Three-dimensional Contact Stress 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.

Predictions of three-dimensional contact stresses of a radial truck tire under different driving modes

In pavement design, vehicle load is typically simplified as vertical circular uniform loading. Due to the vehicle dynamic effect and deformation of a tire, non-uniform three-dimensional contact stresses are produced at the contact interface between the tire and pavement under different driving modes. For this paper, an 11R22.5 truck radial tire was selected. Considering the geometric nonlinearity and large deformation of the tire and nonlinear characteristics of tire-pavement contact, the Neo-Hookean and Rebar models are used to simulate the hyperelastic rubber material and rubber-cord composite material, respectively. The three-dimensional contact stress distribution under static, free rolling, acceleration, braking, and cornering modes was simulated and analyzed. The results show that inflation pressure, axle load, and friction coefficient of the tire significantly affect the three-dimensional contact stress distribution. Further, three-dimensional stresses are non-uniformly distributed, rather than in the traditional simplified circular uniform load. The three-dimensional stress distribution of tire-pavement in different driving modes is also significantly different. The vertical and lateral stresses in the state of cornering are the largest, the longitudinal stress in the state of braking is the largest as well. The research results provide reference for future pavement design and pavement damage analysis.

Three-dimensional contact stresses of a slick solid rubber tyre on a rigid surface

The main aim of this paper is to quantify the three-dimensional contact stresses imposed by a single slow-moving (or rolling) slick solid rubber tyre on a relatively rough contact surface, such as stiff asphalt concrete or airport concrete surfacing layers. The results indicated the tyre-contact patch of a slick solid rubber tyre to be of rectangular shape for a vertical tyre loading range between 20 kN and 100 kN. The rectangular tyre contact shape was confirmed with static paper prints, as well as an electronically measured contact patch with the stress-in-motion pad device. The study included load calibration using a mass load scale, and a stress-in-motion device. These were used with an existing full-scale accelerated pavement test device, referred to as the heavy vehicle simulator. In addition, simplistic multi-layer linear elastic modelling was used to quantify differences between stress and strain responses of two types of two relatively 'stiff' based pavements, such as an asphalt concrete base and Portland cement concrete base, on similar subbase and subgrade layers. Notable differences were obtained, which could potentially influence further detailed studies on the performance of full-scale slick solid rubber tyres on typical multi-layered pavements.

Thermomechanical Coupling of a Hyper-viscoelastic Truck Tire and a Pavement Layer and its Impact on Three-dimensional Contact Stresses

A thermomechanical coupling between a hyper-viscoelastic tire and a representative pavement layer was conducted to assess the effect of various temperature profiles on the mechanical behavior of a rolling truck tire. The two deformable bodies, namely the tire and pavement layer, were subjected to steady-state-uniform and non-uniform temperature profiles to identify the significance of considering temperature as a variable in contact-stress prediction. A myriad of ambient, internal air, and pavement-surface conditions were simulated, along with combinations of applied tire load, tire-inflation pressure, and traveling speed. Analogous to winter, the low temperature profiles induced a smaller tire-pavement contact area that resulted in stress localization. On the other hand, under high temperature conditions during the summer, higher tire deformation resulted in lower contact-stress magnitudes owing to an increase in the tire-pavement contact area. In both conditions, vertical and longitudinal contact stresses are impacted, while transverse contact stresses are relatively less affected. This behavior, however, may change under a non-free-rolling condition, such as braking, accelerating, and cornering. By incorporating temperature into the tire-pavement interaction model, changes in the magnitude and distribution of the three-dimensional contact stresses were manifested. This would have a direct implication on the rolling resistance and near-surface behavior of flexible pavements.

