Spring (device)

Classification

Springs can be classified depending on how the load force is applied to them.

Tension/extension spring

The spring is designed to operate with a tension load, so the spring stretches as the load is applied to it.

Helical coil springs designed for tension.

Tension springs in a folded line reverberation device.

Compression spring

Designed to operate with a compression load, so the spring gets shorter as the load is applied to it.

Torsion spring

Unlike the above types in which the load is an axial force, the load applied to a torsion spring is a torque or twisting force, and the end of the spring rotates through an angle as the load is applied.^[7] Often used in torsion bar vehicle suspension systems.

There are many other ways to potentially classify and subclassify springs, such as their shape - coil springs are common, but so are leaf springs, for example. Garter springs are arc springs with a specific arc in mind; both are typically made by bending a coil spring into a position.

Common types

The most common types of spring are:

Balance spring

Also known as a hairspring. A delicate spiral spring used in watches, galvanometers, and places where electricity must be carried to partially rotating devices such as steering wheels without hindering the rotation.

Cantilever spring

A flat spring fixed only at one end like a cantilever, while the free-hanging end takes the load.

Coil spring

Also known as a helical spring. A spring (made by winding a wire around a cylinder) is of two types.

• Tension or extension springs are designed to become longer under load. Their turns (loops) are normally touching in the unloaded position, and they have a hook, eye or some other means of attachment at each end.
• Compression springs are designed to become shorter when loaded. Their turns (loops) are not touching in the unloaded position, and they need no attachment points.

Arc spring

A pre-curved or arc-shaped helical (coiled) compression spring, which is able to transmit a torque around an axis.

Garter spring

An arc spring where the arc is a full circle. They can be compression or extension springs.

Volute spring

A volute spring. Under compression the coils slide over each other to afford longer travel.

Vertical volute springs of a Stuart tank

A coil spring in the form of a cone so that under compression the coils are not forced against each other, thus permitting longer travel.

Hollow tubing spring

Can be either extension springs or compression springs. Hollow tubing is filled with oil and the means of changing hydrostatic pressure inside the tubing such as a membrane or miniature piston etc. to harden or relax the spring, much like it happens with water pressure inside a garden hose. Alternatively tubing's cross-section is chosen of a shape that it changes its area when tubing is subjected to torsional deformation: change of the cross-section area translates into change of tubing's inside volume and the flow of oil in/out of the spring that can be controlled by valve thereby controlling stiffness. There are many other designs of springs of hollow tubing which can change stiffness with any desired frequency, change stiffness by a multiple or move like a linear actuator in addition to its spring qualities.

Leaf spring

A flat spring used in vehicle suspensions, electrical switches, and bows.

V-spring

Also known as Chevron spring.^[8][9] Used in antique firearm mechanisms such as the wheellock, flintlock and percussion cap locks. Also used as a door-lock spring, such as in antique door latch mechanisms.^{[10][failed verification]}

• 
  A spiral torsion spring, or hairspring, in an alarm clock.
• 
  A heavy-duty coil spring designed for compression
• 
  The English longbow – a simple but very powerful spring made of yew, measuring 2 m (6 ft 7 in) long, with a 470 N (105 lbf) draw weight, with each limb functionally a cantilever spring and the entire bow acting as an extension arc spring.
• 
  Selection of various arc springs and arc spring systems (systems consisting of inner and outer arc springs).
• 
  Leaf spring on a truck

Other types

Other types include:

Belleville washer

A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated landmines)

Constant-force spring

A tightly rolled ribbon that exerts a nearly constant force as it is unrolled

Gas spring

A volume of compressed gas.

Ideal spring

An idealised perfect spring with no weight, mass, damping losses, or limits, a concept used in physics. The force an ideal spring would exert is exactly proportional to its extension or compression.^[11]

Mainspring

A spiral ribbon-shaped spring used as a power store of clockwork mechanisms: watches, clocks, music boxes, windup toys, and mechanically powered flashlights

Negator spring

A thin metal band slightly concave in cross-section. When coiled it adopts a flat cross-section but when unrolled it returns to its former curve, thus producing a constant force throughout the displacement and negating any tendency to re-wind. The most common application is the retracting steel tape rule.^[12]

Progressive rate coil springs

A coil spring with a variable rate, usually achieved by having unequal distance between turns so that as the spring is compressed one or more coils rests against its neighbour.

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.

Wave spring

various types of spring made compact by using waves to give a spring effect.

Hooke's law

An ideal spring acts in accordance with Hooke's law, which states that the force with which the spring pushes back is proportional to the distance from its equilibrium length: $${\displaystyle F=-kx}$$ where

x is the displacement vector – the distance from its equilibrium length.

F is the resulting force vector – the magnitude and direction of the restoring force the spring exerts

k is the rate, spring constant or force constant of the spring, a constant that depends on the spring's material and construction. The negative sign indicates that the force the spring exerts is in the opposite direction from its displacement

Most real springs approximately follow Hooke's law if not stretched or compressed beyond their elastic limit.

Coil springs 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 nonlinearly with displacement.

If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.

Simple harmonic motion

Since force is equal to mass, m, times acceleration, a, the force equation for a spring obeying 's law looks like:

${\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,}$

The mass of the spring is small in comparison to the mass of the attached mass and is ignored. Since acceleration is simply the second derivative of x with respect to time,

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

This is a second order linear differential equation for the displacement ${\displaystyle x}$ as a function of time. Rearranging:

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

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

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

${\displaystyle A}$ and ${\displaystyle B}$ are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with ${\displaystyle B=0}$ (zero initial position with some positive initial velocity) is displayed in the image on the right.

Energy dynamics

In simple harmonic motion of a spring-mass system, energy will fluctuate between kinetic energy and potential energy, but the total energy of the system remains the same. A spring that obeys Hooke's law with spring constant k will have a total system energy E of:^[13] $${\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}}$$ Here, A is the amplitude of the wave-like motion that is produced by the oscillating behavior of the spring.

The potential energy U of such a system can be determined through the spring constant k and its displacement x:^[13] $${\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}}$$ The kinetic energy K of an object in simple harmonic motion can be found using the mass of the attached object m and the velocity at which the object oscillates v:^[13] $${\displaystyle K=\left({\frac {1}{2}}\right)mv^{2}}$$ Since there is no energy loss in such a system, energy is always conserved and thus:^[13] $${\displaystyle E=K+U}$$

Frequency & period

The angular frequency ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant k and the mass of the oscillating object m:^[14][13]

$${\displaystyle \omega ={\sqrt {\frac {k}{m}}}}$$

The period T, the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by:^[15][13]

$${\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {m}{k}}}}$$

The frequency f, the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period:^[13]

$${\displaystyle f={\frac {1}{T}}={\frac {\omega }{2\pi }}={\frac {\sqrt {k}}{2\pi {\sqrt {m}}}}}$$