Page 238 - Advances In Productive, Safe, and Responsible Coal Mining

Engineered noise controls for miner safety and environmental responsibility 217

conduct testing in such chambers due to the large dimensions of these machines rel-
ative to the dimensions of these chambers. In these cases, tests may have to be con-
ducted in the field, and for mining equipment, this often means testing underground
and in confined spaces. For large complex machines, test protocols may become quite
complicated with a large number of measurements required. In some instances, it may
not be possible to conduct measurements under actual operating conditions. Because
of concerns about ignition sources, most acoustic measurement systems cannot be
used at the working face of a coal mine. In such cases, modeling of machine dynamics
and noise radiation may be the best approach.
Numerical models for dynamic and acoustic prediction constitute the most com-
mon means to conduct noise control development for different types of mining equip-
ment. When numerical models of a significant sound-radiating component are created,
the first step is to validate them using data obtained from experimental tests. This val-
idation process guarantees that the models are an accurate representation of actual
parts/components.
Once validated, numerical models can be used to explore various noise control
alternatives readily. Therefore, some of the benefits of using these models involve
increasing the efficiency of the process and reducing the cost incurred in the fabrica-
tion of physical prototypes that would have to be built and tested if these models were
not available.
There are different methods to build these numerical models; however, the most
commonly used are the boundary element method (BEM), the finite element method
(FEM), and the hybrid finite element/statistical energy analysis (FE/SEA). It is not the
purpose of this chapter to elaborate on each of these methods, but rather to provide an
overview of the benefits and applicability of each of these methods in the mining
industry, as described later. There is extensive literature that explains in detail each
of these methods.
In acoustics, the boundary element method provides a way to solve the wave equa-
tion by discretizing the boundary and solving integral equations for each element that
are mathematically equivalent to the original partial differential equation [4]. The
main advantage of this method is that only the boundary of the domain needs to be
discretized. This advantage is more significant when the domain is exterior to the
boundary, such as in sound radiation and scattering problems. In terms of analysis fre-
quency, the BEM constitutes an effective tool for low to mid frequencies (below
1000Hz) due to discretization requirements. As a rule of thumb, six elements per
wavelength are recommended when using the BEM in order to obtain acceptable
results [5].
The finite element method also provides a way to solve the wave equation
governing acoustic phenomena. In contrast to the BEM, this method requires that
the entire domain be populated with elements. This requirement increases signifi-
cantly the number of unknowns, especially for three-dimensional problems. However,
matrices that arise from this formulation have a sparse structure that simplifies their
solution and reduces the computational effort.
The hybrid finite element/statistical energy analysis combines a deterministic
method (finite element analysis) with a statistical method (statistical energy analysis).