Meta tags:

Headings (most frequently used words):

wear, friction, and, of, viscosity, history, static, dynamic, tribology, contents, etymology, significance, fundamental, concepts, physics, applications, research, see, also, footnotes, references, external, links, early, jost, report, tribosystem, tribofilm, stribeck, curve, lubrication, transport, manufacturing, fields, societies, laws, coefficients, rolling, surfaces, origin, cohesion, theory, measurements, as, function, temperature, pressure, measures, adhesive, abrasive, fatigue, corrosive, rubbing, or, fretting, erosion, factors, affecting, rate, measurement,

Text of the page (most frequently used words):
the (585), and (219), wear (132), friction (118), displaystyle (104), which (69), that (65), tribology (62), are (55), this (52), #surfaces (52), contact (49), edit (47), force (43), with (41), between (40), for (38), can (38), two (34), viscosity (34), material (31), vec (29), text (28), doi (28), from (27), tribological (27), materials (25), systems (23), also (23), possible (23), surface (22), used (22), such (22), lubrication (21), fluid (21), over (21), main (20), motion (20), more (19), coefficient (19), has (18), engineering (18), static (18), not (17), there (16), load (16), dynamic (16), research (15), sliding (15), relative (15), metal (15), temperature (15), these (15), case (15), layer (15), isbn (14), mechanical (14), physics (14), will (14), energy (14), applied (14), due (14), into (14), science (13), machine (13), steel (13), rolling (13), oil (13), pressure (13), first (13), coefficients (13), may (12), fundamental (12), manufacturing (12), history (12), laws (12), studies (12), but (12), study (12), lubricants (12), phenomenon (12), body (12), type (12), what (12), 978 (11), adhesive (11), law (11), article (11), where (11), wheel (11), involved (11), area (11), they (11), fluids (11), deformations (11), use (10), was (10), other (10), rubbing (10), conditions (10), amontons (10), lubricant (10), reduce (10), occurs (10), following (10), some (10), have (10), only (10), velocity (10), 100 (10), under (9), different (9), state (9), issn (9), society (9), deformation (9), phenomena (9), hardness (9), means (9), abrasive (9), given (9), point (9), while (9), then (9), plane (9), block (9), normal (9), wikipedia (8), value (8), international (8), 1007 (8), been (8), system (8), elastic (8), its (8), frictional (8), forces (8), caused (8), another (8), same (8), log (8), toggle (7), you (7), all (7), mechanics (7), solid (7), bibcode (7), processes (7), theory (7), jost (7), report (7), low (7), behavior (7), impact (7), one (7), components (7), obtain (7), equation (7), fact (7), therefore (7), proportional (7), oils (7), speed (7), flow (7), test (7), depends (7), theta (7), term (7), page (6), cs1 (6), articles (6), march (6), description (6), shape (6), s2cid (6), resistance (6), analysis (6), power (6), bearings (6), properties (6), during (6), leonardo (6), occur (6), applications (6), presence (6), each (6), environment (6), fields (6), transport (6), high (6), complex (6), results (6), most (6), observed (6), particles (6), very (6), phase (6), plastic (6), factors (6), structure (6), when (6), cause (6), both (6), corrosive (6), water (6), than (6), hard (6), even (6), since (6), third (6), sin (6), cos (6), left (6), right (6), move (6), table (5), august (5), 2019 (5), index (5), chemistry (5), how (5), external (5), physical (5), methods (5), 1016 (5), copper (5), lubricating (5), steels (5), 2018 (5), fretting (5), corrosion (5), made (5), design (5), consumption (5), solids (5), field (5), coulomb (5), second (5), fatigue (5), process (5), now (5), application (5), environmental (5), important (5), their (5), intensity (5), order (5), example (5), times (5), easily (5), distance (5), rate (5), depending (5), certain (5), increase (5), created (5), because (5), thermal (5), changes (5), oxides (5), local (5), causes (5), described (5), above (5), roughness (5), three (5), mass (5), layers (5), cost (5), result (5), constant (5), alpha (5), function (5), observe (5), stress (5), weight (5), savings (5), subsection (5), contents (4), search (4), available (4), september (4), 2026 (4), references (4), german (4), short (4), data (4), polymer (4), independent (4), 2022 (4), free (4), links (4), elsevier (4), michael (4), 2012 (4), green (4), technology (4), journal (4), peter (4), popov (4), valentin (4), balitskii (4), kolesnikov (4), 3390 (4), hydrogen (4), 2017 (4), s40544 (4), products (4), technologies (4), 2005 (4), global (4), tabor (4), november (4), der (4), reye (4), help (4), related (4), vinci (4), according (4), additive (4), space (4), contaminants (4), introduced (4), form (4), adhesion (4), damage (4), desired (4), including (4), tribologists (4), problems (4), extreme (4), through (4), losses (4), areas (4), sectors (4), tool (4), necessary (4), thus (4), required (4), however (4), condition (4), must (4), before (4), evaluate (4), way (4), removed (4), known (4), mechanisms (4), called (4), ratio (4), various (4), delta (4), less (4), decrease (4), crystalline (4), erosion (4), pure (4), many (4), time (4), lead (4), much (4), bodies (4), asperities (4), precisely (4), increasing (4), types (4), could (4), viscometers (4), determine (4), allows (4), air (4), equal (4), considered (4), shear (4), acting (4), were (4), vert (4), ice (4), wood (4), account (4), stribeck (4), curve (4), his (4), hide (4), sidebar (4), view (3), contacts (3), additional (3), using (3), non (3), commons (3), categories (3), style (3), sources (3), volume (3), containing (3), greek (3), retrieved (3), states (3), national (3), common (3), aspects (3), computational (3), june (3), review (3), superlubricity (3), erdemir (3), ali (3), learning (3), 642 (3), cite (3), 2021 (3), 2013 (3), 2024 (3), performance (3), self (3), mixing (3), influence (3), computer (3), artificial (3), intelligence (3), information (3), sciences (3), image (3), processing (3), techniques (3), particle (3), manganese (3), 2000 (3), associated (3), chemical (3), 2nd (3), john (3), plates (3), book (3), film (3), coatings (3), costs (3), emissions (3), neale (3), bowden (3), frank (3), philip (3), david (3), archard (3), 1860 (3), theodor (3), 108 (3), gold (3), macroscopic (3), 2016 (3), 1966 (3), measures (3), mechanism (3), laboratory (3), based (3), improve (3), mutual (3), movement (3), societies (3), relevant (3), affected (3), particular (3), outer (3), aims (3), increasingly (3), become (3), reducing (3), importance (3), human (3), increases (3), biotribology (3), brakes (3), divided (3), direct (3), effects (3), experimental (3), ring (3), role (3), any (3), slides (3), interactions (3), useful (3), developments (3), measurements (3), small (3), after (3), method (3), measurement (3), severe (3), level (3), change (3), size (3), harder (3), suitable (3), depend (3), microscopic (3), itself (3), films (3), create (3), contribute (3), cases (3), loads (3), comb (3), impurities (3), foreign (3), consists (3), interaction (3), part (3), figure (3), conclusion (3), smooth (3), significant (3), variables (3), newtonian (3), placed (3), describes (3), relationship (3), exact (3), operatorname (3), question (3), consider (3), gradient (3), divide (3), number (3), relatively (3), immobile (3), them (3), just (3), seen (3), slip (3), widely (3), compression (3), inner (3), tangential (3), frac (3), able (3), subjected (3), reduction (3), usually (3), does (3), glass (3), ptfe (3), out (3), found (3), word (3), tribofilm (3), knowledge (3), tribosystem (3), concepts (3), developed (3), carbon (3), dioxide (3), million (3), residential (3), generation (3), world (3), published (3), early (3), coins (3), tools (3), topic (2), languages (2), about (2), privacy (2), policy (2), terms (2), apply (2), wikimedia (2), creative (2), attribution (2), license (2), edited (2), url (2), maint (2), periodical (2), issues (2), needing (2), language (2), long (2), date (2), ancient (2), 2020 (2), wikidata (2), metallurgy (2), degradation (2), control (2), matter (2), informatics (2), interdisciplinary (2), april (2), popular (2), martin (2), 2004 (2), 126101 (2), pmid (2), 2007 (2), 444 (2), nosonovsky (2), triboinformatics (2), bhushan (2), bharat (2), link (2), georg (2), 030 (2), springer (2), zhang (2), 109543 (2), triboint (2), matrix (2), resonant (2), acoustic (2), fuels (2), environmentally (2), friendly (2), nitrogen (2), spark (2), ignition (2), engine (2), set (2), stachowiak (2), 2223 (2), 7690 (2), 017 (2), automotive (2), tribotechnical (2), big (2), elit (2), scientific (2), practical (2), integrated (2), comparison (2), recognition (2), classify (2), debris (2), 019 (2), austenitic (2), cast (2), irons (2), karl (2), microstructure (2), 2015 (2), tests (2), popova (2), elena (2), years (2), rabinowicz (2), cambridge (2), university (2), press (2), structural (2), deposited (2), cathodic (2), arc (2), evaporation (2), 107246 (2), vol (2), feynman (2), lectures (2), american (2), education (2), holmberg (2), kenneth (2), 1995 (2), handbook (2), classic (2), 1098 (2), rsbm (2), biographical (2), memoirs (2), fellows (2), royal (2), 1969 (2), 1953 (2), flat (2), frederick (2), für (2), moritz (2), 1885 (2), 535 (2), theoretical (2), und (2), alloys (2), dowson (2), duncan (2), 1997 (2), pdf (2), present (2), position (2), industry (2), needs (2), later (2), became (2), footnotes (2), removal (2), instrument (2), tribocorrosion (2), interface (2), british (2), list (2), organizations (2), welding (2), see (2), numerous (2), group (2), chinese (2), institute (2), council (2), engineers (2), open (2), micro (2), scales (2), nanotribology (2), glaciers (2), minimize (2), along (2), entire (2), minimal (2), joints (2), typical (2), classical (2), well (2), forming (2), clutches (2), elements (2), ranges (2), traditionally (2), concentrated (2), formation (2), significantly (2), modify (2), behaviour (2), increased (2), sophisticated (2), achieve (2), plays (2), work (2), piece (2), replacement (2), greater (2), distribution (2), include (2), applying (2), often (2), fairly (2), accelerate (2), reality (2), superficial (2), levels (2), radioactive (2), tracer (2), finally (2), best (2), reduced (2), strongly (2), composition (2), real (2), length (2), traveled (2), instead (2), express (2), medium (2), moderate (2), usury (2), provide (2), assessment (2), dimensionless (2), suffered (2), degree (2), resist (2), others (2), deform (2), find (2), affecting (2), either (2), causing (2), parameters (2), angle (2), movements (2), within (2), displacement (2), come (2), oxide (2), oxygen (2), continually (2), positive (2), being (2), repeated (2), turn (2), immediate (2), slide (2), teeth (2), off (2), breaking (2), good (2), try (2), inclusions (2), expansion (2), cutting (2), rub (2), serious (2), who (2), involves (2), inserting (2), fusion (2), distinguish (2), concerns (2), machinery (2), worn (2), parts (2), replaced (2), problem (2), economic (2), please (2), like (2), textbook (2), obtained (2), evaluating (2), measured (2), moves (2), capillary (2), tube (2), keep (2), mind (2), exp (2), get (2), 00715 (2), outside (2), fixed (2), range (2), dissipation (2), initially (2), want (2), reynolds (2), laminar (2), rho (2), said (2), contained (2), newton (2), immediately (2), zero (2), thanks (2), deeper (2), understanding (2), achieved (2), concept (2), equivalent (2), make (2), address (2), inclined (2), tangent (2), allow (2), studied (2), deformed (2), circle (2), tan (2), define (2), returns (2), directly (2), realistic (2), strength (2), far (2), further (2), component (2), comes (2), lower (2), single (2), expressed (2), cohesion (2), heat (2), bumps (2), new (2), decompression (2), permanent (2), large (2), regions (2), atom (2), origin (2), deposition (2), would (2), thin (2), going (2), put (2), derives (2), four (2), supporting (2), continuously (2), once (2), opposes (2), starts (2), happens (2), detail (2), capable (2), horizontal (2), rubber (2), cement (2), dry (2), 001 (2), lubricated (2), shows (2), nonuniform (2), valid (2), apparent (2), section (2), learn (2), citations (2), reliable (2), talk (2), tribosystems (2), biology (2), mtco (2), euros (2), 000 (2), total (2), overcome (2), despite (2), considerable (2), still (2), significance (2), highlighted (2), economy (2), community (2), physicist (2), together (2), cavendish (2), simple (2), charles (2), recent (2), objects (2), doubles (2), etymology (2), appearance (2), upload (2), file (2), read (2), donate (2), menu (2), add, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, disclaimers, site, agree, registered, trademark, profit, organization, foundation, inc, sharealike, rendered, parsoid, last, utc, hidden, unfit, errors, 1453, dmy, dates, https, org, php, title, oldid, 1377618353, yale, lux, israel, poland, czech, republic, japan, bnf, france, united, gnd, authority, databases, category, soft, condensed, nuclear, mining, mineralogy, microelectronics, crystallography, domains, characterization, ceramic, classes, branches, bernhard, adrienne, archived, original, obscure, built, past, future, look, wiktionary, dictionary, dienwiebel, verhoeven, gertjan, pradeep, namboodiri, frenken, joost, heimberg, jennifer, zandbergen, henny, 26811802, 15089689, 1103, physrevlett, 2004phrvl, 92l6101d, letters, graphite, jean, michel, 52772, hasan, syam, 242, 247398788, 1680, jsuin, 00027, 229, innovations, algorithms, topology, springerlink, 238793302, 23680, 23681, ostermeyer, shilko, evgeny, vasiljeva, olga, eds, 2195, 9862, 60123, 60124, tracts, multiscale, biomechanics, inorganic, organic, paulo, davim, 31683, youwang, zhu, xiuchong, kang, xiao, lei, liu, chenxu, 0301, 679x, 194, composite, prepared, powder, alexander, valerii, abramek, karol, olexiy, eliasz, jacek, havrylyuk, marya, ivaskevych, lyubomir, kolesnikova, ielyzaveta, 