ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS

A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.

Influence of Angle of Attack and Lateral Force between Wheel and Rail on Wear of Rail ——a Laboratory Study

Angle of attack and lateral force are two important parameters influencing wheel rail wear. This paper deals with the question of influences of the angle of attack and the lateral force on the wear of rail. A series of experiments are conducted on 1/4 JD 1 Wheel/Rail Tribology Simulation Facility. The angles of attack selected in the tests are 0°16′30″, 0°37′40″ and 1°0′0″ respectively. The lateral forces selected in the tests are 0.694 kN, 1.250 kN and 2.083 kN, respectively corresponding to the lateral forces of 25 kN, 45 kN and 75 kN measured in the field, with the aim of keeping the same ratio of L/V between laboratory and field conditions. It is found that the larger the angle of attack is, the more serious the wear of rail is. The relation of rail wear rate versus angle of attack is non linear, and the relation of rail wear rate versus lateral force is approximately linear. The influence of angle of attack is more serious than that of lateral force. For the tractive wheelset, the wear index involving linear and quadratic function terms of angle of attack has good agreement with the limited experimental data. Some conclusions are given.

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.

Lateral Force Characteristics of Cartridge Valve Core

The flow field of eccentric conical crevices is formed into the working process of hydraulic valves.Therefore, the valve core is readily subjected to a large lateral force which affects the dynamic response speed.Here, a new type of cartridge valve core structure is proposed to solve this problem. The numerical simulationmethod is applied to analyze the flow characteristics of clearance flow field on velocity distribution, pressuredistribution, valve core motion speed, and leakage. The results using computational fluid dynamics (CFD) showthat the guide groove is set on the surface of the cartridge valve core, increasing the connecting length of thevalve core, forming a uniform radial pressure distribution and velocity distribution, effectively reducing the lateralforce, and at the same time ensuring that the leak is not too big. These findings provide theoretical guidance anda basis for optimizing cartridge valve to reduce the occurrence of jamming and improve the response frequency.

Chiral lateral optical force near plasmonic ring induced by Laguerre–Gaussian beam

Owing to the good adjustability and the strong near-field enhancement,surface plasmons are widely used in optical force trap,thus the optical force trap can achieve excellent performance.Here,we use the Laguerre–Gaussian beam and a plasmonic gold ring to separate enantiomers by the chiral optical force.Along with the radial optical force that traps the particles,there is also a chirality-sign-sensitive lateral force arising from the optical spin angular momentum,which is caused by the interaction between optical orbit angular momentum and gold ring structure.By selecting a specific incident wavelength,the strong angular scattering and non-chiral related azimuthal optical force can be suppressed.Thus the chiral related azimuthal optical force can induce an opposite orbital rotation of the trapped particles with chirality of different sign near the gold ring.This work proposes an effective approach for catchingand separating chiral enantiomers.

Numerical Study on Characteristics of Supercavitating Flow Around the Variable-Lateral-Force Cavitator

A control scheme named the variable-lateral-force cavitator, which is focused on the control of lift force, drag force and lateral forces for underwater supercavity vehicles was proposed, and the supercavitating flow around the cavitator was investigated numerically using the mixture multiphase flow model. It is verified that the forces of pitching, yawing, drag and lift, as well as the supercavity size of the underwater vehicle can be effectively regulated through the movements of the control element of the variable-lateral-force cavitator in the radial and circumferential directions. In addition, if the control element on either side protrudes to a height of 5% of the diameter of the front cavitator, an amount of forces of pitching and yawing equivalent to 30% of the drag force will be produced, and the supercavity section appears concave inwards simultaneously. It is also found that both the drag force and lift force of the variable-lateral-force cavitator decline as the angle of attack increases.

Lateral ice force acting on a vertical cylinder

In general, forward directed ice force is only considered by the designer. But experiments prove that thelateral ice force caused by the uneven contact between ice sheet and the pile also exists. The lateral ice force does notobject to normal or Gumbel distribution, and is not relevant to the forward directed one in numerical value. Preventivemeasures should be taken to avoid the damage caused by the lateral ice force to the structure in design phase.

Lateral magnetic stiffness under different parameters in a high-temperature superconductor levitation system

Magnetic stiffness determines the stability of a high-temperature superconductor(HTS)magnetic levitation system.The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods.The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement,which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters.In this paper,we study the influences of some physical and geometrical parameters,including the strength of the external magnetic field(B0)produced by a rectangular permanent magnet(PM),critical current density(Jc),the PM-to-HTS area ratio(α),and thickness ratio(β),on the lateral stiffness by using a numerical approach under zero-field cooling(ZFC)and field cooling(FC)conditions.In the first and second passes of the PM,the lateral stiffness at most of lateral positions essentially increases with B0 increasing and decreases withβincreasing in ZFC and FC.The largest lateral stiffness at every lateral position is almost produced by the minimum value of Jc,which is obviously different from the lateral force–Jc relation.Theα-dependent lateral stiffness changes with some parameters,which include the cooling conditions of the bulk HTS,lateral displacement,and movement history of the PM.These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.

