Search

Friction hysteresis results from an oscillating friction force at a contact interface. At nano-scale, this phenomenon is affected by the roughness of the contact interface and adhesion. In nanotribology, therefore, it is highly desirable to understand and predict this behavior to estimate the energy loss and possible wear. This paper presents a boundary element model (BEM) for the adhesive friction hysteresis contact at the interface of two bodies of arbitrary geometry. In the model, adhesion is represented by means of a Dugdale approximation of the total work of adhesion at local areas with a very small gap between the two surfaces. The amplitude of the oscillating tangential displacement is very small compared to the contact area which means that the interface does not experience gross-sliding between the two surfaces (the contact remains in the pre-sliding state). Hence, the frictional contact is divided into sticking and slipping regions, defined based on the local values for shear stress and normal pressure, and the rate of relative displacement. The model is first verified by comparing the numerical and analytical (Mindlin theory) solutions for the contact of a smooth ball and a flat of identical materials under a fixed normal force and an oscillating friction force. Then, the problem is solved at the smooth interface between a rigid ball and an elastic flat for various values of the work of adhesion. It is shown that as the work of adhesion increases, both static friction force and pre-sliding displacement increase due to the increase in the contact repulsive force. In addition, the rough interface between a glass ball against a silicon wafer and a DLC (Diamond-Like Carbon) coating is considered. Since adhesion depends on the interface roughness, the corresponding contact repulsive force is different for these interfaces. For the smoother interface, a larger contact repulsive force and consequently, a larger static friction force and pre-sliding displacement are obtained.

A new magnetorheological honing (MRH) process has been developed for internal surface finishing of cylindrical workpieces with different diameters. The process makes use of the tool with radial polarized curved permanent magnet strips and a smart magnetorheological (MR) polishing fluid for finishing the internal surface of the cylindrical workpieces. The MRH tool has the uniqueness that its radial curved permanent magnets can move inwards or outwards just like a honing tool so that the different diametric sizes of the internal surface of the cylindrical components can be finished. In the present work, a mathematical model has been developed for predicting the change in surface roughness while finishing the internal surface of ferromagnetic cylindrical workpieces. An analytical approach is adopted to evaluate the magnitude of magnetic flux density at different points in the working gap where MR polishing fluid is present. While finishing the internal surface of ferromagnetic cylindrical workpieces, a magnetic field is also contributed in the working gap due to the effect of iron particles (present in the MR polishing fluid) and the ferromagnetic cylindrical workpiece. The present developed mathematical model evaluates the magnitude of magnetic flux density in the working gap by also considering the contribution of the magnetic effect of iron particles and the ferromagnetic cylindrical workpiece. Theoretically calculated magnetic flux density distribution in the working gap is validated with the experimentally and also through finite element (FE) analysis using Maxwell Ansoft V13 software. With the evaluated values of magnetic flux density at various points in the working gap, the magnetic normal force exerting over the active silicon carbide (SiC) particle has been evaluated. The computed magnetic normal force exerting over the active SiC particle is utilized to calculate the removal of material in terms of decrease in surface roughness values with various finishing cycles. Also, the developed mathematical model for the present MRH process has been validated by performing the experimentations with same parameters and conditions as selected in modeling for the different number of finishing cycles. Results acquired from the mathematical model are found in close relation to the results obtained from experimentations with the maximum percentage error of 8.06% and least of 1.03%. The developed mathematical model for MRH process can be used to predict the process's finishing performance for various ferromagnetic cylindrical workpieces which can make it useful for industries.

This article describes frictional and electrical contact behaviors of electroplated brass under fretting conditions. Fretting tests using a crossed cylinder configuration are conducted. Cylindrical-type specimens are made of tin-plated and gold-plated brass. The ratio of the maximum tangential force to normal force is calculated. The ratio is 0.85 for the self-mated tin-plated brass and 0.55–0.6 for the self-mated gold-plated brass. The results show that the evolution of the dimensionless electrical resistance can be described with a Kachanov-type damage form. Two parameters, the electrical resistance rate constant and electrical resistance exponent, are determined to describe the evolution of the electrical resistance. The results also reveal that the rate constant is affected by the test temperature.

