Page 125 - Advances In Productive, Safe, and Responsible Coal Mining

Developing effective proximity detection systems for underground coal mines 109

ð
ð
Shell x, y, zj BÞ or Shell ρ, α, β, γj BÞ ¼
8
2 2 2
1a
> 2 2 2 1=2 x y z
ð x + y + z Þ ¼ a + b ðÞ
>
>
x + y + z
> 2 2 2
>
>
>
>
> 2 2 2
> or ρ ¼ a cos α cos β cos γð Þ + b ð 1bÞ
>
(7.1)
<
for a + b > L=2
>
a ¼ c a B 1c
> d a
> ðÞ
>
>
>
> d b
> b ¼ c b B ð 1dÞ
>
>
>
for B > 0
:
The shell shape function (1c) has two positive constants, c a , the shell base shape con-
stant, and, d a , the shell shape changing constant. Similarly, the shell size function (1d)
has two positive constants, c b , the shell base size constant, and, d b , the shell size
changing constant. These four constants have fixed values for a given steady magnetic
field and completely describe the magnetic field in its defined space. These constants
are defined by the physical distribution characteristics of a given magnetic field that is
determined by many factors: primarily the length of the ferrite core, permeability of
the core material and medium, the number of turns of the coil, the current flowing
through the coil, and the impedance of the generator. These constants can also be
determined empirically using data from magnetic-field measurements.
The ratio of a to b is called the shell shape changing ratio, and it is a good indicator
of the variation of the shell shape from spherical. Its value is uniquely determined by
the value of B, as shown in Eq. (7.2). No two shells have the same shell shape changing
ratio, and, therefore, no two shells have the same shape. It has been observed that,
typically 0<c a <c b and 0<d a <d b , and that as the value of B increases, the ratio
a/b will also increase. As B is larger close to the generator, the ratio a/b increases close
to the generator, resulting in greater deviation from a spherical shape to a more deeply
concaved shell. Conversely, further from the generator, the value of B is smaller yield-
ing a ratio a/b that is smaller, and the resulting shell will be more spherical in shape.
a c a B d a c a
¼ ¼ B d b d a (7.2)
b c b B d b c b
With a single B reading, it is only possible to determine the shell on which the mea-
surement is made. The exact distance between the sensor and the generator cannot be
directly determined since the shell is never a perfect sphere, and points at different
locations on the shell will have different distances to the generator.
7.4.3 Effect of worker posture
The mining process requires workers to change posture and position based on several
factors such as roof height, machinery location, and mine ventilation. Previous studies
have addressed worker positioning around the CMM rather than posture [10,11].
Some investigations unrelated to mining have focused on wireless and embedded