Face Friction Research Articles

NUMERICAL MODELLING OF A 3D RAIL RCF ‘SQUAT’‐TYPE CRACK UNDER OPERATING LOAD

The analysis is based on the 3D FE model of the rail Rolling‐Contact‐Fatigue (RCF) ‘squat’‐type crack, which tends to be common in tracks with high‐speed passengers and mixed traffic. The model incorporates the section of rail and a wheel of real geometry, in which the wheel is rolling over the running band of rail containing the ‘squat’‐type crack. The state of stress in the vicinity of the crack front is determined, and consequently the values and ranges of the stress intensity factors (SIFs) KI , KII andKIII at the crack front are calculated for the cycle of rolling. To simulate loading conditions occurring in practice, residual, bending and thermal stresses acting in the presence of the tractive force were taken into account. The results indicate a significant role of face friction and tractive force in the loading mechanism at the ‘squat’. The longitudinal and lateral residual stresses may also influence the loading cycles, especially for the cases with reduced friction between the crack faces. Reduction of the face friction coefficient to values close to zero creates conditions for crack propagation driven by the shear mode mechanism. These results were obtained under a project sponsored by the ERRI D173 Committee, Utrecht, The Netherlands.

Characterising frictional behaviour in sheet metal forming

Abstract A two-level multi-variable design of experiment (DoE) approach was used to investigate the influence and interaction of lubricant type, die surface finish, contact pressure, sheet metal coating and draw speed on friction. For this DoE, the flat face friction test (FFF) and the draw bead simulator (DBS) were used to measure the coefficient of friction. The experiments were run in random order with at least three replicates. The Yates algorithm was employed to determine the significance of the main effects and their interactions. It was found that the Zincanneal coating lowers friction and reduces variation within a specific test condition. The DBS results illustrated an insensitivity of the variables investigated to the friction coefficient. However, the rough DBS die was sensitive to blank coating. The polished surface of the FFF test illustrated a similar insensitivity.

Crack Face Friction Effects on Mode II Stress Intensities for a Surface-Cracked Coating in Two-Dimensional Rolling Contact

This work focuses on the effects of crack free friction on Mode II stress intensity factors, KII, for a vertical surface crack in a two-dimensional finite element model of TiN/steel subject to rolling line contact. Second-order extrapolation of KI and KII from nodal stresses ahead of the crack tip is found to be a more consistent technique than linear extrapolation. Results indicate that maximum KJJ values, which occur when the load is adjacent to the crack, may be significantly reduced in the presence of crack face friction. The reduction is more significant for thick coatings than for thin. Crack extension and increased layer thickness result in increased KII values. The effect of crack face friction on compressive KI values appears negligible. Comparative results are presented for MoS2/steel and diamond-like carbon/Ti systems. Presented at the 51st Annual Meeting in Cincinnati, Ohio May 19–23, 1996

Analysis of double edge-cracked iosipescu specimens under biaxial loads

This paper addresses the possibility of using the biaxial losipescu test fixture, employing double edge-cracked specimens, for characterizing the intralaminar mixed-mode fracture properties of unidirectional polymer matrix composite materials. The finite element method has been used in conjunction with the modified crack closure integral method for computing the crack tip strain energy release rates under mixed-modes I and II. For cracked specimens loaded under shear and compression, the structurally non-linear contact problem has been combined with the linear fracture analysis in order to evaluate the effects of crack face friction, loading angle, and applied external load on the crack tip energy release rates.

An upper-bound cutting model for oblique cutting tools with a nose radius

The geometry of practical cutting tools is complex, and usually involves both non straight cutting edges and obliquity. It is of great practical importance to be able to predict cutting forces and chip flow directions for such tools. The authors demonstrate the use of a simplified geometry together with an upper bound model to predict the direction of chip flow. The model proposed includes a requirement for approximate force equilibrium as a method of estimating rake face contact area. A comparison of the results with those from earlier models and with experimental data is provided. Finally a proof of the Stabler chip flow hypothesis is given: it is shown that the hypothesis is only valid for the case of zero rake face friction.

