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Dynamic Analysis
In
every engineering analysis, the required accuracy is
dependent on the overall, size, cost and importance
of the equipment being designed.
Most
internationally recognized computational methods such
as CEMA (Conveyor Equipment Manufacturer's Association)
make numerous simplifying assumptions in order to keep
engineering analysis within reason. The most important
simplification is the treatment of the belt as a rigid
body during both acceleration and deceleration. Although
this may be a common practice in the solution of dynamic
problems, it can lead to inaccuracies in conveyor design
which can lead to problems with component life and performance.
Today,
dynamic solutions are possible by dividing a conveyor
system into a series of masses and springs and solving
with a time based finite element methodology.
"Perhaps
the greatest benefit that can be derived from the
use of these analysis tools is the "feeling"
an experienced conveyor designer can develop for a
conveyor as a flexible arrangement of many interacting
components. From this feel, the designer can from
the very beginning of the design process, arrange
the system so as to minimize or eliminate unwanted
dynamic effects, thereby producing a more reliable
and robust conveyor system."
E.
J. O'Donovan, "Dynamic Analysis- Benefits For
All Conveyors", Presented at SME Annual Meeting
1993
Why
do Dynamic Analysis?
Identify Transient Belt Tensions
Prevent Belt Sag
Prevent Drive Slippage
Test Acceleration Control Algorithms
Test Stopping or Braking Algorithms
Predict Takeup Travel and Velocity
Size Backstops
Analysis
Technique
The
figure at right shows a simple conveyor system as a
series of masses and springs during steady state running.
In this condition, the belt velocity is close to constant
all around the conveyor. The initial running conditions
are derived from static analysis. A drive torque is
equivalent to the difference in belt tension on either
side of the drive pulley (Effective Tension).
The
next figure shows the same system a short time (dt) after
the torque has been removed (drive shut off). This change
leaves the torque unbalanced and the pulley decelerates
rapidly. The velocity difference shortens the spring upstream
and leangthens the spring downsteam while all other springs
stay the same. The change in spring extension results
in tension changes in the belt. The end result is that
a wave of decreasing tension propagates down the carry
side while a wave of increasing tension propagates down
the return side. These are commonly referred to as tension
and compresion waves or transient tensions.
Specific
Data Developed
During the transient conditions of starting and stopping,
belt velocities between remote points on a conveyor
can vary dramatically.
Belt
tensions which dictate critical design parameters such
as takeup size, pulley and structure loads can also vary
significantly due to belt elasticity.
An
accurate determination of Drive Torque and Horsepower
is critical to the selection and application of all
drive train components including motors, reducers, pulleys,
couplings and holdbacks.
Everything
starts at the drive pulley and the transmission of torque
from the motor to the belt. Competent Drive Slip analysis
can be essentual in the development of reliable control
algorithms.
The
design and placement of the take up mechanism must be
compatible with the belt elasticity and starting and stopping
characteristics of the entire conveyor system in order
to perform properly.
Why
do Dynamic Analysis? 
The
figure at right shows a simple conveyor system as a
series of masses and springs during steady state running.
In this condition, the belt velocity is close to constant
all around the conveyor. The initial running conditions
are derived from static analysis. A drive torque is
equivalent to the difference in belt tension on either
side of the drive pulley (Effective Tension). 
The
next figure shows the same system a short time (dt) after
the torque has been removed (drive shut off). This change
leaves the torque unbalanced and the pulley decelerates
rapidly. The velocity difference shortens the spring upstream
and leangthens the spring downsteam while all other springs
stay the same. The change in spring extension results
in tension changes in the belt. The end result is that
a wave of decreasing tension propagates down the carry
side while a wave of increasing tension propagates down
the return side. These are commonly referred to as tension
and compresion waves or transient tensions. 
During the transient conditions of starting and stopping,
belt velocities between remote points on a conveyor
can vary dramatically. 
Belt
tensions which dictate critical design parameters such
as takeup size, pulley and structure loads can also vary
significantly due to belt elasticity.
An
accurate determination of Drive Torque and Horsepower
is critical to the selection and application of all
drive train components including motors, reducers, pulleys,
couplings and holdbacks. 
Everything
starts at the drive pulley and the transmission of torque
from the motor to the belt. Competent Drive Slip analysis
can be essentual in the development of reliable control
algorithms. 
The
design and placement of the take up mechanism must be
compatible with the belt elasticity and starting and stopping
characteristics of the entire conveyor system in order
to perform properly. 
