When two unequal pulleys of different materials are connected by an open belt drive system, the ratio of tensions depends upon:

Explanation: 

Belt drives are called flexible machine elements. Flexible machine elements are used for a large number of industrial applications, some of them are as follows.

• Used in conveying systems
• Used for transmission of power.
• Replacement of a rigid type of power transmission system. 

Two types of belt drives,

Open belt drive

In an open belt drive system, the rotation of both the pulleys is in the same direction

dL = Diameter of the larger pulley, dS = Diameter of the smaller pulley, αL = Angle of wrap of the larger pulley, αS = Angle of wrap of the smaller pulley, C = Center distance between the two pulleys, T₁ = tension on tight side, T₂ = tension on loose side

While determining the angle of contact and power transmitted by belt-drive, it must be remembered that it is the angle of contact at the smaller pulley, if both the pulleys are of the same material.

Basic Formulae αL = 180° + 2β, αS = 180° - 2β

\(\beta = {\sin ^{ - 1}}\left( {\frac{{{d_L} - {d_S}}}{{2C}}} \right)\)

The ratio of tensions is given as, 

\(\frac{T_1}{T_2}=e^{\alpha μ}\)

where, μ =  coefficient of friction