Page 168 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 5.8 Vibration Damper 155

In spite of the simplicity of the torsional damper, the mathematical analysis
for its behavior is rather complicated. For instance, the flywheels can slip continu­
ously, for part of the cycle, or not at all, depending on the pressure exerted by the
spring bolts. If the pressure on the friction ring is either too great for slipping or
zero, no energy is dissipated, and the damper becomes ineffective. Maximum
energy dissipation takes place at some intermediate pressure, resulting in optimum
damper effectiveness.
Obviously, the damper should be placed in a position where the amplitude of
oscillation is the greatest. This position generally is found on the side of the shaft
away from the main flywheel, because the node is usually near the largest mass.

Untuned viscous vibration damper. In this section, we discuss another
interesting application of a vibration damper, which has found practical use in
suppressing the torsional vibrations of automobile engines. In a rotating system
such as an automobile engine, the disturbing frequencies for torsional oscillations
are proportional to the rotational speed. However, there is generally more than
one such frequency, and the centrifugal pendulum has the disadvantage that
several pendulums tuned to the order number of the disturbance must be used. In
contrast to the centrifugal pendulum, the untuned viscous torsional damper is
effective over a wide operating range. It consists of a free rotational mass within a
cylindrical cavity filled with viscous fluid, as shown in Fig. 5.8-2. Such a system is
generally incorporated into the end pulley of a crankshaft that drives the fan belt,
and is often referred to as the Houdaille damper.
We can examine the untuned viscous damper as a 2-DOF system by consider­
ing the crankshaft, to which it is attached, as being fixed at one end with the
damper at the other end. With the torsional stiffness of the shaft equal to K
in. - Ib/rad, the damper can be considered to be excited by a harmonic torque
The damper torque results from the viscosity of the fluid within the pulley
cavity, and we will assume it to be proportional to the relative rotational speed
between the pulley and the free mass. Thus, the two equations of motion for the
pulley and the free mass are

J6 + K6 + c^6 —(f)^ —
(5.8-1)
J j - c { d - 4 > ) = 0

Figure 5.8-2. Untuned viscous
damper.