Torsion spring

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Torsion coefficient of links here.

A torsion spring is a spring that acts with torque or rotation; namely, a flexible elastic object that stores mechanical energy when twisted. When twisted, it gives a force (actually torque) in the opposite direction, proportional to the number (angle) it is twisted. There are two types. A torque rod is a straight rod of metal or rubber worn around the shaft with a torque applied to the tip. The finer forms used in sensitive instruments, called torsional fibers consist of silk, glass, or quartz fibers under pressure, which are twisted about their axis. Another type, helical torque spring, is a helix-shaped metal rod or wire (coil) that is subjected to axis spin wicks with sideways force (bending moment) is applied. to the end, turning the coils tighter. This terminology can be confusing because in helical torque springs the force acting on the wire actually emphasizes the voltage, not the torsional (shear) voltage.

Video Torsion spring

Torsion coefficient

Selama mereka tidak berputar melampaui batas elastis mereka, pegas torsi mematuhi bentuk sudut hukum Hooke:

${\ displaystyle \ tau = - \ kappa \ theta \,}  ÂÂ$

di mana ${\ displaystyle \ tau \,}  ÂÂ$ adalah torsi yang diberikan oleh pegas di newton-meter, dan ${\ displaystyle \ theta \,}  ÂÂ$ adalah sudut putaran dari posisi ekuilibriumnya dalam radian. ${\ displaystyle \ kappa \,}  ÂÂ$ adalah konstanta dengan satuan newton-meter/radian, yang banyak disebut sebagai koefisien torsi pegas , modulus elastis torsi , rate , atau hanya konstanta pegas , sama dengan perubahan torsi yang diperlukan untuk memutar pegas melalui sudut 1 radian. Ini analog dengan konstanta pegas dari pegas linear. Tanda negatif menunjukkan bahwa arah torsi berlawanan dengan arah putaran.

Energi U , dalam joule, disimpan dalam pegas torsi adalah:

${\ displaystyle U = {\ frac {1} {2}} \ kappa \ theta ^ 2} Â Â$

Maps Torsion spring

Penggunaan

Some familiar usage examples are a strong and helical spring torque that operates clothing clothing and traditional spring type mousetraps traps. Other uses are in large circular torsion springs used to compensate for the weight of garage doors, and similar systems are used to help open boot covers on some sedans. Small, coiled torque springs are often used to operate pop-up doors found on small consumer items such as digital cameras and compact disc players. More specific uses:

• The torque rod suspension is a thick steel torque spring bar attached to the vehicle body at one end and to a lever arm attached to the wheel axis in the other. It muffles road shocks as the wheels pass through the mounds and rough road surfaces, pushing a ride for passengers. Torque rod suspension is used in many modern cars and trucks, as well as military vehicles.
• The rocking bar is used in many vehicle suspension systems also using the principle of torsion spring.
• The pendulum torque used in the torque pendulum clock is the weight of the wheel that is suspended from its center by the wire torque spring. It rotates around the spring axis, twisting it instead of swinging like a regular pendulum. The spring force reverses the rotation direction, so the wheels oscillate back and forth, pushed at the top by the clock gears.
• Torque springs consisting of crooked or veined ropes are used to store potential energy to empower some types of ancient weapons; including a Greek ballista and a Roman scorpio and a catapult like onager.
• The spring balance or spring in a mechanical watch is a smooth spiral torque spring that pushes the balance wheel back to its center position as it spins forward and back. The balance wheel and the spring function together with the torque pendulum above in keeping watch for the watch.
• The D'Arsonval movement used in the mechanical meter-type pointer to measure electric current is a type of torque balance (see below). A wire coil attached to the pointer bends in a magnetic field against the resistance of the torsion spring. Hooke's law ensures that the angle of the pointer is proportional to the current.
• A DMD or digital micromirror device chip is at the heart of many video projectors. It uses hundreds of thousands of small mirrors on small torque springs made on the silicon surface to reflect light onto the screen, forming an image.

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Torque balance

The torque balance , also called torque pendulum , is a scientific tool for measuring very weak strength, usually credited to Charles-Augustin de Coulomb, who created it in 1777, but independently was invented by John Michell around 1783. Its most famous use was by Coulomb to measure the electrostatic forces between charges to establish Coulomb's Law, and by Henry Cavendish in 1798 in the Cavendish experiment to measure the force of gravity between two masses to calculate the Earth's density, then to the value for the gravitational constant.

The torque balance consists of a rod hanging from the center by a thin fiber. Fiber acts as a very weak torque spring. If an unknown force is applied at right angles to the end of the bar, the bar will rotate, rotate the fiber, until it reaches equilibrium where the torque or torque of the fiber balance 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 constants of the fiber, so a very weak force causes a large rotation of the bar.

