Normal Interaction Forces Research Articles

Dynamic Modeling and Behavior of Cylindrical Roller Bearings Considering Roller Skew and the Influence of Eccentric Load

At high speeds, skew and skid may frequently occur for the rollers in cylindrical roller bearings, especially when under eccentric load, as the uneven load distribution along the generatrix of the roller further aggravates this phenomenon. In this paper, a dynamic model of a cylindrical roller bearing was established, taking into account roller skewing and interactions with the cage. Firstly, the interaction between the roller and the raceway was calculated by slicing the roller along its generatrix. Furthermore, the computation of the interaction between the roller and the cage is based on elastic theory, taking into account pocket clearance. Subsequently, the dynamic equations for both rollers and cage were derived. Based on this foundation, an investigation was conducted to reveal how rotational speed, radial loads, and moment loads affect roller slipping, skewing characteristics, and interactions with the cage under uneven load conditions. The findings indicate a direct proportionality between roller slipping and bearing speed while exhibiting an inverse relationship with load magnitude. Additionally, it was observed that both bearing speed and load have a direct influence on roller skewing angle. Moreover, normal interaction force between the roller and cage demonstrates a direct proportionality to bearing speed while inversely correlating with load magnitude.

Quantitative dynamic force microscopy with inclined tip oscillation.

In the mathematical description of dynamic atomic force microscopy (AFM), the relation between the tip–surface normal interaction force, the measurement observables, and the probe excitation parameters is defined by an average of the normal force along the sampling path over the oscillation cycle. Usually, it is tacitly assumed that tip oscillation and force data recording follows the same path perpendicular to the surface. Experimentally, however, the sampling path representing the tip oscillating trajectory is often inclined with respect to the surface normal and the data recording path. Here, we extend the mathematical description of dynamic AFM to include the case of an inclined sampling path. We find that the inclination of the tip movement can have critical consequences for data interpretation, especially for measurements on nanostructured surfaces exhibiting significant lateral force components. Inclination effects are illustrated by simulation results that resemble the representative experimental conditions of measuring a heterogeneous atomic surface. We propose to measure the AFM observables along a path parallel to the oscillation direction in order to reliably recover the force along this direction.

Semi-Autogenous Wet Grinding Modeling with CFD-DEM

The paper highlights the features of constructing a model of a wet semi-autogenous grinding mill based on the discrete element method and computational fluid dynamics. The model was built using Rocky DEM (v. 4.4.2, ESSS, Brazil) and Ansys Fluent (v. 2020 R2, Ansys, Inc., United States) software. A list of assumptions and boundary conditions necessary for modeling the process of wet semi-autogenous grinding by the finite element method is presented. The created model makes it possible to determine the energy-coarseness ratios of the semi-autogenous grinding (SAG) process under given conditions. To create the model in Rocky DEM the following models were used: The Linear Spring Rolling Limit rolling model, the Hysteretic Linear Spring model of the normal interaction forces and the Linear Spring Coulomb Limit for tangential forces. When constructing multiphase in Ansys Fluent, the Euler model was used with the primary phase in the form of a pulp with a given viscosity and density, and secondary phases in the form of air, crushing bodies and ore particles. The resistance of the solid phase to air and water was described by the Schiller–Naumann model, and viscosity by the realizable k-epsilon model with a dispersed multiphase turbulence model. The results of the work methods for material interaction coefficients determination were developed. A method for calculating the efficiency of the semi-autogenous grinding process based on the results of numerical simulation by the discrete element method is proposed.

Frictional viscoelastic based model for spherical particles collision

In this paper, collision of two balls in three dimensions with regard to energy loss and friction is studied. This investigation intends to propose the procedure which can determine the condition of pure sliding, sliding with rolling or sticking, and rolling or sticking at the beginning of contact. Furthermore, the other aim of this research is to suggest the closed-form relation for post-collision angular and linear velocities in which the possibility of three regimes of impact, pure sliding, sliding with rolling, and pure rolling, are considered. In this investigation, viscous Hertz contact force describes the normal interaction force. Moreover, stick regime is not taken into account and during sliding, Coulomb friction is considered as a tangential force, which is endorsed by collision experimental data in case the collision regime is not stick regime. Considering aforementioned issues along with employing momentum conservation, the condition for the possibility of transformation of sliding to sticking or rolling during collision, and furthermore, the analytical relation for post-collision velocities are achieved. Eventually, in order to demonstrate the procedure of solving two balls collision, numerical examples are presented.

