Contact Slip Research Articles

A dislocation-based model for shear cracks in arbitrary orientations under contact loading

Mechanical transmission components are generally under the risk of contact fatigue, resulting in cracks initiated from the subsurface. When subject to compressive stress, these cracks might be forced to be closed, thus their faces are in partial slip contact. Under such conditions, the interactions of stick and slip zones cannot be directly determined, which is one of the greatest challenges of contact fatigue problems. In this study, the distributed dislocation technique is adopted to investigate the stick–slip friction along the alignment of shear cracks in arbitrary orientations in a half-plane under contact loading. The unknown dislocation density describing the crack face displacement is iteratively calculated based on the stress conditions and then introduced to update the surface gap between contacting bodies. The complex expressions of the influence coefficients used to determine the stress and displacement induced by the dislocations are derived and the FORTRAN codes are provided in the Supplementary Materials. A step-by-step loading method is proposed to progressively capture the slip history of crack faces. The model is also capable of simulating rolling contact problems. The results are comparable to those predicted using the finite element method with more robust convergence properties. The effects of friction coefficient, crack alignment, and locations of crack faces are discussed in detail. The model paves the foundation for further studies on competing mechanisms of crack propagation and crack face wear, and provides insights into the frictional fracture of materials under contact loading.

Analysis of Traction Coefficient Subject to Rail Cleaning Effect Based on Tribomachine Measurements

The proper representation of friction contact conditions between each wheel and the rail is necessary to accurately model the behaviour of a heavy haul locomotive since friction conditions at the wheel-rail interface affect the locomotive’s dynamic performance under traction and braking conditions. In normal operations, a phenomenon commonly known as rail cleaning effect occurs. The rail cleaning effect causes increased friction coefficients between the following wheel treads and the rail head. The wheel-rail interaction causes the third body layer to be partly or wholly eliminated from the surfaces in contact and generates new layer. An experimental analysis of the changes in friction coefficients under simulated locomotive wheel-rail contact conditions, in terms of contact pressure and slip, is presented in this paper. For this study, data processing equations are presented to obtain the experimental traction coefficient and slip. Furthermore, the rail cleaning effect is examined under different slip conditions. The experiment shows the traction coefficient increases for a given number of cycles until reaching a steady value, demonstrating that the rail cleaning effect is measurable in various slip conditions on a twin disc machine.

A novel dynamic dry friction model for applications in mechanical dynamical systems

This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.

Heterogeneity in tribologically transformed structure (TTS) of Ti–6Al–4V under fretting

Fretting wear is a surface degradation process caused by oscillatory motion and contact slipping. During gross slip, high local stresses and plastic deformation in the surface and subsurface can lead to the creation of a nanosized grained structure called Tribologically Transformed Structure (TTS). The current paper studies the formation of TTS in an alpha-beta Ti–6Al–4V alloy under fretting loading while changing the contact pressure and the number of fretting cycles.Cross-sections of wear scars are observed after polishing and chemical etching. Above a threshold pressure of 300 MPa, TTS appears early in the contact (before 1000 cycles) along with two other structures: a Third Body Layer (TBL) made of compacted debris and a General Deformed Layer (GDL) which is the plastic zone under the TTS. TTS first appears as islands and merges in the middle of the contact after enough cycles. Below 200 MPa, only TBL and GDL are formed. At 200 MPa, only small, localized TTS is found. All structures have the same chemical compositions as the initial bulk material except for the nitrided TBL. TTS has a very high hardness compared to the bulk. TTS was carefully extracted using a Focused Ion Beam (FIB) and its microstructure was observed with a Transmission Electron Microscope (TEM). It shows extreme grain refinement and is composed of two alternated zones. The first zone I is composed of α grains with a size of 20–50 nm with crystallographic texture. Zone II comprises nanosized equiaxed grains whose sizes range from 5 to 20 nm without texture. The results made it possible to establish a scenario of the appearance of the TTS according to the conditions of contact pressure and number of fretting cycles.