Ultrasonic assisted magnetic abrasive finishing (UAMAF) integrates ultrasonic vibrations with magnetic abrasive finishing (MAF) process to finish the workpiece surface more efficiently as compared to MAF. In this work, mechanism of material removal has been discussed. A kinematic analysis of an abrasive particle and an analysis of material removal during UAMAF is presented. The total material removal during finishing is attributed to two simultaneous and independent phenomena — a steady state material removal and a transient material removal. The steady state removal mainly depends on the finishing condition and remains constant throughout the finishing time, while transient removal is primarily associated with the surface roughness of the workpiece. A finite‒element analysis of electromagnet was performed to calculate magnetic‒flux density in the finishing region to evaluate the normal force acting on the active abrasive particles. The steady state material removal was modeled as a function of velocity and normal force using the process physics. The transient material removal was modeled as a function of the volume of instantaneous irregularities available on the workpiece surface. The developed model predicted the material removal rate (MRR) in UAMAF as a function of supply voltage, working gap, angular speed of the electromagnet, amplitude and frequency of ultrasonic vibration, hardness and initial surface roughness of the workpiece. The model brought out that there was an exponential relationship between MRR and finishing time.

Friction is not considered in the calculation of load capacity for spiral bevel gears according to either ISO or AGMA gear standard, and friction effects on the bending, contact and shear of the gears have rarely been discussed. In this regard, the present work establishes analytical solutions to calculate bending and contact strength for spiral bevel gears incorporating friction on the tooth surface, which are verified by ISO gear standard and finite element method (FEM). The bending strength is calculated based on Lewis cantilever beam approximation, utilizing the modified normal force and the friction component. The modified normal force is derived at the highest point of single tooth contact (HPSTC) in the normal equivalent gear. Follow Hertz contact theory, the contact strength is calculated when the modified normal force and the friction component are exerted at the lowest point of single tooth contact (LPSTC) in the normal equivalent gear. The calculated bending and contact stresses agree well with those obtained from the FEM analysis while considering the influence of friction. Both theoretical predictions and FEM analysis have shown that friction has a crucial effect on load capacity of a spiral bevel gear drive, and that it exerts stronger influence on the bending strength (compared with the contact strength). When friction coefficients become larger (with the same input torque), the bending stress considering only the modified normal force decreases at HPSTC, whereas it increases if both the modified normal force and the friction component are included. In comparison, the contact stress will increase at LPSTC under both scenarios. Furthermore, it is illustrated that shear strength check of the tooth is necessary as large friction occurs in the contact zone. This developed analytical solution can be well applied to the determination of load capacity of spiral bevel gears, especially under harsh working conditions or in the demand for higher performance.

In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed.

Piezoelectric ultrasonic motor is an electromechanical coupling system, which is driven by the interface friction between the stator and the rotor/slider. A novel friction model is developed to study the stick–slip motion in a linear piezoelectric ultrasonic motor using longitudinal and bending modes. In this model, the influence of the ultrasonic oscillation on the dynamic friction coefficient is taken into account, which is described by a friction law related to the vibration amplitude at the interface. In addition, the friction contact model involves intermittent separation non-linearity induced by the variable normal force, which can result in complex stick–slip–separation motion at the contact interface. Analytical transition criteria between stick and slip are established by using the switch model. Based on the developed model, numerical simulations are performed to analyze the force transmission between the stator and the slider involving stick–slip motion. A transformed phase plane is proposed to study various states of the contact interface (stick, slip and separation), on which slip–separation, stick–slip, stick–slip–separation, and pure stick motions are intuitively characterized. The influence of some input parameters on the stick–slip motion is analyzed. Furthermore, the low-voltage dead-zone behavior is clarified by stick motion.

Recent research has shown that energy losses named as ‘relaxation damping’ can occur even with an infinite coefficient of friction using the method of dimensional reduction (MDR) which is strictly applicable to axis-symmetric elastic contact problems. If the solution with infinite coefficient of friction is regarded as a limiting case of ‘very large’ friction, this limiting solution is often useful because it will typically be much simpler than that obtained assuming a finite coefficient of friction, and it is likely to give reasonable estimates for the actual dissipation in cases that are far from the gross slip (sliding) limit. Using the advantage of relaxation damping, we shall give a generalized proof that is independent of the MDR. We shall also extend the proof to problems in which the applied loads follow a general trajectory in three-dimensional vector space. Further, we shall demonstrate how the energy dissipation per cycle varies with an increasing normal force, showing that relaxation damping could be useful as a limit in cases where there is significant variation in a normal force.