The role of copolymer composition on the specific ion and thermo-response of ethylene glycol-based brushes

Thermoresponsive ethylene glycol based comb-polymer brushes were studied as a function of copolymer composition in aqueous electrolyte solutions. Homopolymer poly oligo(ethylene glycol) methyl ether methacrylate (POEGMA300) and statistical copolymer brushes with 60 mol% OEGMA300 and 40 mol% (di(ethyleneglycol) methyl ether methacrylate) (MEO2MA) underwent a monotonic swollen to collapsed transition with increasing temperature. Neutron reflectometry and ellipsometry measurements showed that the higher ethylene glycol content of the homopolymer brush led to a higher degree of swelling for a given temperature, with the transition occurring over a wider temperature range than the copolymer brush. Dynamic atomic force microscopy force measurements revealed minimal impact of probe velocity on normal interaction forces for the homopolymer brush. In contrast, a significant increase in both repulsion and adhesion was observed for the copolymer brush. Exposure to potassium thiocyanate solutions increased the degree of swelling at any given temperature while potassium acetate showed the opposite behaviour for both brush compositions. However, the homopolymer brushes displayed a greater increase in swelling due to thiocyanate and reduced collapse due to acetate.

Transformation of sliding motion to rolling during spheres collision

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.

Use of discrete element modeling to study the stress and strain distribution in cyclic torsional shear tests

In this research, a torsional cyclic shear test was modeled using the 3D discrete element method (DEM). The results are compared against experimental data and micro-mechanical aspects of the soil during the loading are discussed. The aim of the work is to study the homogeneity of strains during this laboratory test and to compare the micro-mechanical behavior of the soil sample for different strain levels. The experimental investigation was performed using a synthetic soil material made of glass beads, which simplifies the modeling and calibration since normal interaction forces do not induce rotation of the particles. Both the model and experimental tests used the same grading distribution and particle size. We showed that the hysteresis cycles can be properly reproduced in terms of shape and magnitude. Thus, we obtained a robust estimation for the secant shear modulus and damping ratio at different strain levels. With this, it was possible to build stiffness degradation and damping increase curve to compare it with experimental data obtained from torsional shear tests. Based on this validation of the DEM model, we discuss the micro-mechanical behavior of the soil and its relation with the macroscopic parameters obtained. It is shown that shear strain distribution on the sample is not uniform and that large values of strains concentrate close to the top of the sample as top rotation increases, which differs from the standard assumption of a constant value across the height of the sample. Additionally, it is observed that at 0.8 times radius, the cumulative torque reaches approximately 90% of the total torque applied to sample.

Static and dynamic theoretical analyses of a scanning tip on suspended graphene surface

Recent research progress shows that graphene exhibits distinct adhesion and friction behaviors. In the paper, the static and dynamic analyses of a diamond tip sliding on suspended graphene surface are conducted via theoretical and numerical research methods, and the adhesion and friction properties between them are investigated. The analytical expression of interaction potential between a diamond tip and graphene surface is derived based on the interatomic pairwise potential, and then, the lateral and normal interaction forces are calculated. The equilibrium heights and adhesion energy of the diamond tip are calculated on three particular sites of graphene surface. The influence of vertical distance between the tip and graphene surface is studied on the maximum static frictional force and initial velocity of tip. What is more, the influence of scanning velocity and damping are also analyzed on the frictional force and dynamic behaviors of the scanning tip, and the “stick-slip” phenomenon is observed and discussed by the numerical calculation.

