Tangential Friction Force Research Articles

Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor–stator contact system

The efficiency of rotating machines can be improved via precisely manufactured bearings with reduced clearances; consequently, the proclivity for rotor–stator contact is increased. A common model used to investigate rotor–stator contact in previous studies is the two degree-of-freedom (DOF) rotor with symmetric support stiffness, where the contact assumes a linear elastic normal restoring force proportional to the rotor–stator interference and a tangential dry Coulomb friction force. Switching between the contacting and non-contacting states creates strong nonlinearity in the equations of motion, and the dynamic response displays a rich profile of behaviors including periodic, quasiperiodic, and chaotic responses via period-doubling, sudden transitions, quasiperiodicity, and intermittency. For the first time, this work emphasizes an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses. The influence of support asymmetry on the nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincaré sections, and bifurcation diagrams. It is found that the cross-coupling stiffness coefficient kxy has negligible effect on the dynamic response until its magnitude is on the same order as the direct stiffness coefficients. Direct stiffness coefficient asymmetry is shown to affect the rotor׳s response, where even small asymmetries can qualitatively change the response. Additionally, the importance of including gravity is investigated, and a method is provided for determining the threshold shaft speed above which gravity can be ignored. The dominant route to chaos is period-doubling for the parameters considered here, though other routes to chaos are seen such as a direct transition from periodic to chaotic motion. Finally, observations pertaining to rotor modeling, design, and fault diagnostics are discussed.

Experimental and numerical investigation of friction element dissipative effects in blade shrouding

Friction forces can be advantageously used as a source of passive damping in various mechanical systems. This paper deals with an experimental modelling and numerical simulation of blades interaction by means of a friction element placed in the shroud between the blade heads. The radial force, which represents the centrifugal force acting on the friction element, determines the values of contact forces between the element and blades. The experimental set-up for a couple of non-rotating blades is described in the paper, and the measured dynamic response of two blades is documented. The same situation is modelled by means of a basic and a more complex dynamical model of two blades with a friction element. The effect of friction is studied for the case of harmonic excitation by suitable frequency and subsequent free vibration attenuation. Both mathematical models are based on the finite element method combined with lumped rigid bodies. The interaction of the friction element and blades is described by normal contact and tangential friction forces derived for particular geometrical parameters of the studied mechanical system. The performed comparison of experimental and numerical results shows the satisfactory agreement and the modelling methodology could be used for possible parameter optimization.

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.

Three–dimensional asymmetrical rolling of an aluminium flat strip using an elastic–plastic finite element method

This study developed a three–dimensional asymmetrical cold rolling finite element method for aluminium flat strips, and analysed the curved deformation of the strip caused by the difference in the rotation speed of the upper and lower rollers, and inconsistency in the radius of the upper and lower roller. As for the determination of the direction of tangential friction force, this study also developed a modification algorithm to adjust to the three–dimensional rolling process. In addition, another rule was devised to identify the neutral point to further the theoretical model develop. A comparison of the part of the computation results derived in this article and the empirical data of relevant studies shows that the finite element method developed in this article is very reasonable. The changes in the rolling force, strip curvature, strain and cross–section bulge of the various points inside a strip are further discussed under different rotation speeds and radii of the upper and lower rollers of the asymmetrical rolling.

Experimental study on wear and spalling behaviors of railway wheel

The current researches of the wear and spalling behaviors of wheel/rail materials focus on the field investigation rather than the mechanism. However, it is necessary and significant for clarifying the mechanism and relationship between the wear and spalling damage of railway wheel to test and reproduce the wheel damages in laboratory. The objective of this paper is to investigate the wear and spalling damage behaviors of railway wheel using a JD-1 wheel/rail simulation facility, which consists of a small wheel serving as rolling stock wheel, and a larger wheel serving as rail. The damage process of wheel roller is explored in terms of the creep ratio, axle load, and carbon content by means of various microscopic examinations. The experimental results show that the wear volume growth of wheel roller is proved to be proportional to the increase of the creep ratio and normal load between simulating wheel and rail. The increase of carbon content of wheel material causes a linear reduction in the wear volume. The microscopic examinations indicate that the rolling wear mechanism transfers from abrasive wear to adhesive and fatigue wear with an increase of tangential friction force, which results in the initiation of fatigue crack, and then aggravates spalling damage on the wheel roller surface. The surface hardness of material depends strongly upon its carbon content. The decrease of the carbon content of wheel material may alleviate spalling damage, but can cause a significant growth in the wear volume of wheel roller. Therefore, there is a competitive relationship between the wear and spalling damage of wheel material. This research proposes an important measure for alleviating or preventing the wear and spalling damage of railway wheel material.

