Tangential Deflection Research Articles

On the properties of Alfvénic switchbacks in the expanding solar wind: The influence of the Parker spiral

Switchbacks—rapid, large deflections of the solar wind's magnetic field—have generated interest as possible signatures of the mechanisms that heat the corona and accelerate the solar wind. In this context, an important task for theories of switchback formation and evolution is to understand their observable distinguishing features, allowing them to be carefully assessed using spacecraft data. Here, we work toward this goal by studying how Alfvénic switchbacks evolve in the expanding solar wind beyond the Alfvén radius, when the background magnetic field also rotates due to the Parker spiral. Using simple analytic arguments based on the physics of one-dimensional spherically polarized (constant-field-magnitude) Alfvén waves, we find that, by controlling the wave's obliquity, a Parker spiral strongly impacts switchback properties. Surprisingly, parallel magnetic-field deflections (switchbacks) can grow faster in a Parker spiral than in a radial background field, even though normalized wave amplitudes grow more slowly. In addition, switchbacks become strongly asymmetric: large switchbacks preferentially involve magnetic-field rotations in the plane of the Parker spiral (tangential deflections) rather than perpendicular (normal) rotations, and such deflections are strongly “tangentially skewed,” meaning switchbacks always involve field rotations in the same direction (toward the positive-radial direction for an outward mean field). In a companion paper [Johnston et al., Phys. Plasmas 29, 072902 1346 (2022)], we show that these properties also occur in turbulent 3D fields with switchbacks, given various caveats. Given that these nontrivial asymmetries and correlations develop purely as a consequence of switchback propagation in the solar wind, our results show that in situ observed asymmetrical switchback features cannot be used straightforwardly to infer properties of sources in the low corona.

CALCULATION OF THE PARAMETERS OF THE WIND TURBINE ROTOR EDDY CURRENT SENSOR

Eddy current sensors are used to measure shaft clearance in wind turbines and to check that there is a thin film of oil in the clearance. In this case, the oil is usually applied under pressure. Because the eddy current sensors are resistant to oil, pressure and temperature, this allows them to operate reliably in these hostile environments. When the gap becomes too large, a maintenance warning is generated. Eddy current sensors help detect axial and radial deflection of the turbine shaft. Radial movement occurs when the shaft is off-center. Axial movement indicates that the shaft is tilted relative to the central axis. Both cannot be eliminated completely. However, with significant deviations, increased bearing wear occurs. If such situations are detected, the turbine should be shut down as soon as possible for maintenance, even before an accident occurs. Finally, eddy current sensors are used to measure forces or torques applied to the nacelle. These influences can be caused by vibration, wind loads or other factors that, over time, can lead to the destruction of the entire structure. Eddy current sensors can also be used to measure axial, radial or tangential deflection of clutch discs, which ensure the safety of the rotor in the event of strong winds. This article provides a method for calculating an inductive sensor. This calculation will allow you to correctly develop a wind turbine eddy current sensor.

Mathematical modeling of an armature assembly in pilot stage of a hydraulic servo valve based on distributed parameters

The dynamic performance of a nozzle-flapper servo valve can be affected by several factors such as the disturbance of the input signal, the motion of the armature assembly and the oscillation of the jet force. As the part of vibrating at high frequency, the armature assembly plays a vital role during the operation of the servo valve. In order to accurately predict the transient response of the armature assembly during the vibration, a mathematical model of armature assembly is established based on the distributed parameters method (DPM) and Hamilton principle. The new mathematical model is composed of three main parts, the modal eigenfunction, modal mechanical response expressions of the spring tube and the motion equation of the other armature assembly. After programing, the purpose of using the DPM to predict the dynamic response of different positions located on the armature assembly is achieved. For verifying the validity of the mathematical model, the finite element method (FEM) and classic model (CM) of armature assembly are applicated by commercial software under the same condition. The comparison results prove that the DPM can effectively predict the axial and tangential deflection of the armature assembly different positions which the CM can’t duing to its over-simplification. A certain error is generated when predicting the axial deformation at different heights by DPM, which is caused by an approximate method to simulate the torsion of the spring tube. The comparison results of the spring tube deflection at different vibration frequencies shows that the adaptability of DPM is significantly higher than the classic model, which verify the model is more adaptable for predicting the dynamic response of the armature assembly.