7583, en14227583, energies, coolant, pistons, rings, kit, gasket, gwidon, 247, 500, 11937, 59306, hdl, 0173, 233, helping, advance, survive, identification, vision, 1109, 8892275, proceedings, xith, conference, electronics, balitska, 11762, app142411762, saturated, peng, shangguan, fan, 3041, polym14153041, polymers, failure, wind, laghari, hassan, haggag, wahyudie, tayfor, elsayed, 2025, 107, eng6060107, eng, texture, wei, feature, detection, diagnosis, balyts, kyi, kawiak, triboengineering, 630, s11003, 006, 0023, 624, rigney, transfer, s0043, 1648, 00425, 245, zum, gahr, heinz, 1987, 42754, wiley, sons, 119, 94453, introduction, dos, santos, claudio, teodoro, barbosa, cássio, jesus, monteiro, maurıcio, cerqueira, abud, ibrahim, vieira, caminha, ieda, maria, mello, roesler, carlos, rodrigo, 175, 44071702, 1590, 2446, 4740, 0710, 169, biomedical, orthopedic, screws, astm, f138, stainless, kim, dae, eun, 348, 018, 0240, 341, criterion, batchelor, 2005entr, szeri, kuprin, 165, resnick, halliday, krane, 2002, 5th, otsuki, matsukawa, 1586, 23545778, 3613807, pmc, 1038, srep01586, 2013natsr, 1586o, 1202, 1716, arxiv, reports, systematic, breakdown, object, locally, obeying, hafner, 1965, 752, 0002, 9505, 1119, 1972241, 1965amjph, 750f, 750, sands, matthew, leighton, robert, richard, 3389, fmech, 00016, frontiers, approaching, golden, age, grand, challenges, copied, source, 284, 0183, 263, 7506, 1198, 2001, oxford, texts, 850777, 2008, 459, 0031, 425, october, 1913, 317, 71069997, 0080, 4606, 0001, 1969jglac, 317t, 1903, 1968, 988, 0021, 8979, 1063, 1721448, 1953jap, 981a, 981, 1859, bornemann, pivot, neue, folge, 255, 235, civilingenieur, zeitschrift, das, ingenieurwesen, zur, theorie, zapfenreibung, incompatibility, rühlmann, teil, olms, verlag, 48741119, technical, mathematical, vorträge, über, die, geschichte, technischen, mechanik, theoretischen, maschinenlehre, damit, zusammenhang, stehenden, mathematischen, wissenschaften, chaston, december, 1974, 112, 0017, 1557, bf03215051, bulletin, coinage, 190, 015, 0074, 183, works, generalized, professional, publishing, 86058, 070, gao, jianping, luedtke, gourdon, ruths, israelachvili, landman, uzi, molecular, scale, 3425, 16643851, 1520, 6106, 1021, jp036362l, 2004jpcb, 3410g, 3410, hutchings, ian, supplement, 360, mitchell, luke, ward, jacob, fiction, nonfriction, 281, department, london, stationery, office, polytechnician, zürich, professor, straßburg, zinc, dithiophosphate, damaging, gradual, tribometer, phases, spacecraft, measure, sclerometer, engineer, 1921, chemicals, substance, italian, polymath, 1452, 1519, galling, modifier, resisting, loaded, touch, joining, without, melting, heating, cold, constrain, bearing, additives, prevent, antiwear, stle, imeche, iop, gesellschaft, tribologie, korean, kts, malaysian, mytribos, japanese, jast, india, tsi, institution, vanishing, topical, newer, ionic, liquids, graphene, exposed, natural, operate, requires, withstand, fluctuations, vapor, model, simulations, combining, disciplines, dynamics, fracture, multiphysics, becoming, devices, smaller, nanoelectromechanical, aided, invention, atomic, microscopy, nems, mems, nanoscopic, geological, faults, geotribology, contrast, traditional, holistically, evaluated, lifecycle, biological, gaining, lifetime, expectancy, hip, knee, concerned, wheels, plain, gears, element, diverse, continental, locomotion, animals, insects, considerably, diversified, loosely, overlap, nano, macro, rail, winter, reduces, requirements, know, leave, unique, fingerprint, tribocontact, topography, aerospace, specifically, composites, mixed, effectively, done, shown, boundary, piston, focused, reliability, ensuring, safe, continuous, operation, nowadays, focus, progressively, operations, frequent, loss, tolerance, dimensions, shift, efficiency, historically, effective, particularly, extends, modern, automated, morphology, diagnostic, approaches, classification, ferrographic, assisted, features, complement, identify, improving, diagnostics, units, operating, service, predictive, maintenance, monitoring, recreate, rates, develop, few, days, evaluation, visual, inspection, profile, occurrence, variations, geometry, investigation, marked, visible, accessible, sufficient, influenced, exhibit, strain, hardening, represents, dimensional, holm, usage, class, height, makes, subdivide, situations, passing, modest, verified, decreases, mutually, soluble, tends, regards, structures, hexagonal, compact, slipping, base, planes, solubility, among, influencing, liquid, hit, abrasion, kinds, subject, intense, vibrations, nanometers, produced, remain, trapped, accelerated, substances, metals, oxidize, corrode, surrounding, acids, recreated, contaminating, clearly, trying, hoc, pollutants, sensible, belong, excellent, abrasives, alternative, deterioration, finger, again, stresses, cycling, frequency, temperatures, intervene, optimal, eliminate, defects, effort, act, softer, tips, cut, against, interpose, eliminated, adequate, finish, bring, filters, weighted, aspect, emission, threatens, health, ecology, researcher, investigated, ernest, inversely, shearing, detach, weaker, represented, problematic, speeds, minor, cavitation, spreading, progressive, involuntary, higher, compatible, rough, violent, construction, entails, nature, functional, negative, sides, indeed, eliminating, erroneously, tend, imagine, correlation, connected, vice, versa, implementation, simultaneously, combined, encyclopedic, neutral, rewrite, written, mainly, versatile, rotational, drop, calculating, viscosimeters, say, leads, implies, atmospheric, kinematic, 210, advancement, mixtures, 1929, dean, davis, assigned, namely, pennsylvania, worst, gulf, coast, intermediate, procedure, reference, chosen, disadvantages, car, engines, refrigeration, pumps, weather, variation, affect, choosing, conclude, underline, kind, diameter, flows, whereas, becomes, turbulent, mathrm, simeq, glycerin, blood, gasoline, introduce, corresponds, varies, amount, simplify, writing, oppose, propto, slab, vary, quantity, ideally, ability, hydrodynamics, exploiting, penetrate, fluidostatic, hydrostatic, mineral, insertion, perfect, avoid, possibilities, perfection, choice, unlike, might, think, fats, characterized, course, intended, readily, former, limited, simplest, calculated, begins, moved, cross, roller, pin, disk, today, digital, machines, tester, software, support, insert, plastically, otherwise, expands, similarly, exhaustive, cks, cas, studying, limits, keeping, correct, formula, follows, considerations, should, moisture, correlate, cdot, implied, complicates, ignoring, junction, joint, bonds, relating, resort, require, substrate, spherical, passes, enlargement, reason, definable, rise, sharp, consequently, effectiveness, dissipated, transformed, break, creation, expended, almost, entirely, recovered, hysteresis, literature, junctions, takes, place, undergo, rupture, nitride, multicomponent, demonstrated, improved, contributes, regarding, clean, union, absence, atoms, hardened, rapid, cooling, working, machined, basic, bulk, interior, internal, linked, undergone, latter, relation, radius, tfrac, imperceptible, passed, subsequent, initial, provides, contribution, front, center, opposition, separation, moment, torque, reaction, excludes, rolls, response, floor, 003, synovial, wet, brass, aluminum, scioled, ski, snow, cardboard, values, exceed, unit, velocities, quantities, always, summarize, experiences, lesser, take, affirm, instantly, taking, stated, modulus, minimum, obtaining, leq, quiet, opposite, deviations, satisfied, macroscopically, theories, simplified, predominantly, empirical, reach, precise, approximate, conclusions, inability, definite, complexity, closely, presents, stationary, latin, frictionem, describe, those, dissipative, producing, opposing, remove, message, discussion, unsourced, challenged, jstor, scholar, books, newspapers, news, adding, linear, entrainment, tribologically, stressed, play, tribofilms, detailed, inputs, outputs, devise, procedures, covering, ball, gear, drives, etc, context, embrace, nanotechnology, medicine, implementing, advanced, tons, 970, 3140, 450, 1460, largest, envisioned, potential, estimated, longer, respectively, protection, originates, remanufacture, spare, equipment, expenditure, attempted, quantify

Text of the page (random words):
s possible to study not only the most external surface of the metal but also the immediately more internal states linked to the history of the metal its composition and the manufacturing processes undergone by the latter it is possible to divide the metal into four different layers crystalline structure basic structure of the metal bulk interior form machined layer layer which may also have inclusions of foreign material and which derives from the processing processes to which the metal has been subjected hardened layer has a crystalline structure of greater hardness than the inner layers thanks to the rapid cooling to which they are subjected in the working processes outer layer or oxide layer layer that is created due to chemical interaction with the metal s environment and from the deposition of impurities the layer of oxides and impurities third body has a fundamental tribological importance in fact it usually contributes to reducing friction another fact of fundamental