Rolling Line Contact Research Articles

A finite-element-aided ultrasonic method for measuring central oil-film thickness in a roller-raceway tribo-pair

Roller bearings support heavy loads by riding on an ultra-thin oil film (between the roller and raceway), the thickness of which is critical as it reflects the lubrication performance. Ultrasonic interfacial reflection, which facilitates the non-destructive measurement of oil-film thickness, has been widely studied. However, insufficient spatial resolution around the rolling line contact zone remains a barrier despite the use of miniature piezoelectric transducers. In this study, a finite-element-aided method is utilized to simulate wave propagation through a three-layered structure of roller-oil-raceway under elastohydrodynamic lubrication (EHL) with nonlinear characteristics of the i) deformed curvature of the cylindrical roller and ii) nonuniform distribution of the fluid bulk modulus along the circumference of the oil layer being considered. A load and speed-dependent look-up table is then developed to establish an accurate relationship between the overall reflection coefficient (directly measured by an embedded ultrasonic transducer) and objective variable of the central oil-film thickness. The proposed finite-element-aided method is verified experimentally in a roller-raceway test rig with the ultrasonically measured oil-film thickness corresponding to the values calculated using the EHL theory.

Three-Dimensional Finite Element Elastic–Plastic Model for Subsurface Initiated Spalling in Rolling Contacts

In this investigation, a three-dimensional (3D) finite element (FE) model was developed to study subsurface initiated spalling observed in rolling line contact of tribo components such as bearings. An elastic–kinematic hardening–plastic material model is employed to capture the material behavior of bearing steel and is coupled with the continuum damage mechanics (CDM) approach to capture the material degradation due to fatigue. The fatigue damage model employs both stress and accumulated plastic strain based damage evolution laws for fatigue failure initiation and propagation. Failure is modeled by mesh partitioning along unstructured, nonplanar, intergranular paths of the microstructure topology represented by randomly generated Voronoi tessellations. The elastic–plastic model coupled with CDM was used to predict both ratcheting behavior and fatigue damage in heavily loaded contacts. Fatigue damage induced due to the accumulated plastic strains around broken intergranular joints drive the majority of the crack propagation stage, resulting in a lower percentage of life spent in propagation. The 3D FE model was used to determine fatigue life at different contact pressures ranging from 2 to 4.5 GPa for 33 different randomly generated microstructure topology models. The effect of change in contact pressure due to subsurface damage and plastic strain accumulation was also captured by explicitly modeling the rolling contact geometry and the results were compared to those generated assuming a Hertzian pressure profile. The spall shape, fatigue lives, and their dispersion characterized by Weibull slopes obtained from the model correlate well with the previously published experimental results.

Effect of Coulomb friction on the deformation of an elastica constrained in a straight channel with clearance

Abstract In this paper we consider the effect of friction force on the contact behavior of an elastica constrained inside a straight channel with clearance. The elastica is fed in the channel through a space-fixed input clamp and protrude out of an elastically suspended output clamp. The two pads of the output clamp are assumed to be pre-compressed. Coulomb friction is assumed to be present on the lateral walls of the channel and in the output clamp. Focus is placed on the relative motion between the input and output ends of the beam. The beam may buckle when the input end is pushed in the channel and the output end is stuck due to friction resistance. Four types of contact patterns between the elastica and the constraining channel walls may occur when the beam buckles; they are rolling point contact, combined rolling and sliding point contact, rolling line contact, and sliding line contact. When the friction resistance at the output end is overcome, the beam will protrude out of the channel. When friction is present between the elastica and the lateral walls, hysteresis occurs when the input end undergoes a load–unload cycle. A small-deformation theory is also developed for the case when the spacing between the constraining walls is small. As expected, the accuracy of the small-deformation theory deteriorates as the spacing of the constraining walls increases.

Effect of friction on the planar elastica constrained inside a circular channel with clearance

In this paper we consider the effect of friction force on the contact behavior of an elastica inside a circular channel with clearance. The elastica is partially clamped at both the input and output ends of the channel. Coulomb friction is assumed to be present at the output end and on the constraining walls. Focused is placed on the relative motion between the input end and the output end of the elastica. Shooting method is adopted to solve for the quasi-static behavior of the elastica movement. Four types of contact patterns between the elastica and the constraining channel walls may occur when the input end moves in and out of the channel; they are rolling point contact, combined rolling and sliding point contact, rolling line contact, and sliding line contact. When the input end undergoes a sinusoidal motion, the output end either ceases to move at all, or follows exactly the input end motion. These two phases of output end motion occur subsequently, one immediately after the other. In general, the output end lags behind the input end. Experimental observations on the lagging phenomenon at the output end confirm the theoretical prediction.

Transient elastohydrodynamic lubrication film thickness in sliding and rolling line contacts

The contact behavior between cam and follower is greatly influenced by the kinematics and dynamics of the whole valve train system. This is the reason that both shape and thickness of the fluid film in the contact gap are mainly determined by applied loads and relative contact speeds as well as the curvatures of contacting elements. Most of the studies about lubricant film behavior between cam and follower have been performed without a consideration of transient effects in the contact gap. For the computational difficulties of transient effects, most contact conditions such as relative contacting speeds have been regarded as quasi-steady state during the whole operating cycle.

