Stick Area Research Articles

Cattaneo–Mindlin plane problem with Griffith friction

The classical Cattaneo–Mindlin problem for elastic halfplanes is extended for a Griffith condition for inception of slip, and otherwise following the standard Coulomb law in the sliding zone. A general solution is found using the idea of superposing normal contact pressure distributions for arbitrary 2D geometry. In particular, the full sliding component of shear is corrected with a distribution in the stick region which is formally equivalent to a JKR solution for the normal contact problem insisting on the stick area. We show that geometry affects the apparent friction coefficient (the maximum tangential load at the inception of slip), since a sudden transition to slip occurs when the stick region reaches a critical size which corresponds to the phenomenon of pull-off in the JKR solution. Example solutions are given for Hertzian geometry, power law punches and a sinusoidal profile.

Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited

Classically, the transition from stick to slip is modelled with Amonton–Coulomb law, leading to the Cattaneo–Mindlin problem, which is amenable to quite general solutions using the idea of superposing normal contact pressure distributions – in particular superposing the full sliding component of shear with a corrective distribution in the stick region. However, faults model in geophysics and recent high-speed measurements of the real contact area and the strain fields in dry (nominally flat) rough interfaces at macroscopic but laboratory scale, all suggest that the transition from ‘static’ to ‘dynamic’ friction can be described, rather than by Coulomb law, by classical fracture mechanics singular solutions of shear cracks. Here, we introduce an ‘adhesive’ model for friction in a Hertzian spherical contact, maintaining the Hertzian solution for the normal pressures, but where the inception of slip is given by a Griffith condition. In the slip region, the standard Coulomb law continues to hold. This leads to a very simple solution for the Cattaneo–Mindlin problem, in which the “corrective” solution in the stick area is in fact similar to the mode II equivalent of a JKR singular solution for adhesive contact. The model departs from the standard Cattaneo–Mindlin solution, showing an increased size of the stick zone relative to the contact area, and a sudden transition to slip when the stick region reaches a critical size (the equivalent of the pull-off contact size of the JKR solution). The apparent static friction coefficient before sliding can be much higher than the sliding friction coefficient and, for a given friction fracture “energy”, the process results in size and normal load dependence of the apparent static friction coefficient. Some qualitative agreement with Fineberg's group experiments for friction exists, namely the stick–slip boundary quasi-static prediction may correspond to the arrest of their slip “precursors”, and the rapid collapse to global sliding when the precursors arrest front has reached about half the interface may correspond to the reach of the “critical” size for the stick zone.

Comments on the paper by G.P. Cherepanov “The contact problem of the mathematical theory of elasticity with stick and slip areas. The theory of rolling and tribology”. JAMM, 2015, Vol. 79, No. 1, pp. 81-101

Comments on the paper by G.P. Cherepanov “The contact problem of the mathematical theory of elasticity with stick and slip areas. The theory of rolling and tribology”. JAMM, 2015, Vol. 79, No. 1, pp. 81-101

Cross Shift In A Vehicle With A Manual Gearbox

The cross shift behaviour of a gearbox in a vehicle will be explained. The elements which are involved will be described. Cross shift in a car under static and dynamic condition will be checked. The results of these tests will be described. The shift track of a six gear transmission in a vehicle is illustrated. All elements where a cross shift stuck can occur will be mentioned. The stuck areas are also described. A solution for this item will be found, where no cross shift stuck can ever happen. I. INTRODUCTION The shifting behaviour of a transmission in a vehicle is one of the most important things during the development phase. In the shifting process many parts are involved. The outer shift mechanism and elements which are not included in the cross shift process will not be mentioned in this paper. Driver needs a good static and dynamic performance of a gearbox. Therefore all possible applications for a transmission have to be checked and analyzed. Only cars with a good working gearbox will be bought. The requirements of a gearbox are increasing. All the tests were done in cooperation with a European car manufacturer. The final product will be build up in a new type of car of this vehicle manufacturer. A lot of investigations in warm and cold conditions were done to fulfil the requirements. In order to assess the state of development and the development progress of the shift quality objective, it is necessary to have measurable criteria. The shift quality is according to (Gebert, 2000), (Kucukay and Gebert, 1997) and (Kucukay and Renoth, 1995) a subjective judgment of the vehicle occupant. This judgment depends on factors such as the switching frequency, the response time, the course of the vehicle acceleration a(t) and the associated jerk, as well as the acoustic impression during the shift. A shifting can be described and characterized over the course of acceleration and jerk (Naruse, et. al., 1993), (Schwab, 1994). II.

