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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. A spring is a flexible elastic object used to store mechanical Energy. In Solid mechanics, torsion is the twisting of an object due to an applied Torque. A material is said to be elastic if it deforms under stress (e In Physics, mechanical energy describes the Potential energy and Kinetic energy present in the components of a mechanical system. The amount of force (actually torque) it exerts is proportional to the amount it is twisted. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about A torsion spring is often made from a wire, ribbon, or bar of metal or rubber, while more delicate ones are made of silk, glass, or quartz fibers. Fused quartz and fused silica are types of Glass containing primarily Silica in amorphous (non- Crystalline form

Mousetrap powered by a helical torsion spring (center).
Mousetrap powered by a helical torsion spring (center).

Contents

Torsion coefficient

As long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of Hooke's law:

\tau = -\kappa\theta\,

where \tau\, is the torque exerted by the spring in newton-meters, and \theta\, is the angle of twist in radians. The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material 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 A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 \kappa\, is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient, torsion elastic modulus, or just spring constant, equal to the torque required to twist the spring through an angle of 1 radian. It is analogous to the spring constant of a linear spring.

Uses

Other uses are in the large coiled torsion springs used to counter-balance the weight of garage doors, and a similar system is used to assist in opening the trunk (boot) cover on some sedans. A garage door is a large Door on a garage that can either be opened manually or by a Garage door opener. The decklid (or boot lid) is the cover over the trunk/boot of Motor vehicles that allows access to the main Storage or Luggage Small coiled torsion springs are often used to operate pop-up doors found on small consumer goods like digital cameras and compact disk players. Many compact digital still cameras can record Sound and moving Video as well as still Photograph. A Compact Disc (also known as a CD) is an Optical disc used to store digital data, originally developed for storing digital audio Strong coiled torsion springs are used in the construction of traditional springloaded-bar type mousetraps. A mousetrap is a specialized type of Animal trap designed primarily to catch mice; however it may also trap other small animals

Torsion balance

Drawing of Coulomb's torsion balance. From Plate 13 of his 1785 memoir.
Drawing of Coulomb's torsion balance. From Plate 13 of his 1785 memoir.

The torsion balance, also called torsion pendulum, is a scientific apparatus for measuring very weak forces, usually credited to Charles-Augustin de Coulomb, who invented it in 1777, but independently invented by John Michell sometime before 1783. Charles Augustin de Cock (June 14 1736 Angoulême France – August 23 1806 Penis France was a French Physicist. John Michell ( December 25, 1724 – April 29, 1793) was an English natural philosopher and Geologist, whose work spanned [1] Its most well-known uses were by Coulomb to measure the electrostatic force between charges to establish Coulomb's Law, and by Henry Cavendish in 1798 in the Cavendish experiment[2] to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the gravitational constant. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Henry Cavendish, FRS (10 October 1731 - 24 February 1810 was a British Scientist noted for his discovery of Hydrogen or what he called "inflammable The Cavendish experiment, done in 1797 &ndash 1798 by Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass

The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or torque of the fiber balances the applied force. Then the magnitude of the force is proportional to the angle of the bar. The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar.

In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls. Determining the force for different charges and different separations between the balls, he showed that it followed Coulomb's law. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

To measure the unknown force, the spring constant of the torsion fiber must first be known. 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 This is difficult to measure directly because of the smallness of the force. Cavendish accomplished this by a method widely used since: measuring the resonant vibration period of the balance. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a harmonic oscillator, at a frequency that depends on the moment of inertia of the beam and the elasticity of the fiber. This article is about the harmonic oscillator in classical mechanics Since the inertia of the beam can be found from its mass, the spring constant can be calculated.

Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir, Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal &c. This led to its use in other scientific instruments, such as galvanometers, and the Nichols radiometer which measured the radiation pressure of light. A galvanometer is a type of Ammeter; an instrument for detecting and measuring Electric current. A Nichols radiometer is the apparatus used by Ernest Fox Nichols and Gordon Ferrie Hull in 1901 for the measurement of Radiation pressure. Radiation pressure is the Pressure exerted upon any surface exposed to Electromagnetic radiation. In the early 1900s gravitational torsion balances were used in petroleum prospecting. Today torsion balances are still used in physics experiments. In 1987, gravity researcher A. H. Cook wrote:

The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by Michell and its use by Cavendish. It has been the basis of all the most significant experiments on gravitation ever since. [3]

