Holes and cylinders are the most commonly produced forms in the modern machine
shop. Usually, the diameter is the critical dimension to be measured, but when a
part needs to interact with other parts, form and surface finish must also be
taken into account. When the diameter is tight, form error can take up a
significant part of the tolerance.There are many standards that describe how
form measurements are to be made. Diametral (two-point diameter) and chordal (vee
block) are probably the must common standards, although they provide the least
amount of real information. Form measurements such as roundness are best done
with a radial method, usually using a form gage.
Form errors are a blueprint of the machining process—the cutting tool, the
machine and the environment all leave their marks on the machined part. Embedded
within the roundness of the part are a series of lobes which can have a large
impact on how the part performs, especially when the part rotates at very high
speeds.
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| This Harmonic Analysis chart shows a
range of harmonics and their amplitude. |
In addition to roundness analysis, quality engineers use harmonic analysis
tools to predict what a part might do under certain conditions. By decomposing
the out-of-roundness trace into a collection of sinusoidal components, called
harmonics, harmonic analyses can provide information about the dominant lobes
found within the part.
By using harmonic analysis you can figure out what creates the lobing
conditions on the part. There are three major contributors to the lobing
condition.
The first harmonic is called the fundamental sinusoid. Its wavelength is the
entire length of the circumference (over 360 degrees) and it measures geometry
errors that repeat once per revolution. These errors tend to be the result of an
eccentric error, such as placing the part off-center when it is first set up in
the machine.
The second harmonic measures errors that repeat twice per revolution, so its
wavelength is one half the fundamental wavelength (over 180 degrees). Second
harmonic problems are often the result of an out-of-squareness condition in the
machine tool, the fixture or the measurement setup.
The third harmonic measures errors that repeat three times per revolution.
Its wavelength is one third of the fundamental wavelength (over 120 degrees). In
the same vein, the Nth harmonic, then, is a sinusoid whose wavelength is the
fundamental wavelength divided by N. Third and higher harmonics problems are
often the result of workpiece clamping, a particular aspect of the manufacturing
process or various sources of vibration. For example, a three-point chuck is apt
to produce an odd number of lobes.
In the bearing industry, performance (lack of noise and vibration) is related
to the presence and magnitude of certain lobes (harmonics).
An interesting example is the case of a marine engine manufacturer who suddenly
encountered a peculiar noise from one of the bearings being supplied by its
bearing supplier. The company checked records and found that testing was being
done to inspect as many as 50 lobes per revolution.
However, dynamic analysis on the engine revealed that the vibration or noise
had a period of roughly 120 cycles per revolution. The harmonic analysis was
expanded to look for shorter wavelength errors and confirmed the presence of a
120-lobed condition. The cause was eventually tracked to some unrelated changes
on the shop floor. The changes had triggered a slight increase in vibration that
was just enough to cause the problem for the engine builder.
With the form equipment available today, harmonic analysis is as easy as
setting up some test parameters. However, the results can be invaluable in
producing better parts and better performing machines.
Article courtesy of MMS Online.
