Stick-slip Region Research Articles

Analysis of Contact Stress Distribution between Rolling Element and Variable Diameter Raceway of Cageless Bearing

The change in contact state between the rolling elements and raceway of a cageless bearing with a variable diameter raceway affect the wear of the bearing, which leads to discrete motion failure of the rolling elements. For this purpose, the contact characteristics as contact form and contact stress between the rolling elements and raceway were determined. A numerical method is proposed to determine the three-dimensional contact stress of a cageless bearing. First, combined with the variable diameter raceway structure characteristics and the motion of rolling elements, the rolling elements and raceway contact stress model was established, and the influence factors of contact stress and the maximum stress distribution were determined. Based on the rolling contact theory, the relative position of the stick-slip region and the tangential stress distribution of the contact area were analyzed. The stress equations for the three-dimensional between rolling elements and variable diameter raceway were obtained by the principle of superposition, and the stress component characteristics of the contact area were numerically simulated. The results show that the main influencing factors of contact stress are: load, structure of variable diameter raceway, spindle speed, friction coefficient µ and the ratio of the stick region and the slip region k. Taking a cageless bearing as an example, the influence of the contact curvature Ri on the contact stress is smaller than that of ri. Increasing ri to make it larger than 1.5 mm and controlling the speed to be lower than 13,950 r/min, the maximum stress appears in the conventional raceway, which is beneficial to alleviate the failure of the variable diameter raceway. There are a slip region and a stick region in the contact area, reducing the friction coefficient µ and increasing the stick-slip coefficient k appropriately can ensure the discrete movement of the rolling elements and reduce the wear of the variable diameter raceway. The error of the stress distribution model is less than 15%, which can predict and characterize the contact stress distribution between the rolling elements and the variable diameter raceway. The theoretical guidance for the development and application of cageless bearings is provided.

Contact analysis of an anisotropic half-domain with micropatterns considering friction

In the present study, a contact problem between a spherical indenter and a half-anisotropic elastic region with a micropattern is solved under normal and tangential forces considering friction. The surface Green's function, and the discrete convolution and fast Fourier transform (DC–FFT) method are used to calculate the displacements on a contact area, and the conjugate gradient (CG) method is used to calculate the contact pressure, the contact area, shear tractions, and the stick-slip region. The influences of the shape and density (the pattern area per unit area) of the micropattern and the material anisotropy in the substrate on the friction property of the substrate are investigated. In the present study, substrates with circular and square micropatterns are used in the analysis. The results of the analysis revealed that the shear tractions are concentrated at the edges and corners of the circular and square patterns, respectively. The apparent friction coefficient varies with the direction of the anisotropic principal axis.

Numerical Analysis of Fretting-Wear With a Hybrid Elastoplastic Friction Model

Fretting-wear is a common problem in different industries, especially when it comes to interactions between metallic components. Flow-induced excitation forces in heat exchangers for instance cause tube-support interactions. The long-term interaction is an important phenomenon, which may cause fretting-wear of the tubes. Experimental tests of the interaction show the occurrence of stick–slip intermittent behavior in the tube response. To precisely simulate the intermittent stick–slip behavior, it is crucial to refine the conceptual model of the coefficient of friction for the entire motion from absolute zero velocity to gross slip phase. The incorporated friction model plays an important role in the determination of the level of fretting-wear in the system. The friction model should satisfy two important criteria. The first important aspect is the strategy of the friction model to detect the cessation of sticking, the beginning of partial-slipping, and establishment of the sliding region. The second important aspect is defining a friction coefficient function for the entire system response to precisely represent the transient stick–slip regions. In the present work, the velocity-limited friction model was compared with the LuGre model, which is a rate-dependent friction model. The effect of varying the break-away force and Stribeck effect on the stick–slip region were also investigated. Furthermore, the criteria to demarcate the stick–slip region in the LuGre model are discussed, and a different method to incorporate the Stribeck effect and presliding damping in the Dahl friction model is proposed. Using the tangential stress distribution in the contact area, a new hybrid spring-damper friction model is developed. The model is able to estimate the elastic, plastic, and partial-slipping distances during the relative motion. The ability of the model to reproduce experimental tests is investigated in the present work.

Is stress accumulating on the creeping section of the San Andreas fault?

