DURABILYTY OF FRICTION PAIRS WITH FUNCTIONALITY IN ABRASIVE RANDOMLY PARTICLES

Transcription

1 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN -459 Paper present at International Conerene on Diagnosis and Predition in Mehanial Engineering Systems (DIPRE 7) 6-7 Otober 7, Galati, Romania DURABILYTY OF FRICTION PAIRS WITH FUNCTIONALITY IN ABRASIVE RANDOMLY PARTICLES Andrei TUDOR, Monia VLASE Politehnia University o Buharest; Tehnial Civil Engineering University o Buharest, Romania tudor@meaomtrpubro ABSTRACT It is shown that the abrasive partiles, whih penetrate in the onvergent joint o rition pairs, an damage the superiial layer o suraes The wear aused by individual partile depends on having both a satisatory understanding o individual interations and a suitable proedure or ombining these under irumstanes when partile geometry has randomly aspets It is evaluated the partile number in the learane o ylindrial bearing Wear determinist and random parameter predited rom the orresponding partile deormation models are shown It is onsidered that the abrasive partiles are ovoid with random variable radius and length The random variable distributions are onsidered to be exponential and normal KEYWORDS: Abrasive wear, bearing, randomly geometry, durability INTRODUCTION Frition ouples operating in inested environments with abrasive partiles are one o durability restrition ase For the onvergent-divergent gaps (intersties), with relative suraes motion, the partiles penetration and their driving into the gap, depend on the gap s geometry, the partile geometry and rition oeiient The harder partiles an proeed rom the exterior ouple environment (dust, sand) or even rom the wear partile detahment in the adhesion or atigue proess [,, 3, 4] Abrasion an our due to: miro-utting by the hard partile sharp edges or its roughness; by raturing due to the rak onvergene; by atigue due to repeated plasti streins; by hard granule, pluking out o the material [3, 4] Miro-utting an be explained by two ouring mehanism: material raturing by shearing in the maximum plasti strein plane; material lakes orming by sharing Lubriant presene is a stimulating ator o the miro-utting by abrasive partiles When the lubriant exists, utting ours at smaller penetrations o the abrasive partile in the material, as when the lubriant doesn`t exists This implies the at that when an abasive partile is rigidly ixed in a sot surae, in the lubriant and load presene, the partile will aelerate the wear proess Partile edges an reate hips or plasti strains whih doesn`t provoke material sheares New abrasive partiles, obtained by bigger partile rature or by wear partile detahment rom ragile materials, ontain more miro-utting edges When the partiles moves, onsiderable plasti strains our whih lead to material hardening, thus the wear intensity inreases and the partile edges are trimed [] Fraturing was marked out to ragile materials (brittled) by studing the rature generation in the superiial layer For the ragile materials, the rature under the penetrator is realised in three ways: or a ertain ore, the ratures are spreding under an about 3 angle