Flap over blunt asymmetric reentry vehicles improves the aerodynamic stability and control. The present study has focused on the reentry aerodynamics of blunt-nosed conical body with flap configurations. Three dimensional, steady, viscous and compressible flow over the reentry body configurations were numerically analyzed by solving Reynolds averaged Navier-Stokes equations and SST K-ω turbulence model. The fundamental governing equations were discretized from the partial differential form to numerical analogue using the finite volume approach. Numerical simulations were carried out to investigate the flow characteristics of the three different reentry body configurations at different pitch angles, flap angles, the Mach numbers, and altitudes. For increment in the pitch angle from 0∘ to 6∘, the axial force coefficient is invariant, while the normal force coefficient linearly increases. It is found that the axial force coefficient is directly proportional to the flap angle and inversely proportional to the Mach number. Presence of flap introduces streamwise vortices and increases the flow complexity after the base to a large extent.

The design, analysis, and experimental investigation of a novel 3D tip-based nanofabrication system with high precision depth control capability is presented in this paper. Based on this system, a new depth control method, namely tip displacement-based closed-loop (DC) depth control methodology is proposed to improve the depth control capability. As the force-depth prediction with the commonly-used depth control method, i.e. the normal force-based closed-loop (FC) method, may depend on the machining speed, the machining direction, and the material properties, etc. Compared with the FC method, the DC method decreases the complexity and the high uncertainty. The tip feed system utilizes a non-contact force, i.e. the electromagnetic force, to adjust the tip displacement. Therefore, the tip support mechanism can be used to accomplish the tip-sample contact detection. Additionally, an active compensation method is proposed to eliminate the tilt angle between the sample surface and the horizontal plane. Otherwise the machining depth will change gradually, i.e. getting deeper or lower. Furthermore, a series of patterns have been fabricated on silicon sample surface with the proposed system and method. The maximum machining depth of a single scan reaches 300 nm, which is much larger than that of an atomic force microscope (AFM)-based nanofabrication system. The experimental results demonstrate that the system has advantages of distinguished depth control capability, high machining accuracy, and excellent repeatability, which diminishes the influence of above-mentioned factors on the machining depth. Also, the method has the potential of machining arbitrary 2D/3D patterns with well-controlled depth and high accuracy.

We analyze the pure bending state, preliminarily considering the pure traction problem, for a fiber with circular cross-section composed by monodispersed Nano Tube (NT) segments, whose length is much lower than the length of the fiber, arranged in a cross-sectional square lattice, possibly inclined with respect to the bending plane. The proposed model accounts for the compliant shear coupling of the constituent NTs along their lateral contact surfaces, and considers that the position of each NT is offset with respect to the neighboring ones by a fixed distance. The shearing of the NTs permits their mobility in longitudinal direction, inducing an internal rearrangement, calculated through energy minimization, that affects the macroscopic response. With a micro-macro approach, the internal actions in the whole fiber are calculated. We find that uniform axial macroscopic strain is associated with constant tensile normal force in the fiber and null moment; correspondingly, constant macroscopic curvature provides a constant bending moment in the plane of bending and null axial force. It is then possible to consider the NT fiber as an equivalent homogeneous beam, whose effective tensile and bending stiffness can be calculated, finding a dependence upon the aspect ratio of the fiber, the aspect ratio of the individual NTs and, more important, the offset of the NTs. The model permits to interpret recent experimental results.

In this study moving contact problem for a rigid cylindrical punch and a functionally graded layer is considered. The punch subjected to concentrated normal force, and moves steadily with a constant subsonic velocity on the boundary. Poisson׳s ratio is taken as constant, and both the elasticity modulus and the mass density are assumed to vary exponentially in depth direction. By using Fourier transform and boundary conditions, the governing equations are reduced to a Cauchy singular integral equation. The numerical solution of the singular integral equation is obtained by using Gauss–Chebyshev integration formulas. Numerical results for the contact area, the contact stress and the normal stresses are given. This study is limited in that the elasticity modulus and the mass density vary with the same function. However, it is the first attempt to investigate the moving contact problem with FGMs.

