Page 231 - The Tribology Handbook

B15 Damping devices

GENERAL CHARACTERISTICS Damping devices are used to provide forces to resist
relative motion and oscillation. The two main types are
UNDAMPED OSCILLATION friction dampers, using friction between solid components
\
and hydraulic dampers using mainly viscous effects.
If an oscillation is damped with a friction damper, the
oscillation decay will follow a straight line (Figure 15.1).
The amplitude of each successive oscillation will be
reduced by 4x
where x = F/k
and F = damping force (newtons)
k = system spring rate (newtondmetre)

' f DAMPING FORCE With a hydraulic damper, the decay of the oscillation
APPLIED HERE follows an exponential curve (Figure 15.2).
Figure 15.1 The decay of oscillations by friction The diagram of the damping action of a hydraulic
damping damper shows the effect of different damping factors.
These are related to the number of cycles that it takes for
EXPONENTIAL CURVE D = 0.1 the system to come to rest after an impact displacement.
This relationship can be used to make an experimental
measurement of the damping factor of an existing system.
The relationship between damping force and velocity
varies with the type of damper and can conveniently be
described by the formula
DAMPING FORCE, APPLIED HERE
F= CP
EXPONENTIAL CURVE D = 0.5 where c = a constant which depends on factors such as the
size of the damper
V = the displacement velocity
n = a constant which depends on the working prin-
ciple of the damper
Figure 15.2 The decay of oscillations by viscous
hydraulic damping Type of damper Value Force characteristic
of n
Friction damper 0 F is constant for all
values of V
~~ ~ ~~ ~
Hydraulic damper with 2 F is proportional to
constant area flow passages V2
Hydraulic damper with 1 F is proportional to V
valves to control the flow
2

MEN1 VELOCIT

1.5
LL
w'
u
a
0
LL1
0
z
Q
5
U
n
0.5
I I I I I I
0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5
NUMBER OF CYCLES TO REST (DECAY) PISTON DISPLACEMENT VELOCITY, v
Figure 15.3 The effect of viscous hydraulic damping Figure 15.4 The dependence of the damping force F
factor on the number of cycles required to come to on the piston velocity V at various values of the
rest after a single impact exponent n
B15.1