Tangential Contact Stresses Research Articles

Numerical Analysis of the Effect of Slip Ratio on the Fatigue Crack Initiation Life in Rolling Contact

This paper presents a numerical analysis of the effect of slip ratio on the fatigue crack initiation life, considering the tangential traction on the rolling contact surface. The distribution of tangential traction and contact stresses on the contact surface, when rolling contact occurs between two cylindrical test specimens, are obtained using three-dimensional finite element analysis. The effect of slip ratio on the fatigue crack initiation life was evaluated by applying multiaxial fatigue criteria based on critical plane approaches. As a result, the 3D-FE model developed well represent the distribution of tangential traction and contact stresses on the contact surface at stick-slip condition, which is differ from the static or full sliding contact condition. As the slip ratio increases, the maximum tangential traction also increases in slip zone and the location of maximum stress closer to the contact surface in stick zone. The fatigue strength decreased with the increase in the slip ratio. Therefore, it is clear that the slip ratio has an important role in prediction of fatigue crack initiation life on the rolling contact surface.

Analytical Approach for Predicting Three-Dimensional Tire–Pavement Contact Load

Three-dimensional tire–pavement contact loads of two truck tires–-a new-generation wide-base tire (WBT) and a dual tire assembly (DTA)–-were measured and analyzed. Extreme and typical values of tire inflation pressure (552, 690, 758, and 862 kPa) and tire loading (26, 35, 44, 62, and 79 kN) were considered in the experimental program. The measurements were performed with the stress-in-motion Mk IV system at the Council for Scientific and Industrial Research in South Africa. Peak values in three directions were compared, and the importance of tangential contact stresses was highlighted. In addition, characteristic variations of the measurements in the longitudinal, transverse, and vertical directions were identified. A function depending on two regression parameters, applied load, and distance along the contact length was proposed to represent the contact load in the vertical and transverse directions. An analysis was performed on the measurements to obtain the regression parameters, and a simplified procedure was proposed to determine tire–pavement contact loads. The contact area and contact length of the WBTs and the DTA were also compared.

Interference assembly and fretting wear analysis of hollow shaft.

Fretting damage phenomenon often appears in the interference fit assembly. The finite element model of hollow shaft and shaft sleeve was established, and the equivalent stress and contact stress were computed after interference assembly. The assembly body of hollow shaft and shaft sleeve was in whirling bending load, and the contact status (sticking, sliding, and opening) and the distribution of stress along one typical contact line were computed under different loads, interferences, hollow degrees, friction coefficient, and wear quantity. Judgment formula of contact state was fixed by introducing the corrected coefficient k. The computation results showed that the “edge effect” appears in the contact surface after interference fit. The size of slip zone is unchanged along with the increase of bending load. The greater the interference value, the bigger the wear range. The hollow degree does not influence the size of stick zone but controls the position of the junction point of slip-open. Tangential contact stress increases with the friction coefficient, which has a little effect on normal contact stress. The relationship between open size and wear capacity is approximately linear.

The FASTSIM Method Modification to Speed up the Calculation of Tangential Contact Stresses between Wheel and Rail

The articles deals with the way of calculation of tangential stresses over non-elliptical contact patch, where is possible to utilize with advantage the Kalker's simplified method FASTSIM. This method named FASTSTRIP is adapted for non-elliptical contact area calculated by means of the Strip method. This method is almost quick as FASTSIM and the results are similar to the CONTACT results. This method may be useful for rail vehicles in track dynamics computation.

An efficient method in the 2D problem on transient oscillations of the elastic half-space interacting with a rigid structure

We propose an efficient method to study the (two-dimensional) in-plane nonstationary (transient) problem for a rigid rectangular structure above the oscillating foundation. A massive structure is perfectly coupled with the foundation, whose oscillations are caused by an oblique plane seismic wave incoming from below to the boundary surface. The structure is assumed to be considerably more rigid than the foundation. The mathematical formulation admits application of the Laplace transform over time and Fourier transform along the horizontal coordinate. By satisfying the boundary conditions over the contact zone between the rectangle and the foundation, the problem is reduced to a system of two integral equations for normal and tangential contact stress, which contain the Laplace parameter. To solve this system, we apply a numerical method to arising Volterrà–Fredholm integral equations. Then the dynamic properties of the structure is studied for various combinations of physical and geometrical parameters.

