Spring (device)

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Helical or coil springs designed for tension

A spring is a flexible 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 annealed steel and hardened after fabrication. Some 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 of a spring is the change in the force it exerts, divided by the change in deflection of the spring. That is, it is the gradient of the force versus deflection curve. For an extension or compression spring it has the units of lbf/in, N/mm, or similar. For a torsion spring it has the units of N·m/rad or ft·lbf/degree, for example. 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, as is the compliance of springs in series.

1 History
2 Types
3 Physics
- 3.1 Hooke's law
- 3.2 Simple harmonic motion
4 Theory
5 Popular mechanics
6 Uses
7 References
8 External links

[edit] History

Simple non-coiled springs were used throughout human history e.g. the bow (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of tweezers in many cultures. The Greek engineer 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.^[1]

[edit] Types

A spiral hair spring

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:

Cantilever spring - a spring which is fixed only at one end.

Coil spring or helical spring - a spring (made by winding a wire around a cylinder) and the 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 more legnth to be shortened.
- 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.

Vertical volute springs of Stuart tank

Hairspring or balance spring - a delicate spiral torsion spring used in watches, galvanometers, and places where electricity must be carried to partially-rotating devices such as steering wheels without hindering the rotation.

Leaf spring - a flat springy sheet, used in vehicle suspensions, electrical switches, bows.

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 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 watches, clocks, music boxes, windup toys, and mechanically powered flashlights

Rubber band - a tension spring where energy is stored by stretching the material.

Spring washer - used to apply a constant tensile force along the axis of a fastener.

A torsion bar twisted under load

Torsion spring - any spring designed to be twisted rather than compressed or extended. Used in 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.

Wave spring - a high stiffness spring ^[2]

[edit] Physics

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_eq=k₁+k₂.

[edit] Hooke's law

Main article: Hooke's law

Springs that are not stretched or compressed beyond their 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:

$F=-kx, \$

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.

[edit] Simple harmonic motion

Main article: Harmonic oscillator

Since force is equal to mass, m, times acceleration, a, the force equation looks like:

$F = - k x = m a. \,$

The displacement, x, as a function of time. The amount of time that passes between peaks is called the period.

But acceleration is just the second time derivative of x, so

$- k x = m \frac{d^2 x}{dt^2}. \,$

Re-arranging results in a differential equation

$\frac{d^2 x}{dt^2} + \frac{k}{m} x = 0, \,$

the solution of which is the sum of a sine and cosine:

$x(t) = A \sin \left( t \sqrt{\frac{k}{m}} \right) + B \cos \left(t \sqrt{\frac{k}{m}} \right). \,$

The graph of this function is displayed in the image on the right.

[edit] Theory

In classical physics, a spring can be seen as a device that stores potential energy by straining the bonds between the atoms of an elastic material.

Hooke's law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension, the force used to stretch it. Similarly, the contraction (negative extension) is proportional to the 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 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 — which is the derivative of energy with respect to displacement — will approximate a linear function.

[edit] Popular mechanics

Contrary to popular belief, springs do not appreciably "creep" or get "tired" with age.^{[citation needed]} 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 exibit 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.