Dry rolling-sliding wear behavior of ER9 wheel and R260 rail couple under different operating conditions

This work aimed to evaluate the effects of contact stress and slip ratio on wear and rolling contact fatigue of ER9 wheel steel and R260 rail steel couple under unlubricated conditions using a dual disk test. It was demonstrated that as either contact stress or slip ratio increased, so did the wear rate and surface damage of both ER9 wheels and R260 rail rollers. The wear rate of the ER9 wheel steel containing proeutectoid ferrite and the smaller structure size of pearlite increased significantly when compared to the rail steel containing fully pearlite in each pair. After testing according to the conditions used in this work, the surface hardness of the pearlitic rail steel was higher than that of the ferrite-pearlite wheel steel. The average hardening ratio of ER9 wheel steel and R260 rail steel was 0.7 and 1.28, respectively. This was consistent with the subsurface deformation angle. With full pearlite in the microstructure of rail steel, the main wear mechanism was predominantly caused by fatigue cracking and peeling, with some adhesive wear. Whereas the most prominent mechanism of the ferrite-pearlite wheel steel was adhesive wear, which was followed by spalling and small fatigue cracks.

Practical wheel/rail tangential contact force model for vehicle dynamics analysis combining Levi-Chartet’s formula with adhesion coefficient-velocity relational expression

This paper describes a practical wheel/rail tangential contact force model for railway dynamics analysis under running in rainy conditions. In our previous studies, it was confirmed that experimental results of tangential contact force measurement are agree well with Kalker’s rolling contact theory under dry condition with low humidity around contact surfaces. Here, it can be considered that if the ambient humidity around the contact surface become high infinity, the contact surface is under wet lubrication conditions. On the basis of this assumption, in this study, a practical estimation model for characteristics of tangential contact force under running in rainy conditions is proposed by combining the relationship between the adhesive coefficient and velocity measured on running experiments using actual railway vehicles and Kalker’s linear rolling contact theory. Therefore, to verify the proposed model, the tangential contact force measurement experiment using a twin-disk rolling sliding machine was carried out. As a result, it is confirmed that estimated formulae based on the proposed model are well agreed with experimental results even under different velocity conditions, comparing the relationship between tangential contact force coefficient and slip ratio. From these verified results, the proposed model is considered to be a practical wheel/rail tangential contact force model for vehicle dynamics analysis under rain conditions, because the proposed model has the advantage of low calculation cost and can be easily applied to vehicle dynamics analysis based on multi-body dynamics theories.

Effect of normal load on the wear and rolling contact fatigue behaviour of AAR class B wheel against R350HT rail in a twin disc simulator

The normal load at the wheel-rail contact interface plays a significant role in wear and rolling contact fatigue (RCF) performance of both wheel and rail steels. In recent years, there has been an increase in axle loads due to increased demand for railway services. This study investigated the effect of normal load on the wear and RCF behaviour of the AAR class B wheel versus R350HT rail using a twin disc wear simulator. The mass loss, surface damage and depth of deformation were used to assess wear and RCF, respectively. From the mass loss results, wear maps were obtained to identify different wear regimes being mild, severe and catastrophic at different contact loads and slip ratios. Scanning electron microscopy was also used to assess the surface damage of wheel and rail steels in order to identify the wear regimes with surface cracking and delamination being observed at higher contact loads indicating severe and catastrophic wear. Furthermore, the RCF crack density was found to be higher on specimens evaluated at higher normal loads with more cracks evident and crack branching forming.

ANALYSIS OF THE INFLUENCE OF THE DISPLACEMENT OF THE GEAR RACK PROFILE OF THE PAIR EVOLUTION GEARING ON THE QUALITY INDICATORS OF THE TRANSMISSION

The article is devoted to the study of the influence of the modification of the paired evolute gearing with convex-concave contact on the quality indicators of transmission, namely, the contact pressure and the speed of slippage in the engagement. Previous studies of evolute gears showed the presence of characteristic zones on the side surface of the tooth, which have worse values of quality indicators than in similar involute gear. One of the ways to remove these zones or to reduce their impact on the load capacity of the transmission is to modify the tooth profile, which will be implemented by shifting the profile of the processing gear rack. A displacement factor is added to the equation of the rail profile curve, which has the same value for the gear and wheel teeth, but the opposite sign. On the basis of the developed equation, the side profiles of the teeth of the gear and the wheel were constructed. Several values of the rack displacement coefficient with a positive and negative sign for the gear teeth are considered. The results of the research allow us to evaluate the influence of the amount and direction of the rail displacement on the curvature of the tooth profiles, the contact pressure in engagement along the height of the tooth, and the relative and absolute speed of sliding. The modifications of the profile of the processing toothed rack proposed in this work will expand the existence of paired evolute gears with a different set of quality indicators. This will make it possible to design gears with rational values of contact pressures and slip speeds when they are used in heavily loaded transmissions created for specific operating conditions. Gears with relatively high slip speeds can be used in road and construction equipment transmissions, which are characterized by low shaft rotation frequency, in which the speed of slip between the teeth does not have a significant effect on the life or efficiency of the transmission. Otherwise, gears with relatively low slip speeds are very relevant when they are implemented in the transmission of modern and promising vehicles with a hybrid or fully electric power unit, especially in the case of passenger cars with high-speed electric motors.