importance regarding oxides is that if you could clean and smooth the surface in order to obtain a pure metal surface what we would observe is the union of the two surfaces in contact in fact in the absence of thin layers of contaminants the atoms of the metal in question are not able to distinguish one body from another thus going to form a single body if put in contact surface engineering techniques such as deposition of hard nitride coatings are widely used to improve tribological behaviour of mechanical components multicomponent coatings including cr v n deposited by cathodic arc evaporation have demonstrated improved wear resistance and friction performance 20 origin of friction edit contact between surfaces is made up of a large number of microscopic regions in the literature called asperities or junctions of contact where atom to atom contact takes place the phenomenon of friction and therefore of the dissipation of energy is due precisely to the deformations that such regions undergo due to the load and relative movement plastic elastic or rupture deformations can be observed plastic deformations permanent deformations of the shape of the bumps elastic deformations deformations in which the energy expended in the compression phase is almost entirely recovered in the decompression phase elastic hysteresis break deformations deformations that lead to the breaking of bumps and the creation of new contact areas the energy that is dissipated during the phenomenon is transformed into heat thus increasing the temperature of the surfaces in contact the increase in temperature also depends on the relative speed and the roughness of the material it can be so high as to even lead to the fusion of the materials involved in friction phenomena temperature is fundamental in many areas of application for example a rise in temperature may result in a sharp reduction of the friction coefficient and consequently the effectiveness of the brakes cohesion theory edit the adhesion theory states that in the case of spherical asperities in contact with each other subjected to a w displaystyle vec w load a deformation is observed which as the load increases passes from an elastic to a plastic deformation this phenomenon involves an enlargement of the real contact area a r displaystyle a_ text r which for this reason can be expressed as a r w d displaystyle a_ text r vec w over d where d displaystyle d is the hardness of the material definable as the applied load divided by the area of the contact surface if at this point the two surfaces are sliding between them a resistance to shear stress t displaystyle t is observed given by the presence of adhesive bonds which were created precisely because of the plastic deformations and therefore the frictional force will be given by f a a r t displaystyle vec f _ text a a_ text r vec t at this point since the coefficient of friction is the ratio between the intensity of the frictional force and that of the applied load it is possible to state that μ t d displaystyle mu t over d thus relating to the two material properties shear strength t displaystyle t and hardness to obtain low value friction coefficients μ displaystyle mu it is possible to resort to materials which require less shear stress but which are also very hard in the case of lubricants in fact we use a substrate of material with low cutting stress t displaystyle t placed on a very hard material the force acting between two solids in contact will not only have normal components as implied so far but will also have tangential components this further complicates the description of the interactions between roughness because due to this tangential component plastic deformation comes with a lower load than when ignoring this component a more realistic description then of the area of each single junction that is created is given by a i 2 w i d 2 α f i d 2 displaystyle a_ text i 2 left frac vec w _ text i d right 2 alpha left frac vec f _ text i d right 2 with α displaystyle alpha constant and a tangent force f i displaystyle vec f _ text i applied to the joint to obtain even more realistic considerations the phenomenon of the third body should also be considered i e the presence of foreign materials such as moisture oxides or lubricants between the two solids in contact a coefficient c displaystyle c is then introduced which is able to correlate the shear strength t displaystyle t of the pure material and that of the third body t tb displaystyle t_ text tb t c t tb displaystyle t c cdot t_ text tb with 0 c 1 displaystyle 0 c 1 by studying the behavior at the limits it will be that for c 0 displaystyle c 