Soft Elasto-Hydrodynamic Lubrication

ORIGINAL PAPERSoft Elasto-Hydrodynamic LubricationEfre´n Andablo-Reyes •Juan de Vicente •Roque Hidalgo-A´lvarez •Connor Myant •Thomas Reddyhoff •Hugh A.SpikesReceived:16February 2010/Accepted:11May 2010/Published online:29May 2010ÓSpringer Science+Business Media,LLC 2010Abstract This article examines the use of ferrofluids to control starvation in lubricated contacts.Starvation in a ball–plate contact is experimentally studied under sliding–rolling conditions using a Mini Traction Machine (MTM).Friction is measured and the experimental results are pre-sented in the form of Stribeck curves.The volume of lubricant is controlled in such a way that no free bulk oil is present in the vicinity of the contact.An abrupt change in the slope of the Stribeck curve in the Hydrodynamic Lubrication zone is interpreted as the onset of starvation.It is then shown that the use of ferrofluids in the presence of a magnetic field distribution can change the conditions at which this onset of starvation occurs.Different magnetic field distributions are tested for different values of load and ferrofluid viscosity.It is proposed that ferrofluid lubricants in conjunction with a suitably positioned magnetic field can be used to promote replenishment,and thus control and reduce lubricant starvation.Keywords Starvation in EHL ÁFerrofluid ÁEHL ÁMagnetic particles1IntroductionThe primary purpose of lubricating a rubbing contact is to reduce friction and wear of the surfaces.The lubrication parameters must be optimized to maintain the contact in its optimal performance conditions.It is important to prevent the contact from being starved of lubricant.Because of wetting issues with low modulus solids,starvation can occur quite easily in the soft elastohydrodynamic (EHL)regime [1–5].Optical techniques have been employed to study starvation and thus to predict whether a contact is operating in the fully flooded regime or in the starved regime.Apart from this,it is also important to develop methods to improve the natural replenishment mechanism when the amount of oil needed to lubricate the contact is restricted,and hence prevent or limit starvation.The best way to do this is to find a method that allows some control via an external parameter,independent of the other con-ventional lubrication parameters.In this article,the frictional properties of a soft ball–plate contact were measured under restricted lubricant supply conditions.The use of ferrofluids is proposed as a novel method to improve the replenishment of lubricant to the contact in the absence of free bulk lubricant.2BackgroundUnder fully flooded conditions,the hydrodynamic lubri-cation regime of a lubricated contact is described by the Reynolds equation.By solving this equation,the film thickness and the pressure in the contact can be found,and therefore the friction acting between the surfaces can be calculated.Based on Reynolds theory,de Vicente et al.[6]developed a model to describe the soft EHL regime in aE.Andablo-Reyes (&)ÁJ.de Vicente ÁR.Hidalgo-A´lvarez Department of Applied Physics,Faculty of Sciences,University of Granada,C/Fuentenueva s/n,18071Granada,Spain e-mail:andablo@correo.ugr.esC.Myant ÁT.Reddyhoff ÁH.A.SpikesTribology Section,Department of Mechanical Engineering,Imperial College London,Exhibition Road,London SW72BX,UKTribol Lett (2010)39:109–114DOI 10.1007/s11249-010-9623-3sliding–rolling ball–plate contact under fullyflooded con-ditions[7].Theoretical results were contrasted with experiments carried out in a Mini Traction Machine(PCS Instruments),with a contact consisting of a19-mm diam-eter stainless steel ball against an elastomer disc.Theory and experiment showed good agreement.For this particular case,the friction in the contact is expressed in terms of the properties,load W,fluid viscosity g and entrainment speed U=(u B?u D)/2,where u B and u D are the surface speed of the ball and disc,respectively.l¼1:46ðg UÞ0:65WÀ0:76 E RþSRR3:8ðg UÞ0:71WÀ0:76E Rþ0:96ðg UÞ0:36WÀ0:11E R!ð1ÞHere SRR denotes the slide-to-roll ratio defined as the ratio of the absolute value of sliding speed,|u B-u D|to the entrainment speed U.R0is the reduced radius in the entrainment direction and E0is the reduced elastic modulus,they are given by1/R0=1/R x1?1/R x2and 2/E0=[(1-m12)/E1?