Advancement and Prospect of Bionic Techniques in the Conservation of the Cultural Heritage

The ancient wall paintings and earthen architecture ruins are the most important part of cultural heritage. Inhabitation and locomotion of animals are major factors that lead to biodegradation and biodeterioration at the cultural heritage sites. In this miniview, based on our team work of cultural relics conservation in recent years, the latest findings domestic and overseas in fields of ethology and bionics were summarized, focusing on the correlated methods and techniques that can be used into cross-over study of cultural relics conservation. Animal's biting, nesting, cocooning, crawling, and scratching are all behavioral process that easily bring damage to cultural heritage, such as ancient murals, architectures, earth ruins and so on. Both modern video record techniques and animal motion trajectory analysis may be taken use to improve the analytic accuracy of gait information for animals that crawling on the surface of cultural relics, which promoted the related study of motor pattern, behavior process, and damage pattern of animals to cultural relics. The three dimensional tiny force sensor with high resolution can be used for measuring normal adhesive force and tangential friction force of animals that contacted the surface of fragile cultural relics, which make animal adhesion modeling and historical relics mechanical model constructing possible, and provide newly evidence for biomechanics process illumination of animals locomotion. Totally, the application of the bionic techniques to the study of animals behavioral characteristics will provide new opportunity to better clarify the biological damaging mechanisms of cultural relics and control animal bioderioration, which will drive the development of cultural relics conservation technology in the near future.

Review of Fundamentals of Road Design by Wolfgang KühnWIT Press, Billerica, MA; 2013; ISBN 978-1-84564-097-2; 327 pp.; $312.

Review of <i>Fundamentals of Road Design</i> by Wolfgang KühnWIT Press, Billerica, MA; 2013; ISBN 978-1-84564-097-2; 327 pp.; $312.

Nanoscale Interfacial Interactions of Graphene with Polar and Nonpolar Liquids

While mechanical and frictional properties of graphene in air have been extensively studied, graphene's nanomechanical behavior in liquids, vital for its operation in rechargeable batteries, supercapacitors, and sensors, is still largely unexplored. In this paper, we investigate the nanomechanics of normal (adhesive and elastic) and tangential (friction) forces between a stationary, moving, and ultrasonically excited nanoscale atomic force microscope (AFM) tip and exfoliated few layer graphene (FLG) on SiO2 substrate as a function of surrounding media-air, polar (water), and nonpolar (dodecane) liquids. We find that, while the friction coefficient is significantly reduced in liquids, and is always lower for FLG than SiO2, it is higher for graphene in nonpolar dodecane than highly polar water. We also confirm that in ambient environment the water meniscus dominates high adhesion for both hydrophobic FLG and the more hydrophilic SiO2 surface, with the lowest adhesion observed in liquids, in particular for FLG in dodecane, reflecting the low interface energy of this system. By using nanomechanical probing via ultrasonic force microscopy (UFM), we observed a profound reduction of graphene rippling and increase of graphene-substrate contact area in liquid environment. Friction force dependence on ultrasonic modulation amplitude suggests that dodecane at the graphene interface produces a solid-like "cushion" of approximately 2 nm thickness, whereas, in water immersion, the same dependence shows a remarkable similarity with the ambient environment, confirming the presence of a water meniscus in air, and suggesting negligible thickness of a similar water "cushion" on graphene. Dependence of friction on local environment opens new pathways for friction management in microfluidic and micro- and nanoelectromechanical systems.