Deformation Characterization of Micro Rolling for Stainless Steel Foil

Physical parameters such as microscopic roughness become very important in micro forming process due to increasing surface to volume ratio. As a very important phenomenon in metal forming process, friction size effects are becoming more attracting for researchers because traditional models are not reliable. In this study, the micro rolling deformation characterization has been investigated with SUS 304 stainless steel considering the effect of lubricant, and there exists a sticking area in the contact zone. The evolution of surface roughness and oil film thickness are analyzed. The foil thickness plays an important role in the tribological features of rolling. All the results have been verified experimentally via the desktop 2-Hi micro rolling mills.

A Numerical Study of the Partial Slip Elliptical Contact under Fretting Conditions

The technologically important elliptical contact undergoing fretting is simulated using previously advanced state-of-the-art numerical tools. The influence of contact ellipse eccentricity on various contact parameters is assessed. An analogy with the circular contact is found when tractions equations are written in dimensionless coordinates in case of similarly elastic materials. However, when an elastic mismatch is introduced, the stick area no longer follows proportionally the established contact area.

Frictional dissipation in elastically dissimilar oscillating Hertzian contacts

We consider the problem of a cyclic Hertzian indentation between elastically dissimilar materials. In the case of loading, the problem was solved by Spence in a series of seminal papers, where he proved a relationship between the solution for a rigid square-shaped punch, to that for a power-law indenter. For example, the stick area is a constant ratio of the contact area, independently on the shape of the punch. “Unfortunately”, on unloading, many of the simple properties of the self-similar loading case are lost, there is a complicated development of an external region of slip which cycles in the two directions (forward and back-slip), and an inner region which continues to slip in the forward direction of the first loading cycle. However, this inner region gradually disappears, and further cyclic loading generates a convergence to a steady state solution which involves residual “locked-in” tangential slip displacements in a permanent stick zone, provided the contact is not fully unloaded. Dissipation in the steady state therefore occurs only in the external region of slip, and we provide some results for the energy dissipation per cycle, as a function of the governing parameters: coefficient of friction, Dundurs’ dissimilarity constant, normal load amplitude. We also show the likely independence of energy dissipation on initial conditions, limited to the possible scenario of overloading. It is seen that dependence of energy dissipation per cycle on load amplitude is closer to quadratic than to cubic, and this may explain some experimental findings which so far were not expected from oscillatory loading of elastically similar half-spaces.

Numerical analysis on the clamping reliability of fixture–workpiece facility considering partial slip

Fixture is a mechanical component to clamp a workpiece and to move it to a specific position. This paper analyses partial slip at the fixture–workpiece interface and addresses the effects of design parameters and working conditions of a fixture–workpiece facility on clamping reliability. A stick ratio, defined as the ratio of the stick area to the entire nominal contact area, is introduced in this study to characterize the clamping reliability. If the value of stick ratio equals to one, the clamping is most reliable, but when it drops to zero, a gross sliding will occur, which means clamping failure. This paper investigates the partial slip phenomenon by solving three-dimensional contacts between elastically dissimilar materials, using the conjugate gradient method (CGM) and discrete convolution-fast Fourier transform (DC-FFT) techniques, but focuses on its industrial applications. Results have demonstrated how the inferential factors, such as material property, normal and tangential loads, operational parameters, and geometric features of the fixture, would affect the clamping reliability, which can be used for guiding the design of the fixture, for example, the choice of material, friction coefficient, fixture’s opening angle, acceleration in manipulation, and so on.

Numerical and Experiment Analysis of Rail Wear

The rolling contact wear is a severe problem and meets with much widespread interest in the world. This paper describes an numerical method and simulation experiment investigation on the rail wear affected by the curve radius and axle load etc. The creep force ,stick/slip areas of contact particles, and friction work of wheel/rail in static condition are analyzed by kalker’s program CONTACT. The effect of curve radius and axle load on rolling wear behaviour of rail is investigated by simulation experiment. The results of numerical and experiment indicates that with the decreasing of curve radius and the increasing of axle load, the wear value of rail increase nonlinearly, especially in the condition of the curve radius is less than 1200m,the wear value of rail increase rapidly. And with the decrease of curve radius, the maximum slippage decrease gradually, and the stick areas decrease while the slip areas increase. The growth speed of friction work of wheel/rail in the condition of smaller curve radius and heavier axle load is faster than in the condition of larger curve radius (straigth line) and lighter axle load.

A quadratic programming formulation for the solution of layered elastic contact problems: Example applications and experimental validation

The development of a quadratic programming formulation for the solution of layered elastic contact problems in the presence of friction is presented in this paper. Conveyor belts , tyred wheels, composite cylinders, and conrod bearings, are classical examples of systems which can be studied using the efficient numerical methodology proposed here. In this type of mechanical assembly, micro-slip between the mating surfaces often occurs and may eventually lead to system failure. Accurately capturing the evolution of slip and stick areas using a computationally inexpensive procedure (as an alternative to full finite element analysis) is therefore key to preventing these failures and to improving the design of various engineering components. The proposed approach is first tested and validated against classical marching-in-time solutions for two-dimensional layered systems in the presence of both static and moving loads. Results are then extended to demonstrate the feasibility of the technique to study systems with multiple slip regions and to solve rolling contact problems of practical interest. Finally, the numerical methodology is successfully applied to the prediction of frictional creep of tyred cylinders. Experimental corroboration has been obtained by testing tyred discs.

