A grinding wheel having a diameter of 200 mm rotates at 3 000 r/min with a tangential force of 40 N on the workpiece. The motor runs at 1 500 r/min and the efficiency of the machine is 72%.

Calculate the torque

1 answer

To calculate the torque, we can use the relationship between tangential force, torque, and the radius of the grinding wheel. The formula for torque (\( T \)) is given by:

\[ T = F \times r \]

where:

  • \( T \) is the torque in Newton-meters (Nm),
  • \( F \) is the tangential force in Newtons (N),
  • \( r \) is the radius in meters (m).
  1. Calculate the radius of the grinding wheel: Given the diameter of the grinding wheel is 200 mm, we can find the radius:

    \[ r = \frac{diameter}{2} = \frac{200 \text{ mm}}{2 \times 1000 \text{ mm/m}} = 0.1 \text{ m} \]

  2. Calculate the torque: We have the tangential force \( F = 40 \) N and the radius \( r = 0.1 \) m. Plugging in the values:

    \[ T = 40 , \text{N} \times 0.1 , \text{m} = 4 , \text{Nm} \]

So, the torque applied to the grinding wheel is 4 Nm.