Subsurface crack mechanisms under indentation loading

A linear elastic fracture mechanics analysis of plane-strain indentation of a homogeneous half-space with a subsurface horizontal crack was performed using the finite element method. Stress intensity factor results obtained for an infinite plate with a central crack subjected to far-field tension and a half-space with a frictionless subsurface horizontal crack under a moving surface point load are shown to be in good agreement with corresponding analytical results. Crack mechanism maps illustrating the occurrence of separation, forward and backward slip, stick, and separation at the crack interface are presented for different indentation load positions and crack face friction coefficients. Results for the stresses in the vicinity of the crack tips and the mode I and mode II stress intensity factors are given for different indentation positions, crack face friction coefficients, and both concentrated and distributed surface normal tractions. Although indentation produces a predominantly shear and compressive stress field, mode I loading conditions are shown to occur for certain indentation positions. However, the magnitude of the mode I stress intensity factor is significantly smaller than that of mode II, suggesting that in-plane shear mode crack growth is most likely to occur in the absence of microstructural defects. The significance of crack face friction and sharpness of the indenter on the subsurface shear mode crack propagation rate is interpreted in terms of the mode II stress intensity factor range and material behavior.

The effect of ambient temperature on the shoe-surface interface release coefficient.

Previous studies of the shoe-surface interface correlated foot fixation with cleat length, configuration, and material composition as well as turf type and surface conditions. Our study examined the effect of temperature on the rotational torsion resistance of artificial turf football shoes. Five football shoe models, a flat-soled basketball-style turf shoe, a natural grass soccer-style shoe, and three multistudded turf shoes, were studied on dry Astro Turf at five temperatures (range, 52 degrees F to 110 degrees F). An assay device, a prosthetic foot mounted on a loaded stainless steel shaft, was used to determine the force necessary to release a shoe from the turf's surface. We used a torque wrench to apply a rotational force so that each shoe was pivoted counterclockwise through an arc of 60 degrees. Our results indicated that release coefficients differ within and among the shoe models at various turf temperatures. We also found that an increase in turf temperature, in combination with cleat characteristics, affects shoe-surface interface friction and potentially places the athlete's knee and ankle at risk of injury. Based on an established risk criterion, which correlated shoe-surface interface combinations in the laboratory with documented clinical occurrences, only the flat-soled basketball-style turf shoe could be designated "safe" or "probably safe" at all five temperatures.

The effect of rolling direction reversal on fatigue crack morphology and propagation

The effect of repeated rolling direction reversal on crack morphology, propagation and RCF life of rail steel is investigated in this paper. It has been established that reversal is of beneficial effect on RCF life. This effect is a function of the reversal regime. An optimum reversal is achieved when the number of rolling cycles per reversal is between 25% and 37% of the uni-directional RCF life cycles of the material. Under such a reversal regime, the RCF life is almost doubled. Rolling direction reversal appears to affect RCF cracking propagation as well as morphology. A new mechanism, the ‘variable crack face friction mechanism’, is proposed to explain this effect.

Improved modelling of cutting force coefficients in peripheral milling

Titanium is one of the most widely used metals in the aircraft and turbine manufacturing industries. Accurate prediction of cutting forces is important in controlling the dimensional accuracy of thin walled aerospace components. In this paper, a general three-dimensional mechanistic model for peripheral milling processes is presented. The effects of chip thickness, rake angle and cutting geometry on chip flow, rake face friction and pressure, and cutting forces are analyzed. A set of closed form expressions with experimentally estimated cutting force factors are presented for the prediction of cutting forces. The model is verified experimentally in the peripheral milling of a titanium alloy. For a given set of cutting conditions and tool geometry, the model predicts the cutting forces accurately for the chip thickness and rake angle ranges tested.

