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Helical or coil springs designed for tension
Helical or coil springs designed for tension

A spring is a flexible elastic object used to store mechanical energy. A helix (pl helixes or helices) from the Greek word έλιξ, is a special kind of Space curve, i A material is said to be elastic if it deforms under stress (e In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Springs are usually made out of hardened steel. The term hardened steel is often used for a medium or high carbon Steel that has been given the heat treatments of Quenching followed by Tempering Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication. Annealing, in Metallurgy and Materials science, is a Heat treatment wherein a material is altered causing changes in its properties such as strength 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). Ferrous, in the chemical science realm indicates a bivalent iron compound (+2 oxidation state (as opposed to Ferric, which indicates a trivalent iron compound (+3 oxidation Phosphor bronze is an Alloy of Copper with 35 to 10% of Tin and a significant Phosphorus content of up to 1% Titanium (taɪˈteɪniəm is a Chemical element with the symbol Ti and Atomic number 22 Beryllium copper, also known as copper beryllium, BeCu or beryllium bronze, is a metal Alloy of Copper and 0

The rate of a spring is the change in the force it exerts, divided by the change in deflection of the spring. In Physics, a force is whatever can cause an object with Mass to Accelerate. That is, it is the gradient of the force versus deflection curve. In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object For an extension or compression spring it has the units of lbf/in, N/m, or similar. In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object Physical compression is the result of the subjection of a material to Compressive stress, resulting in reduction of Volume. For a torsion spring it has the units of N·m/rad or ft·lbf/degree, for example. A torsion spring is a spring that works by torsion or twisting that is a flexible elastic object that stores Mechanical energy when it is twisted Newton metre is the unit of moment ( Torque) in the SI system The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 The foot-pound force, or simply foot-pound (symbol ft·lbf or ft·lb) is a unit of work or Energy (a scalar 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. Different definitions exist depending on the specific field of application

Contents

History

Simple non-coiled springs were used throughout human history e. g. the bow (and arrow). A bow is a Weapon that projects arrows powered by the elasticity of the bow 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. Ctesibius or Ktesibios or Tesibius ( Greek Κτησίβιος ( fl Bronze is any of a broad range of Copper alloys, usually with Tin as the main additive but sometimes with other elements such as Phosphorus

Coiled springs were introduced in the 15th century. A Coil spring, also known as a helical spring, is a mechanical device which is typically used to store energy and subsequently release it to absorb shock or to maintain [1]

Types

A spiral hair spring
A spiral hair spring
A volute spring. Under compression the coils slide over each other, so affording longer travel.
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:

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:

The most common types of spring are:

Vertical volute springs of Stuart tank
Vertical volute springs of Stuart tank
Leaf spring on a truck
Leaf spring on a truck

Other types include:

A torsion bar twisted under load
A torsion bar twisted under load

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 keq=k1+k2.
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 keq=k1+k2.

Hooke's law

Main article: 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:

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. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material

Coil springs and other common springs typically obey Hooke's law. A Coil spring, also known as a helical spring, is a mechanical device which is typically used to store energy and subsequently release it to absorb shock or to maintain There are useful springs that don't: springs based on beam bending can for example produce forces that vary nonlinearly with displacement. This article describes the use of the term nonlinearity in mathematics

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. A tape measure or measuring tape is a flexible form of Ruler.

Simple harmonic motion

Main article: Harmonic oscillator

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

F = m a \quad \Rightarrow \quad -k x = m a. \,
The displacement, x, as a function of time. The amount of time that passes between peaks is called the period.
The displacement, x, as a function of time. This article is about the harmonic oscillator in classical mechanics In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the The amount of time that passes between peaks is called the period. Frequency is a measure of the number of occurrences of a repeating event per unit Time.

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,

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

This is a second order linear differential equation for the displacement x as a function of time. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the Rearranging:

\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). \,

A and B are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with B = 0 (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 atoms of an elastic material. Potential energy can be thought of as Energy stored within a physical system History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A material is said to be elastic if it deforms under stress (e

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. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the Solid mechanics is the branch of Mechanics, Physics, and Mathematics that concerns the behavior of solid matter under external actions (e In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object In Physics, a force is whatever can cause an object with Mass to Accelerate. Similarly, the contraction (negative extension) is proportional to the compression (negative tension). Physical compression is the result of the subjection of a material to Compressive stress, resulting in reduction of Volume.

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. Tensile strength \sigma_{UTS} or S_U is the Stress at which a material breaks or permanently deforms 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. A quadratic function, in Mathematics, is a Polynomial function of the form f(x=ax^2+bx+c \\! where a \ne 0 \\! In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Mathematics, the term linear function can refer to either of two different but related concepts

Popular mechanics

Contrary to popular belief, springs do not appreciably "creep" or get "tired" with age alone. Creep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses It occurs as a result of long term exposure to levels of 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.

Uses

References

  1. ^ Springs How Products Are Made, 14 July 2007. Suspension is the term given to the system of springs, Shock absorbers and linkages that connects a Vehicle to its Wheels Suspension A Slinky is a Coil -shaped Toy invented by mechanical engineer Richard James in Philadelphia Pennsylvania A pogo stick is a device consisting of a pole with a handle at one end footpads on the other and a spring which supports the stick and user when on the ground A dashpot is a mechanical device a damper which resists motion via viscous Friction.
  2. ^ [http://www.sdp-si.com/eStore/CoverPg/Springs.htm
  3. ^ Smalley Steel Ring Co. Retaining Rings, Snap Rings and Wave Springs - About Our Springs

External links

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