Page 121 - Shale Shakers Drilling Fluid Systems

104 SHALE SHAKERS AND DRILLING FLUID SYSTEMS
The term "G"-force is sometimes used incor-
rectly to describe a "G"-factor. In the above example, tension in the string, will be significantly higher
the "G"-force on Earth would be 200 pounds and the
"G"-force on Jupiter would be 600 pounds.
Calculating the "C"-Factor
Accelerations are experienced by an object or
mass rotating horizontally at the end of a string.
A mass rotating around a point with a constant
speed has a centripetal acceleration (C a), which
can be calculated from the equation:
C a = rco 2
where r is the radius of rotation
w is the angular velocity in radians per
second
This equation can be applied to the motion of
a rotating weight on a shale shaker to calculate
an acceleration. The centripetal acceleration of a
rotating weight in a circular motion, with a diam-
eter (or stroke) of 2r in inches, rotating at a
certain rpm (or co), can be calculated from the
above equation.
Combining all of the conversion factors to convert
the units to feet per second squared:
Normally this centripetal acceleration is expressed as
a ratio of the value to the acceleration of gravity:
Shale shakers are vibrated by rotating eccentric
masses. A tennis ball rotating at the end of a
3-foot string, and a 20-pound weight rotated at the
same RPM at the end of a 3-foot string, will have
the same centripetal acceleration and the same
"G"-factor. Obviously, the centripetal force, or the
for the 20-pound weight.
The rotating eccentric weight on a shale shaker
is used to vibrate the screen surface. The vibrating
screen surface must transport solids across its
surface for discard and allow fluid and solids smaller
than the screen openings to pass through to the
mud tanks. If the rotating weights rotate at a
speed or vibration frequency that matches the
natural frequency of the basket containing the
screen surface, the amplitude of the basket's vi-
bration will continue to increase and the shaker
will be destroyed. This will occur even with a very
small rotating eccentric weight. For example, con-
sider a child in a swing on a playground. The
application of a small force each time the swing
returns to full height (amplitude), soon results in
a very large amplitude. In this case, the "forcing
function" (the push each time the swing returns)
is applied at the natural frequency of the swing.
When the forcing function is applied at a fre-
quency much larger than the natural frequency,
the vibration amplitude depends on the ratio of the
product of the unbalanced weight (w) and the
eccentricity (e) to the weight of the shaker's vibrat-
ing member (W). This can be expressed as:
The vibration amplitude is one half of the total
stroke length.
The peak force, or maximum force, on a shaker
screen can be calculated from Newton's second
law of motion:
where a is the acceleration of the screen.
For circular motion, the displacement is de-
scribed by the equation:
The velocity is the first derivative of the displace-
ment dx/dt and the acceleration is the second de-
2
2
rivative of the displacement d x/dt This means
that the acceleration would be:
The maximum value of this acceleration occurs
when the sine function is one. Since the displace-
ment (X) is proportional to the ratio of we/W for