Research on Partial Slip Contact Behaviors Under Temperature Effects

Research on Partial Slip Contact Behaviors Under Temperature Effects

INEW method for experimental-numerical locomotive studies focused on rail wear prediction

Locomotive-track interaction is commonly represented by a complex mechanical system which is modelled in numerical studies. Numerical studies alone are not enough to precisely describe the behaviour of this mechanical system due to the various elements that can only be delivered from field and laboratory experimental programs. One such element is wheel-rail wear that has been found to contribute a considerable portion of the total cost of maintaining heavily used railway systems. Simulation studies are typically used for predicting wear of wheels and rails, but the majority of these do not consider in-train forces nor provide detailed modelling of traction and braking events and often rely on historic wear rates for comparable materials, reducing the accuracy of the wheel-rail volume loss estimation. This paper proposes a methodology for wear rate experimental measurements that allow improving the accuracy of wear analyses using dynamic simulations. The proposed method considers in-train forces by performing longitudinal train simulations whose results are then implemented on a detailed locomotive vehicle dynamic model with a traction mechatronic system co-simulation approach. The wheel-rail contact stress and slip results are then post-processed into a Dynamic Load Spectrum that contains contact stress and wheel slip occurrences. The Dynamic Load Spectrum was used to measure the wear rates for Australian AS60 head hardened rail steel material operating in combination with Class B wheel steel material. The experimental program delivered more realistic wear rates that correspond to actual industry operational scenarios. The measured wear rates were used to estimate the rail material volume loss for a specific train trip.

Study on fretting fatigue crack initiation of scaled railway axles in consideration of fretting wear

The objective of this study is to investigate the fretting fatigue crack initiation of press-fitted railway axles. Fretting fatigue tests were conducted on scaled railway axles, and the fretting wear and crack at the fretted zone were analyzed. Based on the test results, FE models which take the fretting wear profiles into account were established. And then, three multi-axial fatigue criteria combined with the theory of critical distance were used to evaluate the fretting fatigue crack initiation. The analysis results show that the contact pressure and slip amplitude within the fretted zone are increased with the evolution of fretting wear, and thus produce a gradual increment of frictional shear stress at the inner side of the fretted zone. This finally leads to the fretting fatigue crack initiation of press-fitted axles. The fretting wear would play a more significant role in fretting fatigue initiation of press-fitted axles in the condition of lower applied stresses and higher loading cycles. As compared with the SWT criterion based on the maximum normal stress and elastic strain amplitude, the criteria considering the shear stress as the main controlling parameter (modified Dang Van criterion and McDiarmid criterion) can give a better-predicted result of the fretting fatigue crack initiation for press-fitted axles.

Analytical approach to estimating the influence of friction slip contact between surrounding rock and concrete lining on mechanical response of deep rheological soft rock tunnels

For a deep-buried tunnel in soft ground, the contact condition between the surrounding rock and lining significantly affects the mechanical response. This is because the slip bond relationship on the contact surface has a direct influence on the tangential slip, resulting in the redistribution of displacement and stress on the contact surface between the surrounding rock and lining. However, previous studies have not paid sufficient attention to this problem, and a well-established method for quantitatively evaluating this influence remains unavailable. Therefore, the influence of the contact behavior between the surrounding rock and lining was examined in this study using an analytical method. First, the concept of friction slip contact and corresponding theoretical equations are proposed based on the real contact behavior between the surrounding rock and lining. Second, considering the friction slip contact between the surrounding rock and lining, a mechanical model of the tunnel excavation-support process was established, and analytical solutions for the stress and displacement of the tunnel within a viscoelastic rock material were realized. Third, the effectiveness and reliability of the proposed solutions were validated. The results could be degenerated to those that do not consider the influence of the mechanical behavior of the contact surface. In addition, there was good agreement between the analytical results and further numerical calculation results. Finally, a comprehensive parametric investigation was conducted, including the influences of the initial release coefficient, friction coefficient, and installation time of the lining. Some useful recommendations for tunnel lining design are provided herein.

