Editing Rolling-element bearing (section)

=== Life calculation models ===
The life of a rolling bearing is expressed as the number of revolutions or the number of operating hours at a given speed that the bearing is capable of enduring before the first sign of metal fatigue (also known as [[spalling]]) occurs on the race of the inner or outer ring, or on a rolling element. Calculating the endurance life of bearings is possible with the help of so-called life models. More specifically, life models are used to determine the bearing size – since this must be sufficient to ensure that the bearing is strong enough to deliver the required life under certain defined operating conditions.

Under controlled laboratory conditions, however, seemingly identical bearings operating under identical conditions can have different individual endurance lives. Thus, bearing life cannot be calculated based on specific bearings, but is instead related to in statistical terms, referring to populations of bearings. All information with regard to load ratings is then based on the life that 90% of a sufficiently large group of apparently identical bearings can be expected to attain or exceed. This gives a clearer definition of the concept of bearing life, which is essential to calculate the correct bearing size. Life models can thus help to predict the performance of a bearing more realistically.

The prediction of bearing life is described in ISO 281<ref name="ISO281:2007" >{{Cite web
 |title=Rolling bearings -- Dynamic load ratings and rating life
 |publisher=ISO
 |year=2007
 |id=ISO281:2007
 |url=http://www.iso.org/iso/catalogue_detail.htm?csnumber=38102
}}</ref> and the [[ANSI]]/American Bearing Manufacturers Association Standards 9 and 11.<ref name="STLE, Zaretsky" />

The traditional life prediction model for rolling-element bearings uses the basic life equation:<ref name="MD, Bearing life" >{{Cite web
 |title=The meaning of bearing life
 |author=Daniel R. Snyder, SKF 
 |website=Machine Design
 |date=12 April 2007
 |url=http://machinedesign.com/bearings/meaning-bearing-life
}}</ref>

<math display="block">
L_{10} = (C/P)^p
</math>

Where:
* <math>L_{10}</math> is the 'basic life' (usually quoted in millions of revolutions) for a reliability of 90%, i.e. no more than 10% of bearings are expected to have failed
* <math>C</math> is the dynamic load rating of the bearing, quoted by the manufacturer
* <math>P</math> is the equivalent dynamic load applied to the bearing
* <math>p</math> is a constant: 3 for ball bearings, 4 for pure line contact and 3.33 for roller bearings

Basic life or <math>L_{10}</math> is the life that 90% of bearings can be expected to reach or exceed.<ref name="ISO281:2007" /> The median or average life, sometimes called [[Mean Time Between Failure]] (MTBF), is about five times the calculated basic rating life.<ref name="MD, Bearing life" />
Several factors, the '[[ASME]] five factor model',<ref name="STLE, ISO281" /> can be used to further adjust the <math>L_{10}</math> life depending upon the desired reliability, lubrication, contamination, etc.

The major implication of this model is that bearing life is finite, and reduces by a cube power of the ratio between design load and applied load. This model was developed in 1924, 1947 and 1952 work by [[:sv:Arvid Palmgren|Arvid Palmgren]] and Gustaf Lundberg in their paper ''Dynamic Capacity of Rolling Bearings''.<ref name="STLE, ISO281" /><ref name="eBearing, ISO281" /> The model dates from 1924, the values of the constant <math>p</math> from the post-war works. Higher <math>p</math> values may be seen as both a longer lifetime for a correctly-used bearing below its design load, or also as the increased rate by which lifetime is shortened when overloaded.

This model was recognised to have become inaccurate for modern bearings. Particularly owing to improvements in the quality of bearing steels, the mechanisms for how failures develop in the 1924 model are no longer as significant. By the 1990s, real bearings were found to give service lives up to 14 times longer than those predicted.<ref name="STLE, ISO281" /> An explanation was put forward based on [[fatigue life]]; if the bearing was loaded to never exceed the [[fatigue strength]], then the Lundberg-Palmgren mechanism for failure by fatigue would simply never occur.<ref name="STLE, ISO281" /> This relied on homogeneous [[vacuum-melted steel]]s, such as [[AISI 52100]], that avoided the internal inclusions that had previously acted as stress risers within the rolling elements, and also on smoother finishes to bearing tracks that avoided impact loads.<ref name="STLE, Zaretsky" /> The <math>p</math> constant now had values of 4 for ball and 5 for roller bearings. Provided that load limits were observed, the idea of a 'fatigue limit' entered bearing lifetime calculations. If the bearing was not loaded beyond this limit, its theoretical lifetime would be limited only by external factors, such as contamination or a failure of lubrication.

A new model of bearing life was put forward by [[Schaeffler Group|FAG]] and developed by [[SKF]] as the Ioannides-Harris model.<ref name="eBearing, ISO281" >{{Cite web
 |title=ISO Adopts SKF Bearing Life Calculations 
 |website=eBearing News
 |date=28 June 2006 
 |url=http://www.ebearing.com/news2006/062801.htm
}}</ref><ref name="Ioannides-Harris" >{{Cite journal
 |first1=Stathis |last1=Ioannides |first2=Ted |last2=Harris 
 |publisher=SKF 
 |year=1985
 |title=A New Fatigue Life Model for Rolling Bearings
}}</ref> ISO 281:2000 first incorporated this model and ISO 281:2007 is based on it.

The concept of fatigue limit, and thus ISO 281:2007, remains controversial, at least in the US.<ref name="STLE, Zaretsky">{{Cite journal
 |title = In search of a fatigue limit: A critique of ISO standard 281:2007
 |author = Erwin V. Zaretsky
 |date = August 2010
 |journal = Tribology & Lubrication Technology
 |pages = 30–40
 |url = http://www.stle.org/assets/document/8-10_tlt_commentary_ISO_Standard_281_2007_Part_II.pdf
 |publisher = Society of Tribologists and Lubrication Engineers (STLE)
 |url-status = dead
 |archive-url = https://web.archive.org/web/20150518100537/http://www.stle.org/assets/document/8-10_tlt_commentary_ISO_Standard_281_2007_Part_II.pdf
 |archive-date = 2015-05-18
|author-link = Erwin V. Zaretsky
 }}</ref><ref name="STLE, ISO281">{{Cite journal
 |title = ISO 281:2007 bearing life standard – and the answer is?
 |date = July 2010
 |journal = Tribology & Lubrication Technology
 |pages = 34–43
 |url = https://www.stle.org/assets/document/tlt_July_cover_story_article.pdf
 |publisher = Society of Tribologists and Lubrication Engineers (STLE)
 |url-status = dead
 |archive-url = https://web.archive.org/web/20131024084224/http://www.stle.org/assets/document/tlt_July_cover_story_article.pdf
 |archive-date = 2013-10-24
}}</ref>