An average of 9 out of 10 aircraft, are found to need propeller balancing.

https://www.acessystems.com/dynamic-propeller-balance/
http://www.expaircraft.com/PropBalance.htm
http://www.propellerman.com/dynamic-balancing.html
Advisory Circular Prop Maintenance

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SYMPTOMS OF IMBALANCE
Cowling and baffling excess wear
Operator and passenger fatigue
Engine mount stiffness rapidly degrades allowing excess engine motion
Accessories towards the rear of the engine are subjected to high vibration levels causing premature failure
Instrument panel instruments are subjected to excessive vibration which dramatically shortens gyro bearing life
Wiring and cabling subject to faster degradation due to continuous vibration

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PROPELLOR TYPES THAT CAN BE BALANCED WITH OUR PROCESS
Fixed pitch with a spinner
Variable pitch with a spinner
Fixed pitch Radial engines with a spinner or means to add or remove weights.
Reverse turning Radial engines with a spinner or means to add or remove weights.
Turbine engines with geared and direct drive. The geared type is very sensitive to propeller unbalance since it causes premature wear in the gear section.

BENEFITS
Minimize vibration
Increase bearing life
Minimize power loss
Minimize audible and signal noises
Minimize structural stresses
Minimize operator annoyance and fatigue
The tachometer error is measured engine internal vibration spectrum is measured and recorded for comparison with desired levels to identify potential problems

HOW OFTEN SHOULD I HAVE THE PROPELLER BALANCED?
How long a balance lasts dependent on the type of operation that the aircraft is subject to.
A tail wheel aircraft can generally operate 300 hours in these conditions while the conventional aircraft may require rebalancing at 150 hours.
Balancing should be completed after any major changes or repairs.

THE BALANCING PROCESS
Balancing a propeller system involves measuring the amount and location of the unbalanced weight while the propeller system is turning, thus the word “dynamic”.

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The amount of unbalance is measured with an accelerometer which is attached to the engine near the propeller; usually on the front engine cross tie bolt on flat engines, or on one of the front crank case bolts on a round engine or a turbine engine.  The accelerometer measures the motion of the front of the engine resulting from the propeller unbalance.

Determining the location of the weight causing the shaking as the propeller rotates is done with an optical pickup attached to the cowling or engine valve cover.  A strip of reflective tape is placed on the back side of one of the propeller blades.  This serves to provide an electrical pulse once each time the propeller rotates.

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With this information about where the propeller blade is located when the accelerometer sees a peak in the vibration, a computation is performed which provides the “where at” information.

The acceleration level measured by the accelerometer provides the “How much” information.

Using this data, the computer calculates the amount of weight to add and, based upon the normal location of the sensors, computes a trial location.  This information is used to install trial and then permanent weight on the propeller assembly as required.