APPLICATION OF COMPUTERS TO STUDY
AND CALCULATION OF PARAMETERS OF TRANSMISSION MINING MACHINES
Maksim Perinskiy (
Source: Proceedings of V All-Ukrainian student scientific conference,
Translation from Russian: Maksim Perinskiy
The dynamic
processes occurring in the transmission,
described the system of equations
that includes the wave partial
differential equations, reflecting the torsional vibration level with distributed
parameters, and equations of motion
of the engine
and the working
tool, appears here as the
boundary conditions:
where: 
- angular velocity
in this section
of the transmission,
- reduced to motor shaft torque
in the transmission,
- coefficient of torsional compliances per unit length
of the shaft,
- coefficient of inertia per unit
length of the shaft, 
Boundary conditions:
by 
: 
by 
: 
here indicated: 
è 
- the current
values of the angular velocity,
respectively, in the initial and
final sections of the transmission;
è 
- the current
values of torque in the
initial and final sections of the transmission.
Initial conditions
are:
The solution
of the reduced
system is carried out based
on the method
of finite differences, informed AA Samara, with the use of
computers. To approximate the partial derivatives
should be used grid model
with an error
of order 
For this
system reduces to:
as a result of net
approximation is obtained:
finite-difference system
has the form:
To construct
the matrix of values of
the tested parameters 
, 
must receive
an initial two vectors (lines)
with 
and 
. This calculation is
performed based on initial conditions.
The implementation of this model allows
to obtain an array of
information about the behavior of
the object's parameters in the
space-time, thus provides a basis
for conclusions about further improvement
design.
As we add
new results it is necessary
to further detail the involvement
of new groups
of parameters, which complicates the mathematical model. However, modern
computer technology by improving the
speed and memory capacity can successfully solve the tasks,
and this determines the prospects for improving
mining equipment.