The driven pulley of a crossed belt drive has an angle of contact of 192° and revolves at 250 rpm while the driving pulley, 250 mm in diameter, revolves at 200 rpm. The drive transmits 30 kW with a coefficient of friction of 0,25 between the surfaces of the pulleys and the belt. The pulley centres of the drive are 800 mm apart.

Question

Calculate:
7.1
Belt speed, in m/s.

Answer 1

To calculate the speed of the belt, we first need to find the circumference of the driving pulley, then the belt speed using the revolutions per minute (rpm) of the driving pulley.

1. Calculate the circumference of the driving pulley:

The diameter of the driving pulley is given as 250 mm. To calculate the circumference (C) in meters, we use the formula:

\[ C = \pi \times D \]

where \(D\) is the diameter in meters.

Converting 250 mm to meters:

\[ D = \frac{250 \text{ mm}}{1000 \text{ mm/m}} = 0.25 \text{ m} \]

Now calculating the circumference:

\[ C = \pi \times 0.25 \approx 0.7854 \text{ m} \]

2. Calculate the belt speed:

The formula to find the belt speed (V) based on the diameter and rpm of the driving pulley is:

\[ V = \frac{C \times N}{60} \]

where \(N\) is the revolutions per minute (RPM).

Given that the driving pulley revolves at 200 rpm:

\[ V = \frac{0.7854 \text{ m} \times 200}{60} \]

Now we calculate this:

\[ V = \frac{157.08}{60} \approx 2.618 \text{ m/s} \]

Thus, the belt speed is approximately 2.62 m/s.