(1-m22)/E2],where R x1,R x2,m1,m2, E1and E2represent the radii,the Poisson’s ratios,and Young modulus of the contacting bodies,respectively.The first term in Eq.1is the Poiseuille contribution to the friction,while the second corresponds to the Couette friction.Studies by de Vicente et al.[6]were carried out under the assumption that the inlet gap was completely filled by lubricant far ahead of the beginning of the Hertz contact.When the amount of free bulk lubricant is restricted,this condition may not be satisfied and hence fullyflooded hydrodynamic lubrication will not necessarily be achieved.In that case,the contact would operate in a regime known as starved EHL,where the functional behavior of thefilm thickness on the lubrication parameters is different.In this regime,thefilm thickness decreases with respect to that expected in fullyflooded conditions.The degree of starvation depends on the operating conditions,such as applied load,entrainment speed and viscosity,as studied by Chiu[1].Cann et al.[4]studied the influence of the volume of lubricant supplied,viscosity,load,and entrainment speed on the oilfilm thickness in a ball–plate contact.They developed a semi-empirical model to describe thefilm thickness in the starved region.Their model relates the starved centralfilm thickness to the height of the oilfilm out of the contact.Jianhai et al.[3]established two criteria to divide fullyflooded lubricated and starved lubricated contact.These criteria involve the upstream position of the meniscus in terms of a meniscus threshold position. Despite the efforts to develop empirical and theoretical models to predict whether a rolling–sliding contact is operating under fullyflooded condition or in the starved lubrication regime,no mechanisms have been proposed to stop or reduce the degree of starvation apart from supply-ing oil directly to the contact.In this study,the use of ferrofluids as lubricants in the presence of a non-uniform magneticfield is proposed as a route for starvation reduction.Ferrofluids are kinetically stable,colloidal,dipolar sus-pensions of superparamagnetic monodomain ferro-or fer-rimagnetic particles dispersed in a liquid carrier.Their rheology is basically that of a Newtonianfluid with the peculiarity that a ferrohydrodynamic magnetic body force appears under the presence of an external magneticfield gradient[8].This property has been investigated to see whether it can be used to improve the performance of rolling and sliding lubricated contacts.Theoretical studies suggest that,under the proper conditions,magneticfluids improve the contact load capacity and help preventing leakage at high operating speed or under the action of gravity[9–11].A successful application of this kind of fluid is the so-called magnetic seal,where thefluid is used to separate two plates that are maintained at different operating pressures[8,12].In this,thefluid is externally manipulated by the application of a magneticfield distri-bution and confined in a desired position.The same mechanism can also be applied to feed lubricant back into the contact using external forces when no free bulk oil is available.Commonly,ferrofluids are opaque media.As a conse-quence,optical techniques cannot be used to determine the film thickness of lubricant in the contact.An indirect method to obtain information of the performance of this replenishment mechanism consists of measuring the fric-tion force in the contact under different running conditions. This way,the performance of the lubricating forces (magnetic and hydrodynamic)is evaluated under different operation conditions of magneticfield strength and distri-bution,fluid viscosity,entrainment speed,and applied load. 3Experimental MethodIn this study,friction measurements were made using a Mini Traction Machine(MTM),which was adapted to study lubrication using magneticfluids.In this apparatus,a ball is loaded and rotated against aflat surface of a rotating disc in the presence of a lubricant.The motion of both parts can be controlled independently to achieve any desired sliding–rolling speed combination and the ball shaft is inclined to minimize spin in the contact.Friction is mea-sured by a load cell attached to the ball motor and,in the MTM,is determined by taking a pair of measurements at the same slide–roll ratio but with the ball moving,respectively,faster and slower than the disc.These two values are then differenced to eliminate any zero load offset in the load cell.The