0 t 0 displaystyle t 0 and for c 1 displaystyle c 1 it returns to the condition in which the surfaces are directly in contact and there is no presence of a third body keeping in mind what has just been said it is possible to correct the friction coefficient formula as follows μ c α 1 c 2 1 2 displaystyle mu frac c alpha 1 c 2 1 2 in conclusion the case of elastic bodies in interaction with each other is considered similarly to what we have just seen it is possible to define an equation of the type a k w displaystyle a k vec w where in this case k displaystyle k depends on the elastic properties of the materials also for the elastic bodies the tangential force depends on the coefficient c displaystyle c seen above and it will be f t c a s displaystyle vec f _ t cas and therefore a fairly exhaustive description of the friction coefficient can be obtained μ c k s displaystyle mu cks friction measurements edit the simplest and most immediate method for evaluating the friction coefficient of two surfaces is the use of an inclined plane on which a block of material is made to slide as can be seen in the figure the normal force of the plane is given by m g cos θ displaystyle mg cos theta while the frictional force is equal to m g sin θ displaystyle mg sin theta this allows us to state that the coefficient of friction can be calculated very easily by means of the tangent of the angle in which the block begins to slip in fact we have μ f a n m g sin θ m g cos θ sin θ cos θ tan θ displaystyle mu f_ text a over n mg sin theta over mg cos theta sin theta over cos theta tan theta then from the inclined plane we moved on to more sophisticated systems which allow us to consider all the possible environmental conditions in which the measurement is made such as the cross roller machine or the pin and disk machine today there are digital machines such as the friction tester which allows by means of a software support to insert all the desired variables another widely used process is the ring compression test a flat ring of the material to be studied is plastically deformed by means of a press if the deformation is an expansion in both the inner and the outer circle then there will be low or zero friction coefficients otherwise for a deformation that expands only in the inner circle there will be increasing friction coefficients lubrication edit main article lubrication to reduce friction between surfaces and keep wear under control materials called lubricants are used 21 unlike what you might think these are not just oils or fats but any fluid material that is characterized by viscosity such as air and water of course some lubricants are more suitable than others depending on the type of use they are intended for air and water for example are readily available but the former can only be used under limited load and speed conditions while the second can contribute to the wear of materials what we try to achieve by means of these materials is a perfect fluid lubrication or a lubrication such that it is possible to avoid direct contact between the surfaces in question inserting a lubricant film between them to do this there are two possibilities depending on the type of application the costs to address and the level of perfection of the lubrication desired to be achieved there is a choice between fluidostatic lubrication or hydrostatic in the case of mineral oils which consists in the insertion of lubricating material under pressure between the surfaces in contact fluid fluid lubrication or hydrodynamics which consists in exploiting the relative motion between the surfaces to make the lubricating material penetrate viscosity edit main article viscosity the viscosity is the equivalent of friction in fluids it describes the ability of fluids to resist the forces that cause a change in shape thanks to newton s studies a deeper understanding of the phenomenon has been achieved he in fact introduced the concept of laminar flow a flow in which the velocity changes from layer to layer it is possible to ideally divide a fluid between two surfaces s 1 displaystyle s_ 1 s 2 displaystyle s_ 2 of area a displaystyle a in various layers the layer in contact with the surface s 2 displaystyle s_ 2 which moves with a velocity v displaystyle v due to an applied force f displaystyle f will have the same velocity as v of the slab while each immediately following layer will vary this velocity of a quantity d v displaystyle dv up to the layer in contact with the immobile surface s 1 displaystyle s_ 1 which will have zero speed from what has been said it is possible to state that the force f displaystyle f necessary to cause a