2 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN -459 with the surae; or a bigger ore, a ragmentation o the ratured material is loalizated; or a ritial ore, the rature has a entral development in its depth The suessive movement o the partiles on the surae leads to a ratures storage and thus, to a material detahment as miro-ragments The material atigue ours in the deormed zone by the hard partile Grooving represents a severe orm o abrasion, with broad and depth srathings, whih an be diretly produed by the ounter-piee (rom gears, the top o the tooth), by harder interposed partiles (or xample, to brake disks), by metali piees and other hard aterials (to ative woking elements o the soil) Srathing is the most mild abrasion orm and it maniests as linear, parallel, isolated srathings et; it an our on dierent piees (tooth lanks o a gear, the liner o a bearing, the liner o a ylinder et), being produed also by harder interposed partiles, some roughness ation et The way in whih the abrasive partiles passes on the worned surae showes two types o wear: - two elements wear; - three elements wear Two elements abrasion supposes that partiles are ixed in one o the ouple element This an be onsidered similar to the abrasion o one surae by the roughness o the onjugated surae Three elements abrasion implies the ree state o the partiles into the gap (interstie), partiles that an slip and roll over the surae The signiiant dierene between the two types o abrasion wear is the veloity or the wear intensity Three elements wear has an wear veloity about times smaller than two elements wear This paper`s goal is to analyse the abrasive wear produed by ovoid partiles with aleatory variable geometry, into a ylindrial slipping bearing gap The initial hypothesis is that the pin`s and liner`s deormations are elasti and the ovoid partiles are peret rigid For example, i the ovoid partile is in ontat with the pin through the big sphere o ovoid and in ontat with the liner through the small sphere o this ovoid, the diretion o the ovoid being radial given the pin, it is determined the abrasive partiles number on the liner unit length, as a untion o dierent non-dimensional parameters: αmax αmin zp = + () α The wrapping angles α max and α min and the angle α partile are determined by geometrial onditions: ψ αmax = βmax + asin sinβ max ( ψ )( + Rap ) ψ min = min + asin sin min ( ψ )( + Rap ) α β β max (,R ap,, ) β ψ χ ξ = and ( ap ap ap ) ( ψ) ψ R χr ξr a os ψ βmin = βmax ψ,r ap,, Thus, the igures and 3 show the variation o partile number to relative learane o bearing and radius o ovoid partile CONTACT MODELLING BETWEEN AN OVOID AND A CYLINDER The abrasive partile is onsidered to be an ovoid, haraterised by two spherial segments o R and r radius and the distane a p between the spheres` entre The non-dimensional values are deined: length oeiient ξ = a p / R, rounding oeiient χ = r/r, partile relative radius R = R/ R The gap (interstie) between the pin and the liner is aharaerised by the relative gap ψ [(R b -R )/R b ], R b bearing radius; R ylinder radius The ovoid positions into the gap between the pin and the liner are presented in igure, thus, the strains and deormations state an be analised or eah ase alone ap Fig Ovoid partile geometry in onvergent joint o bearing

3 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN z p ψ, 7, 5, 5 z 4 p ψ, 6, 5, zp z p ψ, 6, 5, 5 R ap = -7 χ = Fig Partiles number vs relative learane z 5 p R, ap,, zp z p R, ap, 5, 3 5 z p R, ap,, 5 ψ ξ = ψ = χ = χ =5 χ = ξ = ξ = ξ =5 where A and ε onstants an be determined with the limit onditions δ = δ or α = α min = or = max δ α α Thus, δ A = and π os αmin + αmax π φ = αmax From the mehanial equilibrium ondition, Fa = ( 3/ min + π z p os ( αmax + αmin + ( i ) R ap ) π i= os αmax α + min os α ( i ) α ) (4) it is determined the maximum non-dimensional ore F a = F /F elasti supported by the ylinder Thus, igure 4 presents the maximum nondimensional ore variation upon the most harged ovoid partile, or a gap with relative interstie ψ=, partile roundness parameter χ=5, three values o the length oeiient ξ = 5,, R ap Fig 3 Partiles number vs radius ovoid partile The exterior F ore distribution upon the abrasive partiles z p is determined in the ollowing simpliying hypothesis: - the ylinder strains are elasti; - the abrasive partiles are rigid, thus, the distribution irle o the ovoid big spheres enters is onentri with the deinite irle o the ylinder speii to the rition ouple - The abrasive partiles number upon the unit ontat length o the ouple is big ( 4 order o magnitude) and the wrapping angle is small ( ), thus, it is aepted that the abrasive partiles number loaded by the exterior harge (F) is a (α) ontat angle ontinuous untion Knowing that between the ore into a ertain point, situated at the α angular distane and the elasti strain, there is a Hertzian relation as: 3/ Fα = δ () where is the Hertzian rigidity in the speii point, being aepted as onstant all along the irular ontat length o the ylinder with the hard partiles I the strain law is known, the speii ore an be dedued For the aepted ase, with the big spheres enters o the ovoid situated on a irle, the ollowing expression is proposed: δ : = A os( α + Φ) (3) F a, R ap, 5, 5 F a, R ap, 5, 5 F a, R ap, 5, R ap Fig 4 Variation o dimensionless load vs relative ovoid radius 3 ELASTIC LOADING CAPACITY OF CYLINDER To evaluate the elasti loading apaity between the rigid, ovoid partile, and the elasti sphere ontat it shall be used the Tresa or von Mises plastiity riteria [, 5] I = max σ σ, σ σ, σ σ (5) T Fa 3 3 IM = ( σ σ) + ( σ σ3) + ( σ3 σ ) where σ, σ, σ 3 are the main non-dimensional stresses in the ontat entre p o The ondition or low avoidane, evaluated with axial low strength σ, is: po σ or po σ I I T ξ = 5 ξ = ξ = 3 ψ = χ = 5 M (5 )