Analysis of the Effect of Trailer Tire Size on the Articulated Vehicle’s Stability

This research paper aims to identify the effect of tire size on the handling characteristics of a trailer attached to a vehicle. In various stability tests, different models with different tires from the market were tested. A successful outcome of this research would generate an efficient tire selection process and improve the handling of a trailer attached to a vehicle while maximizing fuel efficiency. In this study, different accurate tire models using the magic formula were developed in vehicle dynamics modelling and simulation software. These models were then simulated on on-road conditions to predict vehicle and trailer behaviour under different conditions within the software. Two distinct tests were conducted, the J-Turn test and the Double Lane change test. The results of these tests were used to evaluate the handling characteristics and decide on a better tire size for the trailer attached to the vehicle.

Simulation of Hydrodynamic Performance of Drag and Double Reverse Propeller Podded Propulsors

The unsteady performance of drag and double reverse propeller podded propulsors in open water was numerically simulated using a computational fluid dynamics （CFD） method. A moving mesh method was used to more realistically simulate propulsor working conditions, and the thrust, torque, and lateral force coefficients of both propulsors were compared and analyzed. Forces acting on different parts of the propulsors along with the flow field distribution of steady and unsteady results at different advance coefficients were compared. Moreover, the change of the lateral force and the difference between the abovementioned two methods were mainly analyzed. It was shown that the thrust and torque results of both methods were similar, with the lateral force results having the highest deviation

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.

Packaging Effects on Fiber Bragg Grating Sensor Performance

In this paper, the effects of packaging material and structure of fiber Bragg grating sensor performance are investigated. The effects of thermal expansion coefficient of different embedding materials on the temperature sensitivities of the FBG sensors are studied both theoretically and experimentally with good agreement, which provides a means for selection of FBG packaging material to achieve desired temperature sensitivity. We also demonstrate a 4-point bending structured FBG lateral force sensor that measures up to 242N force with well-preserved reflection spectrum, whereas for 3-point bending structure, multiple-peaks start to occur when applied force reaches 72N.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

Coupling simulation of fluid structure interaction in the stirred vessel with a pitched blade turbine

The interaction between fluid and a down-pumping pitched blade turbine fixed with a flexible shaft in the stirred vessel, as a typical fluid structure interaction phenomenon, was simulated by coupling the Computational Fluid Dynamics and Computational Structural Dynamics. Based on the verification of the simulated impeller torque and dimensionless shaft bending moment with experimental result, the dimensionless shaft bending moment and various loads acting on impeller(including lateral force, axial force and bending moment) were discussed in detail. By separating and extracting the fluid and structural components from those loads, the results show that the shaft bending moment mainly results from the lateral force on impeller although the axial force on impeller is much larger. The impeller mass imbalance increases the shaft bending moment and the lateral force on impeller, but has little influence on the axial force and bending moment acting on impeller. The dominant frequencies of impeller forces are macro-frequency, speed frequency and blade passing frequency, and are associated with the impeller mass imbalance.

Finite Element Analysis for Groove Wander Prediction of Passenger Car Tires with the Longitudinal Tread Grooves

A finite element modeling technique is employed in this paper to predict the groove wander of longitudinal tread grooved tires. In generally, groove wander is the lateral force acting on a vehicle’s wheel resulting from the combination of rain grooves. If the lateral force of tire is generated by groove wander, unexpected lateral motion of vehicle will happen and it makes drivers uncomfortable. This paper describes the effect of groove wander according to the shape condition of tire tread groove and highway groove using the finite element analysis based on a static loading or a steady-state rolling assumption. The road groove can be located anywhere relative to the longitudinal tread groove. Therefore, the lateral force of the tire is changing depending on the location of the groove road. The numerical results for groove wander prediction of the longitudinal tread grooved tires are compared with the subjective evaluation. It is found that the waveform for the tire with varying grooved road position has a peak-to-peak lateral force in order to estimate the rating of groove wander. The effect of the road groove width and the pitch length on the peak-to-peak lateral force of tire is discussed. It is found that the prediction of FEA-based groove wander model using finite element analysis will be useful for the reliability design of the tire tread pattern design.

Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method

A method for analysing the vehicle-bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities(PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel-rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors(derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.