The numerical solution of Cauchy singular integral equations with application to fracture

The present study investigates a numerical algorithm for solving systems of Cauchy singular integral equations of the second kind such as those which often occur in the analysis of interface crack problems. The algorithm takes advantage of many standard subroutines for performing numerical integrations and can be easily applied to equations which are defined over different intervals of the dependent variable. The solution technique is illustrated by analyzing two homogeneous center cracked panels: one loaded in tension and the other loaded in shear and bending. In the second example problem, the presence of crack face friction strongly couples the underlying singular integral equations. The numerical results are compared to closed form elasticity solutions and are shown to be extremely accurate. In addition, the study also illustrates the feasibility of using various assumed forms of the undetermined functions. By assuming these slightly altered forms, many rather complex problems are either solved directly or reduced in complexity.

Crack Propagation in Rolling Line Contacts

The stress intensity factors for short straight and branched subsurface cracks subjected to a Hertzian loading are calculated by the finite element method. The effect of crack face friction on stress intensity factors is considered for both straight and branched cracks. The calculations show that the straight crack is subjected to pure mode II loading, whereas the branched crack is subjected to both mode I and mode II, with ΔKI/ΔKII < 0.25. Although KI is small, it strongly influences KII by keeping the branched crack faces apart. Based on the ΔKII values and Paris’s crack growth model, the number of stress reversals required to grow a crack in a rolling component from an initial threshold length to the final spalling length was estimated. It was found that the crack propagation period is small compared with the expected bearing fatigue life. Therefore, crack propagation is not the rate controlling factor in the fatigue failure of bearings operating under normal loading levels.

Finite element analysis of interface cracking in sliding contacts

The sliding failures of the Au/Ni/Cu multilayer structure used in electrical contacts have been found to be related to interfacial delamination. In this paper a plane strain finite element model for the growth of an interface crack in an elastic-plastic two-layer half-space is presented for a sliding contact. The elastic theories of interface cracking are briefly reviewed and the limitations of elastic solutions to the present problem are discussed on the basis of the finite element calculations. The elastic-plastic analysis has shown that the size of the plastic zone around the crack tips is comparable to the crack length and the coating thickness. Plastic deformation at crack tips expands primarily in two directions as predicted by a slip line field for a closed interface crack. The crack tip sliding displacement (CTSD), a measure of the growth rate of a closed interface crack, is calculated. Both the surface sliding friction and the crack face friction are found to have significant effects on the plastic zone size and the CTSD. The surface sliding friction tends to increase the plastic zone size and enhance the relative displacement of the crack faces in the direction of the friction force. The crack face friction, by contrast, considerably reduces the plastic zone size and the CTSD. The implications of these findings are also discussed.

Laminar heat transfer in the oil groove of a wet clutch

Numerical results for the analysis of heat transfer to laminar flow in radial grooves of wet clutch friction faces are presented. It is shown that a thin oil film intervening between the friction face and the metal separator plate has an important effect on the overall heat transfer coefficient between the metal plate and the oil flowing in the groove. Experiments carried out under continuously slipping conditions on an actual clutch are described and the measured overall heat transfer coefficients are compared to the results of the numerical analysis. The agreement between the numerical and the experimental results is within an r.m.s. deviation of 10.7%. The experimental error is estimated tobe 10.1%. The good agreement allows the use of numerically calculated heat transfer coefficients for a complete thermal analysis of the wet clutch.

A finite element and fatigue threshold study of shelling in heavy haul rails

A finite element study has been made of subsurface rail-wheel contact stresses in a heavy haul railway rail, and the near-threshold fatigue behaviour investigated for both standard carbon and head-hardened rail steels under mode II and mode III shear-loading conditions. Small, semielliptical regions of shear mode growth were found in the mode III tests and are thought to be equivalent to shell cracks. Mode I branch cracks arising from these are similarly believed to correspond to the generation of a transverse defect. Gauge corner shear stresses from the finite element analysis are used together with threshold stress intensity factor ranges from the fatigue tests on standard carbon rail in a fracture mechanics model of the transition from a shell to a transverse defect. When the effects of crack face friction and residual stress in the rail head are incorporated into the model, excellent agreement is obtained between the predicted size of a shell and that found from fractographic examinations of failed rail samples.

