This document discusses methods for balancing rotating machinery using a mobile phone stopwatch to time oscillations. The Timed Oscillation Method involves attaching a swing mass to the rotor and using a phone stopwatch to time oscillations. Times are plotted against position and the maximum/minimum times are used to calculate an imbalance correction mass. This method was successfully used to balance pump impellers and fans. The document also discusses trial and error balancing without instrumentation by drilling holes in positions that cause rotor oscillations to vary.

1. BALANCING USING YOUR MOBILE PHONE
By Ray Beebe
Unbalance is one of the most common causes of high vibration in machines. If the
largest vibration component in the spectra is at 1X (i.e. at the frequency
corresponding to rotation speed) then unbalance is the likely cause. Balancing is
therefore a regular maintenance activity in many workplaces. Ray Beebe explains a
method that has been successfully used on rotors large and small, with the only
instrumentation required for balancing being the stopwatch feature of a mobile
phone.
It is assumed that the severity of vibration has been assessed as unacceptable according to sources such as
the relevant part of ISO 10816 (Ref 1). Even if a machine’s vibration meets such criteria, it may be
causing annoying vibration of adjacent parts.
Looseness is another of the most common causes, and a check of foundation tightness is recommended
before proceeding to balancing. If the unbalance is due to deposition on the rotor, such as with fans
handling dirty gas, the rotor should be cleaned. In cases where a deposit is difficult or expensive to
remove, it may be expedient to balance out its effect until a more convenient time for cleaning.
The Timed Oscillation Method
This method has been used successfully for short rotors such as overhung fans up to 2m diameter, and for
pump impellers. It has also been used on smaller fans with two bearings that are nearer to what are
considered “long” rotors. The rotor must be in rolling element bearings, or set up on a mandrel and
parallel ways, and not be affected by crosswinds.
For field balancing, the usual safety precautions for opening any machine must of course be taken so that
the machine cannot be switched on while the work is in progress.
I do not know the source of the method, but I learnt it in my first job at a power station in the 1960s.
Published in Ref 2, the equation is derived from the theory of the compound pendulum.
 Mark numbers around the rotor, evenly spaced. For bladed rotors, mark at the blades.
 Choose a swing mass to fasten (by clamp or magnet) on the rotor, to give to-and-fro oscillation
time of about 20 seconds. (This gives some allowance for reaction time in operating the
stopwatch feature of your mobile phone)
 With the swing mass fixed to the rotor at Position 1, turn the rotor so that the mass is at one
horizontal position and stationary.
 Release the rotor and let it swing freely under its own inertia – do not push it in any way.
 Time the to-and-fro oscillation from the horizontal position. The left part of the sketch below
illustrates the process.
 Turn the rotor so that the mass is at the horizontal position on the other side, and repeat.
 Calculate the mean time of swing for this position, and plot on a graph of time against position
as shown in the sketch. With position numbers evenly spaced, one position appears twice - at
the start and the end of the position axis.
 Move the swing mass to Position 2, etc. and repeat the process.
 Connect the graphed points with a smooth sine wave shape, and read off the maximum and
minimum times of swing: T and t.

