11/26/1998

There is an ongoing thread on the RCM NG concerning the balancing of a 
crankshaft, with a some discussion of how to make the equipment to do 
it. Having used high-end equipment and being certified in vibration 
analysis, I thought this could be done in DIU way.

With some help in electronics a useable device can be built (possibly 
from one or more of the electric folks on RCM). My practical 
electronics ability can, at best, be described as "able to lengthen 
shorts quickly"!

Onward;

Balancing is a discipline that falls within the large envelope of 
"Vibration analysis or Vibration Spectrum analysis" so some discussion 
of vibration and analysis is in order.

Vibration is the term used to describe the motion (oscillation) of an 
object from its natural state, or place of rest. In machinery vibration 
may be caused by a great number of things including;

Unbalance or eccentricity of rotating parts
Looseness
Misalignment of shafting or bent shafting
Bad belts
Oil whirl (in plain bearings)
Constant velocity problems
Electromagnetic force
Resonance
There are some others relating to pumps and fans, I’ve listed enough!

The components of vibration are;

Displacement (Movement, expressed in mils (.001")
Velocity (Speed, expressed in inches per second)
Acceleration (Force, expressed in G’s)

Frequency (expressed in cycles per minute)
Phase (expressed in degrees)

Displacement, Velocity, and acceleration are all linked, and are best 
understood by looking at a sine wave with max velocity occurring at 0 
degrees and 180 degrees, max acceleration at 90 degrees and 270 degrees 
and displacement the total value from 90 degrees to 270 degrees.

Frequency is useful to determine the exact culprit when you’re having a 
bad vibration day.

Phase is useful in comparing one vibration with another, or one against 
a fixed reference (balancing).


	Early equipment used seismic velocity transducers, which 
consisted of a moving coil cutting through a magnetic field. Almost all 
of these had the problem of the coil moving with the magnetic field at 
lower frequencies. These are still used but for the DIU folks I think 
an accelerometer may be better suited.

	Also, vibrations can be complex, with a seismic transducer the 
output includes AC voltage from ALL sources of vibration (an 
oscilloscope will show all of these in real time and it can be quite 
confusing!). To confound the problem if the AC voltage is converted to 
DC, (so it may be easily read) different vibration amplitudes depending 
on frequency and phase tend to add or subtract from the total reading.  
To allow for this a tuner is used to filter the AC input and zero in on 
any given frequency.

	Early machines also used a strobe to measure phase, this could be 
triggered by the input of the transducer (not so nifty without the use 
of filters) or by an internal oscillator which was used to "freeze" the 
rotating part. Original amplitude readings and phase references were 
noted, trial weights were then affixed and new readings were noted.  A 
simple vector plot was used to calculate the amount of weight and angle 
of correction needed to achieve balance.


	On to types of Unbalance;

1. Static unbalance, (the center of gravity is parallel to the axis of 
rotation), this type of unbalance may be corrected on knife-edges.

2. Couple unbalance, (the center of gravity crosses through the axis of 
rotation at the midpoint of the rotor). This type of unbalance will 
show equal vibration amplitudes at each end of the rotor but the phase 
of unbalance will be 180 degrees apart, this type of unbalance is more 
easily corrected by dynamic balancing.

3. Semi-static unbalance, (the center of gravity crosses the center of 
rotation in someplace other than the midpoint of the rotor). This type 
of unbalance will have unequal vibration amplitudes at either end and 
the phase will be 180 degrees apart, this type of unbalance is also 
more easily corrected by dynamic balancing.

4. Dynamic unbalance, (the center of gravity is neither parallel to, 
nor intersects with the axis of rotation). This is the most common type 
of unbalance, with vibration phase indications neither the same, nor 
180 degrees apart. 


On to rotor types, (rigid or flexible)

1. If a rotor is operating at or below 70 percent of its’ critical 
speed, it is considered a rigid rotor, and when balanced at one speed 
it will be in balance at all speeds.

2. If a rotor is operating at 70 percent of its’ critical speed it is 
considered to be a flexible rotor, and must be balanced within the 
operation range intended for the rotor. This means the rotor may have 
some unbalance below, and often above the operating range intended for 
the rotor.

Here critical speed must be discussed. A rotor is said to have reached 
critical speed when the rotor turns about its’ center of gravity and 
not its’ intended axis. As a rotor reaches 70 percent of critical 
speed, vibrations will increase, as the rotor begins to flex due to the 
force applied by its’ center or gravity (the amount depending on 
structure and machine rigidity). As the rotor speed is increased 
vibrations will also increase until the rotor assumes another mode 
shape or a "catastrophic" failure occurs. A rotor may have more than 
one critical speed, and a rotor can have a critical speed of "zero" 
(I’m not going into that here).


	Understanding planes of balance correction, (single, two, or 
multi-plane)

1. "Single plane balancing" is the correction of an unbalance condition 
by placing or removing weight in a single plane around the axis of 
rotation. This correction method is the simplest to use and a common 
guideline for use is with rotors having a length to diameter ratio 
(L/D) X RPM of;
	a. 0.5 or less and rotor speeds up to 2000RPM or,
	b. More than 0.5 and less than 2 with rotor speeds up to 200RPM
	c. More than 2 with a rotor speed up to 100RPM

2. "Two plane balancing" is the correction of an unbalance condition by 
placing or removing weight in two correction planes, (usually at the 
ends of a rotor) around the axis of rotation. Guidelines for use are 
with rotors having a length to diameter ratio (L/D) of;
	a. .05 or less with rotor speeds over 2000RPM
	b. More than 0.5 and less than 2 with rotor speeds from 200 to 
	   2000RPM or below 70 percent of the first rotor critical speed.
	c. More than 2 with rotor speeds from 100RPM up to 70 percent of 
	   the first rotor critical speed.

3. "Multi-plane balancing" is the correction of an unbalance condition 
by placing or removing weight in three or more correction planes around 
the axis of rotation. It is recommended that any rotor operating at or 
above 70 percent of critical speed be balanced using multi-plane 
techniques.

I should state that in most cases "two plane" balancing is the norm, I 
have never seen an electric motor shop (rotors with (L/D) of 3 or more) 
or automotive machine shop (crankshafts with (L/D) of from 4 to 6) 
truly multi-plane balance. More often the better of these shops employ 
a "Two Plane Static Couple" solution, which will usually work very well 
through a rotors’ first critical speed and mode shape.

Along with the above I’ll post a "no-phase" method of balancing (maybe 
two) in the RCM site.  I’m going to have to generate some vector charts 
and convert them to JPG format first. If this goes well maybe we can 
get to two plane and static couple solutions...