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 ).