4 4 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN -459 It an be deined the elasti loading apaity o the sphere-rigid ovoid ontat as p o /σ ratio For the untion harateristis (rition oeiient, ontat angle β) situated on the /IM urve, it an be evaluated the elasti loading apaity p o /σ For the untion harateristis situated above the /I M urve, the deormation state is plasti and the stresses and deormation state an be determined with the plastiity theory For the untion harateristis situated under the /I M urve, the wear partile appearane is deined by the elasti atigue ater a speii yle number (Wöhler urve type) Regarding the ritial deormations o the transition rom elasti state to the plasti one, it is onsidered the penetration (the intererene) o the p o pressure, or whih the von Mises invariant reahes the limit value Thus, using the Hertz equation system an obtain: h π po π σ Eo har = = ( hk) = = Rr Eo IM (6) For higher h ar values, the deormations are plasti and they are determined with the Henky s slip-lines When the untional onditions determine the abrasive, rigid partile to reate on the ounter piee (sphere or plane tablet) plasti deormations, the lowing limit o the equivalent stress is reahed, evaluated using the von Mises or Tresa parameter The elasti loading apaity is deined that the maximum ontat pressure (p max ) whih realizes the elastiity strength o materials We onsider that dimensionless parameter (p omax ) as a report o the maximum ontat pressure and the yielding strength o material For example, igure 5 shows the elasti loading apaity as a untion to rition oeiient, or some loal ontat point onditions (relative depth o ylinder z/a - a Hertzian radius:,, ) Fig 5 Elasti loading apaity vs rition oeiient The durability o rition pair with elasti strain an be evaluated by the atigue Wőhler urve type A hypotheses is made, aepted by many researhes [4, 5], that or a speii normal and tangential ore, the rigid abrasive partile has a plasti penetration in the ontra-piee, until the ontat area beomes suiient large, thus, the deormations gets elasti 4 THE WEAR MODEL FOR PLASTICALLY CONTACT To evaluate the ontat surae o a rigid partile with a plane plasti deormed, the Henky s slip-line method is used It is onsidered the plasti strain state The ovoid partiles rom the gap determine dierent ontat angles with the ylinder The partiles eets upon the strain state are determined by the adhesion angle, deined by rition angle,, and the attak angle (α) [6, 7, 8] The ollowing angles are deined, whih are speii to strain Henky lines: ( ) ε = 5 aos ; φ = α ε ; sin( α ) η = asin For the speii onditions o the ontat between a small sphere (mirometri radius) and a ylinder (millimeter radius), it is determined the wear proess by Arhard oeiient Funtion to utting (α) and adhesion (ε) angles an be analyze two ases When utting angle α<ε, the Arhard s wear parameter has expression [5] 3 γ ka = sin( ε) sin( α) + γ r pan π + 5 sin( α) os ( α) + sin( α) tan η where ( α ) + os( ε α ) ( α ) + sin( ε α ) = A sin n = A os n π A n = + + ε α η The shearing deormation sin( φ ) γ = sin ε sin ε sin α (7) and yielding strain by tangential stress γ = E m / τ with the melting energy per unite o volum e (E m ), and yielding strength (τ ) The Arhard s wear parameter, or the utting angle, α>ε, will be ( 5 sin( α ) sin( α) ) 35 γ ka = + (8) γ Figure 6 shows the Arhard s wear parameter as a untion to utting angle o abrasive partile or three materials yielding strain