Numerical simulation of lateral control in supersonic cross jet flow

To investigate the effect of angle of attack and jet position on the lateral control force in the cross jet flow,the paper firstly simulated the supersonic cross jet flow by the numerical methods. The calculated longitudinal wall pressure distribution agreed well with the experimental results. Jet force amplification factor in longitudinal direction and center of interaction force were used to evaluate the actual performance of lateral control force in jet interaction. Moreover,normal interaction force accumulation coefficient was introduced to analyze how four characteristic areas on the body surface affect the lateral control force in jet interaction.The numerical results indicate that the lateral control force in jet interaction,which is equivalent to a normal force,together with a nose-down moment around center of jet,are not equal to the jet force in design. The wake zone of low pressure is a determinant factor affecting the actual performance of lateral control force. As the angle of attack increases,the strength of the interaction pressure in the wake zone decreases,which will enhance the lateral control force. With the jet location moving backward,the scope of the wake zone diminishes,which will improve the actual performance of lateral control force.

Interaction forces in RC beams strengthened with near-surface mounted rectangular bars and strips

The flexural performance of a reinforced concrete (RC) beam can be improved using the near-surface mounted (NSM) FRP strengthening technique. In the NSM technique, grooves are first cut in the concrete cover, and FRP bars are then placed in the grooves using a suitable bonding adhesive. In such an FRP-strengthened RC beam, debonding failure at the two bar ends may occur due to local high interaction forces in the bar-end regions between the RC beam and the FRP bars. This paper presents a theoretical investigation into these interaction forces in RC beams strengthened with NSM FRP rectangular bars (including FRP strips with a narrow rectangular section as a special case). By introducing and defining two interfacial stiffness parameters, an analytical solution for the tangential and the normal interaction forces between the beam and the NSM bars is first obtained based on the analytical solution developed by Smith and Teng for beams strengthened with an externally bonded FRP plate. The accuracy of the analytical solution is demonstrated by comparing its predictions with those from a 3-D linear elastic finite element (FE) model. The numerical results from both the analytical solution and the 3-D FE model confirms the existence of high interaction forces in the bar-end regions as the cause for bar-end debonding failure which has been commonly observed in tests. While the present paper is focused on RC beams strengthened with NSM rectangular bars, the proposed approach is general and is applicable to a range of similar problems such as RC beams strengthened with NSM bars of other cross-sectional shapes (e.g. circular and elliptical shapes) as well as timber beams strengthened with NSM bars.

The Electrochemical Surface Forces Apparatus: The Effect of Surface Roughness, Electrostatic Surface Potentials, and Anodic Oxide Growth on Interaction Forces, and Friction between Dissimilar Surfaces in Aqueous Solutions

We present a newly designed electrochemical surface forces apparatus (EC-SFA) that allows control and measurement of surface potentials and interfacial electrochemical reactions with simultaneous measurement of normal interaction forces (with nN resolution), friction forces (with μN resolution), and distances (with Å resolution) between apposing surfaces. We describe three applications of the developed EC-SFA and discuss the wide-range of potential other applications. In particular, we describe measurements of (1) force-distance profiles between smooth and rough gold surfaces and apposing self-assembled monolayer-covered smooth mica surfaces; (2) the effective changing thickness of anodically growing oxide layers with Å-accuracy on rough and smooth surfaces; and (3) friction forces evolving at a metal-ceramic contact, all as a function of the applied electrochemical potential. Interaction forces between atomically smooth surfaces are well-described using DLVO theory and the Hogg-Healy-Fuerstenau approximation for electric double layer interactions between dissimilar surfaces, which unintuitively predicts the possibility of attractive double layer forces between dissimilar surfaces whose surface potentials have similar sign, and repulsive forces between surfaces whose surface potentials have opposite sign. Surface roughness of the gold electrodes leads to an additional exponentially repulsive force in the force-distance profiles that is qualitatively well described by an extended DLVO model that includes repulsive hydration and steric forces. Comparing the measured thickness of the anodic gold oxide layer and the charge consumed for generating this layer allowed the identification of its chemical structure as a hydrated Au(OH)(3) phase formed at the gold surface at high positive potentials. The EC-SFA allows, for the first time, one to look at complex long-term transient effects of dynamic processes (e.g., relaxation times), which are also reflected in friction forces while tuning electrochemical surface potentials.

