Page 75 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Field Balancing

LAWS OF SIN & COS

O α

β T

O + T γ

Figure 5-5. Solving the Balancing Triangle

cos is used first to determine the length of b (T vector). Since b 2
2
2
2
2
2
= a + c – 2ac cos β substituting yields b = 5 + 3.5 – 35 cos (60),
2
and cos(60) = .50000 (from trigonometric tables). Thus b = 19.75
or b = 4.44409.
Using the law of the sine the angle α is found by sin α/sin
β = a/b or sin α = sin β × (a/b). Substituting sin α = sin(60) (5/
4.44409), and sin(60) = .866025 (from trigonometric tables). Thus,
sin α = .866025 × 1.125089 = .974356 and α = 77 degrees (from
trigonometric tables).
Note that the answers obtained with the mathematical solu-
tions are more accurate than answers obtained graphically. How-
ever, the two answers are so close that the resultant correction
weight and its location will be about the same.

REVIEW

The basic steps required in the single plane balancing pro-
cess:

1. Operate the rotor at the balancing speed, and with the ana-
lyzer filter tuned to 1 × rpm, measure the amplitude of the
vibration in mils, and using a strobe light, note the position
of the phase reference mark. Record the amplitude and phase
angle as the original run.