8.13:
Flat Belts: Problem Solving
A flat belt 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.
Pulley B rotates clockwise and drives Pulley A, causing tension T2 at one end of the belt and tension T1 at the other.
Given that the maximum allowable tension T2 is 1000 N and the coefficient of static friction between the belt and pulleys is 0.4, what is the maximum moment on pulley A?
The belt-to-surface contact angle, calculated from the system's geometry, is 140 degrees.
The belt-to-surface contact angle in radians and the coefficient of static friction values are substituted into the expression for belt tensions to obtain T1.
As pulley B rotates clockwise, a tension difference created at pulley B generates a moment at pulley A.
A free-body diagram for pulley A is drawn, and the moment equilibrium condition is applied.
The radius and tension values are substituted to obtain the maximum moment.
8.13:
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.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. Pp 439 ‒ 441.
- Meriam, J.L.; Kraige, L.G. and Bolton, J.N. (2020). Engineering Mechanics ‒ Statics. Hoboken, New Jersey: John Wiley. Pp 372.
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P. (2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill. Pp 469-470.