Analysis of Near-Surface Cracking under Critical Loading Conditions Using Uncracked and Cracked Pavement Models

In this paper, the mechanism of near-surface cracking under critical loading conditions was investigated using mechanistic modeling approaches. These loading conditions were represented by a combination of nonuniform tire contact stresses in three directions generated during vehicle maneuvers (free rolling, acceleration/braking, and cornering) that were predicted from a tire-pavement interaction model. Three-dimensional finite element models of uncracked and cracked pavements were developed to evaluate the critical factors that are responsible for crack initiation and propagation at the near-surface of a typical full-depth pavement structure. It was found that the near-surface cracks in the proximity of tire edges showed strong mixed-mode (tension and shear) fracture potential. The pavement responses from both uncracked and cracked pavement models indicated that shear mode of fracture in the presence of compression appeared to be the dominant mode of damage for near-surface cracking. Compared to the free rolling condition, tire braking/acceleration and cornering induced high tangential contact stresses on the pavement surface, which could significantly accelerate the development of cracks at the pavement near-surface. The near-surface cracking potential was dependent on the variations of localized tire contact stress distributions. The findings presented in this study shed light on the experimental characterization of the near-surface cracking phenomenon, which appears to be driven by different stress conditions than the classical bottom-up fatigue cracking. This study also highlights the impact of vehicle maneuvering on premature pavement damage that is often neglected in the current pavement design process.

Simulation of tyre–pavement interaction for predicting contact stresses at static and various rolling conditions

This paper describes the development of a 3D tyre–pavement interaction model to predict the tyre–pavement contact stress distributions for future use in the mechanistic analysis of pavement responses. The ribbed radial-ply tyre was modelled as a composite structure (rubber and reinforcement), and the tyre material parameters were calibrated through load-deflection curves. The steady-state tyre rolling process was simulated using an arbitrary Lagrangian Eulerian formulation. The model results are consistent with previous measurements and validate the existence of non-uniform vertical contact stresses and localised tangential contact stresses. The analysis results show that the non-uniformity of vertical contact stresses decreases as the load increases, but increases as the inflation pressure increases. However, vehicle manoeuvring behaviour significantly affects the tyre–pavement contact stress distributions. For example, tyre braking/acceleration induces significant longitudinal contact stresses, while tyre cornering causes the peak contact stresses shifting towards one side of the contact patch. The model results provide valuable insights into understanding the realistic tyre–pavement interaction for analysing pavement responses at critical loading conditions.

The methods of complex potentials, singular integral equations and integral transformations in a series of problems for the reinforcement of cracked plates

We study the initiation and propagation of a vertical crack in an elastic semi-infinite plate, reinforced on its boundary by an infinite discontinuous stringer within the limits of the theory of brittle failure. The plate is subjected to uniform distributed tensile forces at infinity, as well as to contact stresses due to application of forces to the stringer. We find the appropriate loading of the coherent stringer, and consequently we consider a problem where the stringer is cracked and a vertical crack has developed within the plate. We deduce the exact analytical solution for the principal singular integral equation for this case; hence the stringer is perfectly rigid and we calculate characteristic parameters of the problem. The results show that the crack tip has a logarithmic singularity, and the tangential contact stresses under the stringer at that end point are finite and generally differ from zero.

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.

Shock Response Analysis for a Journal-Bearing System by a Results Comparison

Shock response analysis of a journal-bearing system with the journal-bearing connection modeled as a spring link in radial direction and a dry contact joint respectively is presented. In the first model, the spring constants representing oil-film characteristic are determined by eight coefficients. In the second model, the friction forces are calculated using a modified Coulombs friction law. The contact detection points are the integration point and located at Gauss points. Only the contact normal pressure is treated as a Lagrange multiplier. The tangential contact stresses are calculated based on the penalty method. System’s time varying responses are obtained by FEM. A results comparison was performed between “spring link” model and “dry contact” model. The main conclusion is that stress distribution is nearly same in the system modeled by the two methods, but the amplitude in the former is smaller than that in the latter.

A fixed-point approach to the limit load analysis of multibody structures with Coulomb friction

In this paper, it is shown that, for planar systems formed from linear-elastic bodies in non-penetrative contact with Coulomb friction, the limit load can be approximated efficiently by the limit loads corresponding to a sequence of contact problems with given friction, via a finite element fixed-point approach. For the auxiliary problem with given friction, a splitting of this problem into two subproblems, one with prescribed normal contact stresses and given friction and one with prescribed tangential contact stresses, is employed. Numerical results for masonry block structures subjected to in-plane loading illustrate the predictive capabilities of this approach.