Characterization of Exponential Cohesive Zone Model for Fracture Assessment of De-Bonded Composite Panels

Composite structures are prone to delamination/de-bond and effective tool to simulate de-lamination is cohesive zone model. Cohesive zone model uses multiple adhesive failure parameters. The influence of adhesive parameters on the delamination and fracture of Double cantilever Beam, subjected to Mode-I loading through finite element simulations is studied usingExponential Cohesive Zone Model (ECZM). Influence of Normal stress (σ), normal deflection (δn) and tangential deflection (δt) on the de-bond propagation is examined.From the analysis it is found that the tangential deflection (δt) has negligible impact on Mode-I loading and fracture of the specimen. Significant effects are seen for the perturbation of Normal stress (σ) and Normal deflection (δn). A Finite element based ECZM for composite layer (HTS/M18) with EPG 2601 adhesive is proposed. The model is validated by comparing with test data.

Closed-form solution considering the tangential effect under harmonic line load for an infinite Euler–Bernoulli beam on elastic foundation

• Analytical solution for dynamic response of infinite beam on foundation is developed. • The elastic foundation considered the horizontal tangential effect. • Double Fourier transformation is used for deduction and the residue theorem is employed to obtain the solution. • The analytical solution for the beam under inclined dynamic load is presented. The dynamic response of an infinite Euler–Bernoulli beam resting on an elastic foundation, which considers the tangential interaction between the beam and foundation under harmonic line loads, is developed in this study in the form of a closed-form solution. Previous studies have focused on elastic Winkler foundations, wherein the tangential interaction between the bottom of the beam and the foundation is not considered. In this study, a series of separate horizontal springs is diverted to the contact surface between the foundation and beam to simulate the horizontal tangential effect. The horizontal spring reaction is assumed proportional to the relative tangential displacement. As the geometric equation and linear-elastic constitutive equation of beam under the condition of small deformation have been presented based on the basic principle of elasticity mechanics, the analysis model is built and the governing differential equations about normal and tangential deflections of beam are deduced. Double Fourier transformation and the residue theorem are used to derive the closed-form solution to this problem. The proposed solution is then validated by comparing the degraded solution with the known results and comparing the numerical solution with the analytical solution. We also discuss the case in which the load direction is not vertical to the beam. Results can be used as a reference for engineering design.

Tangential deflection and formation of counterstreaming flows at the impact of a plasma jet on a tangential discontinuity

AbstractIn this letter we report three‐dimensional particle‐in‐cell simulations of the interaction between a nonpenetrable magnetosheath jet and the magnetopause, for northward interplanetary magnetic field. The magnetopause is modeled as a tangential discontinuity with no magnetic shear. We investigate the deflection of the plasma jet in the direction tangential to the magnetopause. We find that as the frontal edge of the jet interacts with the magnetopause, the electrons and ions are scattered in opposite directions, tangential to the magnetopause, by the energy‐dependent gradient‐B drift. This effect is more effective on the nonthermal particles that tend to accumulate at the two sides of the jet and sustain a polarization electric field in the direction normal to the discontinuity surface. The electric drift of the bulk of particles under the action of this polarization electric field explains the deflection and counterstreaming at the impact of the plasma jet on the tangential discontinuity.

Experimental Investigation of the Scaling-Off Location and the Slag Mass in Pulverized Coal-Fired Boiler with Water-Cooled Slag Removal

It is of great importance to acquire precisely the scaling-off location and the extent of slagging in the furnace to conduct combustion adjustment and avoid the dropping of bulk slag. An experimental platform where slag cooling is simulated was built, and the features of heat and mass transfer during the cooling process of the slag were studied. The experimental results show that during the cooling process of the high-temperature slag, the closer the measuring point is to the drop point of the slag, the faster its temperature rises, by a large margin. Meanwhile, the average temperature of the water in the upper layer shot up first and then decreased, while the temperature of the relatively deep water (≥3 cm) tended to rise gradually. In addition, the temperature rise of the cooling water and the bursting water evaporation are in direct proportion to the mass of the slag and are in linear relation to the temperature of the slag. About 20% of the slag heat is taken by bursting evaporation, and 80% is conducted to the cooling water. In a thermal power plant’s 440 t/h pulverized coal-fired boiler with water-cooled slag removal, a temperature matrix with eight measuring points was arranged in the slag extractor. The location and mass of the slag in the furnace were determined, and the reason for slagging in the furnace was analyzed, in order to make fine adjustments to the parameter of air supply, to improve the tangential circle deflection in the furnace further, and to avoid the dropping of bulk slag quenching the fire, which guarantees that the boiler can run safely and stably.

