50 was repeated because of technical problems that happened during the first test. After samples preparation, two phases were carried out. The first phase corresponds to the
 application of normal and shear stresses. Regarding the second phase, 20 thermal cycles were applied, varying the soil temperature between 14 °C and 32 °C.
 The mechanical results showed a good agreement compared to standard direct shear tests. The thermo-mechanical results showed that the succession of soil expansion and contraction upon heating and cooling respectively lead to an accumulated irreversible contraction and continuous shearing displacement after each thermal cycle with different magnitudes, depending on the soil density and stress level. In addition, the rate of these incremental irreversible displacements decreases when the cycle number increases. Moreover, the increase in the stress levels will lead to an increase in the accumulated lateral displacement after 20 cycles, and this increment is significant in loose sand compared to dense sand under the same mechanical conditions. Overall, the thermally induced sand-concrete interface displacements are affected by stress level and strongly depend on the sand density. The thermally induced settlement may be critical in the case of floating energy piles under high mechanical load, and greater than 45% may lead to greater in the case of loose soil would be greater than 0.3 mm. Finally, this study suggests that using a homogeneous stress design method for energy geostructures may adversely affect the design.