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Contact Mechanics and Tribology Match

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Contact Mechanics and Tribology Match FEATURE ARTICLE Jeanna Van Rensselar / Contributing Editor Beneath the Why contact mechanics and tribology are a natural match KEY CONCEPTCONCEPTSS • CoContacntact mechanics iiss a sometimes oveoverlookedrlooked bbutut ccriticalritical asaspectpect of ttribology.ribology. • FriFrictionction rereductionduction iiss maximizmaximizeded by lleveragingeveraging the dydynaminamic bbetweenetween ssurfaceurface mmaterialaterial gengineeringg aandnd lublubricationrication genengineering. gineering. g. ••A Atetexturedxtured bbearinbearingg susurfacrface acts ass a lublubricantricant ,reservoirreservoir,, sstoringtoring daandnd ddispens-ispens- ing ththee llubricantubricant directly taatt ththee ppotinintt of ccontactontact wherwheree iitt makes mmostost ssense.ense. 52 • JULY 2015 TRIBOLOGY & LUBRICATION TECHNOLOGY WWW.STLE.ORG surface: Leveraging both disciplines together can yield results neither can achieve alone. WHEN THE THEORY OF CONTACT MECHANICS WAS FIRST DEVELOPED IN 1882, lubricants were not factored into the equation at all. Experts say that may be due to the lack of powerful ana- lytical and numerical tools that necessitated simplicity.1 The omission of lubrication from contact mechanics theory was resolved four years later when Osborne Reynolds developed what is now known as the Reynolds Equation. It describes the pressure distribution in nearly any type of fluid film bearing. WWW.STLE.ORG TRIBOLOGY & LUBRICATION TECHNOLOGY JULY 2015 • 53 Even with that breakthrough, how- WHY IS IT THE STRIBECK CURVE?4 ever, it was decades later before contact mechanics was actually factored into Fundamental to both contact mechanics and tribology, the Stribeck curve is named after tribology. Richard Stribeck. Developed in the first half of the 20th Century, it defines the form of the Today tribology is an integral com- friction curve for liquid-lubricated surfaces and is a foundational tribology element. ponent of contact mechanics, but con- Stribeck performed his research at Berlin’s Royal Prussian Technical Testing Institute tact mechanics still doesn’t have the (now the BAM Federal Institute for Materials Research and Testing) around 1900. Similar same status in tribology. Experts say work was previously performed at the same institute 15 years earlier by Adolf Martens it’s time for a change. and 15 years before that by Robert H. Thurston at the Stevens Institute of Technology in Currently, machine elements are Hoboken, N.J. required to work under increasingly So why is the curve attributed to Stribeck, though both Thurston and Martens severe conditions such as thinner lu- achieved similar results considerably earlier? Possibly because Stribeck published in one brication, minimum lubrication and of the most important journals for engineers at that time, Germany’s Zeitschrift des Ver- higher temperatures. Because of this, eins Deutscher Ingenieure (VDI). Martens published his results in the lesser known Journal the effect of surface topography on lu- of the Royal Prussian Technical Testing Institute. bricated contacts is more relevant than ever. This is especially true for heavily loaded lubricated contacts, which are very dependent on the correct descrip- tion of surface roughness and its associ- Principles of contact mechanics numerical data. If a solid surface ated behavior. Today, with the help of are applied in all tribology-related has inherently very low friction, faster computers, better software and disciplines that involve the contact of it may be difficult to distinguish significantly more efficient numerical one or more solid surfaces; this would between friction from solid contact methods, it’s possible to start modeling include just about every discipline. versus lubricant shearing. It is also surface failure modes in real time.2 In fact, contact mechanics is one very difficult to generate theoretical of the fundamental tools for designing Stribeck curves that are quantitatively bearings. It lays the foundation for race- correct.” way profile design and surface rough- ness specifications. For example, the HISTORY Today tribology is an profile of the rough surface needs to be In 1882 Heinrich Hertz solved the integral component of considered in order to predict the mini- contact problem of two elastic bodies mum effective film thickness. For bear- with curved surfaces. He published contact mechanics, but ings operating in a mixed or boundary his theory in the seminal work On the lubrication environment, contact me- Contact of Elastic Solids and is consid- contact mechanics still chanics is even more important. ered the father of contact mechanics. doesn’t have the same Researchers are able to create Hertz’s solution became the foundation coupled models