The cardiac cycle effects on the coronary arterial geometry and hemodynamics: An in vivo CT angiography study

Epidemiological studies have proposed heart rate as an independent risk factor for cardiovascular disease [1]. Animal studies demonstrated that elevated heart rate and heart rate fluctuation are associated with plaque formation [2]. A subgroup analysis of the BEAUTIFUL study has shown the significance of lower heart rate in patients with stable coronary disease and left ventricular dysfunction [3]. Endothelial shear stress (ESS) is the tangential frictional force of the flowing blood on the endothelium. Low ESS promotes atherosclerosis through endothelial receptors and a mechanotransduction cytoplasmic process [4,5]. Molecular viscosity (MV) represents the intrinsic blood resistance as the friction between the adjacent parallel fluid layers. The Edinburg Artery Study suggested that highMV promotes ischemic heart disease and is a risk factor of cardiovascular disease in addition to conventional ones [6]. Mechanical forces and cardiac motion play a possible key role in atherosclerosis. During cardiac cycle coronary arteries are subject to forces which may affect the localization of plaque growth. Curvature refers to the deviation from straightness and is an index of the mechanical forces exerted on the coronary arteries, depicting the flexibility of a vessel during the cardiac cycle [7]. We investigated 22 subjects (19 men, mean age 62 ± 12.1 years) undergoing coronary computed tomography angiography for the investigation of suspectedmoderate/low risk coronary artery disease or with known coronary artery disease but unable to undergo invasive coronary angiography. All patients provided written informed consent and the institutional Medical Ethics Committee approved the study. The studyprotocol conforms to theethical guidelines of the1975Declaration of Helsinki. The authors of this manuscript have certified that they comply with the Principles of Ethical Publishing in the International Journal of Cardiology. Multislice computed tomography (128-slice) was performed in held inspirationwith SOMATOMDefinition AS+ SIEMENS. Based on

The Vibration Characteristics of Steam Turbine Blades with New Friction Damping Structures

The hysteresis curves that show the relationship between the tangential friction force and relative displacement of the contact surface were measured. The equivalent stiffness and damping of the friction contact surface under different normal loads were computed by harmonic balance method (HBM). The finite element model of steam turbine blades with new friction damping structures was established. The effects of friction between the contact surfaces were considered by using spring damping elements to connect the friction damper and the blade. The equivalent stiffness and damping which were calculated by the experiment results were applied to the spring damping elements under different rotational speeds. Based on the natural frequencies which were computed by finite element analysis, the Campbell diagram of the whole blades was obtained. The results showed that there were no 3-coincide points in the working speed range.

Behavioural Modelling of Lips Seal Made with Polytetrafluoroethylene Enriched by Glass Fibers

Polytetrafluoroethylene reinforced with glass fibers is a composite material widely used in industry mainly for the manufacture of seals at the level of the rotary shafts of vehicles and stationary floor machines such as turbines and compressors. However, due to elastic and viscous-plastic properties of this material, it wears quickly under the influence of some external parameters during operation. There are therefore material loss, increased clearance and loss of sealing. This work summarises a series of tests carried out with this material in order to analyse the variation of the friction coefficient due to the roughness of the work piece brought into contact with the PTFE, the linear velocity of contact between them and material yield strength. To do this analysis, we used the method of unconventional design of experiments to model the behaviour of material and consequently make decisions to reduce this wear. The results are shown and deeply analysed in the following text as a polynomial mathematical model, graphs, contours and response surfaces illustrating the holding of this material under the effect of the three parameters mentioned above. The previous PTFE samples enriched with chopped glass fibers are not subjected to axially force this time, contrary to the force applied radially. The advantage of this method is the relative linear velocity at the contact sample-disc and the applied pressure remains constant. Under the action of the weight “P” applied on the sample, it comes into friction with the rotating disc whose roughness changes from experience to another; it is expressed by the values of Ra. Tangential friction force appears at the point of contact and is equilibrated by measured force Fm on the lever. The calculation of the moment relative bench axis caused by 2 forces gives the coefficient of friction. Knowing the values of frictional force Ft by calculation and the weight P, we determine then the friction coefficient.