rolling motion in a fluid contained between two plates is proportional to the area of the two surfaces and to the speed gradient f a d v d y displaystyle f propto a dv over dy at this point we can introduce a proportional constant μ displaystyle mu which corresponds to the dynamic viscosity coefficient of the fluid to obtain the following equation known as newton s law f μ a d v d y displaystyle f mu a dv over dy the speed varies by the same amount d v displaystyle dv of layer in layer and then the condition occurs so that d v d y v l displaystyle dv dy v l where l displaystyle l is the distance between the surfaces s 1 displaystyle s_ 1 and s 2 displaystyle s_ 2 and then we can simplify the equation by writing f μ a v l displaystyle f mu a v over l the viscosity μ displaystyle mu is high in fluids that strongly oppose the motion while it is contained for fluids that flow easily table of viscosity coefficients μ displaystyle mu for some fluids fluid μ displaystyle mu co 2 1 5 10 5 pa s air 1 8 10 5 pa s gasoline 2 9 10 4 pa s water 90 c 0 32 10 3 pa s water 20 c 1 0 10 3 pa s blood 37 c 4 0 10 3 pa s oil 20 c 0 03 pa s oil 0 c 0 11 pa s glycerin 1 5 pa s to determine what kind of flow is in the study we observe its reynolds number r e ρ l v μ displaystyle re rho lv over mu this is a constant that depends on the fluid mass ρ displaystyle rho of the fluid on its viscosity μ displaystyle mu and on the diameter l displaystyle l of the tube in which the fluid flows if the reynolds number is relatively low then there is a laminar flow whereas for r e 2000 displaystyle mathrm re simeq 2000 the flow becomes turbulent to conclude we want to underline that it is possible to divide the fluids into two types according to their viscosity newtonian fluids or fluids in which viscosity is a function of temperature and fluid pressure only and not of velocity gradient non newtonian fluids or fluids in which viscosity also depends on the velocity gradient viscosity as a function of temperature and pressure edit temperature and pressure are two fundamental factors to evaluate when choosing a lubricant instead of another consider the effects of temperature initially there are three main causes of temperature variation that can affect the behavior of the lubricant weather conditions local thermal factors like for car engines or refrigeration pumps energy dissipation due to rubbing between surfaces in order to classify the various lubricants according to their viscosity behavior as a function of temperature in 1929 the viscosity index v i was introduced by dean and davis these assigned the best lubricant then available namely the oil of pennsylvania the viscosity index 100 and at the worst the american oil of the gulf coast the value 0 to determine the value of the intermediate oil index the following procedure is used two reference oils are chosen so that the oil in question has the same viscosity at 100 c and the following equation is used to determine the viscosity index v i l o test l h 100 displaystyle v i l o_ text test over l h times 100 this process has some disadvantages for mixtures of oils the results are not exact there is no information if you are outside the fixed temperature range with the advancement of the technologies oils with v i more than 100 which can not be described by the method above in the case of oils with v i above 100 you can use a different relationship that allows you to get exact results v i 10 n 1 0 00715 100 displaystyle v i 10 n 1 over 0 00715 100 n log h log o test log v displaystyle n operatorname log h operatorname log o_ text test over operatorname log v where in this case h displaystyle h is the viscosity at 100 f 38 c of the oil with v i 100 and v displaystyle v is the kinematic viscosity of the study oil at 210 f 99 c we can therefore say in conclusion that an increase in temperature leads to a decrease in the viscosity of the oil it is also useful to keep in mind that in the same way an increase in pressure implies an increase in viscosity to evaluate the effects of pressure on viscosity the following equation is used μ μ 0 exp α p displaystyle mu mu _ 0 exp alpha p where μ displaystyle mu is the pressure viscosity coefficient p displaystyle p μ 0 displaystyle mu _ 0 is the viscosity coefficient at atmospheric pressure and α displaystyle alpha is a constant that describes the relationship between viscosity and pressure viscosity measures edit to determine the viscosity of a fluid viscosimeters are used which can be divided into 3 main categories capillary viscometers in which the viscosity of the fluid is measured by sliding it into a capillary tube solid drop visc...