that consider both for contact mechanics and is still rel- status in tribology; the lubricant behavior and the solid evant today. experts say it’s time contact between the rough surfaces Hertzian contact stress usually re- (the relationship between lubricants fers to the stress close to the area of for a change. and asperities); this is essential for contact between two different-sized generating a Stribeck curve (see Stribeck spheres. In tribology, Hertzian contact Curve sidebar). This also has opened up stress is the stress within pairs of parts the possibility of designing surfaces that operate in the same system (the matched to lubricants (i.e., surface ball and socket of a hip replacement CONTACT MECHANICS texturing and controlled machining). or rolling elements and raceways of a Contact mechanics is the study of how But STLE-member Rob Jackson, bearing in a gearbox). Hertzian contact solids that touch each other at one or professor of mechanical engineering stress assumes the following: more points change shape. Central to at Auburn University, the only school 5 contact mechanics are the pressures offering a tribology minor, has this • There is very little pressure on ei- and adhesions perpendicular to the caveat, “The Stribeck curve is a ther sphere and the surfaces have contacting surfaces (the normal direc- popular method often employed to very little yield. tion).3 Contact mechanics is a some- characterize the lubrication regime • The surfaces are continuous and times overlooked but critical aspect of by the friction coefficient. It can non-conforming; the area of contact tribology. be created from experimental or is a point or line. 54 • JULY 2015 TRIBOLOGY & LUBRICATION TECHNOLOGY WWW.STLE.ORG NA-LUBE® KR Series Broadest Range of Alkylated Naphthalenethalene ® SPECIALTY CHEMICALS NEW BROADEST RANGE NA-LUBE NA-LUBEA-LUB NA-LUBEA-LUB Property KR-00KR-008 KR-009R-00 Supported with Custom Solutions KR-007A NA-LUBE® KR synthetic base oils are available in a Visc. @ 40˚C 22 cSt 36 cSt 39 cSt broad viscosity range from 22-193 cSt at 40°C and Visc. @ 100˚C 3.8 cSt 5.6 cSt 5.7 cSt 3.8-20 cSt at 100°C. King has the expertise and capabilities to customize products to meet your Noack Volatility 39.0% 12.0% 7.7% specific performance requirements. Pour Point < -48˚C -33˚C -33˚C EXCELLENT SOLUBILITY Extremely Versatile Solubility NA-LUBE® KR Series synthetic base oils provide excellent additive solubilizing properties in a wide selection of natural and synthetic base oils and are highly effective as base oil modifiers. LOW VISCOSITY PLUS Low Volatility NA-LUBE® KR-009 alkylated naphthalene combines low viscosity with low volatility for enhanced fuel economy. EXCELLENT STABILITY Highest Thermal-Oxidative Stability NA-LUBE® KR Series synthetic base oils have exceptional thermal-oxidative stability to provide excellent varnish control and to help extend drain intervals. www.kingindustries.comg www.kingindustries.comg www.kingindustries.comg www.kingindustries.comg ndustries.com www.kingindustries.comg ndustries.com for Specialty www.kingindustries.comCallgCallndustt ries.com Alkylated Naphthalene www.kingindustries.com...and..andandg ask a ndust our chemists chemtries which co Alkylated Naphthalene product is best for you! www.kingindustries.com 1-800-431-7900 Toll Free www.kingindustries.com • Each sphere can be considered an Shortly after the JKR model was Hertz’s theory significantly more relevant. elastic half-space. developed, Derjaguin, Muller and Timken Co. scientist and ASME • The surfaces are frictionless. Toporov developed the DMT model— Fellow Xiaolan Ai explains, “Numerical which also accounts for adhesion. Both simulations have come to a stage where So basically all this assumes that the JKR and DMT models still are used they can take any digitized surface the surfaces are smooth and friction- today, and both are still valid. The profile into consideration and study the less, that there is elastic deformation difference is that each model is more effect of roughness under more realistic and half of each surface represents the applicable to certain materials. The conditions. However, experimental entire sphere. So while no one would trick is determining which model to studies are not quite up to modern argue that Hertz’s theory is valid, its ap- use—another field of study in itself. standards.” plicability was and is limited to contact In the 1950s Bowden and Tabor between surfaces that are smooth and were the first to take into account the CONTACT MECHANICS where the contact is lightly loaded and importance of surface roughness for AND BEARINGS frictionless. bodies in contact—this is the point Part of the reason that Hertz failed to In 1970 Johnson, Kendall and of intersection for contact mechanics take asperities into account was the Roberts discovered a similar solution and
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