An efficient numerical analysis of starved thermohydrodynamically lubricated rolling line contacts

Effect of starvation in thermohydrodynamically lubricated high rolling speed line contacts has been investigated numerically by using an efficient numerical method in which temperature variations across the lubricant film is approximated by the second-order of Legendre polynomial. Mechanism of starvation at the contact has been set by creating gradual reduction in the length of the computational domain from the inlet side. In the solution, the lubricant has been assumed to be a Newtonian fluid. Minimum film thickness and rolling traction coefficient under fully flooded and starved conditions have been computed in this work. The rolling traction coefficient, minimum film thickness, and maximum mid film temperature rise in the starved line contact are found to be lesser than the fully flooded contact condition.

A Boundary Element Procedure for the Solution of the Elastohydrodynamic Lubrication Problem of Rolling Line Contacts by a Newtonian Fluid

A Boundary Element Procedure for the Solution of the Elastohydrodynamic Lubrication Problem of Rolling Line Contacts by a Newtonian Fluid

Prevention of interfacial slippage in isothermal pure rolling line contact elastohydrodynamic lubrication under heavy loads

The contact-lubricant interfacial slippage, near and in the inlet zone, significantly reduces the load-carrying capacity of elastohydrodynamic lubrication (EHL) in isothermal pure rolling line contacts under heavy loads. The EHL load-carrying capacity can be significantly improved by the prevention of this interfacial slippage. Equations are derived for predicting the critical interfacial limiting shear stress, which is the least for preventing this interfacial slippage. These equations can be used for designing the EHL system of which the load-carrying capacity is not reduced by this slippage.

Surface fatigue of molybdenum and Al-bronze coatings in unlubricated rolling/sliding contact

Surface fatigue phenomenon of Mo and Al-bronze coatings was investigated by using two-disc machine under various loadings. Life to flaking and life to complete surface failure of two different types of coatings on low carbon steel substrates were determined in rolling line contact with hardened steel disc as the counter surface. The experimental findings revealed that Mo coatings had superior life to surface failure when compared to Al-bronze coatings under pure rolling and rolling/sliding contacts. The life to flaking decreased for Al-bronze particularly with an increase in the load. An increase in the slip ratio had a negative effect on the Al-bronze coatings giving rise to a very severe wear and sudden surface failures. Optical microscopy and scanning electron microscopy studies also indicated that Mo coatings were subjected to relatively mild wear as compared to those of Al-bronze coatings.

Wear of metal/PTFE coatings in rolling line contact

The paper presents results of an investigation to assess the performance of aluminium bronze coatings and molybdenum coatings both filled with PTFE and deposited on steel substrate in rolling line contact. The experimental results show that both types of coating studied have an outstanding wear and surface fatigue resistance. Under pure rolling conditions, the aluminium bronze coating was found to be more wear resistance than molybdenum coating. However, after 1.2 × 106 load cycles under the normal load of 36 N and 98 N, both coatings did not suffer any serious surface damage. Optical and scanning electron microscopy studies indicated that surface asperity peaks present in the coating supported the load. PTFE initially present in the coating was mainly lost due to a mild adhesive wear resulting in transfer film formation on the steel couter-surface. This, in turn, provided efective solid lubrication for the contact zone.

EHL Film Thickness Limitation Theory Under a Limiting Shear Stress

It is numerically shown that the elastohydrodynamic lubrication (EHL) film thickness has a limit under an assumed limiting shear stress of the contact-lubricant interface in isothermal pure rolling line contacts. The prediction of the central film thickness limit is made, and well matches experiments. The present theory shows that, in elastohydrodynamic line contacts, the central film thickness is of molecular scale and part of the contact area is in non-continuum film lubrication when the equivalent cylinder curvature radius is less than the critical one. This critical radius depends on the load and the contact-lubricant interfacial limiting shear stress at low pressures.

Study of surface roughness effects in elastohydrodynamic lubrication of rolling line contacts using a deterministic model

A sinusoidal surface roughness model is adopted for the analysis of the effects of roughness amplitude and wavelength on pressure profile, film shape, minimum film thickness and coefficient of friction in a steady state EHL line contact. The influence coefficients used for the evaluation of surface displacements are calculated by utilizing a numerical method based on Fast Fourier Transform. Significant reduction is observed in the minimum film thickness due to surface roughness. Such reduction is quantified by roughness correction factor, C R, and a relationship between C R and non-dimensional surface roughness amplitude A is derived as: C R=1−0.7823 A 0.8213. This equation may prove to be of interest from designer's viewpoint. The friction coefficient is found to increase appreciably with increasing amplitude and decreasing wavelength of surface roughness.