Force distribution for a flat belt drive with a concentrated contact load

An equation based on the classical Euler formula is derived to investigate the normal and tangential belt force distribution of a flat belt drive when a concentrated contact load is applied on the pulley. This loading condition occurs in an abrasive belt grinding. The belt force equation presented in this paper has a constant coefficient of friction. Analytical results show good agreement with the experimental results and the authors' previous work, which is based on a surface model of the belt friction face with a varying coefficient of friction. The equation developed from the Euler formula is suggested for practical design due to its sufficient accuracy and simplicity.

Closure to “Discussions of ‘The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks’” (1989, ASME J. Tribol., 111, pp. 396–398)

Closure to “Discussions of ‘The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks’” (1989, ASME J. Tribol., 111, pp. 396–398)

Dynamic Performance of the Stepped Hydrostatic Circumferential Gas Seal

Theoretical analysis of dynamic tracking and leakage characteristics of a self-centering, hydrostatic, stepped gas seal is presented. The equations of motion are solved numerically, taking into account shaft speed and whirl, pressure ratio across the seal, fluid film properties and face friction effects. The analysis is limtied to low axial Reynolds numbers and negligible tangential hydrodynamic pressure buildup. Became the model neglects azimuthal pressure gradients, the analyzed seals must be either axially short or limited to small eccentricities. An analytical tracking criterion is established for high pressure ratios for preliminary design purposes. Presented at the 43rd Annual Meeting in Cleveland, Ohio May 9–12, 1988

The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks

A two-dimensional model of a surface initiated rolling contact fatigue crack has been developed. The model takes into account the effects of frictional locking between the faces of the crack, and the influence of fluid pressure acting on the crack faces. The model has been used to investigate three possible mechanisms for propagating the cracks: mode II crack growth due to the cyclic shear stresses caused by repeated rolling contact; crack growth due to fluid forced into the crack by the load; and crack growth due to fluid trapped inside the crack. The predictions of the theory are compared with the behaviour of contact fatigue cracks.

The influence of residual stresses on rolling contact mode II driving force in bearing raceways

This paper evaluates the effects of rolling-contact-generated residual stresses on the mode II cyclic stress intensity range ΔK II that drives subsurface crack growth in a rim subjected to repeated rolling contacts. It treats the circumferential residual stresses generated in high strength bearing steels in the early life (2 ⩽ N ⩽ 10 7 contacts) and the higher levels existing in the later life (10 8 ⩽ N ⩽ 10 10 contacts). ΔK II is evaluated for repeated, two-dimensional, frictionless rolling contact, for small, planar, subsurface cracks under linear elastic fracture mechanics conditions. The calculations are performed as a function of hertzian pressure, relative crack depth, crack inclination, and crack face friction for the two sets of residual stress fields. The results are compared with observations of crack growth and spalling. The work shows that the later life residual stresses substantially reduce the ΔK II values for rough cracks at all but the smallest inclinations, favoring the formation of shells.

A Preliminary Analysis of Subsurface Crack Branching Under a Surface Compressive Load

This paper presents the results of a preliminary analysis of the branching behavior of a horizontal subsurface crack subjected to a moving compressive surface load. The purpose of the analysis is to provide some fundamental understanding concerning the behavior of subsurface contact fatigue cracks, including the onset of pitting or delamination. The analysis is approximate inasmuch as the traction-free boundary condition at the surface is only partially satisfied, and the history dependent effects arising from crack face friction are not included. The results show that mode I branching crack growth is possible even though the stress field is largely compressive. Nevertheless, based on a simple competing failure mode model the results indicate that within the limits of the analysis, nonbranching mode II growth is likely to be the dominant mode of propagation.