Flat Belts: Problem Solving

Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used to determine the maximum moment on a pulley. For instance, consider a flat belt that wraps around two pulleys, A and B, with radii of 30 cm and 10 cm, respectively. The angle between the belt and the horizontal is 20 degrees at the pulleys. As pulley B rotates clockwise and drives pulley A, tension T₂ is caused at one end of the belt, while tension T₁ is created at the other.

The belt-to-surface contact angle, β,  must be calculated to determine the maximum moment. This angle is obtained from the system's geometry and found to be 140 degrees. As a result, the belt-to-surface contact angle in radians, along with the coefficient of static friction value, 0.4, is substituted into the expression for belt tensions.

Considering that the maximum allowable tension T₂ is 1000 N, the calculated value of T₁ is 376.93 N. As pulley B rotates clockwise, a tension difference is created at pulley B, generating a moment at pulley A. Considering a free-body diagram for pulley A, the moment equilibrium condition can be applied.

The radius and tension values are then substituted to obtain the maximum moment as 186.921 N.m.