In our last Balancing How-To, I stated that an initial trial weight is sometimes a guess. Sometimes based on experience, and sometimes on common sense. But if you prefer to be a little more scientific about it, there are ways to calculate a good trial weight.
There are a few requirements to calculate a trial weight:
In many instances, a trial weight is calculated to generate a centrifugal force equal to 10% of the rotor’s weight. NOTE: Not 10% of rotor weight – 10% of the rotor’s centrifugal force. Also, if the rotor is operating above 3600 RPM, a calculation of 5% of the rotor’s weight is recommended.
To Calculate Centrifugal Force – Cƒ = mrω²
Let’s try it in an example. We have a fan, running at 600 rpm, with a rotor weight of 400 lb., and we have an 18 radius of where the trial weights will be placed.
If we want a centrifugal force equal to 10% of the rotor, we use (.1 x 400 lb) = 40 lb.
Convert speed from RPM to Hz (600/60) = 10 Hz.
To get the speed in radians – (2π) (10 Hz) = 62.83 rad/sec
To get ω² – 62.83² = 3947.84 rad/sec²
m= _____ 40 lb _____ = 0.00056
Now that we have the mass, we need to calculate for the weight – W=mg
W=(0.00056)(386.4)=0.217 lb or (.217)(16 oz in a pound) = 3.472 oz
A Simplified Calculation
Trial weight = 56375.5 x rotor weight
_______________RPM² x radius
______________56375.5 x 400 lb = 3.478 oz.
_______________600rpm² x 18”
Knowing the speed of the machine and the radius of weight placement is easy. What was typically more difficult for me was knowing the rotor weight. If you can find it, the simplified calculation formula works well. If you feel comfortable in estimating it, just be careful, and lean toward the light side. FYI-steel weighs about 500 pounds per cubic foot.
If you keep records on balancing rotors (and your probably should), you can often calculate a good trial weight by knowing the previous balance job.
As an example:
3.5 oz. = 9.114 oz/in/sec .42 in/sec – 0.036 in/sec
If the new unbalance is .4 in/sec
Remember, this assumes there have been no changes made to the rotor since the previous balance. If the rotor is dirty, it is different, and should probably be cleaned before attempting balancing.