Spring (device) 316617 223874134 2008-07-06T07:52:26Z 216.86.113.233 io [[Image:Springs 009.jpg|thumb|right|250px|[[Helix|Helical]] or ''coil'' springs designed for tension]] A '''spring''' is a flexible [[Elasticity (physics)|elastic]] object used to store mechanical [[energy]]. Springs are usually made out of [[hardened steel]]. Small springs can be wound from pre-hardened stock, while larger ones are made from [[annealing (metallurgy)|annealed]] steel and hardened after fabrication. Some [[ferrous|non-ferrous metals]] are also used including [[phosphor bronze]] and [[titanium]] for parts requiring corrosion resistance and [[beryllium copper]] for springs carrying electrical current (because of its low electrical resistance). The [[rate (mathematics)|rate]] of a spring is the change in the [[force]] it exerts, divided by the change in [[deflection (engineering)|deflection]] of the spring. That is, it is the [[gradient]] of the force versus deflection [[curve]]. An [[tension (physics)|extension]] or [[physical compression|compression]] spring has units of force divided by distance, for example lbf/in or N/m. [[torsion spring|Torsion springs]] have units of force multiplied by distance divided by angle, such as [[newton metre|N·m]]/[[radian|rad]] or [[ft·lbf]]/degree. The inverse of spring rate is compliance, that is if a spring has a rate of 10 N/mm, it has a compliance of 0.1 mm/N. The stiffness (or rate) of springs in parallel is [[additive function|additive]], as is the compliance of springs in series. ==History== Simple non-coiled springs were used throughout human history e.g. the [[Bow (weapon)|bow]] (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of tweezers in many cultures. [[Ctesibius of Alexandria]] developed a method for making [[bronze]] with spring-like characteristics by producing an alloy of bronze with an increased proportion of tin, and then hardening it by hammering after it is cast. [[Coiled springs]] were introduced in the 15th century.<ref>[http://www.madehow.com/Volume-6/Springs.html Springs] How Products Are Made, 14 July 2007.</ref> The first spring-powered [[pocket watch]] was created by [[Peter Henlein]] in 1524, followed by the first spring-powered [[clock]]s by Henlein and [[Taqi al-Din]] in 1556, and the first spring-powered [[astronomical clock]] by al-Din in 1559.<ref name=Hassani>{{cite web|author=[[Salim Al-Hassani]]|title=The Astronomical Clock of Taqi Al-Din: Virtual Reconstruction|publisher=FSTC|url=http://muslimheritage.com/topics/default.cfm?ArticleID=947|date=19 June 2008|accessdate=2008-07-02}}</ref><ref name=Hill>{{cite web|author=[[Donald Routledge Hill]] and [[Ahmad Y Hassan]]|title=Engineering in Arabic-Islamic Civilization|url=http://www.history-science-technology.com/Articles/articles%2011.htm|work=History of Science and Technology in Islam|accessdate=2008-07-03}}</ref> ==Types== [[Image:Montre Tribaudeau Besancon 01.jpg|thumb|right|250px|A spiral hair spring]] [[Image:volute spring.jpg|thumb|right|250px|A volute spring. Under compression the coils slide over each other, so affording longer travel.]] Springs are classified according some of its properties. Depending on load it can classifies as: *Tension/Extension spring *Compression spring *Torsional spring In tension/extension and compression there is axial load. On the other hand in the torsional spring there is torsional force. Depending on spring material it can be classified as: *Wire/Coil spring *Flat spring The most common types of spring are: *[[springboard|Cantilever spring]] - a spring which is fixed only at one end. *[[Coil spring]] or [[helix|helical]] spring - a spring (made by winding a wire around a cylinder) and the [[Cone (geometry)|conical]] spring - these are types of [[torsion spring]], because the wire itself is twisted when the spring is compressed or stretched. These are in turn of two types: **''Compression springs'' are designed to become shorter when loaded. Their turns are not touching in the unloaded position, and they need no attachment points. ***A ''[[volute]]'' spring is a compression spring in the form of a cone, designed so that under compression the coils are not forced against each other, thus permitting longer travel. **''Tension springs'' are designed to become longer under load. Their turns are normally touching