Centrifugal pendulum

This article covers the machine element used to dampen vibrations. For the historical mechanism in steam engines see centrifugal governor . Centrifugal pendulum is also an alternative name for the conical pendulum .

The centrifugal pendulum is a type of vibration damper for damping torsional or torsional vibrations . Due to the speed proportionality, the centrifugal pendulum is also referred to as an adaptive damper.

background

In order to achieve an optimal damper effect to reduce vibration amplitudes, dampers are matched to the frequency of the excitation . In the case of spring-mass systems, the spring constant and the oscillating mass are decisive. To dampen vibrations in systems with variable excitation frequency, the stiffness of the damper must change quadratically with the excitation frequency for a broadband effect, which is not possible with conventional springs.

Mode of action / functional principle

With the centrifugal pendulum, the restoring force is not created by a spring, but, as with the thread pendulum, by acceleration. The natural frequency of the thread pendulum depends on the acceleration due to gravity and the thread length : ${\displaystyle f_{p}}$ ${\displaystyle g}$ ${\displaystyle l}$

${\displaystyle f_{p}={\frac {1}{2\pi }}{\sqrt {\frac {g}{l}}}}$

In contrast, the centrifugal pendulum mass is attached to a rotating disk, whereby the centrifugal force of the disk rotating at the frequency becomes effective instead of gravity : ${\displaystyle f_{s}}$

With

${\displaystyle f_{p}={\frac {\omega _{s}}{2\pi }}{\sqrt {\frac {r-l}{l}}}}$

and

${\displaystyle \omega _{s}=2\pi \ f_{s}}$

applies

${\displaystyle {\frac {f_{p}}{f_{s}}}={\sqrt {\frac {r-l}{l}}}={\sqrt {\frac {L}{l}}}}$

It denotes the distance between the pendulum mass and the axis of the disk and its angular velocity . is the distance of the pendulum suspension point from the axis of the disc. The damper frequency is therefore proportional to the speed and can be precisely adjusted by choosing and . ${\displaystyle r}$ ${\displaystyle \omega _{s}}$ ${\displaystyle L=r-l}$ ${\displaystyle L}$ ${\displaystyle l}$

In many cases of rotational irregularities , an excitation frequency dominates, which is also in a fixed ratio to the speed. With a 4-cylinder 4-stroke engine this is engine order and it results in the following relationship: ${\displaystyle m:n=2}$

${\displaystyle 2={\sqrt {\frac {L}{l}}}}$

Because the resonance is always tuned, the oscillation amplitude of the pendulum is increased and the damping effect is given even with small pendulum masses.

The alternative use of dual mass flywheels has the disadvantage of a constant resonance frequency, so that the resonance cannot be exploited. Rather, the system is designed for the non-resonant case and resonance is avoided. This is then at the lower end of the low speed range that is desirable for low fuel consumption .

literature

• Hans Dresig , Franz Holzweißig : Maschinendynamik , Springer, 2011, ISBN 978-3-642-16009-7 , doi : 10.1007 / 978-3-642-16010-3 , limited preview in the Google book search.