Interaction analysis of back-to-back mechanically stabilized earth walls

Back-to-back mechanically stabilized earth walls （BBMSEWs） are encountered in bridge approaches, ramp ways, rockfall protection systems, earth dams, levees and noise barriers. However, available design guidelines for BBMSEWs are limited and not applicable to numerical modeling when back-to-back walls interact with each other. The objective of this paper is to investigate, using PLAXIS code, the effects of the reduction in the distance between BBMSEW, the reinforcement length, the quality of backfill material and the connection of reinforcements in the middle, when the back-to-back walls are close. The results indicate that each of the BBMSEWs behaves independently if the width of the embankment between mechanically stabilized earth walls is greater than that of the active zone. This is in good agreement with the result of FHWA design guideline. However, the results show that the FHWA design guideline underestimates the lateral earth pressure when back-to-back walls interact with each other. Moreover, for closer BBMSEWs, FHWA design guideline strongly overestimates the maximum tensile force in the reinforcement. The investigation of the quality of backfill material shows that the minor increase in embankment cohesion can lead to significant reductions in both the lateral earth pressure and the maximum tensile force in geosynthetic. When the distance between the two earth walls is close to zero, the connection of reinforcement between back-to-back walls significantly improves the factor of safety.

An experimental methodology for the concurrent characterization of multiple parameters influencing nanoscale friction

A structured transdisciplinary method for the experimental determination of friction in the nanometric domain is proposed in this paper.The dependence of nanoscale friction on multiple process parameters on these scales,which comprise normal forces,sliding velocities,and temperature,was studied via the lateral force microscopy approach.The procedure used to characterize the stiffness of the probes used,and especially the influence of adhesion on the obtained results,is thoroughly described.The analyzed thin films were obtained by using either atomic layer or pulsed laser deposition.The developed methodology,based on elaborated design of experiments algorithms,was successfully implemented to concurrently characterize the dependence of nanoscale friction in the multidimensional space defined by the considered process parameters.This enables the establishment of a novel methodology that extends the current state-of-the-art of nanotribological studies,as it allows not only the gathering of experimental data,but also the ability to do so systematically and concurrently for several influencing variables at once.This,in turn,creates the basis for determining generalizing correlations of the value of nanoscale friction in any multidimensional experimental space.These developments create the preconditions to eventually extend the available macro-and mesoscale friction models to a true multiscale model that will considerably improve the design,modelling and production of MEMS devices,as well as all precision positioning systems aimed at micro-and nanometric accuracy and precision.

Synergistic nano-tribological interaction between zinc dialkyldithiophosphate(ZDDP)and methyl oleate for biodiesel-fueled engines

In biodiesel-fueled compression-ignition(CI)engines,dilution by unburned biodiesel has been found to have adverse effects on the boundary lubrication properties of additives in fully formulated engine lubricants.Such dilution of engine lubricants could be even more pronounced for CI engines running on higher blend concentrations of biodiesel.Given the nanoscopic nature of the interaction,this study seeks to determine the nano-tribological properties of an engine lubricant additive(e.g.,zinc dialkyldithiophosphate(ZDDP))when diluted with a fatty acid methyl ester(e.g.,methyl oleate).Using lateral force microscopy(LFM)together with a fluid imaging technique,the lowest nanoscopic friction forces and coefficient of friction values(0.068-0.085)were measured for ZDDP when diluted with 70 vol%of methyl oleate.These values are also observed to be lower than those measured for neat ZDDP and neat methyl oleate,respectively,under similar conditions.Subsequently,interpreting the data with the Eyring thermal activation energy approach,it could then be elucidated that the lower frictional losses observed for the contact lubricated with this volumetric mixture are a result of the lower potential energy barrier and activation energy required to initiate sliding.These energy values are approximated to be 2.6%and 28.9%(respectively)lower than that of the contact lubricated with neat ZDDP.It was also found that the mixture,at this volumetric concentration,possesses the highest possible pressure activation energy(load-carrying capacity)along with the lowest possible shear activation energy(shearing),potentially indicating optimum tribological conditions for boundary lubrication.Thus,the findings of this study suggest that an optimum concentration threshold exists in which a synergistic nano-tribological interaction between additives and fatty acid methyl esters can be attained,potentially reducing boundary frictional losses of lubricated conjunctions.Such findings could prove to be essential in effectively formulating synergistic additive concentrations for engine lubricants used in biodiesel-fueled CI engines.

Capillary grip-induced stick-slip motion

We present capillary grip-induced stick-slip motion,a nanoscale tribological effect,where the role of a nanoscale confined water meniscus formed between a buckled sharp tip and a glass or mica surface is addressed by shear dynamic force measurement.We obtained the effective elasticity,viscosity,conservative(elastic)and non-conservative(viscous)forces,energy dissipation,and lateral force using small oscillation,amplitude-modulation,and shear-mode quartz tuning fork-atomic force microscopy(QTFAFM).We distinguished the conservative and non-conservative forces by investigating the dependence of normal load and relative humidity,slip length,and stick-slip frequency.We found that the confined nanoscale water enhances the lateral forces via capillary grip-induced stick-slip on a rough surface,resulting in an increase of static lateral force(3-fold for both substrates)and kinetic lateral force(6-fold for glass,3-fold for mica).This work provides quantitative and systematic understanding of nanoscale tribology properties in humid ambient conditions and is thus useful for control of friction as well as characterization of tribology in nanomaterials and nanodevices.