in the unloaded position, and they have a hook, eye or some other means of attachment at each end. [[Image:Volutespring.jpg‎|right|thumb|Vertical volute springs of [[Stuart tank]]]] * Hairspring or [[balance spring]] - a delicate spiral torsion spring used in [[watch]]es, [[galvanometer]]s, and places where electricity must be carried to partially-rotating devices such as [[steering wheel]]s without hindering the rotation. *[[Leaf spring]] - a flat springy sheet, used in vehicle [[suspension (vehicle)|suspension]]s, electrical [[switch]]es, [[bow (weapon)|bow]]s. [[Image:leafs1.jpg|right|thumb|250px|Leaf spring on a truck]] * [[V-spring]] - used in antique [[firearm]] mechanisms such as the [[wheellock]], [[flintlock]] and [[percussion cap]] locks. Other types include: *[[Belleville washer]] or Belleville spring - a disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated [[land mine|landmines]]). *[[Gas spring]] - a volume of gas which is compressed. *[[Ideal Spring]] - the notional spring used in physics: it has no weight, mass, or damping losses. *[[Mainspring]] - a spiral ribbon shaped spring used as a power source in [[watch]]es, [[clock]]s, [[music box]]es, windup [[toy]]s, and [[mechanically powered flashlight]]s *[[Rubber band]] - a tension spring where energy is stored by stretching the material. *Spring [[Washer (mechanical)|washer]] - used to apply a constant tensile force along the axis of a [[fastener]]. [[Image:Torsion-Bar with-load.jpg|thumb|right|A torsion bar twisted under load]] *[[Torsion spring]] - any spring designed to be twisted rather than compressed or extended. Used in [[Torsion beam suspension|torsion bar]] vehicle suspension systems. *[[Negator spring]] - a thin flat metal band that is coiled similar to a tape rule. This type of spring produces a constant force throughout a long displacement.<ref>[http://www.sdp-si.com/eStore/CoverPg/Springs.htm Springs]</ref> *[[Wave spring]] - a high stiffness spring <ref>[http://www.smalley.com/wave_springs/about_springs.asp Smalley Steel Ring Co. Retaining Rings, Snap Rings and Wave Springs - About Our Springs<!-- Bot generated title -->]</ref> ==Physics== [[Image:SpringsInParallel.svg|right|thumb|280px|Two springs attached to a wall and a mass. In a situation like this, the two springs can be replaced by one with a spring constant of ''k''<sub>eq</sub>=''k''<sub>1</sub>+k<sub>2</sub>.]] ===Hooke's law=== {{main|Hooke's law}} Most springs (not stretched or compressed beyond the [[elastic limit]]) obey Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length: :<math> F=-kx, \ </math> where : ''x'' is the displacement vector - the distance and direction in which the spring is deformed : ''F'' is the resulting force vector - the magnitude and direction of the restoring force the spring exerts : ''k'' is the '''spring constant''' or '''force constant''' of the spring. [[Coil spring]]s and other common springs typically obey Hooke's law. There are useful springs that don't: springs based on beam bending can for example produce forces that vary [[nonlinear]]ly with displacement. There are also linear springs which don't follow Hooke's law: a Negator spring (the spring that a self retracting [[tape measure]] uses) provides a constant force.{{Fact|date=June 2008}} ===Simple harmonic motion=== {{main|Harmonic oscillator}} Since force is equal to mass, ''m'', times acceleration, ''a'', the force equation for a spring obeying [[Hooke's law]] looks like: :<math>F = m a \quad \Rightarrow \quad -k x = m a. \,</math> [[Image:Periodampwave.svg|thumb|right|280px|The displacement, ''x'', as a function of time. The amount of time that passes between peaks is called the [[Wave period|period]].]] The mass of the spring is assumed small in comparison to the mass of the attached mass and is ignored. Since acceleration is just the second time [[derivative]] of x, :<math> - k x = m \frac{d^2 x}{dt^2}. \,</math> This is a second order linear [[differential equation]] for the displacement <math>x</math> as a function of time. Rearranging: :<math>\frac{d^2 x}{dt^2} + \frac{k}{m} x = 0, \,</math> the solution of which is the sum of a [[sine]] and [[cosine]]: :<math> x(t) = A \sin \left( t \sqrt{\frac{k}{m}} \right) + B \cos \left(t \sqrt{\frac{k}{m}} \right). \, </math> <math>A</math> and <math>B</math> are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with <math>B = 0</math> (zero initial position with some positive initial velocity) is displayed in the image on the right. ==Theory== In [[classical physics]], a spring can be seen as a device that stores [[potential energy]] by straining the bonds between the [[atom]]s of an [[Elasticity (physics)|elastic]] material. [[Hooke's law]] of [[theory of elasticity|elasticity]] states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its [[Tension (mechanics)|tension]], the [[force]] used to stretch it. Similarly, the contraction (negative extension) is proportional to the [[Physical compression|compression]] (negative tension). This law actually holds only approximately, and only when the deformation (extension or contraction) is small compared to the rod's overall length. For deformations beyond the [[Tensile strength|elastic limit]], atomic bonds get broken or rearranged, and a spring may snap, buckle, or permanently deform. Many materials have no clearly defined elastic limit, and Hooke's law can not be meaningfully applied to these materials. Hooke's law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. Any smooth function of one variable approximates a [[quadratic function]] when examined near enough to its minimum point; and therefore the force &mdash; which is the [[derivative]] of energy with respect to displacement &mdash; will approximate a [[linear function]]. == Popular mechanics == Contrary to popular belief, springs do not appreciably "[[Creep (deformation)|creep]]" or get "tired" with age alone.{{Fact|date=September 2007}} Spring steel has a very high resistance to creep under normal loads. For instance, in a car engine, valve springs typically undergo about a quarter billion cycles of compression-decompression over the engine's life time and exhibit no noticeable change in length or loss of strength. But for good measure, springs can be replaced when doing a valve job. The sag observed in some older [[automobiles]] suspension is usually due to the springs being occasionally compressed beyond their yield point, causing plastic deformation. This can happen when the vehicle hits a large bump or pothole, especially when heavily loaded. Most vehicles will accumulate a number of such impacts over their working life, leading to a lower ride height and eventual bottoming-out of the suspension. In addition, frequent exposure to road salt accelerates corrosion, leading to premature failure of the springs in the car's suspension. Weakening of a spring is usually an indication that it is close to complete failure. <!--Must explain how torsion and bending springs work, i.e. how they can be analyzed in terms of infinitesimal rod springs, and that they too satisfy Hooke's law. Must also note that a helical spring is a torsion spring, not a simple rod spring. --> ==Uses== *[[Vehicle suspension]] *[[Slinky]] *[[Pogo Stick]] *[[Dashpot]] ==References== {{reflist}} ==External links== {{wikibooks|Physics Study Guide|Springs}} {{commons|Spring (device)|Spring (device)}} *{{cite web |last=Wright |first=Douglas |title=Introduction to Springs |work=[http://www.mech.uwa.edu.au/DANotes/springs/home.html Springs], [http://www.mech.uwa.edu.au/DANotes/ Notes on Design and Analysis of Machine Elements] |publisher=Dept. of Mechanical & Material Engineering, Univ. of Western Australia |url=http://www.mech.uwa.edu.au/DANotes/springs/intro/intro.html |accessdate=2008-02-03}} *{{cite web |last=Silberstein |first=Dave |date=2002 |title=How to make springs |publisher=[http://home.earthlink.net/~bazillion/ Bazillion] |url=http://home.earthlink.net/~bazillion/intro.html |accessdate=2008-02-03}} *[http://www.allrite.com/compdwg.pdf Design A Compression Spring] *[http://www.spring-makers-resource.net/index.html The Resource for Spring Design and Manufacture] [[Category:Springs (mechanical)]] [[af:Veer (toestel)]] [[ar:زنبرك]] [[cs:Pružina]] [[da:Fjeder]] [[de:Feder (Technik)]] [[es:Muelle elástico]] [[eo:Risorto]] [[fa:فنر]] [[fr:Ressort]] [[gl:Resorte]] [[io:Resorto]] [[it:Molla]] [[he:קפיץ]] [[nl:Veer (mechanica)]] [[ja:ばね]] [[no:Fjær (teknikk)]] [[nds:Fedder (Mechanik)]] [[pl:Sprężyna]] [[pt:Mola]] [[ru:Пружина]] [[sk:Pružina]] [[sl:Vzmet]] [[fi:Vieteri]] [[sv:Fjäder (teknik)]] [[vi:Lò xo]] [[tr:Yay (makina elemanı)]] [[zh:弹簧]]