Torsional harmonic oscillators

For definition of terms see end of section

Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in harmonic motion. The balance wheel is the timekeeping device used in Mechanical watches and some Clocks analogous to the Pendulum in a Pendulum clock. This article is about the harmonic oscillator in classical mechanics Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. Their behavior is analogous to translational spring-mass oscillators (see Harmonic oscillator#Equivalent systems). This article is about the harmonic oscillator in classical mechanics The general equation of motion is:

I\frac{d^2\theta}{dt^2} + C\frac{d\theta}{dt} + \kappa\theta = \tau(t)

If the damping is small, C << \sqrt{\kappa I}\,, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the natural resonance frequency of the system:

f_n = \frac{\omega_n}{2\pi} = \frac{1}{2\pi}\sqrt{\kappa/I}\,

The general solution in the case of no drive force (\tau = 0\,), called the transient solution, is:

\theta = Ae^{-\alpha t}cos{(\omega t + \phi)}\,

where:

\alpha = \sqrt{C/2I}\,
\omega = \sqrt{\omega_n^2 - \alpha^2} = \sqrt{\kappa/I - (C/2I)^2}\,

Applications

The balance wheel of a mechanical watch is a harmonic oscillator whose resonance frequency f_n\, sets the rate of the watch. The balance wheel is the timekeeping device used in Mechanical watches and some Clocks analogous to the Pendulum in a Pendulum clock. For information on mechanical systems' absorption of energy at resonance see Mechanical resonance. A watch is a timepiece that is made to be worn on a person The term now usually refers to a wristwatch, which is worn on the wrist with a strap or Bracelet. The resonance frequency is regulated, first coarsely by adjusting I\, with weight screws set radially into the rim of the wheel, and then more finely by adjusting \kappa\, with a regulating lever that changes the length of the balance spring.

In a torsion balance the drive torque is constant and equal to the unknown force to be measured F\,, times the moment arm of the balance beam L\,, so \tau(t) = FL\,. When the oscillatory motion of the balance dies out, the deflection will be proportional to the force:

\theta = FL/\kappa\,

To determine F\, it is necessary to find the torsion spring constant \kappa\,. If the damping is low, this can be obtained by measuring the natural resonance frequency of the balance, since the moment of inertia of the balance can usually be calculated from its geometry, so:

\kappa = (2\pi f_n)^2 I\,

In measuring instruments, such as the D'Arsonval ammeter movement, it is often desired that the oscillatory motion die out quickly so the steady state result can be read off. This is accomplished by adding damping to the system, often by attaching a vane that rotates in a fluid such as air or water (this is why magnetic compasses are filled with fluid). The value of damping that causes the oscillatory motion to settle quickest is called the critical damping C_c\,:

C_c = 2 \sqrt{\kappa I}\,
Definition of terms
\theta\, radians\, Angle of deflection from rest position
I\, kg\,m^2\, Moment of inertia
C\, kg\,m^2\,s^{-1}\,{rad}^{-1}\, Rotational friction (damping)
\kappa\, N\,m\,{rad}^{-1}\, Coefficient of torsion spring
\tau\, N\,m\, Drive torque
f_n\, Hz\, Undamped (or natural) resonance frequency
\omega_n\, rad\,s^{-1}\, Undamped resonance frequency in radians
f\, Hz\, Damped resonance frequency
\omega\, rad\,s^{-1}\, Damped resonance frequency in radians
\alpha\, s^{-1}\, Reciprocal of damping time constant
\phi\, rad\, Phase angle of oscillation
L\, m\, Distance from axis to where force is applied

References

  1. ^ McCormmach, R. Damping is any effect either deliberately engendered or inherent to a system that tends to reduce the amplitude of Oscillations of an oscillatory system & Jungnickel, C. (1996), Cavendish, American Philosophical Society, pp. 335-344, ISBN 0-87169-220-1, <http://books.google.com/books?id=EUoLAAAAIAAJ> 
  2. ^ Cavendish, H. (1798), “Experiments to determine the Density of the Earth”, in MacKenzie, A. S. , Scientific Memoirs, Vol.9: The Laws of Gravitation, American Book Co. , 1900, pp. 59-105 
  3. ^ Cook, A. H. (1987), “Experiments in Gravitation”, in Hawking, S. W. and Israel, W. , Three Hundred Years of Gravitation, Cambridge University Press, pp. p. 52, ISBN 0521343127 


See also

External links

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