Tire–pavement interaction modelling: hyperelastic tire and elastic pavement

The interaction between deformable tire and pavement was studied using the validated finite element model; the full understanding of tire–pavement contact has implications for pavement damage prediction and pavement life-cycle assessment (fuel consumption estimation). The tire’s rubber and reinforcement were considered hyperelastic and linear elastic, respectively, with material constants obtained from the tire manufacturer (rubber) and laboratory testing (reinforcement). On the other hand, the pavement was assumed linear elastic supported by linear elastic springs. This assumption was made as a first step to examine the impact of using a deformable-on-deformable tire–pavement system to predict energy in the tire and contact stresses. The effect of the pavement stiffness on contact area, tire deflection, three-dimensional contact stresses, surface deflection, internal energy of the tire and its components, the work performed by the contact forces, and dissipation caused by friction was also studied. The elastic modulus of the pavement affected the contact area, while the elastic constants of the springs were more relevant for tire deflection. In addition, stiffness of the pavement had a varying effect on each component of the three-dimensional contact stresses: vertical contact stresses remained almost constant and longitudinal ones were the most affected. The symmetry of the surface deflection decreased and the friction dissipation increased 10.2% as the elastic modulus changed from the smallest to the highest value. Finally, the work performed by the vertical contact forces was significantly higher than by the in-plane loads, and the stiffness of the pavement affected rolling resistance force, which is related to fuel consumption.

Contact Phenomenon of Free-Rolling Wide-Base Tires: Effect of Speed and Temperature

AbstractThe finite-element method was used to quantify the effect of temperature and speed on contact area, deflection, and three-dimensional contact stresses of a free-rolling wide-base tire. The tire model comprised material properties identified in the laboratory and/or provided by the tire manufacturer (hyperviscoelastic rubber and linear elastic reinforcement) and accurate geometry. The model was validated using measured deflection and contact area. The analysis matrix consisted of 81 cases resulting from a combination of three loads, tire-inflation pressures, speeds, and temperatures. Four criteria were used to compare contact stresses: range, average, root-mean-square error, and coefficient of determination. Speed and temperature influence the contact area more than deflection. Longitudinal contact stresses were the most affected, followed by transverse contact stresses. In general, under constant load and tire-inflation pressure, the influence of temperature was more significant on the considered ...

Introducing realistic tire–pavement contact stresses into Pavement Analysis using Nonlinear Damage Approach (PANDA)

Realistic tire–pavement interface contact areas and stresses were incorporated into the Pavement Analysis using Nonlinear Damage Approach (PANDA) user interface (PUI). PANDA is a software library developed to simulate the complex thermo-viscoelastic–viscoplastic–viscodamage responses of the pavement to mechanical and environmental loads. The PUI is an interface generating a finite element representation of the pavement within PANDA. The application of realistic tire loading is necessary to calculate accurate pavement responses. The PUI incorporates a database of tire contact areas and stresses obtained from tire finite element simulations. The database includes tire interface characteristics with pavements for various applied loads, tire inflation pressures, vehicle speeds and scenarios of different rolling simulations. A parametric study was conducted to investigate the effect of simulations of tire contact stresses that match field measurements on viscoelastic and viscoplastic pavement responses. Pavement responses are greatly affected using realistic tire loading contact stresses and contact geometry as compared to simplified contact models. The impact on rutting and damage predictions cannot be ignored if reliable projections of pavement performance are to be made. This study confirms the importance of considering realistic three-dimensional contact stresses to design and analyse pavements.

Airfield Pavement Response Caused by Heavy Aircraft Takeoff

The effect of wheel configuration on critical airfield pavement responses during takeoff was calculated, and variables, usually omitted in conventional pavement analysis, were considered. The numerical analysis matrix consisted of two takeoff speeds, two inflation pressures, two pavement structures, and four wheel configurations. One of the pavement structures was built at the National Airport Pavement Test Facility and had been previously described in the literature. The method used in this study advanced current knowledge in two respects. First, the study examined not only the tensile strains at the bottom of the asphalt concrete (AC) layer (fatigue cracking) and vertical strain on top of the subgrade (rutting) but also the transverse surface strain (surface cracking) and vertical shear strains (near-surface cracking and rutting). Second, several assumptions about existing methods were advanced. These assumptions included (a) nonuniform three-dimensional contact stresses instead of uniform one-dimensional vertical stresses over a circular contact area, (b) viscoelastic and nonlinear material characterization for AC and granular material under high stress levels in lieu of a linear elastic model, and (c) load variation with time to reflect takeoff. Transverse surface strain and vertical shear strain in the subgrade were most affected by wheel configuration. In addition, the variables had varying influence on pavement responses and wheel interaction. For instance, takeoff speed affected vertical strain on top of the subgrade but did not affect transverse surface strain. Tire inflation pressure modified wheel interaction for shear strain in the AC but not in the subgrade.