Finite Element Modeling of the Nano-scale Adhesive Contact and the Geometry-based Pull-off Force

Nano-scale adhesive contact mediated by intermolecular van der Waals forces has become a typical fundamental problem in many areas. Interpretation and control of the strength and efficiency of the nano-scale adhesive contacts require a proper modeling considering the actual interfacial forces, the varying contact area, and clearance. In this article, the finite-element (FE) method is developed to model the nano-scale adhesive contact of elastic bodies with an adhesive pressure derived from the interatomic interaction Lennard-Jones potential, which permits numerical solutions for a variety of interface geometries. Compared with the analytical results from conventional Hertz, JKR, and DMT models, the validity of the FE model is verified. For nano-scale contact, the assumption of equivalent radius adopted in the Hertz model is initially investigated and proved to be improper for nano-scale adhesive contact due to the distribution variations of interfacial force caused by local contact geometry. Then adhesive contact behaviors of four typical nano-scale contact geometries inspired by tip shapes of bio-adhesive pads are investigated in detail, which are flat punch tip, sphere tip, mushroom tip, and empty cup tip. The simulation results indicate that the nano-scale tip geometry plays a dominant role on the pull-off strength. Within the investigated geometries, cup tip results in a highest adhesion efficiency followed by flat punch tip, sphere tip, and mushroom tip, respectively, which are highly geometry dependent and verified by former experimental results. The dominant effect is found coming from the contact area ratio of the adhesive area to the sticking area or the whole contact area. The FE modeling can serve a useful purpose in revealing the nano-scale geometry-based adhesion contact for surface topography design in MEMS to avoid stiction failure and for the artificial sticky feet in bionics to increase adhesion strength.

Contact-layer method in adhesive mechanics: Adhesive strength during normal detachment

The contact-layer method is used to solve the problem of stressed-deformed state and strength in the adhesive attachment model, designed for normal detachment tests. The influence of different model and experimental parameters on the normal destructive stress measured in experiments is studied. It is shown that tangent stresses are distributed nonuniformly over the sticking area and that the strength in the model is determined by the competition of normal and maximum tangent stresses.

Prediction of Contact Temperature Distribution during Fretting Fatigue in Titanium Alloys

Fretting is a critical problem to the manufacturers and operators of turbine engines, reducing the useful life of fan, compressor, and turbine blade components. The fretting action between the two components in contact leads to temperature rise, which in most cases, may be significant enough to cause a number of adverse effects. The knowledge of the temperature profiles inside the material is very important because it enables the prediction of possible oxide formation and the development of thermal stresses. To this end, the temperature profile for Ti-6Al-4V alloys has been predicted in this work utilizing a heat flow channel (HFC) model. The model requires as input the material constants (thermal conductivity, thermal diffusivity, and flow stress), the material surface characteristics (roughness and asperity spacing), the frictional conditions between the two surfaces, as well as the external parameters (frequency, amplitude of oscillation, magnitude of contact area). The analysis enabled the determination of the temperature field as a function of time and the three spatial coordinates. The model showed that the temperature increases quite rapidly at the beginning of the process and reaches an essentially constant value after approximately 1000 cycles. The predictions revealed a rapid decay of temperature with the thickness of the specimen, while the temperature drop was found to be much smoother in the other two specimen directions. Additionally, a first-order validation of the model was achieved by determining the oxygen concentration in fretting-fatigued Ti-6Al-4V specimens, where it was found that an increased oxygen concentration existed in the fretting area compared to the non-contact and stick areas.

A numerical model for the point contact of dissimilar materials considering tangential tractions

This paper presents a three-dimensional numerical model for the simulation of the contacts of elastically dissimilar materials. This model is based on the Boussinesq–Cerruti integral equations relating normal and tangential surface tractions to surface displacements and employs the static friction law to identify the onset of local micro-slip. An iterative conjugate gradient method (CGM) is utilized to determine the unknown contact and stick area efficiently and accurately with the assistance of the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model leads to the solutions of surface real contact and stick areas, pressure, tangential tractions, and the subsurface stress field. It is verified through the comparison of the numerical results with analytical solutions. Simulations are performed for a ball and half-space contact with the normal loading alone first, and then the results for the contact with increasing tangential loading are also presented. The effects of shear tractions on the contact area, the stick zone, pressure and the intensity of von-Mises stress are discussed.

