Categories: Machinery Diagnostics,Machinery Maintenance,Other Topics

A Vector Approach to Single Plane Balancing

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By on February 7, 2019

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)

3 – 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

6 – 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”

About the Author

Mike Keohane has been involved in machinery reliability since 1985. He started as a field service engineer for IRD Mechanalysis. Prior to that he was a wireline logger for Schlumberger Well Services. He joined VibrAlign in 1992 and supports clients in Georgia, South Carolina, Alabama and the Florida Panhandle. In addition to precision alignment, he has field experience in vibration analysis, field and shop balancing, oil analysis and ultrasonics. Mike holds a BSME from Michigan State University. Mike and his wife and two children currently live in Peachtree City, GA.

2 responses to “A Vector Approach to Single Plane Balancing”

  1. Roberto Colaneri says:

    Hi Michael,
    in the formula Correction weight = Trial weight x “O”/”T”
    CW = 100 x 7/9 = 77.7 grams and not 55.5 grams.
    Thank you for share this article.

  2. Michael Keohane says:


    Thank you for reading and catching my error and taking the time to reply! Keeps me on my toes! We will correct it. If you have an ideas for future blog posts please let us know. We love to hear from our readers.



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