Effects of Nonuniform and Three-Dimensional Contact Stresses on Near-Surface Cracking

Near-surface cracking, sometimes referred to as top-down cracking, is one of the predominant distress types in flexible pavements. The incidence of near-surface cracking has increased in recent years with the increased construction of relatively thick (hot-mix asphalt layer > 200 mm) flexible pavements. However, understanding the mechanisms of near-surface cracking and its integration into pavement design protocols remains a challenge. Analysis of this problem can be complex because of multiaxial stress states in the vicinity of tires. The near-surface response to nonuniform tire contact stresses is investigated, and the potential for crack occurrence near the surface is analyzed in a typical relatively thick flexible pavement. The generalized finite element method (GFEM) is used to analyze pavement structure. This method provides a computational framework for the arbitrary orientation of cracks in a finite element mesh that is particularly useful for mixed-mode fracture problems. A three-dimensional (3-D) model for a typical pavement structure with a thick bituminous layer is created, and 3-D and nonuniform tire–pavement contact stresses are applied to the pavement surface. Aggregate-scale cracks are inserted at various locations and orientations in the pavement. Results of this numerical study indicate that complex stress states in the presence of strong mode mixity may cause shear or tensile fracture in flexible pavements. The importance of novel computational methods such as the GFEM to the discovery and understanding of mechanisms governing the premature failure of pavements is highlighted.

Prediction of Three-Dimensional Contact Stress and Ligament Tension in the Ankle During Stance Determined from Computational Modeling

Our goal was to quantify and visualize the three-dimensional loading relationship between the ligaments and articular surfaces of the ankle to identify and determine the stabilizing roles of these anatomical structures during the stance phase of gait. We applied discrete element analysis to computationally model the three-dimensional contact characteristics and ligament loading of the ankle joint. Physiologic loads approximating those at five positions in the stance phase of a normal walk cycle were applied. We analyzed joint contact pressures and periankle ligament tension concurrently. Most ankle joint loading during the stance phase occurred across the articular surfaces of the joint, and the amount of ligament tension was small. The tibiotalar articulation showed full congruency throughout most of the stance phase, with peak pressure developing anteriorly toward the toe-off frame. Of the periankle ligaments, the deep deltoid ligament transferred the most force during the stance phase (57.2%); the superficial deltoid ligament transferred the second-most force (26.1%). The anterior talofibular ligament transferred force between the talus and fibula continuously, whereas the calcaneofibular ligament did not carry force during gait. The distal tibiofibular ligaments and the interosseous membrane were loaded throughout the stance phase. Force transmission through the ankle joint during the stance phase is predominantly through the articular surfaces, and the periankle ligaments do not play a major stabilizing role in constraining ankle motion. The medial ligaments have a more important role than do the lateral ligaments in stabilizing the ankle joint. In addition to ligament insufficiency, other factors, such as varus tilt of the tibial plafond, may be important in the development of recurrent instability. Continuous loading of syndesmosis ligaments provides a theoretical basis for evidence of syndesmosis screw breakage or loosening. The analysis method has potential applications for clarifying ankle joint function and providing a basis for comparison between normal and abnormal joint conditions.

