Page 173 - Robot Builders Source Book - Gordon McComb

4.5 Damping of Harmful Vibrations 161

conclusion that there must be some value of c at which a maximum amount of energy
is absorbed during the relative movement of the vibrating masses, and at which the
vibrational amplitude of mass Mis thus minimized. Denoting a> a/Q.=f, it can be proved
that the minimum vibrational amplitude of the main mass M is reached when

For this condition the vibrational amplitude flj of the main mass M can be estimated
from the expression

The last specific case applied to the model shown in Figure 4.55 that we will consider
here describes the situation where c * 0, and k 2 = 0; that is, when masses M and m are
connected only by means of the absorber. Such an absorber is called a Lanchester
damper; it is based on viscous friction. The implementation of such a damper for indus-
trial purposes can have various forms. An example is shown in Figure 4.57. This design
consists of two discs 1 freely rotating on bearings 2. The latter are mounted on bushing
3 fastened onto the vibrating shaft 9. This bushing has disc 4 with friction gaskets 5.
Springs 6 can be tuned by bolt 7 and nut 8 to develop the required factional torque.
The optimum amplitude (the minimum vibrational amplitude) in this case is esti-
mated by the Formula (4.58). (Obviously, for rotational vibration the masses and stiff-
nesses must be replaced by the appropriate concepts: masses by moments of inertia,

FIGURE 4.57 Lanchester damper—cross section.
TEAM LRN