Torsion of rough elastic half-space by rigid punch

Torsion of an elastic half-space by a rigid punch is investigated. The boundary of the half-space is assumed to be rough. Two geometries of the punch-parabolic and flat end are considered. It is shown that the contact area consists of stick and slip zones. This fact, which is well-known in the classical torsional contact of the elastic half-space with the smooth surface and the parabolic punch, also holds true for the flat-ended punch if the boundary roughness is involved. The partial slip problems are reduced to the integral equations, which are solved numerically. The presented results show the effects of boundary roughness on the shear stresses, size of the stick area and the relation between the twisting moment and the angle of twist.

Interlocking Performances on Non-Oriented Electrical Steels

Interlocking performance as fastened strength and magnetic deterioration by interlocking were investigated. The thickness of a surface insulation coating affected the interlocking fastened strength. Sheets with a thin coating resulted in a better interlocking performance than those with a thick coating due to the lubricating effect by resin as coating materials. Sheet gauge affected the interlocking fastened strength. The fastened strength of thin gauge sheet was less than that of a thick one, because of the reduction of the sticking area of interlocking protuberances. The protuberance shapes affected the fastening strength. The rectangular types are stronger than the circular ones, due to the ‘hooked by corners’ effect. Magnetic deteriorations by interlocking was caused by the core loss increased by the obstruction of magnetic flux flows and eddy current loss through the laminations. The core loss increased by the eddy current loss through the laminations was 78% of all deterioration by interlocking.

Development of Elastic Finger-like Sensor for Control of Grasping Force (Control of Grasping Force in Arbitrary Direction Using Spherical Sensor with Strain Gages Arranged on Perpendicular Axes)

A two axial finger-shaped sensor is developed for controlling grasping force so that an object is lifted with appropriate grasping force at any grasping direction. It consists of silicone rubber having spherical surface and strain gauges arranged in two perpendicular axes. First, the relationship between stick area and the internal strain distribution of the sensor are calculated using FE (finite element) analysis when the sensor is in contact with an object. It is necessary to detect the shear strain distributed in the sensor in order to grasp the object with appropriate force. Then, the method for estimating stick area of the sensor is proposed using FE analysis. Finally, the grasping force control is achieved using the constructed system. It is shown that arbitrary objects with various weight and friction coefficients are lifted using the developped sensor and control method.

Development of Elastic Robot Finger having Rides which can Detect a Distribution of Contact Condition

An elastic robot finger has been developed for controlling grasping force when weight and frictional coefficient of grasped object are unknown. First, geometry of the finger is designed. The elastic finger has ridges at the surface to divide the contact area. Geometry of the ridges is trapezoid like human ridges. It also has a pair of tactile sensors embedded per one ridge similar to human fingertips. The surface of the whole finger is curved so that normal reaction force distributes unequally. A Finite Element (FE) model of the elastic finger was made to conduct a dynamic contact analysis using a FE method in order to design the elastic finger in detail. Then the elastic finger was made to confirm the results of FE analyses. At a result, it was confirmed by calculation and experiment that the elastic finger can detect the incipient slippage of the ridge that occurs near the edge of contact area and can deduce the stick area ratio. This result in useful for controlling grasping force when the weight and friction coefficient between the elastic finger and grasping object are unknown.

Properties of equal bodies in contact with friction

The properties of a reduced friction model for elastic bodies with general surfaces in contact are explained, and it is proved that the tangential friction problem can be reduced to the normal problem. The tangential solution results as the difference of the full slip traction for actual contact and a smaller contact area, which represents the stick area (or multiple areas). The local traction in the slip area opposes the relative motion in the same way as the normal relative approach opposes the contact pressure, as required by Coulomb’s slip inequality. The stick inequality for the traction is identical with the contact condition of positive pressure. A superposition method for general loading scenarios is explained and an example is calculated at the end. The force displacement relation of the reduced friction model agrees well with the FEM solution, even for dissimilar materials, because the dissimilarity effect is small in practical applications. Since numerical solutions of frictional contact are rare in literature, an example for a contact area with a hole is presented.

Stick/slip Distribution on the Fingerpad and Response of Tactile Receptors when Human Grasp an Object.

Grip force and contact condition including stick/slip are measured to investigate the mechanism of dynamical transmission of contact information to tactile afferents in precision grip of human. A system for measuring normal/tangential forces and stick/slip condition between the human finger and grasping object is made. As a result of measurement, it is found that the increase ratio of the grip force and the change in stick area are mutually related. Contact condition is also calculated using a FE (finite element) analysis. It is found that the stick/slip condition shows the similar phenomena as experiment. Change in SED (strain energy density) at the Meissner's corpuscles' location shows local maximum at the slip area. The relationship among the SED at the location of Meissner's corpuscles, the deformation of the finger and the stick/slip condition in precision grip is shown. In other word, a model for transmitting the dynamic information from the contact condition to tactile afferent responses during precision girp is constructed.