Damping constant

Physical size
Surname	Translation damping constant
Formula symbol	${\displaystyle d,k,D}$
Size and unit system unit dimension SI kg · s -1 M · T −1

Physical size
Surname	Rotation damping constant
Formula symbol	${\displaystyle \Gamma }$
Size and unit system unit dimension SI kg · m 2 · s -1 M · L 2 · T −1

The damping constant ( formula symbols in part also or the latter can easily lead to confusion with the degree of damping ) is the proportionality factor of a linear damping element. The damping coefficient . The generated damping force or the generated damping torque results from: ${\displaystyle d}$ ${\displaystyle k}$ ${\displaystyle D;}$ ${\displaystyle \beta ={\frac {d}{2m}}}$

• for a translational movement : from the damping constant, multiplied by the speed in the damping element ( ) ${\displaystyle {\vec {F}}=-d\,{\dot {\vec {x}}}}$
• for a rotational movement : from the damping constant, multiplied by the angular velocity in the damping element ( ). ${\displaystyle {\vec {M}}=-\Gamma \,{\dot {\vec {\varphi }}}}$

For example, in the following equation of motion of a damped oscillation, a damping constant occurs ( here is a spring stiffness ): ${\displaystyle d}$ ${\displaystyle k}$

${\displaystyle m{\ddot {x}}+d{\dot {x}}+kx=0.}$

Application in the analysis of linear vibration systems: linear systems are mathematically much easier to deal with than non- linear ones . Real attenuation, e.g. B. by shock absorbers , but are mostly non-linear. In order to treat them in a mathematically simplified manner, linearization is often carried out.

The unit of the damping constant is

• for a translational movement: ${\displaystyle \mathrm {N\cdot s/m} }$
• for a rotational movement: ${\displaystyle \mathrm {Nm\cdot s} .}$

Examples of damping elements are shock absorbers (translational) and torsional vibration dampers or viscous couplings (rotational, e.g. viscosity dampers ).

See also

• Damping factor