A punching machine carries out 5 holes per minute. Each hole of 30 mm dia in 40 mm thick plate requires 10 NM of energy per mm^2 of the sheared area. The punch has a stroke of 90 mm. find the power of the motor required if the mean speed of the flywheel if 20 m/s. If the total fluctuation of speed is not to exceed 2% of the mean speed. Determine the mass of the flywheel?
To find the power of the motor required, we first need to calculate the work done in punching one hole and then determine the time required to punch one hole.
1. Calculate the area of the sheared hole:
The diameter of the hole is 30 mm. The area of a circular hole is given by A = π * r^2, where r is the radius.
The radius of the hole is half of the diameter, so r = 30 mm / 2 = 15 mm.
Thus, the area of the hole is A = π * (15 mm)^2.
2. Calculate the energy required to shear the area of one hole:
The energy required per mm^2 of the sheared area is given as 10 Nm/mm^2.
Therefore, the energy required to shear the area of one hole is E = 10 Nm/mm^2 * A.
3. Calculate the work done in punching one hole:
The work done is W = E * area, where area is the thickness of the plate.
The thickness of the plate is 40 mm, so area = 40 mm.
Therefore, the work done in punching one hole is W = E * area.
4. Calculate the time required to punch one hole:
The punching machine carries out 5 holes per minute, which means it takes 1/5 minutes to punch one hole.
Since there are 60 seconds in one minute, the time required to punch one hole is t = (1/5) * 60 seconds.
5. Calculate the power of the motor required:
Power is defined as the work done per unit time, so Power = W / t.
Therefore, the power of the motor required is Power = (E * area) / ((1/5) * 60) watts.
Now, let's find the power of the motor required.
6. Calculate the power:
Substitute the values of E, area, and t into the formula:
Power = (10 Nm/mm^2 * A * 40 mm) / ((1/5) * 60) watts.
Simplify the equation and convert mm^2 to m^2:
Power = (10 Nm/mm^2 * π * (15 mm)^2 * 40 mm) / ((1/5) * 60) watts.
Power = (10 Nm * (π/1000) * (15/1000)^2 * 40) / ((1/5) * 60) watts.
Power ≈ 0.0188 watts.
Thus, the power of the motor required is approximately 0.0188 watts.
To determine the mass of the flywheel, we require information about the flywheel design, such as its moment of inertia or the coefficient of fluctuation of speed. Please provide more details so that I can help you calculate the mass of the flywheel.