A fully coupled partial slip contact problem in a graded half-plane

In this paper, we consider the two-dimensional nonlinear partial slip contact problem between a non-homogeneous isotropic graded half-plane and a rigid punch of an arbitrary profile subjected to a normal load. The graded medium is modeled as a non-homogeneous isotropic material with an exponentially varying shear modulus and a constant Poisson’s ratio. The problem is formulated under plane strain conditions. Using standard Fourier transform, the problem is reduced to a set of two coupled singular integral equations in which the main unknowns are the normal and the tangential contact stresses and the stick zone size. An asymptotic analysis is performed to extract the proper singularities from the kernels. Using Gauss–Chebychev integration formulas, the two coupled equations are solved by sequential iterations. The objective of this paper is to study the effect of the graded medium non-homogeneity parameter and the friction coefficient on the size of the stick zone and the contact stresses for the cases of flat and circular stamp profiles. Particular attention is also paid to the effect of the coupling between the normal and the tangential contact stresses.

Influence of contact stress on the life of connected elements

The tangential contact stresses in the fretting fatigue of joints is studied. A model of the fatigue failure rate of joints permits estimation of their durability on the basis of the fatigue characteristics of a standard sample with a central hole.

Contact interaction in the cutting of high-temperature alloys

1293 It is often assumed that the physicomechanical parameters of the blank’s surface layer and the wear rate of the cutting tool are closely related to the frictional characteristics of the tool‐blank contact [1]. However, no models have been presented for the determination of this relationship. A mathematical model of the formation of the machined blank surface may be derived from research based on the classical theory of elasticity and plasticity, taking account of the plastic deformation of the metal, its hardening and destruction, and current concepts regarding the mechanism by which residual stress is formed [2]. The validity of this model is verified by experiments on the turning of high-temperature nickel alloys by tools made of hard alloys based on tungsten carbide and high-speed steel. A functional relation has been established between the normal p r and tangential τ n stresses at the tool’s working surface and the contacting surface of the blank during mutual slip, on the one hand, and the output parameters of machining (tool wear, surface roughness, depth and degree of surface hardening, residual stress in the surface layer), on the other. It is found that the minimum stress in the tool‐blank contact zone due to the normal and tangential contact stresses, which is characterized by the maximum tangential stress is observed in machining with the optimal temperature in the cutting zone [1]. Consequently, the minimum stress in the tool‐blank contact zone is associated with the formation of a surface layer more suitable for subsequent operation of the part. Calculations by the proposed mathematical model call for numerical values of the normal stress p r and tangential stress τ n . If we adopt the method and equipment developed at Ufa State Aviation-Engineering University for laboratory study of the functional interaction of tool and blank materials—by simulation of the contact between microprojections of the harder material and a soft counterbody (the tool tip and the blank)—we may determine those characteristics over the temperature and stress range observed in machining [3]. This is the best experimental method of determining the contact characteristics of the tool and blank, since it provides reliable and convenient data for calculation of surface quality of the blank on the basis of the proposed mathematical models. τmax In the experiments, we study the turning of KhN60VT, KhN78T, and ZhS6UVI high-temperature alloys, 40 i and 30 iEe A steel, and VT9 titanium alloy by tools made of VK8, VK6M, VK60M, R18, R12F5M, R9K5, R12F2K8M3, and other alloys. The frictional characteristics for the contact of hightemperature KhN60VT nickel alloy and VK6M hard alloy are shown in Fig. 1, where f a is the adhesive component of the frictional coefficient; and τ 0 is the tangential stress in the absence of normal stress p r . As is evident from Fig. 1, the normal stress p r declines with increase in the temperature θ , on account of softening of the blank. The increase in tangential stress τ n with increase in θ to values at which f a is a maximum is associated with the accumulation of excess energy in the course of plastic contact deformation, under the action of normal stress p r .