Parametric Instability of Dual-Ring Structure With Motionless and Moving Supports

This work is to study parametric vibration of a dual-ring structure through analytical and numerical methods by focusing on the relationships between basic parameters and parametric instability. An elastic dual-ring model is developed by using Lagrange method, where the radial and tangential deflections are included, and motionless and moving supports are also incorporated. Analytical results imply that there are four kinds of parametric excitations, and the numerical results show that there exist stable and unstable areas separated by transition curves or straight lines, and even crossover points. The relationships are determined as simple expressions in basic parameters, including discrete stiffness number and wavenumber. Whether the parametric resonance can be excited or not depends on the values of support stiffness, rotating speed, and natural frequency. Vibrations at the crossover points are also addressed by using the multiscale method. Comparisons against the available results regarding ring structures with moving supports are also made. Extensions of this study, including the use of powerful Sinha method to deal with the parametric vibration, are suggested.

Parametric instability induced by traveling magnetic load within permanent magnet motors

Magnetic load can cause excessive noise and vibration or even parametric instability, damaging permanent magnet (PM) motors on a permanent basis. This work investigates the parametric vibration of a ring stator with an aim to identify mechanical–magnetic coupling parametric vibration. An analytical model is developed by using energy method, where the stator is treated as a thin smooth ring having radial and tangential deflections and subjected to traveling magnetic load. The modeling leads to a partial differential equation with time-variant coefficients depending on pole/slot combination, excitation order, permanence order, and wave number. Principal instability boundaries are identified by multi-scale method as simple closed-form expressions. The expressions govern the relationships between mechanical–magnetic parameters and instability’s occurrence or suppression. Results show that there exist unstable regions that cannot be detectable directly by traditional treatment widely employed when using the multi-scale method, and thus, an alternative avenue is presented. Analytical results are well compared against the numerical ones from the Floque’t theory. The analytical results can find application in parameter’s selection at preliminary design stage of the PM motors to keep stable running.

On Cutter Deflection Profile Errors in End Milling: Modeling and Experimental Validation

In the present paper three dimensional cutter deflections and the corresponding profile errors during end milling are predicted by finite element and bond graph modeling approach. The deflections have been modeled considering the cutter as a cantilever beam fixed at the collet end. Rayleigh beam model is used for modeling to consider the shear force effect, and Castigliano's theorem of strain energy is used to predict the deflections due to radial, tangential, and axial cutting forces. The tool-workpiece contact region is sliced into small elements to apply the forces on the entire contact region and predict deflections more accurately. The predicted deflections at different parametric settings are compared with experimental measurements by measuring the geometric accuracy of the cut profiles. The depth of cut has the most significant influence on profile deviations, while feed and speed have marginal effects. The results reveal that the predictions by finite elements and the bond graph closely matches with the experimental results, and errors of the machined profile are significantly influenced by the radial and tangential deflections. The axial deflection is negligible and leads to insignificant deviation in depth of the cut profile. The proposed model shows that the bond graph simulation takes significantly less computational time and space as compared to the finite element technique.

Control Port Influence on Swirl, Operating, and Flow Characteristics of a Mini-Vortex Amplifier on Glove Box Service

Abstract Vortex amplifiers (VA) use fluidic phenomena to modify flow through a containment breach, when used to protect glove box workers from exposure to the contents. The influence of control port geometry on swirl, operating characteristics, global flow, and momentum characteristics is studied experimentally. Shape and size of the control flow channels and the pressure applied at the tangential ports are critical in determining the trajectory of the jet issuing from the tangential ports and deflection of radial flow and vortex strength. Dominance of control-to-exit area ratio is confirmed. A clear improvement in performance is noted for a practical geometry derived from shaped passages of the device. Flow and momentum characteristics provide additional design data. The relationship of swirl number to output flow is demonstrated. Global flow and momentum characteristics provide insight into design and operation that is useful when avoiding back diffusion.

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions.

Tribological method to objectify similarity of vague tactile sensations experienced during application of liquid cosmetic foundations

To develop objective estimation methods for the tactile sensations experienced during the application of liquid cosmetic foundation (i.e., emulsion foundations (EFs)), a tribotester based on the mechanical properties of human skin was used in lubrication experiments with EF samples. From the time-varying signals of the tangential spring deflection obtained in reciprocating rubbing tests for small sample amounts, trajectories (i.e., plots of the tangential spring deflection against the tangential drive position) were obtained. Using characteristic trajectory shapes (e.g., a shape like a ribbon with jagged edges) makes it possible to evaluate the similarity of vague tactile sensations without sensory testing.

