Linear Variable Differential Transformer Research Articles

Maximum Energy Density for Evaluation of the Dynamic Accuracy of LVDT Sensors Applied in the Energy Industry

This paper presents a proposal in which the maximum energy density criterion is used to evaluate the dynamic accuracy of LVDT (Linear variable differential transformer) sensors for applications in the energy industry. The solutions proposed in the paper are based on a mathematical model of the LVDT sensor, represented by its frequency response. The mathematical foundations required for the synthesis of such a model and the formulae and algorithm necessary to determine the maximum energy density for the integral-square error criterion are presented. Numerical and simulation calculations are performed using MathCad 15 and MATLAB R2014a programs. The solutions presented in this paper can constitute a basis for the selection of LVDT sensors for applications in the energy industry, with a view to achieving accurate diagnostic measurements.

Evaluation of Concrete Fatigue Damage with Elastic Wave-based Measurement Techniques

Fatigue damage is a progressive and permanent change in the internal material structure due to cyclic loading. The cyclic loads can be due to wind, waves, temperature variation, and traffic loads. Each cyclic load application introduces micro-damages that accumulate to induce failure. Detecting these micro-damages requires sensitive measuring techniques. Hence this research compares the sensitivity of different measuring techniques applied to fatigue experiments of concrete. The applied NDT are the passive acoustic emission technique (AET) and active ultrasonic measurements. In addition, linear variable differential transformers (LVDTs) are applied as a reference measurement. Accordingly in this research, cylindrical concrete samples are subjected to monotonic and cyclic Brazilian splitting tests. The cylinders are 100 mm in diameter and 150 mm in length. The cyclic load is applied to these samples with a loading frequency of 5 Hz. During the tests, the damage evolution is monitored with AET, ultrasonic measurements and LVDTs. There are eight AE sensors attached to the sample. The two LVDTs are positioned at the center of the sample's front and back side. Besides passively monitoring the acoustic emissions, the AET sensors are also used to do active ultrasonic measurements. The research reports the comparison conducted on the deformations and cracks measured with the LVDTs, the damage growth identified with the AET, and the change in the ultrasonic pulse velocity measurements. In addition, the study also presents the damage analysis capacity of the methods across different types of loading: monotonic, constant amplitude, and stepped fatigue loading. The comparison shows that combination of AET and ultrasonic velocity measurement is a sensitive indicator for damage growth.

The initial structural health monitoring system of the Nibelungen Bridge Worms

As an essential part of the validation project for the German Research Foundation-funded Priority Program SPP 100+, an initial structural health monitoring system has been implemented on the Nibelungen Bridge in Worms. The aim of this system is to monitor the general behavior of the bridge for further development of condition indicators and to provide real data to all project partners to validate their methods. In this scope, 20 sensors, including radiation, humidity, temperature, inclination, linear variable differential transformer (LVDT), and acceleration sensors, have already been installed on the bridge. The quality of the recorded data, including measurement technical traceability, completeness, and reliability, shall be guaranteed. Subsequently, both the raw data and the first statistically evaluated values, such as the maximum, average, and minimum values, are saved. These raw and first-hand data are made available to the involved partners in a possible real-time manner. In addition, a web-based visualization platform has also been established. Therefore, users can access the deviation of the measured values from different sensors in the most direct way. The measured results of this initiated SHM system are compared and validated with numerical simulation results. Further supplementation of additional sensors, extension, and improvement of this initial system are aimed to be achieved in the future.

