Page 6 - Combined_41_OCR

wheels, for instance. But this com­
pensation is not completely satisfac­
tory.
Upper skin in tension
r -Wrw2-
\
\
’ Shear forces
Lower skin in compression on elastomer

Conventional Damped
solid beam laminated
beam

If the disc and shaft above are sup­
Second mode ported by a bearing at each end and
spun, a rotating vector force of
Wroj2 pounds results. W is the disc
weight, (j is the angular velocity
in radians per second, and r is the
Third mode radial distance (inches) from the cen­
ter of the shaft out to the center of
gravity of the system.
The shaft and bearings must absorb
and transmit not only the weight of
the rotor but also a new force, one
that rotates; one which, at high ro­
tational speeds, may be greater than
the rotor weight. A numerical ex­
ample: 1 oz-in. of unbalance, though
above consists of three sketches, each vibration. Some modes are more like­
taken at a different frequency. An ly than others to cause failure in a small, will cause a force of ±114 lb
electromagnetic shaker furnished a particular installation. The frequencies at 8000 rpm.
In most rotating elements, such as
forcing function to a pair of beams. causing such critical modes are called motor armatures or engine crank­
The shaker frequency was adjusted critical frequencies. shafts, mass is distributed along the
first to excite the fundamental shape Intense sounds can excite vibra­ shaft rather than being concentrated
of vibration bending (also called the tions, especially in thin panels. Damp­ in a disc. Such a unit may be sta­
first mode or fundamental mode). ing treatments on the panels are very tically balanced, but when it is spun,
Then it was readjusted to higher fre­ effective in reducing such vibration
quencies that excited the second and (and in reducing sound that is radi­ severe unbalanced forces may be
transmitted to shaft and bearings.
third modes. ated by resonating panels).
If the solid beam at the left is Obviously such a unit is not truly
“plucked” (as with shock), causing Rotational Unbalance: Where rotat­ balanced; since this new unbalance is
apparent only during rotation, it is
it to vibrate at one or more of the ing engines are used in ships, auto­ called dynamic unbalance.
frequencies and patterns shown, the mobiles, aircraft, or other vehicles,
vibration will gradually die out, be­ where turbines are used in vehicles
cause of the internal damping of the and pumping stations, where pro­ Unbalancing Unbalancing
beam (hysteresis). The right-hand pellers are used in ships and aircraft,
cantilever beam is made of two thin where motors are used in machine
metal layers joined by a layer of a tools and appliances—in all of these
viscoelastic damping material. Shear and many other varied applications,
forces exist between metal and damp­ unbalance of the rotating members is
er that convert vibratory motion into a common source of vibration.
heat faster than with the solid beam.
At very low vibration frequencies,
transmissibility = 1 at all points
along the beams. At certain higher Static and Dynamic
(resonance) frequencies, transmissi­
Dynamic Unbalance Unbalance Only
bility grows larger. The points of
minimum amplitude are nodes; the
points having maximum amplitude If the two unbalances of this un­
are antinodes. Maximum bending restrained simplified system are exact­
occurs at the attachment point and ly equal, are 180 deg apart, and the
at the antinodes—locations where fa­ If the simple disc-shaft system shown rotor is otherwise uniform and identi­
tigue failures usually occur. is placed on knife-edges, it will come cal, this system will be statically
These three sketches suggest that to rest with the heavy side down. balanced. However, as the shaft ro­
the severity of a vibration often de­ This type of unbalance is called static tates, the rotor wll generate centrif­
pends upon where it is measured. unbalance, since it can be detected ugal forces that are out of phase
Ratios of 1000/1 or more (D anti- and measured statically. If a weight with each other. If these forces are
node/D node) have been measured. W' is attached at some radius r' not countered by two new rotating
Finding a representative location for to the side opposite the heavy side, forces, rotation will cause the center-
a vibration pickup is often difficult. so that the disc has no preferred posi­ line of the rotor to trace out two
Several modes of vibration can oc­ tion, the product W'r' is the value cones, as on the right. For simple
cur at once if several exciting fre­ of the original unbalance. static unbalance, the rotor run-out
quencies are present, as in shock and Static balancing is a simple tech­ will take the form of an oversize
in complex and wide-band random nique, often used on automobile cylinder, as on the left.
120 Machine Design