contact studied was that of a PDMS elastomer ball (Sylgard TM 184,supplied by Dow Corning)against an aluminium disc.A mold having a spherical cavity of 19mm diameter was used to fabricate the elastic balls.The Sylgard components were mixed,degassed in a vacuum chamber,placed inside the mold and cured at a temperature of 60°C for a period of 1h in a vacuum oven.From this,bubble-free,elastomer spheres with a non-deformed radius of 19mm and Young modulus of 3MPa were prepared.The MTM aluminium disc had Young’s modulus 69GPa.The Poisson’s ratio of the elastomer and aluminium was taken as 0.3and 0.5,respectively,so the reduced elastic modulus was 8MPa.All the tests were carried out at room temperature at a slide–roll ratio SRR =0.50.Friction was measured over an entrainment speed range of U =0.005–1m/s,at applied loads of W =3,5,and 7N.A radially symmetric magnetic field distribution cen-tered at the point contact was achieved by placing circular permanent magnets under the aluminium disc.The strength and shape of the distribution was easily changed by varying the number of magnets in the arrangement as shown in Fig.1The diameter of the magnets was 6mm,which fully covers the larger Hertz contact radius,which has a value of 1.3mm at a load of 7N.The magnetic field distributions corresponding to the different magnet configurations are labeled as maximum,medium,and minimum.The magneticfield reached at the centre of the contact was 150,50,and 25mT,respectively.Ferrofluids used here were provided by FerroTec,Co.and all of them have the same M (H )superparamagnetic Langevin type dependence (saturation magnetization 24.3±0.7kA/m),but different Newtonian viscosities 46,200,and 560mPa s.The carrier fluids are synthetic ester and synthetic hydrocarbon,for the first and the last two ferrofluids,respectively.Also,density and surface tension is the same for all the fluids.Considering a particle size log-normal distribution and using the Langevin function,a value of 9nm was obtained for the average particle diameter,with a polydispersity around of 20%[13].Par-ticle volume fraction is around 5.5vol%for the three lubricants,assuming a saturation magnetization for bulk magnetite of 447kA/m.A rheological characterization of the ferrofluids was performed (results not shown for brevity).Neither shear-thinning nor viscoelasticity were observed in the range of shear rates of interest.For every test,one drop of 500l l of ferrofluid was deposited in the vicinity of the contact at rest conditions.As soon as the oil was placed around the contact it was trapped by the magnetic field.The amount of oil is then restricted to the oil trapped by the magnetic field.4Results and DiscussionIn both fully flooded and starved conditions,entrainment speed U ,fluid viscosity g ,and load capacity W control the contact friction.Therefore,each of these parameters will be studied,introducing at the same time the magnetic field as a controllable external parameter.4.1Entrainment Speed UThe scaling number U g determines the film thickness and thus the regime in which the contact operates.Initially the fluid viscosity was held constant and the effect of speed on lubrication studied.Figure 2shows the friction coefficient versus the entrainment speed U ,for a viscosity of 200mPa s,a load of 7N and the maximum magnetic field distribution.Mixed and hydrodynamic lubrication regions are shown in the range of entrainment speed swept in the figure.Despite the limitation in lubricant supply,this curve shows a similar behavior of a contact under fully flooded conditions for entrainment speeds up to approximately 0.6m/s.The log–log slope in the hydrodynamic regime is 0.4±0.07.This value is similar to the value of 0.33,calculated by considering a simple Couette flow,and assuming that the fully flooded film thickness is propor-tional to U 0.67[6].Moreover,this result is differentfromFig.1Schematic representation of the adapted Mini Traction Machine.The three magnet set-ups are representedthat obtained by solving Reynolds equation under the assumption of fullyflooded condition,having a more complex behavior described by Eq.1.When the speed becomes larger than0.6m/s,a change in the slope is seen; this is believed to be the critical point that divides full lubrication and starved lubrication and to result from the lack of lubricant to achieve the fullyfloodedfilm thickness.In the starved