Prediction of Three-Dimensional Contact Stress and Ligament Tension in the Ankle During Stance Determined from Computational Modeling

Prediction of Three-Dimensional Contact Stress and Ligament Tension in the Ankle During Stance Determined from Computational Modeling

Modelling wear and crack initiation in rails

Wear and crack initiation of steel rails is a problem of great significance to the railway industry. A high wear rate shortens the life of rails and the frequent rail replacement is expensive in terms not only of resources but also of track access time and delays affecting timetables. In addition, railhead profiles change gradually as the rails are worn and the greater the wear rate, the more often the rails need to be reground to maintain good train running performance. In contrast, a low wear rate means that cracks have time to develop in the plastically deformed rail steel and these may propagate deeper into the rails with potentially disastrous consequences. Finding the optimum combination of wear and grinding to maintain railhead profile and prevent cracks from growing is key to running a safe and cost-efficient railway. The large number of variables arising from track geometry, train dynamics, and wheel and rail profiles leads to wide variation in contact patch size and location. The two-dimensional model of ratcheting wear developed by Kapoor et al. has been developed to model the damage accumulation near the surface of the rail on the basis of a full three-dimensional contact stress distribution. Different rail steel microstructures can also be modelled and the effects of microstructure on wear and crack initiation are explored.

Report on the Prediction of Surface-Initiated Longitudinal Wheel Path Cracking in Asphalt Pavements

ABSTRACT Almost all mechanistic flexible pavement design procedures implicitly assume that fatigue cracks originate at the bottom of the bound layers and propagate upwards towards the surface of the pavement. However, observations from cracked roads in many countries have shown that the cracking originated from the surface of the pavement rather than at the base, particularly for thick flexible constructions. Many researchers have been trying to confirm that surface-induced cracking can be explained by the presence of tensile and/or shear stresses (strains) at (or near to) the pavement surface. A standard analysis of a pavement structure loaded by a uniform vertical contact stress shows that small horizontal stresses and strains can be generated due to negative curvature effects although it should be noted that the maximum (principal) strain at the pavement surface (at approximately 45o to the surface) can be of a similar magnitude to the horizontal tensile strain at the base of the asphalt layers. In addition, the inclusion of the complex three-dimensional contact stress distribution generated between the tyre and the pavement surface has been shown to produce high local values of horizontal tensile stress and strain at the pavement surface which could drive surface-induced cracking. However, other factors such as ageing of the surface material and temperature-induced stiffness gradients are also likely to be important.

Bearing failure analysis of mechanically fastened joints in composite laminates

An experimental investigation was performed to study the effects of stacking sequence and clamping force on delamination bearing strengths of mechanically fastened joints in carbon/epoxy composite laminates using acoustic emission (AE) technique. The experimental work of the study was presented in [H.J. Park, Effects of stacking sequence and clamping force on the bearing strengths of mechanically fastened joints in composite laminates, Compos. Struct., submitted], and this paper summarizes the analytical work. The major focus of the analytical work was to develop an effective methodology for assessing the delamination bearing strength of joints in finite composite laminates in conjunction with an accurate three-dimensional contact stress analysis via an efficient quasi-three-dimensional finite element procedure based on layerwise theory. The contact phenomena and stress distribution in the vicinity of joints in composite laminates are investigated in detail. The delamination bearing failure strengths of mechanically fastened joints in composite laminates are predicted using modified Ye-delamination failure criterion based on layerwise finite element contact stress analysis. The effects of stacking sequence and clamping pressure are considered. The accuracy and applicability of the proposed methodology are confirmed by comparisons to the referenced experimental data and previous investigations.

Effects of Friction on Three-Dimensional Contact Stresses in Pin-Loaded Laminated Composites

An investigation is performed to study the effects of friction on the three-dimensional (3D) stress state around pin-loaded holes in laminated composites. The composite pinned joints are modeled as a linear elastic contact problem with friction; therefore, the interactions between the pin with the laminate follow the law of Coulomb friction. An analytical solution for the 3D stress state involved in this problem is developed based upon the variational principle of complementary energy. Compared to the previous research based on a two-dimensional stress assumption, the present solution is innovative, since the out-of-plane effects (i.e., edge effects) near the pin-loaded holes are considered. The present formulations are restricted to the laminated composites with bi-directional fiber orientations, because all the traction and displacement boundary conditions can be satisfied in such type of laminates. Numerical results for pin-loaded cross-ply laminates with different coefficients of friction are presented. It is shown that the effects of friction on the magnitude and distribution of the 3D stress state around pin-loaded holes in laminated composites are significant.