2.  Calculate the size of balance mass required from:
Balance mass = Swing mass × 22
22
tT
tT


 Make a balance mass, and fix it on the rotor at position of maximum swing time. The fixing
must of course be sufficiently strong not to allow the mass to fly off at operating speed. If
welded, allow for the mass of the weld.
o If the correction is to be made by removing mass from the rotor, remove it from the
position of minimum swing.
o If the correction mass is at a different radius to that of the swing mass, then calculate the
mass size to achieve the same moment (i.e. Mass × Radius).
 If required, verify the result by repeating the swing test for three spaced points.
Application to balance pump impellers
The method was developed and used for each impeller of a high-speed 10-stage pump of the ring-section
design (where each stage impeller is assembled in turn with its matching stationary section). We clamped
parallel ways to the bed of a milling machine. A mandrel was made to suit the impeller and a pot magnet
used as the swing magnet.
The correction was made on the adjacent milling machine using an end cutter. A table was calculated
and drawn up giving the depth of cut required in each case. The position was marked clearly on the
impeller, and it was passed to the machinist who cut the required mass from the back shroud.
The method gave satisfactory results. At the time, the only balancing machine available could only hold
the total rotor assembly, and corrections would be made on each of the end impellers. Arguably, the
impeller-by-impeller method gave a more satisfactory result.
Balancing by trial and error
Another method that may be satisfactory does not require any instrumentation. A story will illustrate the
method.
Among the cars that I have owned was a second-hand 1971 Ford Falcon (in-line 6 cylinder 4 litre
engine). It came with an after-market twin extractor exhaust system. This gave a “boy racer” burble, and
the salesman explained that it was the cause of severe vibration of the whole car that was evident at
around 90 km/h.
I tolerated this for some time before deciding that with my growing knowledge of vibration problem
solving, and fresh from solving a pump problem, I should be able to fix it. With the bonnet up, I revved
the engine, expecting to see the exhaust pipes shake about when the critical speed range was reached. To

3. my surprise, they did not move at all from an equilibrium position. Then I placed my hand on the
alternator and was horrified to feel it shaken off by its rough vibration! I should have figured this out
much earlier, because the alternator support bracket had been repaired by brazing, and I had replaced it
with a new one.
I removed the alternator, leaving the rotor in its end casing bearing. When spun by hand and allowed to
come to rest, it settled at the same angular position each time. So, I drilled holes in this “heavy” pole face
until the spin test showed the position at rest to vary each time.
On reassembling and back in the car, the vibration no longer occurred. This alternator must have slipped
through manufacturing QC unnoticed. (When telling this story, I usually leave out the bit about having
to ask our instrument workshop people to repair the screw thread that I had mangled just a little!)
Methods of balancing
This table outlines the several methods available.
Situation Method Equipment needed Comments
Rotor out of machine Balancing machine Balancing machine -usually done
by an external service
Refer ISO 1940/1-1986(E)
for criteria
Timed oscillation
(single plane)
Parallel ways, rotor in mandrel.
Stop watch. Swing mass (e.g. pot
magnet for small rotors).
Systematic method. Can use on short
and some longer rotors.
Trial & error (single
plane)
Parallel ways, rotor in mandrel.
Swing masses of various sizes.
Sometimes cost-effective.
Rotor in machine
("field", "in situ")
 Off-speed
Timed oscillation
Trial & error
Rotor must be in anti-friction
bearings
See above
 On-speed Single plane
(sometimes called
“static” balancing)
Vibration 1X and phase angle
measurement
For "short" rotors. 3 runs. Can do in
one shot with past history data.
Vibration measurement, no phase
angle
The “4 Runs” method (or less, with
50% chance of correct position for
balance weight). Assumes that the
vibration is predominantly 1X. (Ref
2).
Two planes (sometimes
called “dynamic
balancing”)
Vibration 1X and phase angle at
each end bearing
For "long" rotors.
4 runs using "Influence coefficients"
method. (Ref 2).
3 runs in some cases, using
"components" method where “static”
(i.e. in-phase) and “dynamic” (i.e.
anti-phase) components are treated
separately (Ref 2).
Multiple planes (but in
field on a rotor often
only two are
accessible)
Vibration and phase angles at each
end bearing
Modal balancing for flexible rotors,
rather like components method.
Computer system is usual.
Some vibration data collector/analyser devices can have capability for field balancing, using a phase
angle reference. I think that the earlier method where a vector diagram is drawn has the advantage of
visualising the process, step by step.
References
1. ISO 10816 Mechanical vibration – Evaluation of machine vibration by measurements on non-rotating parts.
(Several parts for specific machine types)
2. Beebe, Ray S Machine condition monitoring, MCM Consultants, 2009 reprint. ISBN 0646250884