The creeping section of the San Andreas fault (CSAF) in central California is a proposed barrier to propagation of large earthquakes. Yet, recent studies show that the creeping section is not entirely uncoupled but is accumulating slip deficit at a rate equivalent to a Mw=7.2–7.4 earthquake every 150years. A critical piece to understanding earthquake potential on the CSAF is determining whether slip deficit is occurring with stress accumulation on stick‒slip regions or without stress accumulation on stable‒sliding regions shadowed by surrounding locked areas. We use a physical model to estimate the spatial distribution of locked, stress‒accumulating areas of the fault constrained by surface creep rate measurements and GPS‒derived velocities. We find that the area of the fault accumulating stress, if ruptured every 150years, would release slip equivalent to at most a Mw=6.75 earthquake, significantly less than the Mw=7.2–7.4, 150year equivalent total slip deficit rate.

Elastic-Plastic Contact Conditions for Frictionally Constrained Bodies Under Cyclic Tangential Loading

A Frictionally constrained condition implies dependence of friction force on tangential displacement amplitude. The condition may occur due to chemical, physical, and/or mechanical interaction between the contacting surfaces. The condition, sometimes also referred to as the presliding condition or partial slip condition, is characterized under fretting. Under such conditions, various experimental studies indicate the existence of two distinguishable regions, that is, stick region and slip region. In the present study, frictionally constrained conditions are identified and the evolutions of stick-slip regions are investigated in detail. Investigations have been performed on self-mated stainless steel and chromium carbide coated surfaces mated against stainless steel, under both vacuum and ambient conditions. Contact conditions prevailing at the contact interface were identified based on the mechanical responses and were correlated with the surface damage observed. Surface degradation has been observed in the form of microcracks and material transfer. Detailed numerical analysis has also been performed in order to understand the energy dissipation and the damage mode involved in the surface or subsurface damage. It has been observed that under frictionally constrained conditions, the occurrence of annular slip features are mainly due to the junction growth, resulting from elastic-plastic deformation at the contact interface. Ratcheting has been observed as the governing damage mode under cyclic tangential loading condition.

Determination of stick-slip stage of single and multiple yarn ends pull-out in para-aramid (Kevlar®) woven fabric

The aim of this study was to understand the stick-slip properties of para-aramid woven fabrics. For this reasons, pull-out test was conducted on para-aramid Kevlar® 29 and Kevlar® 129 woven fabrics. The force–displacement curve from each fabric sample was obtained. The stick-slip region and accumulative retraction force region were defined based on the force–displacement curve. It was found that stick-slip and accumulative retraction forces depend on fabric density and the number of pulled ends in the fabric. Stick-slip and accumulative retraction forces in the multiple yarn pull-out test were higher than those of the single yarn pull-out test. Stick-slip and accumulative retraction forces in single and multiple yarn pull-out tests in the dense K29 fabric were higher than those of the loose K129 fabric. In addition, long fabric samples showed high stick-slip force compared to that of the short fabric samples.

Three-dimensional transient rolling contact analysis of similar elastic cylinders

Because most fatigue cracks in wheel and rail take place by rolling contact between wheel and rail in railway industry, it is critical to understand the rolling contact phenomena, especially for the three-dimensional situation. In this paper the steady-state and transient rolling contact problem of three-dimensional elastic bodies has been studied. The transient conditions were controlled by the applied relative slip. The variation of tangential traction and stick-slip region on rolling contact surface were obtained using the finite element method. The three-dimensional distribution of tangential traction and contact stresses on the contact surface are investigated. Results show that the distribution of tangential traction and contact stresses on the contact surface varies rapidly as a result of the variation of stick-slip region. The tangential traction is very close in form to Carter's distribution that contact region divided into stick and slip region. The contact stress at the leading edge is greater than at the trailing edge and the transient distance increases with small slip.

Transient rolling of cylindrical contacts with constant and linearly increasing applied slip

The transient start problem of a rolling cylindrical contact has been studied. The transient conditions were controlled by the applied relative slip. Two cases with start of rolling from stationary contact were investigated, with constant and with linearly increasing applied slip. At each instant during the transition stage, it was assumed that the traction distribution could be approximated with the Carter traction for steady-state tractive rolling. Based on this distribution, approximate expressions were derived for the transient rolling distance and transient behaviour of the tangential load. The transient period could end in gross sliding or steady-state creep with the Carter traction distribution and stick–slip regions in the contact. The expressions and the transient traction distributions were validated numerically using FEM. Simulations with constant applied slip showed that when rolling started from a tangentially unloaded and unstrained position, the steady-state traction distribution by Carter was a good approximation of the actual transient traction distribution. The solution was accurate for transient rolling lengths longer than a quarter of the contact width. The transient behaviour depended on the bulk geometry of the structures. For the relatively stiff structure with two elastic steel cylinders, small amounts of relative slip and high coefficients of friction, the transient rolling distance, L 0, could become large. In the present study, examples with L 0 ≈ 40 ⋅ a were identified. Thus, situations exist for which the transient conditions might be important. The transient distance increased with smaller slip, larger coefficient of friction, lower bulk stiffness, higher contact normal loads and for more compliant materials. The spur gear contact interaction with varying slip was considered as a case study.

