Distribution Of Interaction Forces Research Articles

Stress state of the grinding tool loaded with tangential force

Purpose. Determining the interaction mechanism of discrete grains through material that binds them in a tool for abrasive material processing in the case of its loading with a tangentially directed cutting force. Methodology. Development and analytical solution to a mathematical model formulated on the basis of static equilibrium of an abrasive grain as a system element of tool grains bound with a material with excellent mechanical characteristics. Findings. A mathematical model has been developed and an algorithm has been formulated to analytically determine the stress-strain state parameters of a tool for abrasive processing of materials, which is loaded with a discrete cutting force, tangential to its working surface. The nature of the dependence of stresses and deformations on mechanical parameters, the quantity of grains and the material binding them in an abrasive tool, loaded with a unit tangential force, has been determined. Originality. The loading of the extreme grains leads to greater displacements, tangents of the shear angles of the material binding the grains. They decrease with increasing quantity of grain rows in the tool or with increasing quantity of grains to the nearest tool edge. Practical value. The distribution of interaction forces of grains and stresses in the material binding them has been determined. The found distribution allows one in the process of developing the tool and technology, in which it is involved, to comprehensively assess the influence of tangential load value of the tool working grain on its stress state and the material containing the grains. The determined stress state makes it possible to predict the number of loading cycles until the simultaneous rational wear of the grain and the destruction of that part of the material that contains it. The linear formulation of the problem makes it possible to take into account the mutual influence of the tangential loads of several grains on the stress-strain state of the tool as a whole.

A Fourier-based elastic continuum solution for jointed pipeline response to tunneling

This paper deals with the problem of tunneling effects on existing jointed pipelines. It extends a recently developed Fourier-based elastic continuum approach which has been applied to continuous pipelines. Unlike the continuous pipeline solution, in which the response in the spatial frequency domain is orthogonal (that is, each frequency response is independent of other frequencies), the joints lead to coupling between the spatial frequencies. Within the paper, closed form expressions are provided for the set of equations describing the coupling and interaction between the spatial frequencies. These expressions can directly be used to solve the global response of the jointed pipeline. The development is based on energy principles, and involves full cross-sectional as well as longitudinal compatibility, and hence may be regarded as more rigorous than previously published elastic continuum solutions which involve various assumptions regarding the distribution of interaction forces and discretization. The results of the suggested solution are compared against previous published, matrix based, solutions, where it is shown that the current method is well suited for the jointed pipeline problem. Finally, the condition of the more simplified Winkler system is addressed and various subgrade reaction models are discussed and compared with the more rigorous elastic continuum solution.

Non-Gaussian tail in the force distribution: a hallmark of correlated disorder in the host media of elastic objects

Inferring the nature of disorder in the media where elastic objects are nucleated is of crucial importance for many applications but remains a challenging basic-science problem. Here we propose a method to discern whether weak-point or strong-correlated disorder dominates based on characterizing the distribution of the interaction forces between objects mapped in large fields-of-view. We illustrate our proposal with the case-study system of vortex structures nucleated in type-II superconductors with different pinning landscapes. Interaction force distributions are computed from individual vortex positions imaged in thousands-vortices fields-of-view in a two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated in point-disordered media present Gaussian distributions of the interaction force components. In contrast, if the media have dilute and randomly-distributed correlated disorder, these distributions present non-Gaussian algebraically-decaying tails for large force magnitudes. We propose that detecting this deviation from the Gaussian behavior is a fingerprint of strong disorder, in our case originated from a dilute distribution of correlated pinning centers.