Experimental and analytical fretting characterisation of pressure armour nub-groove contact in flexible marine risers

This paper presents the development of a test rig for the characterisation of fretting in the nub-groove contacts of pressure armour layers in flexible marine risers and an analytical design tool called EASY-FRET (Engineering Analysis SYstem for FRETting) for fretting wear, fatigue and stress analysis of fretting contacts. The test rig characterisation includes both partial and gross slip fretting regimes under representative three-dimensional crossed-cylinder contact pressure and slip fretting loading conditions, identified from finite element global-local modelling of the complex geometrical-loading configuration. The analytical design tool simulates wear and associated fretting fatigue indicator parameters. The ability to predict the fretting wear and fretting fatigue in flexible marine risers will allow for less conservative design.

Experimental study on fretting damage in the interference fit area of high-speed train wheels and axles based on specimen

Taking the high-speed train axles as the object, this paper designs and produces fretting fatigue specimens that simulate the interference fit of the high-speed train axles and conducts the fretting damage test on the interference fit area of the axles under rotating bending loads. The interrupted fretting fatigue tests were conducted based on the fretting fatigue limit to study the distribution, the damage of the wear debris and the characteristics of crack initiation of the specimen shaft in the contact area of the interference fit. Research shows that the fatigue limit of high-speed train axle materials is significantly reduced due to fretting damage in the interference fit area. The closer to the outer edge of the contact slip zone, the more concentrated the wear debris, the more severe the fretting fatigue damage. When the amount of wear debris reaches its maximum, the load cycle occurs 1 million cycles. Fretting wear and fretting fatigue coexist in the interference fit specimen under rotating bending loads, accompanied by the formation of third-body oxides between the contact surfaces.

Surface Roughness Explains the Observed Water Contact Angle and Slip Length on 2D Hexagonal Boron Nitride.

Hexagonal boron nitride (hBN) is a two-dimensional (2D) material that is currently being explored in a number of applications, such as atomically thin coatings, water desalination, and biological sensors. In many of these applications, the hBN surface comes into intimate contact with water. In this work, we investigate the wetting and frictional behavior of realistic 2D hBN surfaces with atomic-scale defects and roughness. We combine density functional theory calculations of the charge distribution inside hBN with free energy calculations using molecular dynamics simulations of the hBN-water interface. We find that the presence of surface roughness, but not that of vacancy defects, leads to remarkable agreement with the experimentally observed water contact angle of 66° on freshly synthesized, uncontaminated hBN. Not only that, the inclusion of surface roughness predicts with exceptional accuracy the experimental water slip length of ∼1 nm on hBN. Our results underscore the importance of considering realistic models of 2D materials with surface roughness while modeling nanomaterial-water interfaces in molecular simulations.

FEM numerical simulation of contact stresses between driving shaft and hub impeller of fuel pump

The aim of the work was to test the contact stresses in the model system of the turbine hub cooperating with the fuel pump drive shaft. The hypothesis of the work was that, by means of FEA, it is possible to assess the contact stresses in the materials of the turbine hub and the fuel pump shaft during torque transmission. A turbine with fibre-reinforced polyphenylene sulphide (PPS) composite cooperating with a stainless steel shaft (X46Cr13/1.4034) in a commonly used D-flat shape joint was selected for the experimental research. To assess contact stresses, the CAD model (NX, Siemens) of the entire turbine was limited to the hub area. The drive shaft is supported in accordance with the bearing in the fuel pump, and the possibility of rotation about the axis along the length of the torque-producing magnet is taken away. The system was loaded with a torque of 200 Nmm on the turbine. The turbine hub and shaft were calculated, taking into account the phenomenon of contact detachment or slip at the value of the friction coefficient of 0.1. The pressure transmission area was found in the area at the edge of the flat surface D-flat and on the opposite side of the D-convexity. The contact stresses on the D-flat side reached values close to the composite strength. The studies did not take into account the technological inaccuracies, thermal deformation, local material properties, and wear. The value of the friction coefficient was not measured in realistic conditions with fuel lubrication. FEA has been achieved, which allows to reduce the cost of experimental research. The proposed model allows for further studies of the influence of elasticity of various materials and structures on contact stresses in order to assess wear resistance.