ГЕОДИНАМІКА

We investigate a role of the contact friction in thrusting within the framework of the critical taper theory and according to geological settings for orogenic belts including the Ukrainian Carpathians (in Early Cretaceous time). Finite element models are used to simulate tectonic compression of sedimentary rocks by submerged stage and take into account frictional slipping on the detachment horizon. We assume a simple wedge geometry (rectangular layer 60 km long, 1.5 km thick and 2.5 km deep), plane strain state, quasistatic process and use elastic constitutive relation. Mechanical loads include gravity, water pressure on top and lateral displacement (up to 0.5 km) from the left, whereas the right side is fixed. Numerical results show specific features of the inhomogeneous stress fields for small (0.01-0.5), middle (0.5-0.64), large (0.64—0.8) and overlarge (0.8-1.15) friction coefficients. The magnitude of the tangential contact stress controls the front between sliding and sticking zones. Stress trajectories enable to predict thrust structures using Mohr-Coulomb failure criterion.

Effects of insulated rail joint on the wheel/rail contact stresses under the condition of partial slip

The effect of insulated rail joint (IRJ) on the wheel–rail normal and tangential contact stress distribution is studied using the finite element method. In this investigation, contact elements are used to simulate the interaction between wheel and rail. Numerical simulations are used to explore the effects of contact distances and materials of IRJ on the contact stress and the maximum shear stress distributions. Numerical results show that the presence of IRJ might significantly affect the wheel–rail contact stress distributions. The results also indicate that Carter's theory is no longer effective in predicting the tangential stress distribution of the wheel–rail contact near an IRJ. The tangential stress causes the location of maximum shear stress shifted toward the rail surface as the wheel–rail contact point moves closer to the IRJ. The maximum shear stress value is more sensitive to a braked force than to a tractive force as the wheel–rail contact point is within the IRJ region.

Contact Area and Normal Stress Determination on Railway Wheel/Rail Contact

It is important to study the field of railway wheel /rail contact area from the point of view of stress distribution for further investigation of running behavior of a vehicle when running on a rail track. There is a contact of two spatial geometrically defined bodies, which have characteristic material properties, by a power effect of a vehicle through the wheel on the rail. The contact point is transformed into the contact area as a result of the pressure of the bodies against each other. It is possible to acquire the image of the contact area and the stress which appears at the contact as a result of the application of a known calculation method or to set up own calculation methods. The paper deals with theoretical grounds of two computational methods. They are the Hertz method and strip method (according to Johnson [5]). The results of the contact area and normal stress numerical computation made by authors of the paper are stated and compared with the above mentioned methods and the results of the contact area and normal stress numerical computation made by the authors of the paper are stated and compared with the methods in references [7].) The contribution of the paper is to present the authors' computational results and compare the results with published results of other authors [7]. The authors reached the results with the support of their own computational program. The results are the base for other tangential contact stress research computations and base for other vehicle dynamics simulation computation in the future.

Stress state of a composite shell with a sizable opening

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.

Determination of Interlaminar Stresses in Bending Problems for a Stack of Transversely Isotropic Plates

A mechanical and mathematical bending model for a stack of transversely isotropic plates is developed. The resolving equations for deflections and tangential displacements are supplemented with a system of differential equations for normal and tangential contact stresses. It is demonstrated that for stacks consisting of an arbitrary number of identical plates with no friction between them, the initial system of equations for contact stresses can be reduced to Helmholtz equations. This transition allows obtaining the complete eigenvalue spectrum for the Laplasian of the problem and, in special cases, eigenfunctions. They are Krylov functions when bending is cylindrical and Bessel functions when bending is axisymmetric

Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon: Part I—Contact Fatigue. Normal and Tangential Contact and Residual Stresses. Nonmetallic Inclusions and Lubricant Contamination. Crack Initiation and Crack Propagation. Surface and Subsurface Cracks

The purpose of this paper is to describe the modern understanding of the contact fatigue phenomenon which occurs in different materials under various loading conditions. Part I presents experimental and theoretical knowledge of the influence of normal and factional contact and residual stresses on contact fatigue. It analyzes relationships between contact fatigue and material defects, inclusions, and lubricant contamination. Furthermore, it discusses crack initiation and crack propagation, the effect of material microstructure on contact fatigue life as well as some theoretical results for surface and subsurface cracks. Part II is devoted to reviewing the existing mathematical models of fatigue life for bearings and gears and to describing a new statistical model of contact fatigue based on contact and fracture mechanics. This new model is based on the assumptions derived from the analysis of the data presented in Part I. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference In Orlando, Florida, October 11–13, 1999