Force / Velocity Relationship

The centrifugal force F acting at the centroid of the material is given by:

F = mv²/gR

Where:

m = mass of material acting at centroid (kg)
v = tangential velocity (m/s)
g = acceleration due to gravity (m/s²)
R = distance from centre of pulley to centroid (m)

NB. Tangential velocity is not equal to nominal belt velocity. It must be calculated thus

v = 2 π Rp where p = pulley rotational speed in rev/s.

When the centrifugal force equals the radial component of the material mass, the material will no longer be supported by the belt and its free fall trajectory will commence. The angular position around the pulley at which this occurs is dependent upon the conveyor belt inclination.

In the analysis and examples, which follow, the trajectories examined are those of the centroid of the material (i.e. the median line). For materials of approximately uniform particle size and density of 800 kg/m³ or more, the upper and lower limits of the material path will closely parallel the median line for falls up to about 2 m below the centre of the discharge pulley. Thereafter the material will tend to diverge.

Light, fluffy materials, high belt velocities and a mixture of large lumps, small lumps and fines will alter the upper and lower limits of the material path. Lumps riding near the top of the material at the discharge point will tend to be thrown further from the pulley. The trajectories of any such lumps may be individually plotted.