Stick–slip phenomenon

File:Static_kinetic_friction_vs_time.png

With stick–slip there is typically a jagged type of behavior for the friction force as a function of time as illustrated in the static kinetic friction figure. Initially there is relatively little movement and the force climbs until it reaches some critical value which is set by the multiplication of the static friction coefficient and the applied load—the retarding force here follows the standard ideas of friction from Amontons' laws. Once this force is exceeded movement starts at a much lower load which is determined by the kinetic friction coefficient which is almost always smaller than the static coefficient. At times the object moving can get 'stuck', with local rises in the force before it starts to move again. There are many causes of this depending upon the size scale, from atomic to processes involving millions of atoms.{{Cite book |last=Persson |first=Bo N. J. |url=http://link.springer.com/10.1007/978-3-662-03646-4 |title=Sliding Friction |date=1998 |publisher=Springer Berlin Heidelberg |isbn=978-3-662-03648-8 |series=NanoScience and Technology |location=Berlin, Heidelberg |doi=10.1007/978-3-662-03646-4}}{{Cite book |last1=Gnecco |first1=Enrico |title=Elements of friction theory and nanotribology |last2=Meyer |first2=Ernst |date=2015 |publisher=Cambridge university press |isbn=978-1-107-00623-2 |location=Cambridge}}

File:Stick-slip.svg

Stick–slip can be modeled as a mass coupled by an elastic spring to a constant drive force (see the model sketch). The drive system V applies a constant force, loading spring R and increasing the pushing force against load M. This force increases until retarding force from the static friction coefficient between load and floor is exceeded. The load then starts sliding, and the friction coefficient decreases to the value corresponding to load times the dynamic friction. Since this frictional force will be lower than the static value, the load accelerates until the decompressing spring can no longer generate enough force to overcome dynamic friction, and the load stops moving. The pushing force due to the spring builds up again, and the cycle repeats.

Stick–slip may be caused by many different phenomena, depending on the types of surfaces in contact and also the scale; it occurs with everything from the sliding of atomic force microscope tips to large tribometers. For rough surfaces, it is known that asperities play a major role in friction.{{Cite book |last1=Bowden |first1=Frank Philip |title=The friction and lubrication of solids |last2=Tabor |first2=David |date=2008 |publisher=Clarendon Pr |isbn=978-0-19-850777-2 |edition=Repr |series=Oxford classic texts |location=Oxford}} The bumping together of asperities on the surface creates momentary sticks. For dry surfaces with regular microscopic topography, the two surfaces may need to creep at high friction for certain distances (in order for bumps to move past one another), until a smoother, lower-friction contact is formed. On lubricated surfaces, the lubricating fluid may undergo transitions from a solid-like state to a liquid-like state at certain forces, causing a transition from sticking to slipping. On very smooth surfaces, stick–slip behavior may result from coupled phonons (at the interface between the substrate and the slider) that are pinned in an undulating potential well, sticking or slipping with thermal fluctuations.Bo N.J. Persson and Nicholas D. Spencer, "Sliding Friction: Physical Principles and Applications", Physics Today 52(1), 66 (1999); doi: 10.1063/1.882557 Stick–slip occurs on all types of materials and on enormously varying length scales.Ruina, Andy. "Slip instability and state variable friction laws.", Journal of Geophysical Research 88.B12 (1983): 10359-10 The frequency of slips depends on the force applied to the sliding load, with a higher force corresponding to a higher frequency of slip.{{cite journal|last1=Rabinowicz|first1=Ernest|date=May 1956|title=Stick and Slip|journal=Scientific American|volume=194|issue=5|pages=109–119 |doi=10.1038/scientificamerican0556-109 }}

Stick–slip motion is ubiquitous in systems with sliding components, such as disk brakes, bearings, electric motors, wheels on roads or railways, and in mechanical joints.{{cite book|last=Ding|first=Wenjing|title=Self-excited Vibration|year=2010|publisher=Springer Berlin, Heidelberg|isbn=978-3-540-69741-1|doi=10.1007/978-3-540-69741-1|pages=140–166}} Stick–slip also has been observed in articular cartilage in mild loading and sliding conditions, which could result in abrasive wear of the cartilage.D.W. Lee, X. Banquy, J. N. Israelachvili, Stick–slip friction and wear of articular joints, PNAS. (2013), 110(7): E567-E574 Many familiar sounds are caused by stick–slip motion, such as the squeal of chalk on a chalkboard, the squeak of basketball shoes on a basketball court, and the sound made by the spiny lobster.{{cite journal |author=S. N. Patek |year=2001 |journal=Nature |volume=411 |pages=153–154 |title=Spiny lobsters stick and slip to make sound |doi=10.1038/35075656 |pmid=11346780 |issue=6834|bibcode=2001Natur.411..153P |s2cid=4413356 }}{{Cite news|url=https://www.nytimes.com/2017/03/17/sports/ncaabasketball/squeaky-shoes-hardwood.html|title=Why Are Basketball Games So Squeaky? Consider the Spiny Lobster|last=Branch|first=John|date=2017-03-17|work=The New York Times|access-date=2017-03-19|issn=0362-4331}}

Stick–slip motion is used to generate musical notes in bowed string instruments, the glass harp{{cite journal|last1=Rossing|first1=Thomas D.|date=1994|title=Acoustics of the glass harmonica|journal=Journal of the Acoustical Society of America|volume=95|issue=2 |pages=1106–1111|doi=10.1121/1.408458

}} and the singing bowl.{{Cite journal |last1=Collin |first1=Samantha R |last2=Keefer |first2=Chloe L |last3=Moore |first3=Thomas R |name-list-style=amp |date=16–19 September 2015 |title=The Etiology of Chatter in the Himalayan Singing Bowl |url=http://viennatalk2015.mdw.ac.at/proceedings/ViennaTalk2015_submission_64.pdf |journal=Proceedings of the Third Vienna Talk on Music Acoustics |series=Bridging the Gaps |volume=138 |issue=3 |pages=120–123|doi=10.1121/1.4933928 |bibcode=2015ASAJ..138.1888K }}

Stick–slip can also be observed on the atomic scale using a friction force microscope. Atomic-scale friction of a tungsten tip on a graphite surface C.M. Mate, G.M. McClelland, R. Erlandsson, and S. Chiang Phys. Rev. Lett. 59, 1942 (1987) The behaviour of seismically active faults is also explained using a stick–slip model, with earthquakes being generated during the periods of rapid slip.{{cite book|last=Scholz|first=C.H.|title=The mechanics of earthquakes and faulting|url=https://books.google.com/books?id=JL1VM5wMbrQC&pg=PA82|access-date=6 December 2011|edition=2|year=2002|publisher=Cambridge University Press|isbn=978-0-521-65540-8|pages=81–84}}

• {{Annotated link |Contact mechanics}}
• {{Annotated link |Friction}}
• {{Annotated link |Lubrication}}
• {{Annotated link |Nanotribology}}
• {{Annotated link |Tribology}}
• {{Annotated link |Tribometer}}

• [https://www.youtube.com/watch?v=idlHxu7TTWU Simulation of stick-slip behaviour in a friction force microscope (movie)]
• [https://nanohub.org/resources/7771 Jianguo Wu, Ashlie Martini, "Atomic Stick-Slip," DOI: 10254/nanohub-r7771.1, 2009]

Category:Mechanical engineering

Category:Friction