Surface fatigue of brittle polymers in rolling line contact

The two-disc machine was used to study surface fatigue in polymethylmethacrylate (PMMA) specimens in rolling line contact. A notch was introduced to the specimen to study the crack growth rate. The form of damage in PMMA disc ranges from the appearance of small cracks on the contact path, leading to the formation of pits and initiation, growth and failure of crazes. A degree of sliding was introduced into the contact between the two discs to study the effect of the tangential force on surface fatigue and crack propagation. The creation of crazes was observed in both rolling and rolling/sliding configurations, but the time of initiation, the appearance, their size and the time to failure were different. An optical microscope and SEM were used to study the morphology of the failure produced. The growth rate in the artificially induced crack was monitored and appeared to be stable with an initial burst of crack extension.

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

J-integral for subsurface crack in circular plate with inner hole under rolling and sliding contact

J-integral for a subsurface horizontal crack in a circular plate with an inner hole under rolling line contact is evaluated according to loading positions with various load conditions, crack length and crack location. Two-dimensional crack is modeled, and the relation between Tresca stress for uncracked model and J-integral is discussed. The loading location which gives the maximum J-integral depends on load condition and crack location, and the presence of friction force increases Tresca stress and J-integral near the surface. Regardless of friction force, crack location that gives maximum J-integral is the same as that of maximum Tresca stress in an uncracked model, and the value of J-integral is propotional to crack length. It is also showed that the variation of an inner radius of a disk does not effect J-integral value.

On Mechanisms of Fatigue Life Enhancement by Surface Dents in Heavily Loaded Rolling Line Contacts

This paper studies mechanisms of surface dents in enhancing the fatigue life of rolling bearings previously reported in Akamatsu et al. (1). First, transient micro-EHL analyses of heavily loaded contacts between rough surfaces with multiple dents are conducted under near rolling conditions. Contacts with various dent dimensions, dent arrangements under different loading and kinematic conditions are investigated. Results show that surface dents generate no favorable micro-EHL effects to enhance the contact fatigue life. Subsequent analyses, in conjunction with other published studies, suggest that the fatigue life enhancement likely comes from the reduced local traction at asperity contacts through the “oil pots” effects of the dents. The effects of the surface dents on contact fatigue life may depend on the lubrication regime in which the contact is operating being favorable in poor lubrication conditions but adverse in well-lubricated contacts. Since rolling bearings are usually designed to operate in a healthy regime of lubrication, fatigue life enhancement by artificially introducing dents on bearing surfaces may not extend to field applications. Presented at the 51st Annual Meeting in Cincinnati, Ohio May 19–23, 1996

Grease lubrication in isothermo‐elastohydrodynamic line contact

AbstractElastohydrodynamic analysis is conducted and a numerical solution is presented for the film thickness in grease lubrication in isothermal, fully‐flooded rolling line contact with or without slip. By making use of a perturbational method, a modified Reynolds equation is established, which can be used with various constitutive equations if the equivalent viscosity can be expressed as a function of the shear rate. Verification of this analysis is carried out by experimentally determining the minimum film thickness with an X‐ray transmission technique, with satisfactory agreement. The effect of temperature on the apparent viscosity of grease is also discussed.

Modeling of Dynamic Friction in Lubricated Line Contacts for Precise Motion Control

A simple dynamic friction model for an elastohydrodynamic lubrication sliding and rolling line contact has been developed. This model uses the technique introduced earlier by Harnoy and Friedland (1). The model includes low-velocity regions where friction is a combination of contact and elastohydrodynamic friction. The study shows that the lime-variable friction is not only a function of instantaneous sliding velocity, but is also a memory function of the velocity history. Simulation of the model for an oscillating velocity exhibits similar hysteresis effects in friction-velocity curves as observed earlier in several experimental studies. The model can be useful for friction compensation to enhance the precision of motion in control systems. Presented at the 50th Annual Meeting in Chicago, Illinois May 14–19, 1995

Kinematics and Lubrication of Camshaft Roller Follower Mechanisms

This study provides a theoretical treatment of the lubrication of a camshaft in rolling contact with an oscillating roller follower. The rocker arm motion was specified as a function of the camshaft angle of rotation. The method of kinematic coefficients was used to determine the camshaft profile and the radius of curvature of the camshaft at the contact interface. The vector loop approach was used to calculate the lubricant entraining velocity. A numerical model for the dynamic elastohydrodynamic lubrication of rolling line contact was developed. This model uses as input the kinematics of the camshaft and roller follower mechanism. The one-dimensional Reynolds and elasticity equations were simultaneously solved using the multigrid multilevel technique to obtain the pressure and film thickness distributions within the lubricant film as a function of time. The time-dependent pressure and film thickness distributions for different loadings and camshaft angular velocities are presented. Presented at the 49th...

Crack propagation in rolling line contacts: Salehizadeh, H. and Saka, N. J. Tribol. (Trans. ASME) (Oct. 1992) 114 (4) 690–697

Crack propagation in rolling line contacts: Salehizadeh, H. and Saka, N. J. Tribol. (Trans. ASME) (Oct. 1992) 114 (4) 690–697