Question

A shaft undergoing torsional vibrations is held fixed at one end, and it has attached at the other end a disk with a rotary inertia of 4 kg m2about the rotational axis. The rotary inertia of the shaft is negligible compared to that of the disk, and the torsional stiffness of the shaft is 8 Nm /rad. The disk is placed in an oil housing, and the associated dissipation is modeled by using an equivalent torsional viscous damper with damping coefficient ct. What should the value of ctbe so that the system is critically damped?.

Answer 1

Answer:

ct = 11.31 N.m.s/rad

Explanation:

Given that

$I=4 \ kg m^2$

Torsional stiffness  ,K= 8 Nm/rad

As we know damping coefficient ct (critical )given as

In simple spring mass system critical damping coefficient given as

$ct=2\sqrt {m.K}$

In  torsional system critical damping coefficient given as

$ct=2\sqrt {I.K}$

Now by putting the values

$ct=2\sqrt {I.K}$

$ct=2\sqrt {4\times 8}$

ct = 11.31 N.m.s/rad