16
The vibration frequency of a plucked string is dependent upon
the tension of that string. As the tension is increased, the vibration
frequency also increases. Laboratory investigations show that
power transmission belts react in a similar manner. Data indicates
that there is a direct relationship between belt tension and a belt’s
natural frequency of vibration. This relationship holds true except
for the very extreme high-tension zones (well above where any
belt system can operate). Using load cells and accelerometers
while applying Newtonian law, the linkage between strand tension
and natural vibration frequency has been deined. It was found
that unlike with a string, the mass of a belt does play a role in the
results. The relationship between tension and frequency has been
determined to be:
T = 4ml
2
f
2
where T = belt tension in newtons (N)
m = mass per unit length expressed as
kilograms/meter (kg/m)
l = span length in meters (m)
f = vibration frequency in hertz (Hz)
String theory ignores lexural stiness. A belt does have some
stiness so the calculated tension for a given frequency will be
slightly higher than the actual tension. For belt spans greater than
0.25m, the above equation will provide results within 10% of the
actual values. Beam analysis may give improved accuracy but the
required inputs are generally too cumbersome for ield application.
The TensionRite® Belt Frequency Meter is a dual function tool.
The optical sensing head uses an invisible infrared beam to detect
vibration while the integral calculator determines the time base and
performs the necessary calculations to support the results shown
in the display window.
The TensionRite® Belt Frequency Meter may be used with all power
transmission belts regardless of type or construction.
2.0 Theory of Operation
Appendix 2.0 Theory of Operation
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