Page 93 - Electric Drives and Electromechanical Systems

86 Electric Drives and Electromechanical Systems

contributions from all the rotational elements, including the idler pulleys, any rotating
load, and the belt:
(3.21)
I tot ¼ I p þ I L
where I p is the sum of the inertias of all the rotating elements. The inertia of the belt
together with any additional load is given by,
MD 2 in
I L ¼ (3.22)
4
where the mass, M, is the sum of the linear load (if present) and the transmission-belt
masses. An external linear force applied to the belt will result in a torque at the input
drive shaft,
D in F
T ext ¼ (3.23)
2
In a linear application, the frictional force, F f , must be carefully determined as it will
result in an additional torque,
D in F f
T f ¼ (3.24)
2
If a belt drive is used as a speed changer, the output speed is a ratio of the pulley
diameters,
D out
n ¼ (3.25)
D in
and the input torque which is required to drive the load torque, T i , is given by,

T out
T i ¼ (3.26)
n
where T out is the torque required by the external application, if present. The inertia seen
at the input to the belt drive is the sum of the inertias of the pulleys, the belt, the idlers,
and the load, considering the effects of the gearing ratio;
I RL þ I p2
I tot ¼ I p1 þ I L þ 2 (3.27)
n
where the inertia of the belt can be calculated from Eq. (3.20) and I p2 is the inertia of the
driven pulley modified by the gear ratio and includes the inertia of any rotational load
I RL , being driven by the output pully. The drive torque which is required can then be
computed; the losses can be taken into account by using Eq. (3.16).
The main selection criteria for a belt or chain is the distance, or pitch, between the
belt’s teeth (this must be identical to the value for the pulleys) and the drive
characteristics. The belt pitch and the sizes of the pulleys will directly determine the
number of teeth which are in mesh at a time, and hence the power that can be
transmitted. The power that has to be transmitted can be determined by the input
torque and speed. The greater the number of teeth in mesh, the greater is the power