In a belt-and-pulley drive, the belt embraces the shorter pulley 165° and runs over it at a mean speed of 1700 m/min with a standard deviation of 51 m/min.
The density of the belt has a mean value of 1 g/ cm3 and a standard deviation of 0.05 g/cm3. The mean and standard deviations of the permissible stress in the belt are 25 and 2.5 kg/cm2, respectively. The coefficient of friction O) between the belt and the pulley is given by μ = 0.25 and σµ = 0.05.
Assuming a coefficient of variation of 0.02 for the belt dimensions, find the width and thickness of the belt to maximize the mean horsepower transmitted.
The minimum permissible values for the width and the thickness of the belt are 10.0 and 0.5 cm, respectively.
Assume that all the random variables follow normal distribution and the constraints have to be satisfied with a minimum probability of 0.95.