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| The '''Archard wear equation''' is a simple [[mathematical model|model]] used to describe sliding [[wear]] and is based around the theory of [[Asperity (materials science)|asperity]] contact. The Archard equation was developed later than the [[Reye's hypothesis]], though both came to the same physical conclusions, that the volume of the removed debris due to wear is proportional to the work done by friction forces. Reye’s model<ref>{{cite journal |first=Th. |last=Reye |title= Zur Theorie der Zapfenreibung|journal=J. Der Civilingenieur |volume=4 |year=1860 |pages=235–255}}</ref> became very popular in Europe and it is still taught in university courses of applied mechanics. This theory has, however, been totally ignored in English and American literature where subsequent works by Ragnar Holm<ref>{{cite book |first=R.|last=Holm| title = Electrical Contacts |place= Stockholm |publisher = H. Gerber |year = 1946 }}</ref> and John F. Archard are usually cited.
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| ==Equation==
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| :<math>Q = \frac {KWL}H</math>
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| where:<ref>{{cite conference|title=Determination of Wear in a Tribo-System |first=Carrie K. |last=Harris |coauthors=Broussard, J.P.; Keska, J.K. |conference=ASEE Gulf-Southwestern Annual Conference |year=2002 |publisher=American Society for Engineering Education |location=Lafayette|url=http://www.chunbotech.co.kr/techinform/ti-03.pdf|accessdate=2009-06-09}}</ref>
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| : ''Q'' is the total volume of wear debris produced
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| : ''K'' is a dimensionless constant
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| : ''W'' is the total normal load
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| : ''L'' is the sliding distance
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| : ''H'' is the [[hardness]] of the softest contacting surfaces
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| Note that <math>WL</math> is proportional to the work done by the friction forces as described by Reye's hypothesis.
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| ==Derivation==
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| The equation can be derived by first examining the behavior of a single asperity.
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| :
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| The local load <math>\, \delta W </math>, supported by an asperity, assumed to have a circular cross-section with a radius <math>\, a </math>, is:
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| :<math>\delta W = P \pi {a^2} \,\!</math>
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| where ''P'' is the yield pressure for the asperity, assumed to be deforming plastically. ''P'' will be close to the indentation [[hardness]], ''H'', of the asperity.
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| If the volume of wear debris, <math>\, \delta V </math>, for a particular asperity is a hemisphere sheared off from the asperity, it follows that:
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| : <math> \delta V = \frac 2 3 \pi a^3 </math>
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| This fragment is formed by the material having slid a distance 2''a''
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| Hence, <math>\, \delta Q </math>, the wear volume of material produced from this asperity per unit distance moved is:
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| :<math> \delta Q = \frac {\delta V} {2a} = \frac {\pi a^2} 3 \equiv \frac {\delta W} {3P} \approx \frac {\delta W} {3H}</math> making the approximation that <math>\,P \approx H</math> | |
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| However, not all asperities will have had material removed when sliding distance 2''a''. Therefore, the total wear debris produced per unit distance moved, <math>\, Q </math> will be lower than the ratio of ''W'' to ''3H''. This is accounted for by the addition of a dimensionless constant ''K'', which also incorporates the factor 3 above. These operations produce the Archard equation as given above.
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| ''K'' is therefore a measure of the severity of wear. Typically for 'mild' wear, ''K'' ≈ 10<sup>−8</sup>, whereas for 'severe' wear, ''K'' ≈ 10<sup>−2</sup>.
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| ==References==
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| <references/>
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| ==Bibliography==
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| *{{cite journal |doi=10.1063/1.1721448 |first=J.F. |last=Archard |title=Contact and Rubbing of Flat Surface |journal=J. Appl. Phis. |volume=24 |issue=8 |year=1953 |pages=981–988}}
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| *{{cite journal |doi=10.1098/rspa.1956.0144 |first=J.F. |last=Archard |coauthors=Hirst, W.|date=1956-08-02 |title=The Wear of Metals under Unlubricated Conditions |journal=Proceedings of the Royal Society |volume=A-236 |pages=397–410}}
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| *{{cite book |title=Wear Control Handbook |last=Peterson |first=M.B. |coauthors=Winer, W.O. |year=1980 |publisher=[[American Society of Mechanical Engineers]] (ASME) |location=New York}}
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| *{{cite book |title = Friction, Lubrication, and Wear Technology |publisher = ASM Handbook |year = 1992 |isbn = 0-87170-380-7}}
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| {{DEFAULTSORT:Archard Equation}}
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| [[Category:Surfaces]]
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| [[Category:Materials science]]
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| [[Category:Equations]]
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Hi there, I am Yoshiko Villareal but I never truly favored that name. I am a manufacturing and distribution officer. He presently life in Arizona and his parents reside close by. Playing crochet is something that I've done for many years.
my blog - auto warranty (stay with me)