Tangential and Quantum Frictional Forces on a Neutral Particle Moving Near a Surface

We calculate tangential forces applied to a ground state atom (nanoparticle) moving with nonrelativistic velocity parallel to the surface of Drude -modelled or Lorentz -modelled half -space using the formalism of fluctuation electrodynamics.The obtained formulae assume the nonretarded regime and arbitrary temperatures of the particle and medium. The quantum frictional force is realized at zero temperature of the particle and medium and can reach about 1/3 of the static value of the Casimir -Polder force in the case of ground state atom. In the case of nanoparticles and nonzero temperature, the tangential forces appears to be both frictional and accelerating. Numerical examples are given for atoms of Na above the surface of Au and MgO nanoparticles above the surface of SiC.

A comparison of Coulomb and pseudo-Coulomb friction implementations: Application to the table contact phase of gymnastics vaulting

In the table contact phase of gymnastics vaulting both dynamic and static friction act. The purpose of this study was to develop a method of simulating Coulomb friction that incorporated both dynamic and static phases and to compare the results with those obtained using a pseudo-Coulomb implementation of friction when applied to the table contact phase of gymnastics vaulting. Kinematic data were obtained from an elite level gymnast performing handspring straight somersault vaults using a Vicon optoelectronic motion capture system. An angle-driven computer model of vaulting that simulated the interaction between a seven segment gymnast and a single segment vaulting table during the table contact phase of the vault was developed. Both dynamic and static friction were incorporated within the model by switching between two implementations of the tangential frictional force. Two vaulting trials were used to determine the model parameters using a genetic algorithm to match simulations to recorded performances. A third independent trial was used to evaluate the model and close agreement was found between the simulation and the recorded performance with an overall difference of 13.5%. The two-state simulation model was found to be capable of replicating performance at take-off and also of replicating key contact phase features such as the normal and tangential motion of the hands. The results of the two-state model were compared to those using a pseudo-Coulomb friction implementation within the simulation model. The two-state model achieved similar overall results to those of the pseudo-Coulomb model but obtained solutions more rapidly.

Erosion simulation of first wall beryllium armour after ITER transient heat loads and runaway electrons action

Beryllium is foreseen as plasma facing armour for the first wall (FW) in ITER in form of Be-clad blanket modules in macrobrush design with brush size about 8–10cm. In ITER significant heat loads during transient events (TE) and runaway electrons impact are expected at the main chamber wall that may leads to the essential damage of the Be armour. The main mechanisms of metallic target damage remain surface melting, evaporation, and melt motion, which determine the life-time of the plasma facing components. The melt motion damages of Be macrobrush armour caused by the tangential friction force and the J×B forces are analyzed for bulk Be and different sizes of Be-brushes. The damage of the FW due to heat loads caused by runaway electrons is numerically simulated.

A Research of V-Belt Transmission Mechanics with Two Same Pulleys

V-belt is made of a special anisotropic material, its material and pulley groove structure make the V-belt drive mechanics complicated. The elasticity limit, seating and unseating effects, radial compliance makes us consider the macro features of the drive and not to consider the material heterogeneity. We focus on the steady mechanics of V-belt drive in the state of sliding friction between groove and belt. The pulley groove leads to two-dimensional radial and tangential friction forces whose direction depends on the relative speed between belt and the pulley along the contact arc. The belt model is analyzed with comparing method which is performed through acquiring the equivalent coefficient of friction, and replacing the coefficient of friction in the flat belt mechanical equilibrium equations for v-belt analysis. Through the sample calculation it is proved that this method is simple and valid for V-belt mechanical analysis.