Fretting contact with finite friction of a functionally graded coating with arbitrarily varying elastic modulus Part 1: Normal loading

The two-dimensional normal contact of a functionally graded coated half-space by a rigid cylindrical punch under the action of a monotonically increasing normal load is considered. Friction with a finite coefficient is assumed between the contact surfaces. The whole contact region is composed of an inner stick region and two outer slip regions. The linear multilayered model is used to model functionally graded materials (FGMs) with arbitrarily varying shear modulus and constant Poisson's ratio under plane strain deformation, i.e. the FGM is divided into several sublayers and in each sublayer the shear modulus is assumed to be a linear function while Poisson's ratio is a constant. With the use of the transfer matrix method and Fourier integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. An iterative method is developed to determine the stick-slip region. Normal and tangential tractions in the whole contact region are calculated. It is found that the stick region depends on the gradient of the functionally graded coating as well as on Poisson's ratio and the friction coefficient. The results also show that appropriate gradual variation in the shear modulus can significantly alter the contact traction. This may lead to suppression of Hertzian cracking at the edges of the contact region and thus modify the contact damage. Therefore, it is believed that FGM coatings would have potential applications in improving the resistance to contact damage at the contact surfaces.

Jamming of three-dimensional prolate granular materials

We have found that the ability of long thin rods to jam into a solidlike state in response to a local perturbation depends upon both the particle aspect ratio and the container size. The dynamic phase diagram in this parameter space reveals a broad transition region separating granular stick-slip and solidlike behavior. In this transition region the pile displays both solid and stick-slip behavior. We measure the force on a small object pulled through the pile, and find the fluctuation spectra to have power law tails with an exponent characteristic of the region. The exponent varies from beta=-2 in the stick-slip region to beta=-1 in the solid region. These values reflect the different origins--granular rearrangements vs dry friction--of the fluctuations. Finally, the packing fraction shows only a slight dependence on container size, but depends on aspect ratio in a manner predicted by mean-field theory and implies an aspect-ratio-independent contact number of <c>=5.25 +/- 0.03.

A new criterion for occurrence of strick-slip motion in drive mechanism

This paper, using Karnopp's model of friction force and phase plane method, studies the stick-slip motion of the flexble drive mechanism. It is explained that a sudden drop of friction force is the essential source of stick-slip motion when the sliding is impending. A new criterion for occurrence of stick-slip motion is established. The stick-slip region and the stable region in a parameter plane are separated by a critical parameter curve. Moreover, for the stick-slip motion of the flexible drive mechanism without viscous damping, a parameter expression is obtained. The results may be used in design of the flexible drive mechanism.

Peel adhesion and viscoelasticity of poly(ethylene-co-vinyl acetate)-based hot melt adhesives. II. The influence of wax

The influence of wax on the viscoelasticity and peel adhesion of poly(ethylene-co-vinyl acetate) (EVA)-based hot melt adhesives was evaluated. Wax does not affect the glass transition temperature of a homogeneous EVA/rosin blend. However, for a heterogeneous EVA/rosin blend, wax addition increases the EVA-rich phase portion, resulting a higher rubbery response. The T-Peel fracture energies of EVA/tackifier/wax blends bonded to polypropylene film are controlled by two factors: (1) a weak boundary layer of wax, which has a deleterious effect on bonding, and (2) on the other hand, an increased rubbery response in the stick-slip region, which tends to strengthen joints. © 1997 John Wiley & Sons, Inc.

The phase-plane analysis of sliding motion

This paper is a report on an investigation of the stick-slip motion which can arise when a body slides along a machined surface, with or without lubrication, at low speeds. This type of motion is encountered in machine-tool practice and can cause serious deficiency in the accuracy and finish of machined surfaces. In any positioning system such a motion is unavoidable. The effect can be reduced by increasing the natural frequency of the driving spring-mass system. Working from the coefficient of friction-velocity relationship the phaseplane trajectory method indicates that as relative speed increases motion passes through the stick-slip region into a region of smooth movement and then at higher speeds into a region of oscillatory motion. The work was carried out on a modified lathe-bed 8 ft. long using loads of up to 500 lb. at speeds from 1/10 in./min up to 100 in./min using a variety of lubricants. Actual results are quoted and analysed for one typical set of conditions. From the experimental results a series of non-dimensional curves can be obtained from which optimum relationships between mass, stiffness and speed can be derived for smoothest motion.