Continuum modeling of ion-selective membranes constructed from functionalized carbon nanotubes

This paper aims to analyze the problem of ion selectivity and, in particular, sodium and chloride ions, through semi-infinite carbon nanotubes decorated by a functional group at the entry. A continuum approach is adopted to model the Van der Waals and the electrostatic interactions using the 6–12 Lennard–Jones and the Coulomb potentials, respectively. Suction energy imparted to the ion in the form of an increased velocity is determined. Moreover, an acceptance condition is obtained in the absence and the presence of functional group to examine whether the rested core is completely sucked into the nanotube or not. With respect to the proposed formulations, numerical results of suction and acceptance energies along with potential energy and interaction force distribution are presented by varying the functional group charge and nanotube radius. Unlike acceptance energy, suction energy configuration is shown to be independent of electrostatic interactions. Our numerical results also indicate that the ion selectivity can be altered by changing the sign and magnitude of functional group charge. In the presence of functional group, it is observed that the acceptance radius of a counterion always reduces and thus the ion can pass through the nanotube more easily.

Continuum study on the mechanics of ion-based carbon nanocones as gigahertz oscillators

There is a growing interest in the development of nanomechanical oscillators operating in the gigahertz range and beyond. This paper introduces a novel nano-oscillator based on a chloride ion inside an open carbon nanocone decorated by functional groups at both small and wide ends. Assuming that the carbon atoms and the electric charges of functional groups are evenly distributed over the surface and the two ends of nanocone, respectively, a continuum-based model is presented through which potential energy and interaction force are evaluated analytically. The van der Waals interactions between ion and nanocone are modeled by the 6–12 Lennard–Jones potential, while the electrostatic interactions between ion and two functional groups are modeled by the Coulomb potential. With respect to the proposed formulations, potential energy and interaction force distribution are presented by varying sign and magnitude of functional groups charge and geometrical parameters (size of small and wide ends of nanocone and its vertex angle). Using the fourth-order Runge–Kutta numerical integration scheme, the equation of motion is also solved to arrive at the time histories of separation distance and velocity of ion. An extensive study is performed to investigate the effects of sign and magnitude of functional groups charge, geometrical parameters, and initial conditions (initial separation distance and initial velocity) on the oscillatory behavior of ion-electrically charged open carbon nanocone oscillator. Numerical results demonstrate that the oscillation frequency of chloride ion inside an uncharged nanocone is respectively lower and higher than those generated inside a nanocone whose small end is decorated by positively and negatively charged functional groups. It is further shown that oscillation frequency is highly affected by the sign of electric charges distributed at the small end of nanocone.

Gigahertz nanomechanical oscillators based on ions inside cyclic peptide nanotubes: a continuum study

The present work aims to investigate the mechanical oscillatory behavior of ions, and in particular \({{\rm Li}^{+}, {\rm Na}^{+}, {\rm Rb}^{+}}\) and \({{\rm Cl}^{-}}\) ions, inside a cyclo[(–d-Ala–l-Ala)4–] peptide nanotube using the continuum approximation along with the 6–12 Lennard–Jones (LJ) potential function. Assuming that each peptide unit is comprised of an inner and an outer tube, the van der Waals (vdW) potential energy and interaction force between an ion and a cyclic peptide nanotube (CPN) are determined analytically. With respect to the present formulations, a detailed parametric study is conducted on the vdW potential energy and interaction force distributions by varying the number of peptide units. Employing the conservation of mechanical energy principle, a novel expression for precise evaluation of oscillation frequency is introduced. To verify the accuracy of the proposed frequency expression, the results obtained from energy equation are compared with the ones predicted through solving the equation of motion numerically. The effects of number of peptide units and initial conditions including initial separation distance and velocity on the oscillatory behavior of various ions inside CPNs are explored. Among the considered ions, \({{\rm Cl}^{-}}\) ion is found to generate the highest frequency. According to the potential energy profile, one oscillatory zone for one peptide unit and different oscillatory zones for more than one peptide unit are observed. Numerical results indicate that optimal frequency decreases with increasing the number of peptide units and almost remains unchanged when the number of peptide units exceeds four.

