Page 73 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Field Balancing

ounces. Next, the exact location for the correction weight must be
determined. Again, we will use the information obtained in our
trial run.
The object of the balancing process is to adjust the length of
the T vector to equal the length of the O vector, and to adjust the
direction of the T vector to be 180 degrees opposite of the O vector.
The T vector can be thought of as a vector whose tail is always
connected to the head of the O vector. Thus to make the T vector
point exactly opposite the O vector, it must be shifted by the angle
between the O vector and the T vector. This angle α was measured
to be 79 degrees.
This is the angle that the trial weight must be moved. In
Figure 5-3, the O + T vector was at 120 degrees, while the O vector
had been at 60 degrees. Thus the reference mark shifted from 60
degrees to 120 degrees in a clockwise direction. Remember, the
weight is moved opposite the reference shift direction, so the cor-
rection weight must be added 79 degrees counterclockwise from
the position of the trial weight.

CAUTION: The correction weight is always shifted in an angle
opposite in direction from the shift of the reference mark. The
angle is measured from the location of the trial weight and not the
reference mark.

REMEMBER: Remove the trial weight after adding the correction
weight.

LAW OF SINE

The solution to the balancing problem in the example above
can also be solved with the trigonometric functions sine and co-
sine. To accomplish this, the law of sine and the law of cos must
be used. Refer to Figure 5-4.
Note in Figure 5-4 that the side a is opposite the angle α; the
side b is opposite the angle β; and the side c is opposite the angle
γ.