Development of contact stress analysis programs using the hybrid method of FEM and BEM

This paper deals with the development of two- and three-dimensional contact stress analysis programs using a method combining the finite element method and the boundary element method. Designed to improve the accuracy of analysis using the hybrid method, a new method for computing the equivalent stiffness matrix is described. Furthermore, the penalty function is applied to introduce the contact conditions. A three-node contact element was used for two-dimensional analysis and five-node contact element, for three-dimensional analysis. Considering the application to general slide movements, a new eight-node contact element has been developed. The programs are applied to the problem of contact between a magnetic disc and a slider. A thin-film of the disc and a slider are modeled using finite elements. The substrate of the disc is modeled using boundary elements. Results confirm the validity and the accuracy of this procedure.

Development of contact stress analysis programs using the hybrid method of FEM and BEM

This paper deals with the development of two- and three-dimensional contact stress analysis programs using a method combining the finite element method and the boundary element method. Designed to improve the accuracy of analysis using the hybrid method, a new method for computing the equivalent stiffness matrix is described. Furthermore, the penalty function is applied to introduce the contact conditions. A three-node contact element was used for two-dimensional analysis and a five-node contact element, for three-dimensional analysis. Considering the application to general slide movements, a new eight-node contact element has been developed. The programs are applied to the problem of contact between a magnetic disk and a slider. A thin-film of the disk and a slider are modeled using finite elements. The substrate of the disk is modeled using boundary elements. Results confirm the validity and the accuracy of this procedure.

Chronic stress tolerance levels for human articular cartilage: Two nonuniform contact models applied to long-term follow-up of CDH

Two computer models of nonuniform contact stress on the articular surface of the human hip were used to study the relationship between chronically excessive articular cartilage contact stress and long-term clinical outcome in a series of patients with congenital dislocation of the hip (CDH). The analyzed database consisted of 409 stylus digitized radiographs from 83 patients with unilateral CDH, who had been treated by closed reduction, and whose average follow-up time was 29.2 y. The first model (nonuniform Legal) involved a three-dimensional contact stress distribution function whose pole was coincident with the resultant force acting through the hip, and which acted over a contact area whose borders were determined soley by bony landmarks. In the second model (Brinckmann), the direction of the pole of the contact stress distribution function was initially unknown; one border of the contact region was determined by radiographic landmarks, while the other border depended upon the pole of the iteratively determined contact stress distribution function. In both models, the contact stress distributions were converted to area engagement histograms, corresponding to the fractional areas of cartilage experiencing specific ranges of stress (0.5 MPa increments). These histograms were integrated over time to calculate a cumulative contact stress overdose, which was then compared to clinical outcome. Reasonable correlations (Spearman p = 0.63−0.66) with patient outcomes were obtained for optimally chosen damage thresholds, although these thresholds were appreciably different (2.0 versus 4.5 MPa) due to the respective modelling assumptions.

Three-dimensional contact stress analysis of a composite laminate with bolted joint

Based on an incremental restricted variational principle formulated and the transformation matrix derived from three-dimensional contact kinematic conditions, a general but effective finite element technique satisfying various contact conditions is established for the three-dimensional contact stress analysis of a composite laminate with bolted joint. The double-lap bolted joint in the thin graphite/epoxy laminate of [ 45 0 /– 45 90 ] s lay-up or in the thick glass-reinforced polyester laminate of various stacking sequences subjected to a bolt load and/or a clamping torque is considered in the analysis. The effects of friction, clearance, bolt elasticity, stacking sequence and clamp-up on the contact tractions around the bolted joint are studied systematically. The distribution of contact tractions through the thickness of the bolt-laminate interface is also shown. The delamination onset of the composite laminate can thus be evaluated accordingly. Several examples are carried out to demonstrate the applicability of the technique developed. Good agreement between the present computed results and the referenced experimental results is noted. The present work would be of help for the design of a composite laminate with bolted joint.