Pressing Strength of Plastic Bottle Couch as a Form of Waste Management Innovation in UMKM Sobotik

Abstract In general, people burn plastic waste openly because they do not know the impact it can cause. Couch from plastic bottles one of the effective alternative innovations. The objective of this study was to determine the strength of the plastic bottle couch from the UMKM Sobotik couch product as the effort to develop creativity in utilizing plastic waste. Plastic bottles that have been glued according to the size and shape designed are given a load (load cell) at the center point of the test object. The shortening of the specimen during compression was observed by two linear variable differential transformers (LVDT) which were placed on the top of the flat surface on different sides of the specimen. The difference in the compressive strength of the plastic bottle couch specimen was based on the variable height of the plastic bottles making up the couch, the cross-sectional shape of the couch, and the position of the fastener (duct tape). There are three types of plastic bottles that make up the couch for this test, namely 1500 ml, 600 ml and 330 ml with the height of each bottle being 290 mm, 226 mm and 170 mm respectively. The results of the compressive load test on the plastic bottles that make up the couch ranged from 241 kgf-621 kgf. The strength of the couch is influenced by the number of adhesives, the location of the adhesive and the shape of the couch. The specimen with the smallest rigidity is a rectangular cross section. Round cross sections tend to have advantages over other cross sections. Due to the pressure received by the test object can be spread evenly throughout the radius of the test object. For a square cross section, there is a cross section that is shorter than the other parts, resulting in non-uniformity of the load received by the parts of the cross section, so that the round shape has great strength.

Evaluation of the single-frequency variometric approach based on low-cost GNSS observations and different satellite combinations for detecting short-term dynamic behaviors

This study presents the capability of the single-frequency (SF) variometric approach (VA) technique with low-cost GNSS observations to detect short-term dynamic behaviors. Harmonic oscillations with amplitudes between 5 and 20 mm and frequencies between 0.3 and 5.0 Hz were generated employing a single-axis shake table to investigate the performance of the SF-VA technique in the structural health monitoring (SHM) system. Besides, a Mw 6.9 Kobe, 1995 earthquake simulation was generated using the shake table to analyze the SF-VA performance for the earthquake early warning (EEW) system. A low-cost u-blox ZED-F9P GNSS receiver and ANN-MB-00 patch antenna were used to collect GNSS observations at a 20 Hz sampling rate during the experiments. The observations were processed using the MATLAB-based open-source PPPH-VA software in real-time (RT) mode, considering eight different satellite combinations. The capability of the SF-VA technique to detect horizontal dynamic behaviors in RT mode was investigated in the frequency and time domains, accepting the displacements from the linear variable differential transformer sensor as a reference. The results in the frequency domain demonstrate that the SF-VA technique with low-cost GNSS observations can successfully detect the peak frequency value of short-term harmonic oscillations up to 5 Hz. Moreover, time domain findings emphasize that the short-time dynamic oscillations can be determined with the SF-VA technique with an accuracy ranging from 0.8 to 6.4 mm. Earthquake simulation experiment results demonstrate that the strong ground motions caused by mega earthquakes can be determined at mm-level by the SF-VA method. The results of both experiments show that multi-GNSS observations contribute to the SF-VA technique considerably. Overall, the findings reveal that the SHM and EEW systems can be operated with low-cost GNSS receivers, and the natural frequency of the man-made structures and accurate displacement values of seismic waveforms can be determined in RT with the SF-VA technique.

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

BackgroundThere 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.ObjectiveAdditive manufacturing capabilities offer consistent patterns using programmable fabrication methods.MethodsIn 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.ResultsThe 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.ConclusionOur results highlight a new pattern fabrication technique that is form factor friendly for digital image correlation in nuclear applications.

Flexural behavior analysis of double honeycomb steel composite encased concrete beams: An integrated experimental and finite element study

This research addresses a critical issue in composite sections—insufficient concrete flow on both sides of the steel beam web, leading to discontinuity in the filler material. The study focuses on double honeycomb beams in concrete-enclosed steel structures, categorizing them as pure and enclosed steel. A two-phase approach, comprising experimental and numerical analyses, was employed. Fabrication of specimens representing both beam types was followed by bending tests using the STD600 apparatus. The primary specimen showcased the significant advantages of composite beams over conventional steel in bending scenarios. In the experimental phase, two practical solutions were introduced—transforming beam profiles into honeycomb configurations and optimizing spatial constraints around the central linear variable differential transformer (LVDT). Finite element models, validated against test results, demonstrated the practicality and accuracy of Abaqus software. The findings highlight superior flexural behavior in composite beams, presenting promising implications for the construction industry.

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.