We begin
by calculating:
-
Circumference of the tire
(c = π x d)
-
The linear velocity of
the tire
-
The spot size resolution desired
-
The camera exposure time
and frame rate needed to meet the stop motion spot
size requirements
-
Will a trigger device
be necessary? If so what type?
-
The anticipated temperature
range
-
The thermal sensitivity
required
-
Which wavelength (3-5µm
called mid wave or 8-10µm called long wave) camera
to select
Assuming a 16-inch wheel and
4-inch sidewall, the circumference of the tire will be 3.1416
x 24 (16+4+4) = 75.3 inches.
Assuming a speed of 60mph, the
linear velocity is 1056 inches (26,822 mm) per second.
Assuming the resolution desired
is 0.2 inches (5mm) ±15% for acceptable motion displacement,
we can calculate the exposure time necessary. We need to
integrate the sensor during the period of time it takes
the tire to move 0.03 inches (0.2 x 15%).
The integration time is calculated as 0.03/1056
or 28.4 microseconds (µs). |
Normal operating temperatures for tires are within the
ambient operating specification of a tire, plus a factor for the
load-induced heating of the
tire under a wide range of load and speed conditions. We
will assume that the maximum temperature a tire will be
subjected to 100°C or 200°F.
Given the uniform material properties of
a tire, we are assuming that the temperature resolution
or sensitivity required for proper analysis of the tire
under various test conditions will be <0.25°C.
Electrophysics offers cameras with spectral
responses in either the mid-IR wavelength region (commonly
referred to as MWIR) or long-IR wavelength region (commonly
referred to as LWIR). Because of the relatively cold temperature
of the tire, an LWIR camera will perform much better due
to Planck's Law. Essentially, this states that as a target
temperature gets hotter, the peak wavelength associated
with that temperature shifts toward shorter wavelengths.
An LWIR system has its peak sensitivity around room temperature,
while a MWIR system has its peak sensitivity around 400°C.
Therefore, an LWIR system can better achieve the short exposure
and sensitivity performance objectives.
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