damping

When damping is defined as the phenomenon that during a vibratable system, in principle, the amplitude of oscillation decreases with time or can no vibration occur depending on circumstances. After energy has been supplied once, the oscillation is based on the interrelation of two forms of energy; z. B. with a mechanical shaft , kinetic energy and potential energy are mutually exchanged. If energy is branched off into a third form of energy - often as heat - this is the cause of the damping.

The term damping is also applied to a weakening phenomenon that is related to oscillation, radiation or wave-like processes, although these are stationary . These processes can take place without a time limit if the energy given off as heat is continuously replaced by other types of energy.

Time-dependent processes

Basis, parameter

The attenuation may be undesirable, e.g. B. in a clockwork that is supposed to oscillate indefinitely. But it may also be desirable, for. B. in an electromechanical measuring mechanism that should come to rest quickly after a change in the measured variable .

In the case of a damped, oscillatory system, a distinction is made between an oscillation case , a creep case and the aperiodic borderline case in between , but which also exhibits creeping behavior. An oscillation is only possible at all if the damping is sufficiently weak. For the mathematical representation, reference is made to the main articles.

In the differential equation of oscillation, damping can be seen in the fact that a term appears with the first derivative of the dependent variable . In the case of mechanical processes, this derivation stands for the speed, the term for the influence of friction .

Weakly damped oscillation with an exponentially decreasing limit

With weak damping, the natural angular frequency of the oscillation is lower than its value with undamped oscillation. The amplitude decays in an exponential relationship with time, so that the oscillation through ${\ displaystyle \ omega _ {d}}$ ${\ displaystyle \ omega _ {0}}$

{\ displaystyle y = {\ hat {y}} \ \ mathrm {e} ^ {- \ delta t} \ sin \ omega _ {d} t}

is writable. Here is called the decay coefficient with . ${\ displaystyle \ delta}$ ${\ displaystyle \ delta> 0}$

An oscillating system with a low degree of damping or high quality can be operated undamped as an oscillator by a constant supply of energy (e.g. under mechanical or electrical voltage) . When excited with an alternating quantity, resonance is possible. By inhibition or by dependent on the deflection (non-linear) damping necessary to prevent the system that builds up until the destruction ( resonance catastrophe ).

Examples of attenuation

mechanics

A vibrating string emits energy through the body of a musical instrument, preferably through the propagation of sound .
Vibrations in the chassis of vehicles are weakened by shock absorbers ; these become hot when driving fast on bumpy roads. The damping comes about through friction brakes, for example through flow resistance due to viscosity when oil is pushed through narrow nozzles. For further possibilities see also under vibration damper .

Electrical engineering

Setting in the aperiodic limit case
Damped oscillating setting

In an oscillating circuit, the electric field and magnetic field exchange their energy. In this case, electrical current primarily delivers energy to the ohmic resistance of the coil .
In the moving-coil measuring mechanism , the conductive coil frame is used as an eddy current brake . It represents a turn in which a current flows proportional to the angular velocity due to electromagnetic induction .

A system that can oscillate comes into its rest position the fastest in the aperiodic borderline case. The most favorable damping to get safely into a rest position, however, is a lower damping, so that an overshoot occurs, whereby the oscillation quickly drops to a narrow range. This settling is particularly useful when static friction is to be expected. For commercially available electromechanical measuring devices, an overshoot of up to 20% of the scale length is permitted with a display change of von of the scale length.

Stationary processes

Basis, parameters

Here, too, there is the undesirable and the desired damping. The latter requires an attenuator .

One specifies for components, transmission paths and systems

the damping factor ${\ displaystyle D = {\ frac {X} {Y}} = {\ frac {1} {V}}}$

where = input variable, = output variable, = transfer or gain factor .

{\ displaystyle X}

{\ displaystyle Y}

{\ displaystyle V}

the logarithmic attenuation , ${\ displaystyle a = \ ln | D | {\ text {Np}} = 20 \; \ lg | D | {\ text {dB}}}$

when the input and output variables are of the same type on which the power depends on the square.

Of the (possibly complex) quantities and , the one whose magnitude is greater than one is used; thus the amount always has a positive logarithm. ${\ displaystyle D}$ ${\ displaystyle V}$