When
performing starting and stopping calculations per
CEMA or DIN 22101 (static analysis), it is assumed
all masses are accelerated at the same time and rate;
in other words the belt is a rigid body (non-elastic).
In reality, drive torque transmitted to the belt via
the drive pulley creates a stress wave which starts
the belt moving gradually as the wave propagates along
the belt. Stress variations along the belt (and therefore
elastic stretch of the belt) are caused by these longitudinal
waves while being dampened by resistances to motion.
It
is, therefore, important a mathematical model of the
belt conveyor that takes belt elasticity into account
during stopping and starting be considered in these
critical, long applications.
A
model of the complete conveyor system can be achieved
by dividing the conveyor into a series of finite elements.
Each element has a mass and rheological spring as
illustrated below.
Many
methods of analyzing a belt’s physical behavior
as a rheological spring have been studied and various
techniques have been used. An appropriate model needs
to address:
1.
Elastic modulus of the belt longitudinal tensile
member
2. Resistances to motion which are velocity dependent
(i.e. idlers)
3. Viscoelastic losses due to rubber-idler indentation
4. Apparent belt modulus changes due to belt sag
between idlers
Since
the mathematics necessary to solve these dynamic problems
are very complex, it is not the goal of this presentation
to detail the theoretical basis of dynamic analysis.
Rather, the purpose is to stress that as belt lengths
increase and as horizontal curves and distributed
power becomes more common, the importance of dynamic
analysis taking belt elasticity into account is vital
to properly develop control algorithms during both
stopping and starting.
See
for more information