In the Coulomb experiment, the torque balance is an insulating rod with a metal-plated ball attached to one end, hung by a silk thread. The ball is filled with static electricity, and a second charged ball with the same polarity is brought close by. Both charged balls fend off one another, rotating the fiber through a certain angle, which can be read from the scale on the instrument. By knowing how much power is required to rotate the fiber through a given angle, Coulomb is able to calculate forces between the spheres. Determining the power for different charges and different separations between spheres, it shows that it follows the law of square reversed proportionality, now known as Coulomb's law.

To measure unknown forces, the spring constants of the twisted fiber must first be known. This is difficult to measure directly because of the lack of style. Cavendish completed this with a method used extensively since: measuring the resonance vibration period of the equilibrium. If the free balance is twisted and released, it will oscillate slowly clockwise and counter to time as a harmonic oscillator, at frequencies that depend on the moment of inertia of the beam and the elasticity of the fiber. Because the inertia of the beam can be found from its mass, the spring constant can be calculated.

Coulomb first developed the theory of torsional fiber and torque balance in his 1785 memoir, Recherches theoretical et experimentales de la desde de torsion et sur l'elasticite des fils de metal & amp; c . This leads to its use in other scientific instruments, such as galvanometers, and Nichols radiometers that measure the pressure of light radiation. In the early 1900s, gravity torque balance was used in petroleum search. Currently, torque balance is still used in physics experiments. In 1987, gravity researcher A.H. Cook writes:

The most important advance in experiments on gravity and other fine measurements was the introduction of Torque balance by Michell and its use by Cavendish. This has been the basis of all the most significant experiments on gravity ever since.

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Torsional harmonic oscillator

Torque balance, torque pendulum and balance wheel are examples of torsional harmonic oscillators that can oscillate with rotational motion around the torque spindle axis, clockwise and anticlockwise, in harmonic motion. Their behavior is analogous to the semi-mass translation oscillator (see Harmonic ocillator # Equivalent systems). Common motion equations are:

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

Jika peredamannya kecil, ${\ displaystyle C \ ll {\ sqrt {\ frac {\ kappa} {I}}} \,} Â$ , seperti halnya dengan pendulum torsi dan roda keseimbangan, frekuensi getaran sangat dekat dengan frekuensi resonansi alami dari sistem:

${\ displaystyle f_ {n} = {\ frac {\ omega n n}} {2 \ pi}} = {\ frac {1} {2 \ pi}} {\ sqrt {\ frac {\ kappa} {I}}} \,} Â Â$

Oleh karena itu, peri diwakili oleh:

${\ displaystyle T_ {n} = {\ frac {1} {f_ {n}}} = {\ frac {2 \ pi} {\ omega _ {n}}} = 2 \ pi {\ sqrt {\ frac {I} {\ kappa}}} \,} Â Â$

Solusi umum dalam kasus tidak ada gaya penggerak ( ${\ displaystyle \ tau = 0 \,}  ÂÂ$ ), disebut solusi transien, adalah:

${\ displaystyle \ theta = Ae ^ {- \ alpha t} \ cos {(\ omega t \ phi}} \,}  ÂÂ$

dimana:

${\ displaystyle \ alpha = C/2I \,} Â Â$

${\ displaystyle \ omega = {\ sqrt {\ omega _ n} ^ 2 - α2}} = {\ sqrt { \ kappa/I - (C/2I) ^ 2}}} \,} Â Â$

Apply

Roda keseimbangan arloji mechanis adalah osilator harmonik yang frekuensi resonan ${\ displaystyle f_ {n} \,} Â Â$ menetapkan laju already. Frekuensi resonansi diatur, pertama-tama dengan menyesuaikan ${\ displaystyle I \,} Â$ dengan sekrup berat yang diatur secara radial ke tepi roda, dan kemudian lebih halus dengan menyesuaikan ${\ displaystyle \ kappa \,} Â$ dengan tuas pengatur yang mengubah panjang musim semi keseimbangan.

Dalam keseimbangan torsi, torsi penggerak adalah konstan dan sama dengan gaya tak dikenal yang akan diukur ${\ displaystyle F \,}  ÂÂ$ , kali momen lengan balok keseimbangan ${\ displaystyle L \,}  ÂÂ$ , jadi ${\ displaystyle \ tau (t) = FL \,}  ÂÂ$ . Ketika gerakan oskilator dari keseimbangan mati, defleksi akan sebanding dengan gaya:

${\ displaystyle \ theta = FL/\ kappa \,}  ÂÂ$

Untuk menentukan ${\ displaystyle F \,}  ÂÂ$ perlu untuk menemukan konstanta pegas torsi ${\ displaystyle \ kappa \,}  ÂÂ$ . Jika redamannya rendah, ini dapat diperoleh dengan mengukur frekuensi resonansi alami dari keseimbangan, karena momen inersia keseimbangan biasanya dapat dihitung dari geometri, jadi:

${\ displaystyle \ kappa = (2 \ pi f_ {n}) ^ {2} Saya \,}  ÂÂ$

Source of the article : Wikipedia