Mobility evaluation of wheeled robots on soft terrain: Effect of internal force distribution

Many applications of wheeled robots include operations in unstructured environments. Optimizing vehicle mobility is of key importance in these cases. Reduced mobility can limit the ability of the robot to achieve the mission goals and can even render it immobile in extreme cases. In this paper, some aspects of the effect of the wheel–ground interaction force distribution on mobility are investigated. A performance index based on the normal force distribution is used to compare different design layouts and vehicle configurations. The validity of this index was assessed using both multibody dynamics simulation and experimental results obtained with a six-wheeled rover prototype. Results confirmed that modifying the system configuration and employing active suspensions to alter the normal force distribution can lead to an increase of traction force available at the wheel–terrain interfaces, thus improving rover mobility. Finally, the study was extended to consider the change of soil properties during operation due to the multipass effect. Optimum load distributions were obtained as the solution of a constrained maximization problem.

A semi-analytical approach for the interaction of carbon nanotori

Based on the continuum approximation together with Lennard-Jones potential, a new semi-analytical method is developed to investigate the van der Waals interaction between two parallel carbon nanotori. Considering that atomistic approaches, such as classical molecular dynamics and density functional theory, are often computationally expensive, the present continuum method can be alternatively used for theoretical modeling of interaction force and energy between nanostructures. Following the present method, a semi-analytical expression is given in terms of double integrals which can be used to obtain the potential energy and interaction force. Investigating the effects of geometrical parameters on the potential energy and interaction force distributions reveals the oscillatory behavior of two parallel carbon nanotori and the plausibility of using them as the ideal traps for atoms and particles.

On the van der Waals interaction of carbon nanocones

Based on the continuum Lennard-Jones model, the van der Waals interaction of two concentric and eccentric carbon nanocones with different or identical sizes are investigated in this paper. Also, on the basis of classical mathematical modeling techniques, a new semi-analytical solution is given to evaluate the van der Waals potential energy and interaction force distributions of two concentric carbon nanocones. Finally, a universal potential energy is presented for the carbon nanocones.

Continuum Modeling of van der Waals Interaction Force Between Carbon Nanocones and Carbon Nanotubes

Using the Lennard–Jones potential, continuum modeling of the van der Waals potential energy and interaction force distributions are investigated for the eccentric and concentric single-walled carbon nanocones inside the single-walled carbon nanotubes. Furthermore, a new semi-analytical solution is presented to evaluate the van der Waals interaction of the nanocone located on the axis of the nanotube. Eccentric and concentric configurations of these nanostructures are also investigated to obtain the preferred position of the nanocone inside the nanotubes. Finally, the optimum radius of a carbon nanotube for which the preferred location of carbon nanocones is along the tube axis is found.

Measuring human–robot interaction on wearable robots: A distributed approach

This paper presents a novel, distributed approach to monitor physical interaction between a user and a wearable robot. We propose to apply a matrix of optoelectronic sensors embedded in a thin and compliant silicone bulk onto the user-robot contact surface. This distributed tactile sensor can measure the pressure distribution on the interaction area without affecting the comfort of the user, and does not require the robot to be specifically designed to house it. Besides the estimation of the interaction force/torque, the distributed approach allows to monitor the pressure on the user’s skin. This information is fundamental to assess the comfort and safety of the users which determine the final acceptability of the robot-mediated rehabilitation. The proposed method is preliminary evaluated on an elbow active orthosis during a repetitive rehabilitation task. Experimental results prove the relevance of this approach for the detection of the user motion intention through a measurement of the interaction force distribution.

A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D- n model can all be explicitly recovered by the current general solution.