Conditions for Worm-Robot Locomotion in a Flexible Environment: Theory and Experiments

Biological vessels are characterized by their substantial compliance and low friction that present a major challenge for crawling robots for minimally invasive medical procedures. Quite a number of studies considered the design and construction of crawling robots; however, very few focused on the interaction between the robots and the flexible environment. In a previous study, we derived the analytical efficiency of worm locomotion as a function of the number of cells, friction coefficients, normal forces, and local (contact) tangential compliance. In this paper, we introduce the structural effects of environment compliance, generalize our previous analysis to include dynamic and static coefficients of friction, determine the conditions of locomotion as function of the external resisting forces, and experimentally validate our previous and newly obtained theoretical results. Our experimental setup consists of worm robot prototypes, flexible interfaces with known compliance and a Vicon motion capture system to measure the robot positioning. Separate experiments were conducted to measure the tangential compliance of the contact interface that is required for computing the analytical efficiency. The validation experiments were performed for both types of compliant conditions, local and structural, and the results are shown to be in clear match with the theoretical predictions. Specifically, the convergence of the tangential deflections to an arithmetic series and the partial and overall loss of locomotion verify the theoretical predictions.

Non-linear thermoelastic analysis of steel arch members subjected to fire

This paper addresses the non-linear thermoelastic behaviour of steel arches acted on by a sustained uniformly distributed load, when subjected to elevated temperatures as caused by fire. The steel arch is restrained at its two ends by elastic translational springs in both the horizontal and vertical directions, as well as by counterpart elastic rotational springs, which simulate a generic semi-rigid connection, or restraint by other members in a frame, or when the arch acts as a large-span roofing element supported and restrained by columns. The study is restricted to the thermoelastic structural response of the steel material and therefore the high-temperature effects of catenary action and yielding are not considered; however the important effect of the second order term in the strain–displacement relationship is included. In order to model structural response of an elastically supported steel arch under thermal loading, an alternative geometric formulation is needed since the tangential and radial deflections and rotations as well as the axial compressive force in the member are substantial at the early stage of the fire. The formulation presented in this paper takes into account the degradation of the stiffness of the steel arch prior to yielding at elevated temperatures and it is argued that there are many situations for which analyses of a real fire situation in the thermoelastic range are valid. It is shown that the proposed model agrees well with independent solutions obtained using finite element analyses. The proposed model has significant potential for use in the analysis of restrained steel arches subjected to uniformly distributed load at elevated temperatures, such as large-span roofs and can provide a foundation for codified procedures in design.

Mechanism of stick-slip associated with Schallamach waves

The mechanism of stick-slip associated with Schallamach waves was investigated using a sliding point contact between a glass hemisphere and a transparent soft-material plate that was driven via tangentially compliant support. The measurement of the tangential deflection and the observation of the contact zone were performed simultaneously. Schallamach waves synchronized with stick-slip were observed. Stick-slip associated with Schallamach waves is likely to occur for low contact load and high driving speed, which apparently contradicts the tendency of general stick-slip. This can be explained by the magnitude of the stick-slip parameter that considers the contact-area variation induced by Schallamach waves.

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.

Optimal design of timber beam

In modern timber structures a large number of beams are loaded with bending Contemporary engineering practice has shown that the effect of tangential stress and deflection of beams are not controlled during the design of this kind of beams. This could produce negative consequences in structure behavior during the exploitation. Using optimal design procedure in this article, the member is designed for bending in two planes. The following criteria must be observed: normal bending stress, shear stress and maximal deflection.

High-Performance Surface-Micromachined Inchworm Actuator

This work demonstrates a polycrystalline silicon surface-micromachined inchworm actuator that exhibits high-performance characteristics such as large force (/spl plusmn/0.5 millinewtons), large velocity range (0 to /spl plusmn/4.4 mm/sec), large displacement range (/spl plusmn/100 microns), small step size (/spl plusmn/10, /spl plusmn/40 or /spl plusmn/100 nanometers), low power consumption (nanojoules per cycle), continuous bidirectional operation and relatively small area (600 /spl times/ 200/spl mu/m/sup 2/). An in situ load spring calibrated on a logarithmic scale from micronewtons to millinewtons, optical microscopy and Michelson interferometry are used to characterize its performance. The actuator consists of a force-amplifying plate that spans two voltage-controlled clamps, and walking is achieved by appropriately sequencing signals to these three components. In the clamps, normal force is borne by equipotential rubbing counterfaces, enabling friction to be measured against load. Using different monolayer coatings, we show that the static coefficient of friction can be changed from 0.14 to 1.04, and that it is load-independent over a broad range. We further find that the static coefficient of friction does not accurately predict the force generated by the actuator and attribute this to nanometer-scale presliding tangential deflections.

Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.