5 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN ka Fig 6 Arhard wear parameter vs utting angle When the utting angle or other parameter is a random variable, it is neessary to analise the eet o probabilisti parameter about wear parameter or rition oeiient [] We deine the wear randomly parameter (I w ), x max x min ( ) I = k x,x,,x x x dx (9) w A n p m when k A (x,x,,x n ) is the Arhard s deterministi wear parameter or the x, x,, x n variable; p (x) requeny untion o stohasti x variable; xm- statisti media o x variable; x min, x max minimum and maximum o stohasti x variable In this paper, we apply this onept to the utting angle, that a stohasti variable The exponential and normal probabilisti laws appear in some tribologial phenomena [, 7, 8] a) The exponential law The requeny untion o utting angle (α) is e ( α ) = exp( α B) () when, the onstant B will be evaluted by the normating rule o requeny untion (th e sume o all probabilisti event is %) The igure 7 shows the eet o rition oeiient about wear random parameter, or some dimensionless nominal ontat pressure, when yielding strain by tangential stress γ = Iwe γ = o α max = 3 α = 3 o med p a = 5 γ r = γ r = 8 = p an = Fig7 Wear exponential random parameter vs adhesion parameter α p a = 5 p = a γ r = 6 It an see, rom igure 8, that the ontat pressure inrea ses proportional the random wear parameter The wear parameter dereas or inreas, when the statisti parameters o utting angle are variable For example, igure 9 shows the eet o variation o the maximum utting angle, when minimum angle is onstant b) The Gauss normal law The requeny untion o utting angle (α) is α α m pn ( α ) = exp π σ α when σ α is standard deviation o utting angle Iwe p a = 3 Fig 8 Wear exponential random parameter vs dimensionless ontat pressure Iwe γ = α max = 3 o α mi = o n p a = α max, o = = = γ r = α m = p = a () Fig 9 Eet o maximum statisti angle about wear random parameter We aept the rule o the 6 th σ α or the maximum and minimum statisti utting angle, when the media and standard deviation are known αmin = αm 3 σα αmax = αm + 3 σα Thus, or example, the wear random parameter as a untion to the adhesion parameter and to the ontat pressure are shown in igure and igure

6 6 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI FASCICLE VIII, 7 (XIII), ISSN -459 IwN Fig Wear normal Gauss random parameter vs adhesion parameter The eet o standard angle deviation (σ α ) about Arhard s wear parameter is shown in igure IwN γ r = σ σ = 3 p a = 3 γ r = σ σ = 3 p a = = p a = = 5 = p a Fig Wear normal Gauss randomly parameter vs ontat pressure 4 CONCLUSIONS Abrasion due to miro-utting by the hard partile sharp edges or its roughness is one important orme to limte the durability o rition pairs Signiiant progress has been made in alulating how miro-mehanial ontats strain a wearing surae and estimating how this may be related to wear rates The abrasive partile is onsidered to be an ovoid, haraterised by two spherial segments and the distane between the spheres entre The partile number o ovoid has been evaluated to relative learane o bearing and radius o ovoid partile It is determined the maximum non-dimensional elasti load supported by the ylinder in ontat with abrasive ovoid The work presented here shown that ovoid partiles an be introdued in onvergent joint and the eet o these partiles on strain and stress The elasti loading apaity o rition pair is evaluated by Tresa or von Mises parameter The durability o rition pair with elasti strain an be evaluated by the atigue Wőhler urve type For higher penetration (intererene) values, the deormations are plasti and they are determined with the Henky s slip-lines The partile eets upon the strain state are determined by the adhesion angle Arhard s wear oeiient an be alulated or plasti ontats as a untion to utting angle and adhesion angle The exponential and normal probabilisti laws are exempliied to analyze the wear parameter The random wear oeiient is predited and an be used to determine the durability o rition pairs REFERENCES Fig Wear normal Gauss randomly parameter vs standard angle deviation It an be notied that the Arhard s wear parameter inreases verry rapidly with the standard deviation I the wear randomly parameter is known, it is possible to estimate the durability o rition pairs, as a untion o geometrial aspets Ikramov, VA, 987, Rasetni metod otenki abrazvovo iznosa, Moskva, Masinostroenie (in Russian) Tudor, A, 99, Contatul real al supraetlor upleor de reare, Buuresti, Editura Aademiei Române (in Rumanian) 3 Kato K, 99, Miro-mehanisms o wear- wear modes, Wear 53, pp Xie, Y Williams, JA, 993, The generation o worn suraes by the repeated interation o parallel grooves, Wear, vol 6-64 pp Maugis, D,, Contat, adhesion and rupture o elasti solid Springer 6 Kopalinsky, EM, Oxley, PLB 995, Explain the mehanis o metalli sliding rition and wear in terms o slip line ield models o asperity deormation, Wear vol 9, pp Laey, P, Torrane AA, 99, The alulation o wear oeiient or plasti ontat, Wear, vol 45, pp Torrane, AA, Bukley, TR, 996, A slip-line ield model o abrasive wear, Wear, vol 96, pp 35-45