Based on a simplified equivalent two-dimensional (2-D) plane strain finite element model with an equivalent normal force obtained from the three-dimensional (3-D) finite element model, the bending fretting fatigue process of 316L stainless steel is simulated numerically by ABAQUS code. In the simulation, the effects of ratchetting and cyclic hardening features on the fretting fatigue process of 316L stainless steel are discussed by implementing an advanced cyclic elasto-plastic constitutive model into ABAQUS code as a user material subroutine (UMAT). The model describes the ratchetting and cyclic hardening features of 316L stainless steel very well. From the numerical simulation, the effects of bending load and normal force on the bending fretting fatigue of 316L stainless steel are addressed, and then the crack initiation locations and the failure lives are predicted by using Smith–Watson–Topper critical plane criteria. Comparison with the corresponding experiments shows that the predicted results are in good agreement with the experimental ones.

Magnetorheological (MR) fluid based finishing process is a nano finishing process applicable to a large variety of materials. A theoretical model of forces (normal and tangential) acting on the workpiece is proposed to improve the in-depth understanding of the mechanism of material removal during MR fluid based finishing process. Two different theories are proposed to model the effect of abrasive particles concentration in the MR fluid. A normal and tangential squeeze force model is also proposed based on the theory of rolling process. A comparison of theoretical and experimental results is carried out to validate the proposed models which show their trends in good agreement.

In this paper, starting from results of Part I (Afferrante et al. [1] ), we develop a procedure to evaluate the frequency dependent receptances of the energy dissipation at the contact interface, which is the quantity of interest in corrugation studies as the most known wear laws assume the local wear proportional to the frictional dissipation. These results are applied to the calculation of the growth rate of corrugation in railway tracks with an initial sinusoidal undulation. In particular, the wheel inertia and the transient contact mechanics effects are considered using a continuum description of the rail (hence neglecting pinned–pinned resonance due to the beam bending between two successive supports) by the simplest model (the Euler beam) which we can use to describe the normal receptance of the rail. The presence of a finite partial slip zone in the contact area can significantly modify the results, partially explaining the scatter of the experimental data collected in the literature. In particular, we found that partial slip affects the predicted apparent wavelength of highest growth of corrugation, and with respect to the full stick conditions, higher tractive ratio increases significantly the growth factors and non-linearity, showing an unexpected absolute maximum of growth at intermediate velocities, and the “resonance-free” regime becomes increasingly not a constant “frequency”, spanning a range of frequency between 700 and 1500 Hz even for a given system and set of loads. Only a full investigation involving all other resonances in the system may clarify further the correspondence with experimental values, since the corrugation “enigma” may be due to a combination of effects.

We study the effect of harmonic oscillations during the steady rolling of a cylinder on a plane in partial slip contact conditions in the limit of small oscillations. The solution is an extension of that given in Barber et al. [1] for infinitely large coefficient of friction. Here, the effect of varying normal load and hence contact area is investigated in detail by analyzing the first order variation of the tangential force and the corresponding relative displacements. In particular, the solution is given in terms of an explicit length scale d in the Flamant solution used as a Green function. Appropriate choice of values of d allows to treat both two-dimensional problems and three-dimensional ones having elliptical contact area sufficiently elongated in the direction of the rotation axis. Also, this analysis can be used as starting point for corrugation calculations in railway tracks, where oscillations in time of the normal forces can result in non-uniform wear and hence in amplification of the corrugation.

The increasing occurrence of drop-impact failure of portable electronics could be traced to the failure of the solder joints that interconnect the integrated circuit (IC) components to the printed circuit board (PCB)—collectively referred to as PCB assembly. The drop impact leads to bending of the PCB assembly within the portable electronics, and the interconnecting solder joints undergo severe deformation to accommodate the differential bending deformation between the IC component and the PCB. This manuscript presents an approximated closed-form analytical solution for the stresses in the solder joints of the PCB assembly subjected to mechanical bending. The PCB assembly is modelled as a tri-layer structure in which the IC component and the PCB are modelled as beams or plates and the solder joints as a continuous layer consisting of infinite number of beams that are capable of carrying normal force, shear force, and moment along its interfaces with the IC component and the PCB. The analytical solutions have been validated against finite element analysis. Design analysis has suggested that the robustness of the PCB assembly against mechanical bending can be increased by increasing the diameter of the solder joints; increasing the in-plane and flexural compliances of IC component and PCB; while reducing the shear and flexural stiffness of the solder joints and reducing the transverse compliant of the PCB assembly.

