A Vector Approach to Single Plane Balancing

Unbalance (Imbalance) is often defined as the unequal distribution of the weight of a rotor about its rotating centerline. A rotor can be balanced either in-place or in a balancing machine assuming unbalance is the issue and weight can be added or removed. Modern balancing instruments will do the math for you. I originally learned by plotting on polar graph paper with an analyzer with a strobe light phase input.


Vector – a quantity having both direction and magnitude

Polar Graph Paper – graph paper with equally spaced concentric circles divided into small arcs

Mils – Peak to Peak vibration displacement, 1 mil = .001 inches. Often used in field balancing

Trial Weight – Amount of weight added to a rotor that changes the unbalance condition

O – Vector representing the original unbalance

O + T – Vector representing the original plus trial weight unbalance

T – Vector representing difference between “O” and (“O”+”T”) This is the effect of the trial weight

A – Angle between “O” and “T”

Solving a single plane balance using vectors and polar graph paper

1 – At running speed measure the amplitude and phase at 1 x rpm. This is plotted as the “O” vector

“O” = 7 mils at 160 degrees

2 – Shut down the machine and add a trail weight of a known amount

Trial Weight = 100 grams (3.53 oz)

– Run the machine and record the new amplitude and phase. A rule of thumb is look for either a 30 degree phase change or a 30% change in amplitude. This vector is plotted as “O” + “T”

“O” + “T” = 5 mils at 70 degrees

4 – Connect the end of the “O” vector to the end of the “O” + “T” vector and label this as “T”

5 – Measure “T”

“T” = 9 mils

– Use the formula Correction weight = Trial weight x “O”/”T”

CW = 100 x 7/9 = 77.77 grams

7 – Measure the angle between “O” and “T” with a protractor

“A” = 35 degrees

8 – The goal is to adjust vector “T” so it is equal and opposite vector “O”

9 – Remove the trial weight and add a correction weight of 77.77 grams 35 degrees from the location of the trial weight

10 – For this example, the correction weight is shifted in the direction opposite the shift of the reference mark from “O” to “O” + “T”

by Acoem contributor | June 13, 2022
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