There are two restoring forces resulting from the deformation
of the belt at the tangency point. The first, illustrated in
Fig. 3b, is geometrically defined by the displacement of the
belt. It can be shown that there is negligible increase in the
local belt fibre tension due to the deflection imposed by
the buckets motions and, accepting this, it can be shown that
the force exerted to the bucket causing it to accelerate it is
defined by the length of belt between the head and tail pulley
centres, and the distance between the buckets attachment
bolts and the lowest point of contact between belt and bucket.
As the bottom of the bucket pushes onto the belt an angle α
will be formed from the attachment point to the lowest point
of bucket contact and a corresponding smaller angle β will
form towards the tail pulley.
Considering Fig. 3b, the magnitude of the force F can be
determined from Eq 1.
F = (sin(α) + sin(β))xT (1)
It should be noted that the tension at the head end will be
greater than the tension at the tail end due to the mass of the
belt and buckets, however the local tension at the point of
deflection is needed in Eq. 1.
Asecond restoring force is aHertzian contact force, generated
as the bucket tries to compresses the belt carcass against
the head pulley face. If the head pulley has rubber lagging,
then this will facilitate a larger deflection due to the increased
compliance at the contact point. The rate of force generation,
and the centre of pressure associated with that contact,
is dependent on the transverse modulus of elasticity of the
belt and the compliance of the lagging material on the head
pulley. In the simulation work to date, these two contributing
restorative forces have not been decoupled and this is a point
for further research.