1 - Guide for the calculation of a transmission

When one  tries to calculate a transmission in order to identify the belt section type, the number of pulley races and their unified primitive diameters, one is always confronted with a large number of formulas, whose meaning is not always immediate. Moreover, the  parameters vary from manufacturer to manufacturer, often with different symbols being used. Besides, it is not easy to understand the logical process which needs to be carried out.

- In this guide we aim to present a fully discussed example of transmissions,
by means of belts, which is not the result of the usual mathematical formulas but, above all, experimental coefficients and tables. It must represent a simple, clear and safe outline. It is an easy-to-perform procedure to arrive at choosing the most suitable pulleys.

- Before turning to the explanatory example we will go over the size symbols used and present some tables and two functional diagrams that represent the material to be consulted during the process which we will follow.

Size symbols used and their respective meaning.
P Nominal power - The power envisaged in order to make use of the utilizer machinery, ie. the power required to operate the machine conducted by the motor.
Pc Correct power - The increased power compared to the nominal power to take into account the transmission of daily service and any negative factors involved.
The corrections will be made using a listed C2 coefficient, which takes into account the conditions of use as well as the working conditions.
Ps Specific power - The power transmitted by each belt. From its value one may immediately work out the number of belts needed for the transmission and hence the number of pulley races.
n1 Number of revolutions of the smallest pulley.
n2 Number of revolutions of the largest pulley.
r = n1/n2 Transmission ratio.
It also results that  r = Dp/dp when a single pair of wheels is envisaged.
L Length of the belt.
Obtained from the manufacturers' tables.
C2 Coefficient that takes into account working conditions.  Reported in the table.
C3 Coefficient that takes into account the length L of the belt.  Reported in the table.
C1 Coefficient that takes into account the angle of wrap of the smallest pulley. Reported in the table
nz Number of belts required for the transmission.
β Angle of wrap of the belt on the smallest pulley.
dp Primitive diameter of the smallest pulley.
Dp Primitive diameter of the largest pulley.
e Interaxis  - Distance between the axes of the two pulleys.

The C1 coefficient reduces the power to be transmitted to the large pulley whenever
the angle ß is less than 180°.  This is chosen from the table provided.
It is always unwise to use a transmission with ß less than 120° since, in these cases, the transmission ratio (r) is very high. In order to increase the angle of wrap it is necessary to increase the interaxis (e) and bring ß within the aforesaid limits.  Furthermore, this is often impossible due to space restrictions. Therefore the transmission ratio is either distributed over the two pairs of pulleys, the advantage being a very compact mechanism, or a belt tensioner is employed.