Design of thin curved sensor to measure contact slip in fretting experiments

This paper proposes a new thin curved sensor/strip to measure the relative slip between pad and specimen under fretting condition. Since the relative contact displacement is an important parameter to categorize the fretting process, the measurement of contact displacement between pad and specimen is necessary. Because of high yield strength and the ability to return to its initial position even with notable deflection, the spring steel have chosen to fabricate the thin curved strip. Before the fabrication, the detailed Finite Element Analysis (FEA) of the thin curved sensor was carried out. The strip consists of different shapes (rectangular, circular and elliptical) of slots and the number of slots in each strip is varied from 2 to 6. The Strain Energy Approach (SEA) has been used to calculate the displacement for the curved strip and it was compared, verified and validated with its FEA and Experimental results. From FEA study of thin curved strip with slots, four configurations were chosen to measure micro level displacement between pad and specimen under fretting experiments. The study reveals that the increasing number and size of holes presented in the curved strip indicate that the increased in displacement and von-Mises stress values which offers the higher flexibility to the strip. The reduction in area and minimum thickness of the curved strip could be the reason for the decrease in the stiffness of the curved strip. This study explores the use of new simple and novel instrument/sensor to capture the micro level relative displacement between the pad and specimen under fretting condition.

A Brake System Coefficient of Friction Estimation Using 3D Friction Maps

The coefficient of friction (COF) is one of the core factors in the evaluation of brake system performance. It is challenging to predict the COF, since it is strongly influenced by several parameters such as contact pressure (p), slip rate (v) and temperature (T) that depend on the driving conditions. There is a need for better models to describe how the brake friction varies under different driving conditions. The purpose of this research is to study the possibility of using 3D friction pvT-maps to estimate the COF of a disc brake system under different driving conditions. The 3D friction pvT-maps are created by filtering results of material tests conducted in a mini-dyno inertia bench. The COF measured under different driving cycles in an inertia dyno bench with the full brake system are compared with the COF estimated by the friction maps coming from the reduced scale dyno bench to investigate the validity of the simulation approach. This study shows that mini dyno bench is suitable to obtain a tribological characterization of the friction pad–disc rotor contact pair and is able to replace the full inertia dyno bench to investigate the brake system performance.

An innovative and efficient solution for axisymmetric contact problem between structure and half-space

In this paper, with displacement increment as variables, the scaled boundary finite element equations of the axisymmetric plate and half-space are respectively derived based on the principle of virtual work. The dual vector is introduced to solve the boundary stiffness matrix. Linear complementary contact conditions are formulated as B-differentiable equations. With discrete, static assumptions of small displacement, B-differentiable equations system was formed by combining the contact conditions and the stiffness matrix of the plate-foundation. The equations can be iteratively solved by B-differentiable Newton method. In numerical experiments, the contact stress, slip and contact status of each contact node pair are compared with the results of the augmented Lagrangian contact algorithm based on FEM. When adopting different load types, thickness-to-radius ratio, plate-foundation stiffness ratio and friction coefficient, the axisymmetric contact problems between plate and half-space are discretized by 120 one-dimensional first-order elements. The applicability, accuracy and effectiveness of B-SBFEM for axisymmetric contact problems are verified by numerical examples.

Adhesion behavior of different droplet on superhydrophobic surface of cotton fabric based on oxygen plasma etching

Oxygen plasma etching followed with spraying of hydrophobic suspension containing SiO2 nanoparticles were used to construct superhydrophobic cotton fabric, and the adhesion behavior of the superhydrophobic surface to deionized water, dye liquor, sterile defibrinated sheep blood, and simulated blood solutions was studied and evaluated in focus. Results of the present study showed the water contact and water slip angles of the superhydrophobic cotton fabric were 158.6° and 7.3° with 5 wt% of hexadecyltrimethoxysilane (HDTMS). The plasma etching imparted uniform strip grooves on the fiber, which together with the deposition of SiO2 nanoparticles constituted a dual-scale rough structure on the fabric surface. FTIR analysis showed the successful combination of HDTMS and SiO2 nanoparticles and covering on the cotton surface. This superhydrophobic surface possessed hydrophobic effect even after 35 times of abrasion and immersion in strong acid or alkali solutions for 8 h. The surface tension and viscosity of simulated blood and sterile defibrinated sheep blood (SDSB) were similar, with a contact angle of only 139.7° and a slip angle above 20°. And their adhesion forces were calculated by the Cassie-Baxter equation to be 30.93 and 37.88 μN. Moreover, the droplets placement of simulated blood and SDSB on the superhydrophobic surface for 2 h caused trace adhesion but no penetration. This indicated that the superhydrophobic surface had anti-adhesion performance to the liquids. In conclusion, it was evident that the superhydrophobic fabric has good application prospects in the field of textiles for daily life and medical protection.