The Lamb's problem for the half-space covered with the pre-stretching layer is studied within the framework of the piecewise homogeneous body model. The three-dimensional linearized theory of elastic waves in initially stressed bodies is used. It is assumed that a time-harmonic point-located normal force acts on the free face plane of the covering layer. A numerical algorithm is also developed. Numerical results are presented for two cases of material pairs: rubber (layer)+aluminum (half-space); and aluminum (layer)+rubber (half-space). These results involve stresses acting on the interface plane and in the covering layer. The influence of the harmonic force frequency and the pre-stretching of the covering layer on the distribution of stresses is analyzed. In particular, it is established that stresses on the interface plane are decreased as the pre-stretching is increased.

The in-plane vibration of a slider-mass which is driven around the surface of a flexible disc, and the transverse vibration of the disc, are investigated. The disc is taken to be an elastic annular plate and the slider has flexibility and damping in the circumferential (in-plane) and transverse directions. The static friction coefficient is assumed to be higher than the dynamic friction. As a result of the friction force acting between the disc and the slider system, the slider will oscillate in the stick-slip mode in the plane of the disc. The transverse vibration induced by the slider will change the normal force on the disc, which in turn will change the in-plane oscillation of the slider. A numerical method is used to solve the two coupled equations of the motion. Results indicate that normal pressure and rotating speed can drive the system into instability. The rigidity and damping of the disc and transverse stiffness and damping of the slider tend to suppress the vibrations. The in-plane stiffness and damping of the slider do not always have a stabilizing effect. The motivation of this work is the understanding of instability and squeal in physical systems such as car brake discs where there are vibrations induced by non-smooth dry-friction forces.

Two elastic cylinders, which in general may be elastically dissimilar, are pressed together by a normal force and slid over one another. A frictional shear traction is developed which also generates heat along the interface. It is assumed that one body is an insulator and that the contact patch traverses the conducting body. In the paper we first solve the coupled thermo-elastic contact problem and then find explicitly the total state of stress in the conducting body. A quantitative assessment of the relative importance of thermal effects on the strength of the contact is then made.

The interfacial stick-slip system present between two infinitely long cylinders, pressed together by a normal force, is considered. The shearing traction distribution is represented in a piecewise-linear sense, using overlapping triangles of shear, which may have both transverse and axial components. Several external force histories are modelled, starting off with a monotonically increasing transverse force (the Cattaneo–Mindlin problem). Subsequently, an axial force is applied, again within the partial slip regime, and finally a complete closed cycle of transverse and axial forces is studied. The stick-slip regime and distribution of shearing traction is displayed at several points within the cycle, and it is shown that a steady state is almost achieved within one cycle of loading.

A normal force moves slowly over the surface of a layer which is pressed against a substrate. Two asymmetric slip zones are generated if the force exceeds a friction dependent critical value. The slip is opposite in direction in the two zones, but due to the lack of symmetry, a net tangential shift of the layer is left behind by the passage of the force. This net shift is generally influenced by the coefficient of friction: for high coefficient, the layer shifts in the direction of motion, while for low coefficient, the shift is opposite. The latter result has been observed experimentally.

Growth in the thickness direction of a long axial surface crack at the inner surface of a thin walled cylinder has been analyzed for loads generated by internal pressure and a thermal gradient through the wall thickness. Plane-strain deformations have been considered. It has been assumed that the cracked cross-section is fully plastic, but that the plastic zone width in the circumferential direction is very small. The cracked cross-section transmits a normal force and a bending moment, which have been considered as external forces on an equivalent cut ring element, to compute the deformation of the cracked cross-aection. An analytical expression has been derived for the crack-opening-displacement, as a function of the loads and the crack depth. Stable and unstable crack growth have been investigated on the basis of a critical crack-opening-displacement and a smoothly rising crack-opening R- curve . The condition for unstable crack growth depends primarily on the magnitude of the internal pressure. A thermal gradient by itself is less likely to cause unstable crack propagation.