regime,the oilfilm thickness is found to be proportional to U-1[4].If the same assumption of a simple Couetteflow is taken,the resulting friction coeffi-cient is proportional to U2.However,the slope found for our measurements is larger,about5.9.In addition to the previous mechanisms proposed for rolling contacts,in rolling–sliding conditions both the disc and the ball are in motion.Due to the movement of the disc,centrifugal forces act on the lubricant,whose magnitude depends on the disc speed and the position of the contact respect to the spinning centre and also on thefluid density.This force is neglected by Reynolds theory,under the assumption of fullyflooded conditions.However,when the amounts of oil are restric-ted and entrainment speed is large enough they play an important role pulling the lubricant out from the Hertz contact to the rim of the plate,hindering the replenishment mechanism and increasing the starvation.4.2Ferrofluid Viscosity gThe viscosity is another important parameter governing the performance of the lubricant in the contact.Results for fluid viscosities of g=46,200and560mPa s are shown in Fig.3As expected from hydrodynamic lubrication theory, the higher the viscosity,the larger the friction coefficient. The critical point between fullyflooded and starved lubrication is reached at lower speeds for the higher viscosity,as shown by the division lines inserted in the figure.This is in agreement with observations obtained fromfilm thickness measurements by other authors,where it was found that thefluidfilm starvation increases with fluid viscosity[1,4].Figure4shows the friction coefficient plotted as function of U g.All the curves collapse to a single one in the fully lubricated regime.However,the same effect is not observed in the starved lubrication regime.At differentfluid viscosities,the critical point occurs at a different value of the parameter U g.4.3Load WFigure5shows the friction coefficient as function of the entrainment speed for a200mPa sfluid.Loads of3,5and 7N were tested at the maximum magneticfield distribu-tion.As described by Eq.1,the friction coefficient decreases with the applied load.For all the loads investi-gated,the transition point occurs at U=0.8m/s(dashed line),and the dependence of friction coefficient on entrainment speed becomes stronger.The values of the slopes after the transition do not differ significantly for different values of W.Hence,the applied load has no sig-nificant influence on the performance in this starved regime.4.4Magnetic Field StrengthOnce the role of the lubrication parameters(U,g,and W)in controlling the occurrence and development of starvation in the contact has been established,it is important to study the influence of the parameter proposed here to control starvation,the magneticfield.The lubricants were chosen so that,regardless thefluid viscosity,the magnetic response was approximately the same.This means that the magnetic lubrication forces are completely controlled by the strength and shape of the external magneticfield distribution,with no variation due to mechanical properties(e.g.density,surface tension).Magnetic body forces appear in the magneticfluid when a magneticfield distribution is applied and are given by l0M(H)H,where l0is the vacuum permeability,M(H)the functionalfluid magnetization and H the magneticfield strength.Thus,these forces depend on the magnetic response of thefluid and the shape and strength of the magneticfield distribution.Due to magnetic forces,the pressure on thefluid is increased,and the main effect of this is the confinement of thefluid around the region of maximumfield,i.e.,in this case around the centre of the contact.All the results shown in the previous subsections were carried out at the maximumfield distribution.The effect of decreasing the strength of the magneticfield is now explored.In Fig.6,Stribeck curves for afluid viscosity of 46mPa s are shown,every curve corresponding to a dif-ferent magnet set-up.As shown above,the load applied did not significantly affect the transition from fullyflooded to starved EHL.So,a value of7N wasfixed.As observed in Fig.6,there was not any significant difference between applying the minimum and medium magneticfield distri-bution.However,when the maximum magneticfield was applied,the contact remained working in the fully lubri-cated regime in the range of speeds studied in