Question

1. A flywheel for a punching machine is used to punch a hole. It is capable of furnishing 3500 N-m of energy during the 1/4 revolution of the process. The flywheel rotates at a maximum of 200 rpm and reduces its speed by 8% during the load stroke. The mean radius of the rim contributes to 95% of the energy requirements with a mean radius of 1016 mm. Determine the total weight of the flywheel if a) neglecting the arm and hub weight, and b) assuming the total weight of the flywheel to be 1.20 that of the rim.

Answer 1

To determine the total weight of the flywheel, we first calculate the angular velocity and moment of inertia of the flywheel. Then, we use the given information to determine the total weight of the flywheel, neglecting the arm and hub weight or assuming the total weight to be 1.20 times that of the rim.

Step-by-step explanation:

First, we need to calculate the total energy furnished by the flywheel during the load stroke. The flywheel rotates 1/4 of a revolution, which is equal to 1/4 x 2π radians. The energy furnished by the flywheel can be calculated using the formula:

E = 1/2 I ω^2

where E is the energy, I is the moment of inertia, and ω is the angular velocity.

Given that the flywheel furnishes 3500 N-m of energy, we can substitute the known values into the formula and solve for ω:

3500 = 1/2 I ω^2

ω = sqrt(2*3500/I)

Next, we need to calculate the moment of inertia of the flywheel. Since the mean radius of the rim contributes to 95% of the energy requirements, we can assume that the flywheel has a uniform density and calculate the moment of inertia using the formula:

I = 1/2 m r^2

where I is the moment of inertia, m is the mass of the flywheel, and r is the mean radius of the rim.

Given that the mean radius of the rim is 1016 mm, we can convert it to meters (1.016 m) and substitute the known values into the formula to calculate the moment of inertia.

Finally, we can calculate the total weight of the flywheel:

a) Neglecting the arm and hub weight: The weight can be calculated using the formula:

W = m g

where W is the weight, m is the mass of the flywheel, and g is the acceleration due to gravity (9.8 m/s^2).

b) Assuming the total weight of the flywheel to be 1.20 times that of the rim: We can calculate the weight of the rim using the formula W = m g, and then calculate the total weight of the flywheel by multiplying the weight of the rim by 1.20.