Atomic Force Microscopy Measurement of Heterogeneity in Bacterial Surface Hydrophobicity

The structure and physicochemical properties of microbial surfaces at the molecular level determine their adhesion to surfaces and interfaces. Here, we report the use of atomic force microscopy (AFM) to explore the morphology of soft, living cells in aqueous buffer, to map bacterial surface heterogeneities, and to directly correlate the results in the AFM force-distance curves to the macroscopic properties of the microbial surfaces. The surfaces of two bacterial species, Acinetobacter venetianus RAG-1 and Rhodococcus erythropolis 20S-E1-c, showing different macroscopic surface hydrophobicity were probed with chemically functionalized AFM tips, terminating in hydrophobic and hydrophilic groups. All force measurements were obtained in contact mode and made on a location of the bacterium selected from the alternating current mode image. AFM imaging revealed morphological details of the microbial-surface ultrastructures with about 20 nm resolution. The heterogeneous surface morphology was directly correlated with differences in adhesion forces as revealed by retraction force curves and also with the presence of external structures, either pili or capsules, as confirmed by transmission electron microscopy. The AFM force curves for both bacterial species showed differences in the interactions of extracellular structures with hydrophilic and hydrophobic tips. A. venetianus RAG-1 showed an irregular pattern with multiple adhesion peaks suggesting the presence of biopolymers with different lengths on its surface. R. erythropolis 20S-E1-c exhibited long-range attraction forces and single rupture events suggesting a more hydrophobic and smoother surface. The adhesion force measurements indicated a patchy surface distribution of interaction forces for both bacterial species, with the highest forces grouped at one pole of the cell for R. erythropolis 20S-E1-c and a random distribution of adhesion forces in the case of A. venetianus RAG-1. The magnitude of the adhesion forces was proportional to the three-phase contact angle between hexadecane and water on the bacterial surfaces.

Characterizing the effect of substrate surface roughness on particle–wall interaction with the airflow method

The effect of surface roughness on particle–wall interaction was studied by the airflow method. Five kinds of monodispersed spherical particles ( D p50 = 11-41 μm) and six test pieces with different surface roughness ( Ra = 0.01-1.64 μm) were used in the experiments. The particles were dispersed on the test pieces to form a monolayer, and entrained in a rectangular air channel. The air velocity increased at a constant rate, and the entrained particles were detected with a laser dust monitor. Microscopic observations showed that particle entrainment occurred in discrete and intermittent events during experiment, thus a statistical parameter, i.e. the particle entrainment efficiency as a function of the air velocity, was defined for evaluating the particle–wall interaction force distribution. The experimental results showed that the air velocity for particle entrainment decreases with the increase of the surface roughness within submicron-scale and reaches a lower limit, while increases to some extent for micron-scale surface roughness. It was also found that the effect of the substrate surface roughness depends on the particle diameter.

Optimal trajectory formation of human reaching movement in crank-rotation task

Opening a door, turning a steering wheel, rotating a coffee mill are typical examples of human movements constrained by the external environment. The constraints decrease mobility of the human arm and lead to redundancy in the distribution of interaction force between the arm joints. Due to the redundancy of force actuation in the constrained motions, there is an infinite number of ways to form the arm trajectory. However, humans form the hand trajectory in a unique way. How do humans resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate these problems, we examine the trajectories of the human arm in a crank-rotation task. To explain the trajectory formation in constrained point-to-point motions, we propose a novel criterion minimizing hand contact force change and torque change over the time of the movement. Our experiments show a close matching between the prediction and the subjects' data. This indicates that in constrained movements the CNS naturally selects a moving contact frame as the criterion for the trajectory formation. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(12): 22–32, 2005; Published online in Wiley InterScience (). DOI 10.1002sscj.20368

Theoretical simulation of noncontact AFM images of Si(111) √3×√3-Ag surface based on Fourier expansion method

A Fourier expansion method is introduced to simulate the noncontact atomic force microscopy (NC-AFM) images in an efficient way, where three dimensional (3D) tip–surface interaction force distribution calculated by the first-principles density functional (LDA) calculations are fitted to an analytical function. As an example of application of this method, we adopt a Si(111) √3×√3 R30°-Ag surface. Force spectroscopies and 2D images for different tip height are presented.