Interaction forces between pipelines and submarine slides — A geotechnical viewpoint

Assessment of interaction forces between deep water pipelines and potential submarine slides, debris flows and turbidity currents is an important aspect of geohazard studies. Historically, interaction forces have tended to be expressed in terms of drag factors, within a traditional fluid mechanics framework, with the drag factors depending strongly on an equivalent Reynolds number for the non-Newtonian debris material. Here, we have followed a more geotechnical approach, allowing the interaction forces to be expressed in terms of a strain-rate dependent shear strength of the debris material, and with the inclusion of a drag term (with fixed drag coefficient) for high velocity, low strength, combinations. This superposition approach treats separately the interaction forces that arise from the strain-rate dependent strength and the inertia of the debris, rather than combining them into a single drag force. A failure envelope is proposed, allowing axial and normal interaction forces to be estimated for any angle of attack of the debris flow.

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net-neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.

Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory

A relationship based on a modified couple stress theory is developed to investigate the flexural sensitivity of a V-shaped cantilever of an atomic force microscope (AFM) taking into account the normal interaction force between the cantilever tip and the sample surface. An approximate solution to the flexural vibration problem is obtained using the Rayleigh–Ritz method. The results show that the sensitivity of the V-shaped AFM cantilever using the modified couple stress theory is smaller than that using the classical beam theory for the lower contact stiffness. However, when the contact stiffness becomes higher, the situation is reversed. Furthermore, as the ratio of cantilever thickness to internal material length scale parameter decreases, the sensitivity of the cantilever decreases.

Normal and Lateral Interactions between Thermosensitive Nanoparticle Monolayers in Water

Static and dynamic interaction forces between two thermosensitive polymeric nanoparticle monolayers grafted onto mica surfaces and immersed in water were studied using a surface forces apparatus. The polymeric nanoparticles (NPs) were made of N,N-diethylacrylamide and had a hydrodynamic diameter of ca. 780 nm at 20 degrees C in aqueous suspension. They were irreversibly grafted onto chemically modified mica surfaces at a constant surface coverage of 2.6 NPs/mum(2). The measured normal forces between two opposing NP monolayers were found to be strongly dependent on the temperature. At temperatures lower than the lower critical solution temperature (LCST), the grafted NPs were swollen, and the normal interaction forces between the two NP monolayers were repulsive. Above the LCST, the NPs collapsed, and attractive forces between the NP layers were measured. The swollen NPs were found to exhibit very low friction forces compared to the collapsed ones. The effect of the sliding velocity on the shear stress was investigated, and the results are in agreement with the so-called adhesive friction model developed for rubber friction. Our results suggest that the water content in the contact area and the interdiffusion of polymer chains are important parameters in determining the friction between polymer-bearing surfaces.

Friction and Normal Interaction Forces between Irreversibly Attached Weakly Charged Polymer Brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.

Flexural sensitivity of a V-shaped cantilever of an atomic force microscope

The flexural sensitivity of a V-shaped cantilever of an atomic force microscope has been analyzed, taking into account the angle between the cantilever and the sample surface, including not only the normal interaction force, but also the lateral force, and an approximate solution is obtained using the Rayleigh–Ritz method. The results show that the effect of the cantilever slope on the sensitivity is significant. The sensitivity increases with decreasing slope when the contact stiffness is low. The flexural vibration mode of the V-shaped cantilever is more sensitive than that of a uniform cross-section cantilever. However, when the contact stiffness becomes large, the situation is reversed. Furthermore, decreasing the width and increasing the leg length increase the flexural sensitivity when the contact stiffness is low. Increasing the tip length increases the flexural sensitivity when the contact stiffness is high.

Automatic deburring utilizing a real-time impedance control strategy

The design, development and testing of a new and improved real-time active impedance control system and its applications in deburring processes are presented. This control system is capable of simulating an active compliant device (mass, spring, and dashpot) to accommodate the effects of the normal interaction forces occurring during the deburring operation. Another useful feature of this control system is that it provides a bandwidth of 25 Hz. The mass, stiffness, and damping coefficients of the impedance controller can be selected or modified, and input by the user via a personal computer to study different behavior patterns in the controlled system. Results of actual deburring tests using this impedance controller incorporating both force and position control strategies are included.