this work, i.e.,starvation was stopped.The same experimental tests are shown in Fig.7,now for a much more viscous ferro-fluid.In this case,the transition point between tribological regimes is clearly shifted to higher speeds for higher values of magneticfield strength.In highly viscous ferrofluids, starvation was not fully stopped even for the highest magneticfields employed in contrast to low viscosity fer-rofluids(cf.Fig.6).Summing up,higher viscosities and higher speeds require higher magneticfields to stop star-vation.It is demonstrated here that the external magnetic field can be used as a lubricant supply control parameter, which can be tuned independently without interfering with the rest of the lubrication parameters.5ConclusionsStarvation is a problem in many lubricated systems.It occurs at high speeds and with high viscosity lubricants and is thus a problem in rolling element bearings operating at low temperatures.It is especially prevalent with low elastic modulus,polymeric bearings where the contact is large and wetting of the surfaces often poor.It has been shown in this article that ferrofluid can be used as a smart lubricant to limit starvation in a sliding–rolling contact where the amount of lubricant is restricted.A non-uniform magneticfield distribution is centered on a sliding non-conforming contact lubricated with ferrofluid. This has the effect of confiningfluid within the region of the contact,thus greatly reducing the total amount of lubricant required.Experiments show that the transition between the fully and starved lubrication regimes can be controlled by modifying the magneticfield distribution.The transition between hydrodynamic and starved regimes depends on thefluid viscosity and not on the applied load,at least in the range covered in this study.The higher the viscosity,the lower the speed associated to the onset of starvation.Hence,it is shown that the higher the viscosity,the higher the magneticfield strength required preventing starvation.As well as helping to control starvation,it is likely that the ability to confine a ferrofluid lubricant close to the location where lubrication is required using a magnetic fluids might also be desirable in situations where viscous drag losses need to be minimized.For example,the application of magneticfields to transmissions could potentially offer increased efficiency by reducing the vol-ume of lubricant in which contacting surfaces are sub-merged.As shown in this work,if an appropriate magnetic field distribution is applied,very small lubricant volumes can be employed without the normally associated risk of starvation.Acknowledgements This work was supported by MICINN MAT 2009-14234-C03-03projects(Spain),by the European Regional Development Fund(ERDF)and by‘‘Junta de Andalucı´a’’P07-FQM-2496project(Spain).References1.Chiu,Y.P.:An analysis and prediction of lubricantfilm starvationin rolling contact systems.Tribol.Trans.17,22–35(1974)2.Guangteng,G.,Cann,P.M.,Spikes,H.A.:A study of parchedlubrication.Wear153,91–105(1992)3.Jianhai,L.,Shizhu,W.:Fullyflooded,starved and parchedlubrication at a point contact system.Wear159,135–140(1992) 4.Cann,P.M.E.,Damiens, B.,Lubrecht, A.A.:The transitionbetween fullyflooded and starved regimes in EHL.Tribol.Int.37,859–864(2004)5.Yin,C.,Yang,P.H.,Tan,H.,Wang,J.:Thermal elastohydrody-namic lubrication of starved elliptical contacts.J.Tribol.Int.42, 964–974(2009)6.de Vicente,J.,Stokes,J.R.,Spikes,H.A.:The frictional proper-ties of Newtonianfluids in rolling-sliding soft-EHL contact.Tribol.Lett.20,273–286(2005)7.de Vicente,J.,Stokes,J.R.,Spikes,H.A.:Rolling and slidingfriction in compliant,lubricated contact.Proc.IMechE J.220, 55–63(2006)8.Rosenweig,R.E.:Ferrohydrodynamics.Dover,New York(1997)9.Chandra,P.,Sinha,P.:Ferrofluid lubrication of externally pres-surized circular plates and conical bearings.Int.J.Eng.Sci.31, 593–604(1993)10.Shah,R.C.,Bhat,M.V.:Ferrofluid squeezefilm in a long journalbearing.Tribol.Int.37,441–446(2004)11.Bali,R.,Sharma,S.K.:Effect of magneticfield in lubrication ofsynovial joints.Tribol.Lett.19,281–287(2005)12.Ravaud,R.,Lemarquand,G.,Lemarquand,V.:Mechanicalproperties of ferrofluid applications:centering effect and capacity of a seal.Tribol.Int.43,76–82(2010)13.Chantrell,R.,Popplewell,J.,Charles,S.W.:Measurement ofparticle size distribution parameters in ferrofluids.IEEE Trans.Magn.14,975–977(1978)。