Dealing with multiple contacts in a human-in-the-loop application

This paper deals with continuous contact force models applied to the human-in-the-loop simulation of multibody systems, while the results are valid in general to all the real-time applications with contacts. The contact model proposed in this work is suited to collisions between massive solids for which the assumption of quasi-static contact holds, and it can be supposed that the deformation is limited to a small region of the colliding bodies while the remainder of them are assumed to be rigid. The model consists of two components: normal compliance with nonlinear viscoelastic model based on the Hertz law, and tangential friction force based on Coulomb’s law including sticktion and a viscous friction component. Furthermore, the model takes into account the geometry and the material of the colliding bodies. The tangential model is a novel contribution while the normal model is completely taken from previous works. For this work, the formulation of the equations of motion is an augmented Lagrangian with projections of velocities and accelerations onto their constraints manifolds and implicit integrator. The whole solution proposed is tested in three applications: the first one is the simulation of a spring–mass system with Coulomb’s friction, which is an academic problem with known analytical solution; the second one is the Bowden and Leben stick–slip experiment; the third one is a simulator of a hydraulic excavator Liebherr A924, which is a realistic application that gives an idea of the capabilities of the method proposed.

Microparticle manipulation on the surface of a piezoceramic actuator

In this paper, a technique called piezoelectric interfacial particle manipulator (PIPM) for the manipulation of single and multiple microparticles on the surface of a piezoelectric actuator is demonstrated. The PIPM is capable of controlled manipulation of single and multiple microparticles ranging in size from 0.5 to 50 µm. Piezoelectrically excited bulk modes of vibration, ranging from 10 kHz to 2 MHz, are used to generate a complex distribution of manipulation forces acting in opposition to particle–surface normal adhesion and tangential frictional forces. The vibration of the PIPM is characterized using a finite element method (FEM) simulation and a theoretical study of the particle–surface interfacial forces. A comparative study of the manipulation forces and the adhesive particle–surface interfacial forces, measured using atomic force microscopy, is performed. The results confirm the ability of the PIPM to overcome adhesion forces ranging from 10 to 250 nN for particles ranging in radii from 10 to 30 µm. Furthermore, reproducible high throughput particle manipulation is demonstrated via the translation of a 25 µm stainless steel particle, over a distance 600 times its radius, with an average speed of 5 mm s−1. Experimental results correlated with theoretical expectations indicate that the PIPM can prove to be a versatile tool for the controlled non-destructive manipulation of single as well as multiple microparticles in the fields of biosensors, tissue engineering, biochips, micro-fabrication and MEMS devices.

Size effect in nanopowder compaction

The process of nanopowder compaction has been studied by the method of granular dynamics. The interaction of particles involves the elastic Hertz forces, tangential friction forces, and dispersive attraction forces. The curves of uniaxial compaction on the “axial pressure-compact density” plane are analyzed. Calculations have been performed for powders with particle sizes from 10 to 100 nm. It is shown that the allowance for dispersive attraction forces ensures adequate description of the size effect in nanopowder compaction.

Nonlinear dynamic analysis of fractional order rub-impact rotor system

Nonlinear dynamic characteristics of rub-impact rotor system with fractional order damping are investigated. The model of rub-impact comprises a radial elastic force and a tangential Coulomb friction force. The fractional order damped rotor system with rubbing malfunction is established. The four order Runge–Kutta method and ten order CFE-Euler method are introduced to simulate the fractional order rub-impact rotor system equations. The effects of the rotating speed ratio, derivative order of damping and mass eccentricity on the system dynamics are investigated using rotor trajectory diagrams, bifurcation diagrams and Poincare map. Various complicated dynamic behaviors and types of routes to chaos are found, including period doubling bifurcation, sudden transition and quasi-periodic from periodic motion to chaos. The analysis results show that the fractional order rub-impact rotor system exhibits rich dynamic behaviors, and that the significant effect of fractional order will contribute to comprehensive understanding of nonlinear dynamics of rub-impact rotor.

From force distribution to average coordination number in frictional granular matter

We study the joint probability distribution of normal and tangential frictional forces in jammed granular media, P μ ( f t , f n ) , for various values of the friction coefficient μ , especially when μ = ∞ . A universal scaling law is found to collapse the data for μ = 0 to ∞ , demonstrating a link between the force distribution P μ ( f t , f n ) and the average coordination number, z c μ . The results determine z c μ for a finite friction coefficient, extending the constraint-counting argument of isostatic granular packing to finite frictional packings.